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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Quasi-coherent structures in the turbulent boundary layer. I - Status report on a community-wide summary of the data

A review is presented of the approach, motivation and early results of a reevaluation of the knowledge collected by the research community during thirty years of research on the structure of turbulent boundary layers. Four distinctions or criteria concerning the need to improve the practices in this field are discussed: data versus inferences, possible versus actual versus significant events, one structure versus many, and one or two flows versus the totality of data. Attention given to the known quasi-coherent structures show that three factors significantly reduce the information available from laboratory data as a basis for forming a complete model of the quasi-coherent structure in the turbulent boundary layer: (1) the necessity to ensemble average probe output with resulting loss of phase information, (2) the inability to see more than one or two of the various types of structures simultaneously, and (3) the inability to see the spatial relations between the various quasi-coherent structures resulting from (1) and (2).

Kline, S. J.↗
NASA NTRS2015

Numerical Modeling of Self-Pressurization and Pressure Control by Thermodynamic Vent System in a Cryogenic Tank

This paper presents a numerical model of a system-level test bed - the multipurpose hydrogen test bed (MHTB) using Generalized Fluid System Simulation Program (GFSSP). MHTB is representative in size and shape of a fully integrated space transportation vehicle liquid hydrogen (LH2) propellant tank and was tested at Marshall Space Flight Center (MSFC) to generate data for cryogenic storage. GFSSP is a finite volume based network flow analysis software developed at MSFC and used for thermo-fluid analysis of propulsion systems. GFSSP has been used to model the self-pressurization and ullage pressure control by Thermodynamic Vent System (TVS). A TVS typically includes a Joule-Thompson (J-T) expansion device, a two-phase heat exchanger, and a mixing pump and spray to extract thermal energy from the tank without significant loss of liquid propellant. Two GFSSP models (Self-Pressurization & TVS) were separately developed and tested and then integrated to simulate the entire system. Self-Pressurization model consists of multiple ullage nodes, propellant node and solid nodes; it computes the heat transfer through Multi-Layer Insulation blankets and calculates heat and mass transfer between ullage and liquid propellant and ullage and tank wall. TVS model calculates the flow through J-T valve, heat exchanger and spray and vent systems. Two models are integrated by exchanging data through User Subroutines of both models. The integrated models results have been compared with MHTB test data of 50% fill level. Satisfactory comparison was observed between test and numerical predictions.

Majumdar, Alok↗
DOE OSTI2021

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗
DOE OSTI2021

Transport Modeling of Kinetically Limited Microscale Extraction Systems: Droplet and Supported Liquid Membrane Separations

Microfluidic droplet extraction devices can be used to efficiently measure solute phase transfer kinetics in liquid–liquid extraction systems. In this work, a droplet extraction apparatus was constructed using off-the-shelf and custom 3D printed parts for less than 110 USD. The interfacial kinetics of the transfer of Pu(IV) between an aqueous nitric acid phase and a 5 v/v% tridodecylamine (TDA) in toluene phase were characterized by determining the extent of Pu(IV) transfer between phases at different flow rates. Forward interfacial rate constants calculated from this data using an analytical model are 5.6 × 10 –3 mm s –1 under extraction (aqueous-to-organic solute transfer) conditions and 3.3 × 10 –3 mm s –1 under stripping (organic-to-aqueous solute transfer) conditions. The analytical model is valid when the rate of solute transfer across the interface between the two liquid phases has pseudo-first-order reversible reaction kinetics and is slow relative to the rate of solute transport to the interface. The change in the outlet concentration with residence time determined using the analytical model was compared with the results of a numerical model accounting for advection/diffusion to the interface in addition to kinetically limited interfacial solute transfer. These calculations revealed that for systems with forward interfacial rate constants greater than approximately 10 –2 mm s –1 , the analytical model must be supplemented with a numerical transport model accounting for an additional advection/diffusion mass transfer resistance. This threshold corresponds to a Damköhler number of one. The measured interfacial kinetic rate constants for Pu(IV)/TDA were used in a supported liquid membrane (SLM) numerical model, which showed that the Pu(IV) phase transfer kinetics are fast enough for use in a practical separation.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2026

Comparison of URANS and LES predictions for the open phase of the OECD NEA CSNI fluid structure interaction CFD benchmark

The OECD NEA CSNI WGAMA CFD Task Group ran a benchmark in 2020 and 2021 to assess the predictive capabilities of coupled fluid structure interaction (FSI) CFD analysis methods. This paper presents the predictions made for the open phase of the benchmark using URANS and LES turbulence modelling approaches, and a comparison of the results to the experimental data. The benchmark comprised a channel containing two inline cylinders in cross-flow. The cylinders were fixed at one end, free at the other, and had measured resonant frequencies and damping properties. The URANS modelling used ANSYS Fluent 2-way coupled to ANSYS Mechanical. The LES modelling used Nek5000, 1-way coupled to Diablo. Comparisons with cross-channel velocity profiles are presented, both for the mean flow and its RMS. Comparisons are also made to the frequency spectra for point measurements of fluid velocity and pressure, and for the accelerations of the free end of each cylinder. URANS predicts the average velocity profiles relatively well, and is able to predict the velocity and acceleration spectra at the shedding frequency. However, the frequency content at the 4th harmonic of the shedding frequency is low in the URANS flow fields, and so does not excite accelerations at the resonant frequency of the cylinders. LES makes better predictions of the average profiles, and the velocity spectra agree well at both the shedding frequency and at higher frequencies. In conclusion, the 1-way coupled LES results show good agreement for acceleration spectra.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Combining Distributed Electrochemical Measurements with a Semi-Empirical Model to Identify Local Variations in Overpotentials for PEM Water Electrolyzers

Abstract A segmented cell and PCB approach was used to demonstrate an advanced technique for measuring and understanding the electrochemical behavior of PEM water electrolyzers. By employing a semi-empirical model, discrete modes of overpotential and their spatial distributions were identified in an operating cell. Distributed area-specific resistance (DASR measurements indicate that local dehydration of the polymer electrolyte membrane is the primary driver of increased polarization, behaving similarly to mass transport-limited currents at low flow rates due to ineffective gas-phase bubble removal. To improve quantification, the overall ohmic overpotential is divided into background (η Ohm,b ) and mass transport-coupled (η Ohm,mt ) components. Two types of anode diffusion media, a baseline PTL and a thin foil liquid/gas diffusion layer (LGDL), were examined. The results show significant variations in η Ohm,b and highlight that ineffective bubble removal leads to pronounced local dehydration. The effect of cell temperature on various overpotentials was also examined. Negligible differences in diffusion overpotential were observed when comparing PEWE performance using the PTL and LGDL, despite major differences in two-phase fluid transport within each diffusion media. This underscores the critical role of the catalyst layer's micro-porous structure in diffusion processes. The study highlights the complex nature and intricacies of mass transport limitations within PEWEs.

Roy, Anirban (ORCID:0000000163803386)↗
NASA NTRS1988

Measured and calculated acoustic attenuation rates of tuned resonator arrays for two surface impedance distribution models with flow

An experiment was performed to validate two analytical models for predicting low frequency attenuation of duct liner configurations built from an array of seven resonators that could be individually tuned via adjustable cavity depths. These analytical models had previously been developed for high frequency aero-engine inlet duct liner design. In the low frequency application, the liner surface impedance distribution is unavoidably spatially varying by virtue of available fabrication techniques. The characteristic length of this spatial variation may be a significant fraction of the acoustic wavelength. Comparison of measured and predicted attenuation rates and transmission losses for both modal decomposition and finite element propagation models were in good to excellent agreement for a test frequency range that included the first and second cavity resonance frequencies. This was true for either of two surface impedance distribution modeling procedures used to simplify the impedance boundary conditions. In the presence of mean flow, measurements revealed a fine scale structure of acoustic hot spots in the attenuation and phase profiles. These details were accurately predicted by the finite element model. Since no impedance changes due to mean flow were assumed, it is concluded that this fine scale structure was due to convective effects of the mean flow interacting with the surface impedance nonuniformities.

Parrott, Tony L.↗
NASA NTRS1990

Inflight replanning for diversions

Current procedures for handling flight plan diversions can require too much of the crew's resources. This increases workload and may compromise safety and cause delays in modifying the flight plan. The goal of NASA Langley Research Center's Diverter research program is to develop guidelines for a prototype pilot decision aid for diversions that will reduce cognitive workload, improve safety, increase capacity and traffic flow, and increase aircraft efficiency. The Diverter program has been partitioned into five phases, the first three of which were performed under contract by Lockheed Aeronautical Systems Company, Marietta, GA. In the first two phases, which have been completed, the system requirements and desired functions were defined and a prototype decision-making aid was implemented and demonstrated on a workstation. In phase three, which is currently under way, the pilot/vehicle interface is being defined and the capability of the prototype is being improved. In the last two phases, which will be performed at NASA Langley Research Center, the interface will be implemented, tied into the prototype aiding software, and installed in an advanced simulation facility for testing. In addition, significant implementation issues may be addressed through flight testing on NASA research aircraft. Information is given in viewgraph form.

Palmer, Michael↗
NASA NTRS1991

Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Baysal, Oktay↗
NASA NTRS1993

Phase 2: HGM air flow tests in support of HEX vane investigation

Following the start of SSME certification testing for the Pratt and Whitney Alternate Turbopump Development (ATD) High Pressure Oxidizer Turbopump (HPOTP), cracking of the leading edge of the inner HEX vane was experienced. The HEX vane, at the inlet of the oxidizer bowl in the Hot Gas Manifold (HGM), accepts the HPOTP turbine discharge flow and turns it toward the Gaseous Oxidizer Heat Exchanger (GOX HEX) coil. The cracking consistently initiated over a specific circumferential region of the hex vane, with other circumferential locations appearing with increased run time. Since cracking had not to date been seen with the baseline HPOTP, a fluid-structural interaction involving the ATD HPOTP turbine exit flowfield and the HEX inner vane was suspected. As part of NASA contract NAS8-36801, Pratt and Whitney conducted air flow tests of the ATD HPOTP turbine turnaround duct flowpath in the MSFC Phase 2 HGM air flow model. These tests included HEX vane strain gages and additional fluctuating pressure gages in the turnaround duct and HEX vane flowpath area. Three-dimensional flow probe measurements at two stations downstream of the turbine simulator exit plane were also made. Modifications to the HPOTP turbine simulator investigated the effects on turbine exit flow profile and velocity components, with the objective of reproducing flow conditions calculated for the actual ATD HPOTP hardware. Testing was done at the MSFC SSME Dynamic Fluid Air Flow (Dual-Leg) Facility, at air supply pressures between 50 and 250 psia. Combinations of turbine exit Mach number and pressure level were run to investigate the effect of flow regime. Information presented includes: (1) Descriptions of turbine simulator modifications to produce the desired flow environment; (2) Types and locations for instrumentation added to the flow model for improved diagnostic capability; (3) Evaluation of the effect of changes to the turbine simulator flowpath on the turbine exit flow environment; and (4) Comparison of the experimental turbine exit flow environment to the environment calculated for the ATD HPOTP.

Cox, G. B., Jr.↗
NASA NTRS2001

Internal Flow Simulation of Enhanced Performance Solid Rocket Booster for the Space Transportation System

An enhanced performance solid rocket booster concept for the space shuttle system has been proposed. The concept booster will have strong commonality with the existing, proven, reliable four-segment Space Shuttle Reusable Solid Rocket Motors (RSRM) with individual component design (nozzle, insulator, etc.) optimized for a five-segment configuration. Increased performance is desirable to further enhance safety/reliability and/or increase payload capability. Performance increase will be achieved by adding a fifth propellant segment to the current four-segment booster and opening the throat to accommodate the increased mass flow while maintaining current pressure levels. One development concept under consideration is the static test of a "standard" RSRM with a fifth propellant segment inserted and appropriate minimum motor modifications. Feasibility studies are being conducted to assess the potential for any significant departure in component performance/loading from the well-characterized RSRM. An area of concern is the aft motor (submerged nozzle inlet, aft dome, etc.) where the altered internal flow resulting from the performance enhancing features (25% increase in mass flow rate, higher Mach numbers, modified subsonic nozzle contour) may result in increased component erosion and char. To assess this issue and to define the minimum design changes required to successfully static test a fifth segment RSRM engineering test motor, internal flow studies have been initiated. Internal aero-thermal environments were quantified in terms of conventional convective heating and discrete phase alumina particle impact/concentration and accretion calculations via Computational Fluid Dynamics (CFD) simulation. Two sets of comparative CFD simulations of the RSRM and the five-segment (IBM) concept motor were conducted with CFD commercial code FLUENT. The first simulation involved a two-dimensional axi-symmetric model of the full motor, initial grain RSRM. The second set of analyses included three-dimensional models of the RSRM and FSM aft motors with four-degree vectored nozzles.

Ahmad, Rashid A.↗
NASA NTRS2004

Acoustic Modeling and Analysis for the Space Shuttle Main Propulsion System Liner Crack Investigation

Cracks were found on bellows flow liners in the liquid hydrogen feedlines of several space shuttle orbiters in 2002. An effort to characterize the fluid environment upstream of the space shuttle main engine low-pressure fuel pump was undertaken to help identify the cause of the cracks and also provide quantitative environments and loads of the region. Part of this effort was to determine the duct acoustics several inches upstream of the low-pressure fuel pump in the region of a bellows joint. A finite element model of the complicated geometry was made using three-dimensional fluid elements. The model was used to describe acoustics in the complex geometry and played an important role in the investigation. Acoustic mode shapes and natural frequencies of the liquid hydrogen in the duct and in the cavity behind the flow liner were determined. Forced response results were generated also by applying an edgetone-like forcing to the liner slots. Studies were conducted for state conditions and also conditions assuming two-phase entrapment in the backing cavity. Highly instrumented single-engine hot fire data confirms the presence of some of the predicted acoustic modes.

Casiano, Matthew J.↗
DOE OSTI2019

Small-scale flow topologies in decaying isotropic turbulence laden with finite-size droplets

The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations. The invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors are computed in the carrier phase. The joint probability density functions of the invariants are calculated and conditioned on different distances from the droplet surface. The results show that outside the viscous region near the interface, the flow topologies favor stable focus/stretching and unstable node/saddle/saddle structures, which is in agreement with those found in canonical homogeneous isotropic turbulence. Inside the viscous layer at the droplet surface, the flow topologies shift from a preference for high-enstrophy/low-dissipation motions to favoring low-enstrophy/high-dissipation. At the droplet surface, there is a strong tendency for boundary-layer-like and vortex-sheet flow topologies in which the strain and rotation rates are positively correlated. Furthermore, an interesting observation is that the shapes of the invariant distributions at the droplet surface are remarkably similar to those reported in the viscous sublayer of turbulent wall-bounded flows. Also, the results show that the smallest hydrodynamic length scale of the carrier fluid turbulence is located at the droplet interface and that this length scale is two to three times smaller than that of the surrounding bulk flow. From a computational viewpoint, this suggests a more stringent spatial resolution requirement for the direct numerical simulation of finite-size droplets in isotropic turbulence than its single-phase counterpart.

42 ENGINEERING↗
NASA NTRS1990

Hot gas ingestion test results of a two-poster vectored thrust concept with flow visualization in the NASA Lewis 9- by 15-foot low speed wind tunnel

A 9.2 percent scale STOVL hot gas ingestion model was tested in the NASA Lewis 9 x 15-foot Low-Speed Wind Tunnel. Flow visualization from the Phase 1 test program, which evaluated the hot ingestion phenomena and control techniques, is covered. The Phase 2 test program evaluated the hot gas ingestion phenomena at higher temperatures and used a laser sheet to investigate the flow field. Hot gas ingestion levels were measured for the several forward nozzle splay configurations and with flow control/life improvement devices (LIDs) which reduced the hot gas ingestion. The test was conducted at full scale nozzle pressure ratios and inlet Mach numbers. Results are presented over a range of nozzle pressure ratios at a 10 kn headwind velocity. The Phase 2 program was conducted at exhaust nozzle temperatures up to 1460 R and utilized a sheet laser system for flow visualization of the model flow field in and out of ground effects. The results reported are for nozzle exhaust temperatures up to 1160 R and contain the compressor face pressure and temperature distortions, the total pressure recovery, the inlet temperature rise, and the environmental effects of the hot gas. The environmental effects include the ground plane contours, the model airframe heating, and the location of the ground flow separation.

Johns, Albert L.↗
DOE OSTI2021

Characterizing the Effect of Capillary Heterogeneity on Multiphase Flow Pulsation in an Intermediate–Scale Beadpack Experiment using Time Series Clustering and Frequency Analysis

An intermediate-scale beadpack drainage experiment was conducted to investigate how simple layered lamination heterogeneity affects CO 2 flow. Two simple layers of capillary barriers are manually packed in the tank and slow drainage was carried out using analog fluids to mimic the capillary- and gravity-dominated CO 2 upward migration process in deep saline aquifers. Nonwetting phase saturation time series clustering analysis and frequency analysis have been conducted on the experimental data. Additionally, modified invasion percolation numerical simulations were done on a digital model of the beadpack to compare to experimental results. Results show that capillary barriers can lead to strong pulsation behavior, which in turn can cause unexpected early breaching through other barriers. The inlet pressure is found to be able to respond to saturation changes in far regions of the domain, indicating that the wetting phase can transmit pressure changes from the other phase. Although static simulations were not able to capture all the dynamic behavior observed in the experiment, Monte Carlo composite simulation results combining many different realizations can better illustrate how the nonwetting phase will behave in the heterogeneous domain. Furthermore, our results suggest the need for CO 2 storage site selection with preference given to aquifers with more capillary barriers with finer grain sizes to avoid flow pulsation and to retard plume upward migration.

58 GEOSCIENCES↗
DOE OSTI2022

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. In this study, we use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. Furthermore, we show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Finally, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Effect of Aluminum Alloying on the Hot Deformation Behavior of Nano-bainite Bearing Steel

Interest in using aluminum in nano-bainite steel, especially for high-carbon bearing steel, is gradually growing. In this study, GCr15SiMo and GCr15SiMoAl steels are introduced to investigate the effect of Al alloying on the hot deformation behavior of bearing steel. Results show that the addition of Al not only notably increases the flow stress of steel due to the strong strengthening effect of Al on austenite phase, but also accelerates the strain-softening rates for its increasing effect on stacking fault energy. Al alloying also increases the activation energy of deformation. Two constitutive equations with an accuracy of higher than 0.99 are proposed. The constructed processing maps show the expanded instability regions for GCr15SiMoAl steel as compared with GCr15SiMo steel. This finding is consistent with the occurrence of cracking on the GCr15SiMoAl specimens, revealing that Al alloying reduces the high-temperature plasticity of the bearing steel. On the contrary, GCr15SiMoAl steel possesses smaller grain size than GCr15SiMo steel, manifesting the positive effect of Al on bearing steel. Attention should be focused on the hot working process of bearing steel with Al.

36 MATERIALS SCIENCE↗
NASA NTRS1996

Numerical Investigation of Slag Behavior for RSRM

It is known that the flow field of the redesigned solid rocket motor (RSRM) is very complicated due to the complex characteristics of turbulent multi-phase flow, chemical reaction, particle combustion, evaporation, breakup and agglomeration etc. It requires multi-phase calculations, chemical reaction simulation, and particle combustion, evaporation, and breakup models to obtain a better understanding of thermophysics for the RSRM design using numerical methods. Also, the slag buildup due to the molten particles is another factor affecting the performance of the RSRM. To achieve this goal, the volume of fluid (VOF) method is used to capture the free surface motion so as to simulate the accumulation of the molten particles (slag) of the RSRM. A finite rate chemistry model is used to simulate the chemical reaction effects. For multi-phase calculations, the Hermsen combustion model is used for the aluminum particle combustion analysis and the Taylor Analogy Breakup (TAB) model is used for the particle breakup analysis. An interphase mas-exchange model introduced by Spalding is used for the evaporation calculation. The particle trajectories are calculated using a one-step implicit method for several groups of particle sizes by which the drag forces and heat fluxes are then coupled with the gas phase equations. The preliminary results predicted a reasonable physical simulation of the particle effects using a simple two dimensional solid rocket motor configuration. It shows that the AL/AL2O3 particle sizes are reduced due to the combustion, evaporation, and breakup. The flow field is disturbed by the particles. Mach number distributions in the nozzle are deformed due to the effect of particle concentrations away from the center line.

Liaw, P.↗