Results for “constitutive flow model” — Page 2

NASA NTRS2016

Reference Solutions for Benchmark Turbulent Flows in Three Dimensions

A grid convergence study is performed to establish benchmark solutions for turbulent flows in three dimensions (3D) in support of turbulence-model verification campaign at the Turbulence Modeling Resource (TMR) website. The three benchmark cases are subsonic flows around a 3D bump and a hemisphere-cylinder configuration and a supersonic internal flow through a square duct. Reference solutions are computed for Reynolds Averaged Navier Stokes equations with the Spalart-Allmaras turbulence model using a linear eddy-viscosity model for the external flows and a nonlinear eddy-viscosity model based on a quadratic constitutive relation for the internal flow. The study involves three widely-used practical computational fluid dynamics codes developed and supported at NASA Langley Research Center: FUN3D, USM3D, and CFL3D. Reference steady-state solutions computed with these three codes on families of consistently refined grids are presented. Grid-to-grid and code-to-code variations are described in detail.

Diskin, Boris↗

NASA NTRS2015

Fluid Flow Nozzle Energy Harvesters

Power generation schemes that could be used downhole in an oil well to produce about 1 Watt average power with long-life (decades) are actively being developed. A variety of proposed energy harvesting schemes could be used to extract energy from this environment but each of these has their own limitations that limit their practical use. Since vibrating piezoelectric structures are solid state and can be driven below their fatigue limit, harvesters based on these structures are capable of operating for very long lifetimes (decades); thereby, possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. An initial survey identified that spline nozzle configurations can be used to excite a vibrating piezoelectric structure in such a way as to convert the abundant flow energy into useful amounts of electrical power. This paper presents current flow energy harvesting designs and experimental results of specific spline nozzle/ bimorph design configurations which have generated suitable power per nozzle at or above well production analogous flow rates. Theoretical models for non-dimensional analysis and constitutive electromechanical model are also presented in this paper to optimize the flow harvesting system.

bimorph↗

DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗

DOE OSTI2025

An adaptive, data-driven multiscale approach for dense granular flows

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.

Dense granular flows↗

NASA NTRS2014

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

Rodio, J. J.↗

DOE OSTI2026

Rates of Sea‐Level Rise Are Highly Sensitive to Ice Viscosity Parameters in Model Benchmarks

Glacier flow plays a major role in current and future rates of globally averaged sea-level rise. The viscosity of glacial ice, controlling the rate of flow, decreases as stress increases and is highly sensitive to the value of the stress exponent, $n$, in the constitutive equation for viscous flow. Glaciologists and climate modelers almost exclusively assume $n=3$ when modeling ice flow and projecting sea-level rise through forward modeling. However, recent work suggests that $n\approx 4$ better fits observations, prompting the question: How sensitive are projections of sea-level rise to the value of $n$? We use an established community ice flow model and standard benchmark experiments designed as an idealized representation of Pine Island Glacier, West Antarctica. While initializing an $n=3$ model to match observations of an $n=4$ ice sheet is possible, we find that incorrectly assuming $n=3$ when in fact $n=4$ dramatically underestimates rates of sea-level rise. The scale of this error grows nonlinearly with the magnitude of the climate forcing, acting to increase projection uncertainties. Additionally, we find that models often account for this stress-dependent rheology mismatch during model initialization in a way that masks this rheological effect in the short term while leaving model outputs vulnerable to larger biases in longer-term projections. Initializations to observations of Pine Island Glacier display similar rheology-mismatch fingerprints to our idealized example.

climate sensitivity↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

NASA NTRS2013

PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils

PowderSim is a calculation tool that combines a discrete-element method (DEM) module, including calibrated interparticle-interaction relationships, with a mesh-free, continuum, SPH (smoothed-particle hydrodynamics) based module that utilizes enhanced, calibrated, constitutive models capable of mimicking both large deformations and the flow behavior of regolith simulants and lunar regolith under conditions anticipated during in situ resource utilization (ISRU) operations. The major innovation introduced in PowderSim is to use a mesh-free method (SPH-based) with a calibrated and slightly modified critical-state soil mechanics constitutive model to extend the ability of the simulation tool to also address full-scale engineering systems in the continuum sense. The PowderSim software maintains the ability to address particle-scale problems, like size segregation, in selected regions with a traditional DEM module, which has improved contact physics and electrostatic interaction models.

Johnson, Scott↗

NASA NTRS1994

Dynamic and Thermal Turbulent Time Scale Modelling for Homogeneous Shear Flows

A new turbulence model, based upon dynamic and thermal turbulent time scale transport equations, is developed and applied to homogeneous shear flows with constant velocity and temperature gradients. The new model comprises transport equations for k, the turbulent kinetic energy; tau, the dynamic time scale; k(sub theta), the fluctuating temperature variance; and tau(sub theta), the thermal time scale. It offers conceptually parallel modeling of the dynamic and thermal turbulence at the two equation level, and eliminates the customary prescription of an empirical turbulent Prandtl number, Pr(sub t), thus permitting a more generalized prediction capability for turbulent heat transfer in complex flows and geometries. The new model also incorporates constitutive relations, based upon invariant theory, that allow the effects of nonequilibrium to modify the primary coefficients for the turbulent shear stress and heat flux. Predictions of the new model, along with those from two other similar models, are compared with experimental data for decaying homogeneous dynamic and thermal turbulence, homogeneous turbulence with constant temperature gradient, and homogeneous turbulence with constant temperature gradient and constant velocity gradient. The new model offers improvement in agreement with the data for most cases considered in this work, although it was no better than the other models for several cases where all the models performed poorly.

Schwab, John R.↗

NASA NTRS2000

Viscoelastic flow modeling in the extrusion of a dough-like fluid

This work attempts to investigate the effect of viscoelasticity and three-dimensional geometry in screw channels. The Phan-Thien Tanner (PTT) constitutive equation with simplified model parameters was solved in conjunction with the flow equations. Polyflow, a commercially available finite element code was used to solve the resulting nonlinear partial differential equations. The PTT model predicted one log scale lower pressure buildup compared to the equivalent Newtonian results. However, the velocity profile did not show significant changes for the chosen PTT model parameters. Past Researchers neglected viscoelastic effects and also the three dimensional nature of the flow in extruder channels. The results of this paper provide a starting point for further simulations using more realistic model parameters, which may enable the food engineer to more accurately scale-up and design extrusion processes.

NASA Discipline Life Support Systems↗

DOE OSTI2020

A Review of Computational Models for the Flow of Milled Biomass Part II: Continuum-Mechanics Models

The design of efficient material-handling systems for milled lignocellulosic biomass is challenging due to their complex particle morphologies and frictional interactions. Computational modeling, including the discrete element method (DEM) and continuum-based finite-element/volume methods, may offer scientific insight and predictive capabilities for the flow of milled biomass in hoppers and feeders. Herein, this article (Part II) presents a review of current state-of-the-art continuum models for the flow of milled biomass, whereas DEM models are reviewed in a companion article (Part I). Advances of numerical methods to solve the global governing equations are discussed first, followed by a comprehensive review of constitutive models for granular materials, including Drucker–Prager, hypoplastic, Cambridge-type, inertial-rheology, and nonlocal granular fluidity models. Specifically, we provide in-depth discussion on the suitability of those models for milled lignocellulosic biomass materials in terms of nonlinear elasticity, dependence of flow strength on pressure, density and shear rate, and compaction (dilation) associated with hardening (softening). Furthermore, our study shows that, despite the recent advances in continuum granular flow modeling, the most suitable constitutive models still need further development to account for material parametrization, multiflow regimes, and multiscale behavior before they can be reliably used to optimize the design and operation of biomass handling systems.

09 BIOMASS FUELS↗

NASA NTRSDate not supplied

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗

NASA NTRSDate not supplied

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗

NASA NTRS1992

Thermomechanical and bithermal fatigue behavior of cast B1900 + Hf and wrought Haynes 188

A thermomechanical fatigue (TMF) high-temperature life prediction method has been evaluated using the experimental data. Bithermal fatigue (BTF), bithermal creep-fatigue (BTC-F), and TMF experiments were performed using two aerospace structural alloys, cast B1900 + Hf and wrought Haynes 188. The method which is based on the total strain version of strain range partitioning and unified cyclic constitutive modeling requires, as an input, information on the flow and failure behavior of the material of interest. Bithermal temperatures of 483 and 871 C were used for the cast B1900 + Hf nickel-base alloy and 316 and 760 C for the wrought Haynes 188 cobalt-base alloy. Maximum and minimum temperatures were also used in both TMF and BTF tests. Comparisons were made between the results of these tests and isothermal tensile and fatigue test data obtained previously. Qualitative correlations were observed between tensile and isothermal fatigue tests.

Halford, G. R.↗

NASA NTRSDate not supplied

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A Liever↗

NASA NTRSDate not supplied

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A. Liever↗

NASA NTRSDate not supplied

High-Fidelity CFD Verification Workshop 2024 Summary: Spalart-Allmaras QCR2000-R Turbulence Model

This paper summarizes solutions submitted for the Reynolds-averaged Navier-Stokes (RANS) test suite of the High-Fidelity CFD Verification Workshop. The goal of the workshop is to establish standards for verification of computational fluid dynamics (CFD) approaches to simulations of steady and unsteady turbulent flows. The RANS verification studies focus on a one-equation Spalart-Allmaras model with quadratic constitutive relation and rotation correction, SA-neg-QCR2000-R. The verification test cases are a two-dimensional subsonic flow around a Joukowski airfoil, a three-dimensional subsonic flow around an extruded NACA 0012 wing in a tunnel, and a subsonic flow around a wing-body configuration developed for verification of solvers participating in the 5 𝑡 ℎ High-Lift Prediction Workshop. The turbulencemodel formulation, geometry, flow conditions, grids, and reference solutions are described in detail. Solutions for the test cases are computed by seven established CFD solvers on adaptedand fixed-grid families using different discretization approaches. While some noticeable differences between solutions remain, the results achieved by contributing solvers show that different solutions computed for the same RANS model on different grid families can converge to a common limit with grid refinement. The apparent requirements for grid convergence are a well designed family of grids that provide sufficient resolution in important areas and a strong solver capable of deep iterative convergence on each grid. For each test case in the study, the variation between aerodynamic forces computed by different solvers on the finest grids of different families is less than 2%.

Boris Diskin↗