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NASA NTRS2004

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

Fridlind, Ann↗

NASA NTRS1993

Numerical modeling of wall-injected scramjet experiments

A wall-injected, hydrogen-fueled scramjet is modeled numerically using a parabolic Navier-Stokes computer code with a k-epsilon turbulence model and finite-rate chemistry. The numerical results are compared to experimental scramjet data taken in a shock tunnel and are found to be in reasonable agreement. Under the conditions studied, the numerical results show that combustion in the scramjet is mainly mixing limited.

Brescianini, C. P.↗

NASA NTRS1981

Numerical modeling of diffusive-convective physical vapor transport in cylindrical vertical ampoules

Diffusive-convective physical vapor transport (PVT) in cylindrical, vertical ampoules of aspect ratio (length/radius) between 0.5 and 10 was modeled numerically. The transport of a crystal forming component through an inert component that undergoes zero net transport was considered. Systems were treated in which: (1) with unequal molecular weight of the components and with temperature gradients typically employed in PVT, convective flow arises dominantly from solutal density gradients; and (2) with equal molecular weight of the components, convective flow can arise only from thermal expansion. It was found that, due to the diffusion-induced horizontal density gradients, buoyancy-driven convective flows are superimposed on the diffusive-advective fluxes without threshold. Net recirculation sets in adjacent to the growing interface, in contrast to the corresponding monocomponent situation where marginally stable convective modes fill the whole fluid space. Depending on the orientation of the main transport direction with respect to gravity, convection can either reduce or enhance the diffusion-induced radial concentration gradients. Significant enhancement of the net transport rate was found to occur only when the whole vapor space between source and growing crystal is filled by a convective recirculation roll. Solutal and thermal convection results are similar; yet for quantitative discussions, thermal and solutal Rayleigh numbers are not interchangeable in contrast to convective situations that lack net mass transport across the fluid space.

Markham, B. L.↗

NASA NTRS2007

Toward Scientific Numerical Modeling

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and verifying that numerical models are translated into code correctly, however, are necessary first steps toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. To address these two shortcomings, two proposals are offered: (1) an unobtrusive mechanism to document input parameter uncertainties in situ and (2) an adaptation of the Scientific Method to numerical model development and deployment. Because these two steps require changes in the computational simulation community to bear fruit, they are presented in terms of the Beckhard-Harris-Gleicher change model.

Kleb, Bil↗

NASA NTRS1998

Numerical Modeling of Solidification in Space With MEPHISTO-4

A pre-flight analysis of the directional solidification of BiSn with MEPHISTO-4 is presented. Simplified Bridgman growth under microgravity conditions is simulated using a two dimensional finite element model. This numerical model is a single domain, pseudo-steady state model, and includes the effects of both thermal and solutal convection. The results show that for all orientations of the applied steady state gravity vector, of magnitude 1 micro-g, the directional solidification process remains diffusion controlled. The maximum convective velocity was found to be 4.424 x 10(exp -5) cm/s for the horizontal Bridgman growth configuration. This value is an order of magnitude lower than the growth velocity. The maximum and minimum values or solute concentration in the liquid at the crystal-melt interface were 13.867 at.% and 13.722 at.%, respectively. This gives a radial segregation value of xi = 1.046% at the interface. A secondary objective of this work was to compare the results obtained to those that consider thermal convection only (no solutal convection). It was found that the convective flow patterns in simulations which included solutal convection were significantly different from those which ignored solutal convection. The level of radial segregation predicted by the current simulations is an order of magnitude lower than that found in simulations which ignore solutal convection. The final aim was to investigate the effect of g-jitter on the crystal growth process. A simulation was performed to calculate the system response to a 1 second, 100 micro-g gravity impulse acting normal to the direction of growth. This pulse is consistent with that induced by Orbiter thruster firings. The results obtained indicate that such a gravity pulse causes an increase in the level of radial solute segregation at the interface from the steady state values. The maximum value of solute concentration in the liquid was found to be 13.888 at.%, the minimum value calculated was 13.706 at.%, yielding a radial segregation value of xi = 1.31% at the interface. These values occurred 126 seconds after the pulse terminated. Thus it is anticipated that the process will remain diffusion controlled even when subjected to such g-jitter.

Simpson, James E.↗

NASA NTRS1984

Numerical Modeling of the Atmosphere

Numerical models and numerical analyses of observations were used to improve the understanding of the physical processes important in global weather and climate. Results from a study of the effect of baroclinic waves on mid-latitude vertical temperature structure show that the waves' vertical eddy heat flux tend to eliminate the potential vorticity gradient near the steering level by causing the static stability to decrease rapidly with height in the lower troposphere above the boundary layer. An empirical study of the relationship between eddy heat fluxes and the meridional temperature gradient has been completed. The results indicate that the feedback in the flux-gradient system is comparable to dissipation on all time scales between the synoptic and the seasonal. The definition of the Eliassen-Palm flux and the Eliassen-Palm and non-acceleration theorems has been generalized to include eddy forcing of condensation. Calculations based on the generalized diagnostics showed that the annual mean eddy forcing of the zonal mean zonal wind is two and one half times stronger when the condensation effects are included.

Stone, P. H.↗

NASA NTRS1984

A slotted test section numerical model for interference assessment

A numerical model of a slotted wind tunnel test section, intended for use with sparsely measured wall pressures in a wall interference assessment procedure, is described. The numerical model includes a discrete finite length wall slot representation and accounts for the nonlinear effects of the dynamic pressure of the slot outflow jet and of the low energy of slot inflow air. By using th numerical model in a wall interference prediction mode, it is demonstrated that accounting for slot discreteness is important in interpreting wall pressures measured between slots, and that accounting for finite slot length and nonlinear effects in the slot boundary condition can yield significant departures from the wall interference predicted using the classical linear homogeneous infinite-length wall representation.

Kemp, W. B., Jr.↗

NASA NTRS2005

3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

Anne Douglass↗

NASA NTRS1980

Thermal Pollution Mathematical Model: Verification of One-Dimensional Numerical Model at Lake Keowee - Volume 2

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Lee, S. S.↗

NASA NTRS1988

Providing operational guidance for the development of sea breeze thunderstorms at the Kennedy Space Center - An experiment using a mesoscale numerical model

The effectiveness of a mesoscale numerical model to provide improved local forecast guidance is evaluated with respect to sea breeze convection storms at the Kennedy Space Center. The model and operational forecast guidance production are described. A case study is presented for sea breeze convection storms and lightning events on July 1, 1986. It is found that the mesoscale numerical model outperforms purely subjective predictions of sea breeze convection. The range of applications for the model are considered.

Lyons, Walter A.↗

NASA NTRS2022

A Framework for Deep Learning Emulation of Numerical Models With a Case Study in Satellite Remote Sensing

Numerical models based on physics represent the state of the art in Earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest generation computers, reducing the ability of modelers to generate simulations for understanding parameter sensitivities and characterizing variability and uncertainty. Thus, surrogate models are often developed to capture the essential attributes of the full-blown numerical models. Recent successes of machine learning methods, especially deep learning (DL), across many disciplines offer the possibility that complex nonlinear connectionist representations may be able to capture the underlying complex structures and nonlinear processes in Earth systems. A difficult test for DL-based emulation, which refers to function approximation of numerical models, is to understand whether they can be comparable to traditional forms of surrogate models in terms of computational efficiency while simultaneously reproducing model results in a credible manner. A DL emulation that passes this test may be expected to perform even better than simple models with respect to capturing complex processes and spatiotemporal dependencies. Here, we examine, with a case study in satellite-based remote sensing, the hypothesis that DL approaches can credibly represent the simulations from a surrogate model with comparable computational efficiency. Our results are encouraging in that the DL emulation reproduces the results with acceptable accuracy and often even faster performance. We discuss the broader implications of our results in light of the pace of improvements in high-performance implementations of DL and the growing desire for higher resolution simulations in the Earth sciences.

Bayesian Deep Learning↗

NASA NTRS1991

GEOSIM: A numerical model for geophysical fluid flow simulation

A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated by finite differences in the meridional plane and spectral decomposition in the azimuthal direction. The user can specify a variety of boundary and initial conditions, and there are five different spectral truncation options. The results of five validation cases are presented: (1) the transition between axisymmetric flow and baroclinic wave flow in the side heated annulus; (2) the steady baroclinic wave of the side heated annulus; (3) the wave amplitude vacillation of the side heated annulus; (4) transition to baroclinic wave flow in a bottom heated annulus; and (5) the Spacelab Geophysical Fluid Flow Cell (spherical) experiment.

Butler, Karen A.↗

NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗

NASA NTRS2000

Numerical Modeling of Drying Residual RP-1 in Rocket Engines

When a Rocket Engine shuts down under a fuel rich environment, a significant amount of unburned RP-1 is trapped In the engine. It is necessary to clean the residual RP-1 prior to subsequent firing to avoid any explosion due to detonation. The conventional method is to dry RP-1 with inert gas such as Nitrogen or Helium. It is difficult to estimate the drying time unless the engine is adequately equipped with instruments to measure the trace of RP-1 during the drying process. Such instrumentation in flight hardware is often impractical and costly. On the other hand numerical modeling of the drying process can provide a good insight for a satisfactory operation of the process. A numerical model can provide answer to questions such as a) how long it takes to dry, b) which fluid is a better dryer for RP-1, c) how to reduce drying time etc. The purpose of the present paper is to describe a numerical model of drying RP-1 trapped in a cavity with flowing nitrogen or helium. The numerical model assumes one dimensional flow of drying fluid in contact with liquid pool of RP-1. An evaporative mass transfer takes place across the contact surface.

Majumdar, Alok↗

NASA NTRS1981

A mesoscale sixth-order numerical modelling system

A numerical simulation system is currently under development for NASA which is intended to improve the modeling of subsynoptic and mesoscale adjustments associated with cyclogenesis, severe storm development and atmospheric transport processes. The model utilizes a standard hydrostatic sigma-p coordinate primitive equation set, with x,y-space differencing accurate to eighth order. A three-step dynamic initialization procedure is employed between the analysis of real-time data and grid interpolation. Results of an 18-hour simulation during which synoptic scale cyclogenesis, subsynoptic scale jet streak adjustments, mesoscale convergence zones and tornadic storms were observed have shown the present model to have the potential for simulating the fine-scale structure of features associated with cyclogenesis and intense squall-line development. The mesoscale model was also found to produce less truncation than the NWS LFM model, although a frictionless version of the mesoscale model somewhat overdeepens and overaccelerates features.

Kaplan, M. L.↗

NASA NTRS1990

Numerical modeling of an arcjet thruster

A numerical model of an arcjet thruster was developed and the results of calculations using this model are compared to the experimental data from a 30 kW arcjet using ammonia as a propellant. The model contains equations for the conservation of mass, radial, axial, and azimuthal momentum, energy, and the radial component of the magnetic field and provides a solution for three components of velocity, temperature, and the axial and radial current as a function of position in an axisymmetric flowfield. The model predicts 12 percent more specific impulse than the experiment when the mass flow and power input are constrained to the experimental values. A major conclusion of this study is that improved procedures for calculating transport properties are necessary if the accuracy of the model is to be improved.

Rhodes, Robert P.↗

NASA NTRS1995

Dynamics of the Antarctic Circumpolar Current. Evidence for Topographic Effects from Altimeter Data and Numerical Model Output

Geosat altimeter data and numerical model output are used to examine the circulation and dynamics of the Antarctic Circumpolar Current (ACC). The mean sea surface height across the ACC has been reconstructed from height variability measured by the altimeter, without assuming prior knowledge of the geoid. The results indicate locations for the Subantarctic and Polar Fronts which are consistent with in situ observations and indicate that the fronts are substantially steered by bathymetry. Detailed examination of spatial and temporal variability indicates a spatial decorrelation scale of 85 km and a temporal e-folding scale of 34 days. Empirical Orthogonal Function analysis suggests that the scales of motion are relatively short, occuring on 1000 km length-scales rather than basin or global scales. The momentum balance of the ACC has been investigated using output from the high resolution primitive equation model in combination with altimeter data. In the Semtner-Chervin quarter-degree general circulation model topographic form stress is the dominant process balancing the surface wind forcing. In stream coordinates, the dominant effect transporting momentum across the ACC is bibarmonic friction. Potential vorticity is considered on Montgomery streamlines in the model output and along surface streamlines in model and altimeter data. (AN)

Gille, Sarah T.↗

NASA NTRS2007

Numerical Modeling of Propellant Boil-Off in a Cryogenic Storage Tank

A numerical model to predict boil-off of stored propellant in large spherical cryogenic tanks has been developed. Accurate prediction of tank boil-off rates for different thermal insulation systems was the goal of this collaboration effort. The Generalized Fluid System Simulation Program, integrating flow analysis and conjugate heat transfer for solving complex fluid system problems, was used to create the model. Calculation of tank boil-off rate requires simultaneous simulation of heat transfer processes among liquid propellant, vapor ullage space, and tank structure. The reference tank for the boil-off model was the 850,000 gallon liquid hydrogen tank at Launch Complex 39B (LC- 39B) at Kennedy Space Center, which is under study for future infrastructure improvements to support the Constellation program. The methodology employed in the numerical model was validated using a sub-scale model and tank. Experimental test data from a 1/15th scale version of the LC-39B tank using both liquid hydrogen and liquid nitrogen were used to anchor the analytical predictions of the sub-scale model. Favorable correlations between sub-scale model and experimental test data have provided confidence in full-scale tank boil-off predictions. These methods are now being used in the preliminary design for other cases including future launch vehicles

Majumdar, A. K.↗