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NASA NTRS1996

Second moment closure analysis of the backstep flow database

A Second Moment Closure computation (SMC) is compared in detail with the Direct Numerical Simulation (DNS) data of Le and Moin for the backstep flow at Re = 5,000 in an attempt to understand why the intensity of the backflow and, consequently, the friction coefficient in the recirculation bubble are severely underestimated. The data show that this recirculation bubble is far from being laminar except in the very near wall layer. A novel 'differential a priori' procedure was used, in which the full transport equation for one isolated component of the Reynolds stress tensor was solved using DNS data as input. Conclusions are then different from what would have been deduced by comparing a full simulation to a DNS. One cause of discrepancy was traced back to insufficient transfer of energy to the normal stress by pressure strain, but was not cured. A significant finding, confirmed by the DNS data in the core region of a channel flow, is that the coefficient that controls destruction of dissipation, C epsilon(sub 2), should be decreased by a factor of 2 when production is vanishing. This is also the case in the recirculation bubble, and a new formulation has cured 25% of the backflow discrepancy.

Parneix, S.↗

NASA NTRS1996

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.

Winckelmans, G. S.↗

NASA NTRS2002

Testing putative hemichordate homologues of the chordate dorsal nervous system and endostyle: expression of NK2.1 (TTF-1) in the acorn worm Ptychodera flava (Hemichordata, Ptychoderidae)

Recent phylogenetic investigations have confirmed that hemichordates and echinoderms are sister taxa. However, hemichordates share several cardinal characterstics with chordates and are thus an important taxon for testing hypotheses of homology between key chordate characters and their putative hemichordate antecedents. The chordate dorsal nervous system (DNS) and endostyle are intriguing characters because both hemichordate larval and adult structures have been hypothesized as homologues. This study attempts to test these purported homologies through examination of the expression pattem of a Ptychodera flava NK2 gene, PfNK2.1, because this gene is expressed both in the DNS and endostyle/thyroid in a wide range of chordate taxa. We found that PfNK2.1 is expressed in both neuronal and pharyngeal structures, but its expression pattem is broken up into distinct embryonic and juvenile phases. During embryogenesis, PfNK2.1 is expressed in the apical ectoderm, with transcripts later detected in presumable neuronal structures, including the apical organ and ciliated feeding band. In the developing juvenile we detected PfNK2.1 signal throughout the pharynx, including the stomochord, and later in the hindgut. We conclude that the similar utilization of NK2.1 in apical organ development and chordate DNS is probably due to a more general role for NK2.1 in neurogenesis and that hemichordates do not possess a homologue of the chordate DNS. In addition, we conclude that P. flava most likely does not possess a true endostyle; rather during the evolution of the endostyle NK2.1 was recruited from its more general role in pharynx development.

NASA Discipline Evolutionary Biology↗

NASA NTRS1991

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.↗

NASA NTRS2005

A Priori Analysis of Subgrid-Scale Models for Large Eddy Simulations of Supercritical Binary-Species Mixing Layers

Models for large eddy simulation (LES) are assessed on a database obtained from direct numerical simulations (DNS) of supercritical binary-species temporal mixing layers. The analysis is performed at the DNS transitional states for heptane/nitrogen, oxygen/hydrogen and oxygen/helium mixing layers. The incorporation of simplifying assumptions that are validated on the DNS database leads to a set of LES equations that requires only models for the subgrid scale (SGS) fluxes, which arise from filtering the convective terms in the DNS equations. Constant-coefficient versions of three different models for the SGS fluxes are assessed and calibrated. The Smagorinsky SGS-flux model shows poor correlations with the SGS fluxes, while the Gradient and Similarity models have high correlations, as well as good quantitative agreement with the SGS fluxes when the calibrated coefficients are used.

turbulence↗

NASA NTRS2010

Instability of a Supersonic Boundary-Layer with Localized Roughness

A localized 3-D roughness causes boundary-layer separation and (weak) shocks. Most importantly, streamwise vortices occur which induce streamwise (low U, high T) streaks. Immersed boundary method (volume force) suitable to represent roughness element in DNS. Favorable comparison between bi-global stability theory and DNS for a "y-mode" Outlook: Understand the flow physics (investigate "z-modes" in DNS through sinuous spanwise forcing, study origin of the beat in DNS).

Marxen, Olaf↗

NASA NTRS2013

Influence of Computational Drop Representation in LES of a Droplet-Laden Mixing Layer

Multiphase turbulent flows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent flows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of pollutant dispersion, etc. Two-phase flows contain millions and sometimes billions of particles. For flows with volumetrically dilute particle loading, the most accurate method of numerically simulating the flow is based on direct numerical simulation (DNS) of the governing equations in which all scales of the flow including the small scales that are responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary. Because of high computational cost, numerical simulations of such flows cannot track all these drops. The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics, and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provide minimal error in flow prediction. For this purpose, several Large Eddy Simulation (LES) of a mixing layer with evaporating drops have been performed by using coarse, medium, and fine grid spacings and computational drops, rather than physical drops. To define computational drops, an integer NR is introduced that represents the ratio of the number of existing physical drops to the desired number of computational drops; for example, if NR=8, this means that a computational drop represents 8 physical drops in the flow field. The desired number of computational drops is determined by the available computational resources; the larger NR is, the less computationally intensive is the simulation. A set of first order and second order flow statistics, and of drop statistics are extracted from LES predictions and are compared to results obtained by filtering a DNS database. First order statistics such as Favre averaged stream-wise velocity, Favre averaged vapor mass fraction, and the drop stream-wise velocity, are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when NR is less than 32, and by the coarse mesh LES reasonably accurately for all NR values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.

Bellan, Josette↗

NASA NTRS2013

Direct Numerical Simulation of Transition in a Swept-Wing Boundary Layer

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing derived from a two-dimensional, partial-differential-equation based eigenvalue computation; and the mode selected for forcing corresponds to the most amplified secondary instability mode which, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. Both the growth of the secondary instability wave and the resulting onset of laminar-turbulent transition are captured within the DNS computations. The growth of the secondary instability wave in the DNS solution compares well with linear secondary instability theory when the amplitude is small; the linear growth is followed by a region of reduced growth resulting from nonlinear effects before an explosive onset of laminar breakdown to turbulence. The peak fluctuations are concentrated near the boundary layer edge during the initial stage of transition, but rapidly propagates towards the surface during the process of laminar breakdown. Both time-averaged statistics and flow visualization based on the DNS reveal a sawtooth transition pattern that is analogous to previously documented surface flow visualizations of transition due to stationary crossflow instability. The memory of the stationary crossflow vortex is found to persist through the transition zone and well beyond the location of the maximum skin friction.

Duan, Lian↗

NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗

NASA NTRS2014

Direct Numerical Simulation and Theories of Wall Turbulence with a Range of Pressure Gradients

A new Direct Numerical Simulation (DNS) of Couette-Poiseuille flow at a higher Reynolds number is presented and compared with DNS of other wall-bounded flows. It is analyzed in terms of testing semi-theoretical proposals for universal behavior of the velocity, mixing length, or eddy viscosity in pressure gradients, and in terms of assessing the accuracy of two turbulence models. These models are used in two modes, the traditional one with only a dependence on the wall-normal coordinate y, and a newer one in which a lateral dependence on z is added. For pure Couette flow and the Couette-Poiseuille case considered here, this z-dependence allows some models to generate steady streamwise vortices, which generally improves the agreement with DNS and experiment. On the other hand, it complicates the comparison between DNS and models.

Coleman, G. N.↗

NASA NTRSDate not supplied

Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature

Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models.The wall geometry and flow conditions of the DNS are representative of the experimental data for a Mach 4.9 turbulent boundary layer that was tested on a two-dimensional planar convexwall model in the high-speed blow-down wind tunnel located at the National Aerothermochemistry Laboratory at Texas A&M University. The favorable pressure gradient is induced bythe streamwise surface curvature. The DNS results will be compared with experimental measurements and RANS computations for the same flow conditions and wall geometry. The DNS datasets will also be analyzed to provide an improved physical understanding of hypersonic boundary-layer turbulence subject to mechanical nonequilibrium, including the validity of Morkovin’s hypothesis and the various available compressibility transformations, as well as to obtain turbulence statistics that are relevant to RANS modeling, including the distribution ofeddy viscosity, the budgets of turbulent kinetic energy and Reynolds stresses, and the velocity-temperature correlations. The RANS predictions will be obtained by using both the commonly used one- and two-equation models that assume a constant turbulent Prandtl number and an algebraic, variable Prandtl number model for the turbulent energy flux.

turbulent boundary layers↗

NASA NTRS2004

Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops : Part 1. Direct numerical simulation formulation and a priori analysis

This paper is organized as follows. In § 2, we present the DNS formulation. This formulation consists of a set of coupled conservation equations for the gas phase and the liquid phase (i.e. the drops). The coupling describing the interaction between the two phases is provided in the gas-phase conservation equations by source terms. In § 3, we analyse the DNS results; in particular, we evaluate the adopted form of the heat and mass fluxes. The gas-phase LES equations are developed in § 4 and assumptions that may simplify these equations are examined using the DNS database. Thereafter, the contribution of the source terms is examined by considering the budget of the LES equations. The final form of the LES equations are then presented, in which only the SGS fluxes and the FSTs need be modelled. A parallel perspective on the importance of the source terms is presented in § 5, wherein the irreversible entropy production (i.e. the dissipation) expression for two-phase flow with phase change is derived and evaluated for transitional DNS and the filtered flow fields. Models for the FSTs appearing in the LES equations are investigated in § 6, while several constantcoefficient SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an a posteriori study.

"Okong'o, Nora A.", 'Bellan, Josette↗

NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in A Mach 4.5 Boundary Layer

We use deep learning, an ensemble variationaltechnique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (Deep-ONets), which have the known ability to learn com-plex nonlinear operators within dynamical systems,are used for machine learning. For the baseline config-uration of a smooth flat plate, the second-mode wavesat the DNS inflow cause a quick nonlinear breakdownof the high-speed boundary layer within the computa-tional domain. Results reported in the present studyvalidate the ability of DeepONets to model the tran-sition delay via a given topography of the roughnesselement. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substan-tially lowered by the DeepONets-based reduced-ordermodel. In comparison to the baseline method of EnVaroptimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition pastthe outflow boundary of the computational domainwhile utilizing almost 5–6 times fewer DNS.

Machine Learning↗

NASA NTRSDate not supplied

Effect of the Reynolds Number on the Freestream Disturbance Environment in a Mach 6 Nozzle

To understand the impact of unit Reynolds number on the acoustic disturbance field inside a high-speed wind tunnel, we use Direct Numerical Simulations (DNS) to model the turbulent boundary layers along the walls of a quasi-two-dimensional nozzle configuration. Intended as a stepping stone to fully three-dimensional simulations of freestream noise inside the NASA 20-Inch Mach 6 Wind Tunnel, the present simulations are based on periodic boundary conditions across the spanwise width of the computational domain that corresponds to about one third of the actual tunnel width. These simulations are performed at four different unit Reynolds numbers, ranging from 3.56e6 to 14.0e6 per meter. The predominantly hydrodynamic fluctuations inside the boundary layer are shown to be nearly unaffected by the presence of freestream forcing associated with the impinging acoustic radiation from the opposite wall. Thus, the Reynolds number trends associated with boundary-layer quantities are consistent with previously published DNS of flat-plate boundary layers at similar Mach numbers and wall temperature ratios. The unsteady disturbance environment within the nozzle core region is found to be approximately spatially homogeneous and purely acoustic in nature. The numerical results are used to make comparisons with tunnel noise measurements by Chou et al. [1,2]. Unlike previous comparisons involving static-pressure fluctuations based on the DNS and pitot-pressure fluctuations measured in the wind tunnel, direct comparisons involving the fluctuations in the same physical quantity, namely, the streamwise mass flux, have been reported for the first time. The predicted decrease in the root-mean-square fluctuations in pressure and mass flux with an increasing unit Reynolds number is in agreement with the measurements in the NASA 20-Inch Mach 6 Wind Tunnel. Additional details of the acoustic radiation field are quantified and should be useful toward a digital synthesis of the tunnel disturbance environment that would enable realistic simulations of the natural transition process.

Turbulence↗

NASA NTRSDate not supplied

Effect of the Reynolds Number on the Freestream Disturbance Environment in a Mach 6 Nozzle

Acoustics↗

NASA NTRS1992

The compositional structure and the effects of exothermicity in an unpremixed planar jet flame

Results are presented of direct numerical simulations (DNS) of a randomly perturbed compressible, spatially developing planar jet under the influence of a finite rate Arrhenius chemical reaction of the type F + O yields Product + Heat. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the data generated by DNS. It is shown that even with this idealized kinetics model, the simulated results exhibit features in accordance with experimental data. These results indicate that the Damkoehler number is an important parameter in determining the statistical composition of the reacting field, and that the results are insensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and rms of the product mass fraction decrease, and those of the reactants mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain indicating a lower reactedness. These trends are consistent with those observed experimentally and are very useful in portraying the statistical structure of non-equilibrium diffusion flames. The DNS generated data are also utilized to examine the applicability of the 'laminar diffusion flamelet model' in predicting the rate of the reactant conversion with finite rate chemistry. This examination indicates that the bounds of the product formation scale reasonably well with those obtained by the flamelet model. However, in the range of the relatively low values of the Damkoehler numbers considered, the scatter of the results is substantially more than that to be completely determined by the closure.

Steinberger, C. J.↗

NASA NTRS1990

Low Reynolds number kappa-epsilon modeling with the aid of direct simulation data

The constant C(sub mu) and the near-wall damping function f(sub mu) in the eddy-viscosity relation of the kappa-epsilon model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary layer flow at two Reynolds numbers each. Various existing f(sub mu) model functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The epsilon-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the epsilon-equation is analyzed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the epsilon-equation are tested against the DNS data, and an improved model is proposed.

Rodi, W.↗

NASA NTRS1992

Direct and large-eddy simulations of three-dimensional compressible Navier-Stokes turbulence

This paper reports results from the numerical implementation and testing of the compressible large eddy-simulation (LES). Relevant quantities from 32-cubed coarse grid LES solutions are compared with results generated from direct numerical simulations (DNS) of three-dimensional compressible turbulence that have been run both with sufficient resolution, at 96 cubed. The 32 cubed LES results overall agree well with their 96 cubed DNS counterparts. Moreover, the new DNS results confirm several recent conclusions about compressible turbulence that have been based primarily on two-dimensional simulations.

Zang, T. A.↗