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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Wall-Modeled Lattice Boltzmann and Navier-Stokes Approaches for Separated Flows

Lattice Boltzmann (LB) and hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are applied to NASA's Revolutionary Computational Aerosciences (RCA) standard test cases for separated flows. A detailed comparison between the performance and accuracy of the two emerging numerical methodologies for turbulence resolving simulations, i.e. the LB and hybrid RANS/LES methods will be presented. This contribution addresses the RCA technical challenge to identify and down-select critical turbulence, transition, and numerical method technologies for 40% reduction in predictive error for standard turbulence separated flow test cases. Results for the 2D NASA wall-mounted hump and the axisymmetric transonic bump including time-averaged pressure coefficient, skin friction, and velocity pro les, as well as resolved and modeled Reynolds stresses for both numerical approaches will be presented and differences between LB and hybrid RANS/LES will be discussed.

Lattice Boltzmann↗
NASA NTRS1980

Numerical solutions of the Navier-Stokes equations for transonic afterbody flows

The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.

Swanson, R. C., Jr.↗
NASA NTRS1992

Parabolized Navier-Stokes methods for hypersonic flows

The development and numerical solution of the Parabolized Navier-Stokes (PNS) equations is discussed. Special emphasis is placed on numerical integration algorithms for PNS solvers, most notably recent applications of upwind schemes. Application of this technology to high speed, high Reynolds number flows was the focus, and modeling techniques for real gas effects and turbulence were discussed. Experiences in validating the UPS upwind PNS flow solver for relatively simple body shapes are presented. The test cases range in complexity from two dimensional perfect gas cases to three dimensional finite rate chemistry cases.

Lawrence, S. L.↗
NASA NTRS1985

Time-dependent Navier-Stokes computations of separated flows over airfoils

The application of both a central-difference and an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using the thin-layer approximation, both algorithms are employed to solve the low Reynolds number laminar flow around a circular cylinder with periodic shedding. Results agree with experimental Strouhal numbers to within about 10 percent. A grid refinement study is conducted using the upwind code for both the thin-layer and complete Navier-Stokes approximations. The circular cylinder solution is shown to be highly dependent upon both grid density outward from the body and grid extent. Finally, the thin-layer central-difference code is used to predict the time-accurate unsteady flow about two stalled airfoils. The NACA 0012 airfoil turbulent solutions are periodic with Strouhal numbers of about 0.1; a strong vortex is periodically shed from the leading edge. The LS(1)-0417 airfoil turbulent solution shows a high frequency oscillatory trailing edge separation. The 20 degree NACA 0012 airfoil solution is massively separated, but shows no evidence of periodicity.

Rumsey, C. L.↗
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 NTRS1979

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

Shamroth, S. J.↗
NASA NTRS1996

Calculation of Turbulent Subsonic Diffuser Flows Using the NPARC Navier-Stokes Code

Axisymmetric subsonic diffuser flows were calculated with the NPARC Navier-Stokes code in order to determine the effects various code features have on the flow solutions. The code features examined in this work were turbulence models and boundary conditions. Four turbulence models available in NPARC were used: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, and the Chien kappa-epsilon and Wilcox kappa-omega two-equation models. The three boundary conditions examined were the free boundary, the mass flux boundary and the subsonic outflow with variable static pressure. In addition to boundary condition type, the geometry downstream of the diffuser was varied to see if upstream influences were present. The NPARC results are compared with experimental data and recommendations are given for using NPARC to compute similar flows.

Dudek, J. C.↗
NASA NTRS1991

Evaluation of a three-dimensional Navier-Stokes solver for transonic flow over a low-aspect-ratio wing mounted in a wind tunnel

A three dimensional Navier-Stokes solver is evaluated for transonic flow over a thin, swept, low-aspect ratio wing. The computational study was undertaken in support of a wind tunnel experimental program. The computational results are compared to experimental surface pressure data obtained in a cryogenic wind tunnel with an adaptive wall test section. The results show favorable agreement over a wide range of conditions, further the numerical results provide additional data of the complex three-dimensional flow field. Differences in the predictions and experiment suggest a need to conduct further experiments to evaluate the adaptive wall testing technique, and to model the tunnel sidewall boundary layer in the computations.

Milholen, William E., II↗
NASA NTRS1988

A Navier-Stokes solver for cascade flows

A computer code for solving the Reynolds averaged full Navier-Stokes equations has been developed and applied using sheared H-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady state calculations. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications in less than 100 multigrid cycles on the finest mesh.

Arnone, A.↗
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 NTRS1987

Navier-Stokes predictions of multifunction nozzle flows

A two-dimensional, Navier-Stokes code developed by Imlay based on the implicit, finite-volume method of MacCormack has been applied to the prediction of the flow fields and performance of several nonaxisymmetric, convergent-divergent nozzles with and without thrust vectoring. Comparisons of predictions with experiment show that the Navier-Stokes code can accurately predict both the flow fields and performance for nonaxisymmetric nozzles where the flow is predominantly two-dimensional and at nozzle pressure ratios at or above the design values. Discrepancies between predictions and experiment are noted at lower nozzle pressure ratios where separation typically occurs in portions of the nozzle. The overall trends versus parameters such as nozzle pressure ratio, flap angle, and vector angle were generally predicted correctly.

Wilmoth, Richard G.↗
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 NTRS1984

Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder

Euler and Navier-Stokes solutions of the supersonic shear flow past a circular cylinder are obtained. These solutions are used to study the basic flow structure around the cylinder. Both the inviscid and viscous calculations show the formation of a large recirculating flow region around the front stagnation point. The calculations further show that the overall size of the recirculating region is approximately the same for the Euler and Navier-Stokes solutions but the inside structure is quite different. The inviscid flow shows only one vortex whereas the viscous flow shows two vortices inside the recirculating flow region. The inner vortex in the Navier-Stokes solution is formed primarily due to the viscous effects near the body surface and its size depends upon the Reynolds number. It is found that with increasing Reynolds number, the inner vortex diminishes in size and the Navier-Stokes solution asymptotically approaches the Euler solution. These results indicate that the Euler equations may correctly predict certain high Reynolds number separation phenomenon in flows with natural inviscid vorticity source.

Kumar, A.↗
NASA NTRS1989

Prediction of turbine rotor-stator interaction using Navier-Stokes methods

Flows in turbomachinery are generally complex and do not easily lend themselves to numerical computation. The flows are three-dimensional and inherently unsteady. Complicated blade geometries and flow phenomena such as separation and periodic transition from laminar to turbulent flow add to the numerical complexity. Nevertheless, the accurate numerical analysis of such flows is a problem of considerable interest and practical importance to the turbomachinery community. Much of the early work in turbomachinery flow prediction focussed on airfoil cascades. While such analyses of flows in isolated airfoil rows have helped improve understanding of the flow phenomena and have gained widespread acceptance in the industrial community as a design tool, they do not yield any information regarding the unsteady effects arising out of rotor-stator aerodynamic interaction. These interaction effects become increasingly important as the distance between successive stator and rotor rows is decreased. Thus, the need exists for analytical tools that treat the rotor and stator airfoils as a system and provide information regarding the magnitude and the impact of the unsteady effects. The focus a three-dimensional, time-accurate, thin-layer Navier-Stokes code that was recently developed to study rotor-stator interaction problems. A system of patched and overlaid grids that move relative to each other is used to discretize the flow field and the governing equations are integrated using a third-order upwind scheme set in an iterative, implicit framework. The code was used to simulate subsonic flow through an axial turbine configuration for which considerable experimental data exists. Grid refinement studies were also conducted as part of the code validation process. The current status of the research, along with planned future directions, are also discussed.

Madavan, Nateri K.↗
NASA NTRS1988

Study of V/STOL flows using the fortified Navier-Stokes scheme

One of the flows inherent in V/STOL operations, the jet in ground effect with a crossflow, is studied using the Fortified Navier-Stokes (FNS) scheme. Through comparison of the simulation results and the experimental data, and through the variation of the flow parameters (in the simulation), a number of interesting characteristics of the flow have been observed. For example, it appears that the forward penetration of the ground vortex is a strong inverse function of the level of mixing in the ground vortex. An effort has also been made to isolate issues which require additional work in order to improve the numerical simulation of the jet in ground effect flow. The FNS approach simplifies the simulation of a single jet in ground effect, but will be even more effective in applications to more complex topologies.

Van Dalsem, William R.↗
NASA NTRS1991

Parabolized Navier-Stokes methods for hypersonic flows

A representative sampling of the techniques used in the integration of the Parabolized Navier-Stokes (PNS) equations is presented. Special atention is given to recent algorithms developed specifically for application to high speed flows, characterized by the presence of strong embedded shock waves and real gas effects. It is shown that PNS solvers are being used in the analysis of sonic boom signatures. Methods for modeling physical effects are discussed, including an overview of commonly used turbulence models and a more detailed discussion of techniques for including equilibrium and finite rate real gas effects.

Lawrence, Scott L.↗
NASA NTRS1990

A three-dimensional upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional flow of chemically reacting air around hypersonic vehicles. The code is a modification of the perfect gas, three-dimensional UPS code of Lawrence et al. (1986) which has been extended in the present study to permit the calculation of hypersonic, viscous flows in chemical nonequilibrium. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for real gas effects. The present code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Results are presented for the hypersonic laminar flow over a cone at 0- and 10-deg angles of attack and for a generic hypersonic vehicle. Calculations are performed assuming either perfect gas, equilibrium air, or finite-rate chemistry.

Buelow, Philip E.↗
NASA NTRS1988

An upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. The algorithm solves the gas dynamic and species continuity equations in a 'loosely' coupled manner. The new code has been validated by computing the laminar flow (at free stream Mach number 25) of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally-differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave where the present code exhibits superior shock capturing capabilities.

Tannehill, John C.↗