- - O N - I E NTNU Trondheim Norges teknisk-naturvitenskapelige universitet
DqktorIngenioravhandling 1997:29 2 2 0 1 Institutt for mekanikk, termo- og fluiddynamikk Trondheim MTF-rapport 1997:149 (D) moners
TA am Computational analysis of the flow field downstream of flow conditioners
Asbjern Erdal February 1997
Thesis for the dr. ing. degree Department of Applied Mechanics, Thermodynamics and Fluid Dynamics Norwegian University of Science and Technology Page 2 DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Abstract
A flow conditioner (FC) is a device installed upstream of a flow meter in order to remove swirl and to correct a distorted flow profile generated by inappropriate installation conditions. Using an FC can reduce installation effects in flow measurements. Numerous attempts have been made to isolate metering stations from piping-induced disturbances, and many different FCs have been designed. Some have proved capable of meeting the flow quality requirements in the metering standards, but doubts have remained about the factors dictating their performance. The design methods used earlier, such as screen theory, cannot give a fundamental understanding of how an FC works. This thesis shows, however, that computational fluid dynamic (CFD) techniques can be a valuable tool to examine several parameters which may affect the performance of an FC. It is, among other things, shown that the flow pattern through a complex geometry, like a 19-hole plate FC, can be simulated with good accuracy by a k-s turbulence model. The calculations illuminate how variation in pressure drop, overall porosity, grading of porosity across the cross-section and the number of holes affect the performance of FCs. These questions have been studied experimentally by researchers for a long time. Now an understanding of the important mechanisms behind efficient FCs emerges from the predictions. The research is documented in 6 papers which step by step study various aspects of the topic. Page 4 Preface
This thesis consists of six papers and an introduction which gives a survey of the matter. The work has been carried out in the period 1992 - 1996. The thesis is based on research performed at K-Lab after my hospitation at The Norwegian Institute of Technology from 1992 to 1993. During this period I have been motivated and inspired by many people both at Statoil, The Norwegian Institute of Technology and Institute for Energy Technology. First of all I will express my deepest and sheerest thanks to my former supervisor in Statoil, Dr. Jan Bosio. His involvement during initiation of this work and inspiration during preparation has been highly appreciated. I wish to thank my academic supervisors Professor Helge I. Andersson and Professor Per-Age Krogstad for their valuable support and advice during this work. I also want to thank my co-authors Dag Lindholm, Dag Thomassen, Lars Even Torbergsen, Stein Rimestad, Anne Synnave Sivertsen and Morten Langsholt for many fruitful discussions. I wish to thank my employer Statoil, represented by my supervisor Dr. Svein Birger Thaule and chief engineer Dr. Karl Sjaen, who have given me the opportunity and resources to prepare this Dr. ing. thesis. Finally, and most important, I will thank my wife Magny and our four children for all patience and support throughout these years. Without this help it would have been difficult to complete the thesis in due time.
Page 5 Page 6 Contents
Abstract...... 3
Preface...... 5
Contents ...... 7
List of papers...... 8
Introduction ...... 9
Orifice plate meters...... 11 Installation effects in orifice meters...... 13 Flow conditioners developed before 1987 ...... 18 Modem flow conditioners ...... 20 Flow conditioners and international metering standards ...... 27 CFD codes and upstream effects...... 29 The Phoenics CFD code ...... 31
Progress in the papers in this thesis...... 32 Paper I...... 34 Paper II...... 36 Paper III...... 37 Paper IV...... 38 Paper V...... 39 Paper VI...... 41
Conclusions ...... 42
References ...... 44
Page 7 List of papers
This thesis is based on the following papers, referred to in the text by Roman numerals :
I : Erdal, A, Lindholm, D and Thomassen, D, Development of a flow conditioner, North Sea Flow Measurement Workshop, Peebles, Scotland, October 1994.
II : Erdal, A, Torbergsen, L E, Rimestad, S and Krogstad, P A, Evaluation of a CFD-model for simulation of simplified flow conditioners, Fluid Flow Measurement 3rd International Symposium, San Antonio, USA, 1995. m: Erdal, A, Sivertsen, A S, Langsholt, M and Andersson, H I, Three-dimensional computation of turbulent flow through a flow conditioner, Proceedings of the 8th International conference on Flow Measurement, Flomeko '96, Beijing, China, pp 718-723, 1996.
IV: Erdal, A. and Andersson, H I, Numerical aspects of flow computation through orifices, Accepted for publication in Flow Measurement and Instrumentation.
V : Erdal, A, Torbergsen, L E, Andersson, HI and Krogstad, P A, Flow development of two simplified and one K-Lab/Laws flow conditioners - experiments and calculations, Accepted for the 1997 ASME Fluids Engineering Division Summer Meeting, Symposium on Devices for Flow Measurement and Analysis. Paper number FEDSM 97-3216.
VI: Erdal, A, A numerical investigation of different parameters that affect the performance of flow conditioners, Submitted to How Measurement and Instrumentation.
Page 8 Introduction
Technological innovations are essential for maintaining the competitiveness for the gas companies. In this context, metering technology represents a key area of expertise for gas companies which buy and sell huge volumes each day. Achieving the highest possible reliability in flow measurements has great economic importance. Neither side in a transaction should be penalised for measuring errors. Figure 1 shows the Norwegian transport system for natural gas to continental Europe. Norway exported 30 billion standard cubic metres through these pipelines in 1995, and plans to export 60 billion standard cubic metres in 2000. An uncertainty of 0.5 to one per cent in the measured volume passing through the sales metering stations represents an annual value of about USD 35-70 million from 2000. Control of uncertainty in the metering stations, and particularly of the parameters that have a negative impact on measurement accuracy, is clearly of primary importance; ref. Bosio and Erdal [Bosio 1996a]. The most commonly used method for metering large gas flows is based on the orifice meter. A significant amount of research has been done in recent years to evaluate the adequacy of specifications for orifice meter installations. To eliminate the effect of poor installation conditions, flow conditioners (PCs) have been recommended upstream of the orifice meter. Substantial efforts have been devoted to developing PCs with good performance. A thorough understanding of the flow field through an PC is critical to any work on optimising the design of these devices. The flow can be studied both experimentally and by computer simulations. This thesis will analyse the flow structure downstream of perforated plate PCs with the aid of computational fluid dynamic (CFD) techniques. With this approach, it is possible to introduce wide-ranging parameters and evaluate their effects using computer methods. Validation experiments for selected cases can demonstrate the method's credibility. The results of this dual numerical and experimental approach should speed up the work of optimising PC design. The work has been inspired by current practice for flow metering in large-scale gas transportation systems, and will focus on orifice meters. But its findings can also shed light on other metering technologies, and contribute to a better understanding of flowmeter performance.
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Figure 1 The Norwegian transport system for natural gas to continental Europe
Page 10 Orifice plate meters For many years, differential pressure meters were the only devices available for measuring flow rates in a pipe. More than a hundred different instruments are now available to measure flow on the basis of at least 10 different principles [O'Brien 1989, Furness 1994]. However, differential pressure meters still hold the largest slice of the market - 40 per cent, according to Furness 1987. Within the group of differential pressure flowmeters, the orifice plate is the type most commonly found in the gas industry for custody transfer metering. The origin of these meters reaches back to the antiquity. Aqueducts built by the Romans supplied water that was "metered" by an orifice at the household. Buyers agreed to pay their water bills in accordance with the size of the orifice bore [Miller 1996]. In modem times, the orifice meter came into wide use at the turn of the century for measuring natural gas. Its popularity rests on design simplicity, low cost, reliability, robustness, user friendliness and accuracy. The principle is based on measuring the pressure drop across an orifice plate installed in the pipe. The rate of flow can be determined from this pressure difference and from knowledge about the characteristics of the flowing fluid. Many forms of orifice plates are available, and alternative positions for pressure tappings are in use. Figure 2 shows a typical orifice meter with D and D/2 pressure tapping. The description of the flow through an orifice plate flowmeter is obtained by applying Bernoulli's equation and the continuity equation across the restriction. Flow through an orifice plate will continue to converge just downstream of the plate, forming a "vena contracta". See Figure 2. Since it cannot be measured experimentally, the area of this vena contracta is not known accurately. To correct for the assumption of nonideal behaviour, a dimensionless discharge coefficient, Cd , is introduced to account for discrepancies in the approximate analysis that relate to viscosity, temperature, pressure, compressibility, Reynolds number, wall friction and other effects. The discharge coefficient is defined as : Cd = actual flowrate/theoretical flowrate. The area of the orifice bore is used for calculating Cd .
Page 11 The final equation is then [ISO 1991]:
qm =-j==■ Si 1 cf J2Appi 4
where:
«i» Mass flowrate [kg/s] d Diameter of orifice [m] D Pipe diameter [m] Diameter ratio d/D P [1] Sl Upstream expansion factor [1] Pi Upstream density [kg/m3] Ap Differential pressure [kg/ms2]
Vena contracts
Figure 2 Diagram of an orifice plate flowmeter with D and D/2 pressure tappings. The figure is illustrating the differential pressure, pressure loss and "vena contracta".
Page 12 The gas expansion factor, 8, is a coefficient used to take into account the compressibility of the fluid. Equations to calculate Cd and gas 8 can be found empirically from data collected in flow laboratories. The value of the discharge coefficient is approximately 0.6 and 8 is normally between 0.9 and 1. Both government regulations and sales gas contracts between companies generally refer to international metering standards, which contain such equations. These standards have been developed jointly by experts representing the worldwide competance of the measurement community, including scientists and meter manufacturers as well as buyers and sellers of the fluids. Development of new standards and revision of existing ones are difficult and time consuming. New standards are only released after careful evaluation of new technologies. This is very understandable, given the high value of the gas involved and the need to achieve international agreement (See Teyssandier 1993). Much research was done on flow through orifice meter at Ohio State University between 1932 and 1935. These experiments were carried out on water using seven pipes, with diameters ranging from 25 to 350 mm. The results were used to derive the mathematical equations which is still applied in the most recent edition of ISO-5167 [ISO 1991]. At the end of the 1970s extensive R&D programmes were initiated both in Europe and in the USA to collect more input for a Cd database. Research was done on several terms with known physical significance, such as fluid type (water, air, natural gas and oil), pipe sizes, tapping points, Reynolds numbers and so forth. This database held about 11 000 records in 1990 and approximately 16 000 measurement points in 1994 [Ref Gallagher 1992, Reader-Harris 1990]. ISO-5167, with the Stolz equation for the Cd , is used in Europe today [ISO 1991], with the USA and Canada utilising the Reader-Harris-Gallagher equation [AGA 1991/API 1990]. Efforts are now under way to update ISO-5167 with an equation similar to the one used in North America [Ref Reader-Harris 1995a], because different standards are causing a number of problems for the multinational gas industry.
Installation effects in orifice meters The classic definition of "fully developed turbulent flow" is stated by Hinze as follows: "For the fully developed turbulent flow in the pipe, the mean-flow conditions are independent of the axial coordinate and axisymmetric, assuming a uniform wall condition" [Hinze 1975].
Page 13 All measurements that contribute to the development of the orifice plate Cd equation have been carried out with fully developed turbulent flow upstream of the meter. Therefore, the equations in the AGA/ISO standards are only valid when such a condition is fulfilled. If the flow field upstream of the orifice meter is distorted, and deviates from fully developed turbulent flow, an error will be introduced in the measurement. This measurement bias is usually referred to as an "installation effect". It is easy to meet the condition of fully developed turbulent flow by installing long straight pipes in a flow laboratory. In practice, such as on an offshore platform or in a plant, space is often limited, and deviations from fully developed turbulent flow will arise whenever the fluid passes through bends or experiences a change of pipe cross-sectional area. A literature survey for the flow field downstream of different pipes and fittings has been performed [Parchen 1988]. To avoid errors from installation effects, the standards include recommendations for the length of straight pipe upstream of an orifice meter. This thesis considers only time-independent distortion of the flow field that originates from upstream pipe configurations. When assessing the effect of pipework configuration, it is important to look into some basic principles. The upstream configuration is often of two types, depending on the resulting velocity field. One involves fittings which distort the flow profile without generating noticeable swirl, and the second those which distort the flow profile and generate bulk swirl [Miller 1996]. When the disturbing elements are all in the same plane, the generated velocity distribution is largely free from rotational movement (bulk swirl). However, the axial velocity profile can be skewed, i.e disturbed in the sense that the velocity at one side of the pipe is much higherthan at the other. The axial velocity profiles in this category can also be flatter or more peaked in the centre line than the ones obtained with a fully-developed velocity distribution. A typical example of this category is a 90° bend. The horizontal and vertical flow profile downstream of a single bend can be seen in Figure 3, together with the secondary flows. An expander or reducer also gives this kind of flow, which is distorted without swirl. In addition, these fittings give axisymmetric velocity profiles, see Figure 4. When the upstream pipework causes the flow to change direction twice in rapid succession in two different planes, considerable rotational movement or swirl will be introduced in the flow. The most typical example of this category is two 90° bends in planes at right angles to each other. This is often called a twisted S-bend. See Figure 5.
Page 14 Secondary flow
Figure 3 Diagram of velocity profiles and secondary flow downstream of a single 90° bend.
Figure 4 Axial velocity profiles downstram of an expander. The profiles are axisymmetric.
Figure 5 Flow rotation downstream of a twisted S-bend.
Page 15 Awareness of the importance of installation effects has grown in recent years. This is particularly true offshore, where mechanical constraints limit space for metering stations. However, it has been shown lately that metering errors of several percentage points can exist even in installations that meet the standards requirements [e g Mottram 1986, Bates 1991, Steenbergen 1995]. Much research has been done on this subject, and some information is now available on the behaviour of orifice meters in perturbated flow. Most often the changes in Cd are positive, which means that calculated Cd , for fully developed condition, is lower than real Cd . The result is an undermeasurement of the flow. If disturbed flow enters the orifice plate, the effect on the meter reading will depend on several parameters. These include axial velocity profile, degree of swirl in the flow, turbulence field, P -ratio, Reynolds-number and the tapping points used [Morrison 1990, Shen 1991, Morrison 1992a, Mattingly 1991, Kamik 1992], Normally, the flow picture upstream of the meter run in a metering station is a combination of different flow categories, and it can be difficult to determine the contribution on Cd from the various parameters. Nor is it simple to decouple the various effects experimentally. Producing an axial velocity profile that is nearly fully developed and also has flow with high swirl presents difficulties, for instance. Experiments with a swirl generator, often used to create tangential velocity, revealed that increasing the swirl angle redistributed axial momentum towards the pipe walls and changed the axial velocity profiles [Morrison 1994]. In a recent paper, however, Morrison et al have tried to split the effects of swirl and axial momentum by assuming that the two effects are independent of each other and contribute linearly to additive changes in Cd [Morrison 1995]. From this work, some general trends can be assessed:
• a peaky velocity profile decreases the pressure drop across the orifice plate and increases Cd
• a flat velocity profile generally increases the pressure drop and decreases Cd
• in swirling flow, centrifugal forces cause the jet to expand faster downstream of the orifice plate - giving an earlier and more rapid pressure recovery that causes the pressure drop to decrease and Cd to increase. • sensitivity to a perturbated axial velocity profile on Cd increases for larger |3 ratios • slight dependence exists for P ratios on Cd for swirling flows, except for high P ratios (above 0.65) which are very sensitive to high swirl.
Page 16 In general, swirl has a much greater effect on flowmeters than asymmetry, and also requires much longer straight lengths of pipe before disappearing. A length of 100 pipe diameters is often required to ensure that severe swirl has negligible effect on a flowmeter [Kreith 1965]. Results from research on installation effects are gradually being implemented in new revisions of the standards. But the delay between availability of testdata and updating of standards is often long. One of the main concerns of the standards today is the straight pipe length required upstream of the orifice plate. In general, several methods are available for dealing with installation effects. Three approaches are widely used in gas metering:
• specification of the required length of straight pipe upstream of the orifice meter based on experimental knowledge about installation effects
• use of other flowmeters, which are less sensitive to flow field distortion.
• insertion of a flow conditioner upstream of the flowmeter.
Much effort has been devoted to specify minimum upstream lengths for orifice metering stations with different upstream configurations. This research is time-consuming and very expensive for high-pressure testing. The problem lies in the impossibility of testing out the effect of all kinds of bends, headers, diffusers, expanders, valves for different pressures, temperatures, flow rates, gas compositions, P ratios, tapping points and pipe roughness. This kind of research can yield much information, but obtaining recommendations that are generally applicable is difficult since so many parameters are involved. Other devices, such as turbine meters [Cabrol 1992, Erdal 1992, van der Kam 1993 and Park 1995] and the new multipath ultrasonic meters [Sakariassen 1996, Halttunen 1990 and van Bloemendaal 1995], are less sensitive to installation effects. Guide vanes and, in some cases, flow straighteners are built into turbine meters as part of the device [Dijstelbergen 1995]. In ultrasonic meters, the number of acoustic paths is chosen to minimise the effect of perturbated flow profiles. Turbine and ultrasonic meters are therefore considered as an alternative to orifice plate for many applications. But change takes time in the gas industry, and orifice meters will continue to be seen in metering stations for many decades. In large pipe installations, the cost of including a straight settling length of some 100 pipe diameters is very expensive. Especially on an offshore platform, as it would also take too much space
Page 17 and be too heavy. An alternative means of controlling the requirements of upstream effects is therefore needed. This can be achieved by placing a flow conditioner (FC) in the pipe. An FC should restore a distorted velocity profile and remove the swirl (such devices are also sometimes called flow straighteners).
Flow conditioners developed before 1987 Numerous attempts have been made in the past to "isolate" flowmeters from piping-induced disturbances. Despite these efforts, much research is still under way to find the proper approach to achieving this objective. The FC seems to be one adequate way to reduce the effect on the meter performance of non adequate installation conditions in flowmeters. FCs can be grouped into four general classes based on their mechanical design - tube bundles, vanes/screens/tabs, perforated plates and combination devices. An overview of the best-known models in the 1980s can be seen in Figure 6. Of these devices, the tube bundle is the only one manufactured commercially and in general use. It consists of a collection of cylindrical parallel tubes assembled tangentially along their axis, fixed together and held within the pipe, figure 6d, 6e and 6f.
Figure 6 The best-known flow conditioners in a b c 1989. a) Etoile b) AGA/ASME c) AMCA d) ISO d e f e) AGA f) ASME g) Zanker h) Mitsubishi i) Sprenkle 9 h i From [Miller 1996]
Page 18 Tube bundles are extensively used in the USA. Both API [API 1990] and AGA [AGA 1991] standards provide for the use of tube bundles as part of the minimum upstream length to assure accurate flow measurement with orifice plates. The ISO-5167 [ISO 1991] standard recommends them for special non-standard fittings. Specifications in the standards allow a great deal of latitude in actual construction. Tube bundle straightening vanes in common use can therefore differ greatly in the number of tubes, length, tube diameter, tube packing (hexagonal or radial), tube-to-tube attachment, mounting within the pipe, and so forth. Until now, tube bundle conditioners have been widely used because of their low cost, easy fabrication and low maintenance expenses. Two vane/screen FCs are shown in Figure 6. One is the Etoile (star) straightener [ISO 1991], shown in Figure 6a. It consists of eight flat, thin plates aligned parallel to the axis of the pipe. These divide the flow cross section into equal portions. The length is equal to twice the diameter of the pipe. The second is the AMCA FC [ISO 1991], which consists of a honeycomb with square meshes. See Figure 6c. Both these FCs should have the vanes and plates to be as thin as possible while providing adequate strength. Vane/screen/tab FCs are designed solely to eliminate swirl. Pressure loss over these FCs are very low, with a pressure loss coefficient - ApFC /(0.5pU2) - of approximately 1 in both cases depending on the plate or cell thickness.
The Mitsubishi FC [Akashi 1979] is a perforated plate with a thickness of 0.13 D and 35 holes of the same size with diameters equal to the plate thickness. As Figure 6h shows, these holes are arranged in a hexagonal configuration. The pressure loss coefficient for this FC is only 1.5, and it has been claimed to achieve fully-developed flow conditions within 10-11 D from the last upstream disturbance. In a study using laser Doppler velocimetry, Spearman et al [Spearman 1991] demonstrated the effectiveness of this FC in removing swirl, but also showed that it was less effective in removing asymmetrical flow in the stream. Some FCs have been made by combining various types of straightener in an attempt to bring together the best features of the individual components. The Tinker conditioner [Zanker 1969] is a perforated plate with holes of certain specified sizes, followed by a channel for each hole formed from the intersection of a number of plates - Figure 6g. Three perforated plates in series with a length equal to one pipe diameter between the successive plates are employed in the Sprenkle FC [Sprenkle 1958]. Perforations are preferably chamfered on the upstream side, and porosity must be greater than 40 per cent (total area of holes in each plate to cross-sectional area of the pipe). The
Page 19 ratio of plate thickness to hole diameter will be at least 1, and the diameter of the holes must be less than or equal to 0.05 D. See Figure 6i. A Sprenkle FC has a high pressure loss coefficient by comparison with the ISO tube bundle and the Zanker FC - about 15, 5 and 5 respectively. As mentioned above, the vane/screen FCs have much lower pressure loss, but these devices are unable to develop the flow profile rapidly . Among the FCs in Figure 6, the Mitsubishi has been shown to be superior in many respects to the others [Humphreys 1984]. However, only the tube bundles have been generally accepted in the measurement community.
Modern flow conditioners Statoil's K-Lab facility at Karste north of Stavanger started to design a higher-performance FC in 1987. This project was initiated by P L Wilcox, then technical manager at K-Lab. The first new FC, called Markl, was developed in cooperation with E M Laws at the University of Salford in the UK. Later, K-Lab also cooperated with Institute for Energy Technology (IFE) in developing FCs. This author joined the project in 1989. K-Lab was primarily interested in making compact metering systems for use on offshore platforms in the North Sea. The traditional orifice meter systems built in accordance with ISO-5167 [ISO 1991] were too large, heavy and costly. In addition, the twisted S-bends that cause swirl are often used offshore, and various research papers indicated that swirl need more than the specified upstream lengths recommended in the ISO-5167 standard to be eliminated and unaffected from installation conditions [i.e. Bates 1991]. It is easy for a porous plate FC to remove swirl. The challenge was to achieve fully developed flow within a short distance downstream of the FC - a maximum of 15 D downstream of the flow perturbance. The first FC was denoted K-Lab/Markl. It was 50 mm thick, with a porosity of 51 per cent and a pressure loss coefficient of 2.4. Incorporating seven rings of holes, it was constructed from 154 tubes. See Figure 7. Manufacturing was not very easy. Its performance was good, but it became clear in 1989 that it would be preferable to make the FC from a perforated plate. On the basis of this experience, K-Lab developed a series of FCs in cooperation with the IFE, called K-Lab/Mark2 to K-Lab/Mark5. They were all 50 mm thick, with a central hole and four rings of holes. All were efficient swirl-killers. The various hole diameters were varied to produce a fully-developed turbulent velocity profile a short distance downstream of the FC. This was to be achieved independently of the swirl and velocity profiles that existed upstream of the FC. Figure 8
Page 20 shows a drawing of Marks, and Table 1 provides the design specifications for these FCs. Tests performed with these FCs were reported in papers by Wilcox, Weberg and Erdal [Wilcox 1990a], Wilcox and Erdal [Wilcox 1990b] and Erdal et al [Erdal 1994], the first paper in this thesis.
Model Ring number Pitch circle diameter Hole diameter Number of holes (r/D) (a/D) Mark2 1 0.86 0.11 22 2 0.62 0.07 16 3 0.43 0.11 11 4 0.21 0.07 8 5 0.00 0.13 1 Mark3 1 0.91 0.07 30 2 0.73 0.09 20 3 0.52 0.10 13 4 0.28 0.11 6 5 0.00 0.11 1 Mark4 1 0.91 0.07 22 2 0.73 0.09 15 3 0.52 0.10 10 4 0.28 0.10 6 5 0.00 0.10 1 Marks 1 0.91 0.07 32 2 0.73 0.09 21 3 0.52 0.09 14 4 0.29 0.10 7 5 0.00 0.12 1
Table 1. Design specifications for the K-Lab Mark2, Mark3, Mark4 and Marks flow conditioners.
Page 21 o DOOOQXO
K-Lab FC model Markl. K-Lab FC model Marks.
A similar perforated-plate FC, called K-Lab/Laws, with a central hole surrounded by two rings of holes, is described by Laws [Laws 1990] and shown in Figure 9. The minimum plate thickness was found to be 0.123 D, but it can be increased without significantly affecting the plate's swirl-removing properties. Pitch circle diameters of the inner and outer rings are 0.4616 D and 0.8436 D respectively. The total number of holes varies between 19 and 23, but 1:6:12 or 1:7:13 configurations are normally used. These FCs have a pressure loss of approximately 2.5, which could be reduced to about 1.8 by chamfering the upstream face of the holes at 45° to a depth of D/64. The FC was compared originally with the Mitsubishi, and found to be superior. Sanderson and Sweetland [Sanderson 1991] and Lake and Reid [Lake 1992] also found the K-Lab/Laws plate to perform best in their comparisons with other FCs. The performance of the Laws and Mark-series FCs is similar [Lindholm 1992], and both are covered by the same patent. In addition to being better known than the K-Lab/Mark models, the K-Lab/Laws model is simpler to manufacture (fewer holes) and suffers slightly lower pressure loss. As a result, this is the only model currently manufactured. A leaflet [Bosio 1996b] provides a record of all K-Lab FCs currently installed in metering systems.
Page 22 Figure 9 The K-Lab/Laws flow conditioner, with hole configuration 1:6:12.
When the project on compact metering systems began at K-Lab a decade ago, enthusiasm in the metering community for FC research was not particularly high. But interest in this technology has changed drastically, and a lot of researchers are currently studying FCs. A sliding vane technique developed at Southwest Research Institute (SwRI), which can relocate the FC without venting the meter run or disconnecting flanges, has saved considerable time and made research more efficient [Morrow 1990]. A lot of work has been done on tube bundles at SwRI in recent years, with the focus on the Cd changes introduced by different location of the tube bundle. The additional uncertainty in the flow measurement, reflecting upstream installation effects, can be up to one per cent for some p ratios, and many researchers have tried to find the optimal installation position for various FCs to minimise the metering error [e.g McFaddin 1989, Kothari 1989, Mattingly 1990, Brennan 1991, Morrow 1992, Gregor 1992, Morrow 1995]. Several researchers found that latitude in the construction of tube bundles can cause variations that influence orifice plate Cd [Kamik 1995 and Stuart 1993]. These findings have made scientists curious to invent a better FC, and competition has almost raged in recent years over the metering conferences to come up with even better flow conditioning devices. Nova in Canada [Kamik 1995] has tried to optimise the K-Lab/Laws FC. Kamik modified and improved the hole distribution pattern and ended up with a 1:8:16 pattern, rather than the 1:6:12 or 1:7:19 typically used in a K-Lab/Laws FC. Two basic designs were evaluated, one with 40 per cent porosity (holes compared to pipe area) and one with 50 per cent porosity. The pressure loss of the plates was 4.5 and 2.5 respectively. Screen theory was used in the design, and tuning was performed to give a velocity profile close to the reference profile for Reynolds numbers greater than 10*. The
Page 23 work resulted in an optimised FC with negligible effect on the measured mass flow through the orifice meter. A similar modification to the K-Lab/Laws plate has been done at the NEL in Scotland by Spearman et al [Spearman 1994]. They used LDV to measure the flow structure when placing different designs of perforated-plate FC downstream of a 90° bend and a twisted S-bend. In a manner similar to the Nova modification, NEL's optimal design has an outer ring of 16 holes and an inner ring of eight holes. But the central hole is replaced by four holes arranged in a square at the centre. See Figure 10. The performance is good, but the pressure loss coefficient is higher (at approximately 3) than the K-Lab/Laws plate. A modification to the K-Lab/Laws FC was made in 1993, and reported during 1994 in a series of papers by Laws and Ouazzane [Laws 1994a and Laws 1994b] and by Laws, Ouazzane and Erdal [Laws 1994c and Laws 1994d], The refined device with tabs and vanes is illustrated in Figure 11. The new design has six radial vanes on the upstream side of the plate, and six short radial tabs on the downstream side. These vanes are intended to straighten flow and reduce the asymmetry in a distorted upstream flow, leaving the plate to operate in a less hostile flow environment. The addition of vanes on the plate significantly improves the overall performance of the FC, giving a device that can produce both acceptable time mean flow and axial turbulence intensity profiles in short upstream and downstream installation lengths with very low pressure loss. In a study, Laws, Ouazzane and Erdal [Laws 1994d] showed that even a 70 per cent porosity plate with a pressure loss coefficient of 0.7 gave remarkably good results, with a total length from the upstream disturbance to the orifice meter of only five-six diameters.
Figure 10 The NEL flow conditioner.
Page 24 Plate
Vanes
Tabs
Figure 11 The K-Lab/Laws flow conditioner with tabs/vanes.
An improved tube-bundle FC has also been developed lately. See Figure 12. It makes use of tubes of different diameters to "grade" the flow resistance in the radial direction and to improve velocity profile shaping combined with an anti-swirl device. Called the Stuart tube bundle, the device is described by Stuart in a couple of papers [Stuart 1993 and Stuart 1994]. This new kind of optimised tube bundle is well within the tube bundle specification as set out in AGA Report No. 3 [AGA 1991]. As a result, application of a Stuart tube bundle design would not require a revision of the metering standard. Stuart tested out different combinations of tube size, and the best delivered a very good performance [Morrow 1995].
Figure 12 The Stuart tube bundle
Page 25 In 1994, Gallagher presented a new combined device consisting of a short tube bundle (1/2 D long) and a perforated plate with three rings of holes, separated by a "settling chamber" 3 D in length. The inner ring has three holes, the middle has eight and the outer has sixteen. This new device has been presented in a couple of papers by Gallagher [Gallagher 1994 and Gallagher 1995] and showed a very good performance. Two other types of FC have also been described in the literature during recent years. The first of these is the Bosh & Hebrad device [Bosch 1984 and Bosch 1990]. It is a development of tube bundles in which the tubes vary in length and diameter. The design of this FC is rigorous and complex, and the pressure loss is relatively high. This device is not in general use in the gas industry for fiscal metering. The other is the Vortab FC, described by Smith et al [Smith 1989]. This FC is a combination of "swirl tab" and "vortex tab" generators. Its overall length is four pipe diameters, which is somewhat long for compact metering systems. The FC was tested by Laws and Reader-Harris [Laws 1993], showing very low pressure drop and relatively good performance. Table 2 gives an overview of current PCs.
FC class Type Head loss Reference Tube bundles ASME 1 ASME 1980 ISO 5 ISO 1991 Bosch & Hebrad 10 Bosch 1984 Stuart 1 Stuart 1993 Vanes/screens/tabs Etoile 1 ISO 1991 AMCA 1 ISO 1991 Vortab 0.70 Smith 1989 Perforated plates Mitsubishi 1.50 Akashi 1979 K-Lab 2 Wilcox 1990a/Laws 1990 NEL 3 Spearman 1994 Combination PCs Sprenkle 15 Sprenkle 1958 Zanker 5 Zanker 1969 K-Lab/Laws with tabs/vanes 2 Laws 1994a Gallagher 2 Gallagher 1994
Table 2 Overview of the various flow conditioners.
Page 26 Flow conditioners and international metering standards As long as the gas market was a national and/or local business, metering was a topic of limited concern except when invoices were received. The first edition of a comprehensive ISO standard for orifice meters was issued as late as 1967! This was more than a decade after natural gas had started to flow in pipelines across European borders. The gas industry has traditionally been very conservative, but its competitiveness has been seriously strengthened over the years. Internationalisation of the gas supply market began in the mid-1950s, and the technical and commercial challenges have increased continously. The speed of technological improvement creates challenges for the user of standards. In the gas metering field, recognised standards have slipped behind as new technologies entered the market. The International Organisation for Standardisation (ISO) has played a central role in the standardisation of flowmeters for the process industry in general, while the American Petroleum Institute (API) and the American Gas Association (AGA) standards have been dominant in the oil and gas industry. However, since all the major gas producers and transporters have become multinationals, the standard organisations - under pressure from the users - are pursuing a process to make the same standards applicable world-wide. To meet the requirements of European Union directives, the Comite Europeen de Normalisation (CEN) has been created in Europe. The Vienna agreement between ISO and the CEN aims to eliminate duplication of effort, and to ensure that standards published by one of the two bodies can be retained as an ISO or CEN standard with a minimum of administrative formalities. See Bosio and Erdal [Bosio 1996a]. As noted above, a great deal of research has been carried out on PCs over the past decade, and many new and better devices than those mentioned in the current standards have been developed. In 1986, an ISO draft document on PCs was written by Hondareyte [Hondareyte 1986]. This work has to be reconsidered, and a group of experts is currently evaluating the state of the art on PCs for ISO. It plans to come up with a performance evaluation of the various flow conditioners. In North America, researchers at various US and Canadian companies are now preparing a White Paper on installation configuration with and without flow conditioners. This group was asked by the API's standardisation committee to cany out an analysis of available data on orifice meter installation effects, to identify problem areas and information gaps, and to recommend potential solutions. The
Page 27 group's mandate also includes the formulation of recommendations for further research. This White Paper will subsequently be used in developing the revised orifice standard [Studzinski 1996]. The group is collecting data on the flow structure downstream of various pipe configurations, with and without PCs, from different test facilities. Where data are not available, further research will be done. The aim is to collect data downstream of 14 selected pipe geometries. These are:
1. single 90° elbow, R/D=l. 5
2. single 45° elbow
3. 90° inspection tee
4. 90° elbow preceded by a spacer longer than 10 D and a pipeline element such as another 90° elbow or a header
5. two 90° elbows (R/D=l .5) in plane with a spacer shorter than 10D (S-bend)
6. a 90° elbow preceded by a valve
7. a valve preceded by a straight pipe
8. a valve preceded by a 90° elbow
9. two 90° elbows (R/D=l .5) in perpendicular planes with and without a short spacer
10. two 90° elbows (R/D=1.5) in perpendicular planes with a spacer longer than 9 D
11. three 90° elbows in different planes
12. headers combined with elbows and spacers
13. an expander (2.5/4) preceded by a spacer and 90° elbow (R/D=l .5)
14. a reducer (3/2) preceded by a straight pipe.
Measurement of the effect on orifice meter Cd after all these pipe configurations, with different PCs installed in various positions, are being collected and evaluated. (3 ratios between 0.2 and 0.75 and Reynolds numbers from 1.5' 10" to 7' 106 should be covered. This is an important but obviously very time-consuming and difficult task. When necessary data points from the test matrix above are collected, an enormous database about flow conditioners will be available. In real life, however, new parameters will always emerge. What will happen if the bend radius (R/D), bend angle, pipe friction,
Page 28 gas composition or FC design change slightly? Can the data in the database then be used, or must more measurements be done? Questions like these will always be raised. Looking at all the variables above that can affect measurement error in an orifice meter station, it is easy to see the need for a tool to predict installation effects and how to cope with them by using a flow conditioner. Even though the simulation will not be 100 per cent correct, it could be useful for pinpointing trends and speeding up laboratory work by selecting the most important cases for measurement. To diagnose a problem within the current standard and recommend an improvement, two sets of data from independent facilities are required by the group. Prediction methods could also be valuable here when special trends need to be illuminated.
CFD codes and upstream effects The use of CFD techniques in metering technology has increased over the past few years. The main reason is the remarkable advances in computer calculating power. In addition, the predictive capabilities of the codes have been improved. Most of the engineering community uses commercial CFD codes, and a dozen different programmes are on the market. A recent paper [Freitas 1995a] presents the results of a series of benchmark simulations using commercial CFD codes. The simulations were performed by the vendors themselves. Five different flow phenomena with varying degrees of complexity for both laminar and turbulent flow were predicted and compared against measured data. In general, the codes gave acceptable results when applied correctly. A key finding of the project was that people who carry out CFD simulations needed very good insight into the solution of the problem to obtain grid convergent results. That CFD programmes never should be used as a "black box" is also clearly demonstrated by Spencer et al in a similar paper [Spencer 1995]. It was found that different experts obtained significant variability in the numerical prediction of the flow in a given configuration when using the same CFD code and turbulence model. Many of the problems to which these codes are applied push the limits and assumptions that the models are based upon. For example, the flow through complicated bends may require more accurate discretisation methods than the second order schemes which are the most advanced in such programmes today. The current state of the art in commercial CFD codes is the standard k-e model and other eddy-viscosity models. Many papers - e g Bradshaw, Launder and Lumley [Bradshaw 1996] - have shown that further research into more advanced turbulence models is required. In
Page 29 particular, the dissipation transport equation used to provide a length (or time) scale in both two-equation and stress-transport models is a major source of error. Despite these limitations, more and more researchers use CFD techniques in conjunction with experiments for guiding and validation. Durst et al. [Durst 1989a and Durst 1989b] have studied the flow through an axisymmetric orifice in a pipe both numerically and experimentally. They found good agreement between calculations using a k-s turbulence model and measurements. Davis and Mattingly [Davis 1997] modelled orifice plates with (3 ratios from 0.4 to 0.7 and with Reynolds numbers - Re^ - in the range 104 to 106. They found that the agreement between computed and experimental discharge coefficients was within four per cent and concluded that computational methods have to be considered a feasible and fertile complement to theoretical and experimental analyses. Sheikholeslami et al [Sheikholeslami 1988] and Barry et al [Barry 1992] subsequently used Fluent to model the variations in orifice meter performance as a function of Re-,, (3 ratio, pipe surface roughness, upstream swirl, and upstream and downstream flow boundary conditions. They reported that an 80 x 60 grid is sufficient to obtain a discharge coefficient within two per cent of the empirical data. Reader-Harris [Reader-Harris 1986 and Reader-Harris 1989] has also used CFD codes to study orifice meters; primarily the discharge coefficient, the effect of pipe roughness on it, and the wall pressure distribution through the orifice. He reported that discharge coefficients can be calculated with a remarkably highaccuracy - within 0.64 per cent. Several authors (e g, Langsholt [Langsholt 1991], Morrison [Morrison 1992b] and Freitas [Freitas 1995b]) have used CFD for parametric studies. Morrison studied the effect of upstream flow conditions on orifice flow meter performance and found a correlation between the second and third order radial moments of momentum, mvr2 and mvr3, and the value of the discharge coefficient. This correlation can be used to estimate the change in the Cd given the inlet velocity profile. Reader-Harris et al [Reader-Harris 1995b] used Fluent to study the magnitude of ACd shift when the upstream velocity profile differs slightly from fully-developed. Their predictions showed that the current ISO-5167 requirements, which consider ±5 per cent deviation from the reference profile to be fully developed, can lead to values of ACd that greatly exceed ±0.2 per cent for large (3 ratios.
The same study predicted the flow structure downstream of different bends and found that good installation design can eliminate some of the more severe flow problems. Thomassen et al
Page 30 [Thomassen 1992] have also evaluated several metering stations both experimentally and by using CFD models to study trends and to provide insight into the flow physics. In improving ultrasonic flow meters, CFD techniques have also been used with good results to study the influence of various upstream bends on the performance of different path configurations [Hilgenstock 1996]. Stang [Stang 1995] showed that this method, in combination with a flowmeter model, gave good accuracy for Reynolds numbers above 30000. Two papers have been found in the literature that compute the flow through a FC. Pasdari and Gimson [Pasdari 1990] simulated the velocity profiles downstream of a perforated plate FC. They obtained good agreement between their predictions and the experimental data, but the grid they used was rather coarse: only 15 cells in the radial direction. Barry et al [Barry 1992] tried to model a 30-degree sector of a tube bundle FC with a finer grid (51 x 51 x 24) using Fluent, but the numerical model constructed did not converge to a satisfactory solution. Possible reasons for this problem were the severe skewness of the grid and large jumps in the grid size. Morrison et al [Morrison 1994] used a CFD model to evaluate several upstream profiles to see which would generate fully-developed turbulence and velocity profiles in the shortest distances, and found that a parabolic velocity profile produces fully-developed turbulent flow in a shorter pipe length than a uniform or power law velocity profile.
The Phoenics CFD code As mentioned above, several commercial codes are available. Before this project began, Statoil and Institute for Energy Technology (DFE) had cooperated on several CFD projects that used Phoenics, so this programme was well known. An evaluation of different codes [Austegard 1991] also showed that Phoenics was better than other codes at generating the body fitted coordinate (BFC) grids needed to model FCs. So version 2.0, and later 2.1.3, of this code was selected for the study. Developing a new code was not considered cost efficient. Phoenics is a CFD software package that runs on PCs, workstations, supercomputers and parallel systems. It solves steady-state or transient two- and three-dimensional problems for laminar and turbulent flow. Numerous turbulence models and many different numerical schemes are built in, but some cannot be used for BFC grids. A great deal of the Fortran source coding is available to assist users, so that new models can be added and existing ones adapted. Phoenics allows users to generate colourful plots of contours, vectors, streamlines and iso-surfaces throughout the simulated geometry,
Page 31 and to view the results from any angle. Text can be added to plots and the final image can be saved for inclusion in reports [Cham 1996], A great deal of time has been devoted in this project to assess the results from the computations and to comparing predictions with measurements. About 2 000 runs have been performed, with CPU times from a few minutes to 100 hours. A large number of parametric studies have been done to find the correct way of using the code, and several errors in Phoenics were discovered during this project. Some of the findings were published at a turbulence modelling seminar at Phoenics developer Cham [Erdal 1995]. It is impossible for the system developers to test the code for all flow problems. Instead, new versions are evaluated for a certain number of test cases. These are available in the Phoenics library. One of the author's simplified orifice models is implemented in the library [Example 110], so the staff at Cham will assess this example before new versions of the software package are released. Phoenics was run initially on an IBM RS6000 model 25 T and subsequently on 380 and R21 models. These are Unix (or AIX) Power PCs. A few test cases were also performed on the Cray Y-MP supercomputer at the Norwegian University of Science and Technology in Trondheim. Because this machine has many users, the total simulation time on it was no shorter than on the Power PC, where nearly all the CPU capacity was available.
Progress in the papers in this thesis The object of this thesis has been to investigate whether it is possible to compute the flow structure downstream of an FC subjected to a distorted flow field, and to try to illuminate some of the parameters that affect the performance. The hypothesis before the project started was that CFD models could be a better approach than trial and error, screen theory or other models which have earlier been used to develop PCs. Very little was known about how a model of a complicated geometry like an FC would perform. It was therefore necessary to advance step by step, starting with simple models and evaluating predictions against experimental data all the time. The air measurements were carried out at the department of applied mechanics, thermo and fluid dynamics at the Norwegian University of Science and Technology in Trondheim and at the IFE in Kjeller near Oslo.
Page 32 Flow problem
Development of FC Paper I
Ring model CFD models Trial and error Screen theory Paper I Papern
3-dimensional study of a FC after bends Paper IQ
Numerical aspects of the CFD problem Paper IV
Comparison of a 1 hole, 9 hole and a 19 hole plate Paper V
Numerical study of different parameters that effect the performance of a FC v Paper VI
Figure 13 Flow chart for the progress in the report
Page 33 Figure 13 summarises the various activities in the project. First, the state of the art in FC development in 1994 was described and results from recent years were reviewed. A preliminary CFD study was then performed on one-hole and nine-hole simplified FCs installed in fully-developed flow. Simulations and measurements were compared, and the results from this study were encouraging. The project went on to assess the predictions of a K-Lab/Laws FC installed downstream of a 90° bend and a twisted S bend (two 90° degree bends out of plane.) The accuracy of the three-dimensional predictions downstream of the FC was better than expected, and CFD methods were shown to be a potentially valuable tool in studying the mechanisms influencing FC performance. Much energy and work were devoted to various numerical aspects of computing flow through restriction plates for optimising the model to achieve the best possible results. When the various calculation methods had been evaluated, the CFD technique was used to compare the flow field downstream of three plates with one, nine and 19 holes. The work was extended in a final paper which used the model to study various FC designs.
Paper I: "Development of a flow conditioner" This paper reviews the major activities in the process of developing a flow conditioner at K-Lab between 1987 and 1994. In the early days of the project, the following goals were listed : • eliminate swirl (within 2°) and generate a fully-developed velocity profile (within five per cent ) at a maximum of 15D downstream from the flow perturbance (requirements from ISO-5167)
• give low pressure drop across the FC
• be simple and cheap to manufacture
• give similar or better measurement accuracy than a standard ISO-5167 installation.
The main research activities in developing a good FC were then described. First, a theoretical design model was developed, in which the cross-sectional area of the FC was discretised into rings. The porosity of each ring is then calculated to obtain a predefined velocity profile and pressure loss in the designed FC. From that model, FCs were designed with different overall porosity ((holearea*100 per cent)/pipe area) between 0.4 and 0.51, and pressure loss coefficients between 2.13 and 4.65. The different FCs were then tested in air at atmospheric pressure. One of the models,
Page 34 called Mark 5, had the lowest pressure loss coefficient of 2.1. This fulfilled the ISO-5167 requirements 15 D downstream of a single 90° bend and a twisted S bend. The performance of the Mark 5 was then tested in natural gas at high pressure. The velocity profiles and swirl angles were measured with a specially-developed Pitot probe. Again, the ISO-5167 requirements were fulfilled. See figure 14 and 15. The orifice meter discharge coefficient was then measured at 100 bar with a Mark 5 installed and with (3 ratios equal to 0.2, 0.6 and 0.75. The distance between the last bend and the orifice meter
was 15 D, and such metering systems are called Short Metering System (SMS). Reynolds numbers
in the tests were between 5 104 and 2107 . The measured Cd showed a deviation within 0.5 per cent compared to the flow through the sonic reference nozzles. The SMS was also compared against base-line Cd data (100 per cent fully-developed flow), and the results were within 0.2 per cent. A comparison between a 15 D SMS with this FC and an ordinary installation with normal ISO requirements for upstream lengths revealed that the SMS with Mark 5 performed similarly or better.
5 °.8 - "5 -2,0 - 3 0,6 - -4,0 -
0,0 0,2 0,4 0, 0,8 1,0 1,2 1,4 1,6 1,8 2,0 power law Re-15.2E-6 Re-S4E-5
0,0 0,2 0,4 0,6 0,8 1,0 12 1,4 1,6 1,8 2,0
Figure 14 Figure 15 Horizontal velocity profile 15D downstream of Horizontal swirl angle profile 15D downstream a twisted S-bend when Mark 5 was used. of a twisted S-bend. Results with and without
Mark5
Page 35 Paper II: "Evaluation of a CFD-model for simulation of simplified flow conditioners" The first paper confirmed the promising potential of FC technology. So the challenge was to collect performance data for a result database and to continue optimising the design of the PCs This paper described the results of a project initiated to evaluate the performance of a CFD code for this purpose. The idea was that if flow profiles downstream of simple perforated plates could be predicted, it might also be possible to predict the flow characteristics downstream of more complex flow conditioners. In this study, a k-S CFD model was used to calculate the flow through obstruction plates with one large or nine small holes. Mean velocity, turbulent kinetic energy, k, and the dissipation rate of turbulent kinetic energy, 8, were all calculated and compared against measured data. The simulation of the velocity profiles and the dissipation rate compared well with the measurements. See Figure 16 as an example. Only the predicted distribution of k differed significantly from the experimental data. The results from the second paper were encouraging. They indicated that it is possible to predict flow development downstream of restriction plates with reasonable accuracy, and that it might be possible to simulate the flow through PCs.
1,2
0,4
0,2 Measured Predicted
o.o 0,0 0,2 0,4 0,6 0,8 1,0 y/R
Figure 16 Predicted and measured velocity profiles 10D downstream of 9H plate
Page 36 Paper III: "Three-dimensional computation of turbulent flow through a flow conditioner" A further step was taken in this paper. The flow through a 90° bend and two right-angle bends out of plane, and thereafter through a 19-hole K-Lab/Laws FC, was predicted and compared against measurements. Three different k-s models were used. Results downstream of the FC compare very well with the measurements. The calculations clearly demonstrate how the various jets are mixed. At
2.5 D downstream of the plate, it is still possible to count the number of holes in the plate from the contour plot. At 5 D, however, the individual jets can no longer be distinguished and, at 10 D, the contour lines are close to fully developed, see Figure 17. It was concluded that simulations of this type can be a valuable tool for designing FCs and assessing their effect. Another conclusion was that more research is needed to improve the calculation of flow through bends. The main characteristics of the velocity field are well predicted with eddy-viscosity models, but the calculated profiles are generally too flat compared with the measurements just downstream of bends. Predictions would probably be improved with more advanced turbulence modelling, such as a full Reynolds stress model. But higher order differencing schemes and finer meshes should also be evaluated to obtain grid-independent solutions.
Figure 17 Contour plot of the axial velocities 2.5D downstream of the 90° bend (A), through the FC (B), and 2.5D (C), 5D (D) and 10D (E) downstream of the plate.
Page 37 Paper IV: "Numerical aspects of flow computation through orifices" If simulation of flow through FCs and common flowmeter installations are to be modelled correctly, the numerics used must be studied carefully. It was decided to investigate the model of a geometrically simple one-hole plate before more complex FCs were modelled. These simulations revealed that considerable care is needed before confident results can be predicted. The main recommendation from this study is that the grid spacing must be approximately 0.001 D just upstream of the plate to resolve the flow field here and to calculate the pressure loss correctly. The study also demonstrates how important it is to use higher-order differencing schemes. Wall functions are evaluated and the non-equilibrium log-law is found to perform better than the standard log law. The grid expansion ratio seems to be less important than expected from other papers. Figure 18 shows how well the pressure drop can be predicted with an appropriate numerical model, in a 46D pipe with an orifice installed 30D downstream of the inlet. The investigation also reveals that the k-S model can provide the flow structure trends in an orifice, but more advanced models are needed for accurate prediction of the part of the flow field where the turbulence level is very high, as it is just downstream of an orifice. Predictions were satisfactory further downstream of the plate, where the turbulence structure is relatively unimportant. A modification of the Chen-Kim k-S model is suggested to improve performance when used to simulate flow through orifices at high Reynolds numbers.
Measured 400.0 -
300.0 - Predicted
200.0 -
co 100.0 -
-100.0 -
-200.0 -
-300.0 - Figure 18 Comparison of calculated and measured axial pressure.
Page 38 Paper V: "Flow development of two simplified and one K-Lab/Laws flow conditioners - experiments and calculations" The numerical experience obtained so far was used to recalculate the flow through two simplified plates with one large and nine small holes in addition to a K-Lab/Laws FC. Finer grids, better numerical methods and additional measurements were used in this study by comparison with paper 2. All plates were installed in fully-developed flow. Mean velocity, turbulent kinetic energy, k, and the dissipation rate of turbulent kinetic energy, £, were all calculated. Critical flow characteristics, such as reattachment point, length of axial jets, turbulent regions and the distance required to re-establish fully-developed flow downstream of the different plates, were reported from the predictions. Comparison between the predicted and measured results reveals that the numerical model is capable of describing the trends in the flow. Another finding is that flow field downstream of a simple one-hole device was more difficult to calculate accurately than the flow downstream a more complex geometry like a 19-hole flow conditioner. It is assumed that the flow structure is largely affected by the turbulence level, which here is inversely proportional to the number of holes in the plates. The higher the turbulence level, the larger is the deviation in the predicted values. See Figure 19. From 10 D and further downstream of the plates, where the turbulence structure was relatively unimportant, the simulations were satisfactory for all plates. k/(Wm)2 a
k/(Wm)2 8.0E-2 2.5D, I o ^ o o 2.5D, II 6.0E-2 * 5D
10D 4.0E-2 15D
2.0E-2 2.5D
5D
O.OE+O■0 ------'------!------'------1------■------i------'------1------■------1— 10D 0.0 0.2 0.4 0.6 0.8 1.0 15D Y/R
Figure 19 Predicted and measured turbulent kinetic energy downstream of 1H plate (a) and 9H plate (b). The measured values are shown by points.
Page 40 Paper VI: "A numerical investigation of different parameters that affect the performance of flow conditioners" In this study, the standard k-S model was used to predict and examine trends and provide
insights into the velocity and turbulence field downstream of various PCs installed in fully-developed flow. Several parameters which may affect turbulent mixing and flow conditioning downstream of a plate were studied. Until now, it was thought that the graded porosity is the most important parameter for an efficient PC. The results from this study indicated that graded porosity is responsible for quickly obtaining a velocity profile close to fully developed. They also confirmed that it is possible to obtain approximately fully-developed velocity profiles a few diameters downstream of the plates with different overall porosity if the grading of porosity is appropriate. But various geometrical parameters, such as hole diameter, number of holes and their arrangement, are even more important. These factors determine the blocked area in the plate, which is responsible for producing turbulence and pressure drop. High k just downstream of the PC determines the mixing level and contributes to the flow conditioning. But a high turbulence level just downstream of the PC also requires a longer downstream pipe length before the flow calms down and becomes hundred per cent fully developed. See Figure 20. This dual behaviour of the turbulence level can explain why two devices with high porosity placed one after the other are capable of producing fully-developed flow within a very short installation length.
r.k/Wm2 5D 0.02 45% 0.018 54%
60%
70%
Figure 20 Turbulent kinetic energy, k, 0.004 5D downstream of 45, 54, 60 0 0.2 0.4 0.6 0.8 1 Y/R and 70 per cent PCs calculated two-dimensionally.
Page 41 Conclusions This thesis describes how the K-Lab flow conditioners were developed. Using a K-Lab FC allows the distance from the last bend to the orifice meter to be reduced to 15 D. The velocity profile and swirl angle upstream of the orifice plate still fulfil the ISO-5167 requirements, which state that the velocity profile should be within ± 5 per cent and the swirl angle less than 2°. The results cited in paper I show that this metering system gives an additional uncertainty of about 0.2 per cent for (3 ratios between 0.2 and 0.75 in natural gas at 100 bar.
Design methods used earlier, such as screen theory, cannot be used to improve FC technology further or to secure a more fundamental understanding of how FCs work. Instead, papers II and III reveal that CFD techniques can be a valuable tool. But paper IV also indicates that considerable care is needed in the design of the numerical model before confident predictions can be made. In paper V, the flow field downstream of plates with different numbers of holes is predicted. Comparisons with measurements show that the k-s model simulates the flow structure downstream of a complex geometry, such as the 19-hole K-Lab/Laws FC, better than the flow downstream of a simple one-hole plate. The reason for this is probably that the standard k-e model has difficulties in accurately predicting the part of the flow field in which the turbulence level is very high, as it is just downstream of the orifice. The paper also indicates that a high level of turbulence causes rapid mixing of the flow, which rapidly results in a velocity profile close to fully developed. But highk also requires a very long distance before the flow calms down, and both velocity and turbulence profiles become hundred per cent fully developed. This trend is studied further in paper VI, and an understanding of the important mechanisms for efficient flow conditioning emerges from papers V and VI. Graded porosity is found to be responsible for quickly creating a velocity profile close to fully developed. This can be obtained with different overall porosity if only the grading of porosity is appropriate. Low overall porosity means higher solidity and larger blocked area in the plate, which is responsible in turn for producing turbulence. A high turbulence level means more mixing and may sometimes be required for making the downstream profile independent of the upstream profile if this is highly disturbed. Unfortunately, however, highly turbulent flow also requires a longer downstream pipe length before the flow is 100 per cent fully developed. These characteristics of plate flow conditioners may explain why combined FCs, like the K-Lab/Laws with tabs and vanes, can be more efficient. If the flow is preconditioned by
Page 42 one device, the flow which enters the second FC needs less mixing and the porosity of that plate can be higher, which again generates less turbulence and needs fewer pipe diameters to become 100 per cent fully developed. These findings now need to be compared with measurements. Hopefully, the experiments will verify the predictions and demonstrate that CFD techniques can be a valuable tool in understanding complex flow.
Page 43 References
AGA 1991 AGA Report no 3 (3rd edition), Concentric, square-edge orifice meters, Part 2 - Specification and installation requirements, American Gas Association, Arlington, Virginia, February 1991. Akashi 1979 Akashi, K, Watanabe, H, Koga, K, Developments of a new rectifier for shortening upstream pipe length of flow meter. Proc IMEKO symposium, Flow Measurement and Control in Industry, Tokyo, Japan, 1979, pp 279-284. API 1990 American Petroleum Institute, Manual of Petroleum Measurement Standards, 3rd edition, American Petroleum Institute, Washington, DC, 1990, Chap 14, Section 3, Part 1. ASME 1980 ASME/ANSI 2530, Orifice metering of natural gas and other related hydrocarbon fuels, Amer Soc ofMech Engrs (ASME), New York, NY, 1980. Austegard 1991 Austegard, A, Evaluering av programsystemene Fluent, Phoenics, Astec, Flow3D og Kamelon for stramningsberegninger (In Norwegian). The Norwegian Institute of Technology, Report 199:51, 1991. Barry 1992 Barry, J J, Sheikoleslami, M Z, and Patel, B R, Numerical simulation of flow through orifice meters, Gas Research Institute, GRI-92/0060.1, 1992. Bates 1991 Bates, IP, Field use of K-Lab Flow Conditioner, North Sea Flow Measurement Workshop, Bergen, 1991. Bosch 1984 Bosch, M, Hebrard, P and Bassiri, H, Experimental and theoretical studies of a new flow conditioner, Proceedings of the International Conference on the Metering of Natural Gas and Liquified Hydrocarbon Gases, February 1984. Bosch 1990 Bosch, M and Hebrand, P, Experimental and Theoretical studies of a new flow conditioner, Proceedings of the International Conference on the metering of Natural Gas and liquified hydrocarbon gases, February 1990. Bosio 1996a Bosio, J and Erdal, A, Gas metering technology - a strategic objective, IEA International Conference on Natural Gas Transmission, 1-4 September 1996, Berlin, Germany.
Page 44 Bosio 1996b Bosio, J, Modem flow conditioner technology. The K-Lab flow conditioner, K-Lab leaflet, 1996. Bradshaw 1996 Bradshaw, P, Launder, B E and Lumley, J L, Collaborative testing of turbulence models, Journal of Fluids Engineering, Vol. 118, pp 243 - 247, June 1996. Brennan 1991 Brennan, JA, Sindt C F, Lewis, M A and Scott, J L, Choosing flow conditioners and their location for orifice flow measurement, Flow Measurement and Instrumentation, Vol 2 January 1991, pp 40-44. Cabrol 1992 Cabrol, J F, Erdal, A and Bosio, J, Installation effects on 6-inch gas turbine meters at 100 bars, 1992 AIChE Spring National Meeting, New Orleans, Louisiana, 1992. Cham 1996 Information about Phoenics. Internet address : http://www.cham.co.uk/ Davis 1977 Davis, R W and Mattingly, G E, Numerical modeling of turbulent flow through thin orifice plates, Symp on Flow in Open Channels and Closed Conduits, Gaithersburg, February 23-25, 1977. Dijstelbergen 1995 Dijstelbergen, H H, Optimal straightening vanes for turbine meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, 1995. Durst 1989a Durst, F, Wang, AB and Founti, M, Similarity phenomena and computations of the flow through an axisymmetric ring-type obstracle attached to a pipe wall, Hydrocomp 89, Dubrovnik, p 484, 1989. Durst 1989b Durst, F and Wang, A B, Experimantal and numerical investigation of the axisymmetric, turbulent pipe flow over a wall-mounted thin obstracle, Seventh Symposium on Turbulent pipe flow over a wall-mounted thin obstracle, Seventh Symposium on Turbulent Shear Flows, Stanford University, August 21-23, 1989. Erdal 1992 Erdal, A, Cabrol, J F, and Bosio, J, Calibration results in natural gas at 2.0, 5.0 and 10 MPa of 6 turbine meters, Proceedings of the 1992 International Gas Research Conference, Vol 1, edited by H A Thompson, Government Institutes, Inc, Rockville, Maryland, pp 638-647, 1992. Erdal 1994 Erdal, A, Lindholm, D, and Thomassen, D, Development of a flow conditioner , North Sea Flow Measurement Workshop, 1994.
Page 45 Erdal 1995 Erdal, A, Sivertsen, A S and Andersson, H I, Numerical methods and turbulence models for calculation of flow development downstream of confined jets. User experiences with Phoenics. Phoenics Turbulence Modelling Seminar, CHAM, London, November 1995. Freitas 1995a Freitas, C J, Perspective: Selected benchmarks from commercial CFD codes, Journal of Fluids Engineering, Vol 117, pp 208-218, June 1995. Freitas 1995b Freitas, C J, Advanced computational simulation of flow phenomena associated with orifice meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995. Pureness 1987 Furness, R A, Design engineers handbook, State of the art review of flow metering, Sterling Book Co, 1987. Pureness 1994 Pureness, R A, Outstanding and contentious issues in flow measurement, Flomeko '94, NEL, Glasgow, 1994. Gallagher 1992 Gallagher, J E and Beaty, R E, Orifice metering research - a user's perspective, North Sea Flow Metering Workshop, 1992. Gallagher 1994 Gallagher, J E, LaNasa, P L and Beaty, R E, Development of Gallagherflow conditioner, Flomeko '94, NEL Glasgow, 1994. Gallagher 1995 Gallagher, J E, Field performance of the Gallagher flow conditioner, Fluid Flow Measurement, 3rd Int Symp, San Antonio, 1995. Gregor 1992 Gregor, J G and Kothari, K M, The effects of flow conditioner location on orifice meter performance, International Gas Research Conference, 1992. Halttunen 1990 Halttunen, J, Installation effects on ultrasonic and electromagnetic flowmeters: a model-based approach, Flow Measurement and Instrumentation, Vol 1, 1990, pp 287-292. Hilgenstock 1996 Hilgenstock, A, Heinz, M and Nath, B, Numerical flow simulation as a tool for developing and calibrating ultrasonic flow meters, Flomeko '96, China, 1996. Hinze 1975 Hinze, J O, Turbulence, 2nd ed, McGraw-Hill, New York, 1975. Hondareyte 1986 Hondareyte, F, Flow straighteners and swirl removers, Publication draft from ISO/TC30/WG16 - N36E, 30 June 1986.
Page 46 Humphreys 1984 Humphreys, J S and Wood, IM, Progress report on several flow straighteners operating in identical hydraulic conditions, Internal NEL report, 1984. ISO 1991 International Organisation for Standardisation, Measurement of fluid flow by means of orifice plates, nozzles and Venturi tubes inserted in circular cross-section conduits running full, Geneva: International Organisation for Standardisation, 1991. Kothari 1989 Kothari, K M, Brennan, J A and Goiter, J, The effect of tube bundle flow conditions on orifice meter discharge coefficients, International Gas Research Conference, 1989. Kamik 1992 Kamik, U, Jungowski, W M, and Botros, K K, Effect of turbulence on orifice meter performance, 1992 OMAE - Volume V-A, Pipeline Technology, ASME 1992. Kamik 1995 Kamik, U, A compact orifice meter/flow conditioner package, Fluid Flow Measurement 3rd International Symposium, San Antonio, 1995. Kreith 1965 Kreith, F and Sonju, 0 K, The decay of a turbulent swirl in a pipe, J Fluid Mech, Vol 22, part 2, pp 257-271, 1965. Lake 1992 Lake, W T and Reid, J, Optimal flow conditioner, North Sea Flow Metering Workshop, Pcables, Glasgow, October 1992. Langsholt 1991 Langsholt, M and Thomassen, D, The computation of turbulent flow through pipe fittings and the decay of the disturbed flow in a downstream straight pipe, Flow Measurement and Instrumentation, January 1991, Vol. 2, pp 45-55. Laws 1990 Laws, E M, Flow conditioning - A new development. Flow Measurement and Instrumentation, Vol 1 April 1990, pp 165-170. Laws 1993 Laws, E M and Reader-Hams, M J, Evaluation of a swirl-vor-tab flow conditioner, Flow Measurement and Instrumentation, Vol 4 1993, pp 101-108. Laws 1994a Laws, E M and Ouazzane, A K, Compact installation for orifice plate flow meters, Flomeko' 94, NEL Glasgow, 1994. Laws 1994b Compact installations for differential flowmeters, Flow Measurement and Instrumentation, Vol 5 1994, pp 79-85. Laws 1994c Laws, E M, Ouazzane, A K, and Erdal, A, Short installations for accurate orifice plate flow metering, FED-VOL 193, Turbulence Control, ASME, 1994.
Page 47 Laws 1994d Laws, E M, Ouazzane, A K, and Erdal, A, Shortening installation lengths using a low loss vaned flow conditioner, North Sea Flow Measurement Workshop, Peebles, 1994. Laws 1995 Laws, E M and Ouazzane, A K, Flow conditioning for orifice plate flow meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, 1995. Lindholm 1992 Lindholm, D, Tests on the 1-7-13 University of Salford flow conditioner in IFE's atmospheric fir rig, IFE report no IFE/KR/F-92/088, 1992. Mattingly 1990 Mattingly, G and Yeh, T, Effects of pipe elbows and tube bundles on 50 mm orifice meters, Seminar on Installation Effects on Flow Metering, NEL, Glasgow, 1990. Mattingly 1991 Mattingly, G and Yeh, T, Effects of pipe elbows and tube bundles on selected types of flowmeters. Flow Measurement and Instrumentation, Vol 2 1991, pp 4-13. McFaddin 1989 McFaddin, S E, Sindt, C S and Brennan, J A, Optimum location of flow conditioners in a 4 -inch orifice meter, Technical note 1330, National Institute of Standards and Technology, 1989. MiHer 1983 Miller, R W, Orifice metering - state of the art. Workshopon fundamental research issues in orifice metering, GRI, Gaithesburg pp 6-30, June 1983. MiUer 1996 Miller, R W, Flow measurement engineering handbook, Third edition, McGraw-Hill Inc, 1996. Morrison 1990 Morrison, G L, DeOtte, R E, Moen, M, Hall, K R and Holste, J C, Beta ratio, swirl and Reynolds number dependence of wall pressure in orifice flowmeters, Flow Measurement and Instrumentation, Vol 1 1990, pp 269-277. Morrison 1992a Morrison, G L, DeOtte, R E, and Beam, E J, Installation effects upon orifice flowmeters, Flow Measurement and Instrumentation, Vol 3 1992, pp 89-93. Morrison 1992b Morrison, G L, Panak, D L and DeOtte, R E, Numerical study of the effect of upstream flow condition upon orifice flow meter performance, OMAE 1992. Morrison 1994 Morrison, G L, Hall, K R, Macek, M L, Ihfe, L M, DeOtte, R E and Hauglie, J E, Upstream velocity profile effects on orifice flowmeters, Flow Measurement and Instrumentation, Vol 5 1994, pp 87-92.
Page 48 Morrison 1995 Morrison, G L, Hauglie, J E and DeOtte, R E, Beta ratio, axisymmetric flow distortion and swirl effects upon orifice flow meters, Flow Measurement and Instrumentation, Vol 6 1995, pp 207-216. Morrow 1990 Morrow, T B, Determination of installation effects from 100 mm orifice meter using a sliding vane technique, Seminar on Installation Effects on Flow Metering, NEL, Glasgow, 1990. Morrow 1992 Morrow, T B and Park, J T, Effects of tube bundle location on orifice meter error and velocity profiles, 1992 OMAE - Volume V-A, Pipeline Technology, ASME 1992. Morrow 1995 Morrow, T B, Orifice meter installation effects in the GRIMRF, Fluid Flow Measurement 3rd International Symposium, San Antonio, 1995. Mottram 1986 Mottram, R C and Rawat, M S, The swirl damping properties of pipe-roughness and the implications for orifice meters installation. Int Conf on Flow Measurement in the Mid-eighties, National Engineering Laboratory, Scotland, 1996. O'Brien 1989 O'Brien, C J, Flowmeter terms, types & successful selection, Intech, pp 30-33, Dec 1989. Parchen 1988 Parchen, R R, Krishna, P, and Nieuwvelt, C, Turbulent flow through pipes and fittings; a literature survey. Report R-910-D, Eindhoven Universityof Technology, Faculty of Physics, Fluid Dynamics Laboratory, Eindhoven, The Netherlands, 1988. Park 1995 Park, J T, Reynolds number and installation effects on turbine meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995. Pasdari 1990 Pasdari, M and Gimson, C J, Design of a new "Flow conditioner" with the aid of Phoenics, Vol. 4, No 2, pp 128 -154, Phoenics Journal of Computational Fluid Dynamics. Reader-Harris 1986 Reader-Harris, M J and Keegans, W, Comparison of computation and LDV measurement of flow through orifice and perforated plates, and computation of the effect of rough pipework on orifice plates, Proc of the Int Symp on Fluid Flow Measurement, Washington, DC, 1986
Page 49 Reader-Harris 1989 Reader-Harris, M J, Computation of flow through orifice plates, Numerical Methods in Laminar and Turbulent Flow, Volume 6, pp 1907-1917, 1989. Reader-Harris 1990 Reader-Harris, M J and Sattary, J A, The orifice plate discharge coefficient equation, Flaw Measurement and Instrumentation, Vol 1 1990, pp 67-76. Reader-Harris 1995a Reader-Harris, M J, Sattary, J A and Spearman, E P, The orifice plate discharge coefficient equation - further work, Flow Measurement and Instrumentation, Vol 6 1995, pp 101-114. Reader-Harris 1995b Reader-Harris, M J, Woodhead, E, Sattary, J A and McEwen, D, Flow conditions downstream of headers. HCP001 (223/94) Part 1. East Kilbride, Glasgow: National Engineering Laboratory, Sept 1995. Sakariassen 1996 Sakariassen, R, Real life experience with multipath ultrasonic gas flow meters, International Pipeline Conference - Volume 2, ASME 1996, pp 1077-1088. Sanderson 1991 Sanderson, M L and Sweetland, D, The effect of four designs of flow conditioner on flowmeter performance. Flow Measurement and Instrumentation Consortium, Category 2A Report No 1, Cranfield, Bedford: Cranfield Institute of Technology, July 1991. Sheikholeslami 1988 Sheikholeslami, M Z, Patel, B R and Kothari, K, Numerical modeling of turbulent flow through orifice meters - a parametric study, 2nd International Conference on Flow Measurement, London, UK, 11-13 May 1988. Shen 1991 Shen, J J S, Characterization of swirling flow and its effects on orifice metering. SPE paper 22865, 66th Annual Conf Exhib Society of Petroleum Engineers, Dallas, TX, 1991. Smith 1989 Smith, C R, Greco, J J and Hopper, P B, Low loss flow conditioner for flow distortion/swirl using passive vortex generation devices, 5th International IMEKO conference on Flaw Measurement, FLOMEKO, Duesseldorf, 9-10 October 1989. Spearman 1991 Spearman, E P, Sattary, J A and Reader-Harris, M J, A study of flow through a perforated-plate/orifice-meter package in two different pipe configurations using laser Doppler velocimetry, Flow Measurement and Instrumentation, Vol 2, April 1991.
Page 50 Spearman 1994 Spearman, E P, Sattary, J A and Reader-Harris, M J, Comparison of velocity profiles downstream of perforated plate flow conditioners, Flomeko '94, NEL Glasgow, 1994. Spencher 1995 Spencher, E A, Heitor, M V and Castro, IP, Intercomparison of measurements and computations of flow through a contraction and a diffuser, Flow Measurement and Instrumentation, Vol 6, No 1, pp 3-14, 1995. Sprenkle 1958 Sprenkle, R E and Courtright, N S, Straightening vanes for flow measurement , Mechanical Engineering, pp 71-95, 1958. Stang 1995 Stang, J, Modelling and simulation of flowmeter installation effects, Norwegian Institute of Technology, PhD thesis, 1995. Steenbergen 1995 Steenbergen, W, Turbulent pipe flow with swirl, Eindhoven University of Technology, PhD thesis. Stuart 1993 Stuart, J, Improvments in flow conditioner design for orifice metering, AG A Distribution/Transmission Conf, Ireland, Florida, 1993. Stuart 1994 Stuart, J W, Experimental results of an improved tube-bundle flow conditioner for orifice metering, Flomeko '94, NEL Glasgow, 1994. Studzinski 1996 Studzinski, W, Kamik, U, Jones, B, Peterson, W, LaNasa, P and Morrow, T, Installation configuration with and without flow conditioners, API - White Paper Draft, March 1996. Teyssandier 1993 Teyssandier, RG, Flow measurement and metering requirements in the oil and gas industry. FED-Vol 159, Devices for Flow Measurement and Control, ASME 1993. Thomassen 1992 Thomassen, D, Langsholt, M and Sakariassen, R, Flow conditions in a gas metering station. North Sea Flow Measurement Workshop, October 1992. vanBloemendaal 1995 vanBloemendaal, K and van der Kam, PM A, Installation effects on multi-path ultrasonic flow meters: The Ultraflow' project, Fluid Flow Measurement, 3rd Int Symp, San Antonio, 1995. van der Kam 1993 van der Kam, PM A and van Dellen, K, The effect of double bends out of plane on turbine meters, Flow Measurement and Instrumentation, Vol 2, No 1, pp 61-68, 1991.
Page 51 Wilcox 1990a Wilcox, P L, Weberg, T and Erdal, A, Short gas metering systems using K-Lab flow conditioners, 2nd International Symposium on Fluid Flow Measurement, Calgary, Alberta, Canada, June 6-8, 1990. Wilcox 1990b Wilcox, P L and Erdal, A, K-Lab Flow Conditioners for use in short metering systems, Seminar on Installation Effects on Flow Metering, NEL, 22 October 1990. Zanker 1969 Zanker, K J, The development of a flow straightener for use with orifice-plate flowmeters in disturbed flow, Paper D-2, Symposium on Flow Measurement, Scotland, 1969, pp 395-415. Paper I
Development of a flow conditioner
Erdal, A, Lindholm, D and Thomassen, D
North Sea Flow Measurement Workshop, Peebles, Scotland, October 1994 N.S.F.M.W. October 1994
DEVELOPMENT OF A FLOW CONDITIONER
Asbjern Erdal, Karst0 Metering and Technology Laboratory, K-Lab, Haugesund, Norway Dag Lindholm, Institute for Energy Technology, IFE, Kjeller, Norway Dag Thomassen, Institute for Energy Technology, IFE, Kjeller, Norway
ABSTRACT subscripts: This paper gives a review of the major activities of the systematic process to develop a flow conditioner (FC) i : Ring number which can be used to reduce the required length of an m : Mean value orifice metering station. o : Stagnation value vc : Vena contracta A theoretical design procedure for the development of a FC is presented together with the main findings from experiments performed in test rigs using air at 1. INTRODUCTION atmospheric pressure and natural gas at high pressure. Orifice meter discharge coefficient (Cd) measurements 1.1 BACKGROUND at 100 bar in natural gas show that Short Metering Systems (SMS) of 15D with the Mark 5 FC installed For over sixty years, the concentric orifice meter has have very good performance. remained the predominant meter for natural gas metering applications. Even if more modem flowmeters appear on the market, orifice meters continue to be a NOMENCLATURE preferred choice by many users because of the simple technology, the existence of well-known standards and A : Cross section area [m2] the long experience with the meters. Unfortunately, the a : Hole diameter [mm] accuracy of an orifice meter is affected by flow Cd : Discharge coefficient [-] perturbances, especially swirl, and even 100D may not D : Internal pipe diameter [m] be enough to fulfil the ISO-5167 requirement of less K : Pressure loss coefficient [] than +/- 2° swirl (ref. 1). n : Number of holes [] m : Number of area rings [] Orifice metering stations offshore are very heavy and P : Pressure [Pa] expensive installations because of the long upstream R : Pipe radius or ring radius [mm] pipelength that are required in ISO-5167 (ref. 2). Re : Reynolds number [-] Therefore a lot of effort is put into developing FCs that U : Axial velocity [m/s] can reduce the upstream length required to eliminate Y : radial position referred to the wall [m] swirl and develop a fully developed velocity profile. A P : Diameter ratio of the orifice meter [-] review of the work done so far is presented by : Ratio of the flow area in vena contracts to the Gallagher and Beaty (ref. 3). pipe area [-] >. : Porosity [-] K-Lab has since 1987 co-operated with IFE and p : Density [kg/m3] University of Salford on the development of a series of FCs. This paper deals only with the development of the Mark series of FC and testing at IFE and K-Lab.
Page 1 of 12 N.S.F.M.W. October 1994
The development was inspired by section 7.4 of 2. DESIGN OF THE FLOW CONDITIONERS ISO-5167. This section states that if the flow conditions immediately upstream of the primary device 2.1 A THEORETICAL DESIGN MODEL can be demonstrated to sufficiently approach those of a fully developed velocity profile (within +/- 5%) and be Initially a simple theoretical model for the flow through free from swirl (within +/- 2°), then the uncertainty the holes in the FC was established. Based on formulas range claimed by the standard remains applicable. It deducted from his theory and some practical was decided to attempt to design a new FC to reach this modifications the new FC was designed. condition within I5D downstream of a flow disturbance, independently of the velocity and swirl A design procedure for the FCs is presented below. It is profiles existing upstream of the FC. based on a simplified theoretical model which calculates the pressure loss through the holes in the FC.
1.2 GOALS FOR THE FC DEVELOPMENT
In the early days of the project, the following goals were listed :
The new FC should : - Eliminate swirl (within +/- 2°). - Generate a fully developed velocity profile (within +/- 5%) maximum 15D downstream of the flow perturbance. - Give low pressure drop across the FC. - Be simple and cheap to manufacture. - Give similar or better measurement accuracy compared to a standard ISO-5167 installation.
Figure 1. 1.3 DEVELOPMENT PROGRAM Discretisation of the flow area
When the design objectives for the FC development The cross sectional area in the flow conditioner is first were identified, a research plan with several activities discretised into rings as shown in figure 1. Each ring was established. The main ones are listed below : area is then described by an inner and outer radius, and includes one or more holes. - Develop a theoretical model for the design of the FCs. The velocity profile immediately upstream of the flow - Manufacture FCs according to the theoretical model. conditioner is assumed flat, while the velocity profile - Test the FCs in air at atmospheric pressure. downstream is assumed fully developed. A "quasi - Develop a tool to measure velocity and swirl (swirl one-dimensional" illustration of the flow profile probe) which can be used in natural gas at North Sea through the flow conditioner is shown in figure 2. conditions (up to 150 bar). - Test the FC in natural gas at high pressure. The area of the flow conditioner is divided into rings, - Acquire orifice meter performance data (Cd) in and each ring is regarded as a separate flow channel. natural gas at high pressure. The outlet velocity shall correspond to the discrete - Make a result database for FCs. velocity in the fully developed profile. The flow through - Obtain general acceptance for the technology. each ring is treated separately, and the holes are dimensioned to introduce a sufficient pressure loss to give near fully developed flow downstream. The pressure loss from a distance upstream of the flow conditioner to a distance downstream through all flow channels are equal.
Page2 of 12 N.S.F.M.W. October 1994
the ring to the mean velocity, U_, can now be derived. The equation reads
A,-
The two terms on the right hand side of eq. (1) express the pressure loss due to the sudden area contraction and enlargement caused by the holes in the ring, respectively. The equation does not take into account
Rat profile Flow conditioner Fully developed profile the friction against the hole walls. For FC plates in which the length of the holes are typically 2-6 times the Figure 2. hole diameter, this is a reasonable simplification. Discretisation of the velocity profile The total pressure loss coefficient is defined as
Consider the flow through one of these flowchannels. It AP0 Ko = (2) can be divided into flow through a sudden contraction, 0.5-p-Ul figure 3, and flow through a sudden enlargement, figure 4. The two parts are first treated separately and where p is the fluid density and P„ the total pressure then coupled through the total pressure loss. The flow is difference over the FC in terms of the stagnation considered one-dimensional and incompressible. pressures.
The porosity of a ring flowchannel is defined as the ratio between the area of the holes to the total ring area. Thus, the porosity of ring no. i can be calculated as
. _ »<7t/4>02 (3)
where n is the number of holes in the ring, a is the diameter of each hole, and R,_, and R, the outer and inner radius of the ring.
Figure 3. Eq. (1) forms the basis of the design procedure. The Turbulent flow through a sudden contraction porosity of each ring will be determined to get a predefined velocity profile and total pressure loss.
The shape of a fully developed velocity profile will change with the Reynolds number up to about 3 10' (for smooth pipes to even higher Re-numbers). According to Wilcox et al. (ref. 4) the ratio U/Um can be represented as a function of the radial distance from the pipe axis by the equation
^=1.173.$", (4)
Here Y is the distance from the pipe wall and R is the internal pipe radius. This formula can be employed for Figure 4. determination of the Upvalues in eq. (1). Turbulent flow through a sudden enlargement
The area of each ring is divided into n holes, each with An equation which relates the total pressure coefficient a diameter a. Physical limitations restrict the diameter of the flow conditioner, Ke, to the ring porosity, X< , and the number of holes by the following constraints: and the ratio between the local velocity in the fully developed profile, U,, corresponding to the location of
Page 3 of 12 N.S.F.M.W. October 1994
a*,-a, >o+2 The design of the FCs was based on the theory above. and For Mark 3 the hole diameters were maximised (point 4 n(a + 2) < 2tt • (i?/+i + Ri)/2 ^ ^ above). Plate thickness, porosity and the number of rings were copied from the Mark 2 conditioner. where R, is the inner radius and R.,, the outer radius of ring i. These constraints ensure that the diameter of Mark 4 was designed to introduce higher pressure loss each hole is smaller than the width of the ring, and that in order to increase the ability to handle more the sum of the hole diameters is less than the asymmetric inlet profiles than the previous versions. circumference of the ring. An additional requirement is The porosity was defined to be 0,40 in this model. of course that the number of holes, n, must be an integer. Mark 5 was designed from the same concept as Mark 3 and Mark 4, but was given larger porosity in order to For a given porosity there is normally not a unique reduce the pressure loss coefficient. For Mark 5 the solution to the above equations. To solve the equations hole diameters were maximised. A pressure loss either the size of each hole or the number of holes have coefficient equal to 2,0 was specified which yields an to be maximised. overall porosity equal to 0.53.
The design of a flow conditioner geometry can then be Some design data are listed in table 1 below : determined by the following steps: FC Porosity Pressure loss 1. Define the porosity (or pressure loss) for the flow coefficient conditioner. Calculate the pressure loss (or porosity) by eq. (1) applied at the radial position Mark 2 0,51 2,38 where the upstream velocity equals the downstream velocity, i.e. U/Um=1.0. Mark 3 0,51 2,57 Mark 4 0,40 4,65 2. Define the number of rings. Select m axial velocities to represent the fully developed axial Mark 4, ch 0,40 3,28 velocity profile and determine the radial Mark 5 0,53 2,13 location of each corresponding ring using eq. (4). Table 1. The prescribed overall porosity of the FCs and the 3. Calculate the porosity of each ring using eq. (1). measured pressure loss coefficients obtainedfrom experiments using air at atmospheric pressure. 4. Calculate the area of each hole and the number of holes in each ring by either maximising the All FCs have one centrehole and 4 concentric rings hole diameter or the number of holes. For this with holes. The thickness is common for all FCs and purpose eq. (3), (5) and (6) are employed. equal to 0.357D. Figure 5 shows the basic layout.
2.2 THE DIFFERENT MODELS
The results from the examination of the performance of Mark 2 have been presented in ref. 4 and 5. This FC show excellent performance as swirl remover, but was not equally good in straightening out asymmetric velocity profiles. Therefore the design of Mark 2 was gradually improved resulting in the Mark 3, Mark 4, Mark 4 ch (chamfered) and culminating in the Mark 5 FC. At an early stage, the decision was taken to maintain a thickness of 50mm for the FC when it was installed in a test rig having an internal pipe diameter equal to 140mm. This eliminated one of the variables in the problem, leaving only the layout of the holes in the cross-section to be optimised. Figure 5. K-Lab Mark 2 flow conditioner
Page 4 of 12 N.S.F.M.W. October 1994
3. EXPERIMENTAL SET IIP FOR THE ATMOSPHERIC TESTS
3.1 THE TEST SECTION
The experiments using air at atmospheric pressure were done in a test rig of plexiglas having an internal pipe diameter equal to 140mm. Air is sucked through the I I I I I I loop by a positive displacement pump yielding constant 1 volumetric flowrate. The pipe Reynolds number in the z* Traverse test section is 2.6 10s. In this project three different directions geometrical disturbances at the inlet to the test section have been used. Figure 7. The twisted S-bend geometry. The points P represent 3.2 THE SINGLE BEND RIG the traverse positions and the points 1 the positions for flow conditioner location. The curvature r/D of the In the single 90°-bend geometry a 9D straightpipe with bends is 1.5D. a perforated plate at the inlet followed by a 90° bend is connected to the test section. The radius of curvature of the bend is 1.5D. The set up is shown in figure 6. Axial 3.4 THE FLAT PROFILE TEST RIG velocity profiles and swirl angle profiles can be measured at ID, 3D, 5D, 10D and 15D, while the FC In order to study the flow disturbances caused by the can be installed 3D, 4D, 5D, 6D, 7D and 8D flow conditioner itself, a special set up referred to as the downstream of the bend. flat profile test rig, was built. The rig consists of a 10D long straight pipe upstream of the flow conditioner with a perforated plate positioned at the pipe inlet. Downstream of the flow conditioner the velocity profiles can be measured at 5D, 6D, 7D, 8D, 9D 10D and 12D. A drawing of the set up is shown in figure 8.
Traverse positions SD 10P 13D i i i Traverse Perforated FC directions plate
Figure 6. Figure 8. The single 90° bend geometry. The points P represent The flat profile test rig the traverse positions, the points I the positions for flow conditioner installation. The curvature of the bend is 1.5D. 3.5 PRIMARY MEASUREMENT DEVICES
3.3 THE TWISTED S-BEND RIG A pitot static tube was used for the axial velocity profile measurements. The swirl angles were measured by a 10mm thick 2 hole cylinder pitot tube. Both these A twisted S-bend with a perforated plate at the inlet is instruments were connected to a differential pressure connected to the test section, and traverses to measure manometer type 5 Airflow manufactured by Airflow the axial velocity profile and the swirl angles can be Development. done at ID, 3D, 5D, 10D and 15D downstream from the second bend. The flow conditioner can be positioned at 3D, 4D, 5D, 6D, 7D and 8D, see figure 7. The length of straight pipe between the two bends is 1.25D, and the radius of curvature of the bends is 1.5D.
Page 5 of 12 N.S.F.M.W. October 1994
4. ATMOSPHERIC TEST RESULTS 4.3 TEST OF THE DISTURBANCE INTRODUCED BY THE FLOW 4.1 INTRODUCTORY REMARKS CONDITIONER ITSELF
Mark 2, Mark 3, Mark 4 and Mark 5 which all have the Axial velocity profiles measured downstream of the same basic layout with one centerhole and 4 concentric Mark 5 FC in the Flat Profile Rig are shown in Figure rings with holes were tested in the air loop. Only the 10. The profile at 5D has almost recovered to fully main conclusions from these experiments will be developed but is still too peaked. At 12D the measured presented here. profile is identical to the fully developed velocity profile in Figure 9. The results obtained with Mark 2 are presented in ref. 4. With Mark 2 the ISO-5167 section 7.4 requirements UTjmean were fulfilled 15D downstream from the single bend and the twisted S-bend.
Mark 3 gave better results than Mark 2. With Mark 3 the ISO-5167 requirements were fulfilled 12D downstream from the bend. Mark 4 was even better and the required length between the bend and the orifice plate was reduced to 1 ID. 5D 8D I CD 12D FuBy developed
Mark 5 exhibited the lowest pressure loss coefficient which is considered as a very important property for a Y/R FC. If a Short Metering System with Mark 5 fulfils the ISO-5167 requirements at 15D downstream of the Figure 10. tested disturbances and has good orifice meter Axial velocity profiles. Mark 5 positioned downstream performance, this FC-model can therefore be of flat velocity profile. considered as an optimum design based upon our requirements mentioned in Section 1.2. In the following attention will only be given to the results 4.4 SINGLE BEND TESTS obtained using Mark 5. Figure 11 and 12 show the velocity profiles in two perpendicular planes when no flow conditioner was 4.2 REFERENCE VELOCITY PROFILE installed. The corresponding swirl angles are presented in Figure 13. The traverse directions are defined in The fully developed velocity profile measured Figure 5. In Figure 14 the results obtained with the flow downstream from 101D lengths of straight pipe is conditioner located at 8D are presented as percentage shown in figure 9. The pipe Reynolds number was deviations in U/Umean from the corresponding ratios in 2.6 10s. The profile will be used as "reference profile" the fully developed profile. in the subsequent graphs. The swirl angles were measured at the same positions U/Umean as the velocities. Maximum deviation between the swirl 1.20 angles measured within the same traverse was 0.5 1.10 degrees, which is comfortably within the ISO-5167 requirement. However, the relative swirl along each 1.00 traverse is measured to within +/- 0.5 degree uncertainty. Thus, a maximum variation in the swirl 0.90 angle measurements of 1 degree means that no swirl actually has been detected in the flow.
0.00 0.50 1.00 1.50 2.00 Y/R
Figure 9. Fully developed velocity profile measured downstream ofl 01D straight pipe. Re= 2.6 10s.
Page 6 of 12 N.S.F.M.W. October 1994
Figure 11. Measured axial velocity profiles downstream of the Figure 14. single 9(f bend. Vertical traverses. No FC was Deviation of the measured axial velocity profile from installed downstream of the flow disturbance. the fully developed profile downstream ofthe 90° bend. Mark 5 was installed 8D downstream of the flow disturbance.
4.5 TWISTED S-BEND
The axial velocity profiles measured downstream of the twisted S-bend with no FC installed in the rig are shown in figure 15 and 16. The corresponding swirl angle profiles are plotted in figure 17. The traverse ID 3D 5D 10D 15D directions are defined in Figure 7. Figure 18 presents the deviation in U/Umean from the corresponding ratios in the fully developed velocity profiles when the FC was installed 8D downstream from the last bend. YR The measurements were done at 15D.
Figure 12. Also for this configuration traverses of the swirl angles Measured axial velocity profiles downstream of the were measured, and again the maximum swirl angle single 9(f bend. Horizontal traverses. No FC was found was 0.5 degrees, which mean that no swirl has installed downstream of the flow disturbance. been detected in the flow.
Swirl angle 4.6 CONCLUSION OF AIR TESTS
The ISO-5167 requirements are satisfied both with respect to the axial velocity profile and the swirl angles 15D downstream of a single 90° bend and a twisted S-bend when Mark 5 is installed 8D downstream of the flow disturbance. Figure 14 and 18 show that the S ID 3D 5D 1GD 15D velocity profile is not completely developed. The aim was however, to satisfy the ISO-requirements, and therefore this performance is acceptable.
Figure 13. Measured swirl angle profilesdownstream of the single 9(f bend. Horizontal traverses. No FC was installed downstream of the flow disturbance.
Page 7 of 12 N.S.F.M.W. October 1994
tTUmean % dev. from U / Umean
ID 3D 5D 10D 1SD Y/R
Figure 18. Y/R Deviation of the measured axial velocity profile from the fully developed profile downstream of twisted Figure15. S-bend. Mark 5 was installed 8 D downstream of the Measured axial velocity profiles downstream of flow disturbance. twisted S-bend. Vertical traverses. No FC was installed downstream of the flow disturbance. 5 EXPERIMENTAL SET-UP FOR THE HIGH PRESSURE TESTS
5.1 HIGH PRESSURE TEST LOOP
The high pressure tests were performed at 100 bar and 37°C in dry natural gas (85% methane, 13% ethane and 2% other components).
All the tests were carried out in a 6 inch nominal bore test section with an internal pipe diameter of 140mm. ID 3D 5D HD 15D The PCs were tested downstream of a single 90° bend and a twisted S-bend similar to those used in the atmospheric air rig.
Y/R The reference flowmeters are a bank of sonic nozzles, built according to ISO-9300, which have been primary Figure 16. calibrated in a gravimetric calibration rig over the Measured axial velocity profiles downstream of range 20 to 100 bar. For the discharge coefficient (Cd) twisted S-bend. Horizontal traverses. No FC was measurements a 6" Daniel Orifice meter (model installed downstream of the flow disturbance. M7591) was used. All applied instruments had calibration certificates traceable to international Swirl aigfe standards.
5.2 SWIRL PROBE
A swirl probe was designed and manufactured to measure velocity and swirl in natural gas up to 150 bar in the test-section. Before the final design was made, the performance of 3 cylindrical Pitot probe was 3D 5D 10D investigated.
The following probes were tested : 10mm diameter 2-holes probe with 60° Y/R between the holes 17mm diameter 2-holes probe with 60° Figure 17. between the holes Measured swirl angle profiles downstream of twisted 17mm diameter 3-holes probe with 36.2° S-bend. Horizontal traverses. No FC was installed between the holes downstream of the flow disturbance.
Page 8 of 12 N.S.F.M.W. October 1994
The results are described and discussed in ref. 6. Based upon this study the swirl probe was designed with a U/Umean 12mm cylinder and 3 holes with 35.4° between the holes.
6.0 HIGH PRESSURE TEST RESULTS
0 .6 - 6.1 REFERENCE VELOCITY PROFILE
As mentioned earlier, the Mark 2 to Mark 5 FCs have 0.2 - been designed to produce a 9th power law velocity profile given by equation (4). From figure 19 it can be 0.0 0.2 0.4 0.( 0.8 1.0 seen that the 9th power law velocity profile fits the Y/R measured velocity profile 341D downstream of a twisted S-bend at a Reynolds number 1.5 107 very well. Figure 20. Thus the 9th power law profile has been used as Horizontal velocity profile 15D downstream of a single reference profile for the high pressure tests. 90° bend. U/Umean U/Umean
Measurement Sth power law ; 9th power law Re=155E*6 Re=6.4E*6
0.0 0.2 0.4 0.6 0.8 1.6 1.1 0,0 0.2 0,4 0,6 0,8 1.0 1,2 1,4 1,6 1,8 2,0
Figure 19. Fully developed velocity profile. Re = 1.5 Iff Figure 21. Horizontal velocity profile 15D downstream of a single 6.2 SINGLE BEND TESTS 9(f bend when Mark 5 is used.
Figure 20 shows the horizontal velocity profile 15D U/Umean downstream of the single bend at 2 different Reynolds numbers when no FC was installed in the rig. It can be seen that some of the measurements are outside the ISO-5167 recommendation. Figure 21 shows the velocity profile when Mark 5 is used. The results are now within the 5% band of the fully developed velocity profile. Both with and without the FC the swirl measured at this position is well within the ISO-5167 requirements. Sthpcwertow R*=15.2E*6 Re=6.4E*6
6.3 TWISTED S-BEND TESTS ' 0,0 0.2 0.4 0,6 0,8 1,0 1,2 Y/R The horizontal velocity profile 15D downstream of the twisted S-bend can be seen in Figure 22. The same Figure 22. profile when Mark 5 is used is shown in Figure 23. Horizontal velocity profile 15D downstream of a twisted S-bend.
Page 9 of 12 N.S.F.M.W. October 1994
Deviation from baseline Cd U/Umean 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 H...... -...... -1.0 '---'---'---'---'------'------!------:------'------i 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 9th pcwer I Pipe Re number in E+05
Beta-0.3 Beta=0.5 Beta=0.6 : ’ 0,0 0.2 0.4 0.6 0,6 1,0 1.2 1.4 1,6 1,8 2,0 Y/R Figure 26. Figure 23. ACd for a 15D SMS with Mark 5. Deviation from Horizontal velocity profile 15D downstream of a "baseline " Cd measurements. twisted S-bend when Mark 5 was used. The swirl angle for this configuration with and without Swirl angle the FC is shown in Figure 24. From the results presented above it is demonstrated both how Mark 5 transforms the velocity profile from distorted to nearly fully developed and how it removes the swirl.
6.4 MEASUREMENTS OF DISCHARGE -4.0 t- COEFFICIENT
0.0 0.2 0.4 0.6 O.i 1.0 1.2 1.4 1.6 1.8 2.0 The aim of the ISO-5167 recommendation is to describe how to build an orifice gas metering station NoFC No FC MarkB MarkS and obtaining a gas measurement-error within Re=15200000 R*= £400000 Re=l5200000 R«=640OCO0 +/- 1.0%.
Figure 24. The ultimate question is then how well a Short Metering System (SMS) with Mark 5 FC and an Horizontal swirl angle profile 15D downstream of a overall length of 15D behaves when it is calibrated. In twisted S-bend. Results with and without Mark 5. figure 25 tests between the flow element and the
Deviation from sonic nozzles upstream disturbances are shown for p-ratios equal to 2.0 |------: 0.2, 0.6 and 0.75. The results show that the Cd deviations from the reference sonic nozzles are within 1.0 ...... +/- 0.5%. The tests were done at 100 bar with Reynolds number between 5 104 and 2 10'.
0.0 ------*------9------*■ Normally the performance of the PCs is compared -1.0 against some "base-line" Cd calibrations. For some common P -ratios (0.3, 0.5 and 0.6) these calibrations -2.0 1------1------!------1------‘------!------1------1------1------1------‘------0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 were carried out at 48D lengths of straight pipe with Pipe Re number in E+06 Mark 5 installed at the inlet. Then the results obtained
Single bend Sbend Single bend Sbend Single bend Sbend at 15D downstream of a twisted S-bend were checked against these "baseline" data. The results are found in • * • o figure 26. It can be seen that all the results are within +/- 0.2%. Figure 25. Calibration of a 15D SMS with Mark 5. Results for different configurations and different beta-ratios.
Page 10 of 12 N.S.F.M.W. October 1994
These "baseline" Cds are also compared against data undermeasuring of the flow (ref. 7) which is also obtained with the upstream length required by shown in figure 27. These testresults (fig. 24) ISO-5167 downstream of a twisted S-bend. The results demonstrate that Mark 5 is an efficient swirl-remover are shown in figure 27. It can be seen that all these Cds and avoid this undermeasuring. are lower than the "baseline" data, and in the worst case the deviation is nearly 0.5%. To summarise, this SMS shows small deviation (within +/- 0.2%) from the "base-line" Cd-data. It also gives better results than a standard ISO-5167 installation Deviation from baseline Cd downstream of a twisted S-bend, confirming that the 1.0 SMS-concept with Mark 5 installed fully compares with 0.8 an ISO-5167 installation as was the project objective. 0.6 0.4 0.2 The interest for PCs in the metering community is 0.0 increasing continuously because the large demand for -0.2 cheaper and better metering systems. The challenge -0.4 -0.6 now is therefore to further collect performance data for -0.8 a result-database and work for general acceptance of -1.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 this technology. All the attention the PCs have received Pipe Re number in E+05 the last couple of years confirms the promising potential of this technology. B«ta=0.3 B«ta=0.5 Bas=0.6
The metering technology evolves all the time, and it is Figure 27. still possible to slightly improve the performance of the PCs. The new tabs/vanes FC is an example of an Cd between normal ISO-5167 installation length encouraging improvement (ref. 8) where K-Lab and downstream from a twisted S-bend and "baseline" Cd University of Salford co-operate. measurements.
7.0 CONCLUSION 6.5 DISCUSSION In this paper the main research activities in developing It has been shown that also at high pressure (100 bar) a good FC is described. The aim was to build a Short Mark 5 effectively eliminates the swirl 15D Metering Systems (SMS) of maximum I5D which downstream of a single bend and a twisted S-bend. The fulfilled the ISO-5167 requirements. velocity profile at this position for the 2 configurations examined is not 100% developed but well within the - First a theoretical design model was developed. ISO-5167 recommendation which was the objective to - From that model PCs with different porosity (between reach for the development project. 0.4 and 0.51) and pressure loss coefficients (between 2.13 and 4.65) have been designed. The measurements of the discharge coefficient show - The different PCs were then tested in air at that the performance of a SMS with a total length of atmospheric pressure. Mark 5, which has the lowest 15D compares with the sonic nozzles within +/- 0.5%. pressure loss coefficient of 2.1, fulfilled the ISO-5167 This is good results as a normal ISO-installation may requirements 15D downstream of a single 90° bend have an uncertainty up to 1%. and a twisted S-bend. - A cylindrical Pitot probe with 3 holes for measuring The Cd-shift between the "base-line" calibration and velocity and swirl in a 6 inch pipe up to 150 bar was the SMS-system is within +/- 0.2% at Reynolds number designed and manufactured. between 6.4105 and 6.3106. Also these results are - The performance of the SMS with Mark 5 was considered very satisfactory as they have been obtained tested at 15D at high pressure. The ISO-5167 at high pressure (100 bar). However this Cd-shift is requirements for fully developed flow were fulfilled. wanted as low as possible, and there is still some room - The SMS with |3 -ratios equal to 0.2, 0.6 and 0.75 for improvement here (+/- 0.1%). were tested against sonic nozzles at 100 bar for Reynolds numbers between 5 104 and 2107 . The results Another finding during these tests is that today's showed a deviation within +/- 0.5% . ISO-5167 recommendation does not require long - The SMS was also compared against "base-line" enough upstream lengths after twisted S-bends for the Cd data for common 3 -ratios, (0.3, 0.5 and 0.6). All removal of swirl. It is well known that swirl cause
Page 11 of 12 the results were within +/- 0.2%. -The comparison between a 15D SMS with Mark 5 and an ordinary installation with normal ISO requirements for upstream lengths, shows that the SMS with Mark 5 performs similarly or better. - Since Mark 5 fulfils the ISO-5167 requirements and gives good Cd performance at 15D, this FC can be applied in Short Metering Systems.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the contributions of Dr. Paul Wilcox from K-Lab who initiated the project in 1987 and Dr. Trond Weberg from EFE who was the main architect behind the theoretical design model.
REFERENCES
/!/ - Kreith, F. and Sonju O K. - The decay of turbulent swirl in a pipe. - J. Fluid Mech. 25 (1965) 257.
Ill - Hannisdal, N.E. - Metering study to reduce topsides weight - North Sea Flow Measurement Workshop, 1992.
131 - GallagherJ.E. and Beaty R.E. - Orifice metering research - a user's perspective - North Sea Flow Measurement Workshop, 1992.
/4/ - Wilcox P., Weberg T. and Erdal A. - Short gas metering systems using K-Lab flow conditioner. - 2nd International Symposium on Fluid Flow Measurement in Calgary, June 6-8,1990.
15/ - Wilcox P. and Erdal A. - Seminar on installation effects on flow metering. - NEL, October 22, 1990.
16/ - Thomassen D. and Prein B. - Examination of the performance of three cylinder pitot probes in swirling flow. - Report no.: IFE/KR/F-87/171
111 - Bates I.P - Field use of K-Lab flow conditioner - North Sea Flow Measurement Workshop 1991.
/8/ - Laws E., Onazzane A.K., Erdal A. - Shortening Installation lengths using a low loss flow conditioner. - North Sea Flow Measurement Workshop 1994. Paper II
Evaluation of a CFD-model for simulation of simplified flow conditioners
Erdal, A, Torbergsen, L E, Rimestad, S and Krogstad, P A
Fluid Flow Measurement 3rd International Symposium, San Antonio, USA, 1995 EVALUATION OF A CFD-MODEL FOR SIMULATION OF SIMPLIFIED FLOW CONDITIONERS
Asbjom Erdal, Statoil/K-LAB P O. Box 308 N-5501 Haugesund, Norway
Lars Even Torbergsen, Stein Rimestad, Per-Age Krogstad Division of Mechanics, Thermo and Fluid dynamics The Norwegian Institute of Technology N-7034 Trondheim, Norway
ABSTRACT
Perforated plate flow conditioners are used to generate a fully developed turbulent flow profile upstream of an orifice meter. It is very time-consuming to measure the effect of a flow conditioner for different upstream flow profiles. Therefore a project is initiated to evaluate the performance of a computational fluid computer code for this purpose. If the code correctly predicts the flow profiles downstream of simple perforated plates, it may also be possible to predict the flow characteristics downstream of more complex flow conditioners. In this study a k-s CFD-model was used to predict the flow downstream of obstruction plates having one large or nine small holes. Both mean velocity, turbulent kinetic energy, k , and the dissipation rate of turbulent kinetic energy, s, were calculated and compared against measured data. The results indicate that it is possible to predict the mean velocity well and that the accuracy of the predicted k and e depends on the complexity of the flow.
INTRODUCTION
The orifice meter is a simple and robust metering device, which is still regarded as one of the most reliable and accurate meters available for flow rate measurement. However, the performance of an orifice meter is strongly affected by flow disturbances arising from upstream pipe installations, for instance bends, headers, valves or pipe restrictions.
The flow rates calculated using the empirical discharge coefficient equation in the international standard for orifice metering (ISO-5167, ref. 1) are correct only if the flow profile is fully developed upstream of the meter. Therefore the standard specifies a minimum upstream length of straight pipe to establish a flow profile sufficiently close to the fully developed profile. These recommended lengths vary depending on the [3-ratio of the orifice plate and the type of upstream pipe configuration. It has been shown that for some configurations, the upstream length specified in the ISO-5167 standard is too short to remove swirl (ref. 2, 3 and 4). This is only one of the parameters which influences the flow. In offshore metering stations the lengths required in ISO-5167 are expensive to make available. Therefore K-Lab has put a lot of effort into developing a flow conditioner (FC) which can eliminate swirl and generate a fully developed velocity profile within a short distance downstream of any disturbances (ref. 4).
Page 1 An experimental research programme for developing a good FC is very time consuming and expensive. Therefore K-Lab has started to evaluate Computational Fluid Dynamics (CFD) models as a tool in assisting in this development. The technique has been used successfully the last years to study the influence of upstream effects in orifice metering stations (ref. 5).
The ultimate goal for this effort is to be able to predict the flow profiles downstream of a FC like the K-Lab/Model Laws (19-21 hole plate) with different upstream flow conditions. But first some basic work was needed on simpler plates with fewer holes and fully developed upstream flow. That will give a more fundamental understanding of how the PC's work and how accurate it is possible to predict the different flow characteristics. This work was initiated because very little information about flow prediction downstream of a perforated FC with circular holes is found in the literature. To the authors knowledge, only two papers have focused on the simulation of the flow downstream of a FC (ref. 6 and 7) and no one has checked the accuracy in predicting the turbulent kinetic energy and the turbulent energy dissipation rate downstream of a perforated plate.
It is well known that swirl and other deviations from a fully developed velocity profile affects the flow rate measured by an orifice meter (ref. 8). Lately it has also been shown that deviation from fully developed turbulence structure upstream of an orifice meter, can influence the metering result (ref. 9). Therefore this paper focuses on the distribution of the velocity, the turbulent kinetic energy, k, and the turbulent energy dissipation rate, s, in the pipe.
Furthermore the paper deals with the ability of a CFD code and a simple k-s model to predict the characteristics of the fully developed flow and the decay of the distutbances introduced by a one-hole plate (1H) and a nine-hole plate (9H).
EXPERIMENTAL SET UP
Test facility All the experimental work has been carried out in a 92 mm diameter (D) smooth pipe rig with an upstream mounted fan shown in figure 1. Air enters and leaves the system at atmospheric condition. Vortices generated by the fan are eliminated in a honeycomb section followed by a 5:1 contraction to the pipe. A 108D straight pipe follows downstream of the contraction in which the turbulent pipe flow developes. The two plates which have been investigated were mounted at the end of this pipe. Measurements were performed at three stations 5D, 10D and 15D further downstream.
Obstruction plates The geometries of the 2 plates are shown in figure 2 and figure 3. Both plates are 11 mm thick. The 1H plate consists of a concentric hole with diameter 64 mm. The 9H plate consists of eight 20 mm diameter holes equally distributed in the angular direction and one hole of 30 mm in the centre. The centre of the eight holes were positioned at a radial distance of 30 mm from the pipe axis. The holes were sharp edged both at the upstream and downstream side. Both plates were designed to have the same flow area.
Page 2 Data acquisition The experiments were carried out at a Reynolds-number of Red = 75000. A pitot-static tube and hot-wire anemometry were used for velocity measurements. Both single and crossed hot-wire probes were manufactured from etched platinum 10% rhodium wire. Distribution of mean axial velocity (U) was measured with a single hot-wire probe. The signal was filtered at 10 kHz. The mean velocity profiles are normalised using the mean velocity integrated across the pipe (U0). Distributions of turbulent kinetic energy were measured with a x-wire probe rotated in two directions to obtain all three normal stresses. The dissipation rate of turbulent kinetic energy was obtained from the single wire data. Parts of the one-dimensional energy spectrum E, (k,) in axial direction displays a range which varies as k, "5/3. s is then calculated from the relation given in equation 1;
(1) where k, = 27cf/U is the wave number.
The pressure drop in the pipe was measured by 10 equally spaced pressure tappings.
NUMERICAL MODEL
Computational code The PHOENICS computer code, version 2.0, running on a IBM RS6000 model 25 T was used to simulate the flow. The turbulence was modelled using the k-e model. Standard coefficients were used. All simulations assumed constant temperature and density, stationary flow and smooth pipe wall.
Grid for fully developed flow The predictions were carried out using 40 radial and 40 streamwise grid points for the 108D pipe. Since the flow was assumed to be axisymmetric, a two-dimensional simulation was performed. In cylindrical polar coordinates the domain was therefore divided into rectangular grid cells. The grid was stretched in the radial direction to produce a finer grid close to the wall. y+ for the first grid point near the wall was approximately 40 for all the grids.
Grid for the 1-hole-plate This grid can be seen in figure 4 and figure 5 where 68 axial and 30 radial points were used. The grid was modelled with cells of varying sizes. A finer grid was used close to the plate in the axial direction and close to the wall because of the large velocity gradients expected in these regions.
35D of straight pipe was modelled upstream of the plate to predict fully developed flow. The plate comprised of 4 cells in axial direction. Radially the plate was simulated by blocking cells 18 to 30. Downstream of the plate a straight pipeof 16D was modelled.
Grid for the 9-hole-plate The axial grid for the 9H plate is the same as used for the 1H plate. Here BFC (body-fitted coordinates) was used to model the pipe and plate. 68 axial, 30 radial and 15 tangential grid points were used. The 9H plate is divided into 8 equal sectors each of 2tu/8 radians and only
Page 3 one of these sectors were simulated. The grid in radial and tangential direction can be seen in figure 6. The centre hole is modelled by the 9 first radial cells.
RESULTS AND DISCUSSION
Fully developed flow The fully developed flow profiles were all measured after 108D straight pipe (See fig. 1).
The measured pressure drop became linear at 15D downstream of the contraction. The Darcy friction factor, f, for the pipe
was measured and predicted to be 0.019. The same value can be found for smooth pipe flow in the Moody diagram. This is a good indication that both the measured and predicted profiles are fully developed.
The measured and predicted mean axial velocity profile scaled with the mean flow, U0, is shown in figure 7. The velocity profiles agree well from the pipe wall to y/R « 0.5. Closer to the centre of the pipe the calculations underestimate the velocity and at the centre line the deviation is 3%.
The predicted and measured distribution of turbulent kinetic energy normalised with the friction velocity u* = is shown in figure 8.
The measured mean velocity and turbulence properties compare well with those reported by Lawn (ref 10). Velocity profiles measured at 108D along two diagonals confirmed that the flow is symmetric within 1% of the local mean velocity and for the axial normal stress within 5%.
The calculated turbulent kinetic energy deviates slightly from the measured values. However, the deviation compares well with those reported by other authors at similar Reynolds-numbers (for instance ref. 11). The predicted and measured dissipation rate of turbulent kinetic energy is presented in Figure 9. The experimental results were derived from single hot-wire data assuming isotropic turbulence in the subrange. For the fully developed flow the spectrum in axial direction (E, (k,)) displayed an extensive range where the energy drops as k, "5/3. Estimating the dissipation rate from equation 1 is therefore expected to be acceptable in the core region where the flow is close to isotropic. Near the pipe wall the estimate is more questionable due to the high degree of anisotropy found in this region.
The predicted dissipation profile compares quite well with the measured data.
1-hole-plate (1H) The 1H plate is axisymmetric. The mean velocity distribution was measured along a number of diagonals with a pitot-static tube at 5D, 10D and 15D to check the symmetry. The deviations observed in mean velocity at 5D was within 1% with respect to the centreline velocity and within 0.5% at 15D.
Page 4 The predicted and measured velocity profiles 5D downstream of the plate are plotted in figure 10, in figure 11 for the 10D results and in figure 12 for the 15D results. In figure 13 the measurements from the three stations are shown to visualize how the profiles develop downstream. The velocity distributions 5D downstream of the plate contain high momentum near the pipe wall. As the flow develops downstream to 15D a mean radial transport of momentum towards the centre of the pipe is evident. At 15D the centre line velocity is within 10% compared to the fully developed upstream profile.
As can be seen from the figures, the calculated and measured results at 10D and I5D compare very well. At 5D the discrepancy is larger, but the predictions follow the trend of the measurements. At the centre line the deviation at 5D is 4 %. The flow is quite complex close to the plate and the k-e model obviously has some problems predicting the flow here accurately.
Figure 14 shows the predicted and measured turbulent kinetic energy at 10D and 15D downstream of the 1H plate. At 15D the measured values are approximately constant from 0.4 < y/R < 1.0. The predicted values are approximately 30% too high in this region. However near the wall the agreement is good. At 10D the predicted values are increasing where the measured values are decreasing, and no similarity can be found between the measured and predicted distributions.
Figure 15 compares the predicted and measured dissipation rates of the turbulent kinetic energy. At 10D and 15D the curves follow each other quite well when y/R >0.1. But at 5D downstream of the plate, the deviation is large and the gradients have opposite signs.
9-hole-plate Also for this plate the mean velocity distribution was measured at different diagonals with a pitot-static tube at 5D, 10D and 15D to check the symmetry. The effect of the geometry is much clearer for this plate with a deviation of 4% at 5D and 1% at 15D. But it was not possible to detect a systematic difference and correlate it to the geometry of the plate. Therefore the deviations must be considered as a measure of the sensitivity of the experimental configuration on flow symmetry. Obviously the flow pattern in the narrow region behind the 9H plate is very complex.
For this plate there is a tendency of flow acceleration in the centre line region caused by the larger centre-hole. In contrast to the 1H plate, there is a mean radial transport from the centre region towards the wall between 5D and 10D. At 15D the axial velocity profile has reached approximately the same shape as for the 1H obstruction at the same station.
The predicted and measured velocity profiles at 5D downstream of the plate is plotted in figure 16, in figure 17 for the 10D results, in figure 18 for the 15D results and in figure 19 for comparison of the measured data.. Also for this plate the calculated and measured results at 10D and 15D compare very well. At 5D the predicted velocity also follows the measurments quite well except near the centre line where the deviation is about 3.5%. The predictions showed no variations in the circumferential direction at 5D. This is consistent with the measurements.
Figure 20 shows the predicted and measured turbulent kinetic energy at 10D and 15D downstream of the 9H plate, and figure 21 compares the predicted and measured dissipation rate. Both k and e are lower downstream of this plate than for the 1H plate. The deviations
Page 5 between the predicted and measured values are smaller, but similar, for this plate compared to the 1H plate.
CONCLUSIONS
Numerical approximations with the standard k-s model were used to predict the mean velocity profile, turbulent kinetic energy and dissipation rate of the turbulent kinetic energy for fully developed pipe flow and at 3 positions (5D, 10D and 15D) downstream of a one-hole and a nine-hole perforated plate. For the fully developed flow, the predicted flow deviates from the measured by 3% at the centre line. The simulation of the velocity profiles at 10D and 15D downstream of the plates compares very well with the measured data. At 5D the predicted values are also close to the measured, but here the deviation was as high as 4% at the centre line.
The k-s model could not predict the turbulent kinetic energy profile accurately close to the plates. For fully developed flow and 15D downstream of the 2 plates the general trend of the profiles could be calculated. Closer to the plates, at 10D, the predicted results were still quite different from the measured data.
The predicted dissipation rate compared well with the measured data for the fully developed flow and at 10D and 15D downstream of the plates. At 5D considerable difference between the predicted and measured values were found.
REFERENCES
111 International Organisation for Standardisation. Measurement of fluid flow by means of orifice plates, nozzles and Venturi tubes inserted in circular cross-section conduits running full. ISO 5167-1, Geneva: International Organisation for Standardisation, 1991.
/ 2 / Kreith, F. and Sonju O K The decay of turbulent swirl in a pipe. J.Fluid Mech. 25 (1965) 257.
/ 3/ Bates I P Field use of K-Lab flow conditioner. North Sea Flow Measurement Workshop 1991.
141 Erdal A., Lindholm D. and Thomassen D. Development of a flow conditioner. North Sea Flow Measurement Workshop 1994.
15/ Thomassen D., Langsholt M. And Sakariassen R. Flow conditions in a gas metering station. North Sea Flow Measurement Workshop 1992.
Page 6 / 6 / - Pasdari M. and Crimson C.J. Design of a new "flow conditioner" with the aid of PHOENICS. Vol. 4, No 2 pp 128 - 154, PHOENICS Journal of Computational Fluid Dynamics.
Ill - GajanP. andHebrardP. Experimental and theoretical study of a new flow conditioner. Flucom'88, Sheffield, pp 347 - 351, September 1988.
/ 8 / - Morrison G.L., Hall K.R., Macek M L., Me L.M., DeOtte R E. and Hauglie J.E. Upstream velocity profile effects on orifice flowmeters. Flow Meas. Instrum., 1994 Volume 5 Number 2.
191 - Kamik U., Jungowski W.M. and Botros K.K. Effect of turbulence on orifice meter performance. 1992 OMAE, Vol. V-A, Pipline Technology, pp. 19 - 29.
/10 / - Lawn C.J. The determination of the rate of dissipation in turbulent pipe flow. J.Fluid Mech. 52, pp. 477 - 505, 1971.
/11 / - Malin MR. and Sanchez L. A revised version of the k-kL turbulence model for near wall flows. Appl. Math. Modelling, 1989, Vol. 13, March.
Page 7 108D straight pipe honeycomb 5D extension obstruction
5:1 contraction
Figure 1. Schematic test rig.
Figure 2. The 1-hole plate, 1H. Figure 3. The 9-hole plate, 9H
Figure 4. The grid in y- and z-direction for the 1H plate and 9H plate.
Page 8 Figure 5. The grid in x- and y-direction for the 1H plate and the pipe upstream and downstream of the plate.
Figure 6. The grid in x- and y-direction for the 9H plate and the pipe upstream and downstream of the plate.
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N n/y-3 Paper m
Three-dimensional computation of turbulent flow through a flow conditioner
Erdal, A, Sivertsen, A S, Langsholt, M and Andersson, HI
Proceedings of the 8th International Conference on Flow Measurement, Flomeko '96, Beijing, China pp 718 - 723, 1996. THREE-DIMENSIONAL COMPUTATION OF TURBULENT FLOW THROUGH A FLOW CONDITIONER
A. Erdal and A. S. Sivertsen (Statoil/K-Lab, P.O.Box 308, N-5501 Haugesund, Norway) M. Langsholt (Institute for Energy Technology, P.O.Box 40, N-2007 Kjeller, Norway) H. I. Andersson (Department of Applied Mechanics, Norwegian University of Science and Technology, N-7034 Trondheim, Norway)
ABSTRACT
A campaign has been started to investigate if it is possible to simulate the confined jets through a perforated plate flow conditioner (FC) with different upstream flow profiles by use of a commercial computational fluid dynamics (CFD) tool. In this study three different k-e models were used to predict the flow through a 90° bend and two right angle bends out of plane (twisted S-bend), and thereafter through a 19-hole K-Lab/Laws FC. The predictions are compared with LDV-measurements. In general, the simulated values compare well with the measurements, but there are however, several areas which are pinpointed here, where more information and validation are required before this technique can be fiilly exploited.
INTRODUCTION
A FC is a device which is installed in order to remove swirl and correct a distorted flow profile. In the past there have been numerous attempts to "isolate" flowmeters from piping induced disturbances. Despite all these efforts, much research is still ongoing to find an optimal FC. In an earlier paper, Erdal et al.1 presented the systematic process to develop a FC. A theoretical design procedure for the development and the main findings from laboratory tests were described. Other researchers have used a combination of screen theory and experiments to develop FCs2,3. In general, research programmes based on measurements are very time consuming and expensive. Therefore K-Lab has started to evaluate CFD models as a tool for assisting in this development. During the last years, this technique has been used successfully to study the influence of upstream effects in flow metering stations 4. A common FC, like the K-Lab/Laws, consists of a perforated plate with a central hole and two rings of holes, Fig. 1A. The ultimate goal for this project is to be able to predict the flow profiles downstream of a FC like the K-Lab/Laws, with different upstream pipe configurations, and also study numerically the effect of the FC on an orifice meter. From a fluid mechanical point of view the interaction between the various jets is complicated. Therefore, a preliminary study has been carried out on simpler plates with fewer holes and fully developed upstream flow3. A k-s model was used to predict the flow downstream of 2 obstruction plates having a single large or nine small holes, respectively. The results from this preliminary study were encouraging. They indicated that it is possible to predict the flow development downstream of restriction plates with reasonable accuracy, and that it might be possible to simulate the flow through FCs. In the present study a further step is taken. A 90° bend and a twisted S-bend are predicted upstream of the FC, and the calculated axial velocities are compared with measurements.
Page 1 Fig. 1. Perforated plate A. The K-Lab/Laws FC. Perforated B. The twisted S-bend. C. The 90° bend. D. Traverse direction.
Row conditioner 5D Row conditioner
EXPERIMENTAL SET UP
The test facility consists of a smooth pipe rig, made in Plexiglass, with an internal pipe diameter (D) of 139mm. Air is sucked through the loop by a positive displacement pump yielding a constant volumetric flowrate. The pipe Reynolds number in the test section is 2105. Fig. 1 presents the two configurations used in the study; a single 90° bend (Fig. 1C) and a twisted S-bend geometry (Fig. IB). The former generates a highly asymmetric velocity profile, while the latter generates strong swirl. Both configurations have a 10.6D straight pipe with a perforated plate at the inlet. The radius of curvature for the bend is 1.42D. The twisted S-bend consists of two such 90° bends separated by a 1.13D straight pipe. The FC is positioned at 5D downstream of the last bend. Measurements were performed at 5 stations; 2.5D upstream of the FC (midway between the bend and the FC) and 2.5D, 5D, 10D and 15D downstream of the FC. A 19 hole K-Lab/Laws FC with a hole arrangement 1:6:12, a plate thickness of 0.123D and a porosity of 0.53 per cent is used in this study; see Fig. 1A. The upstream edges of the apertures are not chamfered. An LDV system was used for the velocity measurements. It has been described in detail by Langsholt6. Briefly, the system is a 300mW Spectra-Physics He-Ne laser and a Dantec 55X Fiberflow 2-D system using 488.5 and 514nm wavelength light. A Bragg cell introduces a shift in the frequency of 40 MHz. The signal processing is carried out in a Dantec FVA 5840 enhanced processor. The measurement volume is approximately 0.6 x 0.1 x 0.1 mm. To get coincidence in the laser beam signals, an optical section made from 0.1mm thick glass was used to transit the beams through the wall. Introducing smoke was necessary to obtain reflection of the light. Special care was taken in positioning the probe.
Fig. 2. A. Grid in the bends. B. Pipe grid. C. FC grid.
Page 2 NUMERICAL MODEL
The Phoenics 2.0 computer code, running on an IBM RS6000 model 380, was used to simulate the flow. Phoenics uses the so-called finite-volume method, where the original partial differential equations are converted into algebraic finite-volume equations, with the aid of discretisation assumptions. Use is made of the conventional staggered-grid arrangement, in which the velocity nodes are placed on the cell faces and the scalar variables in the cell centres. Central differencing is employed for the diffusion terms. The convection terms are discretised using the hybrid-differencing scheme. The Simplest algorithm is used to solve the finite-volume equations. The calculation procedure is organised in a slab-by-slab manner, in which all dependent variables are solved at the current slab before the solver routine moves to the next slab. (See Phoenics encyclopaedia 7 for further details.) Appropriate relaxation of the flow variables is necessary in order to obtain convergence. Both inertial and linear relaxation are employed. The former is normally applied to the velocity variables, whereas the latter is applied to the pressure, the turbulent kinetic energy and its dissipation rate. The two geometries, as shown in Fig. IB and Fig. 1C, were both simulated as a sequence of separate, but interlinked, Phoenics runs. Specially designed software ensures correct transformation of the boundary conditions between the modules in a sequence, and precautions were made to avoid that elliptic effects should corrupt the simulations. This method invites to different discretisation through the geometry, it makes is possible to change turbulence model and to use a less dense grid in the inlet geometry, compared to what is required in the FC containing module. The geometry was split into two modules: 1) the inlet geometry (single bend/twisted S-bend) and 2) a section of straight pipe including the FC. The cross-sectional grid used in the bends can be seen in Fig. 2A. The FC containing module was described in a different cross-sectional mesh type, illustrated in Fig. 2B, which was easier to adapt to the geometry of the FC, shown in 2C. The grid consisted of (30 radial x 120 tangential x 62 axial) cells. The axial distribution was 15 cells (slabs) upstream of the FC, 4 cells within the FC and 43 cells on the downstream side. In these calculations the linear relaxation factor used was approximately 0.4 and the inertial usually 0.1. Phoenics was run until the sum of the absolute residual sources over the whole solution domain was less than one per cent of the reference quantities, based on the total inflow of the variables in question. In addition, checks were made to verify that the dependent variables at some selected locations fluctuated less than 0.1 per cent between successive iteration cycles. All geometries use the Body Fitted Coordinate (BFC) option of Phoenics. The normal log-law was used to bridge the viscous sub-layer. Three turbulence models were tested; the standard k-e, the Chen-Kim model (CKM) and a modified Chen-Kim k-e model 8 (MCKM).
RESULTS
First the two bend geometries were calculated with relatively coarse grids to study the effect of different turbulence models. The CKM is known to give good results for bends, but when the turbulence level is too high, it overpredicts the dissipation rate and a modification (MCKM) of one of the constants is necessary 8. Fig. 3A shows the simulated axial velocities, scaled with the bulk velocity (Wm), 2.5D downstream of the 90° bend with a 20 x 20 x 62 mesh. Fig. ID shows the transverse direction for the horizontal (H) and vertical (V) profiles. The ordinate in Fig. 3, 4 and 5 is offset by 0.5 units. It can be seen in Fig. 3A, that the predicted values from the k-e model and the CKM are very similar. When there is a significant difference, as at Y/D-0.8 on the vertical traverse, the standard k-e model compares better with the measured
Page 3 W/Wm W/Wm
Horizonte!
Y/D v y Fig. 3 A. Predicted and measured axial velocity Fig. 3B. Predicted and measured axial profiles 2.5D downstream of the 90° bend with velocity profiles 2.5D downstream of the different turbulence models. 90° bend with different grids. The MCKM turbulence model is used.
W/Wm W/Wm
i Horizontal i Horizontal! 1.6
1.0 1.0 -u 0.8 ^
Fig. 4A. Predicted and measured axial velocity Fig. 4B. Predicted and measured axial profiles 2.5D downstream of the twisted velocity profiles 2.5D downstream of the S-bend with different turbulence models. twisted S-bend with different grids. The k-e turbulence model is used.
data. The best results are obtained with the MCKM. The overall agreement between the calculated and measured velocities along the vertical traverse is best for this model, and also for the horizontal profile it compares best, at least when Y/D is between 0.2 and 0.8. Therefore, further calculations with finer grids were carried out by use of this model. Fig. 3B shows the results for 4 different meshes. The figure reveals that grid refinement from (20 x 20 x 62) to (40 x 40 x 80) changes the predictions and generally improves the results. Fig. 6A shows the contour plot for the axial velocity at this location. The main characteristics of the highly asymmetric velocity profile are well predicted, but Fig. 3B shows that the model is not capable of calculating the velocities with high accuracy; the profiles are too fiat and close to the wall the deviation is almost ten per cent. There may be several reasons for this. It is likely that the predictions would be improved if more advanced turbulence modelling, such as a full Reynolds stress model (RSM), was employed. Further, higher order differencing schemes and finer meshes should be evaluated to obtain grid independent solutions. With the current version of the CFD code, it is not possible to obtain converged solutions with second order
Page 4 Fig. 5. W/Wm Predicted and measured axial 2.4 — velocity profiles, vertical Measured 2.5D traverse, at 2.5D, 5D and 10D downstream of the PC. Measured The modified Chen-Kim model is used.
Measured 10D
Computed
schemes or RSM with BFC grid. In future releases of Phoenics, these features will be implemented, and refinements can be tested. Fig. 4 A shows the predicted axial velocities 2.5D downstream of the twisted S-bend with a (20 x 20 x 71) mesh and the same turbulence models as in Fig. 3A. For this geometry the predictions with the various models gave similar results, but in general the standard k-s model compared best with the measured data. Therefore this model was used in the further calculations. Fig. 4B shows the simulated results with finer meshes. The difference in the results is negligible when the axial grid is increased from 71 to 107, and also very little when it is increased from 20 to 40 in the X and Y direction. Also for this configuration the main characteristics of the flow are well predicted, but the calculated profiles are too fiat compared to the measurements. It is well known that eddy-viscosity models have problems to represent the swirl exactly, so more sophisticated models are needed to improve the simulations. Anyway, the predicted flow pattern through the bends gives a good representation of the distorted flow downstream of the different configurations. The results from the finest grids were used as inlet boundary conditions to the pipe with the FC, to study if it was possible to calculate this complex flow. The simulation of the FC-module was made with both the k-e model and the MCKM. As expected from earlier studies 8 , the results were better with the latter model and only these simulations are presented here. The results with the velocity field of the 90° bend as input, can be seen in Fig. 5 and Fig. 6. In the first of these figures, both predicted axial velocities and LDV measurements are shown for the vertical traverse, which is the highly asymmetric profile upstream of the FC. Generally the predictions and measurements compare very well downstream of the plate. Only close to the wall velocities for some of the profiles are underpredicted. Fig. 3B shows that in general the incoming flow profile is also too low close to the wall. As mentioned earlier, it must be emphasised that these results are not fully grid independent since higher order schemes aren't used. The mesh used here, (30 x 120 x 62), should probably also be refined, but with the current hardware it is impractical with finer grids since a simulation like this needs 33 hours to reach convergence. These good results are obtained even though the upstream profiles from the bend could have been predicted more accurately. A possible explanation is that the FC is capable of redistributing the flow field whatever the upstream profile look like, so that incorrect upstream velocities do not affect the downstream flow considerably.
Page 5 A B C D E
Fig. 6. Contour plot of the axial velocities 2.5D downstream of the 90° bend (A), through the FC (B), and 2.5D (C), 5D (D) and 10D (E) downstream of the plate.
Fig. 6 shows the predicted contour plots at 2.5D upstream of the K-Lab/Laws FC, inside the plate and at 2.5D, 5D and 10D downstream of it. The figure qualitatively demonstrates how the skewed velocity profile is transported through the FC and how quickly it develops downstream of the plate. It is interesting to note how efficiently the FC isolates the downstream side from the highly distorted upstream flow field. The acceleration of the velocities upstream of the blocked part of the FC redistributes the flow so that the maximum axial velocity through all the holes in the outer and inner rings are similar. The figure also demonstrates how the various jets are mixed. At 2.5D it is still possible to count the number of holes in the plate from the contour plot, but at 5D the individual jets can no longer be distinguished, and at 10D the contour-lines are nearly fully developed. The simulations with the FC downstream of the twisted S-bend give similar results as the calculations downstream of the 90°.
CONCLUSIONS
Three-dimensional axial velocity profiles through a 90° bend and a twisted S-bend, followed by a straight pipe with a K-Lab/Laws FC, are predicted. The results downstream of the FC compare very well with the measurements. Simulations of this type can be a valuable tool in designing and assessing the effect of FCs in the future. First, some additional studies must be carried out with higher order schemes and finer grids to assure that the predictions are grid independent. The performance of the modified Chen-Kim k-s model is satisfactory downstream of the plate, but more advanced turbulence models are needed to improve the calculation of flow through bends.
REFERENCES
1. AErdal, D.Lindholm and D.Thomassen, North Sea Flow Meas. Workshop, (1994). 2. E.Laws, Flow Meas. Instrum., 1 (1990), 165. 3. U.Kamik, Fluid Flow Measurement 3rd International Symposium, San Antonio, (1995). 4. D.Thomassen, MLangsholt and R Sakariassen, North Sea Flow Meas. Workshop, (1992). 5. A Erdal, L E.Torbergsen, S.Rimestad and P.A.Krogstad, Fluid Flow Measurement 3rd International Symposium, San Antonio, (1995). 6. M Langsholt, (in Norwegian), IFE-report: DFE/KR/F-96/076, (1996). 7. Phoenics encyclopaedia; online user-manual, Cham Limited, Bakery House, 40 High Street, Wimbledon Village, London SW195AU, UK, (1996). 8. A Erdal, K-Lab report: K-Lab/R/170, (1996).
Page 6 Paper IV
Numerical aspects of flow computation through orifices
Erdal, A and Andersson, HI
Accepted for publication in Flow Measurement and Instrumentation Numerical aspects of flow computation through orifices
A. Erdal Statoil/K-Lab P O Box 308 N-5501 Haugesund, Norway Phone: 4752772388 Telefax: 4752772210
H.I.Andersson Division of Applied Mechanics, Norwegian University of Science and Technology, N-7034 Trondheim, Norway
Keywords: CFD; orifice; numerical methods; turbulence models Abbreviated title: Flow through orifices
ABSTRACT The use of computational fluid dynamics (CFD) tools for modelling and analysing process systems has increased in recent years. A campaign has begun to investigate whether it is possible to simulate metering stations that include flow conditioners (FCs) and orifice meters. However, more information and validation are required in several areas before the technique can be fully exploited. This study was initiated prior to the start of full pipe simulation to investigate various grid effects, coordinate arrangements, wall boundary conditions, differencing schemes and turbulence models that can predict more accurate flow values through an orifice. The calculations were carried out in two-dimensional axisymmetric flow. The findings can be used in modelling both FCs and orifice plates.
Page 1 NOMENCLATURE Ar Cell aspect ratio, h/h^ Cd Orifice plate discharge coefficient D Pipe diameter d Inside diameter of orifice E Roughness parameter (8.6 for smooth walls) h Orifice height, (D-d)/2 k Turbulent kinetic energy p Pressure Pk Production of k R Pipe radius, D/2
RCq Reynolds number calculated from D and bulk velocity u* Friction velocity V Radial velocity W Axial velocity y+ Dimensionless wall distance
3 Orifice plate beta ratio, d/D
s Dissipation rate of turbulent kinetic energy
k von Karman constant (0.41)
Page 2 1. INTRODUCTION The most commonly used method for metering large gas flows uses an orifice meter, which is a geometrically simple device. In international trade, this method is implemented in accordance with international standards such as ISO-5167-1 1. The discharge coefficient - Cd - for orifice meters is normally obtained using empirical equations. These are based on experimental data that are derived under controlled laboratory conditions with fully developed flow upstream of the orifice meter. In many field installations, however, it is not possible or practical to operate under conditions similar to those found in the flow laboratories. Departure from these conditions will change the characteristics of the flow field, and thereby alter the discharge coefficients. As a result, much effort has been devoted to developing a perforated plate flow conditioner (FC), which can generate the required flow structure within a short distance downstream of any disturbance 2. To help improve FCs and metering technology, computational fluid dynamics (CFD) models have been tested in recent years to study trends and to provide insight into the flow physics 3,4. The use of such codes by the engineering community has increased dramatically in the past few years 5. For this technique to be applied successfully to practical problems, so many features in the programmes are needed that it would be too expensive and time-consuming for companies to develop their own code. It will be much more convenient and cost-efficient to purchase a commercial CFD code. This study adopted the general-purpose Phoenics programme6. Everyone who assess calculations from CFD programmes finds that they never should be used as a 'black box'. That is clearly demonstrated by Spencer et al. in a recent paper7 . They found that different experts obtained a significant variability in the numerical prediction of the flow in a given configuration when using the same CFD code and turbulence model. If simulation of flow through FCs and common flowmeter installations are to be modelled correctly, the numerics used must be scrutinised very carefully. It was therefore decided to make a careful study of the model of a geometrically simple one-hole plate before more complex FCs were modelled. The results from this study can be used for modelling both orifice metering stations and multihole FCs. In an earlier paper, Erdal et al.3 described the flow field downstream of a one-hole plate - see Figure 1 - installed in fully developed flow. This case will be used here to explore different aspects of the numerical model in order for possible problems to be identified and discussed.
Page3 2. LITERATURE REVIEW OF ORIFICE MODELLING Information on the predicted flow structure downstream of pipe restriction plates is scarce in the literature. In a couple of papers, Durst et al.8 '9 have studied the flow through an axisymmetric ring-type obstacle in a pipe both numerically and experimentally. They found good agreement between the calculations using a k-e turbulence model and the measurements, but the pressure drop over the plate was not reported. Most of the other researchers who have published numerical calculations on this subject have been interested in metering and have focused on the pressure drop over an orifice plate. Davis and Mattingly 10 modelled orifice plates with beta ratios from 0.4 to 0.7 and with Reynolds numbers - Re^ - in the range 104 to 106. They found that the agreement between computed and experimental discharge coefficients is within four per cent. Sheikholeslami et al.11 and Barry et al.12 used Fluent to model the variations in orifice meter performance as a function of Reynolds number, beta ratio, pipe surface roughness, upstream swirl, and upstream and downstream flow boundary conditions. They reported that an 80 x 60 grid is sufficient to obtain the discharge coefficient within two per cent of the empirical data. Reader-Harris 13-14 has also used CFD to study orifice meters; primarily the discharge coefficient, the effect of pipe roughness on it, and the wall pressure distribution through the orifice. He reported that discharge coefficients can be calculated with a remarkably high accuracy - within 0.64 per cent. Several authors (e.g. Langsholt15, Morrison 16 and Freitas17 ) have used CFD for parametric studies, and many researchers have measured the flow field downstream of an orifice plate - e.g. Morrison et al.18
3. COMPUTATIONAL CODE The Phoenics computer code, version 2.1.3, running on an IBM RS6000 model R21, was used to simulate the flow. This programme is applicable to steady or unsteady, one-, two- and three-dimensional turbulent or laminar flows using Cartesian, cylindrical-polar or curvilinear coordinates (BFC). In this paper, it has been used only to calculate two-dimensional turbulent flow with cylindrical-polar coordinates. Phoenics uses the finite-volume method, in which the original partial differential equations are converted into algebraic finite-volume equations with the aid of discretisation assumptions. Use is made of the conventional staggered-grid arrangement, in which the velocity nodes are placed on the cell faces and the scalar variables in the cell centres. The control volumes for the velocities are staggered with respect to the control volumes for the scalar variables.
Page 4 The partial differential equations for all variables are integrated over each control volume to obtain finite-volume equations. Central differencing is employed for the diffusion terms. The convection terms are discretised using second order schemes: a linear upwind scheme (LUS) for the axial velocity and van Leer harmonic scheme (VANLH) for the other variables. This combination was found to be very robust for the current case. The outcome is a coupled set of algebraic finite-volume equations. All variables at a grid node are expressed in terms of the values at neighbouring grid points. The Simplest19 algorithm is then used to solve the finite-volume equations. The calculation procedure is organised in a slab-by-slab manner, in which all dependent variables are solved at the current slab before the solver routine moves to the next slab. The slabs are thus visited in turn, from the lowermost to the uppermost, and a complete series of slab visits is referred to as a sweep through the solution domain. For elliptic calculations, like for flow through an orifice, many sweeps are carried out until the solution converges. In addition, the pressure equation is solved in a simultaneous whole-field manner at the end of each sweep. Appropriate relaxation of the flow variables is necessary in order to obtain convergence. Both inertial and linear relaxation are employed. The former is normally applied to velocity variables, whereas the latter is applied to turbulent kinetic energy and its dissipation rate. In these calculations, the linear relaxation used is normally 0.5 and the inertial usually 0.02. Phoenics was run until the sum of the absolute residual sources over the whole solution domain was less than a half per cent of the reference quantities, based on the total inflow of the variables in question. In addition, checks were made to see that the dependent variables at some selected locations fluctuated less than 0.1 per cent between successive iteration cycles.
4. NUMERICAL MODEL The axisymmetric one-hole plate in Figure 1 was modelled in two dimensions. Both the pressure drop and the flow field downstream of the orifice have earlier been measured and were used to anchor the calculations 3,20,21. These measurements were carried out in a 92 mm diameter (D) smooth pipe rig at ReD=75000. The plate consists of a concentric hole with a diameter d=64 mm, giving a [3 ratio of 0.7. The plate is 11 mm thick. Measurements are available for fully developed flow and at four stations, 2.5D, 5D, 10D and 15D downstream of the restriction.
Page 5 A sector of the pipe from the axis to the wall is used to simulate the pipe with the plate. Cells were concentrated axially in the area close to the plates and radially near the plate lip and near the pipe wall. 30D of straight pipe was modelled upstream of the plate to assess the flow field and pressure drop in fully-developed flow. Downstream of the plate, a straight pipe of 16D was modelled. At the pipe inlet, fully-developed conditions obtained from an earlier simulation were used for W, k and e, wheras V=0. The static pressure at the outflow boundary
is specified as zero. Cylindrical-polar co-ordinate system is used.
The turbulence was modelled using the k-e mode with standard coefficients. Unless otherwise stated, the wall function technique given by Launder and Spalding was applied 23.
5. RESULTS Mesh size A grid independency study was performed to find a mesh that was sufficiently fine to provide an accurate solution. During the investigation, predictions with the cells concentrated in various regions were carried out to check the effect on the simulated variables. First, the calculated flow-field downstream of the orifice was investigated. These tests revealed that k was much more grid-dependent than the mean axial velocity, W, in this region. The reason is that the gradients are much larger of k than of the axial velocity close to the plate. Therefore, the simulated turbulent kinetic energy at 2.5D downstream of the plate, where measurements were available, was used to assess the grid dependency. Figure 2 shows the calculated k at this location with a 60 x 150 (radial x axial) grid and a 90 x 300 grid. It can be seen that the results are almost identical except in a limited region around Y/R = 0.45. Since the grid dependency on the axial velocity is even smaller and decreases further downstream of the plate, the marginal grid dependency was found to be acceptable in this study; and 60x 150 cells were found to be optimal. In this mesh, 61 cells were used in the streamwise direction upstream of the plate, the orifice was represented by 15 cells and 74 cells were placed in the downstream part of the pipe. A similar grid has also been used by several other scientists. These include Sheikholeslami et al.11, who found that 60 x 80 cells gave a grid independent solution, Reader-Harris 14, who used 55 x 80, and Durst et al.8 , whose finest grid was 56 x 212. But Figure 2 also compares the calculated k at 0.5D with the above-mentioned grids. Here, the difference in the two
Paged calculations is slightly larger. If the focus for an orifice study is the flow field just downstream of an orifice, therefore, the mesh size should be at least 90 x 300.
Grid spacing around the orifice Orifice meter research has shown that the upstream edge of the plate must be sharp. This is reflected in the ISO standard 1, which requires the edge radius of the orifice lip to be less than 0.0004D. In numerical modelling of the plate, this means that the pressure drop through a sharp-cornered orifice is very sensitive to the grid - not in the entire domain, but in the immediate vicinity of the leading edge of the orifice, probably mainly in the axial direction. A sensitivity study was therefore carried out to investigate how small the cells upstream of the orifice have to be. A number of calculations were performed with the mesh divided into several regions. Each region had a fixed length and contained a constant number of cells. The plate itself was one region, and there were other cell regions upstream, downstream and on the inner side of the orifice. By varying the grid expansion ratio in the regions close to the plate, the distance between the orifice and the adjacent grid lines could be changed while the grid size remained the same. This method was used to determine a correlation between the pressure drop and the distance from the orifice to the nearest grid point. It was more convenient to check the pressure drop over the whole pipe, Ap, then over the orifice alone. The difference in Ap reflects the variation in the pressure drop through the plate, since the grid only varied close to the orifice in these calculations. First, the distance to the grid points nearest to the upstream orifice lip was considered. The calculated y+ at the orifice lip was used to measure the axial grid distance from the plate. Three test series were carried out: the first with mesh size 30 x 150, the second with 60 x 150 and the third with 90 x 300 cells. The axial thickness of the upstream cells, hz, varied between 0.0 ID to 0.0002D. Results from these calculations can be seen in Figure 3. They clearly show that Ap is very
grid-dependent. When hz is reduced from 0.01D to 0.001D, Ap increased from approximately
350 Pa to 450 Pa. The pressure drop appears to converge towards a fixed value because Ap seems to be constant when hz is further decreased to 0.0002D. This result, which shows that the upstream grid node must be closer than 0.001D, is in good agreement with the edge radius requirement in the ISO standard 1,14. Similar conclusions for the cell placement around
Page 7 sharpedged bodies have been obtained previously (e.g. Castro and Jones 22). An hz=0.001D upstream of the orifice is therefore recommended in the optimal mesh, and this hz was also used in the previous calculations shown in Figure 2. The trend in these calculations, and the predicted Ap when hz < 0.001D, are almost the same with 30, 60 and 90 cells in the radial
direction. This indicates that a low axial cell length, hz, is more critical than a low radial cell length, hy just upstream of the orifice. It also shows that the placement of the cells is more
important for Ap calculations than the total number of cells in the mesh. It is possible to obtain better results with a 30 x 150 grid than with a 90 x 300 grid if the axial cell length upstream of the leading edge is smaller in the first grid. The same test was carried out by considering the node distance on the inner side and on the downstream side of the plate, but no significant correlation between the pressure drop and the cell distance was found here. Figure 4 compares the predicted axial pressure in the entire pipe with measured data from Torbergsen and Krogstad21. The figure gives a good illustration of the pressure evolution in a pipe with an orifice: the decrease caused by the upstream wall, the build-up just upstream of the plate and the substantial drop over the plate followed by the recovery, which falls off again at the end because of wall friction. Calculated total pressure-drop compares very well with the measured data. The main difference is that the measured data are somewhat lower downstream of the plate and recover more slowly than predicted. The pressure here is probably overpredicted because the mean velocity close to the wall is underpredicted just downstream of the orifice (ref. Figure 9 which compares simulated and measured velocity profiles at 2.5D downstream of the plate). The calculated pressure drop over the orifice has also been checked against the ISO standard. This plate is thicker than an orifice plate used in metering stations, and the plate is not bevelled on the downstream side. But the standard should give an indication of how accurately Ap over the plate is calculated. By using the Stolz equation in the ISO standard for the given
qm, and assuming incompressible flow, ApIS0 is 575.6 Pa while Ap^ is 578.4 Pa from ID upstream of the plate to ID downstream of the plate. This marginal deviation of approximately 0.5 per cent, together with the measurements in Figure 4, indicate that this numerical model gives a good prediction of pressure drop in the pipe.
Page 8 Mesh expansion ratio Because the axial cell length just upstream of the orifice has to be very short, approximately 0.001D, high grid expansion ratios - Gr - have to be implemented when calculating flow through an orifice. Otherwise, with a uniform grid, about 1000 cells are needed in the axial direction for every pipe diameter. But it is known from the literature 7 that Gr should preferably be kept below 1.2 everywhere to avoid serious numerical errors from grid non-uniformities. In the current case, 30D of straight pipe is simulated upstream of the orifice. In the first 29D, the flow is fully developed. This area was simulated with various grids that have different Gr, and they all gave identical results. The reason, of course, is that the axial gradients of mean
velocities, k and e are zero in this area. Around the orifice, however, flow gradients are very high. In Figure 3, Gr varied between 1.1 and 2.5 and between 1.6 and 2.5 for the results with
approximately constant Ap. These results indicate that the effect from Gr cannot be large in this case. It is always difficult to separate different grid effects. In the predictions shown in Figure 3, both Grand the cell aspect ratio - Ar=hz/hy - are changed. Some tests were therefore performed
to quantify the effect of Gr on the grid-sensitive calculated Ap from another perspective. In these simulations, the important hz upstream of the plate was fixed to 0.001D, while the mesh expansion ratio of the 20 next upstream cells was varied between 1.4 and 2.75. The test was carried out for 30 x 150, 60 x 150 and 90 x 300 grids. The results for pressure drop in the pipe can be seen in Figure 5. Between an expansion ratio of 1.5 and 2.3, the effect on the pressure is veiy small, only in the order of 0.3 per cent. With expansion ratios above 2.3, however, the effect of G, is larger. The effect of the mesh expansion was also studied on the radial side downstream of the orifice, where similar deviations were found. It can therefore be concluded that a grid expansion ratio below two has marginal influence on the calculated pressure drop. This finding is likely to be depending on the differencing scheme used, which here is LUS for the axial velocity and VANLH for the other convection terms22.
Aspect ratio The choice of the optimal grid cell aspect ratio is not trivial in most computational fluid flow problems. Normally, the aspect ratio is of the order of unity, but some flow types may dictate
Page 9 much higher or lower aspect ratios. Here, the leading truncation error term is of second order, so the functional value ,8, can be written as:
8 = 6a + %-yy + -~-f + higher order terms (1) 2 dz 1 2 dy
If the y component of the truncation error is dominant, selective grid refinement in this direction is more cost effective than global refinement, and vice versa. In this case, the optimal domain found consists of a long straight pipe in which A, at the beginning of the pipe is approximately 100. The aspect ratio gradually decreases and becomes less then one close to the orifice. At the cell adjacent to the orifice lip, A, is 0.3 in the 60 x 150 mesh. Within the orifice it is about one, and then it gradually increases again further downstream. Demuren and Wilson 23 has shown that the need to resolve boundary layers may dictate much higher aspect ratios than one. That is in good agreement with the present calculations. In a boundary layer, the flow gradient is in the radial direction, and therefore h^ must be smaller than hz. The opposite is the case in the cells just upstream of the orifice. Here the flow is parallel with the plate, the velocity gradient is in the axial direction, and good results are obtained with an Ar of 0.3 at the plate lip. During the grid independency study it was observed that A, could have a significant effect on the pressure drop. The predictions were first tested with a 30 x 150 grid, then with 60 x 150 and thereafter with 90 x 150 grid points. The results from the two first test series gave similar results, but on the third mesh the calculated pressure drop was 12 Pa (2.7 per cent) lower. The calculations were repeated on a 90 x 300 mesh, with results similar to the first two meshes. These tests therefore indicate that an optimal range exists for values of A, upstream of the leading edge of the orifice. Further investigations are required to verify this phenomenon.
Wall functions To avoid the need to account for viscous effects in the turbulence model, wall functions are employed to bridge the viscous sub-layer and provide near-wall boundary conditions for the mean flow and turbulence transport equations. The wall conditions are connected by means of empirical formulae to the first grid node, which is presumed to lie outside the viscous sub-layer in the fully-turbulent region. Two main types of wall functions are used in the literature. All the
Page 10 users of Fluent 11,12,18 have used the log-law of the wall, while Durst 8,9 and Reader-Harris 14 have used the relation given by Launder and Spalding 24. The log-law is appropriate to a near-wall layer in local equilibrium. Normally, it is implemented as:
JJ _ HEy+) (2)
U*~ K
The other option is the non-equilibrium log-law wall function, which can be written:
Ujk In (EC^JkY/v)
where Y is the distance from the wall. The first method uses u* as the characteristic velocity, whereas Jk fulfills this role in the second approach, which is believed to be better in recirculation zones. The wall functions defined in (2) and (3) are implemented in the source term in the momentum equation which contains and expression for the friction factor. In both methods u* is then eliminated 25. For fully-developed flow, they are both reduced to the conventional logarithmic law of the wall. The flow is then in local equilibrium near the wall, and convective transport and diffusion can be neglected. Accordingly, production of turbulent kinetic energy approximately balances the dissipation rate e. This criterion is used in the first method to determine k and s near the wall in
accordance with the following equations:
u*2 k ycr (4)
8 = K Y (5)
The non-equilibrium log-law calculates the near-wall value of k from its own transport equation by setting the diffusion of energy to the wall equal to zero. The shear stress and k are assumed to be constant across the near-wall cell. An analytical integration over the control volume gives
Page 11 an expression for the production of turbulent kinetic energy - Pk, - and the dissipation rate s. Pk
and s are then represented as:
* 2 u U (6) ^ 27
C^./4t3/2ln(ECg4 Jk Y/v) E = (7) 2k Y
In the actual configuration, there will be a small recirculation zone just upstream of the orifice and a larger one downstream of the plate. Therefore, theory requires the non-equilibrium log-law to be used in this example. Since both methods are in current use, however, it is interesting to study the difference in the calculated results and to try to quantify the deviation between the two approaches. 46D of pipe are simulated in the actual model with the orifice located at 30D. The first grid line near the wall was set to 1.8 mm, which corresponds to a y+ of about 35. In Figure 6, the ratio P/E near the pipewall is plotted for the whole simulated pipe. The calculation is carried
out with the non-equilibrium wall function to obtain a picture of this ratio. In the fully
developed pipe upstream of the plate, it can be seen that the near-wall layer is in local equilibrium, i.e. Pk» s. But 0.2D downstream of the orifice the ratio decreases to 0.43, and then
gradually, increases again. At 5D, the predicted ratio is 0.52, at 10D 0.85 and at 13D it is
approximately one again. From this figure, it can be concluded that the assumption for using the local equilibrium log law is not valid for the first 10D downstream of the plate, and that the calculated values in the nodes close to the wall will probably be incorrect if this option is adopted. In Figure 7, the simulations are carried out using both methods and compared with measured values of k at approximately the same distance from the wall. Again, the turbulent kinetic energy is used to illustrate the numerical issues because this flow variable is much more sensitive than the velocities. Upstream of the plate and after 9D downstream of the plate, where J?Je equals 0.8, the two wall functions give identical results. In the first 9D region following
the orifice, however, it is evident that the measured values of k are not reproduced with the
local equilibrium log law. In fact, the calculated k is lower than in fully developed flow just
Page 12 downstream of the obstacle, and at 2.5D the predicted k is 20 times lower than the measured value! Applying the non-equilibrium log law, the trend in the values is correctly calculated but the actual values are too low. At 2.5D downstream of the orifice, the measured value is 69 per cent higher than the calculated value, at 5D 66 per cent, at 10D 25 per cent and at 15D 16 per cent above than the predicted level. Because the different wall functions affect the near-wall flow variables, they also change the calculated pressure drop over the orifice. For this configuration, the total pressure drop in the pipe was calculated with both methods, and the computed value with the log law wall function was 2.8 per cent lower than with the non-equilibrium log law; see Table 1. This is an important observation when the flow through an orifice meter is calculated. In the simulations, the non-equilibrium log-law wall function is also used on the upstream side of the plate wall. This should strictly be used only for y+ > 30, but in the current calculation the resulting y+ value was approximately seven at the orifice lip, see Figure 3, and it was even lower closer to the pipe wall, where a small recirculation zone exists. It is therefore doubtful whether this use of wall functions is appropriate here. In Phoenics, the wall function switches from the log law to the viscous wall function, u+ = y+, when y+ < 11.5. In this case, the calculated eddy viscosity is very low at the grid points nearest to the upstream side of the orifice, so that it should be in order to use the viscous wall function here. Theoretically, a more correct method might be to use a low-Reynolds number model upstream of the orifice plate where the grid must be placed very near the wall. The computations could then be carried out right down to the plate surface.
Differencing schemes A key aspect of the numerical simulation of fluid-flow phenomena is the discretisation of the convection terms in the finite-volume equations. With the staggered grid approach applied here, the central issue is the specification of an appropriate relationship between the converted variable in the cell centre and its value at each of the cell faces. To estimate the truncation error in numerical schemes, the solutions from the default hybrid-differencing scheme were compared with two higher-order schemes. The default hybrid-differencing scheme (HDS) used in Phoenics was tested first (See Phoenics encyclopaedia 26, the on-line manual, for further references to the different schemes.)
Page 13 The HDS uses the first-order upwind-differencing scheme, which omits physical diffusion when the cell Peclet number exceeds 2, but otherwise reverts to the second-order central-differencing scheme and retains physical diffusion. Second, the well known quadratic upwind interpolation for convection kinematics (Quick) was used in the calculation. This second-order scheme uses a quadratic fit through two upwind nodes and one downwind cell centre. It is well known that Quick increases accuracy compared with HDS, but it can also display non-physical oscillations in regions with steep gradients, which are typical for the flow through an orifice. Phoenics has implemented a number of different second-order schemes, and many of these were tested. A combination of the linear upwind scheme (LUS) and the van Leer harmonic scheme (VANLH) was selected because it was found to be numerically stable and easy to converge. LUS, which is often referred to as the second-order upwind scheme in the literature, was used for the axial velocity. This scheme calculates the face value of the convected variable by linear extrapolation from the two upwind cell centres, and is therefore completely upwind-based. VANLH was used on the radial velocities, k and s. This is a second-order non-linear scheme with good convergence behaviour. Results from these simulations revealed that the schemes had little effect on the calculated velocities, a large impact on the calculated turbulent kinetic energy and dramatically altered the calculated pressure in the hole domain. The test in which Ap was calculated for the whole
domain with different grids was also carried out with different schemes on the 60 x 150 mesh.
The results can be seen in Figure 8. The calculations with HDS seem not to approach a limit when the axial cell-length adjacent to the upstream side of the plate is reduced. A further refinement of the grid upstream of the orifice seems to be necessary with this scheme to obtain an accurate solution. The second-order schemes improve the resolution and give predictions much closer to the measured data. In fact, LUS plus VANLH reproduce almost exactly the experimental data. Since the latter schemes are more stable than Quick and reproduce the measured data better, these schemes were selected in the current study. Table 1 summarises the deviation in the predicted values with the different schemes carried out on the optimal grid described earlier. The difference between the Quick and LUS plus VANLH predictions was five per cent, so this test shows that the selected scheme is very important when pressure drop over an orifice is studied. Third order schemes, which are not implemented in Phoenics, will probably give a pressure drop that is again slightly different from those obtained here. This
Page 14 sensitivity to schemes is crucial when seeking to calculate the mass flow through an orifice meter, because the value of the pressure drop is being used to calculate the flow rate through the meter.
Turbulence model The success of numerical prediction methods depends to a great extent on the performance of the turbulence model used. In Figure 9, the axial velocity profiles resulting from the Phoenics simulations are plotted together with the measured velocity profiles at various distances downstream of the orifice plate. In Figure 10, the equivalent turbulent kinetic energies are compared with the measurements. It can be seen that the k-s model predicts the basic flow
characteristics observed in the experiments, but the details could not be adequately achieved.
Downstream of a sharp-edged orifice plate, the importance of the turbulence is very high compared with fully-developed flow, and this case represents a stringent test for the turbulence model. The turbulent kinetic energy was underpredicted 2.5D downstream of the plate, and the deceleration of the axial velocity was overpredicted with maximum deviations at the centreline of 40 per cent and 11 per cent for k and W, respectively. Further downstream, at 10D and 15D, where the flow has further recovered towards fully-developed, the turbulence structure is relatively unimportant and the predictions are satisfactory. These simulations and measurements are carried out at ReD=75000. The literature was scanned for tabulated experimental data on orifice measurements at other Reynolds numbers. The only experimental data which was found came from Wang27 . They were obtained in a 0.05m pipe at low Re,,, approximately 7000, on a one-mm plate with (3=0.5. To assess the
current turbulence model, and to study the performance at this low Reynolds number, their
experimental set-up was calculated with a 60 x 150 grid. The results from the predictions are similar to those obtained by Durst 8,9 , but not completely identical. The main differences in the numerical models are that Durst et al. used a collocated variable arrangement and a combination of central differencing and upward differencing schemes. Figure 11 compares the predictions of the important turbulent kinetic energy with Wang's data at four positions downstream of the orifice plate. z/h=16 and z/h=32 in the Figure 11 correspond to 2.5D and 5D for the one-hole plate (16.4 and 32.8 z/h respectively) in Figure 10. At these two locations, the prediction at the lowest Re compares much better with the experimental data. The reason
Page 15 could lie in the difference in plate thickness (one mm versus 11 mm), the P-ratio (0.5 versus
0.7) or the difference in Re (7 000 versus 75 000). Durst et al. obtained similar results for thick
and thin obstacles, so this is probably not the reason. On the other hand, Agarwal28 showed that characteristic flow parameters such as reattachment and separation points vary both with P
-ratio and especially with Reynolds number. It is therefore possible that the k-e model cannot
capture the variation of the complex flow when Re is changing.
The flow downstream of orifices recovers in essentially the same basic manner, and several interesting features can be noted from Fig. 11. Close to the wall (at 1.5D or z/h=6), the simulated k is too high compared to the measured values. It is well known that the standard k-e
turbulence model does not respond properly to flows with strong axial strains. Therefore, k is slightly overpredicted at 1.5D, but the trend in the k values are accurate. It is also possible that the inertia forces (e.g. pressure and centrifugal forces) dominate at the way out of the orifice before the turbulent forces increase and become dominant. At 2.5D (10 z/h), the calculated k is peaky around y/R = 0.5, i.e. at the radial position where the orifice hole is located, and too low at the centre line. The trend at this location is very similar to the high Re case at 2.5D (16 z/h) which here is located further downstream measured in height distances. At these locations, the turbulence model does not fully succeed in capturing the variation of k across the pipe. The dissipation rate of k has been overpredicted near the centre of the pipe. Further downstream, the turbulence level is decreased and the predicted values are again close to the measured. In view of the well-known deficiencies in the standard k-s model, several researchers have
tried to modify the model, especially the modelling of the s-equation. Chen and Kim29
proposed a modification which should improve the dynamic response of the e-equation. They
introduced an additional time scale, k/Pk, where Pk is the volumetric production rate of k. The idea was to increase s and thereby decrease k when the mean strain is strong, P/e > 1, and to
decrease e when the mean strain is weak (P/e < 1). This feature is known to offer advantages in separated flows and where the turbulence is not in local equilibrium. The Chen-Kim modification should thus improve predictions in the current model, where k is first
overpredicted just after the plate, and then underpredicted where P/e is less than one. Figure
12 and Figure 13 show the results when the flow through the one-hole plate is calculated with
Page 16 this model. As can be seen, the result is much poorer than with the standard model. This observation may reflect the fact that most turbulence models have been developed and verified for flows with very mild strain rates compared with the current example. But this model also shows that the turbulence terms in the equations of motion make a large contribution to the overall momentum balance. Proper modelling of the turbulent kinetic energy is important for correct prediction of the axial velocity. Excessively low k in orifice flow always gives rise to too high W, and vice versa. It is likely that the predictions would be improved if more advanced turbulence modelling, such as a full Reynolds stress model, was employed. But if orifice flow or flow conditioners are to be studied in a limited Reynolds number range, it must be possible to improve the standard
k-e model to obtain better results than those shown in Figures 9 and 10. The ideas behind the
Chen-Kim model are correct, but it seems that the model constants are not tuned for such high turbulence levels. Figure 13 reveals that the modification in the s-equation has a distinct effect on the orifice model, but that the dissipation is too high. To compensate for this unwanted
effect, the Chen-Kim model can be adjusted. The total source term per unit volume in the Chen-Kim model is:
Pk (8) P(Ce3 S + CEi)|Pi
where C83 is zero in the standard k-e model.
Here, CS3 =0.25 and Cei=1.15, so this parenthesis corresponds roughly to Cgl=1.44 in the
standard model when P/e is approximately one. From the current calculations, k is seen to be too low when the turbulence is high and where P/e is much lower than one (cf. Figure 6). This can be improved if Cg3 is made a function of
the P/e value close to the wall. An optimal relation is found to be:
Ce3 = 0.33^-0.08 (9)
Page 17 Results obtained with the modified Chen-Kim model are shown in Figures 14 and 15. It can be seen that the results compare much better with the measurements than the predictions with the standard k-s model in Figs. 9 and 10. No experimental data are available closer to the orifice,
so the modification is not tested out there. But it is often interesting to know what happens a few diameters downstream of a flow conditioner, for instance, and an empirical orifice model like this can then be valuable until more sophisticated solutions, like those mentioned by Leschziner and Rodi 30, are implemented in commercial CED codes. It should be emphasized
that the calculated Ap over the orifice is the same with the modified Chen-Kim and with the k-
s model.
6. CONCLUSIONS A study has been conducted with a commercial CFD programme to evaluate various numerical effects in calculating the complex flow through a geometrically simple orifice. Both the pressure drop and the flow variables downstream of the plate are simulated and compared with measured data. The predictions reveal that considerable expertise and care are needed before confident results can be predicted, especially for the pressure drop. Table 1 summarises some of the effects that influence the calculated pressure drop through the orifice. The main recommendation from this study is that the grid spacing hz must be approximately 0.00 ID just upstream of the plate to resolve the flow field here and to calculate the pressure loss correctly. The study also demonstrates how important it is to use higher-order differencing schemes. In addition, the non-equilibrium log-law is recommended for calculating both the pressure drop and k; but it is also shown that the wall function should be improved. The grid expansion seems to be less important than expected from other papers. This study appears to indicate that there is an optimal range of the aspect ratio of the grid cells upstream of the orifice, but this subject needs to be investigated further. The predicted velocities and turbulent kinetic energy at different locations downstream of the orifice are linked firstly to the turbulence model. The study shows a negative correlation between the predicted k and W downstream of the orifice: excessively low k gives too high W,
and vice versa. The k-e model can provide the trends in the flow field in an orifice, but more
advanced models are needed, in which the flow behaviour is significantly affected by the
Page 18 turbulence structure. Further downstream of the orifice, where the turbulence structure was relatively unimportant, the predictions of k and W were satisfactory. A modification of the
Chen-Kim k-e model is suggested to improve performance when used to simulate flow through orifices at a given Reynolds number. This model, which replaces a model-constant with a function of P/e, can probably be used to calculate the flow field downstream of flow conditioners with better results. REFERENCES
1. ISO 5167-1, Measurement of fluid flow by means of pressure differential devices, Orgfor Standardisation, Geneva, 1991
2. A Erdal, D Lindholm and D Thomassen, Development of a flow conditioner, North Sea Flow Measurement Workshop, October 1994.
3. A Erdal, L E Torbergsen, S Rimestad and P A Krogstad, Evaluation of a CFD model for simulation of simplified flow conditioners, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995.
4. D Thomassen, M Langsholt and R Sakariassen, Flow conditions in a gas metering station. North Sea Flow Measurement Workshop, October 1992.
5. C J Freitas, Perspective: Selected benchmarks from commercial CFD codes, Journal of Fluids Engineering, Vol 117, pp 208-218, June 1995.
6. The Phoenics beginner's manual, Cham TR/100, Cham Limited, Bakery House, 40 High Street, Wimbledon Village, London SW19 5AU, UK, 1991.
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8. F Durst, A B Wang and M Found, Similarity phenomena and computations of the flow through an axisymmetric ring-type obstacle attached to a pipe wall, Hydrocomp 89, Dubrovnik, p 484, 1989.
9. F Durst and A B Wang, Experimental and numerical investigation of the axisymmetric, turbulent pipe flow over a wall-mounted thin obstracle, Seventh Symposium on Turbulent Shear Flows, Stanford University, August 21-23, 1989.
10. R W Davis and G E Mattingly, Numerical modeling of turbulent flow through thin orifice plates, Symp on Flow in Open Channels and Closed Cond, Gaithersburg, February 23-25, 1977.
11. M Z Sheikholeslami, B R Patel and K Kothari, Numerical modeling of turbulent flow through orifice meters - a parametric study, 2nd International Conference on Flow Measurement, London, UK, 11-13 May 1988.
Page 20 12. J J Barry, M Z Sheikoleslami and B R Patel, Numerical simulation of flow through orifice meters, Gas Research Institute, GRI-92/0060.1, 1992.
13. M J Reader-Hams and W Keegans, Comparison of computation and LDV measurement of flow through orifice and perforated plates, and computation of the effect of rough pipework on orifice plates, Proc of the Int Symp on Fluid Flow Measurement, Washington, DC, 1986
14. M J Reader-Harris, Computation of flow through orifice plates, Numerical Methods in Laminar and Turbulent Flow, Volume 6, pp 1907 -1917, 1989.
15. M Langsholt and D Thomassen, Computer modeling of fluid flow through orifices, Int. Conf. on Flow Measurement in the Mid 80's, National Engineering Laboratory, 9-12 June 1986.
16. G L Morrison, D L Panak and R E DeOtte, Numerical study of the effect of upstream flow condition upon orifice flow meter performance, OMAE 1992.
17. C J Freitas, Advanced computational simulation of flow phenomena associated with orifice meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995.
18. G L Morrison, R E DeOtte, G H Nail and D L Panak, Mean velocity and turbulence fields inside a P-0.50 orifice flow meter, AIChE Spring National Meeting, 1992.
19. S V Patankar, Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, 1980.
20. L E Torbergsen and P A Krogstad, Measurements downstream of two perforated plates, MTF report 1995:112, Department of Applied Mechanics, Thermo and Fluid Dynamics, Norwegian Institute of Technology, N-7034 Trondheim, Norway, 1995. 21. L E Torbergsen and P A Krogstad, Flow through a 9-hole perforated plate mounted downstream of two 90-degree bends, MTF report 1995:117, Department of Applied Mechanics, Thermo and Fluid Dynamics, Norwegian Institute of Technology, N-7034 Trondheim, Norway, 1995.
22. I P Castro and J M Jones, Int. J. Num. Methods in Fluids, Vol. 7, pp 793-823, 1987.
Page 21 23. AO Demuren and R V Wilson, Estimating uncertainty in computations of two-dimensional separated flows, Journal of Fluids Engineering, Vol 116, pp 216-220, June 1994.
24. B E Launder and D B Spalding, The numerical computation of turbulent flow, Comp Meth in Appl Mech & Eng, Vol 3, pp 269-289, 1974.
25. MR Malin and D B Spalding, Turbulence Models in Phoenics, Cham report TR/320, Cham Limited, Bakery House, 40 High Street, Wimbledon Village, London SW19 5AU, UK, 1996.
26. Phoenics encyclopaedia; online user-manual, Cham Limited, Bakery House, 40 High Street, Wimbledon Village, London SW19 5AU, UK, 1996.
27. A B Wang, Stromungen in Rohren mit ringformigem Hindemis, Der Technischen Fakultat der Universitat Erlangen-Numberg, Dr. Ing. thesis, 1991.
28. N K Agarwal, Mean separation and reattachment in turbulent pipe flow due to an orifice plate, Journal of Fluids Engineering, Vol 116, pp 373-376, June 1994. 29. Y S Chen and S W Kim, Computation of turbulent flows using an extended k-e turbulence closure model, Nasa CR-179204, 1987.
30. M A Leschziner and W Rodi, Calculation of annular and twin perallel jets using various discretization schemes and turbulence-model variations, J. Fluids Eng., Vol 103, pp 352-360, 1981.
Mesh size h2 upstr orifice Diff scheme Wall function p loss in pipe dev.ffom meas. p 60 x 150 0.00 ID LUS+VANLH Non eq loglaw 448.9 Pa 0.2 % 30 x 150 0.00 ID LUS+VANLH Non eq log law 450.8 Pa 0.6 % 90 x 150 0.00 ID LUS+VANLH Non eq log law 438.1 Pa -2.2 % 90 x 300 0.00 ID LUS+VANLH Non eq log law 450.7 Pa 0.6 % 60 x 150 0.01D LUS+VANLH Non eq log law 335.1 Pa -25.2 % 60 x 150 0.001D LUS+VANLH Log law 436.3 Pa -2.8 % 60x150 0.00 ID HDS Non eq log law 354.6 Pa -20.8 % 60 x 150 0.001D Quick Non eq log law 418.8 Pa -6.5 % Table 1. An overview of some numerical effects on the calculation of pressure drop through an orifice.
Page 22 D—92mm
Figure 1. The simulated pipe and orifice. Plate thickness is 11mm. The figure is not drawn to scale.
5 0.2
Figure 2. Predicted turbulent kinetic energy at 0.5D and 2.5D downstream of orifice with two different grids.
Page 23 h+ at the upstream plate lip
Figure 3. Correlation between predicted pressure drop A p and axial cell length upstream of the plate (hz=hz-u * /v). The points represent /?|= 0.0ID, 0.005D, 0.003D, 0.002D, 0.001D, 0.0005D, 0,0003D and 0.0002D.
500.0 Measured 400.0
300.0 Predicted
200.0
100.0
-100.0
-200.0
-300.0
Figure 4. Comparison of calculated and measured 21 axial pressure.
Page 24 458.0 30 x 150 456.0 60 x 150 454.0
90 x 300 452.0
450.0
448.0 -
446.0
Grid expansion ratio upstream of orifice lip
Figure 5. Comparison of calculated pressure drop Ap and grid expansion ratio Gr upstream of orifice lip.
Figure 6. Predicted P/s along the pipe wall. Non-equilibrium wall function.
Page 25 1.2E-1 Log law
1.0E-1 Non eq. log I.
8.0E-2 Measured
6.0E-2 -
4.0E-2
2.0E-2
0.0E+0
Figure 7. Comparison between predicted and measured 20 k close to the wall.
LUS+VANLH
425,0
QUICK
h+ at the upstream plate lip
Figure 8. Correlation between pressure drop and axial cell length upstream of the plate calculated with different differencing schemes.
Page 26 Figure 9. Predicted and measured 20 velocity profiles at some different positions downstream of the orifice.
Figure 10. Predicted and measured 20 k at some different positions downstream of the orifice.
Page 27 32z/h
16z/h
10z/h
6z/h
Measured
Figure 11. Predicted velocity profiles downstream of a thin orifice at Re^ =7.000 compared with Wang's measurements 27 .
Figure 12. Measured 20 velocity profile at 2.5D downstream of the plate compared with predictions from the standard k-e model and the Chen-Kim model.
Page 28 Measured
Chen-Kim
Figure 13. Measured 20 k at 2.5D downstream of the plate compared with predictions from the standard k-8 model and the Chen-Kim model.
Figure 14. Predicted and measured 20 velocity profiles downstream of the orifice. Modified Chen-Kim is used.
Page 29 Figure 15. Predicted and measured 20 k downstream of the orifice. Modified Chen-Kim is used.
Page 30 Paper V
Flow development of two simplified and one K-Lab/Laws flow conditioners - experiments and calculations
Erdal, A, Torbergsen, L E, Andersson, HI and Krogstad, P A
Accepted for the 1997 ASME Fluids Engineering Division Summer Meeting, Symposium on Devices for Flow Measurement and Analysis Paper number FEDSM 97-3216 The 1997 ASME Fluids Engineering Division Summer Meeting FEDSM'97 June 22-26, 1997 Copyright © 1997 ASME
FEDSM97-3216
FLOW DEVELOPMENT DOWNSTREAM OF TWO SIMPLIFIED AND ONE K-LAB/LAWS FLOW CONDITIONERS - EXPERIMENTS AND CALCULATIONS
Asbjern Erdal Statoil/K-Lab P.O.Box 308 N-5501 Haugesund, Norway
L. E. Torbergsen, H.I.Andersson and P.A. Krogstad Department of Applied Mechanics, Thermo- and Fluid Dynamics Norwegian University of Science and Technology N-7034 Trondheim, Norway
ABSTRACT ReD Reynolds number calculated from D and bulk The standard k-s turbulence model was used to predict velocity the flow in a pipe downstream of 2 obstruction plates having U,V,W Tangential, radial and axial mean velocity 1 large or 9 small holes, and one 19-hole K-Lab/Laws flow wc Axial centre velocity conditioner. Both mean velocity, turbulent kinetic energy, k, W0 Average pipe velocity calculated from the 5:1 and the dissipation rate of turbulent kinetic energy, 8, were contraction calculated. From the predictions critical flow characteristics w„ Bulk velocity calculated from the measured axial velocity such as reattachment point, length of axial jets, turbulent Dimensionless wall distance regions and the distance required for the restablishment of y+ fully developed flow downstream of the different plates are a Kolmogorov constant reported. A comparison between measured and simulated P Orifice plate beta ratio, d/D results reveal that the numerical model is capable of s Dissipation rate of turbulent kinetic energy describing the trends in the flow. But just downstream of the plates, it is more difficult to calculate accurately the flow field of a simple one hole device than a more complex INTRODUCTION geometry like a 19-hole flow conditioner. It is assumed that Metering of natural gas with an orifice plate is a widely the flow structure is largely affected by the turbulence level, used practice within the natural gas industry. A significant which here is inversely proportional with the number of amount of research has been done in recent years to evaluate holes in the plates. The higher the turbulence level, the the adequacy of specifications for orifice meter installations. larger is the deviation in the predicted values. From 10D and To shorten the length of the meter run and improve further downstream, where the turbulence structure was accuracy, flow conditioners (FCs) have been recommended relatively unimportant, the simulations were satisfactory for upstream of the orifice meter. Substantial efforts have been all plates. devoted to developing FCs with good performance. A thorough understanding of the flow field through an FC is critical to any work on optimising the design of these NOMENCLATURE devices. The flow can be studied both experimentally and by D Pipe diameter a numerical method. This report will analyse the flow d Inside diameter of orifice structure downstream of perforated plate FCs with the aid of E, (k,) One-dimensional energy spectrum computational fluid dynamic (CFD) techniques. With this k Turbulent kinetic energy approach, it is possible to introduce wide-ranging k, Wave number parameters and evaluate their effects using computer R Pipe radius, D/2
1 Copyright © 1997 by ASME methods. Validation experiments for selected cases should been published. Nallasamy (1987) used PHOENICS and demonstrate the method's credibility. The results of this dual found that the k-e turbulence model predicts the location, numerical and experimental approach should speed up the shape and size of the recirculation zones with acceptable work of optimising FC design. A common FC like the accuracy. However, the redevelopment of the flow beyond K-Lab/Laws consists of a perforated plate with a central hole the point of reattachment was slow compared to the and two rings of holes, Figure 1. In essence, the associated measurements. Zhu and Shih (1994) have studied a similar flow problem consists of several turbulent jets confined in a problem and found that a recently proposed realisable pipe. The features of such a flow are common to many flows Reynolds stress algebraic equation model (which they call involving several streams of different velocities in industrial RRSAE) is superior to the k-s model for all the flows apparatuses, such as in combustion chambers. considered.
Figure 1. K-Lab/Laws FC Figure 2.1H plate
In an earlier paper, Erdal et al. (1995) used a k-e based CFD-model to predict the flow downstream of 2 obstruction DIAGONAL II DIAGONAL I plates. The results from this preliminary study were encouraging. In the present study a further step is taken. Finer grids, better numerical methods and additional measurements are used to study the flow downstream of two simplified plates having one large (1H) or nine small holes (9H) (cf. Figure 2 and Figure 3) and one K-Lab/Laws FC. There are two objectives in the present study. The first is to test the feasibility of the turbulence model for the flow through FCs. The second is to establish more information about the flow downstream of FCs. Previous computations of the flow through a FC have been performed by Pasdari and Gimson (1991). Their main area of interest was the velocity profile produced downstream of the FC. They obtained excellent agreement Figure 3. 9H plate between their predictions with the PHOENICS code and the experimental data. The grid they used was rather coarse; only 15 cells in the radial direction. Barry et al. (1992) tried EXPERIMENTAL SET UP to model a 30-degree sector of a tube bundle FC with a finer grid (51x51x24) using FLUENT. But the numerical model Test Facility constructed did not converge to a satisfactory solution. The measurements were carried out in a 92mm diameter Possible sources for this problem were the severe skewness (D) smooth pipe rig powered by an upstream mounted fan, of the grid and large jumps in the grid size. Durst et al. shown in Figure 4. Air enters and leaves the system at (1989) studied the flow through an axisymmetric ring-type atmospheric conditions. Vortices generated by the fan are obstacle in a pipe and found good agreement between eliminated in a honeycomb section followed by a 5 : 1 experiments and calculations using a k-E turbulence model. contraction upstream of the pipe. A 108D straight pipe Several authors have used numerical modelling to study the follows downstream of the contraction. The length of the flow through thin orifice plates (Davis and Mattingly, 1977), pipe is sufficient to assure that fully developed turbulent pipe and the general findings are that the k-e model can provide flow exists in the downstream part of the pipe. The 1H and a reasonably accurate description of the flow. Some papers 9H plates which have been investigated in this test rig, were on numerical studies of axisymmetric confined jets have mounted at the end of this pipe, and the pipe was extended
2 Copyright © 1997 by ASME further downstream. Measurements were performed at the The single-wire signal was filtered at 10kHz and sampled at end of the 108D straightpipe and at four stations, 2.5D, 5D, 20kHz. In order to estimate the dissipation rate from the 10D and 15D downstream of the two plates. Kolmogoroff law, a range in the energy spectrum which The K-Lab/Laws FC was tested in IFE's atmospheric air varies as k"5'3 must be identified. The width of this range rig (Langsholt, 1996). decreases when moving towards the wall. Estimation of the dissipation rate from the energy spectrum also relies on an implicit assumption of isotropy in the small scale turbulent motion. This assumption is known to break down when the 125Hi3raight pipe velocity gradient is large. Therefore, larger errors in the jneycomb 1H/9H plate. dissipation rate are expected near the wall. Distributions of turbulent kinetic energy were measured with a 5 ]xm x-wire probe with a wire spacing of 0.5mm and *5:1 contraction an angle between the wires of 90°. The probe was rotated in two directions to obtain all three normal stresses. The average pipe velocity W„ was calculated from the pressure difference across the 5:1 contraction with an accuracy better than 1%. The uncertainty of the measured mean velocity and normal stresses downstream of the two plates is expected to Figure 4. Test rig decrease with increasing distance from the plate. The deviation between W0 and W„, the average bulk velocity calculated from the measured axial velocity, are within 4.5% Obstruction plates everywhere. At 5D, 10D and 15D the measured axial The geometries of the 1H and 9H plates are shown in intensity for both plates varies between 5% and 25% when Figure 2 and Figure 3. Both plates are 11mm thick. The 1H y/R > 0.05, with the highest intensities obtained near the plate consists of a concentric hole with diameter d=64mm, wall. According to Tutu and Chevray (1975) an intensity of giving a contraction ratio P=d/D of 0.696. The 9H plate 30% corresponds to a maximum error of 3% in the mean consists of eight 20mm diameter holes equally distributed in axial velocity and 5.3% in axial fluctuations when using a the angular direction and one hole in the centre. The centres single hot wire, and 12.9% in radial and tangential turbulent of the eight holes were positioned at a radial distance of velocities obtained using x-wire probes. For most of the 30mm from the pipe axis. The holes were sharp edged both flow, the turbulence intensity is considerably lower than at the upstream and downstream sides. Both plates were 30%, so the accuracy is expected to be better than this. designed to have the same flow area, and therefore the same The experiments on the K-Lab/Laws FC were carried out effective |3. The K-Lab/Laws plate is a standard 19-hole FC at a Reynolds number of ReD = 2105. A two dimensional without chamfering, described in Laws (1990). LD V system was used for velocity measurements (Langsholt, 1996).
Data acquisition The experiments on the 1H and 9H plates were carried NUMERICAL MODEL out at a Reynolds number of Re,, = 75000. Hot-wire The PHOENICS computer code, version 2.1.3, running anemometry, operated in constant temperature mode (CTA), on an IBM RS6000 model R21 was used to simulate the was used for velocity measurements. Both single and crossed flow. The turbulence was modelled using the k-s model. hot-wire probes were manufactured from etched Platinum- Standard coefficients were used. PHOENICS applies the 10% Rhodium wire. Distributions of mean and turbulent so-called finite-volume method. Here the staggered-grid axial velocity, and dissipation rates, were measured with a arrangement is used, in which the location of the velocity 2.5 |xm single hot-wire probe, with an active wire length to nodes are placed on the cell feces and the scalar variables in diameter ratio (//d) w =200. The dissipation rate was obtained the cell centres. Central differencing is employed for the from the Kolmogoroff spectrum law for the one-dimensional diffusion terms. The convection terms for the energy spectrum. The Kolmogoroff constant was set to a = two-dimensional 1H plate are discretised using a linear upwind scheme for the axial velocity and van Leer 0.53 and the dissipation rate was obtained from the relation Harmonic scheme for the other variables, while the hybrid-differencing scheme is used for the three-dimensional cases. The Simplest algorithm is used to solve the finite-volume equations. The calculation procedure is organised in a slab-by-slab manner, in which all dependent variables are solved at the current slab before the solver routine moves to the next slab. (See PHOENICS
3 Copyright © 1997 by ASMS encyclopaedia (1996) for further details.) Appropriate PHOENICS was run until the sum of the absolute residual relaxation of the flow variables is necessary to obtain sources over the whole solution domain was less than 0.5 per convergence. Both inertial and linear relaxation are cent of the reference quantities, based on the total inflow of employed. The former is normally applied to the velocity the variables in question. In addition, checks were made to variables, whereas the latter is applied to the pressure, the verify that the dependent variables at some selected locations turbulent kinetic energy and its dissipation rate. In these fluctuated less than 0.1 per cent between successive iteration calculations, the linear relaxation factor used was cycles. Cylindrical-polar co-ordinate system is used for the approximately 0.4 and the inertial usually 0.1. two-dimensional 1H plate, and the three-dimensional The 1H FC was used to test out different grids because geometries applied the body fitted coordinate (BFC) option this is an axisymmetric and geometrically simple case which of PHOENICS. The non-equilibrium log-law was used to can be modelled in two dimensions. A sector of the pipe bridge the viscous sub-layers near the pipe wall and the plate from the axis to the wall, 71/8 for the 9H plate and 71/6 for walls. The first grid line near the wall was set to 0.75mm the K-Lab/Laws FC, was adopted to simulate the pipe with which corresponds to a y+ of about 30 for all models. the FCs. Cells were concentrated axially in the area close to the plate and radially near the wall. Three D of straight pipe was modelled upstream of the plate. Downstream of the FC, RESULTS AND DISCUSSION a straight pipe length of 50 D was modelled. At the pipe inlet, fully-developed conditions obtained from an earlier Mean velocity field simulation were used for W (axial velocity), k (turbulent The 1H plate is axisymmetric and the flow downstream kinetic energy) and E (dissipation rate of turbulent kinetic is therefore expected to be axisymmetric. The mean velocity energy), whereas U=0 and V=0 (tangential and radial was measured with a pitot-static tube along a number of velocity). All grids consisted of 60 radial and 250 axial cells. diagonals and variations in the angular direction at 5D In the tangential direction, 1, 10 and 20 cells were used for downstream are within 1% with respect to the centre line the 1H, the 9H and the K-Lab/Laws FC respectively. The velocity and within 0.5% at I5D. This was accepted as a axial distribution was 46 cells (slabs) upstream of the FC, 12 sufficient proof of axisymmetry, and further measurements cells within the FC and 192 cells on the downstream side. are therefore presented for one diagonal only. Figure 6a The 9H grid can be seen in Figure 5. A grid independency compares the mean velocity, scaled with Wm, from 2.5D to study was performed and this grid was found to be 15D. The velocity distribution at 2.5D contain high sufficiently fine to provide an accurate solution (Erdal, momentum in the core region with a measured centre 1996). A similar grid has also been used by several other velocity Wc =1.86W m , due to the acceleration of the flow scientists, e.g. Sheikholeslami et al. (1988) who found that through the contraction. The calculated axial velocity profile 60x80 cells gave a grid independent solution. To check if the at 2.5D follows the trend in the measurements, but the grid with skewed cells caused errors in the solution, the centre line velocity is overpredicted by 11%. At 5D the same kind of grid as in Figure 5 was used to calculate the peak in the centre line velocity is reduced to Wc=l.llWm , flow downstream of the 1H plate. No difference was found which is caused by a mean radial transport towards the wall. when the results were compared with computations on the Also at this location the calculated centre velocity is much regular grid for the 1H plate. higher than the measured. But at 10D the calculations only slightly overpredict the centre line velocity. At 15D the calculated and measured values coincide. The overall features of the simulated orifice flow field are visualised through the contourlines in Figure 7. Upstream of the 1H plate a fully developed turbulent pipe flow is found. As the flow approaches the orifice the axial flow exhibits some inward radial turning. The contour lines upstream of the plate show increasingly larger inward radial velocities. As expected, the flow is not able to make the 90° comer at the upstream base of the orifice plate, and a small recirculation zone results. In order to accommodate the additional radially inward mass flow, the centreline velocity increases and the centreline flow accelerates axially as it passes through the orifice. The upstream axial acceleration causes a jet to issue from the hole. A large recirculation zone is present downstream of the orifice. The jet spreads as the flow progresses further downstream resulting in a reattachment of the flow at the pipe wall and the eventual re-development Figure 5. The grid in lateral "plane" for the 9H plate into a fully developed turbulent pipe flow. Table 1
4 Copyright © 1997 by ASME r W/Wm 3
V J
W/Wm
W/Wm
W K-Lab/Laws
Figure 6. Predicted and measured velocity profiles downstream of 1H plate (a), 9H plate (b) and K-Lab/Laws FC (c). The measured values are shown by points. Each profile following 2.5D is successively offset by 1 unit 0.025
Figure 7. Contourlines of calculated axial velocity and k ID upstream to 5D downstream of 1H plate, 9H plate and K-Lab/Laws FC. The wall is at the top of the figures and the centre line at the bottom.
5 Copyright © 1997 by ASME Table 1. The characteristic locations for the plates, as lower compared to the 1H plate. Similar to the 1H plate the deduced from the computer simulations. The lengths are measured Wc at 15D is within 10% of the fully developed scaled with D. upstream profile, although the deviation near the wall is smaller. This is believed to be due to the much shorter recirculation zone downstream of this plate (ref. Table 1). 1H 9H K-Lab/Laws Also for this plate the calculated and measured results vary FC somewhat at 2.5D and 5D, but the discrepancy is less than Upstream separation -0.03 -0.03 -0.03 for the 1H plate. At 2.5D the deviation is within 6 %, and at Downstream reattachment 1.22 0.5 0.3 10D the calculated and measured values are again almost equal. The overall features of the simulated flow field Length of axial jets - 1.3 1.9 through the 9H plate are visible in Figure 7, and Length of "jet-like - 2.3 3.0 summarised in Table 1. The flowpattem here is similar to turbulent zone" that described for the 1H plate, but the strong jet Fully developed 48 39 24 downstream of the 1H plate is now divided into 9 weaker jets. The calculated position of the upstream separation point is similar for the 1H and 9H plate (-0.03D), but the downstream reattachment point is located at 0.5D compared summarises some salient characteristics of the flow. to 1.22D for the 1H plate. The length of the axial jets (where A closer examination of the axial velocity (Figure 7) the value of the circumferential axial velocity profiles was reveals that the axial velocity is actually slightly higher at constant within 1%) is 1.3D for the 9H plate. This value is the plate lip than on the pipe centre line. This is a direct not calculated for the 1H plate since this plate is result of the orifice acting as an obstacle to the flow and axisymmetric. forcing the fluid nearer the wall to move radially inward The results from the simulations of a 19-hole before issuing through the orifice itself. The radial location K-Lab/Laws FC are shown in Figure 6c and Figure 7c and of the flow maximum has previously been measured by Durst et al. (1989) and Morrison et al. (1992), but they summarised in Table 1. Here the k-e model gave much found it just downstream of the plate. It is of particular better agreement with the experiments. The maximum interest to notice the gradual spreading and slowing of the deviations between the measured and calculated results are jet downstream of the 1H plate. The measured orifice jet at only 3% (2.5D), 1.5% (5D), 1% (10D) and 2% (15D). Both 2.5D is reduced to a much flatter profile at 5D and 10D measurements and predictions showed some variation in the where Wc is lower than for the fully developed profile. circumferential direction at 2.5D. Table 1 show that the Unlike the free jet, which increases in mass flow because of downstream reattachment point is located at 0.3D which is entrainment of the surrounding fluid, the pipe orifice jet has closer to the plate compared to the 9H restriction. It can no net mass flow gain or loss. The orifice jet spreads out also be seen that the 19 jets here prevail further downstream because of an increase in cross-sectional area available to the than the 9 jets downstream of the 9H plate. This unexpected flow. Some turbulent exchange of mass between the jet and result is probably caused by lower turbulent mixing the recirculation zone will take place, but the net exchange downstream of this FC. From the calculations it was also is zero, since the mass is conserved inside the pipe. found that the velocity profile downstream of this plate The mean velocity distribution was also measured along requires 9.5D to be within 5% of fully developed pipe flow, different diagonals with a pitot-static tube to check the which is the requirement for measurements to fulfil the symmetry downstream of the 9H plate. The deviation from specifications of the international metering standard axisymmetry was obvious for this plate, with a maximum ISO-5167 (1991). The calculations also show that there is a deviation between measurement and simulation at 5D of 4% long distance from this location to where the flow is 100% compared to the centre line velocity and 1% at 15D. It was, fully developed, which is at 24D. This position for the 1H however, not possible to detect a systematic angular and 9H plate are at 48D and 39D, respectively. Probably this variation and correlate it to the geometry of the plate. long development length is needed because of the high turbulence level, which seems to be a key parameter for the Therefore the deviations must be considered as a measure of instabilities generated by the plate. The flow pattern behind understanding of the flow structure. the 9H plate consists of 9 interacting jets. Bradshaw (1965) described how fluid that emerges from a plane as a pattern of jets has a tendency to stick together in random groups, Turbulent field because they can only entrain fluid from each other. This is Distributions of calculated and measured turbulent probably the explanation for the asymmetric behaviour of kinetic energy are shown in Figure 8. In addition Figure 7 the flow in the narrow region behind the 9H plate. Figure 6b shows the contours of the calculated k. It is characteristic for shows how the predicted and measured mean velocity the 1H plate that it generates a much larger distortion than the 9H and the K-Lab/Laws plates. The 9H plate profile, scaled with Wm, develop from 2.5D to 15D. At 2.5D measurements at 2.5D are presented along two different the centreline velocity Wc = 1.58W m which is about 17%
6 Copyright © 1997 by ASME radii (defined in Figure 4) with an angular separation of the 1H plate, at 10D and 15D, where the flow has further 71/8. Radius I, which intersects the centre of three of the recovered towards fully developed, the turbulence structure holes, displays higher intensities compared to measurements is relatively unimportant and the predictions are satisfactory. along radius II, which intersects the centre hole only. It is also of particular interest here to note that it is more Maximum k at 2.5D for the 9H plate is only 30% compared difficult for the k-8 model to calculate accurately the flow to the 1H plate. Further downstream k evolves in a similar field of a simple one hole device than a more complex way as for the 1H plate. At 15D, k is approximately the geometry like a 9H plate or a 19-hole flow conditioner. This same for the two plates. The centre line value is still about is probably caused by the lower turbulence level downstream twice the value of the fully developed flow. As can be seen of the latter plates. Measurements of k are not available for from the figures, the calculated and measured results the K-Lab/Laws FC, but the predictions at 2.5D show that compare well for the 9H plate. At 5D, and in particular at the turbulence level is 1/3 compared with the 9H plate. This 2.5D downstream of the 1H plate, considerable differences results also in lower turbulent mixing of the jets which was between the predicted and measured values were found. noticed in Table 1. In addition it must be mentioned that the K-Lab/Laws measurements were carried out at a Reynolds number of Re0 = 200000 compared to 75000 for the 1H and z \ 9H plates. This may also slightly influence the flow k/(Wm)= development and the performance of the turbulence model. The cause of the rapid rise in k behind the 1H plate is the high mean velocity gradient just downstream of the plate, which causes high turbulence production. The eddies generated in the shear layer grow in diameter as they radially spread momentum across the shear layer via turbulent diffusion. This action transports high speed fluid from the orifice jet to the recirculation zone and simultaneously convects low speed fluid from the recirculation zone into the orifice jet. The same mechanism occurs for all the plates. But for the 9H and K-Lab/Laws plates the velocity gradients are much lower and are located between the holes and between the holes and the wall. It can be seen a strong turbulent region with contour-lines similar to a jet in Figure 7 (her called "jet-like turbulent zone ”) downstream of the 1H plate which persist approximately 4D downstream of the plate. A similar trend has been measured 2.50, II 6.0E-2 by Morrison et al. (1992). For the 9H plate, the "jet-like turbulent zone" disappear after about 2.3D and for
4.0E-2 K-Lab/Laws plate the individuals vanish at 3.0D. Also here the low turbulence level downstream of the K-Lab/Laws FC implies low turbulent mixing and can thus explain the long 2.0E-2 downstream extent of the "turbulent jets" Figure 9 compares the predicted and measured Q.OE+O dissipation rates of the turbulent kinetic energy, e. At 10D and 15D the curves for both 1H and 9H are almost identical for y/R >0.1. Also at 5D for the 9H plate, the calculated and Figure 8. Predicted and measured turbulent kinetic measured £ coincide. But 5D downstream of the 1H plate, energy downstream of 1H plate (a) and 9H plate (b). The the deviation is larger and the radial gradients of the measured values are shown by points calculated and measured values have opposite signs.
(Note that the scale on the y-axis is different in Figure 8a CONCLUSIONS and Figure 8b.) The correct order of magnitude of k is The flow field downstream of a 1H and a 9H obstruction obtained, but not the correct radial distribution. At the same plate, and a K-Lab/Laws FC has been computed and the locations the mean axial velocity is poorly predicted. The results are compared against measured data. It is reason for this is probably that in the immediate vicinity of demonstrated that the standard k-e turbulence model can the plate the forces arising from turbulent Reynolds stresses provide reasonably accurate descriptions of the flow through dominate and therefore the behaviour of the turbulence perforated plates with many holes. The numerical results model in this region is very critical. Further downstream of agree less well with the experimental data for a one hole
7 Copyright © 1997 by ASME REFERENCES Barry, J.J., Sheikholeslami, M.Z. and Patel, B.R., 1992, "Numerical simulation of flow through orifice meters", 6.0E-2 GR1-92/0060.1. Bradshaw, P., 1965, "The effect of wind-tumal screens 4.0E-2 on nominally twodimensional boundary layers", J.Fluid 2.0E-2 Mech., Vol. 22, pp. 679-687. Davis, R.W. and Mattingly, G.E., 1977, "Numerical 1.0 0,2 0,4 0,6 0,8 1,0 modeling of turbulent flow through thin orifice plates", Symp. on Flow in Open Channels and Closed Cond., pp. 491-522. Durst, F., Wang, A.B. and Found, M., 1989, "Similarity phenomene and computations of the flow through an axisymmetric ring-type obstacle attached to a pipe wall", Hydrocomp 89, Dubrovnik, pp. 484-499. Erdal, A., Torbergsen, L.E., Rimestad, S., and Krogstad, 2.0E-2 P.A., 1995, "Evaluation of a CFD-model for simulation of simplified flow conditioners", 3rd Int. Symp. Fluid Flow 1,0E-2 Measurement. Erdal, A, 1996, "Numerical aspects of flow computation through orifices", K-Lab report: K-Lab/R/I70. l,0 0,2 0,4 0,1 0,8 1,0 ISO 5167, 1991, "Measurement of fluid flow by means of orifice plates", Int. Org. for Standardisation, Geneva. Langsholt, M, 1996, "LDV-mMinger av hastighets- Figure 9. Predicted and measured dissipation rate of profiler og turbulensegenskaper oppstrams og nedstrems for turbulent kinetic energy at 5D, 10D and 15D downstream en Laws stromningsretter" , IFE-report: IFE/KR/F-96/076, in of 1H (a) and 9H (b) plate. The measured values are Norwegian. shown by points Laws, E.M., 1990, "Flow conditioning - A new development", FlowMeas. Instrum., Vol. 1, pp. 165-170. Morrison, G.L., DeOtte, R.E., Nail, G.H. and Panak, orifice plate. Downstream of this plate, the turbulence level D.L, 1992, "Mean velocity and turbulence fields inside a (3 = is much higher than for the other devices because the high 0.50 orifice flow meter", AIChE Spring National Meeting. mean velocity gradient causes high turbulence production. Nallasamy, M„ 1987, "Computation of confined The performance of the k-£ model seems to be correlated turbulent coaxial jet flows", J. Propulsion, Vol. 3, pp. with the turbulence level. Further downstream, where the 263-268. turbulence structure is less important, the downstream Pasdari, M. and Gimson, C.J., 1991, "Design of a new evolution towards fully developed pipe flow from the "Flow Conditioner" with the aid of Phoenics", PHOENICS strongly perturbed flow through the plates was well J. CFD, Vol. 4, pp. 128-154. reproduced. The agreement for k and S was also very good Phoenics encyclopaedia, 1996, Cham Limited, 40 High here. Street, Wimbledon Village, London SW195AU, UK. Sheikholeslami, M.Z., Patel, B.R and Kothari, K., 1988, Several critical flow characteristics are predicted in this "Numerical modeling of turbulent flow through orifice study. The calculated upstream recirculation zone is small for all plates, only O.03D. The downstream separation point, meters - a parametric study", 2nd International Conference on Flow Measurement, London. was 1.22D (1H), 0.5D (9H) and 0.3D (K-Lab/Laws). The Turn, N.K. and Chevray, R_, 1975, "Cross-wire trend here was as expected, shortest distance for the 19 hole anemomentry in high intensity turbulence", J.Fluid Mech., plate. More interesting was the length of the axial jets, which was longer for the K-Lab/Laws FC than for the 9H Vol. 71, pp. 785-800. plate. Similar, the "jet-like turbulent zones ” prevail further Zhu, J. and Shih, T.H., 1994,"A numerical study of downstream for the K-Lab/Laws FC than for the 9H plate. It confined turbulent jets", J.Fluids Eng., Vol. 116 pp. was also interesting to notice the very long distance before 702-706. the flow became fully developed downstream of the 1H and 9H plate. Again the reason seems to be the high turbulence level downstream of the plates with fewer holes, which causes high mixing and long pipe lengths are required before the flow settles down.
8 Copyright © 1997 by ASME Paper VI
A numerical investigation of different parameters that affect the performance of flow conditioners
Erdal, A
Submitted to Flow Measurement and Instrumentation A numerical investigation of different parameters that affect the performance of a flow conditioner
A Erdal Statoil/K-Lab PO Box 308 N-5501 Haugesund, Norway
Abstract Recent work with computational fluid dynamics (CFD) tools has shown that this technique can help to improve flow conditioner (FC) and metering technology. In this study, CFD models are used to examine trends and provide insights into the velocity and turbulence field downstream of various FCs installed in fully-developed flow. Several parameters which may affect turbulent mixing and flow conditioning downstream of a plate are studied. These include the overall porosity, the grading of porosity along the radius, the wetted perimeter and the number of holes in the plates. It seems that graded porosity is responsible for quickly obtaining a velocity profile close to fully developed. The blocking area, which is correlated with porosity, is responsible for the pressure drop and the production of turbulent kinetic energy. The latter controls the mixing level and modifies the velocity profile further downstream. High turbulence level downstream of the FC requires longer distance before the flow structure is 100 per cent fully developed. This mechanism probably explain why the combined FCs can be more efficient.
Introduction All flowmeters in common use are sensitive to the structure of the flow as it approaches the meter. A flow conditioner (FC) is a device installed upstream of flowmeters to remove swirl and correct a distorted flow profile. Numerous attempts have been made to "isolate" flowmeters from piping-induced disturbances by designing an FC that performs well, but much research is still going on to produce an optimal device. Several methods are applied in developing FCs. The simplest involves a kind of "trial and error" approach, in which the device is installed upstream of the meter and the secondary effects on the change in the discharge coefficient - Q - of an orifice plate, for example, is investigated for different pipe configurations. Efficient FCs can be found by using this method, but it contributes very little to understanding how different parameters affect the performance of a device. Another method utilises a theoretical design procedure to develop FCs. Erdal et al1 have described a simplified Ring model that was used to develop several different perforated plate FCs. These are designated the K-Lab/Mark2 to K-Lab/Mark5. One is shown in Figure 1. In this
Page 1 approach, the number of rings with holes is defined together with the porosity or pressure loss. The model helps to optimize the number of holes or hole area. While it is useful in designing FCs, the geometries had to be tuned with experiments. In developing the K-Lab/Laws FC, depicted in Figure 2, screen theory was used during the design process. A pressure loss coefficient, K=Ap/(0.5ptt2), for this FC was approximately 2.7. According to the theory, the result should be a downstream velocity independent of upstream velocity 2. But later results from Laws et al3 suggest that FC behaviour is not related to screen theory calculations, because it is difficult to find a correlation between the pressure loss coefficient and the performance of an FC. Kamik4 also reports that there are so many assumptions involved in this theory that geometries designed with its aid require empirical tuning. To help improve FCs, models based on computational fluid dynamics (CFD) have been tested out in recent years 5,6. It is shown that the flow through a complex geometry can be calculated relatively accurate by a k-e turbulence model. In this study, CFD models are applied to studying the effects of various design parameters. The technique yields a great deal of information. Even if the models used do not describe the turbulent flow with complete accuracy, they are very useful for obtaining insights into trends that are difficult or very time consuming to secure experimentally. An installation including an FC like those shown in Figures 1 and 2 may typically require some 12-15 pipe diameters (D) of straight pipe length after a disturbance before the flow structure is almost fully developed. Normally, an upstream settling length of 3-4 D is used between the source of a disturbance and the device to obtain a flatter velocity profile upstream of the FC. Just downstream of the plate, a turbulent mixing zone occurs within the first 1-2 D. This is where individual jets formed by the holes in the plate cause high localised peaks in both turbulence and velocity. Both asymmetry in the flow profiles and remaining swirl are largely destroyed in this mixing zone. The porosity of these FCs varies across the cross-section to permit greater flow through the centre of the pipe than in the wall region. Normally, a settling length of about 9-11 D downstream is required. To be able to develop more efficient FCs, better understanding of the mechanisms that control the operation of the devices are needed. This is because some doubts still remain concerning the factors that dictate the performance. A pressure drop always occurs over the FCs, but this characteristic is no longer regarded as the key parameter for performance. It is now thought7 that the most important aspect of an efficient flow conditioner is the grading of porosities across the cross-section. But are there other important factors? Can plates with different overall porosities ((hole area • 100%) /pipe area) give equal flow structure downstream of the plates? Which parameters influence turbulent mixing and flow development downstream of the plate? Do the number of holes have any effect if graded porosity is the same? What is the relationship between turbulent mixing and
Page 2 pressure loss? These questions will be studied numerically in this paper by comparing predictions downstream of different K-Lab/Laws FCs placed in fully-developed flow.
Numerical model The Phoenics 2.1.3 computer code, running on an IBM RS6000 model R21, was used to simulate the flow. Phoenics uses the finite-volume method, in which the original partial differential equations are converted into algebraic finite-volume equations with the aid of discretisation assumptions. Use is made of the conventional staggered-grid arrangement, in which the velocity nodes are placed on the cell faces and the scalar variables in the cell centres. Central differencing is employed for the diffusion terms. The convection terms are discretised using the hybrid-differencing scheme. The Simplest algorithm is used to solve the finite-volume equations. The calculation procedure is organised in a slab-by-slab manner, in which all dependent variables are solved at the current slab before the solver routine moves to the next slab. (See Phoenics encyclopaedia 8 for further details.) Appropriate relaxation of the flow variables is necessary to obtain convergence. Both inertial and linear relaxation are employed. The former is normally applied to the velocity variables, whereas the latter is applied to the pressure, the turbulent kinetic energy and its dissipation rate. A sector of the pipe from the axis to the wall is used to simulate the pipe with the FCs. Cells were concentrated axially in the area close to the plate and radically near the wall. Three D of straight pipe was modelled upstream of the plate. Downstream of the FC, a straight pipe length of 20 D was modelled. At the pipe inlet, fully-developed conditions obtained from an earlier simulation were used for W (axial velocity), k (turbulent kinetic energy) and e (dissipation rate of turbulent kinetic energy), whereas U=0 and V=0 (tangential and radial velocity). The Reynolds number of the pipe was 2105 and the internal pipe diameter was 139 mm in all the calculations. The grid consisted of (20 tangential x 60 radial x 150 axial) cells. The axial distribution was 46 cells (slabs) upstream of the FC, 12 cells within the FC and 92 cells on the downstream side. Typical grids to model a K-Lab/Laws FC are shown in Figure 3. A grid independency study was performed and this grid was found to be sufficiently fine to provide an accurate solution 9. Some two-dimensional calculations were also carried out. The two- and three-dimensional models were identical, except for the number of cells in the tangential direction (1 x60x150 grid used here). In these calculations, the linear relaxation factor used was approximately 0.4 and the inertial usually 0.1. Phoenics was ran until the sum of the absolute residual sources over the whole solution domain was less than 0.5 per cent of the reference quantities, based on the total inflow of the variables in question. In addition, checks were made to verify that the dependent variables at some selected locations fluctuated less than 0.1 per cent between successive iteration cycles. All geometries use the body fitted coordinate (BFC) option of Phoenics. The
Page 3 non-equilibrium log-law was used to bridge the viscous sub-layer near the pipe wall and the plate walls. The standard k-s turbulence model was used.
Results Comparison with measurements The turbulent mixing zone occurs within the first few pipe diameters downstream of the plate. Since most of the asymmetry and the remaining swirl are destroyed here, it is important that the calculated variables give a good picture of flow in this zone if FCs are to be improved. Figure 4 compares predicted axial velocities with measurements available at 2.5 D downstream of an FC installed in fully-developed flow. The device used was a 19-hole K-Lab/Laws FC with a hole arrangement of 1:6:12, a plate thickness of 0.123 D and a porosity of 0.53 per cent. An LDV system was used for the velocity measurements. The experimental set-up was described in Erdal et als. It can be seen that the simulated values compare very well with the measurements. The maximum deviation is always less than three per cent. Turbulent kinetic energy, k, is not measured, but experience indicates that k can be predicted fairly well if the axial velocity is correctly calculated 9. With more sophisticated turbulence models and higher order schemes, the results could probably have been even better. But these findings show that the predictions are good enough for studying trends in the flow structure downstream of flow conditioners.
Grading of porosity across the cross-section Many experiments show that FCs with low pressure loss coefficient, K, perform better than FCs with much higher K. These observations led Laws and Ouazzane 7 to suggest that the most important factor in an FC that performs well is grading of porosity. If this assumption is correct, it may be possible to design an FC in a different way but with the same porosity grading, and obtain similar flow conditioning downstream of it. Some ideas from the simplified theoretical model described by Erdal et al1 can be used to study this hypothesis. In this design procedure, the cross sectional area in the FC is first discretised into rings as shown in Figure 5a. The porosity of a ring, X,-, is defined as the ratio between the area of the holes in the ring to the total ring area. Thus, the porosity of ring no. / can be calculated as
m-(ie/4)-£Z?
where n is the number of holes in the ring, a. is the diameter of each hole in the ring, and Rw and R, the outer and inner radius of the ring. In the model, the porosity of each ring is calculated to obtain a predefined velocity profile and pressure loss in the designed FC. The graded porosity, Xi,X2and X3, is the same in Figures 5b and 5c. If grading of porosity alone is crucial for the performance of an FC, flow
Page 4 conditioning of the devices in Figures 5b and 5c should give approximately the same flow profiles some diameters downstream of the plates. To evaluate this theory, a CFD ring model of the 1:6:12 K-Lab/Laws FC with an overall porosity of 53 per cent was constructed (Figure 5b). Fully-developed flow was simulated upstream of the plate in order to use a two-dimensional grid. The calculated axial velocities were compared with predictions through a three-dimensional FC, as shown in Figure 5c. The results five D downstream of the plates are plotted in Figure 6. It can be seen that agreement is very poor. The difference in W at the centre line is nine per cent. The same kind of calculation was also carried out with a simpler plate that had only nine holes: eight in the middle and eight outer, ref. Figure 7. Again, predictions based on the two methods failed to give similar results. This means that graded porosity alone is not the only parameter involved in flow conditioning. Other effects, as the geometrical differences, have to be more important. One other characteristic parameter that differs slightly between the two models is friction in the holes, which is related to the wetted perimeter. Table 1 shows the length of the wetted perimeter in the FC, which is highest in the ring model. The difference is 19 per cent in the middle holes (ring two), and 11 per cent between the outer holes (ring three). This difference may change the shear stress so much that both turbulence level and mean velocities downstream of the two plates can be different.
Ring no. Wetted perimeter, Wetted perimeter, Diffinthe hole model (m) ring model (m) wetted perimeter 1 - Central hole 0.09 0.09 0% 2 - Middle holes 0.50 0.40 19% 3 - Outer holes 0.80 0.72 11%
Table 1. Differences in the wetted perimeter between the hole and ring model for a K-Lab/Laws FC with a 53 per cent 1:6:12 configuration.
This idea was tested out with a hole and a ring model of a plate designed with the same wetted perimeter and graded porosity. To simplify the problem, a nine-hole plate as shown in Figure 7 was used. The hole diameters and the radial distance to the outer holes (R%) were calculated to obtain the above requirements. The models are illustrated in Figure 8. Axial velocities calculated with the two models can be seen in Figure 9. The predicted values were now much closer, with a maximum deviation at the pipe centre of four per cent five D downstream of the plates. These numerical experiments indicate that the wetted perimeter can affect the flow conditioning downstream of a plate. But the results are not identical, probably because the geometrical differences in the modelled plates is an even more important factor.
Page 5 Different overall porosity Laws7 reports that various K-Lab/Laws FCs with porosities from 50 to 70 per cent have been tested. The pressure loss coefficients for these plates varied between 2.4 and 0.7. Only minor differences in the performance of the plates could be detected, and all the plates were able to generate time mean flow conditions close to fully developed. This phenomenon was studied further here with two-dimensional models. First, the graded porosity in the ring model described above was slightly modified until calculated axial velocities 2.5 D downstream of the plates were approximately fully developed. The new porosity for this plate was 54 per cent. From this plate, some new models were created with their overall porosity changed to 45, 60 and 70 per cent. Table 2 shows the design of these ring model plates as well as the predicted pressure drop, K, over the plates. Ap was found as the difference between the calculated pressure drop in the pipe with and without the plate. The values are similar to those measured by Laws7 .
Porosity r2(m) r3 (m) drl (m) dr2 (m) dr3 (m) K 45 0.03197 0.05699 0.01249 0.006614 0.005138 4.45 54 0.03197 0.05699 0.01365 0.008120 0.006000 1.74 60 0.03197 0.05699 0.01442 0.008820 0.006851 1.57 70 0.03197 0.05699 0.02558 0.01029 0.007990 0.77
Table 2. Ring models with different porosity that all give an approximately fully-developed axial velocity profile five D downstream of the plate.
Figure 9 shows the calculated axial velocity profiles and turbulent kinetic energy at 2.5, 5 and 15 D downstream of the plates. The jets downstream of the 70 per cent plate seem to spread out more slowly than the others and can still be seen 2.5 D downstream of the plate. At five D all the calculated velocity profiles fulfil the ISO-5167 10 requirements, which specify a velocity profile plus/minus five per cent from fully developed. These predictions confirm that it is possible to obtain velocity profiles close to fully developed downstream of FCs with different overall porosity if grading of porosity is appropriate. The turbulent kinetic energy, k, is quite different downstream of the plates, as shown in Figure 10. The higher the porosity, the lower the turbulence and the pressure drop. See Table 2. At 2.5 D, the predicted k value at the centreline is approximately 2.9 times higher downstream of a 45 per cent plate than a 70 per cent device, and the deviation at five D is even higher. The only difference between these modelled plates is the distance between the rings. When the blocked area is large, the recirculation zone becomes longer and so does the mean velocity gradient between the rings. The latter causes high turbulent production. More blockage
Page 6 also results in increased forces to redistribute the axial momentum through the plates, which again causes a large pressure drop. It is of particular interest here to note that the highturbulent kinetic energy found for plates with lower porosity has an effect on flow development further downstream of these plates, since the flow profiles do not stop changing until all variables, including k, are fully developed. Even if the axial velocities at five D are close to fully developed, the mean velocities continue to change, especially for the low porosity plates with the highest k values. Figure 10 shows the axial velocity and k 15 D downstream of the different plates. It is recognised that even here the turbulent kinetic energy has not fully decayed for any of the plates. The 70 per cent plate has a k profile and an axial velocity profile close to fully developed. It can also be seen here how the axial velocity in the centre of the pipe have been reduced at this location for the plates with the highest k level. This example shows the importance of studying the turbulent kinetic energy downstream of FCs. Even if a plate - such as the 45 per cent version - is able to yield an axial velocity profile that fulfils the ISO-5167 requirements only a few pipe diameters downstream of the FC, a long downstream distance may be required before the flow structure is fully developed. The 70 per cent plate requires a longer distance than the other plates before the jets from the perforations have coalesced because the downstream turbulence level and mixing are both lower. Thanks to the low k level, this plate therefore reaches fully-developed flow before the other plates with lower porosity. It is also interesting to note that this plate has the lowest pressure loss coefficient. But a 70 per cent plate may not show such a good performance if the FC is placed in a distorted velocity profile where good mixing is essential. Kamik4 reported that a 40 per cent plate FC was necessary to make the downstream profile independent of the upstream profile.
The number of holes in the K-Lab/Laws FC Figure 2 shows a K-Lab/Laws FC with one centre, six middle and 12 outer holes, known as a 1:6:12 hole configuration. It is possible to design the FC with the same graded porosity, but with a different hole configuration. Typically 1:7:13 2 is often used, and Kamik4 has reported excellent results with a 1:8:16 hole arrangement. The geometry and also the wetted perimeter will be different if the hole configuration is changed. To study how great those effects are, the flow through 1:7:14 and 1:8:16 plates is simulated for a plate with 53 per cent porosity. Table 3 summarises the differences in the hole radii and wetted perimeters for the three plate configurations. It can be seen that the wetted perimeter increases slightly by 7.4 and 13.4 per cent respectively when the hole configuration rises to 1:7:14 and 1:8:16. The 1:7:14 configuration was modelled with a 2nll sector of the pipe, and the 1:8:16 model with a 2%/8 sector. See Figure 3.
Page 7 Ring no Hole Hole radius Wetted % dev from config (m) perimeter (m) wetted perim K in 1:6:12
2 - Middle hole 1:6:12 0.013 0.50 - 1.723 3 - Outer hole 1:6:12 0.011 0.80 - 2 - Middle hole 1:7:14 0.012 0.54 7.4 1.708 3 - Outer hole 1:7:14 0.0099 0.87 7.4 2 - Middle hole 1:8:16 0.011 0.57 13.4 1.687 3 - Outer hole 1:8:16 0.0092 0.93 13.4
Table 3. Hole radius and wetted perimeter for a 53 per cent K-Lab/Laws FC with 1:6:12, 1:7:14 and 1:8:16 configurations.
To compare the evolution of the axial velocity and k, these values are plotted at 0.12, 1, 2.5 and 10 D downstream of the plates. The predictions are presented in Figures 11 and 12. The first of these figures is plotted between the outer holes, and the latter along a radii through the middle of an outer hole. (The first and the tenth tangential cells respectively in Figure 3.) In general, the results in Figures 10 and 11 are very similar. However, small but significant differences are also present. The wetted perimeter is largest for the 1:8:16 plate. If the friction in the holes determines the pressure loss, this plate should have the largest K. But the opposite is the case: K for the 1:8:16 plate is 1.687 compared to 1.723 for the 1:6:12 configuration. It is therefore assumed that the wetted perimeter does not represent the most important factor in determining pressure loss or flow structure downstream of the plates. Instead, the differences in geometry are proposed as a key parameter for performance. The two-dimensional results discussed above show that large solid areas in the plates create high turbulence. In this case, too, the turbulent production seems to be important for flow development. Here, the blocked area between the holes in the second and third ring are smaller for the FCs with more holes. At the same time, hole diameters are smaller and the solid area between the rings is larger for these FCs. The result is that turbulence production in the 1:6:12 plate can be higher in one region and lower in a neighbouring region by comparison with the 1:8:16 FC, and it is more difficult to guess which of the configurations will give the highest overall turbulence production. Some characteristics can be observed from these calculations. The central hole is the same in all three models, but the middle holes and outer holes are smaller in the 1:7:14 and the 1:8:16 configurations. This is reflected in Figures 11 and 12, which show that axial velocities in the central jet are identical 0.12 D downstream of the plates. The turbulent kinetic energy in the centre is also very similar downstream of the three configurations at this position. It can also be
Page 8 seen from Figure 11 that the recirculation zones between the holes are largest for the 1:6:12 plate, which has the largest blocked area in this case. On the other hand, the solid plate between the outer holes and the pipe wall is smallest in this FC, which again results in the lowest k here at 0.12 D. See Figure 12. The predictions at 1 D and 2.5 D show that turbulent kinetic energy is slightly higher for the 1:6:12 plate, as is the case for K. This results in higher turbulent mixing of the jets, as seen in Figure 11. At 2.5 D, the 1:7:14 plate shows the lowest axial velocity in the centre, and the turbulence level is similar to the 1:8:16 model. At 10 D, all velocity profiles are approximately fully developed, but turbulent kinetic energy still deviates from the desired profiles. Results from the different configurations vary slightly but significantly. As in the previous example, the centre velocities decrease in this case from a peaked profile to fully developed, and then becomes less than fully developed for a while before increasing again. Again this trend is strongest for the 1:6:12 profile with the highest turbulence level. The 1:7:14 plate has the lowest turbulence level and is the first to reach fully-developed flow. These examples also illustrate a phenomenon that has prompted some discussion in the literature: the existence of a "cross-over point". This term is used to define the optimum location for a FC that gives zero deviation in the orifice discharge coefficient (CJ: a shorter distance to the orifice yields a negative ACd while a longer distance yields a positive one. The axial velocity profiles in this case, which are higher than fully developed at the centreline up to a certain position and then "overdevelop" and become lower further downstream before finally reaching the fully-developed status, could explain why such a "cross-over point" occurs (see Figure 10 and 12). The three FCs all fulfil the ISO-5167 requirements at 10 D. But recent research shows that these requirements may be too crude for obtaining zero deviation in the orifice discharge coefficient (C^)11. The current ISO standard has been used as the performance criterion when developing FCs1. No requirements are specified for the turbulence profile. In future, these requirements may be strengthened from close to fully-developed velocity profile to fully-developedflow profile. The design of the FCs should then be modified slightly. This study reveal that the FC which quickly generates a velocity profile close to fully developed may not be the FC which first reaches a fully-developed turbulence profile.
Page 9 Conclusions Until now, it has been thought that graded porosity is the most important parameter for a high-performance FC. To evaluate this hypothesis, the velocity profile downstream of a two dimensional ring model plate and a normal FC with the same graded porosity was simulated. This experiment did not yield comparable results. One of the factors contributing to the difference could be the wetted perimeter, which is larger in a plate perforated with holes than in one with rings. But further studies have revealed that various geometrical parameters, such as diameter, number of holes and their arrangement, are even more important. These factors determine the blocked area in the plate, which seems in this case to be a key parameter responsible for production of turbulence and pressure drop. In this study, the turbulence level downstream of the plates and the pressure loss coefficient are correlated parameters. The level of turbulent kinetic energy is very important for flow conditioning, since it determines the degree of mixing and also affects the final development of the velocity profile. This study confirms that it is possible to obtain approximately fully-developed velocity profiles a few diameters downstream of the plates with different overall porosities if grading of porosity is appropriate. But it also reveals that the turbulence profile downstream of the plates can be quite different. Low porosity produces much turbulence. The present results also show that the flow structure downstream of plates with the same graded porosity but different hole configuration is very similar. All gave velocity profiles 10 D downstream of the plates that are within ISO-5167 requirements. But they also showed significant variation in the turbulence level, which in turn affects the distance before the flow is fully developed. These predictions were carried out for fully-developed flow, with no asymmetry or swirl in the velocity upstream of the plates. The flow profiles downstream of the FCs with highporosity first reached fully-developed flow. But it is assumed from earlier research4 that other upstream configurations that generate distorted flow profiles may require more mixing to condition the flow. These characteristics of plate flow conditioners can explain why combined FCs, like the K-Lab/Laws with tabs and vanes can be more efficient. If the flow is preconditioned by one device, the flow which enters the second FC need less mixing and the porosity of that plate can be higher, which again generates less turbulence and need fewer pipe diameters to become 100 per cent fully developed. Measurements performed by Laws, Ouazzane and Erdal 12 confirm that a 70 per cent porosity combined plate appear to be slightly better than a 50% and a 60% version.
Page 10 References
I . Erdal, A, Lindholm, D and Thomassen, D, Development of a flow conditioner, North Sea Flow Meas Workshop, (1994). 2. Laws E M, Flow Meas Instrum, Flow conditioning - a new development, 1 (1990), 165. 3. Laws, E M and Chesnoy, A, The design and development of flow conditioning devices, FED-Vol 159, Devices for Flow Measurement and Control, ASME (1993). 4. Kamik, U, A compact orifice meter/flow conditioner package, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995. 5. Erdal, A, Torbergsen, L E, Rimestad, S and Krogstad, P A, Evaluation of a CFD model for simulation of simplified flow conditioners, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995. 6. Erdal, A, Sivertsen, A S, Langsholt, M and Andersson, H A, Three-dimensional computation of turbulent flow through a flow conditioner, FLOMEKO '96, Beijing, China, October 1996. 7. Laws, E M and Ouazzane, A K, Flow conditioning for orifice plate flow meters, Fluid Flow Measurement 3rd International Symposium, San Antonio, March 1995. 8. Phoenics encyclopaedia: on-line user-manual, Cham Limited, Bakery House, 40 High Street, Wimbledon Village, London SW19 5AU, UK (1996). 9. Erdal, A, K-Lab report: K-Lab/R/170 (1996). 10. ISO 5167-1, Measurement of fluid flow by means of pressure differential devices, Org for Standardisation, Geneva (1991). 11. Reader-Harris, M J, Woodhead, E, Sattary, J A and McEven, D, Report on flow conditions downstream of headers for the header consortium, Report HCP001 (223/94); National Engineering Laboratory, East Kilbride, Glasgow, UK, September 1995. 12. Laws, E M, Ouazzane A K and Erdal, A, Shortening installation lengths using a low loss vaned flow conditioner, North Sea Flow Measurement Workshop, Peebles, 1994.
Page 11 Figure 1. The K-Lab/Mark5 FC.
Figure 2. The K-Lab/Laws FC.
Page 12 Figure 3. The grid in the radial and tangential direction used to model the flow through a K-Lab/Laws FC. The left grid represents an FC with 1:6:12 hole configuration and the right a 1:8:16 configuration.
W/Wm
Predictions
Measurements
Figure 4. Predicted and measured axial velocities 2.5D downstream of a K-Lab/Laws FC.
Page 13 Figure 5. Illustration of the basic principles in the simplified Ring model.
W/Wm
Ring model
Hole model
Figure 6. Predicted axial velocities 5D downstream of a K-Lab/Laws FC calculated with a hole and a Ring model, cf. Figure 5.
Page 14 Figure 7. The 9 hole plate.
Figure 8. The design of a 9 hole plate with the same graded porosity and wetted perimeter.
Page 15 Figure 9. Predicted and measured axial velocities 5D downstream of a 9 hole plate with the same graded porosity and wetted perimeter.
Page 16 W/Wm
1.2 F- Fully dev. k/Wm 0.05 r
k/Wm 0.02 0.018 0.016 0.014 0.012
0.008 0.006 0.004
Fully dev.
0,005
Figure 10. Axial velocity and turbulent kinetic energy, k, downstream of45, 54, 60 and 70 per cent FCs calculated two-dimensionally.
Page 18 W/Wm 0.12D 1:6:12
1:7:14
1:8:16
k/Wm 0.12D
1:6:12
1:7:14
1:8:16 0.15 -
Figure 11. Axial velocity and turbulent kinetic energy, k, downstream of 1:6:12, 1:7:14 and 1:8:16 configurations of a K-Lab/Laws FC. The calculations are plotted through a radius which goes between the outer holes.
Page 19 W/Wm 0.12D
1:6:12
1:7:14
1:8:16
WAA/m
1:6:12
1:7:14
1:8:16
W/Wm
1:6:12
1:7:14
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0,8 -/
Page 20 WA/Vm 10D
k/Wm 0.12D
1:6:12
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1:6:12 0,05 - 1:7:14 0,04 - 1:8:16
Page 21 k/Wm'
1:6:12
1:7:14
1:8:16
k/Wm'
Fully dev.
Figure 12. Axial velocity and k downstream of 1:6:12, a 1:7:14 and a 1:8:16 configurations of a K-Lab/Laws FC. The calculations are plotted through a radius which intersects an outer hole.
Page 22