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NASA NTRS1988

Transonic aeroelastic analysis of launch vehicle configurations

A numerical study of the aeroelastic stability of typical launch vehicle configurations in transonic flight is performed. Recent computational fluid dynamics techniques are used to simulate the transonic aerodynamic flow fields, as opposed to relying on experimental data for the unsteady aerodynamic pressures. The flow solver is coupled to an appropriate structural representation of the vehicle. The aerodynamic formulation is based on the thin layer approximation to the Reynolds-Averaged Navier-Stokes equations, where the account for turbulent mixing is done by the two-layer Baldwin and Lomax algebraic eddy viscosity model. The structural-dynamic equations are developed considering free-free flexural vibration of an elongated beam with variable properties and are cast in modal form. Aeroelastic analyses are performed by integrating simultaneously in the two sets of equations. By tracing the growth or decay of a perturbed oscillation, the aeroelastic stability of a given constant configuration can be ascertained. The method is described in detail, and results that indicate its application are presented. Applications include some validation cases for the algorithm developed, as well as the study of configurations known to have presented flutter programs in the past.

Filgueirasdeazevedo, Joao Luiz↗

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 NTRS1988

Three-dimensional incompressible Navier-Stokes computations of internal flows

Several incompressible Navier-Stokes solution methods for obtaining steady and unsteady solutions are discussed. Special attention is given to internal flows which involve distinctly different features from external flows. The characterisitcs of the flow solvers employing the method of pseudocompressibility and a fractional step method are briefly described. This discussion is limited to a primitive variable formulation in generalized curvilinear coordinates. Computed results include simple test cases and internal flow in the Space Shuttle main engine hot-gas manifold.

Kwak, D.↗

NASA NTRS1988

Bipolar coordinates for computation of transition duct flows

Numerical simulation techniques for flows in jet-engine transition ducts with changing cross sections are developed and demonstrated. The boundary-conforming grids required are generated using bipolar coordinates, and the singularities arising at the no-slip boundaries are treated as described by de Vahl Davis (1979) and Tsai and Levy (1987). Grids for several typical configurations are employed in computations with the three-dimensional laminar/turbulent viscous-flow solver of Levy et al. (1983), and the results are presented graphically. The scheme used to deal with singularities is shown to be robust, suggesting that the bipolar grids may be applicable to Navier-Stokes computations.

Madabhushi, R. K.↗

NASA NTRS1989

Computation of viscous incompressible flows

Incompressible Navier-Stokes solution methods and their applications to three-dimensional flows are discussed. A brief review of existing methods is given followed by a detailed description of recent progress on development of three-dimensional generalized flow solvers. Emphasis is placed on primitive variable formulations which are most promising and flexible for general three-dimensional computations of viscous incompressible flows. Both steady- and unsteady-solution algorithms and their salient features are discussed. Finally, examples of real world applications of these flow solvers are given.

Kwak, Dochan↗

NASA NTRS1988

Flow Analysis of Space Shuttle Feed Line 17-inch Disconnect Valve

A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle External Tank/Orbiter propellant feed line disconnect flapper valves with upstream elbows. The full Navier-Stokes code, INS3D, is modified to handle interior obstacles. Grids are generated by SVTGD3D code. Two dimensional initial grids in the flow cross section with and without the flappers are improved by elliptic smoothing to provide better orthogonality, clustering and smoothness to the three dimensional grid. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 x 10(exp 6). The results will serve as a guide to improved design and enhanced testing of the disconnect.

Kandula, Max↗

NASA NTRS1978

Semidirect calculation of steady two- and three-dimensional flows

This paper describes a semidirect method for rapidly solving steady-state viscous flows described by the complete Navier-Stokes equations. The current results are for two-dimensional incompressible flows in general channels at arbitrary Reynolds numbers, but work in progress on compressible and three-dimensional flows is also described. The basic concept of semidirect methods is to use the recently developed fast (direct, or noniterative) linear solvers to solve linearized equations, which are then iterated to solve the nonlinearity. The method used here is an extension of the Split NOS method (Roache, 1975)

Roache, P. J.↗

NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗

NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

NASA NTRS1988

A solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method.

Rosenfeld, Moshe↗

NASA NTRS1976

Recent computation of viscous effects in transonic flow

The paper describes some improvements to a method of solving the time-dependent Reynolds-averaged Navier-Stokes equations for two-dimensional compressible flows for describing the coupling between viscous and inviscid regions in transonic flows. Mesh patching is implemented at the sublayer-boundary layer interfaces and the boundary layer-inviscid flow interface. Mesh stretching is geometric and is small in regions of large gradients and large in regions of small gradients, thus preserving second-order accuracy. Mesh lines are arranged so as to accommodate MacCormack's rapid solver for hyperbolic systems and a wider class of turbulent transport models. Results of computations of transonic flows over lifting airfoils are compared with experimental data and other solutions.

Deiwert, G. S.↗

NASA NTRS1989

Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2

A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.

Swisshelm, Julie M.↗

NASA NTRS1988

Three dimensional flow simulation with application to aeroelastic analysis

The three-dimensional flowfield about realistic launch vehicle configurations is simulated using the Reynolds-averaged Navier-Stokes equations. Turbulent mixing is accounted for by means of the two-layer Baldwin and Lomax (1978) algebraic eddy viscosity model. The Beam and Warming (1976) implicit approximate factorization algorithm is used for the solution of the finite difference equations. Applications include the study of the flowfield about a hemisphere-cylinder configuration both in the subsonic and supersonic flight regimes, and about two hammerhead payload configurations at transonic speeds. A method is also described which permits incorporating this flow solver into a complete algorithm to perform time-domain aeroelastic stability analyses. The vehicle is modeled as a free-free beam and modal superposition techniques are used for the structural-dynamic formulation. Aeroelastic analyses were performed for the hammerhead configurations.

Azevedo, Joao Luiz F.↗

NASA NTRS1989

Numerical solution of unsteady incompressible viscous flows in generalized moving coordinate systems

A solution method of the time-accurate, incompressible Navier-Stokes equations in generalized curvilinear moving coordinate systems is presented in this paper. Accuracy is achieved by a conservative finite-volume discretization which satisfies the geometric conservation laws in generalized moving coordinate systems. The solution method is second-order accurate in space and first-order accurate in time. A fractional step solution method is used to efficiently solve the discrete equations. The unknowns, namely the pressure and the volume-fluxes, are chosen to facilitate the formulation of a consistent Poisson equation and to obtain a robust Poisson solver with favorable convergence properties. The method is validated by comparisons to other numerical and experimental solutions. The comparisons show good agreement.

Rosenfeld, Moshe↗

NASA NTRS1983

Shock-capturing parabolized Navier-Stokes model /SCIPVIS/ for the analysis of turbulent underexpanded jets

A new computational model, SCIPVIS, has been developed to predict the multiple-cell wave/shock structure in under or over-expanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive turbulent mixing process occurring behind the disc are handled in a detailed fashion. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial marching solution can be obtained. The iterative coupling of SCIPVIS with a potential flow solver for the analysis of subsonic/transonic external streams is under development.

Dash, S. M.↗

NASA NTRS1986

Finite element solver for 3-D compressible viscous flows

The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.

Reddy, K. C.↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRS1987

Wall jet analysis for circulation control aerodynamics. Part 1: Fundamental CFD and turbulence modeling concepts

An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented.

Dash, S. M.↗