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NASA NTRS1976

Viscid-inviscid interaction of incompressible separated flows

A flow model has been devised to deal with the viscid-inviscid interaction of a class of two-dimensional incompressible separated flow problems. It is suggested that the corresponding inviscid flow of these problems is described by the free streamline theory with few unspecified parameters and their values are, in turn, determined by the viscous flow considerations. The problem of a flow past a backward facing step is selected for study in detail. The viscous flow components of turbulent jet mixing, recompression, and reattachment are delineated and studied individually. When they are later combined, it is found that the point of reattachment behaves as a saddle-point-type singularity in the system of differential equations describing the viscous flow process. This feature is employed to the determination of the aforementioned free parameters and thus the establishment of the overall corresponding inviscid flow field. The resulting base pressure coefficient for the specific case agrees reasonably well with the available experimental data.

Chow, W. L.↗

NASA NTRS1993

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗

NASA NTRS1989

Time dependent viscous incompressible Navier-Stokes equations

Information on time dependent incompressible Navier-Stokes equations is given in viewgraph form. Information is given on streamfunction equations for unsteady incompressible flow, the streamfunction algorithm for unsteady incompressible flow, and a multigrid solver for the laminar implicit equations.

Goodrich, John W.↗

NASA NTRS1986

Incompressible viscous flow simulations of the NFAC wind tunnel

The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.

Champney, Joelle Milene↗

NASA NTRS1992

Computation of incompressible viscous flows through turbopump components

A finite-difference, three-dimensional, incompressible Navier-Stokes formulation for calculating the flow through turbopump components is presented. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line-relaxation method. Both steady and unsteady flow calculations can be performed using the presented algorithm. In this paper, the equations are solved in steadily rotating reference frames by using the steady-state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using the Baldwin-Lomax model. Numerical results are compared with experimental measurements and good agreement is found between the two. Time-accurate calculations will be reported in future publications.

Kiris, Cetin↗

NASA NTRS1984

Fourier-Legendre spectral methods for incompressible channel flow

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

Zang, T. A.↗

NASA NTRS1981

Weighted-mean scheme for solving incompressible viscous flow

The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.

Huynh, Q. Q.↗

NASA NTRS1984

A solution procedure for three-dimensional incompressible Navier-Stokes equation and its application

An implicit, finite-difference procedure is presented for numerically solving viscous incompressible flows. For convenience of applying the present method to three-dimensional problems, primitive variables, namely the pressure and velocities, are used. One of the major difficulties in solving incompressible flows that use primitive variables is caused by the pressure field solution method which is used as a mapping procedure to obtain a divergence-free velocity field. The present method is designed to accelerate the pressure-field solution procedure. This is achieved by the method of pseudocompressibility in which the time derivative pressure term is introduced into the mass conservation equation. The pressure wave propagation and the spreading of the viscous effect is investigated using simple test problems. The present study clarifies physical and numerical characteristics of the pseudo-compressible approach in simulating incompressible flows. Computed results for external and internal flows are presented to verify the present procedure. The present algorithm has been shown to be very robust and accurate if the selection of the pseudo-compressibility parameter has been made according to the guidelines given.

Kwak, D.↗

NASA NTRS1994

Progress In Incompressible Pump Flow Calculations

Steady and unsteady flows for propulsion systems are efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard kappa - epsilon model equations. The resulting computer code is applied to the flow analysis inside an advanced rocket pump impeller in steadily rotating reference frames. Numerical results are compared with experimental measurements. The effects of exit and shroud cavities with the leak-age flow are investigated. Time-accurate incompressible Navier-Stokes formulation with the overlapped grid scheme capability was evaluated by using MIT flapping foil experiment. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗

NASA NTRS1993

Symmetry breaking in vortical flows over cones - Theory and numerical experiments

A stability analysis suggests that inviscid incompressible flow, independent from angle of attack and regardless whether attached or separated, over slender cones is only marginally stable in regions of decelerating circumferential flow. Reducing slenderness or surface curvature lowers the energy level of harmonic perturbations, and, thus, reduces their impact on the overall stability of flows over slender cones. Associating the notion of instabilities in such flows with the onset of vortex asymmetries provides a model for explaining a variety of flow phenomena in Navier-Stokes simulations of laminar incompressible flows over three right circular cones at moderate to high angles of attack.

Hartwich, Peter M.↗

NASA NTRS1994

Symmetry breaking in vortical flows over cones -- theory and numerical experiments

A stability analysis suggests that inviscid incompressible flow, independent from angle of attack and regardless whether attached or separated, over slender cones is only marginally stable in regions of decelerating circumferential flow. Reducing slenderness or surface curvature lowers the frequency spectrum of the harmonic perturbations and, thus, reduces their impact on the overall stability of flows over slender cones. Associating the notion of instabilities in such flows with the onset of vortex asymmetries provides a model for explaining a variety of flow phenomena in Navier-Stokes simulations of laminar incompressible flows over three right circular cones at moderate to high angles of attack.

Hartwich, Peter M.↗

NASA NTRS1973

Two-dimensional laminar incompressible separated flow past airfoils

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.

Plotkin, A.↗

NASA NTRS1991

A pressure based method for the solution of viscous incompressible turbomachinery flows

A new technique was developed for the solution of the incompressible Navier-Stokes equations. The numerical technique, derived from a pressure substitution method (PSM), overcomes many of the deficiencies of the pressure correction method. This technique allows for the direct solution of the actual pressure in the form of a Poisson equation which is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. Two dimensional internal flows are computed with this method. The prediction of cascade performance is presented. The extention of the pressure correction method for the solution of three dimensional flows is also presented.

Hobson, Garth Victor↗

NASA NTRS1992

A compressible near-wall turbulence model for boundary layer calculations

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects.

So, R. M. C.↗

NASA NTRS1974

Theory of discrete vortex noise

A solution is obtained for the noise induced by vortex shedding from the trailing edge of a semiinfinite flat plate. The method of solution for the potential flow is based on a procedure whereby an inner incompressible flow is matched to an outer acoustic field. Acoustic wave fronts are calculated and compared qualitatively with schlieren photographs of similar flows. The acoustic directivity pattern is obtained, and the extreme sensitivity of this parameter to the incompressible flow near the trailing edge of the plate is investigated.

Davis, S. S.↗

NASA NTRS1992

Incompressible viscous flow computations for the pump components and the artificial heart

A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

Kiris, Cetin↗

NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Gunzburger, M. D.↗

NASA NTRS1980

On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries

An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.

Moin, P.↗