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NASA NTRS2004

Increasing Accuracy in Computed Inviscid Boundary Conditions

A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number of time derivatives of surface-normal velocity (consistent with no flow through the boundary) up to arbitrarily high order. The corrections for the first-order spatial derivatives of pressure are calculated by use of the first-order time derivative velocity. The corrected first-order spatial derivatives are used to calculate the second- order time derivatives of velocity, which, in turn, are used to calculate the corrections for the second-order pressure derivatives. The process as described is repeated, progressing through increasing orders of derivatives, until the desired accuracy is attained.

Dyson, Roger↗
NASA NTRS2020

Desorption Kinetics of O and CO from Graphitic Carbon Surfaces

The desorption of O/CO from graphitic carbon surfaces is investigated using a one-dimensional model describing the adsorbate interactions with the surface phonon bath. The kinetics of desorption are described through the solution of a master equation for the time-dependent population of the adsorbate in an oscillator state, which is modified through thermal fluctuations at the surface. The interaction of the adsorbate with the surface phonons is explicitly captured by using the computed phonon density Of states (PDOS) of the surface. The coupling of the adsorbate with the phonon bath results in the transition of the adsorbate up and down a vibrational ladder. The adsorbate-surface interaction is represented in the model using a Morse potential, which allows for the desorption process to be directly modeled as a transition from bound to free (continuum) state. The PDOS is a property of the material and the lattice; and is highly sensitive to the presence of defects. The effect of etch pits along with random surface defects on the PDOS is considered in the present work. The presence of defects causes a redshift and broadening of the PDOS, which in turn changes the phonon frequency modes available for adsorbate coupling at the surface. Using the realistic PDOS distributions, the phonon-induced desorption (PID) model was used to compute the transition and desorption rates for both pristine and defective systems. Mathissen’s rule is used to compute the phonon relaxation time for pristine and defective systems based on the phonon scattering times for each of the different scattering processes. First, the desorption rates of the pristine system is fitted against the experimental values to obtain the Morse potential parameters for each of the observed adatoms. These Morse potential parameters are used along with the defective PDOS and phonon relaxation time to compute the desorption rates for the defective system. The defective system rates (both transition and desorption) were consistently lower in comparison with the pristine system. The difference between the transition rates is more significant at lower initial states due to higher energy spacing between the levels. In the case of the desorption rates, the difference between the defective and pristine system is more significant at higher temperatures. The desorption rates for each of the system shows an order of magnitude decrease with the strongly bound systems exhibiting the greatest reduction in the desorption rates.

Swaminathan-Gopalan, Krishnan↗
NASA NTRSDate not supplied

Integrated Bosch Process System Models for In-Situ Oxygen and Carbon Production

In-Situ Resource Utilization (ISRU) technology is a vital component to NASA’s mission of a sustainable presence on the Moon and Mars. Local resources can be leveraged to reduce resupply frequency and mass. Elements of the Bosch process, combined with the carbothermal reduction process, can produce oxygen on the lunar surface with minimal consumables. The Bosch process can also produce oxygen on the Martian surface by using the CO 2 -rich environment. Between both systems, adsorption pump, solar thermal energy, carbon formation reactor, and water recovery subsystems are modeled and integrated to create a functional model in MATLAB software. The model is used to simulate performance of the system and reduce mass, power, and volume requirements. This integrated system model provides a tool to scale ISRU technologies for oxygen and carbon production. The MATLAB model is created by developing a system of independent subsystem models that are solved for their quasi-steady state values which can be integrated with respect to time to determine the change in current states. A flexible time stepping method is used to ensure a high level of accuracy during periods of rapid change while still making use of a simple explicit integration method. The flexible time step is calculated for each independent subsystem and the minimum value from those is used as the overall time step. A flexible time step is calculated by dividing a resolution value, or the maximum change per time step, by the variables current rate of change. The maximum value from all points in space is used for subsystem models that contain multiple values. The process is done for every variable that is being monitored in each subsystem and the global minimum is used as that iteration’s timestep. Several assumptions used in the MATLAB model for fluid flow dynamics, such as 1-D gas flow through the sorption pump, are supported by modeling in Ansys Fluent software. The Lunar oxygen production system is outlined in Fig. 1. The carbothermal reduction subsystem uses solar energy to heat a mixture of lunar regolith and carbon powder to produce carbon monoxide. To begin, the carbon monoxide feeds to the modified Bosch subsystem along with hydrogen gas. The reactants then enter the carbon formation reactor where water and carbon powder are produced. Solar thermal energy is used to add energy to the reactor, but waste heat from the carbothermal process is another potential heat source. The water is collected and electrolyzed to produce hydrogen which reenters the Bosch subsystem, and the oxygen is stored for downstream use. The carbon powder is collected and feeds back into the carbothermal subsystem. The Martian oxygen production system uses the full Bosch process and is outlined in Fig 2. A CO 2 adsorption pump thermally cycles to scrub and pressurize CO 2 from the environment. Along with an initial supply of hydrogen, the reactants enter the Reverse Water Gas Shift Reactor (RWGSR) which produces carbon monoxide and water. Carbon monoxide and unreacted hydrogen enter the carbon formation reactor to produce water and carbon powder. The water is collected from both reactors and electrolyzed to reintroduce hydrogen and store oxygen for propellant production or life support. Carbon is removed from the carbon formation reactor and stored. The adsorption pump utilizes rapid cycle temperature swings within a stack of zeolite coated surfaces. The subsystem model solves 1-D quasi-steady conservation laws of the quasi-steady form, shown in Eq. 1, for the gas stream and heat exchange liquid to predict performance parameters such as breakthrough capacity and optimum cycle time. The source term S is used to capture interactions between the fluid flows and the sorbent. A quasi-steady-state scheme is used where no time derivatives appear in the governing equations, except for those in the source terms. This results in an autonomous system, where ∂F/∂x = ƒ(F). The fluxes F are provided at the inlet, and an explicit method is used to solve for the spatial distribution of F. The heat and mass flows to the sorbent are then extracted from the source terms. These flows are numerically integrated to produce a 1-D solution for the system’s state as a function of both time and space. The body of the adsorption pump is separated into two semi-independent models: the heat exchanger fluid flow and gas flow through the zeolite coated surfaces. Both models are solved using the above-described method to find a 1-D solution as a function of space and interact only once a timestep is taken. The interaction point is the sorbent through which all heat transfer between the two models must occur. Sorbent mass adsorption is calculated using the Lagergren model, shown in Eq. 2, where the transfer coefficient, λ D , is found by solving a system of nondimensionalized equations derived by using the heat and mass transfer analogy for transport phenomena. Using Grade 544 Type 13X zeolite as the sorbent material, the equilibrium concentration, θ eq , is calculated using the k-site Langmuir isotherm and fit parameters. Additionally, the enthalpy of adsorption used in the model is computed by interpolation of available data [1]. The subsystem model was validated using the Rapid Cycle Temperature Swing Adsorption (RC-TSA) pump. The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC). The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC).

In situ Resource Utilization↗
NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗
NASA NTRS1984

Vectorized schemes for conical potential flow using the artificial density method

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.

Bradley, P. F.↗
NASA NTRS1990

A multiblock multigrid method for the solution of the three-dimensional Euler equations

A general multiblock, multigrid method for the solution of the Euler equations has been developed. Two types of numerical methods were investigated, van Leer's flux-vector-splitting and Roe's flux-difference-splitting, with MUSCL type differencing used in both methods. An explicit two-step method and a multi-stage Runge-Kutta method have been tested. Results are presented for test cases of a channel flow, nozzle exhaust flow, and a transonic wing.

Cannizzaro, Frank E.↗
NASA NTRS1992

Improving the efficiency of aerodynamic shape optimization procedures

The computational efficiency of an aerodynamic shape optimization procedure which is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newton's method in lieu of an alternating direction implicit (ADI) methodology to calculate the highly converged flow solutions which are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. A substantial factor of 8 decrease in computational time for the optimization process was achieved by implementing both of the design improvements.

Burgreen, Greg W.↗
NASA NTRS1995

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.

Saleeb, Atef F.↗
NASA NTRS1995

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.

Li, Wei↗
NASA NTRS1978

Pilot-optimal augmentation synthesis

An augmentation synthesis method usable in the absence of quantitative handling qualities specifications, and yet explicitly including design objectives based on pilot-rating concepts, is presented. The algorithm involves the unique approach of simultaneously solving for the stability augmentation system (SAS) gains, pilot equalization and pilot rating prediction via optimal control techniques. Simultaneous solution is required in this case since the pilot model (gains, etc.) depends upon the augmented plant dynamics, and the augmentation is obviously not a priori known. Another special feature is the use of the pilot's objective function (from which the pilot model evolves) to design the SAS.

Schmidt, D. K.↗
NASA NTRS1990

Integrated identification and robust control tuning for large space structures

System identification is studied for the explicit purpose of supporting modern H-infinity robust control design objectives. In the analysis, the true plant is not assumed to be in the identification model set. An integrated identification/robust control problem is posed in which the optimal solution guarantees the best robust performance relative to the system information contained in a given experimental data set. A numerical example demonstrating an approximate solution to the problem indicates the usefulness of the approach.

Yam, Y.↗
NASA NTRS1990

Diabatic forcing and initialization with assimilation of cloud and rain water in a forecast model: Methodology

The focus of this part of the investigation is to find one or more general modeling techniques that will help reduce the time taken by numerical forecast models to initiate or spin-up precipitation processes and enhance storm intensity. If the conventional data base could explain the atmospheric mesoscale flow in detail, then much of our problem would be eliminated. But the data base is primarily synoptic scale, requiring that a solution must be sought either in nonconventional data, in methods to initialize mesoscale circulations, or in ways of retaining between forecasts the model generated mesoscale dynamics and precipitation fields. All three methods are investigated. The initialization and assimilation of explicit cloud and rainwater quantities computed from conservation equations in a mesoscale regional model are examined. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed. The explicit cloud calculations were purposely kept simple so that different initialization techniques can be easily and economically tested. Precipitation spin-up processes associated with three different types of weather phenomena are examined. Our findings show that diabatic initialization, or diabatic initialization in combination with a new diabatic forcing procedure, work effectively to enhance the spin-up of precipitation in a mesoscale numerical weather prediction forecast. Also, the retention of cloud and rain water during the analysis phase of the 4-D data assimilation procedure is shown to be valuable. Without detailed observations, the vertical placement of the diabatic heating remains a critical problem.

Raymond, William H.↗
NASA NTRS2005

The Use of Mascons to Resolve Time-Variable Gravity from GRACE

We have analyzed GRACE Level 1B data to resolve time-variable gravity using a local mascon approach. The spherical harmonic solutions released to date resolve the signal from surface hydrology over land areas at spatial scales of 750 to 1000 km over one month intervals [Wahr et al., 2004; Tapley et al., 2004]. In our local approach, we solve explicitly for the mass of water in surface blocks using only the KBRR data collected as GRACE overflies the region of interest. The local representation of gravity minimizes leakage of errors from other areas due to aliasing or mismodelling. In this paper, we report on the analysis of GRACE data from January 2003 through August 2004 over three regions: the Amazon, the Indian subcontinent, and the continental United States. We solve for mass change at 10-day intervals using 4 deg x 4 deg blocks. We give an overview of our latest results, and we present the results of error analyses, and comparisons to both hydrology models and in-situ data.

Lemoine, Frank G.↗
NASA NTRS2005

Computation of the Streamfunction and Velocity Potential for Limited and Irregular Domains

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, while the given velocity vectors can be accurately reconstructed from the computed streamfunction and velocity potential. Because the formulation of the minimization problem allows for circumventing the explicit specification of separate boundary conditions on the streamfunction and velocity potential, the algorithm is easily applicable to irregular domains. By using an advanced minimization algorithm with the use of adjoint techniques, the method is computationally efficient and suitable for problems with large dimensions. An example is presented for coastal oceans to illustrate the practical application of the algorithm.

velocity↗
NASA NTRS1987

Numerical solutions of chemically reacting and radiating flows

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten-degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formulation. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field.

Mani, M.↗
NASA NTRS1975

Calculation of shock-separated turbulent boundary layers

Numerical solutions of the complete, time-averaged conservation equations using several eddy-viscosity models for the Reynolds shear stress to close the equations are compared with experimental measurements in a compressible, turbulent separated flow. An efficient time-splitting, explicit difference scheme was used to solve the two-dimensional conservation equations. The experiment used for comparison was a turbulent boundary layer that was separated by an incident shock wave in a Mach 2.93 flow with a unit Reynolds number of 5.7 x 10 to the seventh power m. Comparisons of predicted and experimental values of surface pressure, shear stress along the wall, and velocity profiles are shown. One of the tested eddy-viscosity models which allows the shear stress to be out of equilibrium with the mean flow produces substantially better agreement with the experimental measurements than the simpler models. A tool is thereby provided for inferring additional information about the flow, such as static pressures in the stream, which might not be directly obtainable from experiments.

Baldwin, B. S.↗
NASA NTRS1976

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Kozdoba, L. A.↗