DOCSLIB.ORG

The Rheology Dependent Region in Turbulent Pipe Flow of a Generalised

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Rheology Dependent Region in Turbulent Pipe Flow of a Generalised 20th Australasian Fluid Mechanics Conference Perth, Australia 5-8 December 2016 The rheology dependent region in turbulent pipe flow of a Generalised Newtonian fluid J. Singh, M. Rudman and H. M. Blackburn Department of Mechanical and Aerospace Engineering Monash University, Clayton, Victoria 3800, Australia Abstract the kinematic fluid viscosity as: Direct numerical simulations (DNS) of turbulent pipe flow of n 1 n = Kg˙ − (1) a Generalised Newtonian (GN) fluid at Ret = 323 are analysed to identify the region where GN rheology has the major influ- + + 1=2 ence. The flow domain is divided into two parts: in y < yup Here, g˙ = (2si jsi j) is the second invariant of the strain rate + + and y > yup, with the viscosity modelled using a power-law tensor s and K, n are the model parameters called the consis- + + + + rheology for y < yup and a uniform viscosity for y > yup. tency and flow index. Equation (1) represents shear-thinning + behaviour when n < 1 i.e. the fluid viscosity decreases with in- Values for yup of 35 and 70 are considered. Results show that creasing shear rate. For n > 1 shear-thickening behaviour is beyond y+ = 70, the GN rheology has no significant effect on observed and for n = 1:0 a Newtonian rheology is recovered. the mean flow or turbulence statistics, and that the effect of GN Shear-thinning behaviour is the most widely observed GN phe- rheology is confined to the near wall. To understand these re- nomena [3]. sults, the turbulent kinetic energy budget of the GN fluid and a Newtonian fluid at the same Ret = 323 are compared. The com- For turbulent pipe flow of Newtonian fluids, it is common to parison shows that the GN viscosity-dependent terms in the bal- split the flow domain into a viscous wall region (y+ < 50) and ance either vanish or do not show rheology dependence beyond an outer layer (y+ > 50) [4]. Here, y+ is the non-dimensional y+ = 70. The current results imply that in Reynolds averaged distance from the wall defined using pipe radius R, fluid viscos- + Navier–Stokes and Large eddy simulations the GN rheology’s ity n and friction velocity ut as y = utR=n. The fluid viscos- effects can be taken care of by modifying the wall functions. ity is known to be important only in the viscous wall region. However, in the case of a shear-thinning fluid where the fluid Introduction viscosity increases with decreasing shear rate (and hence with Since Reynolds’ experiments in 1883, studies of wall bounded distance from the wall), the extent of the viscous region is not turbulent flows have significantly contributed in our understand- well known. ing of turbulence. Pipe flow is a subset of wall bounded flows DNS is a powerful tool in understanding wall bounded turbu- which has the characteristic feature of an enclosed geometry, lence. In this study we use a powerful feature of DNS, (i.e. making it easiest to realise in experiments compared to (for ex- the ability model unreal physics), to identify the region where ample) channel flow [2]. Pipe flow also has direct industrial shear-thinning behaviour is important. This is done by running relevance as pipeline transport is the most common method of DNS in which shear-thinning rheology is used only in the near- transporting fluids in industrial processes. There is a vast lit- wall region and Newtonian rheology is used away from the wall. erature available on turbulent pipe flow of Newtonian fluids, The results will show if non-uniform viscosity and viscosity however, studies that aim to develop understanding in non- fluctuations away from the wall have any effect on the overall Newtonian pipe flow turbulence are far less common. turbulent pipe behaviour, and confirm where they must be con- Non-Newtonian fluids are very common in many industrial ap- sidered. This result will have implications for the development plications including mining, polymer processing, waste water of turbulence models suitable for GN fluids in higher Reynolds treatment etc., as well as in nature. They are different from numbers flows. Newtonian fluids as they do not show a constant viscosity (shear stress divided by shear rate). The viscosity of a non-Newtonian Computational Details fluid will often depend on shear rate, shear history and in some applications they show partial elastic behaviour. Generalised Numerical Method Newtonian (GN) fluids are a subclass of non-Newtonian fluids We use the Semtex code [1] which is a spectral element-Fourier for which the viscosity can be defined as a function of the in- DNS code [1] to solve the following governing equations. stantaneous shear rate alone. The viscosity of many fluids such as fine particle suspensions, sewage sludge, paint, some poly- ¶u=¶t + u ∇u = ∇p + ∇ t + f ; with ∇ u = 0: (2) meric solutions, some bodily fluids such as blood etc. can be · − · · well approximated by the GN assumption. These are the fluids Here, u is the velocity vector, p, t and f are pressure, shear of interest here. stress tensor and body force, each divided by the fluid density. We will refer to them as pressure, shear stress and body force The mathematical expression that relates shear stress (or alter- despite this scaling.. The shear stress t is defined using the GN natively viscosity) of a GN fluid to the local instantaneous shear assumption as t = 2n(g˙)S. rate is termed a rheology model. The parameters of this model are determined from the experimentally measured shear stress In the current simulations the pipe is periodic, 10D long and versus shear rate curve (i.e. a shear rheogram). In this study we discretised with 288 Fourier modes in the axial direction. The use a power-law rheology model which is a simple and com- pipe cross-section is covered by 297 spectral elements that use mon model that nevertheless expresses the rheology of some 10th order Gauss-Lobatto-Legendre polynomials. Implemen- materials quite well. The power-law rheology model defines tation of a pressure gradient in the Fourier direction is imple- mented via the body force term by setting fz = ¶p=¶z. The non-uniform viscosity of the non-Newtonian fluid is handled + by decomposing it into a spatially constant nre f and a spatially in the viscous sub-layer (y < 5). Unlike Newtonian fluids, varying component n nre f . The spatially constant component shear-thinning fluids do not follow the Newtonian law of wall − + + + + nre f is treated implicitly whereas n nre f is treated explicitly in i.e. Uz = y in the viscous sub-layer (¶Uz =¶y = 1) (see the − + + 6 time. For more details see [1] and [6]. inset plot in figure 1c). Instead, ¶Uz =¶y increases slightly in the viscous sub-layer as the fluid becomes more shear-thinning, Mesh Spacing and Simulation Parameters with the explanation being complex and tangential to the dis- cussion here. Deviation between the U+ profiles of the PL sim- We define the generalised and friction Reynolds numbers as: z ulations and the Newtonian log-law is due to shear-thinning as noted in [6, 7]. ReG = UbD=nw Ret = utR=nw (3) Here, D and R are pipe diameter and radius, Ub is the bulk ve- I locity (flow rate per unit area), ut is the friction velocity de- 4 1=2 II fined as u = (tw=r) where the mean wall shear stress is t III tw = (D=4)¶p=¶z. In equation (3) the mean wall viscosity nw (a) w is chosen as the viscosity scale as suggested in [7]. For a power- ν/ν 2 law fluid nw is easily written as: 1=n 1 1=n nw = (K =r)(tw) − (4) 0 1 10 100 + The non-dimensional distance from the wall is defined as y+ = 25 y I (R r)ut=nw, where r is the radial distance from the pipe centre. 20 − II In the current simulations (ReG = 11000, Ret = 323), the near (b) 15 III + + + z y r U wall mesh spacing is D = 1 and D( q) = 7. A uniform mesh 10 spacing of Dz+ = 25 is used in the axial direction. 5 We consider three cases with decreasing width of the non- 0 Newtonian rheology domain. First we run the simulation where 1 10 100 + 1.2 y+ PL rheology is assumed at all y (case I). The fluid vis- 1.1 + cosity is modelled via equation 1 with the model parameters rz S 1 K = 345:35 10 6 Pa s n and n = 0:6. In the other two PL 0.8 − − = 2 × + + 0.9 cases, we limit the non-Newtonian domain up to y = yup (see (c) + 1 5 table 1) and beyond that use a uniform viscosity which is set /∂y 0.4 I + + z equal to the mean viscosity observed in case I at the same yup. II An additional simulation is run with Newtonian rheology, i.e. ∂U III 0 a constant viscosity that is set equal to the mean wall viscosity 1 10 100 nw in the PL simulations. A fixed axial forcing fz = 0:01165 N y+ 1 m− is used in all simulations. Figure 1: Profiles of (a) the mean viscosity and (b) the mean Case y+ n =n up N w axial velocity plotted in wall units. Dotted lines in (b) show the I 323 – + + + + classical Newtonian law of wall Uz = y , Uz = 2:5lny +5:5. II 70 2.6 The effect of switching the rheology model is negligible on the III 35 2.0 mean axial velocity profiles. Newt. – 1 Table 1: Upper limit of the non-Newtonian domain in different The effect of restricting PL rheology to the near wall region is + + cases.
Load more

Recommended publications
  • Simulation of Turbulent Flows
    Simulation of Turbulent Flows • From the Navier-Stokes to the RANS equations • Turbulence modeling • k-ε model(s) • Near-wall turbulence modeling • Examples and guidelines ME469B/3/GI 1 Navier-Stokes equations The Navier-Stokes equations (for an incompressible fluid) in an adimensional form contain one parameter: the Reynolds number: Re = ρ Vref Lref / µ it measures the relative importance of convection and diffusion mechanisms What happens when we increase the Reynolds number? ME469B/3/GI 2 Reynolds Number Effect 350K < Re Turbulent Separation Chaotic 200 < Re < 350K Laminar Separation/Turbulent Wake Periodic 40 < Re < 200 Laminar Separated Periodic 5 < Re < 40 Laminar Separated Steady Re < 5 Laminar Attached Steady Re Experimental ME469B/3/GI Observations 3 Laminar vs. Turbulent Flow Laminar Flow Turbulent Flow The flow is dominated by the The flow is dominated by the object shape and dimension object shape and dimension (large scale) (large scale) and by the motion and evolution of small eddies (small scales) Easy to compute Challenging to compute ME469B/3/GI 4 Why turbulent flows are challenging? Unsteady aperiodic motion Fluid properties exhibit random spatial variations (3D) Strong dependence from initial conditions Contain a wide range of scales (eddies) The implication is that the turbulent simulation MUST be always three-dimensional, time accurate with extremely fine grids ME469B/3/GI 5 Direct Numerical Simulation The objective is to solve the time-dependent NS equations resolving ALL the scale (eddies) for a sufficient time
    [Show full text]
  • ESSENTIALS of METEOROLOGY (7Th Ed.) GLOSSARY
    ESSENTIALS OF METEOROLOGY (7th ed.) GLOSSARY Chapter 1 Aerosols Tiny suspended solid particles (dust, smoke, etc.) or liquid droplets that enter the atmosphere from either natural or human (anthropogenic) sources, such as the burning of fossil fuels. Sulfur-containing fossil fuels, such as coal, produce sulfate aerosols. Air density The ratio of the mass of a substance to the volume occupied by it. Air density is usually expressed as g/cm3 or kg/m3. Also See Density. Air pressure The pressure exerted by the mass of air above a given point, usually expressed in millibars (mb), inches of (atmospheric mercury (Hg) or in hectopascals (hPa). pressure) Atmosphere The envelope of gases that surround a planet and are held to it by the planet's gravitational attraction. The earth's atmosphere is mainly nitrogen and oxygen. Carbon dioxide (CO2) A colorless, odorless gas whose concentration is about 0.039 percent (390 ppm) in a volume of air near sea level. It is a selective absorber of infrared radiation and, consequently, it is important in the earth's atmospheric greenhouse effect. Solid CO2 is called dry ice. Climate The accumulation of daily and seasonal weather events over a long period of time. Front The transition zone between two distinct air masses. Hurricane A tropical cyclone having winds in excess of 64 knots (74 mi/hr). Ionosphere An electrified region of the upper atmosphere where fairly large concentrations of ions and free electrons exist. Lapse rate The rate at which an atmospheric variable (usually temperature) decreases with height. (See Environmental lapse rate.) Mesosphere The atmospheric layer between the stratosphere and the thermosphere.
    [Show full text]
  • Hydraulics Manual Glossary G - 3
    Glossary G - 1 GLOSSARY OF HIGHWAY-RELATED DRAINAGE TERMS (Reprinted from the 1999 edition of the American Association of State Highway and Transportation Officials Model Drainage Manual) G.1 Introduction This Glossary is divided into three parts: · Introduction, · Glossary, and · References. It is not intended that all the terms in this Glossary be rigorously accurate or complete. Realistically, this is impossible. Depending on the circumstance, a particular term may have several meanings; this can never change. The primary purpose of this Glossary is to define the terms found in the Highway Drainage Guidelines and Model Drainage Manual in a manner that makes them easier to interpret and understand. A lesser purpose is to provide a compendium of terms that will be useful for both the novice as well as the more experienced hydraulics engineer. This Glossary may also help those who are unfamiliar with highway drainage design to become more understanding and appreciative of this complex science as well as facilitate communication between the highway hydraulics engineer and others. Where readily available, the source of a definition has been referenced. For clarity or format purposes, cited definitions may have some additional verbiage contained in double brackets [ ]. Conversely, three “dots” (...) are used to indicate where some parts of a cited definition were eliminated. Also, as might be expected, different sources were found to use different hyphenation and terminology practices for the same words. Insignificant changes in this regard were made to some cited references and elsewhere to gain uniformity for the terms contained in this Glossary: as an example, “groundwater” vice “ground-water” or “ground water,” and “cross section area” vice “cross-sectional area.” Cited definitions were taken primarily from two sources: W.B.
    [Show full text]
  • Computational Turbulent Incompressible Flow
    This is page i Printer: Opaque this Computational Turbulent Incompressible Flow Applied Mathematics: Body & Soul Vol 4 Johan Hoffman and Claes Johnson 24th February 2006 ii This is page iii Printer: Opaque this Contents I Overview 4 1 Main Objective 5 2 Mysteries and Secrets 7 2.1 Mysteries . 7 2.2 Secrets . 8 3 Turbulent flow and History of Aviation 13 3.1 Leonardo da Vinci, Newton and d'Alembert . 13 3.2 Cayley and Lilienthal . 14 3.3 Kutta, Zhukovsky and the Wright Brothers . 14 4 The Navier{Stokes and Euler Equations 19 4.1 The Navier{Stokes Equations . 19 4.2 What is Viscosity? . 20 4.3 The Euler Equations . 22 4.4 Friction Boundary Condition . 22 4.5 Euler Equations as Einstein's Ideal Model . 22 4.6 Euler and NS as Dynamical Systems . 23 5 Triumph and Failure of Mathematics 25 5.1 Triumph: Celestial Mechanics . 25 iv Contents 5.2 Failure: Potential Flow . 26 6 Laminar and Turbulent Flow 27 6.1 Reynolds . 27 6.2 Applications and Reynolds Numbers . 29 7 Computational Turbulence 33 7.1 Are Turbulent Flows Computable? . 33 7.2 Typical Outputs: Drag and Lift . 35 7.3 Approximate Weak Solutions: G2 . 35 7.4 G2 Error Control and Stability . 36 7.5 What about Mathematics of NS and Euler? . 36 7.6 When is a Flow Turbulent? . 37 7.7 G2 vs Physics . 37 7.8 Computability and Predictability . 38 7.9 G2 in Dolfin in FEniCS . 39 8 A First Study of Stability 41 8.1 The linearized Euler Equations .
    [Show full text]
  • Introduction to Turbulent Flow
    CBE 6333, R. Levicky 1 Introduction to Turbulent Flow Turbulent Flow. In turbulent flow, the velocity components and other variables (e.g. pressure, density - if the fluid is compressible, temperature - if the temperature is not uniform) at a point fluctuate with time in an apparently random fashion. In general, turbulent flow is time-dependent, rotational, and three dimensional – thus, methods such as developed for potential flow in handout 13 do not work. For instance, measurement of the velocity component v1 at some stationary point in the flow may produce a plot as shown in Figure 1. In Figure 1, the velocity can be regarded as consisting of an average value v1 indicated by the dashed line, plus a random fluctuation v1' v1(t) = v1 (t) + v1'( t) (1) Figure 1 Similarly, other variables may also fluctuate, for example p(t) = p (t) + p'( t) (2) ρ(t) = ρ (t) + ρ'( t) (3) The overscore denotes average values and the prime denotes fluctuations. Turbulence will always occur for sufficiently high Re numbers, regardless of the geometry of flow under consideration. The origin of turbulence rests in small perturbations imposed on the flow; for instance, by wall roughness, by small variations in fluid density, by mechanical vibrations, etc. At low Re numbers such disturbances are damped out by the fluid viscosity and the flow remains laminar, but at high Re (when convective momentum transport dominates over viscous forces) they can grow and propagate, giving rise to the chaotic phenomena perceived as turbulence. Turbulent flows can be very difficult to analyze. In this handout, some of the simplest concepts pertinent to turbulent flows are introduced.
    [Show full text]
  • Wind Power Meteorology. Part I: Climate and Turbulence 3
    WIND ENERGY Wind Energ., 1, 2±22 (1998) Review Wind Power Meteorology. Article Part I: Climate and Turbulence Erik L. Petersen,* Niels G. Mortensen, Lars Landberg, Jùrgen Hùjstrup and Helmut P. Frank, Department of Wind Energy and Atmospheric Physics, Risù National Laboratory, Frederiks- borgvej 399, DK-4000 Roskilde, Denmark Key words: Wind power meteorology has evolved as an applied science ®rmly founded on boundary wind atlas; layer meteorology but with strong links to climatology and geography. It concerns itself resource with three main areas: siting of wind turbines, regional wind resource assessment and assessment; siting; short-term prediction of the wind resource. The history, status and perspectives of wind wind climatology; power meteorology are presented, with emphasis on physical considerations and on its wind power practical application. Following a global view of the wind resource, the elements of meterology; boundary layer meteorology which are most important for wind energy are reviewed: wind pro®les; wind pro®les and shear, turbulence and gust, and extreme winds. *c 1998 John Wiley & turbulence; extreme winds; Sons, Ltd. rotor wakes Preface The kind invitation by John Wiley & Sons to write an overview article on wind power meteorology prompted us to lay down the fundamental principles as well as attempting to reveal the state of the artÐ and also to disclose what we think are the most important issues to stake future research eorts on. Unfortunately, such an eort calls for a lengthy historical, philosophical, physical, mathematical and statistical elucidation, resulting in an exorbitant requirement for writing space. By kind permission of the publisher we are able to present our eort in full, but in two partsÐPart I: Climate and Turbulence and Part II: Siting and Models.
    [Show full text]
  • Transition to Turbulence in Non-Newtonian Fluids: an In-Vitro Study Using Pulsed Doppler Ultrasound for Biological Flows
    TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Dipankar Biswas December, 2014 TRANSITION TO TURBULENCE IN NON-NEWTONIAN FLUIDS: AN IN-VITRO STUDY USING PULSED DOPPLER ULTRASOUND FOR BIOLOGICAL FLOWS Dipankar Biswas Dissertation Approved: Accepted: __________________________ __________________________ Advisor Department Chair Dr. Francis Loth Dr. Sergio D. Felicelli __________________________ __________________________ Committee Member Dean of the College Dr. Yang H. Yun Dr. George K. Haritos __________________________ __________________________ Committee Member Vice Provost Dr. Abhilash Chandy Dr. Rex D. Ramsier __________________________ __________________________ Committee Member Date: Dr. Alex Povitsky __________________________ Committee Member Dr. Peter H. Niewiarowski ii ABSTRACT Blood is a complex fluid and has been established to behave as a shear thinning non-Newtonian fluid when exposed to low shear rates (<200s-1). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high shear rates. Shear thinning fluids have been shown to exhibit differences in transition to turbulence compared to that of Newtonian fluids. Incorrect assumption of the transition point in a simulation could result in erroneous prediction of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and standard blood analogs in a straight rigid pipe and an S-shaped pipe under a range of steady flow conditions. Reynolds number for blood was defined based on the viscosity at a shear rate of 400s-1.
    [Show full text]
  • Aircraft Wake Turbulence
    AERONAUTICAL AUSTRALIA INFORMATION AERONAUTICAL INFORMATION SERVICE CIRCULAR (AIC) AIRSERVICES AUSTRALIA GPO BOX 367, CANBERRA ACT 2601 Phone: 02 6268 4874 Email: [email protected] H30/17 Effective: 201710200300 UTC AIRCRAFT WAKE TURBULENCE 1. INTRODUCTION 1.1 This AIC provides basic information on wake vortex behaviour, alerts pilots to the hazards of aircraft wake turbulence, and recommends operational procedures to avoid or deal with wake turbulence encounters. 2. WHAT IS WAKE TURBULENCE? 2.1 All aircraft generate wake vortices, also known as wake turbulence. When an aircraft is flying, there is an increase in pressure below the wing and a decrease in pressure on the top of the aerofoil. Therefore, at the tip of the wing, there is a differential pressure that concentrates the roll up of the airflow aft of the wing tip. Limited smaller vortex swirls exist also for the same reason at the tips of the flaps. Behind the aircraft all these small vortices mix together and roll up into two main vortices turning in opposite directions, clockwise behind the left wing (seen from behind) and anti-clockwise behind the right one wing (see Figure 1). 3. CHARACTERISTICS OF WAKE VORTICES 3.1 Wake vortex generation begins when the nose wheel lifts off the runway on take-off and continues until the nose wheel touches down on landing. 3.2 Size: The active part of a vortex has a very small radius, not more than a few metres. However, there is a lot of energy due to the high rotation speed of the air. (AIC H30/17) Page 2 of 20 3.3 Intensity: The characteristics of the wake vortices generated by an aircraft in flight are determined initially by the aircraft’s gross weight, wingspan, aircraft configuration and attitude.
    [Show full text]
  • The Effect of Turbulence on the Aerodynamics of Low Reynolds Number Wings
    Engineering Letters, 18:3, EL_18_3_09 ______________________________________________________________________________________ The Effect of Turbulence on the Aerodynamics of Low Reynolds Number Wings S. Watkins, S. Ravi, and B. Loxton low Reynolds number range (less than 100,000, see Figure 1). Abstract—Tests on 3-D and nominally 2-D airfoils are In this range complex flow phenomena exist within the presented relevant to micro air vehicle (MAV) flight. Thin, boundary layer. A review paper by Pines et al [3] points to the pressure-tapped, flat airfoils were testing at a Reynolds number lack of knowledge of the fundamental flow physics in this of 75000 under a range of turbulence characteristics. régime, which is needed to accurately model the steady and Turbulence intensity was varied from 1.2 to 12.6% and the longitudinal integral length scale was varied from 0.17 to 1.21m. unsteady environments that MAVs encounter during flight. The overall trend when the intensity was increased was to In smooth flow, the performance of airfoils at Reynolds reduce the lift curve slope but increase the maximum lift numbers above 500,000 is well understood; however the coefficient. When the length scale was increased and the performance deteriorates rapidly at Reynolds numbers below intensity was held nominally constant, the lift curve slope 500,000 and is relatively poorly documented Mueller [4]. At increased and the maximum lift coefficient reduced. The these low Reynolds numbers extensive low energy laminar largest variation in lift with increasing intensity was found at between 5 and 10 degrees where a reduction in lift of up to 28% flow can be present resulting in subsequent early separation was found.
    [Show full text]
  • 16-1 Attachment 3 Glossary of Terminology for Hydraulics & Scour
    Memo to Designers 16-1A • December 2017 LRFD SupersedesSupersedes MemoMemo toto DesignersDesigners 1-231-23 DatedDated OctoberOctober 20032003 Attachment 3 Glossary Of Terminology For Hydraulics & Scour Definitions (refer to AASHTO LRFD-BDS-CA Section 2.2) Common terminology has been defined below for easy reference. Abutment Scour Abutment scour is essentially a form of scour at a short contraction. Accordingly, scour is closely influenced by flow distribution through the short contraction and by turbulence generated and dispersed in the form of eddies and vortices, by flow entering the short contraction. Aggradation General and progressive buildup (long term) of the longitudinal profile of a channel bed due to sediment deposition. Backwater The increase in water surface elevation relative to its elevation occurring under natural channel and floodplain conditions. It is induced by a bridge or other structure that obstructs or constricts the free flow of water that occurs in a channel. Bank Protection: Engineering works for the purpose of protecting streambanks from erosion. Base Flood Discharge associated with the 100-year flood recurrence interval. Base floodplain Floodplain associated with the flood with a 100-year occurrence interval. Bedrock The solid rock exposed at the surface of the earth or overlain by soils and unconsolidated material. Bridge Waterway The cross-sectional area of a bridge opening available for flow, as measured below a specified stage and normal to the principal direction of flow. Bulking Increasing the water discharge to account for high concentrations of sediment in the flow. Channel Profile A plot of the stream channel elevations relative to distance separating them along the length of the channel that generally can be assumed as a channel gradient.
    [Show full text]
  • Wake Turbulence Dangerous
    Wake Turbulence • • IS Dangerous ill\ll~illumnm g)ffi~~TI\J rnorn~g)TI Publication Department of Civil Aviation, Australia In our flying training days, perhaps especially for those of us who learnt to fly in Tiger Moths, one of the measures of a skilfully executed steep turn was ~ the ability to strike one's own "slip-stream ff at the ~ :i~\l(~t~, , completion of a full 360 degree turn. In light train­ "" ing aeroplanes the effect of this encounter was little more than a sudden jolt which, though it might momentarily throw the aeroplane about, could be easily corrected with the controls. Inconsequential though its effects were, the sharpness of this "slip­ stream ff and the suddenness with which it was met and passed, left no possible doubt of its identity-it was in fact quite unlike any other form of turbul­ ence which we had experienced at that stage of our flying careers. As our flying training progressed, we probably experienced slip-stream encounters in other phases of flight-at the completion of a loop while practising aerobatics, or at odd times while learning to fly in formation. Until comparatively recent years, these "slip­ stream ff effects were generally attributed to the wash Fig. 1: Diagram showing direction of rotation of wing tip of the aircraft's propeller. With the advent of large vortices generated behind an aircraft in flight. multi-engined aircraft with high wing loadings how­ ever, it was found that by far the larger proportion of an aircraft's wake is produced by vortex turbul­ ence, generated at the wing tips of the aircraft, as a side effect to the lift which the aircraft's wings are producing.
    [Show full text]
  • Viscous Flow in Ducts Reynolds Number Regimes
    Viscous Flow in Ducts We want to study the viscous flow in ducts with various velocities, fluids and duct shapes. The basic problem is this: Given the pipe geometry and its added components (e.g. fittings, valves, bends, and diffusers) plus the desired flow rate and fluid properties, what pressure drop is needed to drive the flow? Reynolds number regimes The most important parameter in fluid mechanics is the Reynolds number: where is the fluid density, U is the flow velocity, L is the characteristics length scale related to the flow geometry, and is the fluid viscosity. The Reynolds number can be interpreted as the ratio of momentum (or inertia) to viscous forces. A profound change in fluid behavior occurs at moderate Reynolds number. The flow ceases being smooth and steady (laminar) and becomes fluctuating (turbulent). The changeover is called transition. Transition depends on many effects such as wall roughness or the fluctuations in the inlet stream, but the primary parameter is the Reynolds number. Turbulence can be measured by sensitive instruments such as a hot‐wire anemometer or piezoelectric pressure transducer. Fig.1: The three regimes of viscous flow: a) laminar (low Re), b) transition at intermediate Re, and c) turbulent flow in high Re. The fluctuations, typically ranging from 1 to 20% of the average velocity, are not strictly periodic but are random and encompass a continuous range of frequencies. In a typical wind tunnel flow at high Re, the turbulent frequency ranges from 1 to 10,000 Hz. The higher Re turbulent flow is unsteady and irregular but, when averaged over time, is steady and predictable.
    [Show full text]