Showing papers on "Flow separation published in 1974"

Viscous Fluid Flow

Abstract: 1 Preliminary Concepts 2 Fundamental Equations of Compressible Viscous Flow 3 Solutions of the Newtonian Viscous-Flow Equations 4 Laminar Boundary Layers 5 The Stability of Laminar Flows 6 Incompressible Turbulent Mean Flow 7 Compressible Boundary Layer Flow Appendices A Transport Properties of Various Newtonian Fluids B Equations of Motion of Incompressible Newtonian Fluids in Cylindrical and Spherical Coordinates C A Runge-Kutta Subroutine for N Simultaneous Differential Equations Bibliography Index

Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number

Abstract: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.

Multistructured Boundary Layers on Flat Plates and Related Bodies

Abstract: Publisher Summary The chapter reviews subdivisions of the boundary layers that become necessary under the impact of sudden stream wise changes. If the boundary layer is supersonic, a new phenomenon occurs that appears to have no counterpart in subsonic flow. It leads to a greater ease of study of the flow properties and helps to overcome the barrier of separation that appears to hinder progress in the incompressible studies. The phenomenon is the free-interaction boundary layer, first observed by Ackeret and independently by Liepmann in their study of the interaction between a shock wave and a boundary layer and more extensively studied subsequently by Liepmann, Chapman, Hakkinen, and many others. These studies show that when a shock, sufficiently strong to provoke separation, strikes a laminar boundary layer, the boundary layer actually separates ahead of the foot of the shock and the flow features of the separation region are independent of the characteristics of the shock and depend only on the local properties of the flow. The chapter provides example for incompressible boundary layers when the fluid is compressible and explains the modifications necessary to allow this effect.

A boundary layer developing in an increasingly adverse pressure gradient

Abstract: This paper deals with a survey of mean flow and fluctuating quantities in a turbulent boundary layer developing on a smooth wall in a pressure domain P(x), where both dP/dx and d2P/dx2 are positive (increasingly adverse). The two-dimensional nature of the flow field was checked by momentum balance, as well as velocity traverses either side of the working section centre-line. Using the integrated form of the momentum integral equation, it was found that the skinfriction term and the summed momentum and pressure terms differed by at most 19%; but for the majority of measuring points they differed by less than 14%. The off-centre-line velocity profiles were indistinguishable from those taken on the centre-line. The flow field was also surveyed for fluctuating components , as well as for u1 spectra. Wherever possible, the results were compared with existing models of boundary-layer development. These comparisons indicated that the only all-embracing model for boundary-layer development is the law of the wall.

Turbulent/non-turbulent decisions in an intermittent flow

Abstract: The purpose of this study is to generalize the experimental method for deciding when a fluid motion can be considered turbulent. The rationale advanced for processing a transducer signal, which indicates the intermittent nature of a turbulent field, is given a probabilistic outlook. In addition an improved detector function is introduced which uses information from longitudinal and lateral fluctuation components.

Effect of the Adverse Pressure Gradient on Vortex Breakdown

Abstract: of the Influence of the Turbulent Boundary Layer on the Pressure Distribution over a Rigid Two-Dimensional Wavy Wall," TN D-6477, Aug. 1971, NASA. 4 Lighthill, M. J., "On Boundary Layers and Upstream Influence II. Supersonic Flows without Separation," Proceedings of the Royal Society, Vol. A217, 1953, pp. 478 and 504; see also Quarterly Journal of Mechanics, Vol. 3, 1950, p. 303. 5 Benjamin, T. B., "Shearing Flow over a Wavy Boundary," Journal of Fluid Mechanics, Vol. 6, 1959, p. 161. 6 Miles, J. W., "On Panel Flutter in the Presence of a Boundary Layer," Journal of Aerospace Sciences, Vol. 26, No. 2, Feb. 1959, pp. 81-93. 7 McClure, J. D., "On Perturbed Boundary Layer Flows," Rept. 62-2, June 1962, M.I.T. Fluid Dynamic Research Lab., Cambridge, Mass. 8 Anderson, W. J. and Fung, Y. C, "The Effect of an Idealized Boundary Layer on the Flutter of Cylindrical Shells in Supersonic Flow," GALCIT Structural Dynamics Rept. SM62-49, Dec. 1962, Graduate Aeronautical Lab., California Institute of Technology, Pasadena, Calif. 9 Zeydel, E. F. E., "Study of the Pressure Distribution on Oscillating Panels in Low Supersonic Flow with Turbulent Boundary Layer," NASA CR-691, Feb. 1967, Georgia Institute of Technology, Atlanta, Ga. 10 Do well, E. H., "Generalized Aerodynamic Forces on a Flexible Plate Undergoing Transient Motion in a Shear Flow with an Application to Panel Flutter," AIAA Journal, Vol. 9, No. 5, May 1971, pp. 834-841. 11 Ventres, C. S., "Transient Panel Motion in a Shear Flow," AMS Rept. 1062, Aug. 1972, Princeton Univ., Princeton, N.J. 12 Garrick, I. E. and Rubinow, S. I., "Theoretical Study of Air Forces on an Oscillating or Steady Thin Wing in a Supersonic Main Stream," TN 1383, July 1947, NACA. 13 Yates, J. E., "A Study of Panel Flutter with the Exact Method of Zeydel," NASA CR-1721, Dec. 1970, Aeronautical Research Associates of Princeton, Princeton, N.J. 14 Do well, E. H. and Ventres, C. S., "Derivation of Aerodynamic Kernel Functions," AIAA Journal, Vol. 11, No. 11, Nov. 1973, pp. 1586-1588.

Measurements of turbulent boundary layer growth over a longitudinally curved 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.

Extension of leading-edge-suction analogy to wings with separated flow around the side edges at subsonic speeds

Abstract: A method for determining the lift, drag, and pitching moment for wings which have separated flow at the leading and side edges with subsequently reattached flow downstream and inboard is presented. Limiting values of the contribution to lift of the side-edge reattached flow are determined for rectangular wings. The general behavior of this contribution is computed for rectangular, cropped-delta, cropped-diamond, and cropped-arrow wings. Comparisons of the results of the method and experiment indicate reasonably good correlation of the lift, drag, and pitching moment for a wide planform range. The agreement of the method with experiment was as good as, or better than, that obtained by other methods. The procedure is computerized and is available from COSMIC as NASA Langley computer program A0313.

Experiments on the Behaviour of an Axisymmetric Turbulent Boundary Layer with a Sudden Circumferential Strain

Abstract: Mean velocity and mean turbulent field measurements are performed for the case of a three-dimensional turbulent boundary layer on an axially rotated cylinder The cylinder model consists of two parts: a stationary section followed by a spinning afterbody Techniques of hot-wire anemometry are employed, which yield complete mean velocity and turbulence measurements in skewed flows The general behaviour of the three-dimensional boundary layer is first discussed: two asymptotic layers analogous to the two-dimensional wall and defect layers are observed; they are shown to evolve from the equations of mean motion The hypothesis of scalar eddy viscosity is investigated in the light of these results Using conventional length scale assumptions together with the Reynolds stress tensor equations, a prediction of curvature effects in the law of the wall region is developed; a result in the present case is a smaller slope of the semi-logarithmic portion of the law of the wall, No assumptions over and above those necessary for plane, two-dimensional flow are required for this analysis The geometry of the model is such that a rapid change in mean rate of strain occurs along the streamlines From the history of the components of the tensor, it is possible to draw some fundamental conclusions concerning the dynamics of the energy dissipation, diffusion and redistribution processes

A model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

Abstract: A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.

Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer

Abstract: A detailed study of the intermittency in the outer region of a flat-plate turbulent boundary layer has been carried out using digital sampling and processing techniques. Conditional averages are used to generate mean and fluctuating components for the turbulent and non-turbulent zones of fluid. More particularly, point averages of these variables, taken with reference to the instantaneous position of the turbulent/non-turbulent interface, have been made to show the distribution of various quantities through the turbulent front. The results indicate that significant differences exist at leading and trailing edges of the turbulent bursts and a more complete picture of the motion of an average large eddy is deduced.

Intermittent momentum transport in a geophysical boundary layer

Abstract: THE development of flow visualisation techniques1,2 has prompted a renewal of interest in investigating the dynamics of turbulent boundary layers. The discovery that turbulence is generated intermittently, in “bursts”3, near the wall, is of particular significance. It has also been found that the ejections and inrushes of fluid that accompany the bursts of turbulence generation are dominant contributors to the Reynolds stress4–6. These ejections and inrushes extend well into the flow. It follows that momentum transport in turbulent boundary layers is an intermittent process and that the intermittency is not confined to the region near the wall where most of the turbulence production takes place.

Drag reduction in the turbulent flow of fiber suspensions

Abstract: An analysis of the velocity profile and pressure drop relationships for turbulent flow of fiber suspensions through smooth tubes was evaluated experimentally over a range of flow rates, tube sizes, fiber concentrations, and fiber geometries (aspect ratios). This work shows that drag reduction in these systems, in marked contrast to that in viscoelastic polymeric fluids, involves processes in the turbulent core of the velocity field. As a result the drag reduction achieved is independent of the scale of the system. The implications of these results with respect to rates of heat and mass transport are considered in a preliminary way. The measurement of such transport rates, and of the turbulent velocity profiles in dilute suspensions, is seen to be of mechanistic interest.

Measurements in an incompressible three-dimensional turbulent boundary layer under infinite swept wing conditions and a comparison with theory

Abstract: First a three-dimensional turbulent boundary-layer experiment is described. This experiment has been carried out with the specific aim to provide 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 is subjected to an adverse pressure gradient, which leads to a threedimensional separation near the trailing edge of the plate. Furthermore, a calculation method for three-dimensional turbulent boundary layers is discussed. This calculation method 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. The agreement is good over a considerable distance, but large discrepancies are apparent near the separation line.

Gas Release During Transient Cavitation in Pipes

Abstract: Some applications are presented of a mathematical model concerning water hammer and release of dissolved gas in pipelines in the case where the pressure drops to the vapor pressure of the liquid transported. Column separation and cavitation in extensive parts of the pipeline, referred to as cavitating flow, are dealt with. A smoothing procedure is adopted in order to suppress nonlinear instability. Gas release is found to cause some damping of pressure waves in cases where only cavitating flow occurs. Gas release at a column separation cavity tends to increase the duration of column separation, whereas gas release in a possible cavitating flow region adjacent to the separation diminishes this duration, thus causing considerable damping of pressure peaks following subsequent column separations. Good agreement is obtained with experimental results available in the literature. Further experimentation is required as regards the parameters on which gas release depends.

Measurements in the thick axisymmetric turbulent boundary layer near the tail of a body of revolution

Abstract: Detailed measurements of pressure distributions, mean velocity profiles and Reynolds stresses were made in the thick axisymmetric turbulent boundary layer near the tail of a body of revolution. The results indicate a number of important differences between the behaviour of a thick and a thin boundary layer. The thick boundary layer is characterized by significant variations in static pressure across it and an abnormally low level of turbulence. The static-pressure variation is associated with a strong interaction between the boundary layer and the potential flow outside it, while the changes in the turbulence structure appear to be a consequence of the transverse surface curvature. In order to predict the behaviour of the flow in the tail region of a body of revolution it is not therefore possible to use conventional thin-boundary-layer calculation procedures.

On laminar boundary-layer separation

Abstract: Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for a number of separated flows and the accuracy of the method is verified.

Solutions for laminar boundary layers with separation and reattachment

Abstract: Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified, and the pressure is deduced from the solution. A stream function/vorticity formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by a successive column iteration scheme. Results are compared with Klineberg and Steger's (1974) separated boundary-layer calculations, and with Briley's (1971) solution of the Navier-Stokes equations for a separated region.

Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer under infinite swept wing conditions

Abstract: On a wind tunnel model measurements have been made of the six components of the Reynolds stress tensor in a three-dimensional incompressible turbulent boundary layer under infinite swept wing conditions in an adverse pressure gradient, with a three-dimensional separation near the trailing edge. These measurements complement the mean velocity measurements that were carried out earlier in the same test set-up (NLR TR 72O92 U). The measurements were carried out with a rotatable X-wire probe. An extensive discussion of the errors involved in this type of measurement is given. Turbulence intensities and turbulent shear stresses have been measured From the mean velocity profiles the velocity gradient is derived azid compared with the shear stress magnitude and direction. An interpretation of the results is included.

Semisimilar Solutions to Unsteady Boundary-Layer Flows Including Separation

Abstract: A study is made of a certain class of flows for which semisimilar solutions to the unsteady two-dimensional laminar boundary-layer equations may be obtained. It is shown that such solutions are possible when the velocity at the edge of the boundary layer, ud(x, f), is an arbitrary function of the variable £ where £ is either x/(l — Bt) or (x + Kt)/(l-Bt). If the constant K is choosen properly the latter case represents the same external flow as the former case but observed in a reference system moving with the unsteady separation point. It is possible, therefore, to study the unsteady separation phenomenon in this reference system where separation is most easily identified and analyzed. Numerical solutions have been obtained for an unsteady linearly retarded flow where ud(x, t) = U^ — A^. These solutions verify the Moore-Rott-Sears model for unsteady boundary-layer separation in which separation appears as a point of vanishing shear and velocity, within the boundary layer, in a reference system moving with separation. Solutions such as those presented here may also be used as test cases for the new numerical techniques where unsteady boundary layers are analyzed using three-dimensional finite difference techniques.

New Method for Supersonic Boundary-Layer Separations

Abstract: An efficient numerical solution algorithm is presented for solving the interacting supersonic laminar boundarylayer problem. The method employs a time dependent approach with the alternating direction implicit (ADI) scheme and directly accounts for the necessary downstream boundary condition. Solutions are presented for MOO = 3 cold wall boundary-layer flow over a family of compression ramps with regions of reverse flow. Good comparison is given with experimental data and Navier-Stokes solutions for M^ =4 and 6, adiabatic wall, separated flow up a 10° compression ramp.

Turbulent transport of heat and momentum in a boundary layer subject to deceleration, suction and variable wall temperature

Abstract: The relationship between the turbulent transport of heat and momentum in an adverse pressure gradient boundary layer was studied. An experimental study was conducted of turbulent boundary layers subject to strong adverse pressure gradients with suction. Near-equilibrium flows were attained, evidenced by outer-region similarity in terms of defect temperature and defect velocity profiles. The relationship between Stanton number and enthalpy thickness was shown to be the same as for a flat plate flow both for constant wall temperature boundary conditions and for steps in wall temperature. The superposition principle used with the step-wall-temperature experimental result was shown to accurately predict the Stanton number variation for two cases of arbitrarily varying wall temperature. The Reynolds stress tensor components were measured for strong adverse pressure gradient conditions and different suction rates. Two peaks of turbulence intensity were found: one in the inner and one in the outer regions. The outer peak is shown to be displaced outward by an adverse pressure gradient and suppressed by suction.

Prediction of Turbulent Separated Boundary Layers

Abstract: Theme A integral boundary-layer method is extended to calculation of separated turbulent boundary layers by treating the pressure as a dependent variable and prescribing the wall shear variation. The boundary-layer method and a suitable potential flow method are used in an iterative procedure to produce a method for predicting the characteristics of separated flows. The interaction between the boundary layer and the inviscid flow is accounted for by augmenting the physical surface by the boundary-layer displacement thickness. Good comparisons are shown between the theory and data for a separated turbulent boundary layer on the wall of a transonic wind tunnel.

A review of turbulence measurements in compressible flow

Abstract: A survey of turbulence measurements in compressible flows is presented. The majority of turbulence measurements at super- and hypersonic speeds were made for the zero pressure gradient, turbulent boundary layer. It was found that the nondimensional turbulent stress terms for the zero pressure gradient flow appear to agree closely with equivalent incompressible measurements in the outer part of the boundary layer. The stress terms were nondimensionalized by the wall value of shear stress and plotted versus the distance from the wall, nondimensionalized by the boundary-layer thickness. Indirect evaluation of the total shear stress distribution from mean velocity measurements for both super- and hypersonic flows (zero pressure gradient, two-dimensional flows) indicate a near universal distribution. These total shear stress curves also agree very closely with measured incompressible shear stress distributions. Recent laser anemometer measurements of the turbulent Reynolds shear stress (puv), reported by Johnson and Rose for a Mach number 2.9 flow, are in reasonable agreement with the expected total shear stress curve over the outer 60% of the boundary layer.

Supersonic, Turbulent Boundary-Layer Separation

Abstract: Although the requirements for computer time and disk storage are still large, they are orders of magnitude less than what would be required by numerical solution with the differential formulation, so that some time-dependent, three-dimensional solutions can at least be considered within the present state of computer development. The accurate prediction of body forces at high Reynolds numbers would require unfeasible amounts of computer time and storage with a rectangular constant-mesh coordinate system and is still beyond the present development of the technique. Further work would be desirable to extend the present technique to nonrectangular, and eventually general, nonuniform curvilinear coordinate systems, so that bodies of general shape can be more efficiently treated.

Boundary-Layer Considerations in the Design of Aerodynamic Contractions

Abstract: Most design methods for aerodynamic contractions are based on an inviscid approach even though the flow quality downstream of the contraction is determined primarily by viscous effects, including possible boundary-layer separation. The present study includes the consideration of boundary-layer behavior by application of the Stratford criterion for turbulent separation to numercially computed wall-pressure distributions. Calculations are presented for a four-parameter family of contractions within which the minimum-length contraction shapes consistent with fully attached boundary-layer flow are determined.

Oscillating Laminar Boundary Layers and Unsteady Separation

Abstract: : The unsteady laminar boundary equations are solved numerically for oscillating outer flow velocity distributions. Some characteristic features of oscillating boundary-layers are observed and checked against existing analytical and experimental data. The response of the point of zero skin friction that marks flow reversal on the wall, to various outer flow oscillatory distributions is studied. (Modified author abstract)