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At least 451 records · Page 25

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NASA NTRS2012

Investigation of Transonic Wake Dynamics for Mechanically Deployable Entry Systems

A numerical investigation of transonic flow around a mechanically deployable entry system being considered for a robotic mission to Venus has been performed, and preliminary results are reported. The flow around a conceptual representation of the vehicle geometry was simulated at discrete points along a ballistic trajectory using Detached Eddy Simulation (DES). The trajectory points selected span the low supersonic to transonic regimes with freestream Mach numbers from 1:5 to 0:8, and freestream Reynolds numbers (based on diameter) between 2:09 x 10(exp 6) and 2:93 x 10(exp 6). Additionally, the Mach 0:8 case was simulated at angles of attack between 0 and 5 . Static aerodynamic coefficients obtained from the data show qualitative agreement with data from 70deg sphere-cone wind tunnel tests performed for the Viking program. Finally, the effect of choices of models and numerical algorithms is addressed by comparing the DES results to those using a Reynolds Averaged Navier-Stokes (RANS) model, as well as to results using a more dissipative numerical scheme.

Stern, Eric↗

NASA NTRS1983

Parabolized Navier-Stokes solutions of separation and trailing-edge flows

A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

Brown, J. L.↗

NASA NTRS1989

Multigrid calculation of three-dimensional turbomachinery flows

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Caughey, David A.↗

NASA NTRS1981

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

NASA NTRS1986

An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows

A new, implicit finite-difference scheme designed to solve the conservative, flux-difference split Navier-Stokes equations is used to compute incompressible vortex flows around delta wings. The completely vectorizable hybrid algorithm is constructed in delta form for steady state solutions independent of the time-step sizes. The scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The governing equations are solved in curvilinear, body-fitted coordinates for treating complex geometries. The computed flow field results are compared with other theoretical and experimental data.

Hartwich, P.-M.↗

NASA NTRS1987

Viscous calculations of supersonic flows past cylinders at angles of attack

Two- and three-dimensional separated flows around cylindrical sections and a body-of-revolution at angles of attack from -10 deg to +20 deg are computed. The blunt-nose-cylinders chosen for the analyses have different configurations, and one of them has a boat-tail. The freestream Mach numbers are 1.5 and 1.6, the unit Reynolds number and the total temperature are 2 million/ft, and 585 R, respectively. Among the possible areas of application for this study are the aerodynamics of separating stores and missiles. The Reynolds-averaged Navier-Stokes equations are solved by an approximately-factored, implicit, upwind-biased, finite-volume algorithm. The convergence to steady state was accelerated using a multigrid strategy. The results helped understanding the structure of the flowfield with varying incidence and configuration, and the suitability of the computational algorithm used for this class of flows. A two-layer algebraic eddy viscosity model is used for the two-dimensional turbulent flows. Laminar three-dimensional calculations are benchmarked through comparisons with wind tunnel test results.

Baysal, O.↗

NASA NTRS1988

Fully-coupled analysis of jet mixing problems. Three-dimensional PNS model, SCIP3D

Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.

Wolf, D. E.↗

NASA NTRS1987

Numerical simulation of three-dimensional unsteady vortex flow using a compact vorticity-velocity algorithm

A numerical algorithm is presented which is used to solve the unsteady, fully three-dimensional, incompressible Navier-Stokes equations in vorticity-velocity variables. A discussion of the discrete approximation scheme is presented as well as the solution method used to solve the resulting algebraic set of difference equations. Second order spatial and temporal accuracy is verified through solution comparisons with exact results obtained for steady three-dimensional stagnation point flow and unsteady axisymmetric vortex spin-up. In addition, results are presented for the problem of unsteady bubble-type vortex breakdown with emphasis on internal bubble dynamics and structure.

Gatski, T. B.↗

NASA NTRS1988

Navier-Stokes calculations of hovering rotor flowfields

Unsteady, thin-layer Navier-Stokes equations written in rotor coordinates are solved using a partially flux-split, implicit numerical algorithm to calculate the flowfields of a hovering rotor blade at subsonic and transonic conditions. Numerical results are in good agreement with experimental data for both nonlifting and lifting rectangular blades. For the lifting case, the rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blades. Alternate methods of calculating the hovering rotor flowfields in blade-fixed mode that have the same circulation distribution as a hovering blade are explored. All of the results presented in this paper were computed on a Cray-2 supercomputer.

Srinivasan, G. R.↗

NASA NTRS1991

Computational studies of a fluid spike as a leading edge protection device for shock-shock interference heating

The effectiveness of a fluid spike as a device to protect leading edges of hypersonic atmospheric flight vehicles from high aerothermal loads produced by complex shock-shock interference is studied. The two-dimensional Navier-Stokes equations are solved using an unstructured cell-centered, fully implicit, flux-difference split algorithm. Adaptively generated unstructured meshes are employed. A type IV shock-shock interference for Mach 8 flow on a cylindrical leading edge with and without a small contraflow supersonic jet (fluid spike) placed at two different locations on the body is solved. A typical flow past a blunt body with a type IV shock-shock interference produces very high pressures and heat fluxes on the leading edge. Present results indicate that a fluid spike displaces the bow shock further in front of the body and modifies the shock-shock interference pattern. This leads to reduced peak pressures and heat fluxes on the body.

Prabhu, Ramadas K.↗

NASA NTRS1992

Research in computational fluid dynamics and analysis of algorithms

Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.

Gottlieb, David↗

NASA NTRS1993

Development of iterative techniques for the solution of unsteady compressible viscous flows

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

Hixon, Duane↗

NASA NTRS1991

Calculation of hypersonic shock structure using flux-split algorithms

There exists an altitude regime in the atmosphere that is within the continuum domain, but wherein the conventional Navier-Stokes equations cease to be accurate. The altitude limits for this so called continuum transition regime depend on vehicle size and speed. Within this regime the thickness of the bow shock wave is no longer negligible when compared to the shock stand-off distance and the peak radiation intensity occurs within the shock wave structure itself. For this reason it is no longer valid to treat the shock wave as a discontinuous jump and it becomes necessary to compute through the shock wave itself. To accurately calculate hypersonic flowfields, the governing equations must be capable of yielding realistic profiles of flow variables throughout the structure of a hypersonic shock wave. The conventional form of the Navier-Stokes equations is restricted to flows with only small departures from translational equilibrium; it is for this reason they do not provide the capability to accurately predict hypersonic shock structure. Calculations in the continuum transition regime, therefore, require the use of governing equations other than Navier-Stokes. Several alternatives to Navier-Stokes are discussed; first for the case of a monatomic gas and then for the case of a diatomic gas where rotational energy must be included. Results are presented for normal shock calculations with argon and nitrogen.

Eppard, W. M.↗

NASA NTRS1993

A comparative study of computational solutions to flow over a backward-facing step

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Mizukami, M.↗

NASA NTRS1996

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗

NASA NTRS2002

Comparison of Evolutionary (Genetic) Algorithm and Adjoint Methods for Multi-Objective Viscous Airfoil Optimizations

A comparison between an Evolutionary Algorithm (EA) and an Adjoint-Gradient (AG) Method applied to a two-dimensional Navier-Stokes code for airfoil design is presented. Both approaches use a common function evaluation code, the steady-state explicit part of the code,ARC2D. The parameterization of the design space is a common B-spline approach for an airfoil surface, which together with a common griding approach, restricts the AG and EA to the same design space. Results are presented for a class of viscous transonic airfoils in which the optimization tradeoff between drag minimization as one objective and lift maximization as another, produces the multi-objective design space. Comparisons are made for efficiency, accuracy and design consistency.

Pulliam, T. H.↗

NASA NTRS1992

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Shuen, J.-S.↗

NASA NTRS1994

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗