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Showing papers on "Hele-Shaw flow published in 1973"


01 Dec 1973
TL;DR: The literature pertaining to the interaction of a sonic or supersonic gaseous jet with a transverse external flow has been reviewed in this article, where the region upstream of a jet in two-dimensional flow is similar to the flow upstream of forward-facing step and the flow associated with a jet from a circular nozzle in a flat plate resembles the flow past a blunt-nosed slender body.
Abstract: : The literature pertaining to the interaction of a sonic or supersonic gaseous jet with a transverse external flow has been reviewed. The flowfields associated with these interactions are complex, and knowledge of them is based largely on results of experiments. Numerous examples of data from flat-plate experiments are presented. These include static pressure distribution, induced forces, flowfield survey, and flow visualization results. Analyses and correlation techniques for jet interaction flows are discussed. The region upstream of a jet in two-dimensional flow is similar to the flow upstream of a forward-facing step, and the flow associated with a jet from a circular nozzle in a flat plate resembles the flow past a blunt-nosed slender body. The single most important variable in determining the scale of these interactions is the ratio of jet momentum flux to the external-flow dynamic pressure.

64 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined axisymmetric flow of a rotating stream numerically to determine conditions under which an isolated eddy will form on the axis of rotation and provided details of the flow structure and were presented for a range of Reynolds numbers and swirl ratios.

62 citations


01 Mar 1973
TL;DR: In this paper, the time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented in conservative form for both generalized orthogonal and axisymmetric coordinates.
Abstract: The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

57 citations


Journal ArticleDOI
Peter W. Scherer1
TL;DR: The use of a suitably defined critical Reynolds number as an aid in the decision to operate on fusiform aneurysms is noted, as well as the limitations imposed on the experimental and theoretical results by the neglect of flow periodicity and nonhomogeneity.

39 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the separated flow over a finite flat plate when the flow at large distances is given by the stream function ψ_∞ = -xy672 and the plate is situated on the x axis from - 1 to 1.
Abstract: Numerical methods are used to investigate the separated flow over a finite flat plate when the flow at large distances is given by the stream function ψ_∞ = -xy and the plate is situated on the x axis from - 1 to 1. The range of nominal Reynolds number is 10-800. Reduced-mesh calculations are used for fine resolution of the flow field in the immediate vicinity of the separation point. Streamlines, equivorticity lines, and shear stress and pressure gradient at the plate surface illustrate the overall structure of the flow. In each case the streamwise pressure gradient is less than that for undisturbed potential flow and the position of separation is consequently downstream of that predicted by classical boundary layer theory. The boundary-layer structure in the vicinity of the separation point shows a direct transition between the regular upstream behaviour and Dean’s (1950) solution right at separation with no sign whatever of intermediate singular behaviour of the type predicted by Goldstein (1948). The implications of these results for the structure of high Reynolds number, steady, laminar flow are discussed.

23 citations


Journal ArticleDOI
TL;DR: In this paper, the non-symmetric stokes flow past a spherical cap is solved by the method of complementary integral representations, in particular the drag and couple are evaluated for the hemispherical cup.
Abstract: The non symmetric stokes flow past a spherical cap is solved by the method of complementary integral representations. In particular, the drag and couple are evaluated for the hemispherical cup.

21 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the sound attenuation in a lined annular duct with flow and derived the eigenvalue equation in the presence of uniform flow by matching the radial component of the particle displacement and acoustic pressure across a vortex sheet located an infinitely small distance from the facing sheet of an acoustic lining.
Abstract: An investigation is made of the sound attenuation in a lined annular duct with flow. The eigenvalue equation in the presence of uniform flow is derived by matching the radial component of the particle displacement and acoustic pressure across a vortex sheet located an infinitely small distance from the facing sheet of an acoustic lining. The eigenvalue equation in the presence of shear flow is developed by matching the acoustic pressure and the radial component of the particle displacement at the interface between the regions of uniform flow and shear flow. Theoretical prediction of the sound‐attenuation spectrum is based on an acoustic‐energy flow in which the effect of the mean flow is taken into account. The results presented in this paper are limited to those which are typical for the geometry of an annular duct. Effects of mean flow Mach number, boundary‐layer refraction, and acoustic impedance on the sound attenuation for a given duct configuration are found to be similar to those in rectangular‐ an...

20 citations


Book ChapterDOI
TL;DR: In this article, a boundary-layer integral approach is combined with a finite-difference relaxation method to calculate viscous interactions between separated flows at subsonic and transonic velocities.
Abstract: A boundary-layer integral approach is combined with a finite-difference relaxation method to calculate viscous interactions between separated flows at subsonic and transonic velocities Results are obtained for separated laminar flows on circular-arc airfoils at zero angle of attack and are compared with data of Collins (1972) Inviscid and viscous flows are covered

19 citations


Journal ArticleDOI
TL;DR: In this article, the singularities of the limiting streamlines are determined by visual studies of flow through a single layer of spheres, and a flow pattern is suggested for Reynolds numbers close to that for a transition to unsteady flow.

19 citations


Proceedings ArticleDOI
L. Morino1
01 Jan 1973
TL;DR: In this article, a general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented, and an integral representation for the velocity potential is obtained for both supersonic and subsonic flow.
Abstract: The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green's function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. This representation reduces properly to the lifting surface theories as well as to other classical mathematical formulas. Under small perturbation assumption, the potential at any point P in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integrodifferential equation relating the potential and its normal derivative on the surface of the body.

17 citations


01 Jan 1973
TL;DR: In this paper, an integrated turbulent kinetic energy (TKE) equation is solved simultaneously with the integral equations for the mean flow, and axisymmetric flows under consideration were predicted with reasonable accuracy.
Abstract: Mixing of coaxial streams is analyzed by application of integral techniques. An integrated turbulent kinetic energy (TKE) equation is solved simultaneously with the integral equations for the mean flow. Normalized TKE profile shapes are obtained from incompressible jet and shear layer experiments and are assumed to be applicable to all free turbulent flows. The shear stress at the midpoint of the mixing zone is assumed to be directly proportional to the local TKE, and dissipation is treated with a generalization of the model developed for isotropic turbulence. Although the analysis was developed for ducted flows, constant-pressure flows were approximated with the duct much larger than the jet. The axisymmetric flows under consideration were predicted with reasonable accuracy. Fairly good results were also obtained for the fully developed two-dimensional shear layers, which were computed as thin layers at the boundary of a large circular jet.

Journal ArticleDOI
TL;DR: In this article, the authors extended the simplified statistical theory developed earlier to the wall shear flows by formulating the contribution of the smaller eddies to the observable properties, which becomes significant very close to the walls, from an available stochastic analysis of the Navier-Stokes equation.
Abstract: The simplified statistical theory developed earlier is extended to the wall shear flows. This is accomplished by formulating the contribution of the smaller eddies to the observable properties, which becomes significant very close to the wall, from an available stochastic analysis of the Navier‐Stokes equation. Turbulent Couette flow is then analyzed by the use of the theory. Comparison of the Couette flow solutions obtained with the available experimental results shows that the present theory satisfactorily describes the rather detailed turbulence structure of the flow field as well as the mean velocity profile and the surface shear.

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations for flow past a paraboloid of revolution are solved using the ideas of van de Vooren and collaborators, and the flow field has been computed for a large range of Reynolds numbers.

Journal ArticleDOI
TL;DR: A second-order numerical method of characteristics based on a bicharistics scheme was developed for the evaluation of steady, supersonic, nonequilibrium, chemically reacting flows as mentioned in this paper.

Journal ArticleDOI
TL;DR: The method of Fourier transforms is used to determine the kernel function which relates the pressure on a lifting surface to the prescribed downwash within the framework of Dowell's (1971) shear flow model as discussed by the authors.
Abstract: The method of Fourier transforms is used to determine the kernel function which relates the pressure on a lifting surface to the prescribed downwash within the framework of Dowell's (1971) shear flow model This model is intended to improve upon the potential flow aerodynamic model by allowing for the aerodynamic boundary layer effects neglected in the potential flow model For simplicity, incompressible, steady flow is considered The proposed method is illustrated by deriving known results from potential flow theory

01 Jan 1973
TL;DR: In this article, the mixing length model was used to compute 22 test cases on free turbulent shear flows and the calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows.
Abstract: Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.

Journal ArticleDOI
TL;DR: In this paper, the flow fields, temperature fields, and arc boundary shapes of magnetically balanced cross-flow arcs have been determined through the specification of two independent variables (e.g., arc current and mainstream velocity), and using appropriate phenomenological relations.
Abstract: Through the specification of two independent variables (e. g., arc current and mainstream velocity), and using appropriate phenomenological relations, the flow fields, temperature fields, and arc boundary shapes of magnetically balanced cross-flow arcs have been determined. Flow through the arc occurs at lower Reynolds numbers, Reo ~ 1; at higher Reynolds numbers a dividing streamline is formed, inside of which double vortex flow is found. Isotherms are nearly circular for the case of flow through the arc. At the higher Reynolds numbers the isotherms are non-circular throughout the cross-section with major axis transverse to the direction of flow.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Mach number and Reynolds number of the main channel flow will exceed the limits of the incompressible and laminar flow assumptions for suction.

Journal ArticleDOI
TL;DR: In this paper, the linear viscous stability theory for stably stratified parallel shear flow is reviewed and some new results are presented, with emphasis placed on results which demonstrate apparent destabilizing effects of diffusivity which lie beyond the scope of inviscid theory.
Abstract: In this paper the linear viscous stability theory for stably stratified parallel shear flow is reviewed and some new results are presented. Attention is focused on recent work on unbounded flows with emphasis placed on results which demonstrate apparent destabilizing effects of diffusivity which lie beyond the scope of inviscid theory. In particular it is shown that self-excited disturbances may exist with phase speeds lying outside the range of basic flow speed and that with strong thermal diffusivity, instability may occur even though the local Richardson number exceeds 0.25 throughout the flow.

Journal ArticleDOI
TL;DR: The entry flow approximation of the Navier-Stokes equation is discussed and then used to solve the problem of the uniform entry flows at medium or high Reynolds numbers.

Journal ArticleDOI
TL;DR: In this paper, the stability of the viscous flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied, and the critical value of the Reynolds number R is a function of a dimensionless rotation parameter, the Taylor number.
Abstract: The stability of the viscous flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied. The critical value of the Reynolds number R, based on the reduced pressure gradient, is a function of a dimensionless rotation parameter T, the Taylor number. A numerical solution of the eigenvalue problem shows that (i) the minimum point for the viscous instability mode associated with plane Poiseuille flow at T=0 disappears at a value of T of about T≃0.4, and (ii) for T≠0 a new instability mode appears as a result of the Coriolis effect on the basic flow and in the perturbation equations. This new instability gives the critical value of R for values of T as small as 0.06.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the interaction between viscous and inviscid flow fields around a body and present a flow model which has the ability of determining interaction effects wityout the possibility of having to choose between an infinite number of possible solutions.
Abstract: : The problem area of the interaction between the viscous and inviscid flowfields around a body is investigated. The study is based on ascertaining a flow model which has the ability of determining interaction effects wityout the possibility of having to choose between an infinite number of possible solutions. The importance of the inclusion of a two-family characteristic net for the outer supersonic flow and the normal momentum for the inner viscous flow is discussed and the necessity of their inclusion in order to have a properly posed model is presented. A result of the numerical analysis based on the flow model is presented and the uniqueness of such results is discussed.

Journal ArticleDOI
01 Jun 1973
TL;DR: In this article, the authors measured mean velocity, the three components of fluctuating velocity and Reynolds shear stress for the turbulent flow downstream of a wall jet blowing over a backward-facing step.
Abstract: Measurements of mean velocity, the three components of fluctuating velocity and Reynolds shear stress are reported for the turbulent flow downstream of a wall jet blowing over a backward-facing step. The results quantify the complexity of this asymmetric flow and demonstrate the extent to which the slot-lip and backward-facing step destroy the jet-like nature of the flow in the near-slot region. Surface flow visualization experiments demonstrate the influence of the slot flow on the reattachment distance.

Journal ArticleDOI
TL;DR: In this article, an implicit finite-difference scheme of the Navier-Stokes equations was developed to obtain the time variations of three velocity components and of the pressure as boundary conditions vary.
Abstract: Three-dimensional, time-dependent, axisymmetric flows of an incompressible Newtonian fluid in an annular tube as well as in a circular one were analyzed numerically. The flow was produced from rest by a pressure drop between the inlet and the outlet of a finite, annular (or circular) tube which was rotating around its axis. An implicit finite-difference scheme of the Navier-Stokes equations was developed to obtain the time variations of three velocity components and of the pressure as boundary conditions vary. Entrance effects on the velocity field, the pressure, and the Bernoulli-sum were analyzed.

01 Dec 1973
TL;DR: In this article, the complete expression of the interaction force between a gas and solid particles at low Reynolds number flow was obtained from both experimental data and theoretical results of the two-phase flow.
Abstract: From both experimental data and theoretical results of the two-phase flow, the complete expression of the interaction force between a gas and solid particles at low Reynolds number flow is obtained. The interaction force contains two terms: one is proportional to the difference between the velocities of the gas and the solid particle with a coefficient as a function of volume fraction Z and the other is proportional to the product of the total pressure of the mixture and the gradient of solid volume fraction. The second term is new. When Z tends to 0, the completion expression of interaction force reduces to the well-known Stokes formula.

01 Jan 1973
TL;DR: The proceedings of a conference on free turbulent shear flows are presented in this article, where the authors collect and process data for a variety of free mixing problems, assess present theoretical capability for predicting mean velocity, concentration, and temperature distributions in free turbulent flows, identify and recommend experimental studies to advance knowledge of free shear flow, and increase understanding of basic turbulent mixing process for application to free sheer flows.
Abstract: The proceedings of a conference on free turbulent shear flows are presented. Objectives of the conference are as follows: (1) collect and process data for a variety of free mixing problems, (2) assess present theoretical capability for predicting mean velocity, concentration, and temperature distributions in free turbulent flows, (3) identify and recommend experimental studies to advance knowledge of free shear flows, and (4) increase understanding of basic turbulent mixing process for application to free shear flows. Examples of specific cases of jet flow are included.

Journal ArticleDOI
TL;DR: In this article, the behavior of the flow of an electrically conducting viscous fluid past an insulated flat plate at a small incidence, θ, is dealt with by the linearized approximation.
Abstract: The flow of an electrically conducting viscous fluid past an insulated flat plate at a small incidence, θ, is dealt with by the linearized approximation. The behavior of the flow at large values of viscous Reynolds number, R , magnetic Reynolds number, R m , and pressure number, S , is studied. Four characteristic types of flow are shown. In the first case: 1≪ R ≦ O (1/sin θ) and κ 1 =(1+ R m / R )-[(1- R m / R ) 2 +4 R m S / R ] 1/2 >0, the flow field reduces to the conventional potential flow satisfying the Kutta-Joukowski condition. In the second case: 1≪ R ≦ O (1/sin θ) and κ 1 0, the flow field consists of a potential field and a wide wake spreading downstream, where the flow is rotational and the velocity almost vanishes. In the last case: O (1/sin 2 θ)≪ R and κ 1 <0, the flow field consists of two wide wakes spreading both up- and downstream.

Journal ArticleDOI
01 Dec 1973
TL;DR: In this article, the basic equations for fluids with microstructure are applied to the steady flow between two parallel plates under the action of a constant pressure gradient, where the flow is governed by a micro-structure parameter α*.
Abstract: The basic equations for fluids with microstructure are applied to the steady flow between two parallel plates under the action of a constant pressure gradient. The flow is governed by a microstructure parameter α*. The classical flow is recovered when α* → ∞, while maximum effects of microstructure correspond to α* → 0. For a Poiseuille flow, the microstructure fluid exhibits resistance to motion greater than or equal to that of the classical flow. For a Couette flow it is shown that for a given applied velocity to the moving plate, the shearing stress at the plate is greater than or equal to that corresponding to the classical flow situation. For a Generalised Couette flow, it is shown that for a given pressure gradient in the direction of flow, the flow is retarded; while for an adverse pressure gradient the back flow is controlled.

ReportDOI
01 May 1973
TL;DR: In this paper, a finite-difference solution technique has been developed for subsonic two-dimensional inviscid flow past lifting airfoils, where the full governing equations of compressible flow are written in terms of a translated velocity potential, continuous throughout the flow field.
Abstract: : A finite-difference solution technique has been developed for subsonic two-dimensional inviscid flow past lifting airfoils. This work is an adaptation of the method used by Sells (1967). The full governing equations of compressible flow are written in terms of a translated velocity potential which is continuous throughout the flow field. This simplifies solutions for bluff airfoils (no Kutta condition) where both angle of attack and lift coefficient are specified. The computational plane is the interior of a unit circle obtained by mapping the flow field into the interior of the circle. A line over relaxation matrix method is used for solution of the partial differential equation which in the iteration scheme is coupled with an algebraic equation. The numerical procedure is accurate and well behaved for all subsonic flow conditions.

01 Jul 1973
TL;DR: In this paper, an integral form of the boundary layer equations with interaction is used and the interaction between the inviscid and viscous flow fields is provided for by use of a thin-airfoil integral.
Abstract: A method is proposed to treat the problem of steady, two-dimensional, laminar, incompressible high Reynolds number separated flow past thin airfoils. An integral form of the boundary layer equations with interaction is used and the interaction between the inviscid and viscous flow fields is provided for by use of a thin-airfoil integral. Documentation of the attempts at obtaining a solution is presented. A survey of the current state-of-the-art of problems involving viscous-inviscid interactions in flow fields with separation is given.