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NASA NTRS1990

A Numerical Method for Direct Simulation of Turbulence in Complex Geometries

The ultimate goal of this work is to study the flow inside a channel with riblets on one of the two walls. The method has been tested for two dimensional flows in the presence of bodies with a geometrical singularity and for three dimensional flows inside domains described by Cartesian coordinates. The results have been compared with previous numerical simulations and with experimental results. The cases considered are: (1) the growth of Orr-Sommerfield waves in plane Poiseulle flow; (2) the flow over a backward facing step; (3) the flow past a wedge; and (4) the flow inside a narrow channel. Finally, the case of a channel with two large riblets on a wall has been simulated. In this case a limited number of grid points is sufficient, and in spite of the slow convergence for the pressure solver, one is able to obtain solutions with a reasonable amount of computer time. At present solutions with very fine grids in all three directions can not be obtained, due to lack of a fast pressure solver for general curvilinear coordinates.

P Orlandi↗

NASA NTRS1975

Numerical study of supersonic turbulent flow over small protuberances

Supersonic turbulent boundary layers over two-dimensional protuberances are investigated, using the numerical finite difference alternating direction implicit (ADI) method. The turbulence is modeled mathematically. The turbulence is represented here by the eddy viscosity approach. The turbulent boundary layer structure as well as an interest in thick boundary layers and much larger protuberance heights than in the laminar case lead to new difficulties. The problems encountered and the means to remove them are discussed.

Polak, A.↗

NASA NTRS1983

TAWFIVE: A user's guide

The Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was developed. A finite volume full potential method is used to model the outer inviscid flow field. First-order viscous effects are modeled by a three dimensional integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness and curvature effects are modeled using a two dimensional strip method. A very brief discussion of the engineering aspects of the program is given. The input and use of the program are covered in great detail.

Melson, N. D.↗

NASA NTRS1990

Scattering of sound by atmospheric turbulence predictions in a refractive shadow zone

According to ray theory, regions exist in an upward refracting atmosphere where no sound should be present. Experiments show, however, that appreciable sound levels penetrate these so-called shadow zones. Two mechanisms contribute to sound in the shadow zone: diffraction and turbulent scattering of sound. Diffractive effects can be pronounced at lower frequencies but are small at high frequencies. In the short wavelength limit, then, scattering due to turbulence should be the predominant mechanism involved in producing the sound levels measured in shadow zones. No existing analytical method includes turbulence effects in the prediction of sound pressure levels in upward refractive shadow zones. In order to obtain quantitative average sound pressure level predictions, a numerical simulation of the effect of atmospheric turbulence on sound propagation is performed. The simulation is based on scattering from randomly distributed scattering centers ('turbules'). Sound pressure levels are computed for many realizations of a turbulent atmosphere. Predictions from the numerical simulation are compared with existing theories and experimental data.

Mcbride, Walton E.↗

NASA NTRS1999

Comparison of AGE and Spectral Methods for the Simulation of Far-Wakes

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This report demonstrates that a good compromise is possible with the Advected Grid Explicit (AGE) method. AGE has proven to be both efficient and accurate for simulating turbulent free-shear flows, including planar mixing layers and planar jets. Its efficiency results from its localized fully explicit finite difference formulation (Bisset 1998a,b) that is very straightforward to compute, outweighing the need for a fairly small timestep. Also, most of the successful simulations were slightly under-resolved, and therefore they were, in effect, large-eddy simulations (LES) without a sub-grid-scale (SGS) model, rather than direct numerical simulations (DNS). The principle is that the role of the smallest scales of turbulent motion (when the Reynolds number is not too low) is to dissipate turbulent energy, and therefore they do not have to be simulated when the numerical method is inherently dissipative at its resolution limits. Such simulations are termed 'auto-LES' (LES with automatic SGS modeling) in this report.

Bisset, D. K.↗

NASA NTRS1975

Supersonic free turbulent mixing layers

A mean turbulent closure method with a length scale function is developed for predicting the reduced spreading rate in high Mach number, high Reynolds number free shear layers. The new feature of the method is the inclusion of effects of the pressure-dilation term which appears in the compressible form of the turbulence energy equation. The model indicates that the pressure-dilation correlation may act as a turbulence energy sink or source depending on whether the transverse gradients of mean Mach number and mean density have the same or opposite signs.

Oh, Y. H.↗

NASA NTRS1988

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Yung, Chain Nan↗

NASA NTRSDate not supplied

Exploring Unstructured Mesh Adaptation for Hybrid Reynolds-Averaged Navier–Stokes/Large Eddy Simulation

Mesh adaptation methods for the Reynolds-averaged Navier–Stokes (RANS) equations are rapidly maturing and beginning to impact the design of aerospace vehicles. RANS turbulence modeling improvements have slowed and may stagnate. Wall-modeled large eddy simulation (LES) and hybrid RANS/LES (HRLES) may provide an improved modeling capability but require specialized expertise to construct appropriate meshes and are considered be too ex-pensive for routine practical use. The realization of the CFD Vision 2030 Study includes improving geometry linkage, mesh generation/adaptation, and turbulence modeling/resolving methods for automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification (i.e., certification or qualification by analysis). An exploration of mesh adaptation for HRLES is performed to document synergies and challenges between mesh adaptation and HRLES. Vortex breakdown over a delta wing is examined to show the improvement of HRLES over RANS turbulence modeling approaches. A high lift configuration is shown to demonstrate complex geometry capability. Research and development opportunities are identified to advocate for continuing investments that may allow HRLES to enter routine practical use as a tool for aerospace vehicle analysis and design.

Michael A Park↗

NASA NTRS1982

Evaluation of four subcritical response methods for on-line prediction of flutter onset in wind-tunnel tests

Four subcritical response methods were evaluated for on-line use in transonic wind-tunnel tests where the flutter model is excited solely by airstream turbulence. The methods were: randomdec, power-spectral-density, peak-hold, and cross-spectrum. Subcritical response data were obtained during tests in the Langley Transonic Dynamics Tunnel of a cantilevered flutter model wing. The test procedure was to maintain a constant Mach number and increase the dynamic pressure (q) in incremental steps. The four methods provided damping trends by which the flutter mode could be tracked and extrapolated to a flutter-onset q. A hard flutter point was obtained at M = 0.82. The peak-mold and cross-spectrum methods gave reliable results and could be most readily used for on-line testing.

Ruhlin, C. L.↗

NASA NTRS1976

Some experience using subcritical response methods in wind-tunnel flutter model studies

Experiences obtained with four methods of predicting flutter of wind-tunnel models from subcritical response data are described. The four methods are: co/quad, randomdec, power spectra density, and the peak-hold spectrum. Model excitation techniques included both forced (sinusoidal sweep) and random (tunnel turbulence). These methods were successfully used to measure the frequency and damping (or an inverse response amplitude proportional to the damping) in the predominant flutter modes. Implementation and application of each method are discussed. Some results and comparisons between methods are presented.

Foughner, J. T., Jr.↗

NASA NTRS2011

Supersonic/Hypersonic Correlations for In-Cavity Transition and Heating Augmentation

Laminar-entry cavity heating data with a non-laminar boundary layer exit flow have been retrieved from the database developed at Mach 6 and 10 in air on large flat plate models for the Space Shuttle Return-To-Flight Program. Building on previously published fully laminar and fully turbulent analysis methods, new descriptive correlations of the in-cavity floor-averaged heating and endwall maximum heating have been developed for transitional-to-turbulent exit flow. These new local-cavity correlations provide the expected flow and geometry conditions for transition onset; they provide the incremental heating augmentation induced by transitional flow; and, they provide the transitional-to-turbulent exit cavity length. Furthermore, they provide an upper application limit for the previously developed fully-laminar heating correlations. An example is provided that demonstrates simplicity of application. Heating augmentation factors of 12 and 3 above the fully laminar values are shown to exist on the cavity floor and endwall, respectively, if the flow exits in fully tripped-to-turbulent boundary layer state. Cavity floor heating data in geometries installed on the windward surface of 0.075-scale Shuttle wind tunnel models have also been retrieved from the boundary layer transition database developed for the Return-To-Flight Program. These data were independently acquired at Mach 6 and Mach 10 in air, and at Mach 6 in CF4. The correlation parameters for the floor-averaged heating have been developed and they offer an exceptionally positive comparison to previously developed laminar-cavity heating correlations. Non-laminar increments have been extracted from the Shuttle data and they fall on the newly developed transitional in-cavity correlations, and they are bounded by the 95% correlation prediction limits. Because the ratio of specific heats changes along the re-entry trajectory, turning angle into a cavity and boundary layer flow properties may be affected, raising concerns regarding the application validity of the heating augmentation predictions.

Everhart, Joel L.↗

NASA NTRS1992

Turbulent transport of a passive-scalar field by using a renormalization-group method

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Hossain, Murshed↗

NASA NTRS2015

Implicit Large-Eddy Simulations of Zero-Pressure Gradient, Turbulent Boundary Layer

A set of direct simulations of zero-pressure gradient, turbulent boundary layer flows are conducted using various span widths (62-630 wall units), to document their influence on the generated turbulence. The FDL3DI code that solves compressible Navier-Stokes equations using high-order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Results are analyzed at two different Re values (500 and 1,400), and compared with spectral DNS data. They show that a minimum span width is required for the mere initiation of numerical turbulence. Narrower domains ((is) less than 100 w.u.) result in relaminarization. Wider spans ((is) greater than 600 w.u.) are required for the turbulent statistics to match reference DNS. The upper-wall boundary condition for this setup spawns marginal deviations in the mean velocity and Reynolds stress profiles, particularly in the buffer region.

Turblent boundary layer↗

NASA NTRS1945

Statistical Analysis of the Characteristics of Repeated Gusts in Turbulent Air

Statistical methods were applied to acceleration and airspeed data obtained with the XC-35 airplane during flights in turbulent air within convective clouds in order to determine the characteristics of repeated or closely spaced gusts pertinent to design problems. Results indicated that, in turbulent air within convective cloud, gusts tend to be contiguous and are seldom found isolated in space. Over-all average spacing between repeated gusts was in good agreement with twice the average gust-gradient distance of 10 chords used in present design.

AUTHORS (2)↗

NASA NTRS1985

On the Computation of Structural Vibrations Induced by a Low-speed Turbulent Flow

A method for numerical evaluation of the vibrations of a cylindrical shell structure induced by a low speed external turbulent flow is discussed. The direction of flow is along the axis of revolution of the shell, and the source of excitation is the pressure fluctuations in the turbulent boundary layer. For the investigation of vibration and noise problems it is usually more desirable to utilize the modal expansion approach. The axisymmetric shell structure can be modeled by the assemblage of conical-shell finite-elements. This modeling allows the eigenfunction psi sub mn (x,theta) to be represented in a rectangular product of a longitudinal modal function f sub mn (x) and a circular harmonic function cos m theta (or sin m theta).

Hwang, Y. F.↗

NASA NTRS2015

Implicit LES of Turbulent, Separated Flow: Wall-Mounted Hump Configuration

Direct simulations (ILES) of turbulent, separated flow over the wall-mounted hump configuration is conducted to investigate the physics of separated flows. A chord-based Reynolds number of Re(sub c) = 47,500 is set up, with a turbulent in flow of Re(sub theta) = 1,400 (theta/c = 3%). FDL3DI, a code that solves the compressible Navier-Stokes equations using high- order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Two different configurations of the upper-wall are analyzed, and results are compared with both a higher Re(sub c) (= 936,000, Re(sub theta) = 7,200, theta/c = 0.77%) experiment for major flow features, and RANS (k-omega SST) results. A lower Rec allows for DNS-like mesh resolution, and an adequately wide span. Both ILES and RANS show delayed reattachment compared to experiment, and significantly higher skin friction in the forebody of the hump, as expected. The upper-wall shape influences the C(sub p) distribution only. Results from this study are being used to setup higher Rec (lower theta/c) ILES.

Implicit LES↗

NASA NTRS1988

Turbulent viscosity

A model for fully developed turbulence is proposed whose predictions compare favorably with those of the direct interaction approximation (DIA) model and whose main equations are easy to handle. Four different expressions for the turbulent viscosity are derived which contain no free parameters. Two of the expressions are given in terms of properties of the turbulent fluid itself; the other two are given in terms of the instability that generated the turbulence and of the properties of the mean flow. The numerical coefficients entering these relations are evaluated and found to be in good agreement with previous theoretical estimates based on Kraichnan's DIA, the renormalization group method, and turbulence modeling. In the case of shear in the mean flow, the Shakura-Sunyaev alpha parameter is shown to be less than 0.01. The four expressions can be generalized to include the effect of rotation and/or magnetic fields.

Canuto, V. M.↗

NASA NTRSDate not supplied

Validation Experiments for Turbulent Separation over an Axisymmetric Body of Revolution

Historically, the flow physics involved with most turbulent separated flows have presented fundamental challenges to validating numerical approaches. As recognized by the CFD Vision 2030 study commissioned by NASA, validation of Reynolds-averaged Navier-Stokes (RANS) models and other scale-resolving methods for turbulent separated flow requires data from advanced, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, a new test platform, referred to as the NASA Axisymmetric Afterbody, was designed to obtain detailed measurements of the flow field undergoing a smooth, adverse pressure gradient induced separation for a fixed Reynolds number, Re = 180,000. The parametric body offers a range of flow states progressing from fully attached, to incipient separation, and finally to small-scale separated flow based on variable afterbody geometries. In an initial effort to evaluate RANS turbulence model capabilities, the present configurations of the axisymmetric model host a mild adverse pressure gradient over the contoured boattail section, inducing incipient turbulent separation, as well as a slightly larger adverse pressure gradient, inducing a small-scale region of turbulent separation. Experiments include steady pressure measurements and 2-D PIV to provide the preliminary dataset for simulation studies, which examine the effect of variable grid domains and RANS turbulence models. This is done in an effort to understand and evaluate the critical variability between solutions for the present model configurations. Results indicate potential discrepancies may be due to the effect of the square tunnel test section walls, relatively large blockage ratio, and slight variability in reference parameters. Ongoing work will focus on higher fidelity experimental campaigns to obtain surface flow visualizations and Stereo-Particle Image Velocimetry (SPIV) to deliver higher spatial resolution of the three-dimensional flow field to aid turbulence modelers.

Validation↗