Showing papers on "Flow separation published in 1975"
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01 Jan 1975
TL;DR: In this article, the authors present an approach for the analysis of flow properties and properties in a 3D manifold with respect to velocity, acceleration, and velocity distribution, and the Bernoulli Equation.
Abstract: PREFACE. CHAPTER 1 Introduction. 1.1 Liquids and Gases. 1.2 The Continuum Assumption. 1.3 Dimensions, Units, and Resources. 1.4 Topics in Dimensional Analysis. 1.5 Engineering Analysis. 1.6 Applications and Connections. CHAPTER 2 Fluid Properties. 2.1 Properties Involving Mass and Weight. 2.2 Ideal Gas Law. 2.3 Properties Involving Thermal Energy. 2.4 Viscosity. 2.5 Bulk Modulus of Elasticity. 2.6 Surface Tension. 2.7 Vapor Pressure. 2.8 Summary. CHAPTER 3 Fluid Statics. 3.1 Pressure. 3.2 Pressure Variation with Elevation. 3.3 Pressure Measurements. 3.4 Forces on Plane Surfaces (Panels). 3.5 Forces on Curved Surfaces. 3.6 Buoyancy. 3.7 Stability of Immersed and Floating Bodies. 3.8 Summary. CHAPTER 4 Flowing Fluids and Pressure Variation. 4.1 Descriptions of Fluid Motion. 4.2 Acceleration. 4.3 Euler's Equation. 4.4 Pressure Distribution in Rotating Flows. 4.5 The Bernoulli Equation Along a Streamline. 4.6 Rotation and Vorticity. 4.7 The Bernoulli Equation in Irrotational Flow. 4.8 Separation. 4.9 Summary. CHAPTER 5 Control Volume Approach and Continuity Equation. 5.1 Rate of Flow. 5.2 Control Volume Approach. 5.3 Continuity Equation. 5.4 Cavitation. 5.5 Differential Form of the Continuity Equation. 5.6 Summary. CHAPTER 6 Momentum Equation. 6.1 Momentum Equation: Derivation. 6.2 Momentum Equation: Interpretation. 6.3 Common Applications. 6.4 Additional Applications. 6.5 Moment-of-Momentum Equation. 6.6 Navier-Stokes Equation. 6.7 Summary. CHAPTER 7 The Energy Equation. 7.1 Energy, Work, and Power. 7.2 Energy Equation: General Form. 7.3 Energy Equation: Pipe Flow. 7.4 Power Equation. 7.5 Contrasting the Bernoulli Equation and the Energy Equation. 7.6 Transitions. 7.7 Hydraulic and Energy Grade Lines. 7.8 Summary. CHAPTER 8 Dimensional Analysis and Similitude. 8.1 Need for Dimensional Analysis. 8.2 Buckingham Theorem. 8.3 Dimensional Analysis. 8.4 Common-Groups. 8.5 Similitude. 8.6 Model Studies for Flows Without Free-Surface Effects. 8.7 Model-Prototype Performance. 8.8 Approximate Similitude at High Reynolds Numbers. 8.9 Free-Surface Model Studies. 8.10 Summary. CHAPTER 9 Surface Resistance. 9.1 Surface Resistance with Uniform Laminar Flow. 9.2 Qualitative Description of the Boundary Layer. 9.3 Laminar Boundary Layer. 9.4 Boundary Layer Transition. 9.5 Turbulent Boundary Layer. 9.6 Pressure Gradient Effects on Boundary Layers. 9.7 Summary. CHAPTER 10 Flow in Conduits. 10.1 Classifying Flow. 10.2 Specifying Pipe Sizes. 10.3 Pipe Head Loss. 10.4 Stress Distributions in Pipe Flow. 10.5 Laminar Flow in a Round Tube. 10.6 Turbulent Flow and the Moody Diagram. 10.7 Solving Turbulent Flow Problems. 10.8 Combined Head Loss 10.9 Nonround Conduits. 10.10 Pumps and Systems of Pipes. 10.11 Summary. CHAPTER 11 Drag and Lift. 11.1 Relating Lift and Drag to Stress Distributions. 11.2 Calculating Drag Force. 11.3 Drag of Axisymmetric and 3D Bodies. 11.4 Terminal Velocity. 11.5 Vortex Shedding. 11.6 Reducing Drag by Streamlining. 11.7 Drag in Compressible Flow. 11.8 Theory of Lift. 11.9 Lift and Drag on Airfoils. 11.10 Lift and Drag on Road Vehicles. 11.11 Summary. CHAPTER 12 Compressible Flow. 12.1 Wave Propagation in Compressible Fluids. 12.2 Mach Number Relationships. 12.3 Normal Shock Waves. 12.4 Isentropic Compressible Flow Through a Duct with Varying Area. 12.5 Summary. CHAPTER 13 Flow Measurements. 13.1 Measuring Velocity and Pressure 13.2 Measuring Flow Rate (Discharge). 13.3 Measurement in Compressible Flow. 13.4 Accuracy of Measurements. 13.5 Summary. CHAPTER 14 Turbomachinery. 14.1 Propellers. 14.2 Axial-Flow Pumps. 14.3 Radial-Flow Machines. 14.4 Specific Speed. 14.5 Suction Limitations of Pumps. 14.6 Viscous Effects. 14.7 Centrifugal Compressors. 14.8 Turbines. 14.9 Summary. CHAPTER 15 Flow in Open Channels. 15.1 Description of Open-Channel Flow. 15.2 Energy Equation for Steady Open-Channel Flow. 15.3 Steady Uniform Flow. 15.4 Steady Nonuniform Flow. 15.5 Rapidly Varied Flow. 15.6 Hydraulic Jump. 15.7 Gradually Varied Flow. 15.8 Summary. Appendix A-1. Answers A-11. Index I-1.
1,166 citations
TL;DR: In this paper, the shape factor of the boundary layer, d*/0 £ = plate length L = lift m = exponent in Cp=x flows, also lift magnification factor (5.1) M = Mach number p = pressure q = dynamic pressure Q = flow rate R = Reynolds number (= u Ox/v in Stratford flows) R6 = Reynolds Number based on momentum thickness uee/v S = Stratford's separation constant (4.10)
Abstract: c. f = chord fraction, see Eq. (5.1) H = shape factor of the boundary layer, d*/0 £ = plate length L = lift m = exponent in Cp=x flows, also lift magnification factor (5.1) M = Mach number p = pressure q = dynamic pressure Q = flow rate R = Reynolds number (= u Ox/v in Stratford flows) R6 = Reynolds number based on momentum thickness uee/v S = Stratford's separation constant (4.10); also peripheral distance around a body or wing area / = blowing slot gap, also thickness ratio of a body u = velocity in x-direction u0 = initial velocity at start of deceleration in canonical and Stratford flows v = velocity normal to the wall V = a general velocity x = length in flow direction, or around surface of a body measured from stagnation point if used in connection with boundary-layer flow
478 citations
TL;DR: In this article, the Navier−Stokes equations were investigated theoretically under slip-boundary conditions and numerical solutions to the equations were obtained using newly developed computer programs for incompressible fluid flows past elliptic cylinders and oblate spheroids, and the influence of slippage on flow separation, vorticity and vortex shedding, as well as on the force coefficients, was discussed.
Abstract: Laminar flows past bodies under slip−boundary conditions are investigated theoretically within the framework of the Navier−Stokes equations The numerical solutions to the equations are obtained using newly developed computer programs for incompressible fluid flows past elliptic cylinders and oblate spheroids The influence of slippage on flow separation, vorticity, and vortex shedding, as well as on the force coefficients, is discussed
470 citations
313 citations
TL;DR: In this paper, a model is proposed which attempts to explain the complete "burst cycle" by viewing the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-body which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up.
Abstract: A model is proposed which attempts to explain the complete ‘burst cycle’. This model views the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-boundary layer which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up. ‘Sweeps’ are thought to represent the passage of a previous burst from further upstream. They appear either to impress on the wall streak the temporary adverse pressure gradient required to bring about its lifting or, alternatively, to provide the outer vortex which rolls up with the vortex associated with the wall streak. The model is also used to explain how the interactions between a burst and a sweep bring about (i) breakup, as well as (ii) new wall streaks further downstream.Arguments are presented to demonstrate that the three kinds of oscillatory growth reported by Kim, Kline & Reynolds (1971) may be associated with just one type of flow structure: the stretched and lifted vortex described by Kline et al. (1967).
243 citations
TL;DR: In the absence of a viable theory for turbulent structure, a summary of the results of recent experimental research can be found in this article, where the authors present fundamental topics that are necessary for a better understanding of turbulent structure.
Abstract: Publisher Summary This chapter presents fundamental topics that are necessary for a better understanding of turbulent structure. In the absence of a viable theory for turbulent structure, the chapter concentrates upon a summary of the results of recent experimental research. Modern experimental investigations employing sophisticated flow visualization and computer-aided data processing techniques have revealed a large amount of new information. These new results are discussed and the nature of existing theoretical investigations is mentioned. The chapter presents an excellent review of the physics of turbulent flow and includes a detailed discussion of the transition process. It also deals with the structure of the fluctuating turbulent flow field. In boundary layer flows, the nature and structure of the flow are controlled by the vorticity that is produced by the passage of initially irrotational fluid over the wall. Vorticity considerations illuminate the detailed development of the boundary layer just as clearly as momentum considerations and allow a compact description of the dynamics of turbulence.
196 citations
TL;DR: In this article, an extended acoustic theory is worked out for a gas-filled resonance tube, and the results show cooling in the section of the tube with maximum velocity amplitude and marked heating in the region of the velocity nodes.
Abstract: New experiments with a gas-filled resonance tube have shown that not only heating, but also cooling of the tube wall is possible and that these phenomena are not restricted to oscillation amplitudes that generate shocks. The present paper concentrates on amplitudes outside the shock region. For this case, an extended acoustic theory is worked out. The results show cooling in the section of the tube with maximum velocity amplitude (and thus dissipation) and marked heating in the region of the velocity nodes. A strong dependence of these effects on the Prandtl number is noted. The results are in good agreement with experiments. Although the theory is not valid for proper resonance conditions, it nevertheless sheds some light on what happens when nonlinear effects dominate.Closely related to the limit of validity of the thermoacoustic theory is the question of transition from laminar to turbulent flow in the viscous boundary layer (Stokes layer). This problem has also been investigated; the results are given in a separate paper (Merkli & Thomann 1975). In the present article laminar flow is assumed.
165 citations
TL;DR: In this paper, a simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer, and the displacement of the shock is assumed limited by a linear restoring mechanism.
Abstract: Pressure fluctuations due to the interaction of a shock wave with a turbulent boundary layer were investigated. A simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer. Displacement of the shock is assumed limited by a linear restoring mechanism. Predictions of peak root mean square pressure fluctuation and spectral density are in excellent agreement with available experimental data.
155 citations
TL;DR: In this article, the authors draw attention to examples of flow separation in natural meander bends and attempt to define an empirical criterion for predicting the onset of separation, which can be used to predict sedimentation and erosion in sinuous channels.
Abstract: IT is generally assumed that downstream flow through meander bends is helicoidal and is accompanied by a transverse, bottom flow component directed towards the inner bank1–3. Thus particles of sediment on a point bar are transported at some angle inwards from the generalised local downstream flow vector4,5. As pointed out by Bagnold2, however, “… a stage must be reached at which the flow along the inner boundary becomes unstable and breaks away from the boundary, leaving an intervening space occupied by a zone of unstable and confused motion …”. The experimental results of Leopold et al.5 leave no doubt that this phenomenon of flow separation (Fig. 1) can be a highly important feature in river hydraulics. Since 1960, however, no workers have extended these initial experimental ideas into field situations. Existing models of sedimentation and erosion in sinuous channels4,5 ignore any possible effects of flow separation. Here we draw attention to examples of flow separation in natural meander bends and attempt to define an empirical criterion for predicting the onset of separation.
136 citations
TL;DR: In this article, a theoretical model is presented which permits the conservation equations of fluid dynamics to be conditioned in a fashion analogous to the experimentalist's technique of "conditioned sampling", which results in predictions of the flow variables within the turbulent flow and of the intermittency.
Abstract: A theoretical model is presented which permits the conservation equations of fluid dynamics to be conditioned in a fashion analogous to the experimentalist's technique of "conditioned sampling". The detailed analysis refers to the best-known sampling condition, outer-edge intermittency; but the model equation may be applicable to other flow situations, wherein conditioning exposes details of the physical phenomena. The analysis results in predictions of the flow variables within the turbulent flow and of the intermittency. Comparison is made with two sets of experimental results for the two-dimensional mixing layer and with a boundary layer.
133 citations
TL;DR: In this article, the stability of the stable boundary layer is modeled as a linear combination of the dimensionless boundary layer height and the stability dependent functions in the geostrophic drag relations.
Abstract: Publisher Summary Modeling of the stable boundary layer is difficult because usually, a transition from turbulent to laminar flow takes place with increasing height, and steady state is usually not reached in the laminar region but may be approached in the turbulent region. This chapter discusses the formulation of a steady-state stable boundary layer, which, in reality, may occur only after a very long time, possibly during the polar night in the arctic. Under most gravitationally stable conditions in the atmosphere, there is always a good likelihood of a turbulent or mixing layer occurring near the surface. With increasing stability, the length scale of the vertical motion becomes independent of the height above the surface, but proportional to the so-called Obukhov length, and under these conditions, the mean velocity and temperature profiles become linear. The chapter presents two most significant results for the stable boundary layer: (1) the dimensionless boundary layer height varies in inverse proportion to the square-root of the stability parameter and (2) the calculated forms of the stability dependent functions in the geostrophic drag relations are in fair agreement with their empirical estimates from the Wangara data.
TL;DR: In this article, boundary conditions at the surface between a porous medium and a free fluid flow were studied. And the results about the matching of different flow regions and boundary conditions are given, as well as examples.
TL;DR: The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle as discussed by the authors, and the change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e.
Abstract: Measurements have been made concerning the fine structure of the turbulence in the part adjacent to the wall of the wall region of a plane turbulent boundary layer. The objective was to gain further information concerning the larger-scale disturbance mechanism which is mainly responsible for the generation of turbulence. Hot-wire anemomet.ry was used and information on the fine structure was obtained by differentiating and filtering the hot-wire signal.The distributions of the Kolmogorov microscale and of the flatness and skewness factors of the axial fluctuating velocity u and its first and second derivative determined at two Reynolds numbers suggest the existence of Reynolds number similarity. In the region y+ 100) the flatness and skewness factors approach values obtained in shear-free turbulence at the same turbulence Reynolds number.The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle. In the viscous sublayer both the fine structure, and the large-scale mechanism of the turbulence are influenced mainly by the inrush phase, while further out in the wall region (y+ > 40) they are influenced by both inrush and ejection. As a result, in the viscous sublayer the average burst periods of the high frequency turbulence components and their flatness factors (of ∂u/∂t and of ∂2u/∂t2) attain values twice those in the outer part.The change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e. (∂u/∂t)2 and (∂2u/∂t2)2. The spectra agree with each other and decrease with increasing frequency, following a power law as predicted by Gurvich & Yaglom (1967). The power law applies to almost the whole frequency range, when the highest, viscous, frequency range is excluded. However, the exponent is different for the viscous sublayer and the outer part of the wall region. In the buffer layer the spectra have two distinct power-law regions. In the lower frequency range the exponent is the same as that for the viscous sublayer, while in the higher frequency range it is the same as that for the outer part of the wall region.
TL;DR: In this article, the stalling characteristics of an airfoil in a laminar viscous incompressible fluid are investigated using an implicit finite-difference scheme and point successive relaxation procedure.
Abstract: The stalling characteristics of an airfoil in a laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behavior of the forces at large times are studied. Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behavior of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles.
TL;DR: In this article, a review of recent developments of certain aspects of the theory of unsteady laminar boundary layers is presented, but the review is not all-embracing in the sense that the theory can be viewed as a theory of un...
Abstract: The purpose of this article is to review recent developments of certain aspects of the theory of unsteady laminar boundary layers. The review is not all-embracing in the sense that the theory of un...
TL;DR: In this paper, the effect of compressibility on the mixing layer was investigated at Mach number 2, and the difference between free and wall-bounded mixing layers was discussed. And the development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.
Abstract: The effect of compressibility on the mixing layer was investigated at Mach number 2.47. Pitot pressure, static pressure, and hot-wire surveys were conducted to investigate the mean flow and the fluctuation quantities. Similarities between supersonic and incompressible mixing layers were observed in normalized velocity profile, normalized power spectral density distribution, and convection velocity distribution. Spreading rate, normalized shear stress, and velocity fluctuation were found to be appreciably smaller than the respective incompressible results; e.g., the momentum thickness growth rates are 0.0073 and 0.035 for supersonic and incompressible flows, respectively. The difference between free and wall-bounded mixing layers is discussed. Development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.
TL;DR: In this paper, the Taylor-Gortler vortices observed in a nozzle wall boundary layer were used to predict the limits of quiet performance for a proposed 20-in. quiet tunnel.
Abstract: High noise levels in conventional supersonic and hypersonic wind tunnels prevent further advances in transition research. Recent data confirm previous results that transition is dominated by tunnel noise when the rms pressure intensities exceed about 1%. High facility noise levels also dominate fluctuating pressure loads under fully turbulent boundary layers. Recent data on the power spectra of surface pressures indicate that the basic structure of turbulent boundary layers may be modified by high facility noise levels. Experimental data for current techniques to control and reduce noise levels in supersonic and hypersonic wind tunnels by laminarization of nozzle wall boundary layers and by noise radiation shields are presented. These results and possible effects of Taylor-Gortler vortices observed in a nozzle wall boundary layer are used to predict the limits of quiet performance for a proposed 20-in. quiet tunnel.
TL;DR: In this article, the importance of unsteady effects on laminar boundary layers was found to diminish rapidly with increasing longitudinal pressure gradients, whereas turbulent separation on airfoils was significantly affected by oscillatory motion when the incidence approached the stall angle.
Abstract: Incompressible laminar and turbulent flows over flat plates and airfoils have been investigated numerically and experimentally in unsteady flow conditions. Important differences were found between laminar and turbulent flat plate flows over a wide range of oscillation frequencies. Also, the importance of unsteady effects on laminar boundary layers was found to diminish rapidly with increasing longitudinal pressure gradients, whereas turbulent separation on airfoils was significantly affected by oscillatory motion when the incidence approached the stall angle. The calculated hysteresis in turbulent separation followed in a qualitative sense the well-known trends of dynamic stall delay and reattachment. However, the numerical analysis failed to indicate some of the important features of dynamic stall observed in the present experiment and in previous studies.
TL;DR: In this paper, the growth rate of the boundary layer thickness over the convex side is almost halved and the skin friction coefficient falls to about 0.9 of the value expected on a plane surface.
Abstract: Measurements are reported for turbulent boundary-layer growth in a prolonged bend where the additional rates of strain produced by streamline curvature influence the turbulent development. The growth rate of the boundary-layer thickness over the convex side is almost halved and the skin friction coefficient falls to about 0.9 of the value expected on a plane surface. The mixing rate on the concave side is increased to about 1.1 times the plane surface value, and the customary evidence of longitudinal rolls appears. These measurements are the first since those of Schmidbauer's (1936) to provide a test of existing curvature correction formulas for curvatures typical of airfoils and turbomachinery without the complications of compressibility. Results have been compared against calculation techniques proposed by Bradshaw (1973), with good agreement.
TL;DR: In this article, the stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally, and a linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials.
Abstract: The stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally. Previous theoretical results concerning the basic laminar flow (part 1) are compared with experimental results. Small and large Reynolds number results are compared with Stokes-flow and boundary-layer solutions. The effect of the radius ratio of the two spheres is demonstrated. A linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials; the differential equations governing these potentials are integrated numerically. It is found that the flow is subcritically unstable and that the observed instability occurs at a Reynolds number close to the critical value of the energy stability theory. Observations of other flow transitions, at higher values of the Reynolds number, are also described. The character of the stability of the spherical annulus flow is found to be strongly dependent on the radius ratio.
TL;DR: In this paper, an explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow, and a nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field.
Abstract: A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over an 18 percent thick circular-arc biconvex airfoil at zero angle of attack and free-stream Mach number of 0.775. A simple mixing-length model is used to describe the turbulence and chord Reynolds numbers of 1, 2, 4, and 10 million are considered. The solution describes in sufficient detail both the shock-induced and trailing-edge separation regions, and provides the profile and friction drag.
01 Jun 1975
TL;DR: In this article, a review of two-dimensional supersonic interactions including separation for laminar and turbulent flows is made, including numerical techniques for calculating these flows, including finite difference and integral methods.
Abstract: : A review is made of two-dimensional supersonic interactions including separation for laminar and turbulent flows. Part 1 discusses recent theoretical developments in interacting flows and presents numerical techniques for calculating these flows, including finite difference and integral methods. Theoretical discussions are presented for both laminar and turbulent interactions. Part 2 reviews recent experimental studies which have been directed towards understanding the fluid mechanics of attached and separated regions of shock wave-boundary layer interaction in the supersonic annd hypersonic flow.
TL;DR: In this article, the fluid mechanics of transpired incompressible turbulent boundary layers under zero and adverse pressure gradient conditions are investigated using an open-ended wind tunnel with a porous floor in the test section and a secondary air system for supply and metering of the transpiration air.
Abstract: The fluid mechanics of transpired incompressible turbulent boundary layers under zero and adverse pressure gradient conditions is investigated using an open-ended wind tunnel with a porous floor in the test section and a secondary air system for supply and metering of the transpiration air. All velocity profiles and turbulence profiles are obtained by linearized constant-temperature hot-wire anemometry. The wall shear stress is determined by measuring the shear stress away from the wall and extrapolating to the wall by integrating the boundary layer equations for the shear-stress profile. Equilibrium boundary layers are obtained when the transpiration velocity is varied such that the blowing parameter and the Clauser pressure gradient parameter are held constant. The experimental results obtained are presented in tabular and graphical forms.
TL;DR: The boundary layer at the minima positions is found to be twice as thick as that at the maxima positions as mentioned in this paper, and turbulent intensities inside the boundary layer are substantially increased as a result of the concave curvature of the surface.
Abstract: The present experiment describes the behavior of a turbulent boundary layer on a concave wall. At the onset of curvature there appears a fairly coherent wavelike transverse profile of mean velocity. This disturbance might be interpreted as a kind of large scale Taylor-Goertler type instability superimposed on a conventional turbulent boundary layer; further downstream the coherence degenerates as the turbulence level increases. Boundary-layer profile measurements were made at positions of maxima and minima of transverse profiles of (U-component) mean velocity. The boundary layer at the minima positions is found to be twice as thick as that at the maxima positions. Also, turbulent intensities inside the boundary layer are substantially increased as a result of the concave curvature of the surface.
TL;DR: Using the dye injection technique, flow at low Reynolds numbers was studied in glass models which simulated arterial bifurcations of varying angles and had varying bluntness of the apex or crotch.
Abstract: Using the dye injection technique, flow at low Reynolds numbers was studied in glass models which simulated arterial bifurcations of varying angles and had varying bluntness of the apex or crotch. Forks bearing small saccular evaginations simulating berry aneurysms were investigated similarly.. At quite low Reynolds numbers in all the models small wave motion was observed at the forks. At higher Reynolds numbers and below the critical values for turbulence, larger Vortices akin to a Karman vortex street were shed from most of the forks. The disturbances were attributed to boundary layer separation and a jet-edge effect.
TL;DR: In this paper, a three-dimensional turbulent boundary-layer experiment is described with the specific aim of providing a test-case for calculation methods, and the results of the calculations are compared with those of the experiment.
Abstract: First a three-dimensional turbulent boundary-layer experiment is described. This has been carried out with the specific aim of providing a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept-wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate was subjected to an adverse pressure gradient, which led to three-dimensional separation near the trailing edge of the plate. Next, a calculation method for three-dimensional turbulent boundary layers is discussed. This solves the boundary-layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. Agreement is good over a considerable distance; but large discrepancies are apparent near the separation line.
TL;DR: In this article, a semi-empirical theory is developed which will predict the behavior of the shear layer across a laminar separation bubble and is applicable down to short bubble bursting.
Abstract: Testing over a range of Reynolds numbers was done for three NACA 65 Profiles in cascade. The testing was carried out in the VKI C-1 Low Speed Cascade Wind Tunnel; blade chord Reynolds number was varied from 250,000 to 40,000. A semiempirical theory is developed which will predict the behavior of the shear layer across a laminar separation bubble. The method is proposed for two-dimensional incompressible flow and is applicable down to short bubble bursting. The method can be used to predict the length of the laminar bubble, the bursting Reynolds number, and the development of the shear layer through the separated region. As such it is a practical method for calculating the profile losses of axial compressor and turbine cascades in the presence of laminar separation bubbles. It can also be used to predict the abrupt leading edge stall associated with thin airfoil sections. The predictions made by the method are compared with the available experimental data. The agreement could be considered good. The method was also used to predict regions of laminar separation in converging flows through axial compressor cascades (exterior to the corner vortices) with good results. For Reynolds numbers below bursting the semiempirical theory no longer applies. For this situation the performance of an axial compressor cascade can be computed using an empirical correlation proposed by the author. Comparison of performance prediction with experiment shows satisfactory agreement. Finally, a tentative correlation, based on the NACA Diffusion Factor, is presented that allows a rapid estimation of the bursting Reynolds number of an axial compressor cascade.
TL;DR: In this paper, the interaction between a boundary layer and an array of single-wavenumber vortices convected at the mean free-stream velocity is studied analytically and numerically.
Abstract: To acquire insight into the role of free-stream turbulence on laminar-turbulent transition, the interaction between a boundary layer and an array of single-wavenumber vortices convected at the mean free-stream velocity is studied analytically and numerically. For small amplitudes, the effect of a spectrum can be obtained by superposition. The flow field is taken to be the sum of the steady laminar field (Blasius) plus a flow field ascribable to the effects of the vortex array. This latter flow field is further subdivided into the portion that exists in the absence of the plate (the vortex array itself) plus a flow field representing the alteration to that array due to the shearing mean flow and no-slip and impermeability conditions at the plate surface. This last portion of the flow field is described by a nonhomogeneous Orr–Sommerfeld equation with phase speed unity and real wavenumber. The forcing function depends on the mean flow and on the free-stream disturbance array. The problem is not an eigenvalu...