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NASA NTRS2000

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗
NASA NTRS1972

An analytic guidance technique for planetary and lunar approach trajectories.

An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.

Carlson, N. A.↗
NASA NTRS1985

A relaxation approach to patched-grid calculations with the Euler equations

A conservative zonal-boundary condition that was used with explicit integration schemes is extended to implicit, upwind, relaxation schemes; in particular to the Osher scheme. The rate of convergence was found to increase considerably with the use of the implicit, relaxation-zonal scheme when compared to the explicit scheme. The relaxation-zonal scheme has also been used in a time-accurate mode. Results demonstrating the time accuracy of the scheme and the feasibility of performing calculations in cases where some parts of the given system move relative to others (for example, rotor-stator configurations) are presented.

Rai, M. M.↗
NASA NTRS1993

On the generalized VIP time integral methodology for transient thermal problems

The paper describes the development and applicability of a generalized VIrtual-Pulse (VIP) time integral method of computation for thermal problems. Unlike past approaches for general heat transfer computations, and with the advent of high speed computing technology and the importance of parallel computations for efficient use of computing environments, a major motivation via the developments described in this paper is the need for developing explicit computational procedures with improved accuracy and stability characteristics. As a consequence, a new and effective VIP methodology is described which inherits these improved characteristics. Numerical illustrative examples are provided to demonstrate the developments and validate the results obtained for thermal problems.

Mei, Youping↗
NASA NTRS1993

Correlated states of a quantum oscillator acted by short pulses

Correlated squeezed states for a quantum oscillator are constructed based on the method of quantum integrals of motion. The quantum oscillator is acted upon by short duration pulses. Three delta-kickings of frequency are used to model the pulses' dependence upon the time aspects of the frequency of the oscillator. Additionally, the correlation coefficient and quantum variances of operations of coordinates and momenta are written in explicit form.

Manko, O. V.↗
NASA NTRS1995

Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion

A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, K. P.↗
NASA NTRS1985

A Relaxation Approach to Patched-Grid Calculations with the Euler Equations

A conservative zonal-boundary condition that was used with explicit integration schemes is extended to implicit, upwind, relaxation schemes; in particular to the Osher scheme, The rate of convergence was found to increase considerably with the use of the implicit, relaxation-zonal-scheme when compared to the explicit scheme. The relaxation-zonal scheme has also been used in a time-accurate mode. Results demonstrating the time accuracy of the scheme and the feasibility of performing calculations in cases where some parts of the given system move relative to others (e.g., rotor-stator configurations) are presented.

Rai, Man Mohan↗
NASA NTRS1977

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗
NASA NTRS1981

A split explicit reformulation of the regional numerical weather prediction model of the Japan Meteorological Agency

The split explicit integration scheme for numerical weather prediction models is employed in a version of the regional numerical weather prediction model of the Japan Meteorological Agency. The finite-difference scheme of the model is designed in the manner proposed by Okamura (1975). The horizontal advection terms in the governing equations are integrated with a time step limited by the wind speed while the terms which describe inertial-gravity oscillations are integrated in a succession of shorter time steps. The physical processes included within the model are precipitation, small-scale convection, surface exchanges of sensible and latent heat, and radiative heating and cooling. An example of a surface pressure forecast over Europe is shown for initial data observed at 0000 GMT 29 December 1979. Quantitative precipitation forecasts over Europe and North America for the 24 h period beginning at 0000 GMT 30 December 1979 are also shown. It is concluded that the model is capable of realistically depicting the evolution of synoptic-scale systems.

Duffy, D. G.↗
NASA NTRS2000

GCSS Idealized Cirrus Model Comparison Project

The GCSS Working Group on Cirrus Cloud Systems (WG2) is conducting a systematic comparison and evaluation of cirrus cloud models. This fundamental activity seeks to support the improvement of models used for climate simulation and numerical weather prediction through assessment and improvement of the "process" models underlying parametric treatments of cirrus cloud processes in large-scale models. The WG2 Idealized Cirrus Model Comparison Project is an initial comparison of cirrus cloud simulations by a variety of cloud models for a series of idealized situations with relatively simple initial conditions and forcing. The models (16) represent the state-of-the-art and include 3-dimensional large eddy simulation (LES) models, two-dimensional cloud resolving models (CRMs), and single column model (SCM) versions of GCMs. The model microphysical components are similarly varied, ranging from single-moment bulk (relative humidity) schemes to fully size-resolved (bin) treatments where ice crystal growth is explicitly calculated. Radiative processes are included in the physics package of each model. The baseline simulations include "warm" and "cold" cirrus cases where cloud top initially occurs at about -47C and -66C, respectively. All simulations are for nighttime conditions (no solar radiation) where the cloud is generated in an ice supersaturated layer, about 1 km in depth, with an ice pseudoadiabatic thermal stratification (neutral). Continuing cloud formation is forced via an imposed diabatic cooling representing a 3 cm/s uplift over a 4-hour time span followed by a 2-hour dissipation stage with no cooling. Variations of these baseline cases include no-radiation and stable-thermal-stratification cases. Preliminary results indicated the great importance of ice crystal fallout in determining even the gross cloud characteristics, such as average vertically-integrated ice water path (IWP). Significant inter-model differences were found. Ice water fall speed is directly related to the shape of the particle size distribution and the habits of the ice crystal population, whether assumed or explicitly calculated. In order to isolate the fall speed effect from that of the associated ice crystal population, simulations were also performed where ice water fall speed was set to the same constant value everywhere in each model. Values of 20 and 60 cm/s were assumed. Current results of the project will be described and implications will be drawn. In particular, this exercise is found to strongly focus the definition of issues resulting in observed inter-model differences and to suggest possible strategies for observational validation of the models. The next step in this project is to perform similar comparisons for well observed case studies with sufficient high quality data to adequately define model initiation and forcing specifications and to support quantitative validation of the results.

Starr, David OC.↗
NASA NTRS1991

Exponential integration algorithms applied to viscoplasticity

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.

Freed, Alan D.↗
NASA NTRS2003

Preliminary Analysis and Simulations of July 23rd Extended Anvil Case

A key focus of CRYSTAL-FACE (Cirrus Regional Study of Tropical Anvils and cirrus Layers - Florida Area Cirrus Experiment) was the generation and subsequent evolution of cirrus outflow from deep convective cloud systems. A preliminary integrated look at the observations of an extended cirrus anvil cloud system observed on 23 July 2002 will be presented, including lidar and millimeter radar observations from NASA's ER-2 and in- situ observations from NASA's WB-57 and University of North Dakota Citation. The observations will be compared to preliminary results of simulations using 1-D and 2-D high-resolution (100 meter) cloud resolving models. The CRMs explicitly account for cirrus microphysical development by resolving the evolving ice crystal size distribution (bin model) in time and space. Both homogeneous and heterogeneous nucleation are allowed in the model. The CRM simulations are driven using the output of regional simulations using MM5 that produces deep convection similar to what was observed. The MM5 model employs a 2 km inner grid (32 layers) over a 360 km domain, nested within a 6 km grid over a 600 km domain. Initial and boundary conditions for the 36- hour MM5 simulation are taken from NCEP Eta model analysis at 32 km resolution. Key issues to be explored are the settling of the observed anvil versus the model simulations, and comparisons of dynamical properties, such as vertical motions, occurring in the observations and models. The former provides an integrated measure of the validity of the model microphysics (fallspeed) while the latter is the key factor in forcing continued ice generation.

Lin, R.-F.↗
NASA NTRS2003

CRYSTAL-FACE Analysis and Simulations of the July 23rd Extended Anvil Case

A key focus of CRYSTAL-FACE (Cirrus Regional Study of Tropical Anvils and cirrus Layers - Florida Area Cirrus Experiment) was the generation and subsequent evolution of cirrus outflow from deep convective cloud systems. Present theoretical background and motivations will be discussed. An integrated look at the observations of an extended cirrus anvil cloud system observed on 23 July 2002 will be presented, including lidar and millimeter radar observation; from NASA s ER-2 and in-situ observations from NASA s WB-57 and University of North Dakota Citation. The observations will be compared to results of simulations using 1-D and 2-D high-resolution (100 meter) cloud resolving models. The CRMs explicitly account for cirrus microphysical development by resolving the evolving ice crystal size distribution (bin model) in time and space. Both homogeneous and heterogeneous nucleation are allowed in the model. The CRM simulations are driven using the output of regional simulations using MM5 that produces deep convection similar to what was observed. The MM5 model employs a 2 km inner grid (32 layers) over a 360 km domain, nested within a 6-km grid over a 600-km domain. Initial and boundary conditions for the 36-hour MM5 simulation are taken from NCEP Eta model analysis at 32 km resolution. Key issues to be explored are the settling of the observed anvil versus the model simulations, and comparisons of dynamical properties, such as vertical motions, occurring in the observations and models. The former provides an integrated measure of the validity of the model microphysics (fallspeed) while the latter is the key factor in forcing continued ice generation.

Starr, David↗
NASA NTRS2011

An Overview of the GEOS-5 Aerosol Reanalysis

GEOS-5 is the latest version of the NASA Global Modeling and Assimilation Office (GMAO) earth system model. GEOS-5 contains components for atmospheric circulation and composition (including data assimilation), ocean circulation and biogeochemistry, and land surface processes. In addition to traditional meteorological parameters, GEOS-5 includes modules representing the atmospheric composition, most notably aerosols and tropospheric/stratospheric chemical constituents, taking explicit account of the impact of these constituents on the radiative processes of the atmosphere. MERRA is a NASA meteorological reanalysis for the satellite era (1979-present) using GEOS-5. This project focuses on historical analyses of the hydrological cycle on a broad range of weather and climate time scales. As a first step towards an integrated Earth System Analysis (IESA), the GMAO is extending MERRA with reanalyses for other components of the earth system: land, ocean, bio-geochemistry and atmospheric constituents. In this talk we will present results from the MERRA-driven aerosol reanalysis covering the Aqua period (2003-present). The assimilation of Aerosol Optical Depth (AOD) in GEOS-5 involves very careful cloud screening and homogenization of the observing system by means of a Neural Net scheme that translates MODIS radiances into AERONET calibrated AOD. These measurements are further quality controlled using an adaptive buddy check scheme, and assimilated using the Local Displacement Ensemble (LDE) methodology. For this reanalysis, GEOS-5 runs at a nominal 50km horizontal resolution with 72 vertical layers (top at approx. 8Skm). GEOS-5 is driven by daily biomass burning emissions derived from MODIS fire radiative power retrievals. We will present a summary of our efforts to validate such dataset. The GEOS-5 assimilated aerosol fields are first validated by comparison to independent in-situ measurements (AERONET and PM2.5 surface concentrations). In order to asses aerosol absorption on a global scale, we perform a detailed radiative transfer calculation to simulate the UV aerosol index, comparing our results to OMI measurements. By simulating aerosol attenuated backscatter, we use CALIPSO measurements to evaluate the vertical structure of our aerosol estimates, in particular in regions where we have larger discrepancies with OMI. Finally, the consistency of our AOD estimates with estimates from MISR, MODIS/Deep Blue, OMI and PARASOL will be briefly discussed.

da Silva, Arlindo↗
NASA NTRS1997

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Jongen, T.↗
NASA NTRS1993

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗
NASA NTRS2012

Integrated Structural/Acoustic Modeling of Heterogeneous Panels

A model for the dynamic response of heterogeneous media is presented. A given medium is discretized into a number of subvolumes, each of which may contain an elastic anisotropic material, void, or fluid, and time-dependent boundary conditions are applied to simulate impact or incident pressure waves. The full time-dependent displacement and stress response throughout the medium is then determined via an explicit solution procedure. The model is applied to simulate the coupled structural/acoustic response of foam core sandwich panels as well as aluminum panels with foam inserts. Emphasis is placed on the acoustic absorption performance of the panels versus weight and the effects of the arrangement of the materials and incident wave frequency.

Bednarcyk, Brett, A.↗
NASA NTRS1983

Fast Euler solver for steady, 1-dimensional flows

A numerical technique to solve the Euler equations for steady, one dimensional flows is presented. The technique is essentially implicit, but is structured as a sequence of explicit solutions for each Riemann variable separately. Each solution is obtained by integrating in the direction prescribed by the propagation of the Riemann variables. The technique is second-order accurate. It requires very few steps for convergence, and each step requires a minimal number of operations. Therefore, it is three orders of magnitude more efficient than a standard time-dependent technique. The technique works very well for transonic flows and provides shock fitting with errors as small as 0.001. Results are presented for subsonic problems. Errors are evaluated by comparison with exact solutions.

Moretti, G.↗