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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

The flutter characteristics of the first AGARD standard aeroelastic configuration for dynamic response, Wing 445.6, are studied using an unsteady Navier-Stokes algorithm in order to investigate a previously noted discrepancy between Euler flutter characteristics and the experimental data. The algorithm, which is a three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1), was previously modified for the time-marching, aeroelastic analysis of wings using the unsteady Euler equations. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time integration with the governing flow equations. In this paper, the aeroelastic method is extended and evaluated for applications that use the Navier- Stokes aerodynamics. The paper presents a brief description of the aeroelastic method and presents unsteady calculations which verify this method for Navier-Stokes calculations. A linear stability analysis and a time-marching aeroelastic analysis are used to determine the flutter characteristics of the isolated 45 deg. swept-back wing. Effects of fluid viscosity, structural damping, and number of modes in the structural model are investigated. For the linear stability analysis, the unsteady generalized aerodynamic forces of the wing are computed for a range of reduced frequencies using the pulse transfer-function approach. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. This stability analysis is used to determine the flutter characteristics of the wing at free-stream Mach numbers of 0.96 and 1.141 using the generalized aerodynamic forces generated by solving the Euler equations and the Navier-Stokes equations. Time-marching aeroelastic calculations are performed at a free-stream Mach number of 1.141 using the Euler and Navier-Stokes equations to compare with the linear V-g flutter analysis method. The V-g analysis, which is used in conjunction with the time-marching analysis, indicates that the fluid viscosity has a significant effect on the supersonic flutter boundary for this wing while the structural damping and number of modes in the structural model have a lesser effect.

Lee-Rausch, Elizabeth M.↗
NASA NTRS1995

Progress in incompressible Navier-Stokes computations for propulsion flows and its dual-use applications

Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.

Kiris, Cetin↗
NASA NTRS1990

Navier-Stokes and Euler solutions for lee-side flows over supersonic delta wings. A correlation with experiment

An Euler flow solver and a thin layer Navier-Stokes flow solver were used to numerically simulate the supersonic leeside flow fields over delta wings which were observed experimentally. Three delta wings with 75, 67.5, and 60 deg leading edge sweeps were computed over an angle-of-attack range of 4 to 20 deg at a Mach number 2.8. The Euler code and Navier-Stokes code predict equally well the primary flow structure where the flow is expected to be separated or attached at the leading edge based on the Stanbrook-Squire boundary. The Navier-Stokes code is capable of predicting both the primary and the secondary flow features for the parameter range investigated. For those flow conditions where the Euler code did not predict the correct type of primary flow structure, the Navier-Stokes code illustrated that the flow structure is sensitive to boundary layer model. In general, the laminar Navier-Stokes solutions agreed better with the experimental data, especially for the lower sweep delta wings. The computational results and a detailed re-examination of the experimental data resulted in a refinement of the flow classifications. This refinement in the flow classification results in the separation bubble with the shock flow type as the intermediate flow pattern between separated and attached flows.

Mcmillin, S. Naomi↗
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS1989

Vortical flow computations on swept flexible wings using Navier-Stokes equations

A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of swept flexible wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The calculations are compared with the experiment when available. Effects of flexibility, sweep angle, and pitch rate are demonstrated for flows with vortices.

Guruswamy, Guru P.↗
NASA NTRS1985

Viscous-inviscid interaction computations using a pseudo Navier-Stokes approach

A new method is presented for the computation of viscous-inviscid interaction. The idea is to treat rotational inviscid flow (of which flows are almost entirely composed) in a thorough manner, and accept an approximation treatment of vorticity as introduced by viscous effects. The approach is to numerically solve the Navier-Stokes equations with the viscous terms determined from an inverse boundary-layer solution. The method falls somewhere between a Navier-Stokes approach and an Euler and boundary-layer equation coupling approach; consequently, it is referred to as a pseudo Navier-Stokes approach. Results from both the Navier-Stokes equations and the pseudo Navier-Stokes approach are presented.

Whitfield, D. L.↗
NASA NTRS1988

On multigrid methods for the Navier-Stokes Computer

The overall architecture of the multipurpose parallel-processing Navier-Stokes Computer (NSC) being developed by Princeton and NASA Langley (Nosenchuck et al., 1986) is described and illustrated with extensive diagrams, and the NSC implementation of an elementary multigrid algorithm for simulating isotropic turbulence (based on solution of the incompressible time-dependent Navier-Stokes equations with constant viscosity) is characterized in detail. The present NSC design concept calls for 64 nodes, each with the performance of a class VI supercomputer, linked together by a fiber-optic hypercube network and joined to a front-end computer by a global bus. In this configuration, the NSC would have a storage capacity of over 32 Gword and a peak speed of over 40 Gflops. The multigrid Navier-Stokes code discussed would give sustained operation rates of about 25 Gflops.

Nosenchuck, D. M.↗
NASA NTRS1981

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Smith, R. E.↗
NASA NTRS1999

A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields

A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.

Georgiadis, Nicholas J.↗
NASA NTRS1986

A comparison of interactive boundary-layer and thin-layer Navier-Stokes procedures

Numerical procedures for solving the thin-shear-layer Navier-Stokes equations and for the interaction of solutions to inviscid and boundary-layer equations are described and evaluated. To allow appraisal of the numerical and fluid dynamic abilities of the two schemes, they have been applied to one airfoil as a function of angle of attack at two slightly different Reynolds numbers. The NACA 0012 airfoil has been chosen because it allows comparison with measured lift, drag, and moment and with surface-pressure distributions. Calculations have been performed with algebraic eddy-viscosity formulations, and they include consideration of transition. The results are presented in a form that allows easy appraisal of the accuracy of both procedures and of the relative costs. The interactive procedure is computationally efficient but restrictive relative to the thin-layer Navier-Stokes procedure. The latter procedure does a better job of predicting drag than does the former. In both procedures, the location of transition is crucial for accurate or detailed computations, particularly at high angles of attack. When the upstream influence of pressure field through the shear layer is important, the thin-layer Navier-Stokes procedure has an edge over the interactive procedure.

Mehta, U.↗
NASA NTRS1990

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

Numerical solutions to the incompressible Navier-Stokes equations are in greater demand than ever before as the field of computational fluid dynamics (CFD) increases its impact as an engineering tool. An implicit upwind-relation finite-difference scheme is developed for solving unsteady incompressible Navier-Stokes equations incorporating an artificial time derivative of the pressure to the continuity equation. The essential features observed in experiments for complicated vortical flows past three round-edged low-aspect-ratio wings at high angles of attack are reproduced both qualitatively and quantitatively.

Hsu, C.-H.↗
NASA NTRS1996

Numerical simulation of jet aerodynamics using the three-dimensional Navier-Stokes code PAB3D

This report presents a unified method for subsonic and supersonic jet analysis using the three-dimensional Navier-Stokes code PAB3D. The Navier-Stokes code was used to obtain solutions for axisymmetric jets with on-design operating conditions at Mach numbers ranging from 0.6 to 3.0, supersonic jets containing weak shocks and Mach disks, and supersonic jets with nonaxisymmetric nozzle exit geometries. This report discusses computational methods, code implementation, computed results, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions. The Navier-Stokes method using the standard Jones-Launder two-equation kappa-epsilon turbulence model can accurately predict jet flow, and such predictions are made without any modification to the published constants for the turbulence model.

Pao, S. Paul↗
NASA NTRS1995

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗
NASA NTRS1986

Hypersonic low-density solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip

Solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip are presented along the stagnation streamline under low-density hypersonic flight conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and Direct Simulation Monte Carlo (DSMC) predictions. With the inclusion of surface-slip boundary conditions in NS calculations, the surface heat transfer and other flow field quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. Therefore, the practical range for the applicability of Navier-Stokes solutions is much wider than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods. The NS solutions agree well with the VSL results for altitudes less than 92 km. An assessment is made of the frozen flow approximation employed in the VSL calculations.

Gupta, R. N.↗
NASA NTRS2002

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗
NASA NTRS1999

Application of an Unstructured Grid Navier-Stokes Solver to a Generic Helicopter Boby: Comparison of Unstructured Grid Results with Structured Grid Results and Experimental Results

An unstructured-grid Navier-Stokes solver was used to predict the surface pressure distribution, the off-body flow field, the surface flow pattern, and integrated lift and drag coefficients on the ROBIN configuration (a generic helicopter) without a rotor at four angles of attack. The results are compared to those predicted by two structured- grid Navier-Stokes solvers and to experimental surface pressure distributions. The surface pressure distributions from the unstructured-grid Navier-Stokes solver are in good agreement with the results from the structured-grid Navier-Stokes solvers. Agreement with the experimental pressure coefficients is good over the forward portion of the body. However, agreement is poor on the lower portion of the mid-section of the body. Comparison of the predicted surface flow patterns showed similar regions of separated flow. Predicted lift and drag coefficients were in fair agreement with each other.

Mineck, Raymond E.↗
NASA NTRS1987

Numerical solution of the Navier-Stokes equations about three-dimensional configurations: A survey

The numerical solution of the Navier-Stokes equations about three-dimensional configurations is reviewed. Formulational and computational requirements for the various Navier-Stokes approaches are examined for typical problems including the viscous flow field solution about a complete aerospace vehicle. Recent computed results, with experimental comparisons when available, are presented to highlight the presentation. The future of Navier-Stokes applications in three-dimensions is seen to be rapidly expanding across a broad front including internal and external flows, and flows across the entire speed regime from incompressible to hypersonic applications. Prospects for the future are described and recommendations for areas of concentrated research are indicated.

Holst, Terry L.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

The unaveraged Navier-Stokes equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗