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NASA NTRS2000

Parallel performance investigations of an unstructured mesh Navier-Stokes solver

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.

Mavriplis, Dimitri J.↗

NASA NTRS2000

Numerical Simulations of Homogeneous Turbulence Using Lagrangian-Averaged Navier-Stokes Equations

The Lagrangian-averaged Navier-Stokes (LANS) equations are numerically evaluated as a turbulence closure. They are derived from a novel Lagrangian averaging procedure on the space of all volume-preserving maps and can be viewed as a numerical algorithm which removes the energy content from the small scales (smaller than some a priori fixed spatial scale alpha) using a dispersive rather than dissipative mechanism, thus maintaining the crucial features of the large scale flow. We examine the modeling capabilities of the LANS equations for decaying homogeneous turbulence, ascertain their ability to track the energy spectrum of fully resolved direct numerical simulations (DNS), compare the relative energy decay rates, and compare LANS with well-accepted large eddy simulation (LES) models.

Mohseni, Kamran↗

NASA NTRS2011

Modeling Vortex Generators in a Navier-Stokes Code

A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.

Dudek, Julianne C.↗

NASA NTRS1987

Application of an upwind Navier-Stokes code to two-dimensional transonic airfoil flow

An upwind-biased implicit approximate factorization Navier-Stokes algorithm is applied to a variety of steady transonic airfoil cases, using the NACA 0012, RAE 2822, and Jones supercritical airfoils. The thin-layer form of the compressible Navier-Stokes equations is used. Both the CYBER 205 and CRAY 2 supercomputers are utilized, with average computational speeds of about 18 and 16 microsec/gridpoint/iteration, respectively. Lift curves, drag polars, and variations in drag coefficient with Mach number are determined for the NACA 0012 and Jones supercritical airfoils. Also, several cases are computed for comparison with experiment. The effect of grid density and grid extent on a typical turbulent airfoil solution is shown. An algebraic eddy-viscosity turbulence model is used for all of the computations.

Rumsey, Christopher L.↗

NASA NTRS1989

Navier-Stokes Simulation Of Turbine Rotor/Stator Interaction

Patched-grid method used to effect three-dimensional Navier-Stokes numerical simulation of flow interacting with both rotor and stator in turbine. Involves use of two or more grids or sets of grids to solve finite-difference versions of Navier-Stokes or other equations of fluid flow. Ability to perform such calculations contributes to understanding of complicated turbomachinery flows and to consequent improvements in designs of turbomachinery.

Rai, Man Mohan↗

NASA NTRS1987

A new algorithm for the Navier-Stokes equations applied to transonic flows over wings

A new algorithm has been developed for the Navier-Stokes equations. For the convective terms, this algorithm employs flux vector splitting together with a locally rotated coordinate system that is aligned with the streamwise direction. The algorithm has been implemented into a Navier-Stokes code, the NASA Ames Research Center's TNS code, and several cases of steady flow have been calculated. The results show improvements over the original method in the code. First, in a case of separated flow, there is better agreement with the experimental results and also there is an absence of numerical oscillations that occur with the original method. Second, in a case with a strong supersonic to subsonic shock wave, comparisons show an improvement in the resolution of the shock wave and the reexpansion singularity.

Goorjian, Peter M.↗

NASA NTRS1984

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗

NASA NTRS1978

Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.

Warsi, Z. U. A.↗

NASA NTRS1978

An efficient explicit-implicit-characteristic method for solving the compressible Navier-Stokes equations

Explicit, implicit, and characteristic finite-difference methods are applied to solve model equations representative of the compressible Navier-Stokes equations. An approach is then formulated for solving the Navier-Stokes equation at high Reynolds numbers. The approach has drastically reduced the computation time required to obtain viscous flow solutions. Computational results for shock wave separated flows are presented.

Maccormack, R. W.↗

NASA NTRS1987

Navier-Stokes analysis of two- and three-dimensional flow field in solid rocket motors with segment joints

A multidimensional implicit Navier-Stokes analysis which uses numerical solution of ensemble-averaged Navier-Stokes equations in a nonorthogonal bodyfitted cylindrical-polar coordinate system has been applied to simulation of the internal flow field in solid-propellant rocket motor chambers with segment joints. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. Computations performed to simulate the axisymmetric flow field in the vicinity of the aft field joint in the Space Shuttle SRB using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot. Calculations were also performed for two cases involving asymmetric three-dimensional flow in the vicinity of the aft field joint in the SRB using 721,525 grid points to estimate circumferential velocities and pressure gradients at the joint.

Sabnis, J. S.↗

NASA NTRS1994

Navier-Stokes and potential theory solutions for ahelicopter fuselage and comparison with experiment

A thin-layer Navier-Stokes code and a panel method code are used to predict the flow over a generic helicopter fuselage. The computational results are compared with pressure data at four experimental conditions. Both methods produce results that agree with the experimental pressure data. However, separation patterns and other viscous flow features from the Navier-Stokes code solution are shown that cannot be easily modeled with the panel method.

Chaffin, Mark S.↗

NASA NTRS1992

Three-dimensional Navier-Stokes heat transfer predictions for turbine blade rows

Results are shown for a three-dimensional Navier-Stokes analysis of both the flow and the surface heat transfer for turbine applications. Heat transfer comparisons are made with the experimental shock-tunnel data of Dunn and Kim, and with the data of Blair for the rotor of the large scale rotating turbine. The analysis was done using the steady-state, three-dimensional, thin-layer Navier-Stokes code developed by Chima, which uses a multistage Runge-Kutta scheme with implicit residual smoothing. An algebraic mixing length turbulence model is used to calculate turbulent eddy viscosity. The variation in heat transfer due to variations in grid parameters is examined. The effects of rotation, tip clearance, and inlet boundary layer thickness variation on the predicted blade and endwall heat transfer are examined.

Boyle, R. J.↗

NASA NTRS1992

Three-dimensional Navier-Stokes heat transfer predictions for turbine blade rows

Boyle, Robert J.↗

NASA NTRS1975

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Bratanow, T.↗

NASA NTRS1993

Navier-Stokes calculations on multi-element airfoils using a chimera-based solver

A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.

Jasper, Donald W.↗

NASA NTRS1991

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Atkins, Harold↗

NASA NTRS1994

Direct simulation Monte Carlo and Navier-Stokes simulations of blunt body wake flows

Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rare faction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefunction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

WAKE STRUCTURE↗

NASA NTRS1994

Direct simulation Monte Carlo and Navier-Stokes simulations of blunt body wake flows

Numerical results obtained with direct simulation Monte Carlo and Navier-Stokes methods are presented for a Mach-20 nitrogen flow about a 70-deg blunted cone. The flow conditions simuulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how the wake structure changes as a function of rarefaction, what the afterbody levels of heating are, and to what limits the continuum models are realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the after body sting are emphasizes in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗