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At least 415 records · Page 23

Modeling of Liquefaction of Cryogenic Propellant in a Tank

Over the past decades NASA has been focusing to develop technology that would to allow for production of cryogenic propellants on the surface of Mars. The in-situ propellant production reduces the amount of propellants needed to be taken to Mars and ultimately to reduce mission cost. Utilizing Martian resources, the produced gaseous propellants (i.e., oxygen and methane) are liquefied and stored prior to use on the Mars ascent vehicle. In this paper, a model for the liquefaction process of gaseous propellants in a cryogenically refrigerated tank is presented. The tank is considered to be cylindrical with elliptical top and bottom domes. A multi-node transient model is developed based on the mass and energy conservation equations and wall-gas and liquid-gas interface mass and heat transfer correlations. Description of the model and predicted results will be presented in the final paper.

Hedayat, A.↗

One-Dimensional Modeling Methodology for Shock Tubes: Application to the EAST Facility

In this work, a one-dimensional methodology for simulating shock tubes is developed. The model accounts for the viscous interactions of the shock with the shock tube wall by adding an area change source term in the 1-D conservation equations corresponding to the boundary layer growth. This source term corresponds to the mass and energy going into the boundary layer. The boundary layer growth is computed using a simple model with a scaling factor. This scale factor is used to tailor a solution to match the deceleration profile of a shock tube test. In doing so, not only will the source term take into account boundary layer losses, it will also cover any effect due to radiative cooling loses from the gas. For this study, the Electric Arc Shock Tube(EAST) facility at NASA Ames Research Center is modeled for Earth reentry conditions. The purpose of this paper is to investigate if anomalies identified for certain conditions in the EAST data are due to shock deceleration. These anomalies include measuring electron number density above equilibrium predictions and observing that radiance profiles can continually increase behind the shock, never reach steady state, for certain shots (typically those less than 10 km/s). An eleven species air mixture is chosen to study the chemistry of the flow. Comparisons of the simulations to the experimental results are presented. Good agreement with the shock deceleration profiles was achieved by tuning in the boundary layer scale factor. The temperature as well as electron number density increases behind the shock, as has also been observed in the experiments. Finally, radiance comparisons between results from NEQAIR and experiments also show good agreement for some shots, but significant discrepancies are still observed for others.

Sharma, Maitreyee↗

One-Dimensional Modeling Methodology for Shock Tubes: Application to the EAST Facility

In this work, a one-dimensional methodology for simulating shock tubes is developed. The model accounts for the viscous interactions of the shock with the shock tube wall by adding an area change source term in the 1-D conservation equations corresponding to the boundary layer growth. This source term corresponds to the mass and energy going into the boundary layer. The boundary layer growth is computed using a simple model with a scaling factor. This scale factor is used to tailor a solution to match the deceleration profile of a shock tube test. In doing so, not only will the source term take into account boundary layer losses, it will also cover any effect due to radiative cooling loses from the gas. For this study, the Electric Arc Shock Tube(EAST) facility at NASA Ames Research Center is modeled for Earth reentry conditions. The purpose of this paper is to investigate if anomalies identified for certain conditions in the EAST data are due to shock deceleration. These anomalies include measuring electron number density above equilibrium predictions and observing that radiance profiles can continually increase behind the shock, never reach steady state, for certain shots (typically those less than 10 km/s). An eleven species air mixture is chosen to study the chemistry of the flow. Comparisons of the simulations to the experimental results are presented. Good agreement with the shock deceleration profiles was achieved by tuning in the boundary layer scale factor. The temperature as well as electron number density increases behind the shock, as has also been observed in the experiments. Finally, radiance comparisons between results from NEQAIR and experiments also show good agreement for some shots, but significant discrepancies are still observed for others.

Sharma, Maitreyee↗

Field Reconstruction from PIV Measurements Employing Bernstein Polynomial Derived Operators

A fluid-dynamic reconstruction algorithm is presented that generates a least-squares best-fit, two-dimensional density field from a prespecified two-dimensional velocity field. This method recasts the mass-conservation equation as a modified Sylvester equation employing high-order operators derived from modified Bernstein polynomial expansions. To demonstrate its practical utility, this analytic methodology is applied to two canonical cases and a Particle Image Velocimetry dataset obtained from a Mach-2, mechanically back-pressured, isolator experiment. This methodology is envisioned to be used in conjunction with hypersonic-diagnostic techniques to aid in the quantification of isolator flow fields. However, also note that this reconstruction technique is well suited to other applications relevant to fluid dynamics, such as obtaining three-dimensional flow field reconstructions.

Bernstein Polynomials↗

Constrained Field Construction Using Bernstein Polynomial Derived Operators

This method recasts the mass-conservation equation as a Sylvester equation employing high-order derivative operators derived from modified Bernstein polynomial expansions. Given prescribed velocity fields, the algorithm yields a constrained, least-squared solution for the associated density field. To demonstrate the practical utility of this methodology, it is applied to a computationally-derived two-dimensional isolator dataset. This reconstruction method is envisioned to be used in conjunction with diagnostic techniques to aid in the quantification of isolator flow fields, since obtaining highly characterized datasets within this engine component is exceedingly difficult.

Isolator↗

Nodal Modeling of Liquid Propellant Feed and Pressurization System

Nodal or network flow modeling plays an important role in the design and operation of the feed and pressurization system of a liquid rocket engine. Model development and execution time is relatively short for nodal codes in comparison to the Navier-Stokes based CFD codes. Nodal models also allow the inclusion of several components into one model to predict the behavior of a larger system. Unlike CFD models, the nodal models do not need very fine discretization of the flow field because they use empirical correlations to model fluid friction and heat transfer. This paper presents several applications of nodal modeling of liquid propellant feed and pressurization systems using the Generalized Fluid System Simulation Program (GFSSP), a nodal code developed at NASA/ Marshall Space Flight Center. GFSSP discretizes the flow field into nodes which are connected by branches. The mass and energy conservation equations and the equation of state are solved to calculate pressure, temperature, and resident mass at the nodes. The momentum equations are solved at the branches to calculate flow rates. Applications include a) tank pressurization by inert gas as well as autogenous pressurization by gaseous propellant, b) submerged pressurization by helium, c) self-pressurization due to boil-off of cryogenic propellant, d) chilldown of a transfer line of a cryogenic propellant feed system, and e) chilldown and filling of a cryogenic tank. Each of the above-mentioned models was verified and validated by comparing with test data.

Nodal Model↗

Nodal Modeling of Liquid Propellant Feed and Pressurization System

Nodal or network flow modeling plays an important role in the design and operation of the feed and pressurization system of a liquid rocket engine. Model development and execution time is relatively short for nodal codes in comparison to the Navier-Stokes based CFD codes. Nodal models also allow the inclusion of several components into one model to predict the behavior of a larger system. Unlike CFD models, the nodal models do not need very fine discretization of the flow field because they use empirical correlations to model fluid friction and heat transfer. This paper presents several applications of nodal modeling of liquid propellant feed and pressurization systems using the Generalized Fluid System Simulation Program (GFSSP), a nodal code developed at NASA/ Marshall Space Flight Center. GFSSP discretizes the flow field into nodes which are connected by branches. The mass and energy conservation equations and the equation of state are solved to calculate pressure, temperature, and resident mass at the nodes. The momentum equations are solved at the branches to calculate flow rates. Applications include a) tank pressurization by inert gas as well as autogenous pressurization by gaseous propellant, b) submerged pressurization by helium, c) self-pressurization due to boil-off of cryogenic propellant, d) chilldown of a transfer line of a cryogenic propellant feed system, and e) chilldown and filling of a cryogenic tank. Each of the above-mentioned models was verified and validated by comparing with test data.

Nodal Model↗

Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

Leonard, B. P.↗

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Klopfer, G. H.↗

Fast, conservative schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) are investigated for the solution of matrix equations resulting from finite-difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. Two implicit AF procedures are presented, and their convergence performance is compared with that of the standard transonic solution procedure: successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. Results indicate a substantial improvement in convergence rate for AF schemes relative to SLOR.

Holst, T. L.↗

Conservative implicit schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.

Holst, T. L.↗

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg, (2) Re = 1000, alpha = 15 deg, (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗

Analysis of two-dimensional incompressible flow past airfoils using unsteady Navier-Stokes equations

The conservative form of the unsteady Navier-Stokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, alpha = 5 deg., (2) Re =1000, alpha = 15 deg., (3) Re = 10,000, alpha = 5 deg. No artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (3).

Ghia, K. N.↗

Computations of unsteady transonic flow governed by the conservative full potential equation using an alternating direction implicit algorithm

A development was the time linearization of the density function. This linearization reduces the solution process from solving just a single equation. Two sample cases were computed. First, a one dimensional traveling shock wave was computed and compared with the analytic solution. Second, a two dimensional case was calculated for a flow field which resulted from a thickening and subsequently, thinning airfoil. The resulting flow field, which included a traveling shock wave, was compared to the flow field obtained from the low frequency, small disturbance, transonic equation.

Goorjian, P. M.↗

Unsteady vortex-dominated flows around maneuvering wings over a wide range of Mach numbers

The problem of unsteady flow around maneuvering wings is solved using the unsteady Euler equations. The unsteady conservative Euler equations are derived for the flow relative motion with respect to a moving (translating and rotating) frame of reference. The resulting equations can handle the most general case for unsteady three-dimensional flow around maneuvering wings or wing-body configurations undergoing six degrees of freedom motion; three translations and three rotations. The equations are solved using two computational schemes; an explicit multistage finite-volume scheme and an implicit approximately factored finite-volume scheme. The computational applications cover two cases. The first case is for a locally conical supersonic flow of rolling oscillation of a sharp-edged delta wing at zero angle of attack. The second case is for a pitching oscillation around a mean angle of attack of a NACA 0012 airfoil in transonic flow.

Kandil, Osama A.↗

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Abramopoulos, Frank↗

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Deshpande, S. M.↗