Solving the Radiation Transport Equation for Fibrous Insulation Using FE-DOM
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Christapher Lang↗
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Results for “Lippmann-Schwinger equation”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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NiCd battery cycle life prediction equation for low Earth orbit
Cycle life analysis of the nickel cadmium battery is given. The life prediction equation is limited to spacecraft in low Earth orbits.
Hafen, D.↗
Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation
Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.
ESG↗
Comparison between the PISO algorithm and preconditioning methods for compressible flow
Two widely used family of algorithms, pressure-based and density-based methods, have been developed for computational fluid dynamics (CFD) problems over the years. Pressure-based methods (such as SIMPLE and PISO) use a Poisson-like equation for updating pressure instead of the continuity equation, while density-based methods use the continuity equation to update density (an equation of state is used to provide density in pressure based schemes and pressure in density based schemes). Pressure-based methods were developed originally for incompressible flows at low Reynolds numbers and were then extended to high Reynolds numbers and compressible applications. On the other hand, density based methods were originally developed for transonic flows and have been extended down to low Mach numbers through the use of preconditioning techniques. We compare these two very different approaches to solving the Navier-Stokes equations in order to gain an understanding of their similarities and differences. Specifically, we consider the PISO scheme as a representative pressure-based method and contrast it with a recently developed preconditioning scheme. We also compare the relative performance of the PISO algorithm with a Euler implicit algorithm that is employed to solve the preconditioned equations by means of a vector stability analysis.
Charles L Merkle↗
A Navier-Stokes Boundary Element Solver
Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.
O Lafe↗
Battery-Charge-State Model
Charge-state model for lead/acid batteries proposed as part of effort to make equivalent of fuel gage for battery-powered vehicles. Models based on equations that approximate observable characteristics of battery electrochemistry. Uses linear equations, easier to simulate on computer, and gives smooth transitions between charge, discharge, and recuperation.
Vivian, H. C.↗
Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection
This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data
Navier Stokes Equations↗
Development of a One-Domain Volume-Averaged Navier–Stokes Solver
The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.
Ablation↗
Battery failure model derived from flaw theory
A previously derived failure model for battery lifetime is discussed in terms of growth rate of the flaw, distribution of flaw sizes, and number of flaws. Equations are presented for determining the failure model for a nickel cadmium battery.
Schulman, I.↗
Analysis of Gas Absorption to A Thin Liquid Film in the Presence of A Zero-Order Chemical Reaction
The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.
S Rajagopalan↗
Effect of Turbulence Models on Criticality Conditions in Swirling Flows
The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon , RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.
Robert E Spall↗
Turbo-Design: Open-Source Radial Equilibrium Turbomachinery Solver: Part I - Turbines
Advances in 3D Geometrical Designs and Cooling have played a significant role in improving the efficiency of turbomachinery. However, these advancements must be effectively translated back to the modeler. Machine learning can facilitate this transition. Specifically, machine learning–based loss models can bridge the gap between 3D and 1D designs, enabling modelers not only to predict velocity triangles but also to extract additional geometric features. Currently, the design tools used at NASA have not been updated to support such integration—until now. TurboDesign is an open-source, Python-based framework that replaces TD2 (LEW-11029-1) and AXOD2 (LEW-16323-1), both of which are radial equilibrium solvers for axial turbines. The goal of this update is to enable the integration of machine learning loss models into radial equilibrium equations. Additionally, TurboDesign is designed to support radial machines. This paper presents the governing equations, the assumptions underlying the code, the integration of legacy loss models, an example of machine learning model integration, and a validation comparison with CFD. All code, tutorials, and documentation are available at: https://www.github.com/nasa/turbo-design
Radial Equilibrium↗
Analysis of Impact Induced Damage and its Effect on Structural Integrity of Space Flight Composite Overwrapped Pressure Vessels
The objective of this research work has been to provide analytical background and support to the ongoing experimental program at NASA, White Sands Test Facility, involving testing composite overwrapped pressure vessels (COPV) for impact damage and cyclic pressurization. Preliminary theoretical basis, including the governing equations for a shallow shell subjected to internal pressure, has been established. Effects of the Griffith type cracks on the structural integrity of the cylindrical vessel were evaluated by methods of Fracture Mechanics. The results indicate that the effective mass of the pressure vessel is an important factor influencing the response to impact events. We also have found that the material properties of the target, contained in the constitutive equations of the composite attached to the Aluminum liner, dominate the impact event in the low velocity range, the material properties become less important, while the target mass distribution and the impactor mass become more significant as the velocity of the impactor increases. Therefore, at high-velocity impact it is not only the kinetic energy of the impactor but also its mass which has a significant effect on the dynamics of the event, and consequently on the induced damage. This work also suggests a methodology for an assessment of the rate of loading effects on the degradation of the material toughness associated with a high-velocity impact where the rate effects become significant. To model the rate dependence of the material response a viscoelastic-plastic constitutive equations were assumed, and on this basis predictions are made regarding the rate dependent material resistance curve. Other dynamic phenomena associated with the impact event have been treated in the framework of the Computational Mechanics using the courtesy of Prof. P. Guebelle and his graduate student at University of Illinois at Urbana-Champaign who have an access to a super-fast computer located on their campus. Finally, the guidelines for a follow-up research program are provided in the body of this report. They address three major areas: theoretical research, numerical studies, and further experimental work.
Michael P Wnuk↗
Extensional Flow Convecting a Reactant Undergoing a First Order Homogeneous Reaction and Diffusional Mass Transfer From a Sphere at Low to Intermediate Peclet and Damkohler Numbers
Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 ≤ Pe ≤ 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 ≤ Da ≤ 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r,Θ) = Σ c n (r)P n (cosΘ) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions P n (cosΘ), the variable coefficient PDE can be reduced to a system of N+1 second order ODEs for the radial functions C n (r), n=0,1,2, ... ,N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N+ 1) first order differential equations as a two-point boundary value problem on 1 ≤ r ≤ r •• . Convergence of the expansion for a specific value of N can thus be established and provides "spectral" behavior as well as the full concentration field c(r,Θ).
N Y Shah↗
Form Factors, Grey Bodies and Radiation Conductances (Radks)
With today's analysis tools, large, complex thermal radiation problems are easily solved; But, as with any analytical tool, lack of an understanding of the fundamental equations and technique limitations may leave you with the wrong answer; Whether you are a new engineer or a seasoned veteran, an understanding of the techniques employed by these powerful analysis tools is crucial.
Fluids↗
Improvements to RANS Modeling for Aeroheating Predictions on Blunt Bodies
Accurate predictions of aeroheating are critical for designing thermal protection systems for planetary entry vehicles. For larger vehicles, turbulence in the boundary layer can substantially increase convective heating. This turbulence must be accurately modeled to ensure the thermal protection system is sufficient. The majority of hypersonic turbulence model development and validation focuses on boundary layers developing over flat-plates or sharp cones; these cases are substantially different than the boundary layer that develops over the heatshield of a blunt body traveling at hypersonic speeds. Planetary missions often use blunt body geometries, such as the 70-degree sphere-cone favored by Mars missions or the 45-degree sphere-cone planned for the upcoming DAVINCI mission. Due to smaller vehicle size and the lower velocities in the stagnation region, planetary entry vehicles have relatively low Reynolds numbers. Surface curvature and high enthalpy gradients create additional challenges. These difficulties must be addressed to obtain high accuracy needed for the ambitious planetary missions in the upcoming decade. This work focuses on both assessing and improving Reynolds-averaged Navier-Stokes (RANS) turbulence models for blunt-body geometries typical of planetary entry vehicles, with a focus on one-equation and two-equation formulations.
Mars2020↗
Emergence of Complex Modes in Lightly Damped Structural Systems
In this short presentation format, we will provide a set of useful equations, relationships, and physical interpretations direct from the damped two-mode interaction problem. We will demonstrate that the results from the two-mode interaction problem are in direct agreement with observed test data. Practical methods for estimating the parameters driving the relations direct from modal test data are provided. We finalize with two examples demonstrating weak and strong interactions.
spaceflight hardware↗
Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor
Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.
LES↗