Showing papers on "Flow separation published in 1969"
TL;DR: In this paper, the authors investigate for turbulent flow the fluid motions very near a solid boundary, and to create a physical picture which relates these motions to turbulence generation and transport processes.
Abstract: The objective of this study is to investigate for turbulent flow the fluid motions very near a solid boundary, and to create a physical picture which relates these motions to turbulence generation and transport processes. An experimental technique was developed which permitted detailed observations of the regions very near a pipe wall, including the viscous sublayer, without requiring the introduction of any injection or measuring device into the flow. This technique involved suspending solid particles of colloidal size in a liquid, and photographing their motions with a high-speed motion picture camera moving with the flow. To provide greater detail, the field of view was magnified.Fluid motions were observed to change in character with distance from the wall. The sublayer was continuously disturbed by small-scale velocity fluctuations of low magnitude and periodically disturbed by fluid elements which penetrated into the region from positions further removed from the wall. From a thin region adjacent to the sublayer, fluid elements were periodically ejected outward toward the centreline. Often there was associated with these events a zone of high shear at the interface between the mean flow and the decelerated region that gave rise to the ejected element. When the ejected element entered this shear zone, it interacted with the mean flow and created intense, chaotic velocity fluctuations. These ejections and resulting fluctuations were the most important feature of the wall region, and are believed to be a factor in the generation and maintenance of turbulence.
700 citations
TL;DR: In this article, a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients is described, where the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.
Abstract: This paper describes a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients. In contrast to previous work on this problem the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.Two wall roughness geometries were chosen each giving a different law of behaviour; they were selected on the basis of their reported behaviour in pipe flow experiments. One type gives a Clauser type roughness function which depends on a Reynolds number based on the shear velocity and on a length associated with the size of the roughness. The other type of roughness (typified by a smooth wall containing a pattern of narrow cavities) has been tested in pipes and it is shown here that these pipe results indicate that the corresponding roughness function does not depend on roughness scale but depends instead on the pipe diameter. In boundary-layer flow the first type of roughness gives a roughness function identical to pipe flow as given by Clauser and verified by Hama and Perry & Joubert. The emphasis of this work is on the second type of roughness in boundary-layer flow. No external length scale associated with the boundary layer that is analogous to pipe diameter has been found, except perhaps for the zero pressure gradient case. However, it has been found that results for both types of roughness correlate with a Reynolds number based on the wall shear velocity and on the distance below the crests of the elements from where the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rotta's condition of precise self preserving flow. Some other implications of this are also discussed.
548 citations
TL;DR: In this paper, a rational theory is developed to explain the initial pressure rise and consequent separation of a laminar boundary layer when it interacts with a moderately strong shock, where the region of interest is divided into three parts: the major part of the boundary layer, which is shown to change under largely inviscid forces, the supersonic main stream just adjacent to the boundary surface, and a region close to the wall, on boundary-layer scale, in which the relative variation of the velocity is controlled by the incompressible boundary layer equations.
Abstract: A rational theory is developed to explain the initial pressure rise and consequent separation of a laminar boundary layer when it interacts with a moderately strong shock. In this theory, which is firmly based on the linearized theory of Lighthill (1953), the region of interest is divided into three parts: the major part of the boundary layer, which is shown to change under largely inviscid forces, the supersonic main stream just adjacent to the boundary layer in which the pressure variation is small; and a region close to the wall, on boundary-layer scale, in which the relative variation of the velocity is large but is controlled by the incompressible boundary-layer equations, together with novel boundary conditions. We find that the first two parts can be handled in a straightforward way and the problem of self-induced separation reduces, in its essentials, to the solution of a single problem in the theory of incompressible boundary layers. It is found that this problem has three solutions, one of which corresponds to undisturbed flow and another describes a boundary layer which, spontaneously, generates an adverse pressure gradient and a decreasing skin friction which eventually vanishes and then downstream a reversed flow is set up. The third solution generates a favourable pressure gradient and is not relevant to the present study. Although there has hitherto been no valid numerical method of integrating a boundary layer with reversed flow, we find that an ad hoc method seems to lead to a stable solution which has a number of the properties to be expected of a separated boundary layer. Comparison with experiment gives qualitatively good agreement, but quantitatively errors of the order of 20% are found. It is believed that these errors arise because the Reynolds numbers at which the experiments were carried out are too small.
504 citations
TL;DR: Flow profiles were studied in two successive generations of large scale symmetrical models of typical junctions of the human bronchial tree, suggesting that flow patterns are complex and parabolic flow cannot be assumed.
332 citations
TL;DR: In this article, a model for the drag exerted on a cloud of spherical particles of a given particle size distribution in low Reynolds number flow is derived, where the drag experienced by a particle depends only on the first three moments of the distribution function.
Abstract: A formula for the drag exerted on a cloud of spherical particles of a given particle size distribution in low Reynolds number flow is derived. It is found that the drag experienced by a particle depends only on the first three moments of the distribution function. A treatment of viscous interaction between N particles to the lowest order is carried out systematically. By appealing to the concept of ‘randomness’ of the particle cloud, equations describing the averaged properties of the fluid motion are derived. The averages are formed over a statistical ensemble of particle configurations. These mean flow equations so obtained are in a form resembling a generalized version of Darcy's empirical equation for the motion of fluid in a porous medium. The physical meaning of these equations is discussed.
324 citations
TL;DR: In this article, the rough surface skin-friction relations previously described in the literature are expanded in scope and range of applicability, and the resulting equations are combined with the momemtum integral equation and an auxiliary equation for the shape factor to provide a calculation method for predicting the growth of the turbulent boundary layer over a rough surface in pressure gradient.
Abstract: Rough surface skin-friction relations previously described in the literature are expanded in scope and range of applicability . The resulting equations are combined with the momemtum integral equation and an auxiliary equation for the shape factor to provide a calculation method for predicting the growth of the turbulent boundary layer over a rough surface in pressure gradient. Several comparisons have been made between the calculation method and available experimental data in zero, favorable, and adverse pressure gradients. The agreement in general is good.
168 citations
TL;DR: In this article, Van Driest's theory was extended to turbulent flow near a nonporous wall, which enables the theoretical calculation of velocity profiles to be performed for a wider range of mass transfer rates, and gives good agreement with experimental data.
Abstract: : Van Driest's theory, which provides a continuous velocity and shear distribution for turbulent flow near a nonporous wall, is extended to turbulent flow near a porous wall. The new, modified theory enables the theoretical calculation of velocity profiles to be performed for a wider range of mass- transfer rates, and it gives good agreement with experimental data.
159 citations
TL;DR: In this paper, a rate equation is proposed to govern the variation of the effective turbulent viscosity, and the effects of generation, convection, diffusion, and decay are each represented by appropriate terms leaving only two empirical constants to be determined by experiment.
Abstract: A rate equation is proposed to govern the variation of the effective turbulent viscosity. The effects of generation, convection, diffusion, and decay are each represented by appropriate terms leaving only two empirical constants to be determined by experiment. This rate equation together with the equations of motion form a closed system applicable to quasiparallel turbulent shear flows. For an incompressible turbulent boundary layer with zero pressure gradient, solutions were obtained by assuming local similarity and a linear growth of the boundary‐layer thickness. Another problem, the turbulent‐nonturbulent interface at the outer edge of the boundary layer was treated by using the further assumption that the large scale motion of the interface has no significant contribution to the Reynolds stress. It can be shown that for a nearly homogeneous domain, Prandtl's mixing length theory is a limiting case of the present theory.
130 citations
TL;DR: In this article, the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows is used to show that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy.
Abstract: An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.
Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements of the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction at all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This transitional flow consists of alternating patches of laminar and turbulent fluid, within each of which the flow characteristics are approximately similar to those of Newtonian fluids. At high Reynolds number conditions with the turbulent field fully developed the velocity profile in the core is flatter under drag-reducing conditions than for turbulent Newtonian fluids, a change dependent on the increased isotropy of the turbulent field of the drag-reducing fluid. These effects appear to be a result of increases in the time scales of the radial fluctuations caused by the fluid properties.
Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.
126 citations
TL;DR: In this paper, numerical solutions for incompressible Newtonian flow around a circular cylinder for Reynolds numbers of 1, 2, 4, 10, 15, 30, 50, 100, and 500 were obtained in the form of vorticity and stream function distributions.
Abstract: Numerical solutions have been obtained for incompressible Newtonian flow around a circular cylinder for Reynolds numbers of 1, 2, 4, 10, 15, 30, 50, 100, and 500 The results are presented in the form of vorticity and stream function distributions The solutions allow detailed characterization of the vortex rings Drag coefficients, pressure distributions, and vortex dimensions are compared with experimental data and with available theoretical predictions for Reynolds numbers up to 50 The agreement with both experimental data and previous theoretical solutions is considered to be excellent
121 citations
TL;DR: In this article, oscillatory tests in pitch and in vertical translation were performed on symmetrical and cambered airfoils, at full-scale Reynolds numbers, to provide dynamic stall data for rotor blade analyses.
Abstract: Oscillatory tests in pitch and in vertical translation were performed on symmetrical and cambered airfoils, at full-scale Reynolds numbers, to provide dynamic stall data for rotor blade analyses. The Mach number range applicable to the retreating side of the rotor disk was covered at frequencies up to the first bending and the first torsional natural frequency. A system with a torsional degree of freedom was also tested. The following key results were found: 1) The negative aerodynamic damping due to stall is highly sensitive to Mach number. 2) Negative aerodynamic damping can be encountered in large-amplitu de plunging motions. 3) The maximum normal force encountered during oscillation is substantially higher than that for static stall. In addition, the flow separation process is discussed.
TL;DR: In this paper, a floating element skin friction meter was designed for use in adverse pressure gradients and the effects of secondary forces on the element, which arise from the pressure gradient, were examined in some detail.
Abstract: This paper describes a floating-element skin friction meter which has been designed for use in adverse pressure gradients. The effects of secondary forces on the element, which arise from the pressure gradient, are examined in some detail. The limitations of various methods of measuring wall shear stress are discussed and the results from the floating element device are compared with measurements taken in a two-dimensional boundary layer using Preston tubes and velocity profiles. As it is planned to use the instrument later for direct measurements of the shear stress in three-dimensional boundary layers, the relevance of the instrument to this situation is also discussed.
TL;DR: In this article, the authors proposed a compressed hypersonic turbulent boundary layers solution by finite difference method, relating mixing length to velocity profile shape factor and the mixing length with the shape factor.
Abstract: Compressible hypersonic turbulent boundary layers solution by finite difference method, relating mixing length to velocity profile shape factor
TL;DR: In this paper, the development of the turbulent boundary layer on a disk rotating in free air, using circumferential and radial momentum-integral equations and an auxiliary equation of entrainment, was made.
Abstract: Calculations have been made of the development of the turbulent boundary layer on a disk rotating in free air, using circumferential and radial momentum-integral equations and an auxiliary equation of entrainment. In the calculations, circumferential velocity profiles are represented by Thompson's (1965) two-parameter family, while radial profiles are given by Mager's (1952) quadratic expression. The circumferential component of skin friction follows from the use of Thompson's profile family for the circumferential velocity. The entrainment, in dimensionless form, is assumed to be determined uniquely by the circumferential velocity profile in the same way as was proposed by Head (1958) for a two-dimensional turbulent boundary layer.Detailed measurements have been made of the development of the turbulent boundary layer on the rotating disk, and the calculations are found to be in excellent agreement with the results when a suitable adjustment is made to Head's two-dimensional entrainment curve.
TL;DR: Fluid flow around sphere at high Reynolds number by measuring pressure distribution, considering boundary layer separation, tunnel blockage, etc as mentioned in this paper, and considering boundary layers separation and tunnel blocksage.
Abstract: Fluid flow around sphere at high Reynolds number by measuring pressure distribution, considering boundary layer separation, tunnel blockage, etc
TL;DR: In this paper, the effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated.
Abstract: The effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated. In the analysis, a similarity argument is used and the necessary empirical information obtained from a constant pressure flow. An allowance is made for the departure from the wall value of the gradient of total shear stress normal to the wall. The results of analysis were used to generate new additive constants for use with Townsend's modified law of the wall velocity profile and subsequently Townsend's profile is found to be in good agreement with the measured velocity profiles in an adverse pressure gradient.
TL;DR: In this paper, the authors considered turbulent flow along the axis of a 90° corner and made measurements of velocities, wall shear stresses and, the turbulent normal stress in the streamwise direction.
Abstract: Turbulent flow along the axis of a 90° corner is considered. Experimental measurements of velocities, wall shear stresses and , the turbulent normal stress in the streamwise direction, have been made. The data are considered both from the point of view of momentum integral and similarity analyses. A suitable momentum integral equation is easily derived but difficult to use due to the form of the terms which must be measured. Similarity techniques give a series of correlations which describe the flow over a narrow range of Reynolds number for which data are available. There is experimental evidence for secondary currents in this type of flow but their analysis presents considerable difficulty.
TL;DR: In this paper, the fluctuating pressure in a turbulent boundary layer is used to calculate fuel element response to turbulent parallel flow, and the response of the fuel element is measured by the velocity of the parallel flow.
Abstract: Fuel elements have been observed to vibrate in turbulent parallel flow. Available data describing the fluctuating pressure in a turbulent boundary layer is used to calculate fuel-element response t...
TL;DR: In this article, a method for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow is described, which involves the numerical integration of the equations of motion by an explicit finite-difference method.
Abstract: A method is described for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow. The method involves the numerical integration of the equations of motion by an explicit finite-difference method. The shear stress is determined by a parallel integration of the turbulent energy equation modified by the inclusion of empirical functions of a form which has proved successful in two dimensions, and the additional assumption is made that the turbulent shear stress acts in the direction of the rate of strain of the mean motion. The treatment of the turbulent energy equation follows closely the work of Bradshaw, Ferriss & Atwell (1967) in two dimensions.Comparison with experiment is found to be substantially more difficult than in two dimensions. Particular difficulty is encountered in translating the recorded details of the experiment into boundary conditions for the calculation. The comparisons submitted here give some indication that the method as a whole performs satisfactorily, but they do not provide a definitive assessment of the validity of the basic assumptions. A plea is made for an experiment to supply data in a suitable form for making a more careful assessment of methods of this type.
01 Oct 1969
TL;DR: Flow field and drag characteristics of several laminar boundary layer tripping elements in hypersonic flow were analyzed in this article, showing that the tripping element has better performance than other trippers.
Abstract: Flow field and drag characteristics of several laminar boundary layer tripping element in hypersonic flow
01 Jan 1969
TL;DR: In this paper, it is shown that fully developed turbulent shear flows exhibit a velocity structure that is more coherent than generally expected, and it is possible to detect an ordered, relatively coherent structure that moves randomly in space and time and has characteristic lifetimes and length scales which are much larger than the dissipation scale of the flow.
Abstract: There is increasing evidence that fully developed turbulent shear flows exhibit a velocity structure that is more coherent than generally expected. It is possible to detect an ordered, relatively coherent structure that moves randomly in space and time and has characteristic lifetimes and length scales which are, in general, much larger than the dissipation scale of the flow.
TL;DR: In this paper, a finite-difference method has been developed for the solutions to the governing partial differential equations for the constant-property turbulent boundary layer Prandtl's mixinglength concept was used to express the apparent turbulent shearing stress according to a hypothesized mixing-length distribution through the boundary layer.
Abstract: A finite-differe nce method has been developed for the solutions to the governing partial differential equations for the constant-property turbulent boundary layer Prandtl's mixinglength concept was used to express the apparent turbulent shearing stress according to a hypothesized mixing-length distribution through the boundary layer The model for the mixing-length distribution is in general agreement with experimental data for a variety of flow conditions The method, an always stable explicit finite-difference formulation that requires no iterative procedures, is numerically more direct than other methods recently proposed and is unique in its evaluation of the apparent shearing stress by using an assumed mixing-length distribution as the only empirical input The predicted skin-friction coefficients and velocity profiles agree well with experimental data for the several comparisons made, which included flows in both favorable and adverse pressure gradients as well as flat plate cases with and without blowing The numerical method presented is not restricted to use with the particular mixing-length model tentatively proposed in this work, but can be used to compare various models and help establish their properties and range of applicability, thereby serving to further understanding of the most fundamental aspects of turbulent flow a c Cf gc I
TL;DR: In this paper, the oscillatory laminar flow of a Newtonian fluid in a circular tube has been investigated when the fluid is subjected to a periodic pressure gradient and a technique has been developed which allows the velocity amplitude to be determined as a function of radius.
Abstract: The oscillatory laminar flow of a Newtonian fluid in a circular tube has been investigated when the fluid is subjected to a periodic pressure gradient. A technique has been developed which allows the velocity amplitude to be determined as a function of radius and the results agree closely with theoretical predictions. The work is being continued with a view to employing the technique for the determination of the rheological properties of viscoelastic fluids.
01 Apr 1969
TL;DR: Turbulent boundary layer laminarization in conical nozzle flow, measuring velocity profiles and friction coefficient was performed in this article, where the velocity profiles were measured by measuring the friction coefficient.
Abstract: Turbulent boundary layer laminarization in conical nozzle flow, measuring velocity profiles and friction coefficient
TL;DR: In this article, a considerable body of experimental data now exists concerning turbulent boundary layers with air injection at the wall, both at subsonic and at supersonic speeds, and these data for Mach numbers up to 6·5 have been analyzed to find the parameters which occur in the law of the wall as deduced from mixing-length theory.
Abstract: A considerable body of experimental data now exists concerning turbulent boundary layers with air injection at the wall, both at subsonic and at supersonic speeds. In the present report these data for Mach numbers up to 6·5 have been analyzed to find the parameters which occur in the law of the wall as deduced from mixing-length theory. Although the absolute values of the parameters are subject to error because of the lack of accurate skin-friction measurements, the trends of these parameters with Mach number and injection mass flow are clearly defined.
01 Jan 1969
TL;DR: Mean velocity and mean turbulent energy field methods of calculating boundary layer behavior based on numerical solutions of equations of motions have been used to calculate boundary layer behaviour as discussed by the authors, and they have been shown to be useful for boundary layer detection.
Abstract: Mean velocity and mean turbulent energy field methods of calculating boundary layer behavior based on numerical solutions of equations of motions
01 Jun 1969
TL;DR: In this paper, skin friction and heat transfer data for hypersonic turbulent layer on flat plates, wind tunnel wall, and cones were used to estimate the heat transfer rate of the turbulent layer.
Abstract: Skin friction and heat transfer data for hypersonic turbulent layer on flat plates, wind tunnel wall, and cones