Showing papers on "Incompressible flow published in 1975"
TL;DR: In this paper, the finite difference procedure and the subgrid scale (SGS) motion model are used to simulate high Reynolds number turbulent flows of incompressible fluids in plane channels and annuli, and the boundary conditions are formulated in a manner consistent with the SGS theory.
1,386 citations
01 Jan 1975
TL;DR: In this article, a finite difference technique is presented for solving the Navier-Stokes equations for an incompressible fluid, based on the Marker-and-Cell method, to facilitate its use by persons with little or no experience in numerical fluid dynamics.
Abstract: : A finite difference technique is presented for solving the Navier-Stokes equations for an incompressible fluid. The technique, based on the Marker-and-Cell method, is simplified to facilitate its use by persons with little or no experience in numerical fluid dynamics. Section I of the report describes the basic algorithm, SOLA, for confined flows; Sec. II describes modifications necessary for free or curved rigid surface boundaries. Each includes a flow chart and a FORTRAN listing. Sample problems show how to incorporate simple modifications into the basic code to adapt it to a variety of problems.
541 citations
TL;DR: In this paper, the shape factor of the boundary layer, d*/0 £ = plate length L = lift m = exponent in Cp=x flows, also lift magnification factor (5.1) M = Mach number p = pressure q = dynamic pressure Q = flow rate R = Reynolds number (= u Ox/v in Stratford flows) R6 = Reynolds Number based on momentum thickness uee/v S = Stratford's separation constant (4.10)
Abstract: c. f = chord fraction, see Eq. (5.1) H = shape factor of the boundary layer, d*/0 £ = plate length L = lift m = exponent in Cp=x flows, also lift magnification factor (5.1) M = Mach number p = pressure q = dynamic pressure Q = flow rate R = Reynolds number (= u Ox/v in Stratford flows) R6 = Reynolds number based on momentum thickness uee/v S = Stratford's separation constant (4.10); also peripheral distance around a body or wing area / = blowing slot gap, also thickness ratio of a body u = velocity in x-direction u0 = initial velocity at start of deceleration in canonical and Stratford flows v = velocity normal to the wall V = a general velocity x = length in flow direction, or around surface of a body measured from stagnation point if used in connection with boundary-layer flow
478 citations
TL;DR: In this article, the Navier−Stokes equations were investigated theoretically under slip-boundary conditions and numerical solutions to the equations were obtained using newly developed computer programs for incompressible fluid flows past elliptic cylinders and oblate spheroids, and the influence of slippage on flow separation, vorticity and vortex shedding, as well as on the force coefficients, was discussed.
Abstract: Laminar flows past bodies under slip−boundary conditions are investigated theoretically within the framework of the Navier−Stokes equations The numerical solutions to the equations are obtained using newly developed computer programs for incompressible fluid flows past elliptic cylinders and oblate spheroids The influence of slippage on flow separation, vorticity, and vortex shedding, as well as on the force coefficients, is discussed
470 citations
Book•
01 Jan 1975
TL;DR: In this paper, the Navier-Stokes Equations were used to model the flow of two Incompressible Non-miscible Viscous Fluids, and the Finite Element method was used to compute the flow.
Abstract: Part I: High-Speed Flows and Grid Adaptation 1.Adaptive Methods in Computational Fluid Dynamics 2.Adaptive Remeshing for Transient Problems With Moving Bodies 3.Finite-Element Solution Scheme for Compressible Viscous Flow 4.Streamline Diffusion Finite-Element Method for Compressible and Incompressile Fluid Flow 5.Alegebraic Grid Generation With Control Points Part 2:Incompressible Flows 6.MIxed Finite-Element Methods for Time-Dependent Problems:Application to Control 7.Numerical Solution of the Navier-Stokes Equations Modeling teh Flow of Two Incompressible Nonmiscible Viscous Fluids 8.Finite-Element Methods for Multiphase and Multicomponen Flows 9.Unsteady Incompressible Flow Computations with the Finite-Element Method 10.Finite-Element Methods for Three-Dimensional Incompressible Viscous Flow PArt 3:Turbulent FLows 11.An Effecient Finite-Element Method for the Computation of Three-Dimensional Turbulent Incompressible Flows 12.Finite-Element Analysis of Enclosed Turbulent Diffusion Flames 13.Analysis of Turbulent Reacting Flows in Combustion 14.Direct Numerical Simulations of a reacting Turbulent Mixing Layer By a Pseudopsectral-Spectral Element Method Part 4:Applications 15.Thermosolutal Convection During Dendritic Solidification of a Binary Alloy 16.New Transient Algorithms for Non-Newtonian Flows 17.Equlibrium, Transport, and Stability of a Plasm in a Tokamak 18.Improved Methodology for Formulating Finite-Element Hydrodynamic Models 19.Magentohydrodynamic Problem in the Aluminum Industry Index
456 citations
TL;DR: In this article, a family of exact solutions to the MHD equations is presented for steady incompressible two-and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams.
Abstract: A family of exact solutions to the MHD equations is presented for steady incompressible two- and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams. The magnetic field in each plasma is strictly parallel to the current sheet, but can have different magnitudes and directions. Resistive and viscous effects are accounted for. These flows are of considerable interest in connexion with the magnetic field merging process. They represent the limit of resistive field annihilation with zero reconnexion.
140 citations
TL;DR: In this paper, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels.
Abstract: In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number.This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn.
138 citations
TL;DR: A wind tunnel study of uniform-density turbulent flow through triangular array rod bundles is described in this paper, where the data include friction factors, local wall shear stresses, and the distributions of mean axial velocity, Reynolds stresses and eddy diffusivities.
121 citations
TL;DR: In this paper, the authors showed that for large values of D, the resistance coefficient γc is much larger than that for the corresponding straight pipe, and the ratio of the entry lengths of the curved pipe and the straight one is proportional to D−1/2 when D is large.
Abstract: A secondary flow is set up when a fluid flows through a stationary curved pipe. The fluid in the middle of the pipe moves outwards and that near the wall inwards. Dean showed that the dynamical similarity of this fully developed flow depends on a non-dimensional parameter is the mean velocity along the pipe, v is the coefficient of kinematic viscosity and a is the radius of the pipe, which is bent into a coil of radius R. Dean's analysis was limited to small values of D. Later, Barua developed an asymptotic boundary-layer theory for large values of D and showed for these values of D that the resistance coefficient γc is much larger than that for the corresponding straight pipe. The present work deals with the flow in a curved pipe as it develops from a uniformly distributed velocity at the entrance to a fully developed profile. Barua's results for the fully developed flow are adopted as downstream conditions in the present work. The ratio of the entry lengths of the curved ipe and the corresponding straight one is shown to be proportional to D−1/2 when D is large. Thus, the entry length for a curved pipe is much shorter than that for the corresponding straight pipe.
112 citations
TL;DR: In this article, the initial flow field of an incompressible, viscous fluid around a circular cylinder, set impulsively to move normal to its axis, is studied in detail, and the nonlinear vorticity equation is solved by the method of matched asymptotic expansions.
Abstract: The initial flow field of an incompressible, viscous fluid around a circular cylinder, set impulsively to move normal to its axis, is studied in detail. The nonlinear vorticity equation is solved by the method of matched asymptotic expansions. Analytic solutions for the stream function in terms of exponential and error functions for the inner flow field, and of circular functions for the outer, are obtained to the third order, from which a uniformly valid composite solution is found. Also presented are the vorticity, pressure, separation point and drag. These quantities agree with the numerical computations of Collins & Dennis. Extended solutions developed by Pade approximants indicate that higher than third-order approximations will yield only minor improvements.
111 citations
TL;DR: In this paper, the effect of compressibility on the mixing layer was investigated at Mach number 2, and the difference between free and wall-bounded mixing layers was discussed. And the development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.
Abstract: The effect of compressibility on the mixing layer was investigated at Mach number 2.47. Pitot pressure, static pressure, and hot-wire surveys were conducted to investigate the mean flow and the fluctuation quantities. Similarities between supersonic and incompressible mixing layers were observed in normalized velocity profile, normalized power spectral density distribution, and convection velocity distribution. Spreading rate, normalized shear stress, and velocity fluctuation were found to be appreciably smaller than the respective incompressible results; e.g., the momentum thickness growth rates are 0.0073 and 0.035 for supersonic and incompressible flows, respectively. The difference between free and wall-bounded mixing layers is discussed. Development of turbulence structure of mixing layer with increasing Reynolds number was also investigated.
TL;DR: In this paper, it was shown that the separation of the pressure strain correlation into a transport and a deviatoric term is not unique, and that the customary separation appears likely to be the wrong choice.
Abstract: It is shown that the separation of the pressure‐strain correlation into a transport and a deviatoric term is not unique, and that the customary separation appears likely to be the wrong choice.
TL;DR: In this article, the McDonald-Fish turbulence model is employed to predict the development of the time-mean flow field, as influenced by the free-stream turbulence level, and a viscous-inviscid interaction model is also employed to account for the elliptic interaction between the shear layer and inviscid free stream.
Abstract: A method is presented for performing detailed computations of thin incompressible separation bubbles on smooth surfaces. The analysis consists of finite-difference solutions to the time-dependent boundary-layer or Navier-Stokes equations for the flow in the immediate vicinity of the bubble. The method employs the McDonald-Fish turbulence model, to predict the development of the time-mean flow field, as influenced by the free-stream turbulence level. It also employs a viscous-inviscid interaction model, which accounts for the elliptic interaction between the shear layer and inviscid free stream. The numerical method is based on an alternating-direction implicit scheme for the vorticity equation. It employs transformations, to allow the free-stream boundary to change in time with the shape of the computed shear layer, and to ensure an adequate resolution of the sublayer region. Numerical solutions are presented for transitional bubbles on an NACA 663-018 airfoil at zero angle of incidence with chordal Reynolds numbers of 2·0 × 106 and 1·7 × 106. These have a qualitative behaviour similar to that observed in numerous experiments; they are also in reasonable quantitative agreement with available experimental data. Little difference is found between steady solutions of the boundary-layer and Navier-Stokes equations for these flow conditions. Numerical studies based on mesh refinement suggest that the well-known singularity at separation, which is present in conventional solutions of the steady boundary-layer equations when the free-stream velocity is specified, is effectively removed when viscous-inviscid interaction is allowed to influence the imposed velocity distribution.
TL;DR: In this paper, a generalized mixed Lagrangian-Eulerian computing technique for incompressible fluid flows is presented, which combines the advantages of two existing techniques such that conservation of both linear and angular momentums is insured.
TL;DR: In this paper, the second-order accurate finite-difference schemes for the Levy-Lees form of the laminar boundary layer equations were investigated for the boundary layer flow with linearly retarded edge velocity.
01 Jan 1975
TL;DR: In this paper, the vorticity distribution is modeled in terms of continuous closed filaments, and it is attempted to track these filaments in a Lagrangian reference frame.
Abstract: Unsteady three-dimensional fluid flows which are characterized by low viscosity and the presence of distinct regions of high vorticity embedded in an otherwise irrotational flow are considered, taking into account the case in which an intermingling of vortex filaments appears. Incompressible flows of the considered type are simulated with the aid of an approach in which the vorticity distribution is modeled in terms of continuous closed filaments. It is attempted to track these filaments in a Lagrangian reference frame.
TL;DR: In this article, a Cartesian orthogonal frame is introduced for viscous incompressible liquid to occupy a volume of three-dimensional Euclidean space E3, where the scale may be chosen in such a way that the density is equal to unity.
Abstract: Let viscous incompressible liquid occupy a volume ~ of three-dimensional Euclidean space E3. Introducing a Cartesian orthogonal frame xl, x2, x3 in E3, we denote a point (xl, x2, x3) by x. Let us denote the velocity and pressure of the liquid at the point x and at the instant t by v(x, t) and p(x, t), respectively, v~(x, t), i-1, 2, 3, being the projections of the velocity on axes x~. The scale may be chosen in such a way that the density is equal to unity. Then according to the Navier-Stokes theory the motion of the liquid caused by external forces f(x, t) will be described by the following system of four equations : 3 v~-vAv+ ~ vkv~,~ = -gradp+f, (1) k=l
TL;DR: In this paper, an expression for the force on a sphere moving with a time-dependent velocity through an incompressible fluid in nonstationary, nonhomogeneous flow is obtained for the case of arbitrary slip on the surface of the sphere.
Abstract: An expression for the force on a sphere moving with a time-dependent velocity through an incompressible fluid in nonstationary, nonhomogeneous flow is obtained for the case of arbitrary slip on the surface of the sphere.
TL;DR: In this paper, the Navier-Stokes equation of motion for two-dimensional, viscous, steady-state incompressible flow past an infinitely long circular cylinder was solved by numerical techniques for Reynolds numbers between 0.1 and 50.
Abstract: The Navier-Stokes equation of motion for two-dimensional, viscous, steady-state incompressible flow past an infinitely long circular cylinder was solved by numerical techniques for Reynolds numbers between 0.1 and 50. From the streamfunction and vorticity fields the pressure at the cylinder surface, the pressure drag, and the frictional drag were computed, and from the latter two the total drag on the cylinder was derived. The values found for the drag compared well with the best theoretical and experimental values reported in literature, suggesting that our flow fields were sufficiently accurate. These flow fields were used to determine the hydrodynamic interaction between simple columnar ice crystals idealized as circular cylinders of finite length L′, of radius aL′, and of Reynolds number NRe,L (67.1≤L′≤2440 µm; 23.5≤ aL′≤146.4 µm;0.2≤NRe,L <20) and spherical water drops of radius aS′ varying between 2 and 134µm. The flow fields used to describe the flow past drops were numerically computed by...
TL;DR: In this paper, the secondary flow in a low aspect ratio incompressible turbulent bounded jet is described in terms of a near, middle, and far field in which the secondary motion is initiated, developed, and decayed, respectively.
Abstract: The secondary flow in a low aspect ratio incompressible turbulent bounded jet is described in terms of a near, middle, and far field in which the secondary motion is initiated, developed, and decayed, respectively. The initiation of the secondary flow is explained by the distortion of the planar vortex loops which bound the jet at the exit plane. In the region away from the bounding plates, the vortex loop distortion is similar to that found in rectangular free jets; however, the bounding plates cause an additional production of streamwise vorticity near the plates which has no counterpart in the free jet flow. Downstream of the jet core region, a large-scale secondary flow developes from this vorticity. Farther downstream the secondary flow decays; the resultant flow may be characterized as a combination of a plane jet and boundary layer flows. This explanation is supported by the vorticity and velocity data of this investigation.
TL;DR: In this article, a simple approximation for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean was proposed.
Abstract: A simple approximation is proposed for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. Approximations for the Lagrangian velocity correlation function and the dispersion are given and compared with exact computer calculations of Kraichnan. Agreement is found to be good except for time-independent velocity fields and singular wavenumber spectral functions.
01 Jan 1975
TL;DR: In this article, numerical solutions for the laminar and turbulent boundary-layer equations for incompressible flows with separation and reattachment are presented, where the separation angularity is avoided by using an inverse technique in which the displacement thickness is prescribed and the pressure is deduced from the resulting solution.
Abstract: Numerical solutions are presented for the laminar and turbulent boundary-layer equations for incompressible flows with separation and reattachment. The separation angularity is avoided by using an inverse technique in which the displacement thickness is prescribed and the pressure is deduced from the resulting solution. The turbulent results appear qualitatively correct despite the use of a two-layer eddy-viscosity model which is generally assumed appropriate only for mild-pressure-gradient flows. A new viscous-inviscid interaction technique is presented in which the inviscid flow is solved inversely by prescribing the pressure from the boundary-layer solution and deducing the new displacement thickness from the solution of a Cauchy integral. Calculations are presented using this interaction procedure for a laminar flow in which separation and reattachment occur on a solid surface.
TL;DR: In this article, the motion of a vortex filament with a narrow core in an inviscid and incompressible fluid otherwise at rest is investigated numerically, and two types of initial conditions, a sinusoidal form with a single Fourier component and that of a superposition of the first and third components, are assumed.
Abstract: Motion of a vortex filament with a narrow core in an inviscid and incompressible fluid otherwise at rest is investigated numerically. Two types of initial conditions, a sinusoidal form with a single Fourier component and that of a superposition of the first and the third components, are assumed. In both cases, interaction between different components occurs owing to the nonlinear property of the governing equation, but the filament does not show random behavior and after a certain time it recurs nearly to the initial state. Analytical treatment is made and the numerical results are confirmed. Next, the case where an external flow field with an axisymmetric potential flow exists is examined, and an onset of randomness is observed. This is considered as due to a computational error amplified through the interaction between the filament and the external flow.
TL;DR: In this article, the axially-symmetric laminar flow of an incompressible viscous fluid resulting from uniform injection through two parallel porous plates is analyzed and exact numerical solution as well as asymptotic solutions for high and low Reynolds numbers are obtained.
Abstract: The axially-symmetric laminar flow of an incompressible viscous fluid resulting from uniform injection through two parallel porous plates is analyzed. An exact numerical solution as well as asymptotic solutions for high and low Reynolds numbers are obtained. It is found that the velocity component normal to the porous plates is everywhere independent of radial position. This property of uniform accessibility may make this flow geometry a useful experimental tool analogous to the rotating disc. The analysis of high Peclet number mass transfer across the center plane of this geometry is presented as an example.
TL;DR: In this article, a numerical technique for solving axisymmetric, incompressible, turbulent swirling flow problems is presented for a coaxial flow configuration of special interest and the calculation results are discussed in regard to their implications for the design of gas turbine combustors.
Abstract: Description of a numerical technique for solving axisymmetric, incompressible, turbulent swirling flow problems. Isothermal flow calculations are presented for a coaxial flow configuration of special interest. The calculation results are discussed in regard to their implications for the design of gas turbine combustors.
TL;DR: In this article, a method for the solution of transient, incompressible viscous flow in two dimensions was described, where dependent variables, stream function and vorticity, were approximated over each triangular element using linear interpolation functions.
01 Feb 1975
TL;DR: In this paper, the spatial stability of two-dimensional incompressible boundary-layer flows is analyzed by using the method of multiple scales, taking into account the streamwise variations of the mean flow, the disturbance amplitude, and the wavenumber.
Abstract: : The spatial stability of two-dimensional incompressible boundary-layer flows is analyzed by using the method of multiple scales. The analysis takes into account the streamwise variations of the mean flow, the disturbance amplitude, and the wavenumber. The theory is applied to the Blasius and the Falkner-Skan flows. For the Blasius flow, the non-parallel analytical results are in good agreement with the experimental data. The results show that the non-parallel effects increase as the pressure gradient decreases.