A review of fundamental equations of the mixture of a gas with small solid particles
Fluid dynamics of gas-particle flow and solid particle behavior in mixed flow
Pai, S. I.↗
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Modeling the Gas Dynamics Environment in a Subscale Solid Rocket Test Motor
Subscale test motors are often used for the evaluation of solid rocket motor component materials such as internal insulation. These motors are useful for characterizing insulation performance behavior, screening insulation material candidates and obtaining material thermal and ablative property design data. One of the primary challenges associated with using subscale motors however, is the uncertainty involved when extrapolating the results to full-scale motor conditions. These uncertainties are related to differences in such phenomena as turbulent flow behavior and boundary layer development, propellant particle interactions with the wall, insulation off-gas mixing and thermochemical reactions with the bulk flow, radiation levels, material response to the local environment, and other anomalous flow conditions. In addition to the need for better understanding of physical mechanisms, there is also a need to better understand how to best simulate these phenomena using numerical modeling approaches such as computational fluid dynamics (CFD). To better understand and model interactions between major phenomena in a subscale test motor, a numerical study of the internal flow environment of a representative motor was performed. Simulation of the environment included not only gas dynamics, but two-phase flow modeling of entrained alumina particles like those found in an aluminized propellant, and offgassing from wall surfaces similar to an ablating insulation material. This work represents a starting point for establishing the internal environment of a subscale test motor using comprehensive modeling techniques, and lays the groundwork for improving the understanding of the applicability of subscale test data to full-scale motors. It was found that grid resolution, and inclusion of phenomena in addition to gas dynamics, such as two-phase and multi-component gas composition are all important factors that can effect the overall flow field predictions.
Eaton, Andrew M.↗
Crack propagation and arrest in pressurized containers
The problem of crack propagation and arrest in a finite volume cylindrical container filled with pressurized gas is considered. It is assumed that the cylinder contains a symmetrically located longitudinal part-through crack with a relatively small net ligament. The net ligament suddenly ruptures initiating the process of fracture propagation and depressurization in the cylinder. Thus the problem is a coupled gas dynamics and solid mechanics problem the exact formulation of which does not seem to be possible. The problem is reduced to a proper initial value problem by introducing a dynamic fracture criterion which relates the crack acceleration to the difference between a load factor and the corresponding strength parameter. The results indicate that generally in gas filled cylinders fracture arrest is not possible unless the material behaves in a ductile manner and the container is relatively long.
Erdogan, F.↗
Thermal-Flow Code for Modeling Gas Dynamics and Heat Transfer in Space Shuttle Solid Rocket Motor Joints
A new, thermal-flow simulation code, called SFLOW. has been developed to model the gas dynamics, heat transfer, as well as O-ring and flow path erosion inside the space shuttle solid rocket motor joints by combining SINDA/Glo, a commercial thermal analyzer. and SHARPO, a general-purpose CFD code developed at Thiokol Propulsion. SHARP was modified so that friction, heat transfer, mass addition, as well as minor losses in one-dimensional flow can be taken into account. The pressure, temperature and velocity of the combustion gas in the leak paths are calculated in SHARP by solving the time-dependent Navier-Stokes equations while the heat conduction in the solid is modeled by SINDA/G. The two codes are coupled by the heat flux at the solid-gas interface. A few test cases are presented and the results from SFLOW agree very well with the exact solutions or experimental data. These cases include Fanno flow where friction is important, Rayleigh flow where heat transfer between gas and solid is important, flow with mass addition due to the erosion of the solid wall, a transient volume venting process, as well as some transient one-dimensional flows with analytical solutions. In addition, SFLOW is applied to model the RSRM nozzle joint 4 subscale hot-flow tests and the predicted pressures, temperatures (both gas and solid), and O-ring erosions agree well with the experimental data. It was also found that the heat transfer between gas and solid has a major effect on the pressures and temperatures of the fill bottles in the RSRM nozzle joint 4 configuration No. 8 test.
Wang, Qunzhen↗
Stability of chromium (III) sulfate in atmospheres containing oxygen and sulfur
The stability of chromium sulfate in the temperature range from 880 K to 1040 K was determined by employing a dynamic gas-solid equilibration technique. The solid chromium sulfate was equilibrated in a gas stream of controlled SO3 potential. Thermogravimetric and differential thermal analyses were used to follow the decomposition of chromium sulfate. X-ray diffraction analysis indicated that the decomposition product was crystalline Cr2O3 and that the mutual solubility between Cr2(SO4)3 and Cr2O3 was negligible. Over the temperature range investigated, the decomposition pressure were significantly high so that chromium sulfate is not expected to form on commercial alloys containing chromium when exposed to gaseous environments containing oxygen and sulfur (such as those encountered in coal gasification).
Jacob, K. T.↗
Petrologic evolution of CM chondrites: The difficulty of discriminating between nebular and parent-body effects
We wish to draw attention to a major controversy that has arisen in the area of CM-chondrite petrology. The problem is important because its resolution will have profound implications for ideas concerning nebular dynamics, gas-solid interactions in the nebula, and accretionary processes in the nebula, among other issues. On the one hand, cogent arguments have been presented that 'accretionary dust mantles,' were formed in the solar nebula prior to accretion of the CM parent asteroid(s). On the other hand, no-less-powerful arguments have been advanced that a significant fraction of the CM lithology is secondary, produced by aqueous alteration in the near-surface regions of an asteroid-sized object. Because most, if not all, CM chondrites are breccias, these two views could coexist harmoniously, were it not for the fact that some of the coarse-grained lithologies surrounded by 'accretion dust mantles' are themselves of apparently secondary origin. Such an observation must clearly force a reassessment of one or both of the present schools of thought. Our objective here is to stimulate such a reassessment. Four possible resolutions of this conflict may be postulated. First, perhaps nature found a way of permitting such secondary alteration to take place in the nebula. Second, maybe dust mantles could form in a regolith, rather than a nebular, environment. Third, it is possible that dust mantles around secondary lithologies are different from those around primary lithologies. Finally, perhaps formation of CM chondrites involved a more complex sequence of events than visualized so far, so that some apparently 'primary' processes postdated certain 'secondary' processes.
Kerridge, J. F.↗
String Potentiometers for Supersonic Split-Line Thrust Vector Amplification Factor Verification
The static fire of NASA’s Mars Ascent Vehicle (MAV) first stage Solid Rocket Motor (SRM1) Demonstration Motor-1 (DM-1) occurred at Edwards Air Force Base (AFB) on April 7, 2023. Among other objectives, this test successfully demonstrated the Thrust Vector Control (TVC) system, including the Technology Readiness Level (TRL) of the Supersonic Split-Line (SSSL) nozzle. An essential characteristic of the SSSL is the thrust vector amplification factor (TVAF) it exhibits; however, empirically quantifying this behavior is difficult due to the limitations of measuring the internal nozzle gas dynamics of a Solid Rocket Motor (SRM) during burn. Using four string potentiometers mounted inside the test chamber connected to the nozzle and motor case and a thrust measurement system (TMS), the TVAF can be derived from the known nozzle and motor geometry. Increasing the accuracy of the TVAF is essential for certain groups working on the MAV including the Guidance, Navigation, and Control (GN&C) group, who prior to DM-1, solely relied on Computational Fluid Dynamics (CFD) data in their Monte Carlo simulations for TVAF. The methodology shown in this paper can be generally applied to any test article implementing a SSSL nozzle, presuming string potentiometers are a viable option and the facility is conducive of their implementation.
Supersonic Split-Line↗
Chondrule formation in lightning discharges
Chondrules represent a significant mass fraction of primitive meteorites. These millimeter-sized glassy droplets appear to be the products of intensive transient heating events. Their size distribution, chemical and mineral composition, texture, isotope composition suggest that chondrules were produced as a result of short-duration melting followed by rapid cooling of solid precursor particles. Gas-dynamics heating, magnetic reconnection, and electrostatic discharges are thought to be the leading candidates to explain chondrule formation. In this paper we summarize our recent theoretical progress on the effects of 'lightning' in the early solar system and also report on preliminary results from our laboratory experiments. Differential settling of various sized dust particles toward the midplane of the nebula is suspected to build large-scale charge separations that episodically relax via the electric breakdown of the nebular gas. The electrostatic discharge os analogous to lightning in the Earth's atmosphere.
Horanyi, M.↗
A Coordinated Microstructural and Isotopic Study ofa Wark-Lovering Rim on a Vigarano CAI
We carried out a coordinated mineralogical and isotopic study of a Wark-Lovering (WL) rim on a Ca,Al-rich inclusion (CAI) from the reduced CV3 chondrite Vigarano. The outermost edge of the CAI mantle is mineralogically and texturally distinct compared to the underlying mantle that is composed of coarse, zoned melilite (Åk~10-60) grains. The mantle edge contains fine-grained gehlenite with hibonite and rare grossite that likely formed by rapid crystallization from a melt enriched in Ca and Al. These gehlenite and hibonite layers are surrounded by successive layers of spinel, zoned melilite (Åk~0-10), zoned diopside that grades outwards from Al,Ti-rich to Al,Ti-poor, and forsteritic olivine intergrown with diopside. These layered textures are indicative of sequential condensation of spinel, melilite, diopside, and forsterite onto hibonite. Anorthite occurs as a discontinuous layer that corrodes adjacent melilite and Al2 diopside, and appears to have replaced them, probably even later than the forsterite layer formation. Based on these observations, we conclude that the WL rim formation was initiated by flash melting and extensive evaporation of the original inclusion edge, followed by subsequent gas-solid reactions under highly dynamic conditions. All the WL rim minerals are 16O-rich (Δ17O = ~−23‰), indicating their formation in an 16O-rich nebular reservoir. Our Al-Mg measurements of hibonite, spinel, and diopside from the WL rim, as well as spinel and Al,Ti-diopside in the core, define a single, well-correlated isochron with an inferred initial 26Al/27Al ratio of (4.94 ± 0.12) × 10−5. This indicates that the WL rim formed shortly after the host CAI. In contrast, the lack of 26Mg excesses in the WL rim anorthite suggest its later formation or later isotopic disturbance in the solar nebula, after 26Al had decayed.
Jangmi Han↗
Explicit expression to predict the erosive burning rate of solid propellants
Using the theory of gas dynamics and heat transfer from a turbulent gas flow to the burning surface of propellant along a permeable wall, an explicit expression is derived to predict the burning rate of the solid propellant with crossflow. Results of the calculation have been compared with experimental data and proved to be correct.
Wang, S.↗
Thermodynamic Modeling of a Solid Oxide Fuel Cell to Couple with an Existing Gas Turbine Engine Model
The Controls and Dynamics Technology Branch at NASA Glenn Research Center are interested in combining a solid oxide fuel cell (SOFC) to operate in conjunction with a gas turbine engine. A detailed engine model currently exists in the Matlab/Simulink environment. The idea is to incorporate a SOFC model within the turbine engine simulation and observe the hybrid system's performance. The fuel cell will be heated to its appropriate operating condition by the engine s combustor. Once the fuel cell is operating at its steady-state temperature, the gas burner will back down slowly until the engine is fully operating on the hot gases exhausted from the SOFC. The SOFC code is based on a steady-state model developed by The U.S. Department of Energy (DOE). In its current form, the DOE SOFC model exists in Microsoft Excel and uses Visual Basics to create an I-V (current-voltage) profile. For the project's application, the main issue with this model is that the gas path flow and fuel flow temperatures are used as input parameters instead of outputs. The objective is to create a SOFC model based on the DOE model that inputs the fuel cells flow rates and outputs temperature of the flow streams; therefore, creating a temperature profile as a function of fuel flow rate. This will be done by applying the First Law of Thermodynamics for a flow system to the fuel cell. Validation of this model will be done in two procedures. First, for a given flow rate the exit stream temperature will be calculated and compared to DOE SOFC temperature as a point comparison. Next, an I-V curve and temperature curve will be generated where the I-V curve will be compared with the DOE SOFC I-V curve. Matching I-V curves will suggest validation of the temperature curve because voltage is a function of temperature. Once the temperature profile is created and validated, the model will then be placed into the turbine engine simulation for system analysis.
Brinson, Thomas E.↗
Low Stretch Solid-Fuel Flame Transient Response to a Step Change in Gravity
The effect of a step change in gravity level on the stability of low stretch diffusion flames over a solid fuel is studied both numerically and experimentally. Drop tower experiments have been conducted in NASA Glenn Research Center's 5.2 Zero Gravity Facility. In the experiments burning PMMA cylinders, a dynamic transition is observed when the steadily burning 1g flame is dropped and becomes a 0g flame. To understand the physics behind this dynamic transition, a transient stagnation point model has been developed which includes gas-phase radiation and solid phase coupling to describe this dynamic process. In this paper, the experimental results are compared with the model predictions. Both model and experiment show that the interior of the solid phase does not have time to change significantly in the few seconds of drop time, so the experimental results are pseudo-steady in the gas-phase, but the solid is inherently unsteady over long time scales. The model is also used to examine the importance of fractional heat losses on extinction, which clearly demonstrates that as the feedback from the flame decreases, the importance of the ongoing heat losses becomes greater, and extinction is observed when these losses represent 80% or more of the flame feedback.
Armstrong, J. B.↗
Development of Flow and Heat Transfer Models for the Carbon Fiber Rope in Nozzle Joints of the Space Shuttle Reusable Solid Rocket Motor
Methodologies have been developed for modeling both gas dynamics and heat transfer inside the carbon fiber rope (CFR) for applications in the space shuttle reusable solid rocket motor joints. Specifically, the CFR is modeled using an equivalent rectangular duct with a cross-section area, friction factor and heat transfer coefficient such that this duct has the same amount of mass flow rate, pressure drop, and heat transfer rate as the CFR. An equation for the friction factor is derived based on the Darcy-Forschheimer law and the heat transfer coefficient is obtained from pipe flow correlations. The pressure, temperature and velocity of the gas inside the CFR are calculated using the one-dimensional Navier-Stokes equations. Various subscale tests, both cold flow and hot flow, have been carried out to validate and refine this CFR model. In particular, the following three types of testing were used: (1) cold flow in a RSRM nozzle-to-case joint geometry, (2) cold flow in a RSRM nozzle joint No. 2 geometry, and (3) hot flow in a RSRM nozzle joint environment simulator. The predicted pressure and temperature history are compared with experimental measurements. The effects of various input parameters for the model are discussed in detail.
Wang, Q.↗
Concentration distributions in cylindrical combustors
Experimental studies have been conducted with the aim to obtain a better understanding of the fluid dynamics of mixing in gas turbine combustors, and solid fuel ramjet combustors subject to spin. The present investigation represents a continuation of studies conducted by So et al. (1984). It is also concerned with the verification of some conclusions reported by Ahmed et al. (1984). Attention is given to the experimental facility and instrumentation, centerline concentration measurements, mean concentration profiles, and a comparison of concentration and axial velocity results in the case of swirling flow.
Ahmed, S. A.↗
An experimental investigation of gas jets in confined swirling air flow
The fluid dynamics of jets in confined swirling flows which is of importance to designers of turbine combustors and solid fuel ramjets used to power missiles fired from cannons were examined. The fluid dynamics of gas jets of different densities in confined swirling flows were investigated. Mean velocity and turbulence measurements are made with a one color, one component laser velocimeter operating in the forward scatter mode. It is shown that jets in confined flow with large area ratio are highly dissipative which results in both air and helium/air jet centerline velocity decays. For air jets, the jet like behavior in the tube center disappears at about 20 diameters downstream of the jet exit. This phenomenon is independent of the initial jet velocity. The turbulence field at this point also decays to that of the background swirling flow. A jet like behavior in the tube center is noticed even at 40 diameters for the helium/air jets. The subsequent flow and turbulence field depend highly on the initial jet velocity. The jets are fully turbulent, and the cause of this difference in behavior is attributed to the combined action swirl and density difference. This observation can have significant impact on the design of turbine combustors and solid fuel ramjets subject to spin.
Mongia, H.↗
Assessment of Various Flow Solvers Used to Predict the Thermal Environment inside Space Shuttle Solid Rocket Motor Joints
It is very important to accurately predict the gas pressure, gas and solid temperature, as well as the amount of O-ring erosion inside the space shuttle Reusable Solid Rocket Motor (RSRM) joints in the event of a leak path. The scenarios considered are typically hot combustion gas rapid pressurization events of small volumes through narrow and restricted flow paths. The ideal method for this prediction is a transient three-dimensional computational fluid dynamics (CFD) simulation with a computational domain including both combustion gas and surrounding solid regions. However, this has not yet been demonstrated to be economical for this application due to the enormous amount of CPU time and memory resulting from the relatively long fill time as well as the large pressure and temperature rising rate. Consequently, all CFD applications in RSRM joints so far are steady-state simulations with solid regions being excluded from the computational domain by assuming either a constant wall temperature or no heat transfer between the hot combustion gas and cool solid walls.
Wang, Qun-Zhen↗
Wind tunnel tests of space shuttle solid rocket booster insulation material in the aerothermal tunnel c
Wind tunnel tests of the space shuttle Solid Rocket Booster Insulation were conducted in the von Karman Gas Dynamics Facility Tunnel C. For these tests, Tunnel C was run at Mach 4 with a total temperature of 1100-1440 and a total pressure of 100 psia. Cold wall heating rates were changed by varying the test article support wedge angle. Selected results are presented to illustrate the test techniques and typical data obtained.
Hartman, A. S.↗
Planetary environments and the conditions of life
Geophysical models of the first 600 Ma ofthe earth's history following accretion and core formation point to a period of great environmental disequilibrium. In such an environment, the passage of energy from the earth's interior and from the sun through gas-liquid-solid domains and their boundaries with each other generated a dynamically interacting, complex hierarchy of self-organized structures ranging from bubbles at the sea-air interface to tectonic plates. The ability of a planet to produce such a hierarchy is speculated to be a prerequisite to the origin and sustenance of life. The application of this criterion to Mars argues against the origin of Martian life.
Chang, S.↗