DOCSLIB.ORG

Characterization of a Turbulent Boundary Layer in Open Channel Flow Using Particle Image Velocimetry Mathew James Stanek Coastal Carolina University

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Characterization of a Turbulent Boundary Layer in Open Channel Flow Using Particle Image Velocimetry Mathew James Stanek Coastal Carolina University Coastal Carolina University CCU Digital Commons Electronic Theses and Dissertations College of Graduate Studies and Research 7-31-2018 Characterization of a Turbulent Boundary Layer in Open Channel Flow Using Particle Image Velocimetry Mathew James Stanek Coastal Carolina University Follow this and additional works at: https://digitalcommons.coastal.edu/etd Part of the Aerodynamics and Fluid Mechanics Commons Recommended Citation Stanek, Mathew James, "Characterization of a Turbulent Boundary Layer in Open Channel Flow Using Particle Image Velocimetry" (2018). Electronic Theses and Dissertations. 48. https://digitalcommons.coastal.edu/etd/48 This Thesis is brought to you for free and open access by the College of Graduate Studies and Research at CCU Digital Commons. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of CCU Digital Commons. For more information, please contact commons@coastal.edu. CHARACTERIZATION OF A TURBULENT BOUNDARY LAYER IN OPEN CHANNEL FLOW USING PARTICLE IMAGE VELOCIMETRY By Mathew James Stanek Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Coastal Marine and Wetland Studies in the Department of Coastal and Marine Systems Science Coastal Carolina University Summer 2018 Dr. Erin E. Hackett, Major Professor Dr. Roi Gurka, Major Professor Dr. Diane Fribance, Committee Member Dr. Richard Viso, CMSS Director Dr. Michael H. Roberts, Dean © Copyright 2018 Coastal Carolina University ii Acknowledgements I would like to thank my advisors Dr. Erin Hackett and Dr. Roi Gurka for their invaluable guidance, patience, and support throughout this project. Without their expertise and guidance this project would not have been possible. I also would like to thank my thesis advisory committee member, Dr. Diane Fribance for her valuable input and knowledge. I am grateful for Coastal Carolina University’s financial support of the flume in the Environmental Fluids Laboratory and for my graduate assistantship. I would like to thank Mr. Kevin Hobbs and Big South Metals for fabricating the recirculating flume facility, as well as his assistance and guidance with modifications throughout the initial stages of this research. I am appreciative of the support and assistance of my peers, namely Doug Pastore, Ian Matsko, A.J. Kammerer, and Krishnamoorthy Krishnan, as well as my other peers in the Environmental Fluids Laboratory. Finally, I am thankful for my parents and brothers for their unwavering support and encouragement. iii Abstract Turbulent boundary layers are influential in numerous applications (e.g. naval architecture, ocean engineering, sediment transport, etc.), yet considerable knowledge gaps still exist. Boundary layers are regions where transfer of mass, momentum, energy, and heat occur within the interface between a fluid and a solid, or between two fluids. Utilization of optical flow measurement techniques to measure the velocity field with high spatial resolution enables non-intrusive investigation of the complex fluid dynamics of boundary layers. In this study two-dimensional Particle Image Velocimetry was employed to investigate, primarily, the overlap layer of a turbulent boundary layer developed in the recirculating flume facility located in the Environmental Fluids Laboratory at Coastal Carolina University. Three locations in the streamwise direction and two locations in the spanwise direction were investigated covering a range of Reynolds numbers, = 32,432 - 65,586. The overarching goal of this research was to i) investigate the flow characteristics of turbulent boundary layers in open channel flow and ii) provide benchmark results for future studies conducted in this facility. We calculated from the two measured velocity components (streamwise and vertical) over two spatial dimensions (streamwise and vertical) various mean flow and turbulent quantities. Results for the facility indicated: i) a distinct overlap layer existed between ~100 < y+< ~400, ii) a shape-factor characteristic of a zero-pressure gradient boundary layer, iii) turbulent intensity is relatively constant over the range of (4-10%), iv) peak of TKE production occurred at the lower limit of the overlap layer and iv) free-surface effects influenced flow up to 20% of the water depth below the surface. Based on results and findings in this study, users should conduct experiments along the channel middle to avoid iv the influence of sidewalls, between 40-80% of the water height to perform measurements in the region of lowest turbulence intensity, and between 0-40% of the water height to perform turbulent boundary layer measurements. v Table of Contents 1 Introduction ................................................................................................................................. 1 2 Boundary Layers ........................................................................................................................ 6 2.1 Turbulent Boundary Layer Overview .............................................................................. 6 2.2 Inner Layer ........................................................................................................................... 8 2.3 Overlap layer: “Law of the Wall” ..................................................................................... 9 2.4 Outer Layer: “Velocity Defect” ...................................................................................... 10 3 Experiments .............................................................................................................................. 15 3.1 Experimental Facility ....................................................................................................... 15 3.2 PIV Setup ........................................................................................................................... 16 3.3 Experiments ....................................................................................................................... 23 3.4 Error Estimation ................................................................................................................ 23 4 Results and Discussion ............................................................................................................ 33 4.1 Mean Flow Characteristics .............................................................................................. 33 4.1.1 Normalized Velocity Profiles .................................................................................. 33 4.1.2 Boundary Layer Characteristics .............................................................................. 37 4.1.3 Mean Spanwise Vorticity ......................................................................................... 40 4.2 Turbulence Characteristics .............................................................................................. 42 4.2.1 Turbulence Intensity ................................................................................................. 42 4.2.2 Reynolds Stresses ...................................................................................................... 43 vi 4.2.3 Turbulent Kinetic Energy ......................................................................................... 43 4.3 Energy Conservation ........................................................................................................ 44 4.3.1 Production .................................................................................................................. 44 4.3.2 Dissipation .................................................................................................................. 45 4.4 Energy Distribution .......................................................................................................... 46 5 Summary and Conclusions ..................................................................................................... 67 6 References ................................................................................................................................. 71 vii List of Figures Figure 1: Boundary layer transitioning from laminar to turbulent. The uniform free-stream velocity ( ) flows from left to right (reproduced here from Khatri et al., 2012). ............. 5 0 Figure 2: Boundary layer showing the concept of the displacement thickness (reproduced here from Schlichting, 1962). Location A shows the velocity profile and B shows the hypothetical displaced velocity profile. ............................................................................ 12 Figure 3: Boundary layer showing the concept of momentum thickness. The area in which the boundary layer is displaced to compensate for the reduction in momentum of the fluid as a consequence of the boundary is shown in blue.......................................................... 13 Figure 4: Sketch of the various wall regions and layers within a boundary layer in a turbulent channel flow, whose locations are defined in terms of y+ (normalized wall units; reproduced here from Pope, 2000).................................................................................... 14 Figure 5: Isometric view of experimental facility (provided courtesy of Jerry Quick). .. 26 Figure 6: Optics configuration for generating a light sheet. The gray box denotes the flume; hence the optics are under the glass section of the flume. The configuration is situated on a rigid structure lifting the configuration 30 cm off the ground. Furthermore,
Load more

Recommended publications
  • A Numerical Comparison of Symmetric and Asymmetric Supersonic Wind Tunnels
    A Numerical Comparison of Symmetric and Asymmetric Supersonic Wind Tunnels by Kylen D. Clark B.S., University of Toledo, 2013 A thesis submitted to the Faculty of Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science Department of Aerospace Engineering and Engineering Mechanics of the College of Engineering and Applied Science Committee Chair: Paul D. Orkwis Date: October 21, 2015 Abstract Supersonic wind tunnels are a vital aspect to the aerospace industry. Both the design and testing processes of different aerospace components often include and depend upon utilization of supersonic test facilities. Engine inlets, wing shapes, and body aerodynamics, to name a few, are aspects of aircraft that are frequently subjected to supersonic conditions in use, and thus often require supersonic wind tunnel testing. There is a need for reliable and repeatable supersonic test facilities in order to help create these vital components. The option of building and using asymmetric supersonic converging-diverging nozzles may be appealing due in part to lower construction costs. There is a need, however, to investigate the differences, if any, in the flow characteristics and performance of asymmetric type supersonic wind tunnels in comparison to symmetric due to the fact that asymmetric configurations of CD nozzle are not as common. A computational fluid dynamics (CFD) study has been conducted on an existing University of Michigan (UM) asymmetric supersonic wind tunnel geometry in order to study the effects of asymmetry on supersonic wind tunnel performance. Simulations were made on both the existing asymmetrical tunnel geometry and two axisymmetric reflections (of differing aspect ratio) of that original tunnel geometry.
    [Show full text]
  • Brief History of the Early Development of Theoretical and Experimental Fluid Dynamics
    Brief History of the Early Development of Theoretical and Experimental Fluid Dynamics John D. Anderson Jr. Aeronautics Division, National Air and Space Museum, Smithsonian Institution, Washington, DC, USA 1 INTRODUCTION 1 Introduction 1 2 Early Greek Science: Aristotle and Archimedes 2 As you read these words, there are millions of modern engi- neering devices in operation that depend in part, or in total, 3 DA Vinci’s Fluid Dynamics 2 on the understanding of fluid dynamics – airplanes in flight, 4 The Velocity-Squared Law 3 ships at sea, automobiles on the road, mechanical biomedi- 5 Newton and the Sine-Squared Law 5 cal devices, and so on. In the modern world, we sometimes take these devices for granted. However, it is important to 6 Daniel Bernoulli and the Pressure-Velocity pause for a moment and realize that each of these machines Concept 7 is a miracle in modern engineering fluid dynamics wherein 7 Henri Pitot and the Invention of the Pitot Tube 9 many diverse fundamental laws of nature are harnessed and 8 The High Noon of Eighteenth Century Fluid combined in a useful fashion so as to produce a safe, efficient, Dynamics – Leonhard Euler and the Governing and effective machine. Indeed, the sight of an airplane flying Equations of Inviscid Fluid Motion 10 overhead typifies the laws of aerodynamics in action, and it 9 Inclusion of Friction in Theoretical Fluid is easy to forget that just two centuries ago, these laws were Dynamics: the Works of Navier and Stokes 11 so mysterious, unknown or misunderstood as to preclude a flying machine from even lifting off the ground; let alone 10 Osborne Reynolds: Understanding Turbulent successfully flying through the air.
    [Show full text]
  • Experimental Study on Turbulent Boundary-Layer Flows with Wall
    Experimental study on turbulent boundary-layer flows with wall transpiration by Marco Ferro October 2017 Technical Reports Royal Institute of Technology Department of Mechanics SE-100 44 Stockholm, Sweden Akademisk avhandling som med tillst˚andav Kungliga Tekniska H¨ogskolan i Stockholm framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie doktorsexamen fredag den 24 November 2017 kl 10:15 i Kollegiesalen, Kungliga Tekniska H¨ogskolan, Brinellv¨agen 8, Stockholm. TRITA-MEK 2017:13 ISSN 0348-467X ISRN KTH/MEK/TR-17/13-SE ISBN 978-91-7729-556-3 c Marco Ferro 2017 Universitetsservice US{AB, Stockholm 2017 Experimental study on turbulent boundary-layer flows with wall transpiration Marco Ferro Linn´eFLOW Centre, KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden Abstract Wall transpiration, in the form of wall-normal suction or blowing through a permeable wall, is a relatively simple and effective technique to control the be- haviour of a boundary layer. For its potential applications for laminar-turbulent transition and separation delay (suction) or for turbulent drag reduction and thermal protection (blowing), wall transpiration has over the past decades been the topic of a significant amount of studies. However, as far as the turbulent regime is concerned, fundamental understanding of the phenomena occurring in the boundary layer in presence of wall transpiration is limited and consid- erable disagreements persist even on the description of basic quantities, such as the mean streamwise velocity, for the rather simplified case of flat-plate boundary-layer flows without pressure gradients. In order to provide new experimental data on suction and blowing boundary layers, an experimental apparatus was designed and brought into operation.
    [Show full text]
  • In Classical Fluid Dynamics, a Boundary Layer Is the Layer I
    Atm S 547 Boundary Layer Meteorology Bretherton Lecture 1 Scope of Boundary Layer (BL) Meteorology (Garratt, Ch. 1) In classical fluid dynamics, a boundary layer is the layer in a nearly inviscid fluid next to a surface in which frictional drag associated with that surface is significant (term introduced by Prandtl, 1905). Such boundary layers can be laminar or turbulent, and are often only mm thick. In atmospheric science, a similar definition is useful. The atmospheric boundary layer (ABL, sometimes called P[lanetary] BL) is the layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. The complexity of this definition is due to several complications compared to classical aerodynamics. i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. BL is assumed to encompass surface-driven dry convection. Most workers (but not all) include shallow cumulus in BL, but deep precipitating cumuli are usually excluded from scope of BLM due to longer time for most air to recirculate back from clouds into contact with surface. Air-surface exchange BLM also traditionally includes the study of fluxes of heat, moisture and momentum between the atmosphere and the underlying surface, and how to characterize surfaces so as to predict these fluxes (roughness, thermal and moisture fluxes, radiative characteristics).
    [Show full text]
  • Effects of Wall Roughness on Adverse Pressure Gradient Boundary Layers
    Effects of Wall Roughness on Adverse Pressure Gradient Boundary Layers by Pouya Mottaghian A thesis submitted to the Department of Mechanical and Materials Engineering in conformity with the requirements for the degree of Master of Applied Science Queen's University Kingston, Ontario, Canada December, 2015 Copyright © Pouya Mottaghian, 2015 Abstract Large-eddy Simulations were carried out on a at-plate boundary layer over smooth and rough surfaces in the presence of an adverse pressure gradient, strong enough to induce separation. The inlet Reynolds number (based on freestream velocity and momentum thick- ness at the reference plane) is 2300. A sand-grain roughness model was implemented and spatial-resolution requirements were determined. Two roughness heights were used and a fully-rough ow condition is achieved at the refer- ence plane with roughness Reynolds numbers 60 and 120. As the friction velocity decreases due to the adverse pressure gradient the roughness Reynolds number varies from fully-rough to transitionally rough and smooth regime before the separation. The double-averaging approach illustrates how the roughness contribution decreases before the separation as the dispersive stresses decrease markedly compared to the upstream region. Before the ow detachment, roughness intensies the Reynolds stresses. After the sep- aration, the normal stresses, production and dissipation substantially increase through the adverse pressure gradient region. In the recovery region, the ow is highly three dimensional, as turbulent structures impinge on the wall at the reattachment region. Roughness initially increases the skin friction, then causes it to decrease faster than on a smooth wall, generating a considerably larger recirculation bubble for rough cases with earlier separation and later reattachment; increasing the wall roughness also leads to larger separation bubble.
    [Show full text]
  • 1 FLUID MECHANICS TUTORIAL No. 3 BOUNDARY LAYER THEORY In
    FLUID MECHANICS TUTORIAL No. 3 BOUNDARY LAYER THEORY In order to complete this tutorial you should already have completed tutorial 1 and 2 in this series. This tutorial examines boundary layer theory in some depth. When you have completed this tutorial, you should be able to do the following. Discuss the drag on bluff objects including long cylinders and spheres. Explain skin drag and form drag. Discuss the formation of wakes. Explain the concept of momentum thickness and displacement thickness. Solve problems involving laminar and turbulent boundary layers. Throughout there are worked examples, assignments and typical exam questions. You should complete each assignment in order so that you progress from one level of knowledge to another. Let us start by examining how drag is created on objects. 1 1. DRAG When a fluid flows around the outside of a body, it produces a force that tends to drag the body in the direction of the flow. The drag acting on a moving object such as a ship or an aeroplane must be overcome by the propulsion system. Drag takes two forms, skin friction drag and form drag. 1.1 SKIN FRICTION DRAG Skin friction drag is due to the viscous shearing that takes place between the surface and the layer of fluid immediately above it. This occurs on surfaces of objects that are long in the direction of flow compared to their height. Such bodies are called STREAMLINED. When a fluid flows over a solid surface, the layer next to the surface may become attached to it (it wets the surface).
    [Show full text]
  • Chapter 5 Frictional Boundary Layers
    Chapter 5 Frictional boundary layers 5.1 The Ekman layer problem over a solid surface In this chapter we will take up the important question of the role of friction, especially in the case when the friction is relatively small (and we will have to find an objective measure of what we mean by small). As we noted in the last chapter, the no-slip boundary condition has to be satisfied no matter how small friction is but ignoring friction lowers the spatial order of the Navier Stokes equations and makes the satisfaction of the boundary condition impossible. What is the resolution of this fundamental perplexity? At the same time, the examination of this basic fluid mechanical question allows us to investigate a physical phenomenon of great importance to both meteorology and oceanography, the frictional boundary layer in a rotating fluid, called the Ekman Layer. The historical background of this development is very interesting, partly because of the fascinating people involved. Ekman (1874-1954) was a student of the great Norwegian meteorologist, Vilhelm Bjerknes, (himself the father of Jacques Bjerknes who did so much to understand the nature of the Southern Oscillation). Vilhelm Bjerknes, who was the first to seriously attempt to formulate meteorology as a problem in fluid mechanics, was a student of his own father Christian Bjerknes, the physicist who in turn worked with Hertz who was the first to demonstrate the correctness of Maxwell’s formulation of electrodynamics. So, we are part of a joined sequence of scientists going back to the great days of classical physics.
    [Show full text]
  • The Atmospheric Boundary Layer (ABL Or PBL)
    The Atmospheric Boundary Layer (ABL or PBL) • The layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. • The complexity of this definition is due to several complications compared to classical aerodynamics: i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. Atm S 547 Lecture 1, Slide 1 Sublayers of the atmospheric boundary layer Atm S 547 Lecture 1, Slide 2 Applications and Relevance of BLM i) Climate simulation and NWP ii) Air Pollution and Urban Meteorology iii) Agricultural meteorology iv) Aviation v) Remote Sensing vi) Military Atm S 547 Lecture 1, Slide 3 History of Boundary-Layer Meteorology 1900 – 1910 Development of laminar boundary layer theory for aerodynamics, starting with a seminal paper of Prandtl (1904). Ekman (1905,1906) develops his theory of laminar Ekman layer. 1910 – 1940 Taylor develops basic methods for examining and understanding turbulent mixing Mixing length theory, eddy diffusivity - von Karman, Prandtl, Lettau 1940 – 1950 Kolmogorov (1941) similarity theory of turbulence 1950 – 1960 Buoyancy effects on surface layer (Monin and Obuhkov, 1954). Early field experiments (e. g. Great Plains Expt. of 1953) capable of accurate direct turbulent flux measurements 1960 – 1970 The Golden Age of BLM. Accurate observations of a variety of boundary layer types, including convective, stable and trade- cumulus.
    [Show full text]
  • Boundary Layers
    1 I-campus project School-wide Program on Fluid Mechanics Modules on High Reynolds Number Flows K. P. Burr, T. R. Akylas & C. C. Mei CHAPTER TWO TWO-DIMENSIONAL LAMINAR BOUNDARY LAYERS 1 Introduction. When a viscous fluid flows along a fixed impermeable wall, or past the rigid surface of an immersed body, an essential condition is that the velocity at any point on the wall or other fixed surface is zero. The extent to which this condition modifies the general character of the flow depends upon the value of the viscosity. If the body is of streamlined shape and if the viscosity is small without being negligible, the modifying effect appears to be confined within narrow regions adjacent to the solid surfaces; these are called boundary layers. Within such layers the fluid velocity changes rapidly from zero to its main-stream value, and this may imply a steep gradient of shearing stress; as a consequence, not all the viscous terms in the equation of motion will be negligible, even though the viscosity, which they contain as a factor, is itself very small. A more precise criterion for the existence of a well-defined laminar boundary layer is that the Reynolds number should be large, though not so large as to imply a breakdown of the laminar flow. 2 Boundary Layer Governing Equations. In developing a mathematical theory of boundary layers, the first step is to show the existence, as the Reynolds number R tends to infinity, or the kinematic viscosity ν tends to zero, of a limiting form of the equations of motion, different from that obtained by putting ν = 0 in the first place.
    [Show full text]
  • Incompressible Skewed Turbulent Boundary Layer on an End Wall of a Curved Two-Dimensional Diffuser Marvin Dale Smith Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1970 Incompressible skewed turbulent boundary layer on an end wall of a curved two-dimensional diffuser Marvin Dale Smith Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Smith, Marvin Dale, "Incompressible skewed turbulent boundary layer on an end wall of a curved two-dimensional diffuser " (1970). Retrospective Theses and Dissertations. 4199. https://lib.dr.iastate.edu/rtd/4199 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact digirep@iastate.edu. 70-18,908 SMITH, Marvin Dale, 1935- INCOMPRESSIBLE SKEWED TURBULENT BOUNDARY LAYER ON AN END WALL OF A C'JRVSD TWO-DIMENSIONAL DIFFUSER. Iowa State University, Ph.D., 1970 Engineering, mechanical I University Microfilms, A XEROXCompany, Ann Arbor, Michigan j. : Art T»T^oT^xtrr»T\ INCOMPRESSIBLE SKEWED TURBULENT BOUNDARY LAYER ON AN END WALL OF A CURVED TWO-DIMENSIONAL DIFFUSER by Marvin Dale Smith A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of Tlie Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subjects; Mechanical Engineering Aerospace Engineering
    [Show full text]
  • Numerical Investigation of the Turbulent Wake-Boundary Interaction in a Translational Cascade of Airfoils and Flat Plate
    energies Article Numerical Investigation of the Turbulent Wake-Boundary Interaction in a Translational Cascade of Airfoils and Flat Plate Xiaodong Ruan 1,*, Xu Zhang 1, Pengfei Wang 2 , Jiaming Wang 1 and Zhongbin Xu 3 1 State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China; 3110104687@zju.edu.cn (X.Z.); wjm0@zju.edu.cn (J.W.) 2 School of Engineering, Zhejiang University City College, Hangzhou 310015, China; wangpf@zucc.edu.cn 3 Institute of Process Equipment, Zhejiang University, Hangzhou 310027, China; xuzhongbin@zju.edu.cn * Correspondence: xdruan@zju.edu.cn; Tel.: +86-1385-805-3612 Received: 24 July 2020; Accepted: 27 August 2020; Published: 31 August 2020 Abstract: Rotor stator interaction (RSI) is an important phenomenon influencing performances in the pump, turbine, and compressor. In this paper, the correlation-based transition model is used to study the RSI phenomenon between a translational cascade of airfoils and a flat plat. A comparison was made between computational results and experimental results. The computational boundary layer velocity is in reasonable agreement with the experimental velocity. The thickness of boundary layer decreases as the RSI frequency increases and it increases as the fluid flows downstream. The spectral plots of velocity fluctuations at leading edge x/c = 2 under RSI partial flow condition f = 20 Hz and f = 30 Hz are dominated by a narrowband component. RSI frequency mainly affects the turbulence intensity in the freestream region. However, it has little influence on the turbulence intensity of boundary layer near the wall. A secondary vortex is induced by the wake–boundary layer interaction and it leads to the formation of a thickened laminar boundary layer.
    [Show full text]
  • 0 Exam: 01 Aerodynamics: Boundary Layer Theory
    Aerodynamics EETAC Final Exams Compilation Perm: 0 Exam: 01 Aerodynamics: Boundary Layer Theory { Multiple Choice Test 2018/19 Q2 7. The boundary layer (BL) integral equations... 1. Under which circumstances may the volume rate-of-change (a) result from integrating the BL local equations in the entail viscous shear stresses? wall-normal coordinate over the BL thickness. (b) result from integrating the BL local equations along (a) Never for incompressible flow. the streamwise coordinate. (b) Always under the Stokes hypothesis. (c) result in as many unknowns as there are equations. (c) Always. (d) differ for laminar and turbulent BLs. (d) Never. (e) None of the other options. (e) None of the other options. 8. How is the D'Alembert's paradox removed and the form 2. What is true about the viscous blockage? drag obtained in an inviscid flow { boundary layer coupling (a) All options are correct. calculation? (b) It corresponds to a massflow reduction in the near-wall (a) By solving the inviscid problem for a second time over region due to the effects of viscosity. a body enlarged by the displacement thickness and (c) It corresponds to a momentum flux reduction in the extended with the wake. near-wall region due to the effects of viscosity. (b) By directly solving the boundary layer equations. (d) It follows from the no-slip condition at the wall due to (c) The paradox remains no matter what. viscous effects. (d) By solving the inviscid problem over the original body. (e) It may be quantified by the displacement and momen- (e) The paradox was never there in the first place.
    [Show full text]