Showing papers on "Flow separation published in 1976"
TL;DR: In this article, a theoretical method for calculating far field noise from an airfoil in an incident turbulent flow is extended to apply to the case of noise produced by turbulent flow past a trailing edge, and some minor points of the theory in reference are clarified.
800 citations
TL;DR: In this paper, the wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques, and it was shown that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value.
Abstract: The wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques. Instantaneous velocity measurements indicate a high degree of coherence over a considerable area in the direction normal to the wall. At y+ = 15, there is some evidence of large-scale correlation in the spanwise direction, but almost no indication of the streamwise streaks that exist in the lower regions of the boundary layer. Conditional sampling showed that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value. The conditionally averaged Reynolds shear stress was approximately an order of magnitude greater than its conventionally averaged value and decayed slowly downstream.
661 citations
TL;DR: In this article, the leading edge geometry of an NACA 0012 airfoil has been studied in incompressible flow at moderately large Reynolds numbers and three different types of stall were produced.
Abstract: Dynamic stall and unsteady boundary layer separation have been studied in incompressible flow at moderately large Reynolds numbers. By varying the leading-edge geometry of an NACA 0012 airfoil, three different types of stall were produced. For most of the configurations studied, including the basic NACA 0012 profile, dynamic stall was found not to originate with the bursting of a leading-edge laminar separation bubble, as is commonly believed. Instead, the vortex shedding phenomenon, which is the predominant feature of dynamic stall, appears to be fed its vorticity by the breakdown of the turbulent boundary layer.
462 citations
TL;DR: In this paper, the wave boundary layer was chosen as a subject for detailed velocity measurements, from which characteristics such as shear stresses, eddy viscosities, energy loss, and boundary layer thickness were determined.
Abstract: The oscillatory flow near the sea bed under a wave motion is always rough turbulent in a coastal zone. This type of an oscillatory boundary layer (or “wave boundary layer”) was therefore chosen as a subject for detailed velocity measurements, from which characteristics such as shear stresses, eddy viscosities, energy loss, and boundary layer thickness were determined.
369 citations
TL;DR: In this article, the transition to turbulence in a purely oscillatory pipe flow was performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values in the range from 105 to 5830) and for values with Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·
Abstract: Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and U, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.
357 citations
281 citations
Book•
01 Jan 1976
TL;DR: Incompressible Laminar Boundary Layers in Compressible Flow as discussed by the authors have been shown to be useful in many applications in one-dimensional compressible flow.
Abstract: The Fluid Medium. Kinematics of a Flow Field. Dynamics of Flow Fields. Irrotational Incompressible Flow About Two-Dimensional Bodies. Aerodynamic Characteristics of Airfoils. The Finite Wing. Introduction to Compressible Fluids. Energy Relations. Some Applications of One-Dimensional Compressible Flow. Waves. Linearized Compressible Flow. Airfoils in Compressible Flows. Wings and Wing-Body Combinations in Compressible Flow. The Dynamics of Viscous Fluids. Incompressible Laminar Flow in Tubes and Boundary Layers. Laminar Boundary Layers in Compressible Flow. Flow Instabilities and Transition from Laminar to Turbulent Flow. Turbulent Flows. Airfoil Design, Multiple Surfaces, Vortex Lift, Secondary Flows, Viscous Effects. Appendices. Tables. Oblique Shock Chart. References. Index.
231 citations
TL;DR: In this article, the average shape of a spot and the mean flow field in its vicinity were measured using hot-wire anemometers, showing that the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location.
Abstract: Artificially initiated turbulent spots in a Blasius boundary layer were investi- gated experimentally using hot-wire anemometers. Electrical discharges generated the spots, which grew in all directions rn they were swept downstream by the mean flow. A typical lateral spread angle of the spots is 10° to each side of t.he plane of symmetry. Conditional sampling methods were used to form ensemble-averaged data yielding the average shape of a spot and the mean flow field in its vicinity. Far downstream a spot exhibits conical similarity and all quantities measured seem to be independent of the type of disturbance which generated the spot in the first place.In plan view, the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free-stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location. The trailing interface is convected at a constant velocity throughout (UTE = 0·5 U∞). In this way the spot entrains laminar fluid through both interfaces, resulting in its elongation it proceeds downstream. The flow near the surface accelerates abruptly as the leading interface passes by, however the acceleration continues within the spot and the velocity attains a maximum near the trailing interface. There is therefore a continuous increase in skin friction towards the trailing interface. Further away from the surface the passage of the spot is marked by deceleration followed by acceleration after the ridge of the spot passes the measuring station. All changes in velocity occur monotonically without causing inflexions or kinks in the ensemble-averaged velocity profiles. Although the displacement and momentum thicknesses change quite rapidly within the spot, the shape factor is practically constant in the interior region (H = 1·5); and the velocity profiles may be very well represented by the universal logarithmic distribution. The spanwise velocity component W is everywhere directed outwards (i.e. away from the plane of symmetry) and increases with increasing z. The component of velocity normal to the surface is directed towards the plate near the leading interface and away from it in the remaining part of the spot.Two-point velocity correlation measurements suggest that the spot may be represented by an arrowhead vortex tube which is convected downstream with a velocity equal to 65 yo of the free-stream velocity. Pluid which is entrained near the plane of symmetry acquires a helical motion towards the extremities of the spot. This motion helps to explain the lateral as well as the longitudinal spread of the spot.
191 citations
TL;DR: In this paper, an experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported.
Abstract: An experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported. Special attention is given to the shock-induced separation phenomenon in the turbulent regime. Measurements presented include surface pressures, streamline and flow separation patterns, and shadowgraphs. For a limited range of free-stream Mach numbers the airfoil flow field is found to be unsteady. Dynamic pressure measurements and high-speed shadowgraph movies were taken to investigate this phenomenon. Comparisons of experimentally determined and numerically simulated steady flows using a new viscous-turbulent code are also included. The comparisons show the importance of including an accurate turbulence model. When the shock-boundary layer interaction is weak the turbulence model employed appears adequate, but when the interaction is strong, and extensive regions of separation are present, the model is inadequate and needs further development.
189 citations
TL;DR: In this paper, the stability of Couette and Poiseuille flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow.
Abstract: The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec = 88.53 and rotation number Ro = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro < 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.
173 citations
TL;DR: In this paper, extensive one-point measurements have been made of the turbulence structure of the mixing layer bounding a normally impinging plane jet with an irrotational core, and the most striking feature is that the return is not monotonic: after decreasing in the region of stabilizing curvature, the Reynolds stresses, triple products, energy dissipation rate and other turbulence quantities overshoot the plane-layer values before finally decreasing.
Abstract: As part of a general investigation of complex turbulent flows, extensive one-point measurements have been made of the turbulence structure of the mixing layer bounding a normally impinging plane jet with an irrotational core. The ratio of shear-layer thickness to streamline radius of curvature reaches a maximum of about 0.2, the sense of the curvature being stabilizing. Downstream of the impingement region the shear layer returns asymptotically to being a classical plane mixing layer. The most striking feature of the results is that the return is not monotonic: after decreasing in the region of stabilizing curvature, the Reynolds stresses, triple products, energy dissipation rate and other turbulence quantities overshoot the plane-layer values before finally decreasing. Some conclusions are drawn about the nature of the turbulent transport of Reynolds stress, and about the representation of this and other processes in calculation methods for complex turbulent flows. An incidental result of the work is a comprehensive set of measurements in a plane mixing layer.
TL;DR: In this paper, the effect of confinement on the mean-drag coefficient, root-mean-square values of both the drag and the lift fluctuations, the Strouhal number of the dominant vortex shedding, and the Reynolds number marking transition from laminar to turbulent flow separation were investigated for various blockage percentages over a wide range of Reynolds numbers around the critical value.
Abstract: The fluctuating lift and drag acting on a long, rigidly supported circular cylinder placed symmetrically in a narrow rectangular duct were investigated for various blockage percentages over a wide range of Reynolds numbers around the critical value. The data obtained permit a full assessment of the effect of confinement on the mean-drag coefficient, the root-mean-square values of both the drag and the lift fluctuations, the Strouhal number of the dominant vortex shedding, and the Reynolds number marking transition from laminar to turbulent flow separation. Besides experimental information on a subject on which little is known so far, the paper provides a basis for the deduction of better correction procedures concerning the effects of blockage.
TL;DR: In this paper, an efficient time-splitting, second-order accurate numerical scheme was used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner.
Abstract: An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.
01 Nov 1976
TL;DR: In this paper, a large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts.
Abstract: A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.
TL;DR: In this article, a two-dimensional compression corner and axisymmetric flare geometries were used in a study of shock wave interaction with a compressible turbulent boundary layer.
Abstract: Two-dimensional compression corner and axisymmetric flare geometries were used in this study of shock wave interaction with a compressible turbulent boundary layer. The study was carried out at a Mach number of 2.9 and over a Reynolds number range of 10 5
TL;DR: In this article, the authors show that the increase in measured rms pressure with reduction of transducer size is not nearly as dramatic as previous work has suggested, and they also compare spectral measurements with piezoelectric and pinhole microphone transducers.
Abstract: Directly comparable spectral measurements with piezoelectric and pinhole‐microphone transducers show pinhole measurements to be significantly in error. The increase in measured rms pressure with reduction of transducer size is not nearly as dramatic as previous work has suggested.
TL;DR: In this article, the effect of small amplitude wall roughness on the minimum critical Reynolds number of a laminar boundary layer is studied under the assumptions normally employed in parallel flow stability problems.
Abstract: The effect of small amplitude wall roughness on the minimum critical Reynolds number of a laminar boundary layer is studied under the assumptions normally employed in parallel flow stability problems. The presence of a single Fourier component of roughness enhances the instability of the flow by introducing a point of inflection and increasing the profile curvature at the critical layer, and the effect becomes increasingly important as the wavelength of the roughness component decreases. Numerical calculations show a 10% reduction in minimum critical Reynolds numbers in the presence of small wavelength roughness with an amplitude of only 1% of the boundary layer thickness.
TL;DR: In this paper, the laminar boundary layer flow engendered by a rotating sphere is investigated using finite-difference approximations and the coordinate normal to the boundary layer is stretched to avoid the possibility of "cramping" the layer without having to use an inordinately large number of grid points.
Abstract: The laminar boundary layer flow engendered by a rotating sphere is investigated using finite-difference approximations. The coordinate normal to the boundary layer is stretched to avoid the possibility of “cramping” the layer without having to use an inordinately large number of grid points. Variation of the step lengths enables the inaccuracies due to the finite-difference representations to be quantitatively assessed at each stage. The results are used to consider the details of the inviscid interaction at the equator where the eruption into a radial swirling jet occurs. The computation of the boundary layer is also continued beyond the equator and leads to a three-dimensional boundary-layer separation.
01 Jan 1976
TL;DR: In this article, numerical solutions of the Navier-Stokes equations are presented for the interactions of a shock wave and a turbulent boundary layer, provided by a relaxation eddy viscosity model that approximates the response of turbulence to a severe pressure gradient.
Abstract: Numerical solutions of the Navier-Stokes equations are presented for the interactions of a shock wave and a turbulent boundary layer. The turbulent closure is provided by a relaxation eddy viscosity model that approximates the response of turbulence to a severe pressure gradient. The relaxation eddy viscosity model was successfully applied for a series of compression ramp configurations in a previous investigation by the authors. In the present analysis, further verification of the eddy viscosity model is attempted by investigating shock impingement on a turbulent boundary layer. Computations were performed for shock generators varying from 7.93° to 12.17°, at a freestream Mach number of 2.96 and a Reynolds number of 1.2 x 107. Numerical results obtained with MacCormack's scheme were compared with experimental measurements of the surface pressure distribution and the location of the separation and reattachment points. The density distribution throughout the entire interacting flowfield was also compared with experimental results obtained from holographic interferograms. In general, all essential features of the experimental observation were duplicated by the numerical computation.
TL;DR: In this paper, the authors show that the interaction region near the centre-line consists of a continuously contorting interface between the hot and cold layers, shaped by the eruption of large eddies across the centreline from either side of the duct and surprisingly little affected by the inevitable fine-scale mixing.
Abstract: Measurements have been made of the turbulent flow in a rectangular duct of aspect ratio 12:1 at a Reynolds number (based on duct height h) using conditional-sampling techniques. The lower boundary layer was heated in the entry region, and the fluctuating output of a resistance thermometer was used to distinguish ‘hot’ and ‘cold’ fluid. Thus separate velocity-fluctuation statistics could be obtained for fluid from the upper and lower boundary layers, even after the two layers had merged. The measurements suggest that the interaction region near the centre-line consists of a continuously contorting interface between the ‘hot’ and ‘cold’ layers, shaped by the eruption of large eddies across the centre-line from either side of the duct and surprisingly little affected by the inevitable fine-scale mixing.In the mean, this time-sharing between ‘hot’ and ‘cold’ fluid gives the impression of two superposed turbulence fields whose mean-square intensities add to give the total intensity. Exact superposition (which cannot take place in a nonlinear system) would imply that one layer had the same turbulent intensity profiles as an isolated boundary layer spreading into a non-turbulent free stream with the same mean velocity profile as the duct flow. The centre-line interaction grows in strength with increasing distance downstream until a steady rate of mutual eddy intrusion and fine-scale mixing is achieved, when the flow is commonly called ‘fully developed’. It is concluded that superposition (timesharing) is a physically reasonable first approximation for use in turbulence models for interacting shear layers: it is argued that better approximations could be obtained if necessary by correlating departures from superposition (i.e. changes in turbulence structure) by means of one or more interaction parameters.
TL;DR: In this paper, it was shown that the condition that determines circulation about an airfoil with boundary layers is identical with the usual inviscid-flow condition based on conservation of total circulation and the Kutta-Joukowski condition, in both steady and unsteady flow.
Abstract: It is shown that the condition that determines circulation about an airfoil with boundary layers is identical with the usual inviscid-flow condition based on conservation of total circulation and the Kutta-Joukowski condition, in both steady and unsteady flow. This implies interesting relationships between the viscous and inviscid models, namely, between boundary-layer vorticity and bound-vortex strength, viscous-wake vorticity and freevortex strength, and vortex/vorticity fluxes, in both steady and unsteady flow. The unsteady aerodynamics of airfoils with rounded trailing edges is discussed in this light, and it is concluded that a dual model is needed, involving a boundary-layer calculation over a smooth body to determine circulation, and a vortex-sheet model to determine the perturbed potential flowfield needed in this calculation, as well as forces and moments on the airfoil.
TL;DR: In this paper, the effects of Mach number, Reynolds number, and corner angle on flare-induced separation of a supersonic, turbulent boundary layer were investigated, and a simple correlation formula was obtained and used to compare results from other investigations and also to correlate incipient separation data.
Abstract: Experimental results are presented for the effects of Mach number, Reynolds number, and corner angle on flare-induced separation of a supersonic, turbulent boundary layer. In particular, measurements were obtained for the variation with flare angle, α, of the ratio l_0/δ_0 of the upstream interaction length to the boundary-layer thickness at the beginning of the interaction for Mach numbers 2≤M≤4.5, boundary-layer thickness Reynolds numbers 10^5 < R_δ < 10^6, and adiabatic wall conditions. The model consisted of a hollow cylinder of 12-in. diameter and 51-in. length. Flares of angle 9°≤α≤40° were attached to the cylinder model at either of two location, viz., at x_c= 14 or 28 in. downstream from the sharp leading edge. Measurements consisted chiefly of surface-pressure distributions. Profiles for the undisturbed (flare-off) boundary-layer were also obtained. By varying the several parameters upstream interaction lengths as large as l_0/δ_0 = 30 were observed. It was found that l_0/δ_0 decreases with increasing Mach number and Reynolds number and, of course, increases with flare angle. It was also found that, for constant α, when l_0/δ_0 is plotted vs the local skin-friction coefficient, C_(f0), the Mach-number dependence disappears. From this observation, a simple correlation formula was obtained and used to compare results from other investigations, and also to correlate incipient separation data. The present results complement the incipient-separation data obtained previously by us in the next higher decade of Reynolds number and further confirm the trends established there. It was also found that, for large α, the separated region upstream of the flare has free-interaction characteristics similar to those of upstream-facing steps at high Reynolds number.
TL;DR: In this article, the authors extended Vickery's method for calculating the drag of plane lattice structures normal to a turbulent stream to cases of increased solidity, incorporating an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body.
Abstract: The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data.
TL;DR: In this paper, it is suggested that turbulent drag reduction occurs on a geophysical scale if the flows transport cohesive sediments and that drag reduction is caused by dynamic interaction between turbulent shear strain in the flow and deformation of aggregates.
TL;DR: In this paper, a method was developed to determine the time-dependent flowfield about an impulsively started circular cylinder, where an outer potential flow model was interfaced with an inner viscous flow region.
Abstract: A method is developed to determine the time-dependent flowfield about an impulsively started circular cylinder. An outer potential flow model is interfaced with an inner viscous flow region. The wake is described by a set of elementary point vortices. The position at which the point vortices are shed from the cylinder is obtained from a solution to the unsteady incompressible laminar boundary-layer equations. A rear shear-layer is postulated to account for backflow induced vorticity. Wake development is detailed from the initial formation of the two symmetric vortices to subsequent asymmetry and eventual alternate shedding. Unsteady pressure distributions, lift and drag forces, and Strouhal number are calculated and compared with experiment.