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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Numerical flux formulas for the Euler and Navier-Stokes equations. II - Progress in flux-vector splitting

The accuracy of various numerical flux functions for the inviscid fluxes when used for Navier-Stokes computations is studied. The flux functions are benchmarked for solutions of the viscous, hypersonic flow past a 10 degree cone at zero angle of attack using first order, upwind spatial differencing. The Harten-Lax/Roe flux is found to give a good boundary layer representation, although its robustness is an issue. Some hybrid flux formulas, where the concepts of flux-vector and flux-difference splitting are combined, are shown to give unsatisfactory pressure distributions; there is still room for improvement. Investigations of low diffusion, pure flux-vector splittings indicate that a pure flux-vector splitting can be developed that eliminates spurious diffusion across the boundary layer. The resulting first-order scheme is marginally stable and not monotone.

Coirier, William J.↗
NASA NTRS1999

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

Grossman, Bernard↗
NASA NTRS2007

Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver

A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.

Kuruvila, Geojoe↗
NASA NTRS1990

Prediction of vortical flows on wings using incompressible Navier-Stokes equations

Grid-density and Reynolds-number effects on integral values and static pressure distributions are presently studied in the steady-state Navier-Stokes solutions obtained for the flow around a round-edged double delta wing using an upwind-relaxation finite-difference algorithm. It is found that while the computed longitudinal aerodynamic coefficients are in good agreement with extant experimental data, the magnitudes of suction-pressure peaks are underpredicted in the vicinity of the trailing edge. It is judged that additional computations employing finer-grid solutions in the vortical flow region are required.

Hsu, C.-H.↗
NASA NTRS1985

Three dimensional CSCM method for the compressible Navier-Stokes equations with application to a multi-nozzle exhaust flowfield

The effective design of three-dimensional flow systems such as a clustered multinozzle shrouded exhaust system requires detailed analysis of the internal flowfield. It is pointed out that new numerical techniques on the most modern vector computers are making these analyses practicable. In this paper, the upwind differenced implicit conservative supracharacteristics method (CSCM) for three-dimensional viscous flow is presented. The new method is an implicit 'method of planes' symmetric Gauss-Seidel relaxation scheme. The data is conveniently stored on successive planes along the streamwise coordinate, and the system of equations is solved twice in each successive plane of the streamwise coordinate. The developed new three-dimensional compressible Navier-Stokes algorithm combines the best features of the storage and computationally efficient space marching procedures with the generality of time dependent techniques to solve flows with elliptic and streamwise separated flows.

Bardina, J.↗
DOE OSTI2024

ECAR-7932 Rev 0 Large Eddy Simulation of MARVEL Reactor Core Subchannel to Evaluate Model Uncertainty of Reynolds-Averaged Navier-Stokes Equation Based Computational Fluid Dynamics Analysis

In the previous work (ECAR-7210), the peak cladding temperature of the MARVEL microreactor has been evaluated by steady-state Reynolds-Averaged Navier-Stokes (RANS) based computational fluid dynamics (CFD) simulations. Although numerical uncertainties of RANS-based CFD simulations has been assessed in ECAR-7210, the model uncertainty of RANS turbulence models must be investigated to resolve the issues related to inaccurate prediction of turbulent heat flux and flow pulsation in a tight lattice rod bundle using the steady-state RANS simulations. Consequently, this ECAR conducted a high-fidelity CFD analysis utilizing Large Eddy Simulation (LES) to generate reference data and investigated the model uncertainty of RANS-based CFD simulations.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.

Jothiprasad, Giridhar↗
NASA NTRS1998

Prediction of Unsteady Transitional Layers in Turbomachinery Using Navier Stokes Equations

The objective of the research reported in this presentation is to develop computational techniques for the prediction of unsteady transitional flows associated with the rotor stator interaction in turbomachinery. Three low-Reynolds number turbulence models are incorporated in two unsteady Navier-Stokes codes (one is pressure based and the other is time marching with Runge-Kutta time stepping) and evaluated for accuracy in predicting the onset and the end of unsteady transitional patches due to wake passing. The best model is then used for modification and improvement for the leading edge effect. An existing steady Navier-Stokes code was modified to include pseudo-time stepping, which provided acceleration from 5 to 25 times that of the original code. A systematic validation procedure was implemented to assess the effects of the grid, artificial dissipation, physical, and the pseudo-time step for an accurate prediction of transitional flows resulting from the rotor-stator interaction. The ability of the Navier-Stokes code to predict the unsteady transitional flow on a turbomachinery blade is demonstrated. The unsteady pressure and velocity fields are in good agreement with the experimental data and the prediction from the Euler/boundary layer approach. The numerical solver was able to capture all zones (wake induced transitional strip, wake induced turbulent strip, calmed region, etc.) associated with wake induced transition in a compressor cascade. Another significant step is the assessment of k-epsilon turbulence models, including the leading edge modifications. Best results were obtained from the FLB model. The LB model predicted earlier inception of the transition and shorter transition length. Modification of the k-epsilon model was found to be essential for an accurate prediction of the unsteady transitional flow in a compressor cascade. The CH model failed to predict the unsteady transitional flow. Predicted boundary layer was turbulent from the leading edge, even with the modification of the k-epsilon model near the stagnation point. A comparison of the instantaneous shape factor, the skin friction coefficient, and the momentum thickness indicates that the Navier-Stokes predictions are reasonably good. Interaction between the upstream wake and stator wake results in shedding of unsteady vortices from the trailing edge and increased dissipation in the stator wake and, as a consequence, increased rate of decay of the stator wake. The procedure developed at Penn State should aid the designers of turbomachinery in allowing for the unsteady transitional flows due to rotor-stator interaction.

Lakshminarayana, B.↗
NASA NTRS1986

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and application

The Rai (1984,85) patch-boundary scheme for the Euler equations is described. The integration methods used to update the interior grid points are are discussed. Stability of patch-boundary schemes and the use of these schemes in Navier-Stokes calculations are mentioned. Results for inviscid, supersonic flow over a cylinder, blast wave diffraction by ramp, and the motion of a vortex in a freestream are presented. These test cases demonstrate the quality of solutions possible with the scheme.

Rai, M. M.↗
NASA NTRS1991

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Klopfer, G. H.↗
NASA NTRS1985

Computational aspects of zonal algorithms for solving the compressible Navier-Stokes equations in three dimensions

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.

Holst, T. L.↗
NASA NTRS1993

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Chang, Sin-Chung↗
NASA NTRS1992

Investigation of forced unsteady separated flows using velocity-vorticity form of Navier-Stokes equations

The phenomenon of forced unsteady separation and eruption of boundary-layer vorticity is a highly-complex, high-Reynolds number flow phenomenon, which abruptly leads to the formation of a dynamic stall vortex as demonstrated earlier by the authors for a NACA 0015 airfoil undergoing constant rate pitch-up motion. This, as well as the results of other researchers, have convincingly demonstrated a complex vortical structure within the state of unsteady separation prior to the evolution of dynamic stall. This phenomenon of vortex eruption, although observed in studying dynamic stall phenomena, is also associated with transition from laminar to turbulence flow and its generic nature has been stressed by many researchers including the present investigators. An unsteady Navier-Stokes (NS) analysis is developed for arbitrarily maneuvering bodies using velocity-vorticity variables; this formulation is nearly form-invariant under a generalized non-inertial coordinate transformation. A fully-implicit uniformly second-order accurate method is used, with the nonlinear convective terms approximated using a biased third-order upwind differencing scheme to be able to simulate higher-Re flows. No explicit artificial dissipation is added. The numerical method is fully vectorized and currently achieves a computational index of 7 micro-seconds per time step per mesh point, using a single processor on a CRAY Y-MP. The simulation results show that the energetic free shear from the leading edge is responsible for the wall viscous layer to abruptly erupt near the center of the counterclockwise rotating eddy in the unsteady boundary layer. Primary, secondary, tertiary and quaternary vortices have been observed before the dynamic stall vortex evolves and gathers its maximum strength. This study will discuss the simulation results of Reynolds number up to Re = 45,000 and will also discuss the efforts of initial acceleration in a specific maneuver, on the evolution of the stall vortex.

Ghia, K. N.↗
NASA NTRS1998

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗
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.↗
NASA NTRS1991

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗
NASA NTRS2001

Application of Aeroelastic Solvers Based on Navier Stokes Equations

The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors and turbines.

Keith, Theo G., Jr.↗