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NASA NTRS1998

Three-Dimensional Hydrodynamic Simulations of the Postimpact Proto-Earth

Astrophysical fluid configurations are susceptible to a variety of nonaxisymmetric instabilities under the combined effects of rotation, self-gravity, and thermal pressure. When strong enough, they can induce rapid transport of mass and angular momentum. Our own previous studies of nonaxisymmetric instabilities in model protostars and protostellar disks show that significant transport can occur on orbital timescales and that material can be ejected to large distances. In this contribution, we present three-dimensional simulations of the circumterrestrial debris belt that may have resulted from a giant impact. Our three-dimensional hydrodynamics code with self-gravity and artificial viscosity is fully second-order in space and time; the equations of hydrodynamics and the Poisson equation are solved on an Eulerian cylindrical grid. In the preliminary calculations presented here, we use a simplified EOS where the central proto-Earth is treated as an n = 1/2 polytropic fluid, surrounded by a more compressible, rapidly rotating, fluid disk that represents silicate vapor. Our initial disk parameters are generated from the endstate data of recent smoothed particle hydrodynamics giant-impact calculations. Ultimately, we wish to detennine under what conditions nonaxisymmetric instabilities grow in the postimpact disk and whether they facilitate the transport of material outside the proto-Earth's Roche Limit, leading to the formation of the Moon. In future work, we hope to include a more realistic EOS and the consequences of heating, cooling, and phase transitions.

Pickett, B. K.↗

NASA NTRS1991

Simulation of cryogenic liquid flows with vapor bubbles

Liquid flows in rocket engine components (such as bearings, seals, and pumps) often involve the formation of vapor bubbles due to local superheating of the fluid (either boiling or cavitation). Under the present effort, an analysis has been developed for liquid flows with vapor bubbles, based on a combined Eulerian-Lagrangian technique, in which the continuous (liquid) phase is treated by solving a system of Eulerian conservation equations, while the discrete (vapor bubble) phase is dealt with by integrating Lagrangian equations of motion in computational coordinates. Vapor bubbles of changing size can be accommodated easily by this analysis, and models for the simulation of bubble formation, growth, and motion have been included. The effect of bubble motion and other bubble processes on the continuous (liquid) phase has been accounted for by appropriate bubble mass, momentum, and energy interchange source terms in the Eulerian conservation equations. To demonstrate the viability of the resulting procedure, the cavitating flow of liquid oxygen through a simplified model of a labyrinth seal has been successfully calculated.

De Jong, Frederik J.↗

NASA NTRS1984

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Przekwas, A. J.↗

NASA NTRS2012

Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash

In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

Dubey, A.↗

NASA NTRS1987

Implicit flux-corrected transport scheme for low-speed flow

A new high-order nonlinear Eulerian convection algorithm, the barely implicit correction (BIC)-FCT method, is presented. The BIC-FCT makes it possible to perform accurate, multidimensional, slow-flow calculations in which the fluid expansion is important. Owing to its low cost even in two dimensions, fairly detailed chemistry models and other physical processes can be included. Areas of BIC-FCT applicability include premixed flames, diffusion flames, and turbulent jet flames.

Patnaik, G.↗

NASA NTRS1984

A Lagrangian method for a two layer shallow water model

One of the biggest drawbacks of Eulerian methods is the presence of the nonlinear convective terms which leads to inaccurate representations of advection and fronts. An alternative and conceptually simpler approach is the Lagrangian approach in which the fluid particles themselves are tracked and equations are derived based on local spatial interaction. In this formulation the nonlinear convective terms do not appear. The main drawback with the Lagrangian formulation, however, is that the local spatial interactions are time dependent. That is, at each time level, one must know the current neighbors of a given particle to accurately compute the forces acting on the particle. The Voroni Mesh which is continuously deforming and always linking nearest neighbors is needed. The effectiveness of a simple Lagrangian method for simulating the onset of a Kelvin-Helmholtz instability in a 2 layer fluid is demonstrated.

Augenbaum, J. M.↗

NASA NTRS1994

Project JOVE

The goal of this project is to investigate new areas of research pertaining to free surface-interface fluids mechanics and/or microgravity which have potential commercial applications. This paper presents an introduction to ferrohydrodynamics (FHD), and discusses some applications. Also, computational methods for solving free surface flow problems are presented in detail. Both have diverse applications in industry and in microgravity fluids applications. Three different modeling schemes for FHD flows are addressed and the governing equations, including Maxwell's equations, are introduced. In the area of computational modeling of free surface flows, both Eulerian and Lagrangian schemes are discussed. The state of the art in computational methods applied to free surface flows is elucidated. In particular, adaptive grids and re-zoning methods are discussed. Additional research results are addressed and copies of the publications produced under the JOVE Project are included.

Lyell, M. J.↗

NASA NTRS2016

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

In this paper, a deterministic model is developed to assess the risk of critical renal stone formation for astronauts during space travel. A Population Balance Equation (PBE) model is used to compute the size distribution of a population of nucleating, growing and agglomerating renal calculi as they are transported through different sections of the nephron. The PBE model is coupled to a Computational Fluid Dynamics (CFD) model that solves for steady state flow of urine and transport of renal calculi along with the concentrations of ionic species, calcium and oxalate, in the nephron using an Eulerian two-phase mathematical framework. Parametric simulation are performed to study stone size enhancement and steady state volume fraction distributions in the four main sections of the nephron under weightlessness conditions. Contribution of agglomeration to the stone size distribution and effect of wall friction on the stone volume fraction distributions are carefully examined. Case studies using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, results also indicate that the highest stone volume fraction occurs next to the tubule and duct walls. This suggests that there is an increased potential for wall adhesion with the possibility of evolution towards critical stone sizes.

Microgravity↗

NASA NTRS2016

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

Crystal Growth↗

NASA NTRS1977

Turbulent diffusion from a quasi-kinematical point of view

An estimate for the coefficient of self-diffusion can be derived whenever the Eulerian velocity spectrum is known. The result is more general than those previously obtained. A comparison is made with computed test-particle diffusion in an inviscid two-dimensional Navier-Stokes fluid.

Salu, Y.↗

NASA NTRS1986

Calculation of confined gas-particle two-phase turbulent flows

Numerical calculations have been carried out for gas-particle confined turbulent flows using a recently developed two-phase turbulence closure model. The present modeling scheme utilizes Eulerian formulations of the transport equations and accounts for the combined effects of interphase slip and turbulent dispersion of particles. A multiple-scale turbulence model is used for the turbulent field modeling of the underlying fluid flow. For the particle size and particle loading considered in this study, the fluid turbulence transport equations must be modified to include the damping effects of particles. Predictions and comparisons are made in the fully developed gas-solid pipe flow and the confined particle-laden jet. Numerical results are in reasonably good agreement with the published experimental information.

Chen, C. P.↗

NASA NTRS1991

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Chen, C. P.↗

NASA NTRSDate not supplied

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, where droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Computational Fluid Dynamics↗

NASA NTRSDate not supplied

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, wherein droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Self-Pressurization↗

NASA NTRS1975

Two-dimensional turbulence in inviscid fluids or guiding center plasmas

Numerical tests of the inviscid equilibrium theory of Kraichnan (1975) are described. The mathematical description applies equally well to the two-dimensional electrostatic guiding center plasma and to the two-dimensional inviscid Navier-Stokes fluid. The predictions of this analytic theory are discussed. A pair of coupled equations are derived for the two-time vorticity autocorrelation in Fourier space and the infinitesimal unit response function G of Kraichnan in the so-called Eulerian direct interaction approximation. Kraichnan's assertion that thermodynamic limits exist for the negative temperature states is questioned.

Seyler, C. E., Jr.↗

NASA NTRS1992

An extended Lagrangian method

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Liou, Meng-Sing↗

NASA NTRS1993

An extended Lagrangian method

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.

Liou, Meng-Sing↗

NASA NTRS1995

An Extended Lagrangian Method

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Liou, Meng-Sing↗