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DOE OSTI2024

Data-driven closure modeling for hypersonic turbulent flows

The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Space construction base support requirements for environmental control and life support systems

A Space Station analysis study is being performed for NASA which identifies cost-effective Space Station options that can provide a space facility capable of performing space construction, space manufacturing, cosmological research, earth services, and other functions. A space construction base concept for the construction of large structures, such as those needed to implement satellite solar power for earth usage, will be used as a basis for discussing requirements that impact the design selection, level of integration, and operation of environmental control and life support systems (ECLSS). The space construction base configuration also provides a basic Space Station facility that can accommodate biological manufacturing modules, ultrapure glasses manufacturing modules, and modules for other services in a building-block fashion. Examples of special problems that could dictate hardware required to augment the basic ECLSS for autonomous modules will be highlighted. Additionally, overall intravehicular (IVA) and extravehicular (EVA) activities and requirements that could impact the basic station ECLSS degree of closure are discussed.

Thiele, R. J.↗

NASA NTRS1998

A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy

Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new boundary conditions. In addition, we show that the interface treatments are conservative. New finite-difference operators of spatial accuracy up to sixth order are constructed: these operators satisfy the SBP property. Finite-difference operators are shown to admit design accuracy (p(sup th)-order global accuracy) when (p - 1)(sup th)-order stencil closures are used near the boundaries if the physical boundary conditions are implemented to at least p(sup th)-order accuracy. Stability and accuracy are demonstrated on the nonlinear Burgers' equation for an twelve-subdomain problem with randomly distributed interfaces.

Carpenter, Mark H.↗

NASA NTRS2013

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Fisher, Travis C.↗

NASA NTRS2011

Open Collaboration: A Problem Solving Strategy That Is Redefining NASA's Innovative Spirit

In 2010, NASA?s Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowd sourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowd sourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot?s closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was "fun" to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

Rando, Cynthia M.↗

NASA NTRS2011

Open Collaboration: A Problem Solving Strategy That is Redefining NASA's Innovative Spirit

In 2010, NASA's Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowdsourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowdsourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6,000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot's closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was fun to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

Rando, Cynthia M.↗

NASA NTRS2005

The SMART Theory and Modeling Team: An Integrated Element of Mission Development and Science Analysis

When targeting physical understanding of space plasmas, our focus is gradually shifting away from discovery-type investigations to missions and studies that address our basic understanding of processes we know to be important. For these studies, theory and models provide physical predictions that need to be verified or falsified by empirical evidence. Within this paradigm, a tight integration between theory, modeling, and space flight mission design and execution is essential. NASA's Magnetospheric MultiScale (MMS) mission is a pathfinder in this new era of space research. The prime objective of MMS is to understand magnetic reconnection, arguably the most fundamental of plasma processes. In particular, MMS targets the microphysical processes, which permit magnetic reconnection to operate in the collisionless plasmas that permeate space and astrophysical systems. More specifically, MMS will provide closure to such elemental questions as how particles become demagnetized in the reconnection diffusion region, which effects determine the reconnection rate, and how reconnection is coupled to environmental conditions such as magnetic shear angles. Solutions to these problems have remained elusive in past and present spacecraft missions primarily due to instrumental limitations - yet they are fundamental to the large-scale dynamics of collisionless plasmas. Owing to the lack of measurements, most of our present knowledge of these processes is based on results from modern theory and modeling studies of the reconnection process. Proper design and execution of a mission targeting magnetic reconnection should include this knowledge and have to ensure that all relevant scales and effects can be resolved by mission measurements. The SMART mission has responded to this need through a tight integration between instrument and theory and modeling teams. Input from theory and modeling is fed into all aspects of science mission design, and theory and modeling activities are tailored to SMART needs during mission development and science analysis. In this presentation, we will present an overview of SMART theory and modeling team activities. In particular, we will provide examples of science objectives derived from state-of-the art models, and of recent research results that continue to be utilized in SMART mission development.

Hesse, Michael↗

DOE OSTI2026

Collaborative Research: Enabling multi-scale studies of magnetic reconnection with interpretable data-driven models

The development of accurate reduced descriptions and improved closures for magnetic reconnection is an important and a long‐standing challenge in plasma physics. The four‐fluid approach, and associated closures, that were investigated have the potential to improve the accuracy of plasma fluid models, capturing physical effects which would otherwise require a kinetic description. If successful, this approach could have an important impact for the modeling of laboratory and space plasmas. The major goals of this project were to develop new machine learning (ML) tools based on sparse and symbolic regression techniques, and to extract interpretable and generalizable reduced models (e.g., in the form of partial differential equations - PDEs) from data generated by first principles plasma simulations. Preserving interpretability of such data‐driven models is key to addressing the long‐standing theoretical and numerical challenges. Prior proof‐of‐principle studies have demonstrated the enormous potential of this approach, by recovering the well‐established hierarchy of plasma equations (from Vlasov to MHD) from data produced by particle‐in‐cell (PIC) simulations. Our goal in this project was to extend and apply these new tools to construct better kinetic closures for magnetic reconnection; to derive better models of particle injection and acceleration by this fundamental plasma process; and to use this understanding to accelerate the development of multi‐scale plasma algorithms. While our immediate focus was on the problem of magnetic reconnection, the tools that were will developed are general and applicable to other areas of plasma physics, and more broadly to many‐body phenomena. We anticipate that the development of these multi‐scale models will have a significant impact across different areas of plasma science, from fusion to space and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

An inverse method for subcritical flows

An exact method is presented for two-dimensional subsonic flow within the limitations of the tangent gas approximation. While Woods (1961) studied these equations and proposed iterative methods for the solution of both the iterative and inverse problems, the inverse method here presented is noniterative and exact. It is shown that the direct Euler solution over the designed airfoil is very close to the input speed distribution, and that the constraints necessitated by upstream condition and closure requirements are easily incorporated.

Daripa, P. K.↗

NASA NTRS1985

Multiple-scale turbulence closure modeling of confined recirculating flows

A multiple-scale turbulence closure scheme is developed for the numerical predictions of confined recirculating flows. This model is based on the multiple-time-scale concepts of Hanjalic et al. (1980) and takes into account the non-equilibrium spectra energy transfer mechanism. Problems concerning new formulation of energy transfer rate equations and subsequent model coefficient redefinition and energy spectrum partition are discussed. Comparisons are made with several experiments of internal recirculating flows for the purpose of model validation. Numerical results using the present model show significant improvement of predictive capability over that obtained with the single-scale k-epsilon model and show promising potential for complex turbulent flow predictions.

Chen, C. P.↗

NASA NTRS1993

Carrying the mass flux terms exactly in the first and second moment equations of compressible turbulence

In compressible turbulence models, it is assumed that the Favre-mean velocities are suitable approximations to the Reynolds-mean velocities in order to close unknown terms. This neglects, in the mean momentum and energy equations, the contribution to the stress and work terms by the mean of the fluctuating Favre velocity, a quantity proportional to the turbulent mass flux. As the stress and work terms do not introduce any new unknown correlations requiring closure in either k-epsilon or Reynolds stress closures and because the exact form of the terms can, with little additional work, be carried there is no need to make any modeling assumptions. In the Reynolds stress equations the viscous terms appear naturally in Reynolds variables while the problem is posed in Favre variables. In the process of splitting the viscous terms into the viscous transport terms, carried in Favre variables, and the dissipation terms, carried in Reynolds variables, important contributions from the mass flux appear. The accurate accounting of these terms is important for any consistent near wall modeling and the retention of the mass flux terms is important in complex compressible turbulent flows.

Ristorcelli, J. R.↗

DOE OSTI2025

The Functor system: a new on-the-fly take on Material Properties based on C++ functions

In the context of solving multiphysics problems, the discretization of the partial differential equations (PDE) at hand often takes the spotlight. However, for most engineering users and even application developers, the discretization of the equations has already been performed. Instead, they are tasked with implementing specific closure relations and material properties. MOOSE has long enabled this using the Materials system. This system relied on the pre-computation of all properties before they are used in the PDE or in postprocessing. In this talk we will introduce the Functor system, which was deployed in MOOSE in 2021, then present a few applications of functors in flow modeling simulations by the NEAMS program. Functors first offer great flexibility in their evaluation. Rather than storing various arrays for material properties, they are evaluated on the fly at the location and state, e.g. current or old value, requested. Unlike regular material properties, several operations such as the time derivative, the divergence and the curl can be requested from a functor. Similar to material properties, functors can be made to depend on arbitrary combinations of variables, functions, postprocessors and other properties. However, unlike material properties, any of these can be substituted for a functor material property. Thanks to this, objects no longer need to be duplicated based on the types of their parameters.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Elevated temperature crack growth

The problem of crack growth in hot path components such as combustor liners is complicated by several practical and theoretical considerations. The loading environment of such components involves high temperature levels and gradients that lead to considerations such as thermal stresses, crack closure, hold time, inelastic strains (both time dependent and independent), and Thermal Mechanical Fatigue (TMF). In general, a good understanding of the influence of these factors on crack growth was not obtained. At the same time, several nonlinear fracture mechanics parameters were suggested for such applications; however, most of the proposed methods were not tested for broad applications such as required for hot section components. It was the purpose of this program to evaluate proposed nonlinear methods by performing a thorough experimental and analytical study. The results illustrated that much progress was made in developing nonlinear methods.

Kim, K. S.↗

NASA NTRS2019

Hybrid Transportation System Integrated Trajectory Design and Optimization for Mars Landing Site Accessibility

NASA’s Mars Study Capability Team continues the agency’s efforts to study and refine the nation’s plan to field a sustainable human Mars campaign. One of the primary open issues left unanswered during previous analysis cycles was the uncertainty of the impact to the vehicle performance requirement to deliver crew and cargo to the same landing site across multiple mission opportunities. The Mars Study Capability Team has recently developed an integrated trajectory optimization and system closure model to solve the complex interplanetary trajectory optimization using both low-thrust and high-thrust maneuvers. This paper demonstrates the capability of this new integrated trajectory design and optimization method as it applies to the landing site accessibility problem for the Hybrid transportation architecture. The results showed that the current vehicle is capable of reaching up to +20 degree latitude and down to -20 degree latitude in every mission opportunity from 2033 to 2052. However, reaching latitudes beyond +/- 20 required more propellant than the spacecraft is currently designed to carry for many of the mission opportunities.

Chai, Patrick R.↗

NASA NTRS1976

Transonic airfoil design using Cartesian coordinates

A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

Carlson, L. A.↗

NASA NTRS1993

Turbulence modelling of flow fields in thrust chambers

Following the consensus of a workshop in Turbulence Modelling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows, and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data to account for the non-isotropic turbulence effects.

Chen, C. P.↗

NASA NTRS1993

Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

Chen, C. P.↗

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.↗