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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A comparative study of Full Navier-Stokes and Reduced Navier-Stokes analyses for separating flows within a diffusing inlet S-duct

A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier Stokes (RNS) initial value space marching solution technique has been applied to a class of separated flow problems within a diffusing S-duct configuration characterized by vortex-liftoff. Both the FNS and the RNS solution technique were able to capture the overall flow physics of vortex lift-off, and gave remarkably similar results which agreed reasonably well with the experimental measured averaged performance parameters of engine face total pressure recovery and distortion. However, the Full Navier-Stokes and Reduced Navier-Stokes also consistently predicted separation further downstream in the M2129 inlet S-duct than was indicated by experimental data, thus compensating errors were present in the two Navier-Stokes analyses. The difficulties encountered in the Navier-Stokes separations analyses of the M2129 inlet S-duct center primarily on turbulence model issues, and these focused on two distinct but different phenomena, namely, (1) characterization of low skin friction adverse pressure gradient flows, and (2) description of the near wall behavior of flows characterized by vortex lift-off.

Anderson, B. H.↗
NASA NTRS1993

A comparative study of full Navier-Stokes and Reduced Navier-Stokes analyses for separating flows within a diffusing inlet S-duct

A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier-Stokes (RNS) initial value space marching solution technique has been applied to a class of separate flow problems within a diffusing S-duct configuration characterized as vortex-liftoff. Both Full Navier-Stokes and Reduced Navier-Stokes solution techniques were able to capture the overall flow physics of vortex lift-off, however more consideration must be given to the development of turbulence models for the prediction of the locations of separation and reattachment. This accounts for some of the discrepancies in the prediction of the relevant inlet distortion descriptors, particularly circumferential distortion. The 3D RNS solution technique adequately described the topological structure of flow separation associated with vortex lift-off.

Anderson, B. H.↗
NASA NTRS1982

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Rubin, S. G.↗
NASA NTRS1984

Incompressible Navier-Stokes and parabolized Navier-Stokes formulations and computational techniques

The differential formulations and computational techniques currently used for the incompressible Navier-Stokes (NS) and parabolic Navier-Stokes (PNS) equations are reviewed. In particular, attention is given to problems associated with the choice of difference equations, the method of solution and the choice of algorithm, the coupling of dependent variables and discretized equations, the application of boundary conditions, and grid generation. A new composite velocity NS and PNS formulation in (u,v,p) variables is presented, and the applicability of a 'forward' difference global pressure iteration for the (u,v,p) PNS system is demonstrated.

Rubin, S. G.↗
NASA NTRS1989

Thickening oscillation of a delta wing using Navier-Stokes and Navier-displacement equations

The problem of unsteady, supersonic, locally conical, vortical flow around a delta wing undergoing thickening oscillation is solved using the unsteady, thin-layer Navier-Stokes equations and the unsteady linearized Navier-displacement equations. The unsteady, thin-layer Navier-Stokes equations are solved using the implicit approximate-factorization finite-volume scheme to compute the conservative components of the flow vector field. With the conservative components known at any time step, the linearized, Navier-displacement equations are solved using the alternating, direction-implicit scheme to obtain the grid points displacements due to known displacement boundary conditions. A grid-displacements limiter, in the form of a low mesh Reynolds number, is used to limit grid-folding in regions of highly reversed flow.

Chuang, Hsin-Kung A.↗
NASA NTRS1985

Stable boundary conditions and difference schemes for Navier-Stokes equations

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Dutt, P.↗
NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗
NASA NTRS1983

Applications of the contravariant form of the Navier-Stokes equations

The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components.

Katsanis, T.↗
NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗
NASA NTRS1980

A remarkable operator version of the Navier-Stokes equation

The Navier-Stokes equation is transformed into a closed nonlinear equation for the convected curl operator. It is shown how Lie algebraic methods can be employed to solve the obtained double-commutator equation. The proposed operator equation provides a way to the further development of the Navier-Stokes fluid flow theory.

Rosen, G.↗
NASA NTRS1987

Algorithm implementation on the Navier-Stokes computer

The Navier-Stokes Computer is a multi-purpose parallel-processing supercomputer which is currently under development at Princeton University. It consists of multiple local memory parallel processors, called Nodes, which are interconnected in a hypercube network. Details of the procedures involved in implementing an algorithm on the Navier-Stokes computer are presented. The particular finite difference algorithm considered in this analysis was developed for simulation of laminar-turbulent transition in wall bounded shear flows. Projected timing results for implementing this algorithm indicate that operation rates in excess of 42 GFLOPS are feasible on a 128 Node machine.

Krist, Steven E.↗
NASA NTRS2005

Factorization of the Compressible Navier-Stokes Equations

The Navier-Stokes equations for a Newtonian ideal gas are examined to determine the factorizable form of the equations relevant to the construction of a factorizable relaxation scheme. The principal linearization of the equations is found by examining the relative magnitude of the terms for short-wavelength errors. The principal part of the operator is then found. Comparison of the factors of the Navier-Stokes and Euler equations differ qualitatively because of the coupling of entropy and pressure through thermal diffusion. Special cases of the factorization are considered.

Roberts, Thomas W.↗
NASA NTRS1987

Simulations of transition and turbulence on the Navier-Stokes computer

The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems.

Krist, S. E.↗
NASA NTRS1998

Ducted-Fan Engine Acoustic Predictions Using a Navier-Stokes Code

A Navier-Stokes computer code is used to predict one of the ducted-fan engine acoustic modes that results from rotor-wake/stator-blade interaction. A patched sliding-zone interface is employed to pass information between the moving rotor row and the stationary stator row. The code produces averaged aerodynamic results downstream of the rotor that agree well with a widely used average-passage code. The acoustic mode of interest is generated successfully by the code and is propagated well upstream of the rotor, temporal and spatial numerical resolution are fine enough such that attenuation of the signal is small. Two acoustic codes are used to find the far-field noise. Near-field propagation is computed by using Eversman's wave envelope code, which is based on a finite-element model. Propagation to the far field is accomplished by using the Kirchhoff formula for moving surfaces with the results of the wave envelope code as input data. Comparison of measured and computed far-field noise levels show fair agreement in the range of directivity angles where the peak radiation lobes from the inlet are observed. Although only a single acoustic mode is targeted in this study, the main conclusion is a proof-of-concept: Navier Stokes codes can be used both to generate and propagate rotor-stator acoustic modes forward through an engine, where the results can be coupled to other far-field noise prediction codes.

Rumsey, C. L.↗
NASA NTRS1998

Ducted-Fan Engine Acoustic Predictions using a Navier-Stokes Code

A Navier-Stokes computer code is used to predict one of the ducted-fan engine acoustic modes that results from rotor-wake/stator-blade interaction. A patched sliding-zone interface is employed to pass information between the moving rotor row and the stationary stator row. The code produces averaged aerodynamic results downstream of the rotor that agree well with a widely used average-passage code. The acoustic mode of interest is generated successfully by the code and is propagated well upstream of the rotor; temporal and spatial numerical resolution are fine enough such that attenuation of the signal is small. Two acoustic codes are used to find the far-field noise. Near-field propagation is computed by using Eversman's wave envelope code, which is based on a finite-element model. Propagation to the far field is accomplished by using the Kirchhoff formula for moving surfaces with the results of the wave envelope code as input data. Comparison of measured and computed far-field noise levels show fair agreement in the range of directivity angles where the peak radiation lobes from the inlet are observed. Although only a single acoustic mode is targeted in this study, the main conclusion is a proof-of-concept: Navier-Stokes codes can be used both to generate and propagate rotor/stator acoustic modes forward through an engine, where the results can be coupled to other far-field noise prediction codes.

Rumsey, C. L.↗
NASA NTRS1989

A dual potential formulation of the Navier-Stokes equations

A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented. The velocity field is decomposed using a scalar and vector potential. Vorticity and dilatation are used as the dependent variables in the momentum equations. Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations. A three-dimensional incompressible flow formulation is also described. An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential). The Helmholtz decomposition theorem allows this splitting of the velocity field. This approach has had only limited use since it increases the number of dependent variables in the solution. However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate. This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity. A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations. Several levels of flow approximation are available within the framework of this method. Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation. Solution efficiency can be enhanced in a straightforward way. For some flows, the vorticity and/or dilatation may be negligible in certain regions (e.g., far from a viscous boundary in an external flow). It is possible to drop the calculation of these variables then and optimize the solution speed. Also, efficient Poisson solvers are available for the potentials. The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed.

Gegg, S. G.↗
NASA NTRS1987

Navier-Stokes and viscous shock-layer solutions for radiating hypersonic flows

Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitude only, whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire II vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura, who used gray-gas radiation model and thin-layer Navier-Stokes equations. Quite good agreement is obtained between the measured and computed values of radiative and convective heating from the VSL code in th medium-to-low altitude flight regime of the Fire II vehicle. At high altitudes, the Navier-Stokes calculations considerably overpredict the Fire II flight data for radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equilibrium assumption and precludes accounting for the collision-limiting phenomenon at high altitudes. Present Navier-Stokes calculations highlight the effect of these assumptions on radiative heating calculations for such conditions.

Gupta, Roop N.↗