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DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn

Rayleigh-Taylor mixing in the presence of a third component with intermediate density is investigated through three-dimensional large-eddy simulation (LES) with a high-order compact finite-difference code. Two configurations are considered: (1) a symmetric configuration in which the Atwood number between the heavy and intermediate components matches the Atwood number between the intermediate and light components and (2) an asymmetric configuration in which the Atwood number between the heavy and intermediate components is an order of magnitude greater than the Atwood number between the intermediate and light components. Mass fraction covariances are extracted, and proposed Reynolds-averaged Navier-Stokes (RANS) closures for density-specific-volume and density-mass-fraction covariances are evaluated in an a priori fashion. Additionally, a multicomponent extension of the k - Φ - L - a - V RANS model [Morgan, Phys. Rev. E 104, 015107 (2021)] is presented which includes model equations for the upper-triangular elements of the mass fraction covariance matrix. This model, referred to as the k - Φ - L - a - C model, is compared against results from LES and against other RANS models. Profiles of average mass fraction, mass-fraction covariance, and density-specific-volume covariance obtained with the k - Φ - L - a - C model are found to agree well with LES data. Finally, the impact of three-component turbulent mixing on average reaction rate is investigated in both premixed and nonpremixed cases by heating the mixing layer and allowing it to undergo thermonuclear (TN) burn. A closure model for average reaction rate is proposed for use with the k - Φ - L - a - C model, and when this model is applied, improved agreement is obtained between LES and RANS in total TN neutron production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗

DOE OSTI2026

Quantum mechanical closure of partial differential equations with symmetries

We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.

Delay embedding↗

NASA NTRS1979

A method of mapping compact structure in radio sources using VLBI observations

A two-part technique is described for determining the angular structure of the compact components of radio sources from VLBI observations. With this technique, the source structure is first approximated, using both amplitudes and closure phases, by a model consisting of circularly symmetric Gaussian components located on a grid of positions on the sky. The second part begins by employing this model to predict the visibility phase corresponding to each observed visibility amplitude; these estimated visibility phases are then adjusted to agree with the observed closure phases. The resulting estimates of the visibility phases and the observed visibility amplitudes are then combined in a direct Fourier transform to produce a 'dirty' source map that is deconvolved via the CLEAN procedure on the basis of the point-source response. Some examples based on data generated from test models are provided.

Cotton, W. D.↗

NASA NTRS1993

Development of computational methods for heavy lift launch vehicles

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Yoon, Seokkwan↗

NASA NTRS1994

Development of advanced Navier-Stokes solver

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Yoon, Seokkwan↗

DOE OSTI2025

Scalar flux transport models for self-similar turbulent mixing

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

Reynolds-averaged Navier Stokes↗

NASA NTRS1983

A turbulence model for three dimensional turbulent shear flows over curved rotating bodies

There exists currently considerable interest in the development of numerical procedures for solving the equations governing three-dimensional fluid flows. In particular, improved calculations of viscous flows on rotating bodies such a turbomachinery rotors are of great importance. The present investigation is mainly concerned with the analysis of the effect of rotation on the dissipation rate equation and the Reynolds stress equations. Attention is given to governing equations and modelling, algebraic Reynolds stress equations, a procedure for implementing the turbulence closure scheme, results for a model representative of centrifugal turbomachinery, and results for axial turbomachinery. The proposed turbulence model is valid for three-dimensional, rotating, and curved flows. The model has all the essential physics of turbulence, mean flow, rotation, and the curvature.

Galmes, J. M.↗

DOE OSTI2023

Capturing sub-grid temperature and moisture variations for wildland fire modeling

Not Available

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗

NASA NTRS1991

A two-equation turbulence model for compressible reacting flows

A two-equation turbulence model (k-epsilon) has been modified to model compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. Computations are carried out using the Navier-Stokes solver SPARK which includes a finite rate chemistry model for hydrogen-air combustion. Initially, planar compressible mixing layers are simulated. Comparisons of the predictions with available experimental data and the predictions of a compressible Reynolds stress closure indicate that the model is well suited for the study of such flows. The decrease in the growth rate of the mixing layer with increasing convective Mach number is well predicted. The model is then tested on a three-dimensional supersonic flow problem where solid boundaries are present. An axisymmetric nonreacting mixing layer flow involving dissimilar gases is evaluated next using the model and the predictions are compared with available experimental data. Finally, two reacting turbulent flow configurations have been studied and comparison of predictions and experimental data has been done. The comparisons indicate that the model predicts the overall features of the test cases very well.

Narayan, J. R.↗

NASA NTRS1995

Application of Navier-Stokes code PAB3D with kappa-epsilon turbulence model to attached and separated flows

A three-dimensional Navier-Stokes solver was used to determine how accurately computations can predict local and average skin friction coefficients for attached and separated flows for simple experimental geometries. Algebraic and transport equation closures were used to model turbulence. To simulate anisotropic turbulence, the standard two-equation turbulence model was modified by adding nonlinear terms. The effects of both grid density and the turbulence model on the computed flow fields were also investigated and compared with available experimental data for subsonic and supersonic free-stream conditions.

Abdol-Hamid, Khaled S.↗

NASA NTRS1987

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Kim, S.-W.↗

NASA NTRS1989

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

Kim, S.-W.↗

NASA NTRS1988

Quick actuating closure and handling system

A quick activating closure and handling system, which utilizes conical sections for locking, was developed to allow quick access to the combustor internal components of the 8 ft High Temperature Tunnel. These critical components include the existing methane spraybar, a transpiration cooled nozzle and the new liquid oxygen (LOX) injection system housed within the combustor. A substantial cost savings will be realized once the mechanism is installed since it will substantially reduce the access time and increase the time available for conducting wind tunnel tests. A need exists for more frequent inspections when the wind tunnel operates at the more severe conditions generated by using LOX in the combustor. A loads analysis and a structural (finite element) analysis were conducted to verify that the new closure system is compatible with the existing pressure shell. In addition, strain gages were placed on the pressure vessel to verify how the pressure shell reacts to transient pressure loads. A scale model of the new closure system was built to verify the operation of the conical sections in the locking mechanisms.

Allred, Johnny W.↗

NASA NTRS1987

On the modelling of non-reactive and reactive turbulent combustor flows

A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

Nikjooy, Mohammad↗

NASA NTRSDate not supplied

Overview of the Predictive Simulation Capability Element of the Plume Surface Interaction Project

As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The GCD PSI Project, planned to be completed over a four year period, contains a Predictive Simulation Capability (PSC) Element focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the PSC Element, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper describes the PSC Element of the PSI Project as well as providing descriptions of recent accomplishments and remaining work. The overall structure of the PSC Element is broken down into four areas of focus. The first area is the Prediction of Plume Flow in low pressure environments. The development approach taken is the augmentation of the existing production-mode computational fluid dynamics (CFD) tool Loci/Chem, with targeted extensions necessary to accurately model rarefied conditions found in both Martian and Lunar applications. Production readiness and validation of predictive capability are the major objectives of this task. The second area is the effect of mixed continuum/rarefied flow on crater development and ejecta sheets. A new CFD application, Loci/GGFS (Gas Granular Flow Solver), is being developed which implements an Eulerian/Eulerian two-phase model of gas- and soil-phases in order to simulate the soil erosion, crater formation, and soil ejecta transport in a fully coupled simulation. This task seeks to verify Loci/GGFS is production-ready as well as perform validation studies to determine the degree of predictive capability achieved by Loci/GGFS. The third area is focused on the details and extension of particle phase modeling of soil. In this task, Discrete Element Modeling (DEM) techniques are used to perform direct simulations of complex soil particles under the action of forcing similar to that to be cause by PSI. The simulation results are then used to construct closures to the Eulerian model of the soil phase used by Loci/GGFS. The fourth area is gas-particle interaction modeling. In this task, experiments are being conducted as well as detailed simulation results are being studied to further understand the complexities of gas-particle interactions in dilute, intermediate, and high soil volume fraction regimes. Improved models of particle drag and the particle turbulent kinetic energy (PTKE) resulting from the interaction of gas flows within particle clouds are the objective of this task.

Jeff West↗