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NASA NTRS2018

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↗

NASA NTRS2018

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

Sharma, Maitreyee↗

NASA NTRS2000

A Unified Wall Boundary Treatment for Viscous and Inviscid Flows in the CE/SE Method

In the setting of the conservation element-solution element (CE/SE) method, a new and unified wall boundary treatment for the Navier-Stokes and Euler Equations is proposed. In essence, the shear stress exerted on the fluid by a wall is modeled as a source term as a part of local spacetime flux conservation in the vicinity of a wall boundary. When the fluid is inviscid, the source term vanishes and the boundary condition reduces to the usual 'slip' condition. On the other hand, when the fluid is viscous, the source-term effect is consistent with the traditional no-slip condition. Numerical results show that the new treatment is robust, efficient, and accurate for viscous and inviscid flows.

Chang, Sin-Chung↗

NASA NTRS1983

The prediction of the noise of supersonic propellers in time domain - New theoretical results

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Farassat, F.↗

NASA NTRS2010

Modeling Vortex Generators in the Wind-US Code

A source term model which simulates the effects of vortex generators was implemented into the Wind-US Navier Stokes code. The source term added to the Navier-Stokes equations simulates the lift force which would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, supersonic flow in a rectangular duct with a counterrotating vortex generator pair, and subsonic flow in an S-duct with 22 co-rotating vortex generators. The validation results indicate that the source term vortex generator model provides a useful tool for screening vortex generator configurations and gives comparable results to solutions computed using a gridded vane.

Dudek, Julianne C.↗

NASA NTRS2011

Modeling Vortex Generators in a Navier-Stokes Code

A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.

Dudek, Julianne C.↗

DOE OSTI2025

Using Calibrated Sodium Data for Preliminary Validation of the SRT Code for Advanced Reactors

Various types of non-light water reactors are currently engaged in the U.S. licensing process. Because of inherent differences compared with well-established large light water reactors, appropriate assessment tools are needed. Specifically, source term analysis, which determines environmental dose impacts from potential accident scenarios, is a crucial part of design and licensing. The U.S. Nuclear Regulatory Commission has emphasized the importance of mechanistic source term analysis for advanced reactor deployments. To align with these needs, Argonne National Laboratory has developed the Simplified Radionuclide Transport (SRT) source term analysis code for metal fuel Sodium-cooled Fast Reactors (SFRs) and microreactors. SRT conducts time-dependent radionuclide transport and retention in SFRs for core and ex-core radionuclide source accident sequences. The main objective of SRT is to provide rapid sensitivity and uncertainty analyses, incorporating parametric uncertainties and summarizing probabilistic results. As part of the code validation process, a study focused on the bubble scrubbing module was performed using an experiment recently carried out by the University of Wisconsin-Madison. Based on the analysis, the modeling approach in SRT provides accurate results for small and large aerosols, while slight underprediction of radionuclide aerosol removal are observed for medium sized aerosols. However, the deviation is minor, considering the highly uncertain phenomenon and range of results, and is in the conservative direction. In addition, uncertainty information derived from the experiments is further implemented, reflecting the actual span of parameters, which leads to enhanced agreement with code predictions. The results demonstrate that SRT provides reasonable predictions for the bubble scrubbing process in sodium pool.

Kam, Dong Hoon↗

DOE OSTI2025

Catastrophic Cooling Instability in Optically Thin Plasmas

The solar corona is the prototypical example of a low-density environment heated to high temperatures by external sources. The plasma cools radiatively, and because it is optically thin to this radiation, it becomes possible to model the density, velocity, and temperature structure of the system by modifying the MHD equations to include an energy source term that approximates the local heating and cooling rates. The solutions can be highly inhomogeneous and even multiphase because the well-known linear instability associated with this source term, thermal instability, leads to a catastrophic heating and cooling of the plasma in the nonlinear regime. Here we show that there is a separate, much simpler linear instability accompanying this source term that can rival thermal instability in dynamical importance. The stability criterion is the isochoric one identified by Parker (1953), and we demonstrate that cooling functions derived from collisional ionization equilibrium are highly prone to violating this criterion. If catastrophic cooling instability can act locally in global simulations, then it is an alternative mechanism for forming condensations, and due to its nonequilibrium character, it may be relevant to explaining a host of phenomena associated with the production of cooler gas in hot, low density plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗

NASA NTRS2004

Part 1 of a Computational Study of a Drop-Laden Mixing Layer

This first of three reports on a computational study of a drop-laden temporal mixing layer presents the results of direct numerical simulations (DNS) of well-resolved flow fields and the derivation of the large-eddy simulation (LES) equations that would govern the larger scales of a turbulent flow field. The mixing layer consisted of two counterflowing gas streams, one of which was initially laden with evaporating liquid drops. The gas phase was composed of two perfect gas species, the carrier gas and the vapor emanating from the drops, and was computed in an Eulerian reference frame, whereas each drop was tracked individually in a Lagrangian manner. The flow perturbations that were initially imposed on the layer caused mixing and eventual transition to turbulence. The DNS database obtained included transitional states for layers with various liquid mass loadings. For the DNS, the gas-phase equations were the compressible Navier-Stokes equations for conservation of momentum and additional conservation equations for total energy and species mass. These equations included source terms representing the effect of the drops on the mass, momentum, and energy of the gas phase. From the DNS equations, the expression for the irreversible entropy production (dissipation) was derived and used to determine the dissipation due to the source terms. The LES equations were derived by spatially filtering the DNS set and the magnitudes of the terms were computed at transitional states, leading to a hierarchy of terms to guide simplification of the LES equations. It was concluded that effort should be devoted to the accurate modeling of both the subgridscale fluxes and the filtered source terms, which were the dominant unclosed terms appearing in the LES equations.

Okong'o, Nora A.↗

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 NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗

NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Kim, John↗

NASA NTRS1998

Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.

Busby, Judy↗

NASA NTRS2004

Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops : Part 1. Direct numerical simulation formulation and a priori analysis

This paper is organized as follows. In § 2, we present the DNS formulation. This formulation consists of a set of coupled conservation equations for the gas phase and the liquid phase (i.e. the drops). The coupling describing the interaction between the two phases is provided in the gas-phase conservation equations by source terms. In § 3, we analyse the DNS results; in particular, we evaluate the adopted form of the heat and mass fluxes. The gas-phase LES equations are developed in § 4 and assumptions that may simplify these equations are examined using the DNS database. Thereafter, the contribution of the source terms is examined by considering the budget of the LES equations. The final form of the LES equations are then presented, in which only the SGS fluxes and the FSTs need be modelled. A parallel perspective on the importance of the source terms is presented in § 5, wherein the irreversible entropy production (i.e. the dissipation) expression for two-phase flow with phase change is derived and evaluated for transitional DNS and the filtered flow fields. Models for the FSTs appearing in the LES equations are investigated in § 6, while several constantcoefficient SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an SGS models are proposed and calibrated in § 7. The present study aims to create simple models so that the modelling approach can be validated by means of an a posteriori study.

"Okong'o, Nora A.", 'Bellan, Josette↗

NASA NTRS2002

Elliptic Grid Generation of Spiral-Bevel Pinion Gear Typical of OH-58 Helicopter Transmission

This paper discusses the source term treatment in the numerical solution of elliptic partial differential equations for an interior grid generation problem in generalized curvilinear coordinates. The geometry considered is that of a planar cross-section of a generic spiral-bevel gear tooth typical of a pinion in the OH-58 helicopter transmission. The source terms used are appropriate for an interior grid domain where all the boundaries are prescribed via a combination of Dirichlet and Neumann boundary conditions. New constraints based on the Green's Theorem are derived which uniquely determine the coefficients in the source terms. These constraints are designed for boundary clustered grids where gradients in physical quantities need to be resolved adequately. However, it is seen that the present formulation works satisfactorily for mild clustering also. Thus, a fully automated elliptic grid generation technique is made possible where there is no need for a parametric study of these parameters since the new relations fix these free parameters uniquely.

Kaul, Upender K.↗

NASA NTRS2007

Enhanced Elliptic Grid Generation

An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.↗

NASA NTRS1984

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

The equations of momentum annd continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in Earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

Huff, R. G.↗