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At least 127 records · Page 7

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NASA NTRS1987

Algorithm implementation on the Navier-Stokes computer

The Navier-Stokes Computer is a multi-purpose parallel-processing supercomputer which is currently under development at Princeton University. It consists of multiple local memory parallel processors, called Nodes, which are interconnected in a hypercube network. Details of the procedures involved in implementing an algorithm on the Navier-Stokes computer are presented. The particular finite difference algorithm considered in this analysis was developed for simulation of laminar-turbulent transition in wall bounded shear flows. Projected timing results for implementing this algorithm indicate that operation rates in excess of 42 GFLOPS are feasible on a 128 Node machine.

Krist, Steven E.↗

NASA NTRS1987

Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices

Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.

Fujii, K.↗

NASA NTRS1987

Navier Stokes solution of the flowfield over ice accretion shapes

The numerical simulation of flow about ice accretion shapes has been accomplished by solving the Navier-Stokes equations using MacCormack's explicit finite difference scheme. The computations were performed on a CRAY-XMP computer. The influence of turbulence is taken into account by means of an algebraic eddy-viscosity model. In order to optimize the grid spacing and to achieve near orthogonality at the surface of the complex ice shapes, a hyperbolic grid generation scheme is utilized. Particular attention is given to the heat transfer process for which good agreement between the numerical and experimental results is achieved. In addition, liquid water droplet trajectories are coupled within the flowfield along with the resulting collection efficiencies using a parabolized Navier-Stokes formulation.

Scott, J. N.↗

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 NTRS1987

Further comparisons of interactive boundary-layer and thin-layer Navier-Stokes procedures

Calculations of the flows over NACA 4412 and GA(W)-2 airfoils with low-speed flow and over NACA 0012 and RAE 2822 airfoils with transonic flow are reported. They were obtained by solving potential flow and boundary-layer equations, and by solving thin-layer Navier-Stokes equations. The results cover a range of angles of attack up to and including stall and allow the evaluation of the numerical and physical features of the two solution methods. The agreement with measurements is acceptable except between the results of the thin Navier-Stokes equations and measurements in subsonic flow at high angles of attack. The interactive boundary-layer method is considerably more efficient requiring considerably less computer time and storage.

Chang, K. C.↗

NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗

NASA NTRS1987

Solution of the two-dimensional Navier-Stokes equations using sparse matrix solvers

The use of direct sparse matrix solvers in the solution of the Navier-Stokes equations is investigated. The Yale Sparse Matrix Package and its implementation in the solution algorithm is described. The streamfunction-vorticity form of the Navier-Stokes equations are discretized and linearized and the resulting system of equations are solved using this package. Several viscous flow problems are investigated, including flow in a cavity and flow around a NACA0012 airfoil. Massively separated flow around a sine wave airfoil is investigated and high Reynolds number solutions are obtained. A solution of the unsteady flow around a Joukowski airfoil at high angle of attack is presented.

Bender, Erich E.↗

NASA NTRS1987

Steady flow past sudden expansions at large Reynolds number. II - Navier-Stokes solutions for the cascade expansion

The equations of motion in the steady laminar flow past a sudden expansion at large Reynolds number, R, reduce to the boundary layer equations as R tends to the freestream valve, when the longitudinal length scale of the separated eddy increases linearly and indefinitely with R. A global Newton method is presently used to obtain finite difference solutions to the steady Navier-Stokes equations up to R of 1000 for a uniform inflow past a cascade of sudden expansions. For large expansion ratio values, the eddy length increases linearly with R; for smaller values, however, where boundary layer equation solutions could not be found, the steady solutions to the Navier-Stokes equations approach the limit of an inviscid eddy in length with increasing R.

Milos, Frank S.↗

NASA NTRS1987

A comparison of numerical flux formulas for the Euler and Navier-Stokes equations

Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.

Van Leer, Bram↗

NASA NTRS1987

Simulations of transition and turbulence on the Navier-Stokes computer

The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems.

Krist, S. E.↗

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 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 NTRS1987

Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver

The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.

Liu, Jong-Shang↗

NASA NTRS1987

Navier-Stokes computations for circulation control airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, Thomas H.↗

NASA NTRS1988

Implementation and analysis of a Navier-Stokes algorithm on parallel computers

The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.

Fatoohi, Raad A.↗

NASA NTRS1988

Applications of the Navier-Stokes equations to wings and complex configurations using a zonal approach

The simulation of a transonic viscous flow over a series of 3-D configurations, ranging from isolated wings to relatively complete aircraft, is presented. A fast, diagonalized Beam-Warming algorithm is used in conjunction with a zonal approach to solve the Euler/Navier-Stokes equations for these applications. The computer code, called Transonic Navier-Stokes, uses four zones for wing configurations and up to 19 zones for more complete aircraft configurations. For the inner zones adjacent to no-slip surfaces, the thin-layer Navier-Stokes equations are solved, while in the outer zones the Euler equations are solved. Numerical results are presented and compared with experiment (when available) for wing calculations and a more complete configuration based on the F-16A aircraft.

Flores, Jolen↗

NASA NTRS1986

The computation of flow past an oblique wing using the thin-layer Navier-Stokes equations

Essential aspects are presented for computing flow past an oblique wing with the thin-layer Navier-Stokes equations. A new method is developed for generating a grid system around a realistic wing. This method utilizes a series of conformal transformations. The thin-shear-layer approximation and an algebraic eddy-viscosity turbulence model are used to simplify the Reynolds-averaged Navier-Stokes equations. An implicit, factored numerical scheme and the concept of pencil data structure are utilized. For the first time, some flow fields caused by the oblique wing in a supersonic free stream are discussed, emphasizing the separated vortex flows associated with such a wing.

Mehta, Unmeel↗

NASA NTRS1988

A point implicit unstructured grid solver for the Euler and Navier-Stokes equations

An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.

Thareja, Rajiv R.↗