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NASA NTRS2015

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

High-Order↗

NASA NTRSDate not supplied

Numerical Implementation of Source Terms to Evaluate Active Porosity Control using a Transpiration Cooled Thermal Protection System

Transpiration cooling has renewed interest of study as a renewable system of thermal protection for atmospheric entry systems. The presence of coolant within the void space of a porous material changes its effective porosity and theorized to lend the external heatshield as a potential means of porous surface control. Effective porosity is explored in two forms: saturation of void space where exiting coolant creates ‘blowing’ over the surface, and partial evacuation of the void space where withdrawal of the coolant creates ‘suction’ on the surface. Thus this study evaluates using transpiration cooling as a as means of active aerodynamic control. The feasibility of the system is evaluated numerically using Reynolds-averaged Navier Stokes based computational fluid dynamics for the aerodynamic assessments by coding source terms of transpiration cooling products at a heat shield surface boundary at the wind side shoulder, creating an asymmetric scheme. Study results show induced moments about the pitch axis incurred following the source terms of a cooling fluid at a near-shoulder location on the heat shield. Lift and drag saw increasing modulation with increase in mass flux rate. Pitch moment was altered a total of 388 N-m between lowest and highest ‘suction’ rates and changed 194 N-m maximum between ‘blowing’ rates.

transpiration cooling↗

NASA NTRS1995

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

NASA NTRS2002

The NASA Microgravity Fluid Physics Program: Knowledge for Use on Earth and Future Space Missions

Building on over four decades of research and technology development related to the behavior of fluids in low gravity environments, the current NASA Microgravity Fluid Physics Program continues the quest for knowledge to further understand and design better fluids systems for use on earth and in space. The purpose of the Fluid Physics Program is to support the goals of NASA's Biological and Physical Research Enterprise which seeks to exploit the space environment to conduct research and to develop commercial opportunities, while building the vital knowledge base needed to enable efficient and effective systems for protecting and sustaining humans during extended space flights. There are currently five major research areas in the Microgravity Fluid Physics Program: complex fluids, multiphase flows and phase change, interfacial phenomena, biofluid mechanics, and dynamics and instabilities. Numerous investigations into these areas are being conducted in both ground-based laboratories and facilities and in the flight experiments program. Most of the future NASA-sponsored fluid physics and transport phenomena studies will be carried out on the International Space Station in the Fluids Integrated Rack, in the Microgravity Science Glovebox, in EXPRESS racks, and in other facilities provided by international partners. This paper will present an overview of the near- and long-term visions for NASA's Microgravity Fluid Physics Research Program and brief descriptions of hardware systems planned to achieve this research.

Kohl, Fred J.↗

NASA NTRS1988

Numerical study of chemically reacting flows using an LU scheme

A new computational fluid dynamic code has been developed for the study of mixing and chemical reactions in the flow fields of ramjets and scramjets. The code employs an implicit finite volume, lower-upper symmetric successive overrelaxation scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a fully-coupled and very efficient manner. The combustion processes are modeled by an 8-species, 14-step finite rate chemistry model whereas turbulence is simulated by a Baldwin-Lomax algebraic model. The validity of the code is demonstrated by comparing the numerical calculations with both experimental data and previous calculations of a cold flow helium injection into a straight channel and premixed hydrogen-air reacting flows in a ramped duct. The code is then used to calculate the mixing and chemical reactions of a hydrogen jet transversely injected into a supersonic airstream. Results are presented describing the flow field, the recirculation regions in front and behind the injector, and the chemical reactions.

Shuen, Jian Shun↗

NASA NTRS1988

Numerical study of chemically reacting flows using an LU scheme

Shuen, Jian Shun↗

NASA NTRSDate not supplied

Progress on the Reduced Gravity Cryogenic Transfer (RGCT) Project

Reduced gravity transfer of cryogenic propellants is crucial to being able to perform planned extended-duration space exploration missions. However, the transfer of cryogenic propellants under reduced gravity conditions has never been demonstrated in a mass-efficient fashion. Efficient cryogenic fluid transfer methods will reduce the transfer time or amount of propellant consumed for chilldown of transfer lines and tanks and ensure successful engine restart or fill of a customer receiver tank. The purpose of the Reduced Gravity Cryogenic Transfer (RGCT) project is to enhance line chilldown, tank chilldown, and tank fill/transfer in a reduced gravity environment through (1) ground and reduced gravity cryogenic testing and (2) numerical model development and validation, which includes empirical, lumped capacitance, and computational fluid dynamics modeling. Technologies developed, data gathered, and models developed and validated under RGCT have played a critical role in enabling longer duration in-space missions. This presentation will provide a description of the ongoing cryogenic propellant transfer ground and reduced gravity testing, numerical modeling, and technology development to-date.

Boiling↗

NASA NTRS2003

The NASA Microgravity Fluid Physics Program: Research Plans for the ISS

Building on over four decades of research and technology development related to the behavior of fluids in low gravity environments, the current NASA Microgravity Fluid Physics Program continues the quest for knowledge to further understand and design better fluids systems for use on earth and in space. NASA's Biological and Physical Research Enterprise seeks to exploit the space environment to conduct research supporting human exploration of space (strategic research), research of intrinsic scientific importance and impact (fundamental research), and commercial research. The strategic research thrust will build the vital knowledge base needed to enable NASA's mission to explore the Universe and search for life. There are currently five major research areas in the Microgravity Fluid Physics Program: complex fluids, niultiphase flows and phase change, interfacial phenomena, biofluid mechanics, and dynamics and instabilities. Numerous investigations into these areas are being conducted in both ground-based laboratories and facilities and in the flight experiments program. Most of the future NASA- sponsored flight experiments in microgravity fluid physics and transport phenomena will be carried out on the International Space Station (ISS) in the Fluids Integrated Rack (FIR), in the Microgravity Science Glovebox (MSG), in EXPRESS racks, and in other facilities provided by international partners. This paper presents an overview of the near- and long-term visions for NASA's Microgravity Fluid Physics Research Program and brief descriptions of hardware systems planned to enable this research.

Kohl, Fred J.↗

NASA NTRS1988

Problems in fluid dynamics

A scheme was developed for the parametric differentiation and integration of gas dynamics equations. A numerical integration of the gas dynamics equations is necessarily performed for a specific set of parameter values. The linear variational equations are obtained by differentiating the exact equations with respect to each of the relevant parameters. The resulting matrix of flow quantities is referred to as the Jacobi matrix. The subsequent procedure is then straightforward. The method was tested for two dimensional supersonic flow past an airfoil, with airfoil thickness, camber, and angle of attack varied. This approach has great potential value for rapidly assessing the effect of design changes. The other focus of the work was on problems in fluid stability, bifurcations, and turbulence.

Sirovich, Lawrence↗

NASA NTRS1993

The validation and application of numerical modelling to supersonic mixing and reacting flows

This study demonstrates that the computational fluid dynamics (CFD) code GASP can be used to predict the features for flowfields representative of scramjet combustors. The validation program undertaken was composed of two parts: a low enthalpy mixing study and a simplified autoignition study. The low enthalpy mixing study was done using low angle helium injection into a Mach 6 airstream over a flat plate. Both matched and overpressurized injection cases were numerically modelled. The agreement with experimental data for the farfield bulk mixing in both cases was reasonable. The combustion studies modelled premixed hydrogen-air reaction with the results being evaluated qualitatively. GASP proved to be highly sensitive to the chemical species present for flow near the ignition temperature, but provided reasonable qualitative results for a subsonic flameholder model.

Vitt, Paul H.↗

NASA NTRS1990

Numerical investigation of the transient SSME fuel preburner combustor flowfield

A computational fluid dynamics (CFD) model with finite-rate reactions, FDNS2DR, has been developed to study the start transient of the Space Shuttle Main Engine Fuel Preburner (FPB) operation. This design tool can predict accurately the severe thermal gradients which are impressed upon the fuel preburner and turbine during the start transient. An axisymmetric configuration with a grid size of 68 x 45 is used to represent the FPB flowfield. The transient upstream boundary conditions are obtained from a one-dimensional Digital Transient Model simulation to better represent the actual operation. The results of the CFD calculation show temperature spikes near the FPB exit whose timing and magnitude agree well with those of the measured turbine inlet temperature data.

Wang, Ten-See↗

NASA NTRS2009

Combined Modeling of Acceleration, Transport, and Hydrodynamic Response in Solar Flares: The Numerical Model - 1

Acceleration and transport of high-energy particles and fluid dynamics of atmospheric plasma are interrelated aspects of solar flares, but for convenience and simplicity they were artificially separated in the past. We present here self consistently combined Fokker-Planck modeling of particles and hydrodynamic simulation of flare plasma. Energetic electrons are modeled with the Stanford unified code of acceleration, transport, and radiation, while plasma is modeled with the Naval Research Laboratory flux tube code. We calculated the collisional heating rate directly from the particle transport code, which is more accurate than those in previous studies based on approximate analytical solutions. We repeated the simulation of Mariska et al. with an injection of power law, downward-beamed electrons using the new heating rate. For this case, a -10% difference was found from their old result. We also used a more realistic spectrum of injected electrons provided by the stochastic acceleration model, which has a smooth transition from a quasi-thermal background at low energies to a non thermal tail at high energies. The inclusion of low-energy electrons results in relatively more heating in the corona (versus chromosphere) and thus a larger downward heat conduction flux. The interplay of electron heating, conduction, and radiative loss leads to stronger chromospheric evaporation than obtained in previous studies, which had a deficit in low-energy electrons due to an arbitrarily assumed low-energy cutoff. The energy and spatial distributions of energetic electrons and bremsstrahlung photons bear signatures of the changing density distribution caused by chromospheric evaporation. In particular, the density jump at the evaporation front gives rise to enhanced emission, which, in principle, can be imaged by X-ray telescopes. This model can be applied to investigate a variety of high-energy processes in solar, space, and astrophysical plasmas.

STOCHASTIC ACCELERATION MODEL↗

NASA NTRS1990

A numerical and experimental analysis of reactor performance and deposition rates for CVD on monofilaments

The computational fluid dynamics (CFD) code FLUENT is adopted to simulate a cylindrical upflow reactor designed for chemical vapor deposition (CVD) on monofilaments. Equilibrium temperature profiles along the fiber and quartz reactor wall are experimentally measured and used as boundary conditions in numerical simulations. Two-dimensional axisymmetric flow and temperature fields are calculated for hydrogen and argon; the effect of free convection is assessed. The gas and surface chemistry is included for predicting silicon deposition from silane. The model predictions are compared with experimentally measured silicon CVD rates. Inferences are made for optimum conditions to obtain uniformity.

Gokoglu, S. A.↗

NASA NTRS1987

Mechanisms by which heat release affects the flow field in a chemically reacting, turbulent mixing layer

The mechanisms by which heat release affects the fluid dynamics in a turbulent reacting mixing layer are studied by direct numerical simulation. In agreement with previous laboratory experiments, the heat release is observed to lower the rate at which the mixing layer grows and to reduce the rate at which chemical products are formed. The baroclinic torque and thermal expansion in the mixing layer are shown to produce changes in the flame vortex structure that act to produce more diffuse vortices than in the constant density case, resulting in lower rotation rates of fluid elements. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques. The density reductions also lower the generation rates of turbulent kinetic energy and the turbulent shear stresses, resulting in less turbulent mixing of fluid elements. Calculations of the energy in the various wave numbers show that the heat release has a stabilizing effect on the growth rates of individual modes. A linear stability analysis of a simlified model problem confirms this, showing that low density fluid in the mixing region will result in a shift of the frequency of the unstable modes to lower wave numbers (longer wavelengths). The growth rates of the unstable modes decrease, contributing to the slower growth of the mixing layer.

Riley, J. J.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1986

Summary of research in applied mathematics, numerical analysis, and computer sciences

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Source record↗

NASA NTRS1988

Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

Chen, S. C.↗