SEARCH · Engineering Papers

Results for “equation of fluid dynamics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 649 records · Page 36

All sources NASA NTRS DOE OSTI

DOE OSTI2025

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

The theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions (3-D) is discussed. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 solar radii where the flow is supersonic) is approximately described by the nonlinear, single fluid, polytropic (magneto-) hydrodynamic equations. Efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations are outlined. The formulation is inviscid and nonmagnetic, but methods allow for the potential inclusion of both features with only modest modifications. One simple, highly idealized, hydrodynamic model stream is examined to illustrate the fundamental processes involved in the 3-D dynamics of stream evolution. Spatial variations in the rotational stream interaction mechanism were found to produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction.

Pizzo, V. J.↗

NASA NTRS2014

Self-Pressurization and Spray Cooling Simulations of the Multipurpose Hydrogen Test Bed (MHTB) Ground-Based Experiment

This paper presents a CFD (computational fluid dynamics) model for simulating the self-pressurization of a large scale liquid hydrogen storage tank. In this model, the kinetics-based Schrage equation is used to account for the evaporative and condensing interfacial mass flows. Laminar and turbulent approaches to modeling natural convection in the tank and heat and mass transfer at the interface are compared. The flow, temperature, and interfacial mass fluxes predicted by these two approaches during tank self-pressurization are compared against each other. The ullage pressure and vapor temperature evolutions are also compared against experimental data obtained from the MHTB (Multipuprpose Hydrogen Test Bed) self-pressurization experiment. A CFD model for cooling cryogenic storage tanks by spraying cold liquid in the ullage is also presented. The Euler- Lagrange approach is utilized for tracking the spray droplets and for modeling interaction between the droplets and the continuous phase (ullage). The spray model is coupled with the VOF (volume of fluid) model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. Droplet ullage heat and mass transfer are modeled. The flow, temperature, and interfacial mass flux predicted by the model are presented. The ullage pressure is compared with experimental data obtained from the MHTB spray bar mixing experiment. The results of the models with only droplet/ullage heat transfer and with heat and mass transfer between the droplets and ullage are compared.

cryogenic fluid storage↗

DOE OSTI2023

Numerical Analysis of Regular Material Point Method and its Application to Multiphase Flows

The material point method (MPM) is gaining wide popularity in engineering research to model and simulate complex multiphase flow dynamics. The method relies on solving the governing equations of motion and transport in a Lagrangian framework using particles also known as material points. The fluid and kinematic properties are stored on the material points while the spatial gradient calculation and temporal integration are performed on a background grid. This Lagrangian framework allows for large deformations, easy integration of constitutive models, and direct import of complex geometries as particles. However, despite their increasing popularity, very few studies have addressed the issues of numerical resolution and stability of MPM techniques. The presence of additional factors such as the number of material points-per-cell, the location of the material points, the CFL-like condition used in time update, and the grid shape functions also increase the complexity of the error analysis when compared to other finite element methods. In this presentation, we analyze the various forms of error incurred in the application of MPM to continuum mechanics and multiphase flows. The effect of the previously mentioned factors on the error dynamics is studied. The application of these principles to canonical and industrial problems is also presented.

high pressure reverse osmosis↗

DOE OSTI2023

Efficient GPU Implementation of Automatic Differentiation for Computational Fluid Dynamics

Many scientific and engineering applications require repeated calculations of derivatives of output functions with respect to input parameters. Automatic Differentiation (AD) is a method that automates derivative calculations and can significantly speed up code development. In Computational Fluid Dynamics (CFD), derivatives of flux functions with respect to state variables (Jacobian) are needed for efficient solutions of the nonlinear governing equations. AD of flux functions on graphics processing units (GPUs) is challenging as flux computations involve many intermediate variables that create high register pressure and require significant memory traffic because of the need to store the derivatives. This paper presents a forward-mode AD method based on multivariate dual numbers that addresses these challenges and simultaneously reduces the floating-point operation count. The dimension of the multivariate dual numbers is optimized for performance. The flux computations are restructured to minimize the number of temporary variables and reduce register pressure. For effective utilization of memory bandwidth, shared memory is used to store the local flux Jacobian. This AD implementation is compared with several other Jacobian implementations on an NVIDIA V100 GPU (V100). For three-dimensional perfect-gas compressible-flow equations implemented in a practical CFD code, the AD implementation of a flux Jacobian based on multivariate dual numbers of dimension 5 outperforms all other GPU AD implementations on V100. Its performance is comparable with the optimized hand-differentiated version. Finally, the implementation achieves 75% of the peak floating-point throughput and 61 % of the peak global device memory bandwidth usage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1982

A numerical solution of the supersonic flow over a rearward facing step with transverse non-reacting hydrogen injection

The present investigation represents an application of computational fluid dynamics to a problem associated with the flow in the combustor region of a supersonic combustion ramjet engine (scramjet). The governing equations are considered, taking into account the Navier-Stokes equations, a molecular viscosity calculation, the molecular thermal conductivity, molecular diffusion, and a turbulence model. The employed numerical solution is patterned after the explicit, time-dependent, unsplit, predictor-corrector, finite-difference method given by MacCormack (1969). The calculation is concerned with the supersonic flow over a rearward-facing step with transverse H2 injection at conditions germane to the combustor region of a scramjet engine. The H2 jet acts as an effective body which essentially shields the primary flow from the rearward-facing step, thus substantially changing the wave pattern in the primary flow.

Berman, H. A.↗

NASA NTRS1995

Combining Comparison Functions and Finite Element Approximations in CFD

In a variety of potential flow applications, the modal element method has been shown to significantly reduce the numerical grid, employ a more precise grid termination boundary condition, and give theoretical insight to the flow physics. The method employs eigenfunctions to replace the numerical grid over significant portions of the flow field. Generally, a numerical grid is employed around obstacles with complex geometry while eigenfunctions are applied to regions in the flow field where the boundary conditions can easily be satisfied. To handle a wider class of computational fluid dynamics (CFD) problems, the present paper extends the modal element to include function approximations which do not satisfy the governing differential equation. To accomplish this task, a double modal series approximation and weighted residual constraints are developed to force the comparison functions to satisfy the governing differential equation and to interface properly with the finite element solution. As an example, the method is applied to the problem of potential flow in a channel with two-dimensional cylindrical like obstacles. The calculated flow fields are in excellent agreement with exact analytical solutions.

Baumeister, Kenneth J.↗

NASA NTRS1998

Electromagnetics and Fluid Dynamics

Previous efforts focused on developing tools for design of low observables were sustained. The final product was the maturation of a high-order accurate finite-volume based code to solve Maxwell's equations. One of the primary achievements was the development and implementation of efficient filtering techniques which enhance the robustness of high-order and optimized schemes without significant adverse impact on accuracy. This has eliminated the stability barrier which restrains the common use of high-order schemes for conservative wave propagation phenomena on curvilinear meshes. A study was performed of crossing shock interactions under conditions of increasing interaction strength and asymmetry. In the first category, the observed computed topological bifurcations were correlated with the formation of various lines of coalescence and divergence evident in experimental and computed surf-ace oil maps. ne flow structure arising from asymmetric interactions was investigated with particular emphasis on: 1) vorticity dynamics, 2) shock-structure and 3) sidewall vortex loading. Several efforts of the prior year were successfully published in archival journals. The high-order algorithms developed for CEM have been implemented into the FDL3DI CFD code are presently undergoing extensive testing. Preliminary results are highly encouraging.

Gaitonde, Datta↗

NASA NTRS1999

A Design Tool for Liquid Rocket Engine Injectors

A practical design tool for the analysis of flowfields near the injector face has been developed and used to analyze the Fastrac engine. The objective was to produce a computational design tool which was detailed enough to predict the interactive effects of injector element impingement angles and points and the momenta of the individual orifice flows. To obtain a model which could be used to simulate a significant number of individual orifices, a homogeneous computational fluid dynamics model was developed. To describe liquid and vapor sub- and super-critical flows, the model included thermal and caloric equations of state which were valid over a wide range of pressures and temperatures. A homogeneous model was constructed such that the local state of the flow was determined directly, i.e. the quality of the flow was calculated. Such a model does not identify drops or their distribution, but it does allow the flow along the injector face and into the acoustic cavity to be predicted. It also allows the film coolant flow to be accurately described. The initial evaluation of the injector code was made by simulating cold flow from an unlike injector element and from a like-on-like overlapping fan (LOL) injector element. The predicted mass flux distributions of these injector elements compared well to cold flow test results. These are the same cold flow tests which serve as the data base for the JANNAF performance prediction codes. The flux distributions 1 inch downstream of the injector face are very similar; the differences were somewhat larger at further distances from the faceplate. Since the cold flow testing did not achieve good mass balances when integrations across the entire fan were made, the CFD simulation appears to be reasonable alternative to future cold flow testing. To simulate the Fastrac, an RP-1/LOX combustion model must be chosen. This submodel must be relatively simple to accomplish three-dimensional, multiphase flow simulations. Single RP-1 pyrolysis and partial oxidation steps were chosen and the combustion was completed with the wet CO mechanism. Soot was also formed with a single global reaction. To validate the combustion submodel, global data from gas generator tests and from subscale motor test were used to predict qualitatively correct mean molecular weights, temperature, and soot levels. Because such tests do not provide general kinetics rates, the methodology is not necessarily appropriate for other than rocket type flows conditions. Soot predictions were made so that radiation heating to the motor walls can be made. These initial studies of the Fastrac were for a small region close to the injector face and chamber wall which included a segment of the acoustic cavity. The region analyzed includes 11 individual orifice holes to represent the LOL elements and the H2 film coolant holes. Typical results of this simulation are shown in Figure 1. At this point the only available test data to verify the predictions are temperatures measured in the acoustic cavity. These temperatures are in reasonable agreement at about 2000R (1111 K). Future work is expected to include improving the computational efficiency or the CFD model and/or using more computer capacity than the single Pentium PC with which these simulations were made.

Farmer, Richard C.↗

NASA NTRS1998

Parallel Domain Decomposition Preconditioning for Computational Fluid Dynamics

This viewgraph presentation gives an overview of the parallel domain decomposition preconditioning for computational fluid dynamics. Details are given on some difficult fluid flow problems, stabilized spatial discretizations, and Newton's method for solving the discretized flow equations. Schur complement domain decomposition is described through basic formulation, simplifying strategies (including iterative subdomain and Schur complement solves, matrix element dropping, localized Schur complement computation, and supersparse computations), and performance evaluation.

Barth, Timothy J.↗

NASA NTRS2004

Aeroacoustic Analysis of a Simplified Landing Gear

A hybrid approach is used to investigate the noise generated by a simplified landing gear without small scale parts such as hydraulic lines and fasteners. The Ffowcs Williams and Hawkings equation is used to predict the noise at far-field observer locations from flow data provided by an unsteady computational fluid dynamics calculation. A simulation with 13 million grid points has been completed, and comparisons are made between calculations with different turbulence models. Results indicate that the turbulence model has a profound effect on the levels and character of the unsteadiness. Flow data on solid surfaces and a set of permeable surfaces surrounding the gear have been collected. Noise predictions using the porous surfaces appear to be contaminated by errors caused by large wake fluctuations passing through the surfaces. However, comparisons between predictions using the solid surfaces with the near-field CFD solution are in good agreement giving confidence in the far-field results.

Lockard, David P.↗

NASA NTRS2011

CO2 Insulation for Thermal Control of the Mars Science Laboratory

The National Aeronautics and Space Administration (NASA) is sending a large (>850 kg) rover as part of the Mars Science Laboratory (MSL) mission to Mars in 2011. The rover's primary power source is a Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) that generates roughly 2000 W of heat, which is converted to approximately 110 W of electrical power for use by the rover electronics, science instruments, and mechanism-actuators. The large rover size and extreme thermal environments (cold and hot) for which the rover is designed for led to a sophisticated thermal control system to keep it within allowable temperature limits. The pre-existing Martian atmosphere of low thermal conductivity CO2 gas (8 Torr) is used to thermally protect the rover and its components from the extremely cold Martian environment (temperatures as low as -130 deg C). Conventional vacuum based insulation like Multi Layer Insulation (MLI) is not effective in a gaseous atmosphere, so engineered gaps between the warm rover internal components and the cold rover external structure were employed to implement this thermal isolation. Large gaps would lead to more thermal isolation, but would also require more of the precious volume available within the rover. Therefore, a balance of the degree of thermal isolation achieved vs. the volume of rover utilized is required to reach an acceptable design. The temperature differences between the controlled components and the rover structure vary from location to location so each gap has to be evaluated on a case-by-case basis to arrive at an optimal thickness. For every configuration and temperature difference, there is a critical thickness below which the heat transfer mechanism is dominated by simple gaseous thermal conduction. For larger gaps, the mechanism is dominated by natural convection. In general, convection leads to a poorer level of thermal isolation as compared to conduction. All these considerations play important roles in the optimization process. A three-step process was utilized to design this insulation. The first step is to come up with a simple, textbook based, closed-form equation assessment of gap thickness vs. resultant thermal isolation achieved. The second step is a more sophisticated numerical assessment using Computational Fluid Dynamics (CFD) software to investigate the effect of complicated geometries and temperature contours along them to arrive at the effective thermal isolation in a CO2 atmosphere. The third step is to test samples of representative geometries in a CO2 filled chamber to measure the thermal isolation achieved. The results of these assessments along with the consistency checks across these methods leads to the formulation of design-guidelines for gap implementation within the rover geometry. Finally, based on the geometric and functional constraints within the real rover system, a detailed design that accommodates all these factors is arrived at. This paper will describe in detail this entire process, the results of these assessments and the final design that was implemented.

CO2↗

NASA NTRS2018

Radiative Heating of Large Meteoroids During Atmospheric Entry

A high-fidelity approach for simulating the aerothermodynamic environments of meteor entries was developed, which allows the commonly assumed heat transfer coefficient of 0.1 to be assessed. This model uses chemically reacting computational fluid dynamics (CFD), coupled with radiation transport and surface ablation. Coupled radiation accounts for the impact of radiation on the flowfield energy equations, while coupled ablation explicitly models the injection of ablation products within the flowfield and radiation simulations. For a meteoroid with a velocity of 20 km/s, coupled radiation is shown to reduce the stagnation point radiative heating by over 60%. The impact of coupled ablation (with coupled radiation) is shown to provide at least a 70% reduction in the radiative heating relative to cases with only coupled radiation. This large reduction is partially the result of the low ionization energies of meteoric ablation products relative to air species. The low ionization energies of ablation products, such as Mg and Ca, provide strong photoionization and atomic line absorption in regions of the spectrum that air species do not. MgO and CaO are also shown to provide significant absorption. Turbulence is shown to impact the distribution of ablation products through the shock-layer, which results in up to a 100% increase in the radiative heating downstream of the stagnation point. To create a database of heat transfer coefficients, the developed model was applied to a range of cases. This database considered velocities ranging from 14 to 20 km/s, altitudes ranging from 20 to 50 km, and nose radii ranging from 1 to 100 m. The heat transfer coefficients from these simulations are below 0.045 for the range of cases, for both laminar and turbulent, which is significantly lower than the canonical value of 0:1. When the new heat transfer model is applied to a Tunguska-like 15 Mt entry, the effect of the new model is to lower the height of burst by up to 2 km, depending on assumed entry angle. This, in turn, results in a significantly larger ground damage footprint than when the canonical heating assumption is used.

Christopher O Johnston↗

NASA NTRS2005

A New Unsteady Model for Dense Cloud Cavitation in Cryogenic Fluids

A new unsteady, cavitation model is presented wherein the phase change process (bubble growth/collapse) is coupled to the acoustic field in a cryogenic fluid. It predicts the number density and radius of bubbles in vapor clouds by tracking both the aggregate surface area and volume fraction of the cloud. Hence, formulations for the dynamics of individual bubbles (e.g. Rayleigh-Plesset equation) may be integrated within the macroscopic context of a dense vapor cloud i.e. a cloud that occupies a significant fraction of available volume and contains numerous bubbles. This formulation has been implemented within the CRUNCH CFD, which has a compressible real fluid formulation, a multi-element, unstructured grid framework, and has been validated extensively for liquid rocket turbopump inducers. Detailed unsteady simulations of a cavitating ogive in liquid nitrogen are presented where time-averaged mean cavity pressure and temperature depressions due to cavitation are compared with experimental data. The model also provides the spatial and temporal history of the bubble size distribution in the vapor clouds that are shed, an important physical parameter that is difficult to measure experimentally and is a significant advancement in the modeling of dense cloud cavitation.

Hosangadi, A.↗

DOE OSTI2020

An Eulerian multimaterial framework for simulating high-explosive aquarium tests

Aquarium tests of cylindrical high-explosive charges provide optical data of the detonation front velocity and shape, propagation of the shock wave in the surrounding water, and expansion rates of the detonation products behind the front. Data from aquarium experiments is often used for calibration of reactive burn models based on phenomenological equations of state (EOS) and reaction rate laws. This paper presents a multimaterial numerical modeling framework to solve the 2D axisymmetric reactive Euler equations for high-explosive aquarium tests, in particular for ammonium nitrate - fuel oil (ANFO) explosives. An extension of the Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the ANFO explosion products, the charge-confining material (polymethyl methacrylate PMMA), and the surrounding water. This study analyzes the sensitivity of calculations (both computational efficiency and numerical accuracy) to different algorithms for the material interface models including the original GFM versus Riemann solver-based strategies. A novel method for defining the left and right states in the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate the overheating error observed in steady-state calculations. Solution convergence and computational efficiency are explored as a function of the spatial and temporal order of the schemes. Results from the computational model with analytical equations of state and fitted reaction rate parameters show very good quantitative agreement with experimentally observed detonation front velocity, reaction products expansion, and shock wave propagation in the surrounding water for a cylindrical ANFO charge encased in PMMA. Finally, the proposed modeling framework, in conjunction with experimental tests, provides a reliable tool to assess equations of state and reaction rate expressions for reactive burn models of confined high explosives.

42 ENGINEERING↗

NASA NTRS2022

Validation of a High-Fidelity Supersonic Parachute Inﬂation Dynamics Model and Best Practice

The parachute inflation dynamics (PID) of a Disk-Gap-Band (DGB) parachute system travelling at supersonic velocities in the high-altitude Earth atmosphere is simulated using a high-fidelity, multiphysics, massively-parallel computational framework. The sensitivity of the simulation results with respect to critical modelling and simulation parameters, including the fluid mechanical governing equations (Euler vs Navier-Stokes with RANS turbulence closure vs Navier-Stokes with LES turbulence closer), the interaction between the flow and the suspension lines (accounted for vs not accounted for), the dynamics of the payload (restrained vs free), and the material model of the heterogeneous fabric canopy (Saint-Venant Kirchoff vs mechanics-informed multiscale neural network), is extensively investigated. The parameter investigation is enabled by advancements to the state-of-the-art in the modelling and simulation of the supersonic parachute inflation process, which are presented as part of the computational framework. The predictive quality of the computational framework in the context of supersonic PID is validated by comparison of the simulation results with the experimental results from NASA’s Advanced Supersonic Parachute Research (ASPIRE) project. Through the validation, best practices for the modelling and simulation of supersonic PID are developed and proposed.

Rabinovitch, Jason↗

DOE OSTI2023

N-particle irreducible actions for stochastic fluids

We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Machine learning accelerated turbulence modeling of transient flashing jets

We report modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ - Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ - Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier-Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit. Published under an exclusive license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗