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NASA NTRS1992

Studies in turbulence

Various papers on turbulence are presented. Individual topics addressed include: modeling the dissipation rate in rotating turbulent flows, mapping closures for turbulent mixing and reaction, understanding turbulence in vortex dynamics, models for the structure and dynamics of near-wall turbulence, complexity of turbulence near a wall, proper orthogonal decomposition, propagating structures in wall-bounded turbulence flows. Also discussed are: constitutive relation in compressible turbulence, compressible turbulence and shock waves, direct simulation of compressible turbulence in a shear flow, structural genesis in wall-bounded turbulence flows, vortex lattice structure of turbulent shear slows, etiology of shear layer vortices, trilinear coordinates in fluid mechanics.

Gatski, Thomas B.↗

NASA NTRS1987

Low Reynolds number modeling of turbulent flows with and without wall transpiration

A full Reynolds-stress closure that is capable of describing the flow all the way to the wall is formulated. The closure is based on the conventional high Reynolds number form of the redistribution model, the inclusion of molecular diffusion, and a modified dissipation model to account for viscous effects near a wall. Two dissipation models are investigated along with two gradient diffusion and two redistribution models. Their respective effects on the calculated flow properties are assessed by comparing them with the data of fully developed turbulent flows and a developing pipe flow with wall transpiration. The near-wall behavior is very well predicted; however, the wall correction to the redistribution modeling is found to have little effect on the calculated results. The overall behavior of the fully developed turbulent flows is best described by a nonisotropic gradient diffusion model, a return-to-isotropy redistribution model, and a dissipation model that accounts for viscous behavior near a wall. This same closure also gives the best prediction of the axial pressure drop behavior along a pipe with a uniform wall suction. Furthermore, the near-wall behavior of such a flow is very well predicted by this closure.

So, Ronald M. C.↗

DOE OSTI2022

Data-driven, multi-moment fluid modeling of Landau damping

Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning architecture to learn fluid partial differential equations (PDEs) of a plasma system based on the data acquired from a fully kinetic model. Here, the learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effect such as Landau damping. Based on the learned fluid closure, the data-driven, multi-moment fluid modeling can well reproduce all the physical quantities derived from the fully kinetic model. The calculated damping rate of Landau damping is consistent with both the fully kinetic simulation and the linear theory. The data-driven fluid modeling of PDEs for complex physical systems may be applied to improve the fluid closure and reduce the computational cost of multi-scale modeling of global systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Second Order Closures for the Radiative Transfer Equation: Some Are Unstable

The largest existing simulations of cosmic reionization model radiative transfer with moment methods that require a closure relation. The two most commonly used closure relations are M1 and OTVET; both close the moment hierarchy at the first moment. We explore the properties of a higher, second-order closure. We show that direct generalizations of M1 and OTVET to one higher order are physically unstable - i.e., the closure equations themselves result in unstable solutions, not just their numerical implementation. In fact, a generalization of OTVET to any order higher than the first one is unstable. We are also able to show that any local (i.e., depending only on the local moments of the radiation field, like M1) second-order closure that depends only on the radiation intensity and radiation flux, but does not explicitly depend on the radiation pressure, is physically unstable. This result restricts the choice of possible second-order closure relations.

Gnedin, Nickolay Y. [Fermilab; Chicago U., Astron.↗

DOE OSTI2021

Direct observations and characterization of crack closure during microstructurally small fatigue crack growth via in-situ high-energy X-ray characterization

This study provides direct observation of the crack closure mechanism of a naturally occurring, tortuous, 3D microstructurally small fatigue crack (SFC) in additively manufactured Inconel 718. In-situ non-destructive characterization is performed using high-energy X-ray diffraction techniques to capture the evolution of the 3D microstructure and micromechanical response in the vicinity of the crack front. Based on the stress state of twelve grains analyzed at the crack tip, the crack closure events of the SFC front was found to be spatially heterogeneous with respect to loading progression governed by the local stress state of the grains (specifically the stress reversal from compression to tension). From this analysis, three grains that displayed different degrees of crack closure were further investigated, based on the orientation of the crack relative to the grains and the associated modality of crack growth. The stress normal to the crack plane and the associated degree of Mode I crack behavior were correlated with events of the crack opening earlier during the loading cycle. This was further corroborated by diffraction spot spreading analysis that quantified the crystallographic lattice distortion caused by the opening crack. Additionally, the detailed characterization of the opening behavior of the grains located at the crack tip and their associated states of stress elucidates the mechanism governing crack closure and will inform future modeling efforts of this phenomenon.

36 MATERIALS SCIENCE↗

NASA NTRS1974

Analysis of two-dimensional free turbulent mixing

The observed large reduction in spreading rate of adiabatic high-Mach-number free turbulent shear layers has been predicted successfully for the first time by a mean turbulent energy closure method using a new model for a specified pressure-dilitation correlation. A physical mechanism that produces this correlation has been hypothesized based on an eddy shock wave concept. This hypothesis indicates that the correlation would act like a turbulence energy sink or source according to whether the transverse gradients of mean Mach number and mean density have the same or opposite signs, respectively.

Oh, Y. H.↗

NASA NTRS1973

Handling properties of diverse automobiles and correlation with full scale response data

Driver/vehicle response and performance of a variety of vehicles in the presence of aerodynamic disturbances are discussed. Steering control is emphasized. The vehicles include full size station wagon, sedan, compact sedan, van, pickup truck/camper, and wagon towing trailer. Driver/vehicle analyses are used to estimate response and performance. These estimates are correlated with full scale data with test drivers and the results are used to refine the driver/vehicle models, control structure, and loop closure criteria. The analyses and data indicate that the driver adjusts his steering control properties (when he can) to achieve roughly the same level of performance despite vehicle variations. For the more disturbance susceptible vehicles, such as the van, the driver tightens up his control. Other vehicles have handling dynamics which cause him to loosen his control response, even though performance degrades.

Hoh, R. H.↗

NASA NTRS1978

The role of atmospheric shear, turbulence and a ground plane on the dissipation of aircraft vortex wakes

Enhanced dispersion of two-dimensional trailed vortex pairs within simplified neutral atmospheric backgrounds is studied numerically for three conditions: when the pair is imbedded in a constant turbulent bath (constant dissipation); when the pair is subjected to a mean cross-wind shear; and when the pair is near the ground. Turbulent transport is modeled using second-order closure turbulent transport theory. The turbulent background fields are constructed using a superequilibrium approximation. The computed results allow several general conclusions to be drawn with regard to the reduction in circulation of the vortex pair and the rolling moment induced on a following aircraft: (1) the rate of decay of a vortex pair increases with increasing background dissipation rate; (2) cross-wind shear disperses the vortex whose vorticity is opposite to the background; and (3) the proximity of a ground plane reduces the hazard of the pair by scrubbing. The phenomenon of vortex bounce is explained in terms of secondary vorticity produced at the ground plane. Qualitative comparisons are made with available experimental data, and inferences of these results upon the persistence of aircraft trailing vortices are discussed.

Bilanin, A. J.↗

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 analysis of transonic cascade flow

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

Arnone, A.↗

NASA NTRS1991

Transonic cascade flow calculations using non-periodic C-type grids

A new kind of C-type grid is proposed for turbomachinery flow calculations. This grid is nonperiodic on the wake and results in minimum skewness for cascades with high turning and large camber. Euler and Reynolds averaged Navier-Stokes equations are discretized on this type of grid using a finite volume approach. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. Jameson's explicit Runge-Kutta scheme is adopted for the integration in time, and computational efficiency is achieved through accelerating strategies such as multigriding and residual smoothing. A detailed numerical study was performed for a turbine rotor and for a vane. A grid dependence analysis is presented and the effect of artificial dissipation is also investigated. Comparison of calculations with experiments clearly demonstrates the advantage of the proposed grid.

Arnone, Andrea↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS1992

Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids

Arnone, Andrea↗

NASA NTRS1992

Flow prediction over a transport multi-element high-lift system and comparison with flight measurements

Accurate prediction of surface-pressure distributions, merging boundary-layers, and separated-flow regions over multi-element high-lift airfoils is required to design advanced high-lift systems for efficient subsonic transport aircraft. The availability of detailed measurements of pressure distributions and both averaged and time-dependent boundary-layer flow parameters at flight Reynolds numbers is critical to evaluate computational methods and to model the turbulence structure for closure of the flow equations. Several detailed wind-tunnel measurements at subscale Reynolds numbers were conducted to obtain detailed flow information including the Reynolds-stress component. As part of a subsonic-transport high-lift research program, flight experiments are conducted using the NASA-Langley B737-100 research aircraft to obtain detailed flow characteristics for support of computational and wind-tunnel efforts. Planned flight measurements include pressure distributions at several spanwise locations, boundary-layer transition and separation locations, surface skin friction, as well as boundary-layer profiles and Reynolds stresses in adverse pressure-gradient flow.

Vijgen, P. M. H. W.↗

NASA NTRS1992

A study of hypersonic swept shock wave/turbulent boundary layer interactions using a conical Navier-Stokes code

A computational study has been performed of sharp fin-induced swept shock wave/turbulent boundary layer interactions at low hypersonic Mach numbers. The objective was to determine if results obtained using a conical Navier-Stokes code, particularly the peak heating and pressure, are adequate for engineering predictions. The advantage of the conical approach is that the problem becomes two-dimensional and requires much less computational effort than a fully three-dimensional calculation. In this code, the standard Baldwin-Lomax model is used for turbulent closure and its performance is studied in some detail. To assess the approach interactive flowfields generated by unswept sharp fins at two angles of attack at each of three hyprsonic freestream Mach numbers (5, 6, 11) have been calculated and the results compared with experimental wall pressure and heat transfer data. Although the conical Navier-Stokes/Baldwin-Lomax approach is reasonably successful at Mach numbers up to 5, the performance deteriorates as the Mach number is increased. Nevertheless, the approach could be a valuable tool in preliminary parametric design studies.

Rodi, Patrick E.↗

NASA NTRS1993

A Navier-Stokes solver for turbomachinery applications

A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-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. A grid independence analysis is presented for a transonic rotor blade. 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.

Arnone, A.↗

NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗