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At least 109 records · Page 6

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NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗

NASA NTRS1973

Nonlinear vibrations of rectangular plates.

A finite-difference method is developed to determine the large amplitude dynamic responses of thin elastic plates subjected to uniform pressure pulse-type loads. Four different sets of boundary conditions are considered. Some specific problems are solved. The results are compared with approximate solutions obtained by Yamaki (1961). The numerical method presented provides an accurate and efficient approximate solution to the problem, and should be useful as a check on other approximate methods. The grid-size and the time-step necessary for obtaining numerical stability depend on the particular problem. For many cases the method converges rapidly and a rather large grid-size and time-step is adequate.

Bayles, D. J.↗

NASA NTRS1975

Implicit approximate-factorization schemes for the low-frequency transonic equation

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Ballhaus, W. F.↗

NASA NTRS1979

The solution of the three-dimensional viscous-compressible Navier-Stokes equations on a vector computer

The development of a vectorized computer code for the solution of the three-dimensional viscous-compressible Navier-Stokes equations is described. The code is applied on the CDC STAR-100 vector computer which is capable of achieving high result rates when a high degree of parallelism is present in the computations. The computational technique is an explicit time-split MacCormack predictor-corrector algorithm. Since a large volume of data is processed and virtual memory utilized, a data management scheme based on interleaving is used. The program has been applied to obtain the solution of the laminar supersonic flow about a family of three-dimensional corners. The equations of motion are expressed in a generalized form relative to a uniform rectangular computational domain. The metric coefficient and boundary conditions must be supplied for the corresponding physical domain. For calculations with 30,000 grid points, a computational rate of 0.00015 seconds per grid point per time step is observed.

Smith, R. E.↗

NASA NTRS1984

A preliminary study of numerical simulation of thermosolutal convection of interest to crystal growth

Calculations were performed with computer models using three types of finite difference methods of thermosolutal convection: horizontal heating of a container filled with a stably stratified solution, finger convection in a container, and finger convection in a horizontally infinite channel. The importance of including thermosolutal convection in models of crystal growth is emphasized, and the difficulties in doing so are demonstrated. It is pointed out that these difficulties, due primarily to the fine structure of the convection, may be partly overcome by the use of fine grids and implicit time stepping methods.

Miller, T. L.↗

NASA NTRS1986

Upwind Navier-Stokes solutions for separated periodic flows

The application of an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using both the thin-layer and complete forms of the Navier-Stokes equations, the low Reynolds number laminar flow around a circular cylinder with periodic shedding is solved. The effect of grid density, grid extent, and time step on the Strouhal number is shown. Results from both sets of equations agree within the experimental data band. Unsteady, laminar flow computations around inclined plates and separated airfoils are also described. Strouhal numbers agree to within 5 percent of experiments for inclined plates. Differences between the complete equations and the thin-layer approximation for separated periodic flows are discussed. Computations of an impulsively started circular cylinder and airfoil yield time-accurate flowfield shapes in good agreement with experimental flow visualizations. The turbulent computation of an airfoil at a high angle-of-attack is massively separated, but shows no evidence of periodicity.

Rumsey, C. L.↗

NASA NTRS1987

Motion and decay of vortex rings submerged in a rotational flow

The interaction between vortex rings of finite strength and an axisymmetric rotational background flow is studied by a singular perturbation method, because it is difficult to use a finite-difference method to analyze the viscous decay in the small core of a vortex ring. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Euler solution for the background rotational flow. Using the method of averaging, a numerical scheme is developed to obtain an Euler solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the interaction between the trajectories and decay rates of the vortex rings and the background rotational flow.

Ishii, K.↗

NASA NTRS1987

Interaction of a decaying vortex ring with a rotational background flow bounded by a solid wall

The interaction between a vortex ring of finite strength and an axisymmetric rotational background flow bounded by a solid wall is studied by a singular perturbation method. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Navier-Stokes solution for the background rotational flow. Using the method of averaging, numerical scheme is developed to obtain a Navier-Stokes solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the separation of the boundary layer on a solid wall and its interaction with the vortex ring.

Ishii, K.↗

NASA NTRS1993

Finite-Difference Algorithms For Computing Sound Waves

Governing equations considered as matrix system. Method variant of method described in "Scheme for Finite-Difference Computations of Waves" (ARC-12970). Present method begins with matrix-vector formulation of fundamental equations, involving first-order partial derivatives of primitive variables with respect to space and time. Particular matrix formulation places time and spatial coordinates on equal footing, so governing equations considered as matrix system and treated as unit. Spatial and temporal discretizations not treated separately as in other finite-difference methods, instead treated together by linking spatial-grid interval and time step via common scale factor related to speed of sound.

Davis, Sanford↗

NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗

NASA NTRS1993

Dynamic stall of an oscillating wing. Part 1: Evaluation of turbulence models

Unsteady flowfields of a two-dimensional oscillating wing are calculated using an implicit, finite-difference, Navier-Stokes numerical scheme using five widely used turbulence models. The objective of this study is to identify an appropriate turbulence model for accurate simulation of three-dimensional dynamic stall. Three unsteady flow conditions corresponding to attached flow, light-stall, and deep-stall of an oscillating wing experiment were chosen as test cases for computations. Results of unsteady airload hysteresis curves, harmonics of unsteady pressures, and instantaneous flow pictures are presented. Comparison of unsteady airloads with experiment show that all models are deficient in some sense and not a single model predicts all airloads consistently and in agreement with experiment for all flow conditions. For the attached flow condition, the Renormalization Group Theory (RNG), the Johnoson-King (J-K), and the Spalart-Allmaras (S-A) models have better performance. The Baldwin-Lomax (B-L) and the Baldwin-Barth (B-B) models fair poorly. At the light-stall condition, the results for the RNG, the J-K, and S-A models are in agreement with experiment for the upstroke but they all over predict the separation shown by the experiment and therefore have bigger hysteresis loops than experimental results. The B-B model results are also in good agreement for upstroke but have poor lift hysteresis for downstroke. It has superior drag and pitching-moment predictions. For deep-stall conditions, the airloads for the RNG, the B -B, and the S-A models have fair agreement with experiment, but the B-B model performed better at the extreme deep-stall condition. Overall, the RNG model provides significant improvement over the B-L model in all flow regimes with no additional computational cost. The Baldwin-Barth model is the most expensive of the models considered here, costing about 2.5 times that of the Baldwin-Lomax model. Finally, a brief discussion of the effects of grid density, time-step size, and numerical dissipation on the unsteady solutions are also presented.

Srinivasan, G. R.↗

NASA NTRS1996

User's Manual for FOMOCO Utilities-Force and Moment Computation Tools for Overset Grids

In the numerical computations of flows around complex configurations, accurate calculations of force and moment coefficients for aerodynamic surfaces are required. When overset grid methods are used, the surfaces on which force and moment coefficients are sought typically consist of a collection of overlapping surface grids. Direct integration of flow quantities on the overlapping grids would result in the overlapped regions being counted more than once. The FOMOCO Utilities is a software package for computing flow coefficients (force, moment, and mass flow rate) on a collection of overset surfaces with accurate accounting of the overlapped zones. FOMOCO Utilities can be used in stand-alone mode or in conjunction with the Chimera overset grid compressible Navier-Stokes flow solver OVERFLOW. The software package consists of two modules corresponding to a two-step procedure: (1) hybrid surface grid generation (MIXSUR module), and (2) flow quantities integration (OVERINT module). Instructions on how to use this software package are described in this user's manual. Equations used in the flow coefficients calculation are given in Appendix A.

Chan, William M.↗

NASA NTRS1995

Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil

Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.

Srinivasan, G. R.↗

NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗

NASA NTRS1995

Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations

The accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. Nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time sub-iterations. Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.

Rumsey, Christopher L.↗

NASA NTRS1995

Scalability of Parallel Spatial Direct Numerical Simulations on Intel Hypercube and IBM SP1 and SP2

The implementation and performance of a parallel spatial direct numerical simulation (PSDNS) approach on the Intel iPSC/860 hypercube and IBM SP1 and SP2 parallel computers is documented. Spatially evolving disturbances associated with the laminar-to-turbulent transition in boundary-layer flows are computed with the PSDNS code. The feasibility of using the PSDNS to perform transition studies on these computers is examined. The results indicate that PSDNS approach can effectively be parallelized on a distributed-memory parallel machine by remapping the distributed data structure during the course of the calculation. Scalability information is provided to estimate computational costs to match the actual costs relative to changes in the number of grid points. By increasing the number of processors, slower than linear speedups are achieved with optimized (machine-dependent library) routines. This slower than linear speedup results because the computational cost is dominated by FFT routine, which yields less than ideal speedups. By using appropriate compile options and optimized library routines on the SP1, the serial code achieves 52-56 M ops on a single node of the SP1 (45 percent of theoretical peak performance). The actual performance of the PSDNS code on the SP1 is evaluated with a "real world" simulation that consists of 1.7 million grid points. One time step of this simulation is calculated on eight nodes of the SP1 in the same time as required by a Cray Y/MP supercomputer. For the same simulation, 32-nodes of the SP1 and SP2 are required to reach the performance of a Cray C-90. A 32 node SP1 (SP2) configuration is 2.9 (4.6) times faster than a Cray Y/MP for this simulation, while the hypercube is roughly 2 times slower than the Y/MP for this application. KEY WORDS: Spatial direct numerical simulations; incompressible viscous flows; spectral methods; finite differences; parallel computing.

Joslin, Ronald D.↗

NASA NTRS2005

Simulation of Unsteady Flows Using an Unstructured Navier-Stokes Solver on Moving and Stationary Grids

We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.

Biedron, Robert T.↗

NASA NTRS2007

Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

Rupesh, K-A. B.↗