The Shape of Turbomachines and the Ongoing Role of Specific Speed

1 2 3 Paul Gostelow *, Aldo Rona , Ali Mahallati

Abstract

A wide-ranging taxonomy of types is given. The requirements of steam turbines and aircraft engines established a traditional approach to aerodynamic design analyzing orthogonal planes. Computers facilitated this and led to a greater reliance on Computational Fluid Dynamics, offering exciting developments in three dimensional modeling. A balance should be sought between analytical, computational and experimental work. In work on an axial flow rig photographic investigations of cavitation over the ISROMAC 2016 rotor tip have given insights including the very abrupt collapse of cavitation bubbles. Although essential for supersonic regions blade sweep can also be used effectively at lower speeds International Symposium on and can provide significant performance improvements. Further integration of the design and Transport research communities should lead to an improved understanding and predictability. One Phenomena and such area is the unexpected appearance of streamwise vortices on blade suction surfaces. Dynamics of This provides a good base for understanding blade sweep and its effects. Rotating Machinery Keywords

Hawaii, Honolulu Shape — Taxonomy — Cavitation — Sweep

April 10-15, 2016 1,2 Department of Engineering, University of Leicester, Leicester, United Kingdom 3 Concepts NREC, White River Junction, Vermont, U.S.A. * Corresponding author: [email protected]

INTRODUCTION turbo – turbinis (L) __ I spin A taxonomy of turbomachines is presented in Fig. 2. Turbomachinery design is a broad field with distant This permits turbomachines of widely varying geometry historical credentials. Figure 1 shows a 2000 year old to be identified, classified and designed. Does it look impulse turbine from Hero of Alexandria. Today’s young cluttered? It is, because we are dealing with a very wide engineer, when confronted with an unusual range of machines. A question will be “are the turbomachine like this, should be able to classify it and techniques for enclosed flow machines applicable to understand how it operates. The student should be open flow machines?” The opportunities and context able to repair it and maybe re-design it to work better. for open flow ones will be addressed first. A question for An essential requirement is for a rotating component to turbines will be “are all the differences in configuration spin. This allows the transfer of energy between a justified, or does it mean that we have not converged on component and a fluid. This paper is a reminder that the optimal solution yet?” The process will be illustrated there are many obstacles to, and diverse ways of with reference to different configurations of achieving, the objective of spinning. compressors, turbines, fans and . A traditional approach to turbomachinery design was to use two different intersecting planes and to address such features as the specific speed for guidance on the overall shape. Computational fluid dynamics (CFD) approaches based on the Navier-Stokes equations and a suitable closure model, are routinely used in the design and analysis of many modern turbomachines. Although the shapes of turbomachines for aircraft gas turbines may seem to have converged, exciting advances are being made in design tools and techniques. There are still enormous challenges, with progress to be made for the economy and the Figure 1. 2000 Year Old Turbine: Hero of Alexandria. environment, in addressing these. The Shape of Turbomachines and the Ongoing Role of Specific Speed — 2

Figure 2. Taxonomy of Turbomachines.

1. APPROACHES AND REQUIREMENTS FOR 1.2 Current Challenges THE DESIGN OF TURBOMACHINES There are still significant challenges, with progress The classification of turbomachines is approached needed for the economy and the environment. For first; this is illustrated by some modern examples of example the recent growth in intermittent solar and wind open and closed turbomachines. The framework power generation increases the run duration for employed for the analysis and design of enclosed axial conventional power turbomachines under off-design flow turbomachines will be considered. Some research conditions at high loads. A wider look at some advances in understanding the roles of vorticity and of opportunities in newer kinds of turbomachine, for which blade sweep in axial turbomachines will be described. designs have not yet converged, is resulting in improvements. Universities and industry have 1.1 Design Methodologies collaborated in the last two decades to produce highly- loaded low pressure turbines. With the advent of digital computers came the traditional approach to the design of enclosed turbines These have been deployed in commercial aircraft and using intersecting two-dimensional planes. Within this major savings in engine weight and cost have been tradition the radial equilibrium equation was solved [1] achieved, but with a penalty in turbine efficiency. and the S1 and S2 planes were identified [2]. The use Research is now aimed at regaining lost efficiency of advanced RANS and LES computational procedures whilst retaining weight and cost advantages. is now routine [3] but some flow features are not always With this great variety of shapes and sizes how does well-predicted, even for enclosed and axial flow the designer set about selecting the most appropriate turbomachines. The difficulties presented by secondary for the application? From dimensional analysis, the flows and three-dimensional flows are discussed. concept of specific speed (Ns) is useful. This works for Relevant research advances in understanding the roles pumps and turbines, in air or water, and is very effective of vorticity and of blade sweep in axial turbomachines for cavitation avoidance. will be described. A recent discovery is that of organized fine-scale streamwise vortical structures on the suction surfaces of turbine blading. This has aerodynamic and heat transfer implications and raises questions of leading edge bluntness, surface curvature and blade sweep. The sweep question seems particularly relevant for most contemporary approaches to the design of free flow turbines. These issues are addressed but largely remain as questions to be resolved. For progress to be maintained it is essential for analytical, computational and experimental work to proceed in a balanced, Low Ns – High Ns – Axial Turbine collaborative and interactive manner. This would best be achieved by the relaxation of traditional disciplinary Figure 3. What Specific Speeds Do the Power barriers in universities and industry. and Head Indicate?

The Shape of Turbomachines and the Ongoing Role of Specific Speed — 3

2. DIMENSIONAL ANALYSIS The established procedures of dimensional analysis are particularly effective in optimizing the shape of a particular turbomachine. The outcome of applying dimensional analysis to turbomachines is the specific speed concept. Because of their differing flow and head characteristics the work-absorbing and work-producing machines result in differing relationships for pumps and turbines. The specific speed of a pump is given by Ns=N (Q1/2H-3/4) . (1)

For a work producing turbomachine, for instance a Figure 4(a) Cavitation Bubbles at Impeller Tip Section turbine, the relationship is Ns = N (P1/2H-5/4) . (2) The specific speed and the related flow and load coefficients provide a common analytical framework for characterizing networks of differently shaped fluid machines. Specific speed is seen in the developing presence of a wide range of new turbomachinery designs; the approach has been developing over many years in aircraft engines and steam turbines. It is also a driving force in pumps and water turbines. It should be a governing factor in how wind and water turbines are to develop. It is no longer necessary to guess their shape. A methodology exists for deducing the shape, Figure 4(b) Abrupt Collapse of Cavitation Bubbles from the earliest Savonius rotor to the modern axial flow wind or water fluid machines. This extreme variety Figure 4(a) shows visualization by fully developed enables differing configurations of fluid machines to be cavitation bubbles in the rotor tip vortex and Fig. 4(b) handled under a common conceptual framework. The shows the abrupt bubble collapse of that cavitation Pelton Wheel of Fig. 3 is a reminder of the traditional mode. The rig was also equipped with miniature distinction between impulse turbines and reaction pressure transducers over the rotor tip aσnd analysis of turbines [3]. Figure 3 also illustrates the enormous the ensuing pressure distributions is ongoing. difference in configuration between hydraulic turbines Earlier investigations had been made by Rains [6] and with low and high specific speeds. others. There remains considerable scope for further 2.1. Cavitation investigation and improvement of flows in axial, mixed flow and centrifugal pumps as well as various types of Dimensional analysis also gives a cavitation number turbine. Developments in cavitation observation on 2 σ = (pa – pv + H)/ (½ ρ v ). (3) pumps and turbines offer considerable scope for performance improvement. This, the Thoma coefficient, is a reliable indicator for cavitation avoidance and can be monitored by real-time 2.2. Blade Sweep signal processing in the operation of water pumps and Figure 5 illustrates how the freedom from the turbines to prevent un-intended cavitation. Acosta [4] traditional radial stacking is made possible by the has identified three modes of cavitation in introduction of canted blades. Fan and turbine turbomachines. These are blade surface cavitation, designers are now taking advantage of these exciting bubble cavitation and tip clearance cavitation. Axial flow aerodynamic design freedoms. These blades pumps are particularly susceptible to cavitation. encounter a wide range of subsonic, transonic and Investigations on the axial flow pump rig at the supersonic relative velocities or specific speeds. University of Technology Sydney have been performed The distinction between sweep and dihedral was by Wong [5]. He observed the different modes, given by Smith and Yeh [7] and is illustrated in Fig.6, clarifying their impact on pump performance. The rig from Lewis and Hill [8]. This shows the definition for an has a transparent casing and the photographic aircraft wing and practical applications for Francis and observations of cavitation were made in the rotor tip axial turbines. The wide variation in shape shows the region and on the blade surfaces. The Shape of Turbomachines and the Ongoing Role of Specific Speed — 4

Figure 5. Swept and Canted Blading. profound impact of sweep encountered by different types of turbine. It is usual to associate sweep with high speed flows such as those on modern aircraft wings. That is only Figure 7. Sweep and Lean Used to Impart one use of aerodynamic sweep and the turbomachinery Inward Body Forces. aerodynamicist will be familiar with a broader and richer family of applications. in loss by applying 13 dihedral. Similar improvements The General Electric CF6-6 engine was one of the were reported by Filippov and Wang [10] from very first of the high by-pass civil engines that are now curvilinear nozzle blading tested in cascade. universal. The CF6 had a supersonic fan in the outer Despite these excellent results relatively little is regions, thus providing an aerodynamic challenge. understood about the basic fluid mechanics of swept However there was an additional need to impart body and leaned flows. The latest engines do seem to be forces on the subsonic air flowing inward to the core of heading in the right direction in thermal efficiency gain the engine. The layout is shown in Fig. 7. This problem with some quite spectacular fan designs (Fig. 9) and was solved by imparting inward body forces, using both some improvements in turbine performance. sweep and lean. Improvements so far have been based largely on the Early steam turbine blading, reported by Deych and power of CFD, and in particular of RANS computations. Troyanovsky [9] (Fig. 8), gave a remarkable reduction However the performance of turbine components is still falling short and this seems to be the result of a failure to accurately predict the 3-D flows. These result from tip leakage and the inevitable vortices, of which there are many different types, some of which are strong. To resolve these dilemmas, and have better accuracy in flow calculation, more research is needed on the physics of the flows. The authors’ research has focused on the state of the blade surface boundary layers and in particular the presence of streamwise vorticity on the convex suction surface of blades (Fig. 10).

Figure 8. Improvement in Steam Turbine Blading Figure 6. Sweep and Dihedral of Lifting Surfaces [8]. Losses by Application of Dihedral [9].

The Shape of Turbomachines and the Ongoing Role of Specific Speed — 5

Figure 9. Advanced Low Pressure System Design (Courtesy Rolls-Royce).

Observation of the streamwise vortices was unexpected; the phenomenon seems to be very Figure 11. Normalized Spacings of Striations. resilient. These are the very fine striations with a small It has now been possible to undertake wider ranging lateral spacing of the order of a millimeter or two, as tests on a circular cylinder. The results from the circular first predicted by Kestin and Wood [11]. Since these cylinder have confirmed those on the turbine cascade. suction surface vortices were first observed other The cylinder was readily suited to variation of the sweep researchers have made similar observations on both angle. In addition to the zero sweep results [11] testing cascades and circular cylinders. had been conducted by Poll [12] with sweep angles The streamwise vortices distort the laminar boundary between 55 and 70. The present results agreed well layer; it is now clear that the laminar layer on a convex with those of Poll and were compatible with the cosine surface is far from two-dimensional. The vortices are rule. also very resilient, surviving separation regions, Figure 11 shows the measured transverse spacing of boundary layer transition and persevering in the these striations normalized by the cosine rule. They subsequent turbulent layer. The streamwise vortices o demonstrate a peak around 30 , indicating that values observed by the authors on turbine blades tend to of sweep above 30 should be approached with caution. survive all the way from the leading edge to the trailing edge. Experimental work was performed on the high speed cascade tunnel at the Canadian National CONCLUSIONS Research Council (NRC) in Ottawa. Subsequent tests A principal requirement of all turbomachines is to spin. were performed on circular cylinders in the 1.5 m tri- This was understood throughout history. A taxonomy of sonic tunnel at the NRC. turbomachinery types is given. This covers a very wide range which is potentially confusing for the new or specialist engineer. The requirements of steam turbines and aircraft engines established a traditional approach analyzing orthogonal planes. Digital computers facilitated this with developments such as the Wu S1 and S2 stream surfaces and the solution of the radial equilibrium equation. It is now more common to use three- dimensional CFD in the later stages of design. This offers exciting developments but also stern challenges. It should always be recognized that the flow through all turbomachines is three-dimensional and unsteady. A balance should be sought between analytical, computational and experimental work. As a result of Dimensional Analysis the concept of Specific Speed is important, especially for pumps and hydraulic turbines that vary widely in shape. In work on an axial flow pump

rig photographic investigations of cavitation over the Figure 10. Visualization of Suction Surface at Me=1.16 rotor tip have given insights including the very abrupt The Shape of Turbomachines and the Ongoing Role of Specific Speed — 6 collapse of cavitation bubbles. This suggests scope for [2] Chung Hua Wu., A General Theory of Three- improvement in the behavior of pumps by careful Dimensional Flow in Subsonic and Supersonic hydrodynamic design. Turbomachines of Axial, Radial and Mixed Flow The use of blade sweep and lean in fans and low Types, NACA TN 2604, 1952. pressure turbines is discussed. Although essential for [3] S. L. Dixon and C. A. Hall., Fluid Mechanics and supersonic regions sweep can also be used effectively Thermodynamics of Turbomachinery, Elsevier, at lower speeds and is capable of providing significant 2010. performance improvements. This is pioneering work for [4] A. Acosta., Cavitation and Fluid Machinery, Conf. CFD and further integration of the design and research Arr.by IMechE, Herriot-Watt University, Edinburgh, communities should lead to better understanding and 1974. predictability. One such area is the unexpected appearance of streamwise vortices on blade suction [5] K. K. Wong., Observations of Cavitation on an surfaces. Although the understanding of this is still Axial Flow Pump Impeller, Master of Engineering incomplete the phenomenon is surprisingly widespread, Thesis, University of Technology, Sydney, as are its implications. Streamwise vorticity provides a Australia, 1994. good base for understanding blade sweep and its [6] D. A. Rains., Tip Clearance Flows in Axial Flow effects, offering the prospect of design guidance for Compressors and Pumps, California Institute of swept blading. Technology, Hydrodynamics and Mechanical. Engineering Laboratories, Report No. 5, 1954. NOMENCLATURE [7] L. H. Smith Jr. and H. Yeh., Sweep and Dihedral Effects in Axial Flow Turbomachinery, Trans ASME H Total head per stage m J. Basic Eng., Pg. 401, 1963. Me Discharge Mach Number [8] R. I. Lewis and J. M. Hill., The Influence of Sweep N Rotational speed deg/s and Dihedral in Turbomachinery Blade Rows, J. Ns Specific Speed m/s Mech. Eng. Sci., 13, 4, 1971. P Power N.m [9] M. E. Deych and B. M. Troyanovskiy., Investigation and Calculation of Axial Turbine Stages, USAF Q Flow coefficient Trans. FTD-MT-65-409, 1965 Re Reynolds Number [10] G. A. Filippov and Zhong-Chi Wang., The Effect of S1,S2 Planes defined by Wu [2] m Flow Twisting on the Characteristics of Guide v Flow velocity m/s Rows, Teploenergetija, 5, 1964. Λ, λ Sweep angle deg [11] J. Kestin and R. T. Wood., On the Stability of Two- λ Lateral spacing between streaks mm Dimensional Stagnation Flow, Journal of Fluid Mechanics, 44, 461-479, 1970. λo Normalized lateral spacing ζ Loss coefficient [12] D. I. A. Poll., Some Observations of the Transition Process on the Windward Face of a Long Yawed σ Cavitation coefficient (Thoma number) Cylinder, Journal of Fluid Mechanics, 150, 329- Subscripts: 356, 1985. a Ambient pressure kPa v Vapor pressure kPa μ Dihedral deg

ACKNOWLEDGMENTS The authors wish to acknowledge the support of the National Research Council of Canada and the University of Leicester.

REFERENCES [1] L. H. Smith Jr., The Radial Equilibrium Equation of Turbomachinery, Trans ASME J. Eng. Power, 88,1, 1966.