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At least 271 records · Page 15

Thermal Model Heat Rate Predictions of the AGR-5/6/7 Experiment

Several fuel and material irradiation experiments have been planned for the U.S. Department of Energy Advanced Gas Reactor Fuel Development and Qualification Program, which supports the development and qualification of tristructural isotropic (TRISO) coated particle fuel for use in high-temperature gas-cooled reactors. The goals of these experiments are to provide irradiation performance data to support fuel process development, qualify fuel for normal operating conditions, support development of fuel performance models and codes, and provide irradiated fuel and materials for post-irradiation examination and safety testing. Originally planned and named as separate fuel experiments, but subsequently combined into a single test train. AGR-5/6/7 will test low-enriched uranium oxycarbide (UCO – a heterogeneous mixture of uranium oxide and uranium carbide) TRISO fuel. The AGR-5/6 portion of the experiment will provide data to support qualification of the selected reference fuel design, while the AGR-7 portion will serve as a margin test, irradiating the fuel beyond normal operating conditions. During irradiation, the temperature in each capsule is controlled by varying the helium / neon gas mixture flowing through the capsule until the desired thermocouple temperature is reached. Further adjustments can be made by changing the lobe power and the neutron filter. Three neutron filters are available to use as the experiment burns up the fissionable fuel. A thermal finite element model has been created for the five capsules comprising the AGR-5/6/7 experiment. Heat rates from a physics analysis are imported into the model along with fast neutron fluence. Graphite shrinkage due to the fast neutron fluence is incorporated into the model. Gas gaps change as a function of fast neutron fluence. Radiation heat transfer is a major contributor in this model. This is a large model with more than 1 million finite element brick elements. More than 150 different parts are modeled in the finite element model and communicate with each other from a heat transfer sense. More than 50 thermocouples are used in the experiment and are compared to actual measurements. The experiment is composed of five separate stainless steel capsules all welded together. This paper presents a method used to predict the gas mixture in the event that all of the thermocouples fail in a particular capsule. Curve fitting of heat rates from previous cycles and projecting them into the future is the basis of the method.

36 MATERIALS SCIENCE↗

Two-Photon Flow Cytometry

Flow cytometry is a powerful technique for obtaining quantitative information from fluorescence in cells. Quantitation is achieved by assuring a high degree of uniformity in the optical excitation and detection, generally by using a highly controlled flow such as is obtained via hydrodynamic focusing. In this work, we demonstrate a two-beam, two- channel detection and two-photon excitation flow cytometry (T(sup 3)FC) system that enables multi-dye analysis to be performed very simply, with greatly relaxed requirements on the fluid flow. Two-photon excitation using a femtosecond near-infrared (NIR) laser has the advantages that it enables simultaneous excitation of multiple dyes and achieves very high signal-to-noise ratio through simplified filtering and fluorescence background reduction. By matching the excitation volume to the size of a cell, single-cell detection is ensured. Labeling of cells by targeted nanoparticles with multiple fluorophores enables normalization of the fluorescence signal and thus ratiometric measurements under nonuniform excitation. Quantitative size measurements can also be done even under conditions of nonuniform flow via a two-beam layout. This innovative detection scheme not only considerably simplifies the fluid flow system and the excitation and collection optics, it opens the way to quantitative cytometry in simple and compact microfluidics systems, or in vivo. Real-time detection of fluorescent microbeads in the vasculature of mouse ear demonstrates the ability to do flow cytometry in vivo. The conditions required to perform quantitative in vivo cytometry on labeled cells will be presented.

Zhog, Cheng Frank↗

Real Time Flame Monitoring of Gasifier and Injectors

This project is a multistage effort with the final goal to develop a practical and reliable nonintrusive gasifier injector monitor to assess burner wear and need for replacement. The project team included the National Energy Technology Laboratory (NETL), Gas Technology Institute (GTI), North Carolina State University, and ConocoPhillips. This report presents the results of the sensor development and testing initially at GTI combustion laboratory with natural gas flames, then at the Canada Energy Technology Center (CANMET), Canada in the atmospheric coal combustor as well as in the pilot scale pressurized entrained flow gasifier, and finally the sensor capabilities were demonstrated at the Pratt and Whitney Rocketdyne (PWR) Gasifier and the Wabash River Repowering plant located in West Terre Haute, IN. The initial tests demonstrated that GTI gasifier sensor technology was capable of detecting shape and rich/lean properties of natural gas air/oxygen enriched air flames. The following testing at the Vertical Combustor Research Facility (VCRF) was a logical transition step from the atmospheric natural gas flames to pressurized coal gasification environment. The results of testing with atmospheric coal flames showed that light emitted by excited OH* and CH* radicals in coal/air flames can be detected and quantified. The maximum emission intensities of OH*, CH*, and black body (char combustion) occur at different axial positions along the flame length. Therefore, the excitation rates of CH* and OH* are distinct at different stages of coal combustion and can be utilized to identify and characterize processes which occur during coal combustion such as devolatilization, char heating and burning. To accomplish the goals set for Tasks 4 and 5, GTI utilized the CANMET Pressurized Entrained Flow Gasifier (PEFG). The testing parameters of the PEFG were selected to simulate optimum gasifier operation as well as gasifier conditions normally resulting from improper operation or failed gasifier injectors. The sensor developed under previous tasks was used to assess the spectroscopic characteristics of the gasifier flame. The obtained spectral data were successfully translated into flame temperature measurements. It was also demonstrated that the reduced spectral data could be very well correlated with very important gasification process parameters such as the air/fuel and water/fuel ratio. Any of these parameters (temperature, air/fuel, and water/fuel) is sufficient to assess burner wear; however, the tested sensor was capable of monitoring all three of them plus the flame shape as functions of burner wear. This will likely be a very powerful tool which should enable significant improvements in gasifier efficiency, reliability, and availability. The sensor technology was presented to the project's industrial partner (ConocoPhillips). The partner expressed its strong interest in continuing to participate in the field validation phase of GTI's Flame Monitor Project. Finally the sensor was tested in the PWR (Pratt & Whitney Rocketdyne) gasification plant located at GTI's research campus and at the ConocoPhillips industrial scale gasifier at Wabash River Indiana. The field trials of the GTI Gasifier sensor modified to withstand high temperature and pressure corrosive atmosphere of the industrial entrain flow gasifier. The project team successfully demonstrated the Gasifier Sensor system ability to monitor gasifier interior temperature maintaining unobstructed optical access for in excess of six week without any maintenance. The sensor examination upon completion of the trial revealed that the system did not sustain any damage and required minor cleanup of the optics.

01 COAL, LIGNITE, AND PEAT↗

High-speed phase contrast imaging of spray breakup of jet fuels under combusting conditions

X-ray phase contrast imaging is conducted at 90,517 Hz on a fuel spray to characterize the breakup of the bulk fuel into ligaments and individual droplets in a single-sector, swirl-stabilized combustor under reacting conditions. Phase contrast imaging is used to qualitatively assess spray breakup for two fuels: Jet-A, which represents a normal viscosity fuel, and a blend of JP-5 (64%) and farnesane (36% by volume), which represents a high-viscosity fuel, at three fuel-flow rates and two air inlet temperatures. Time-series images of the fuels show that atomization occurs much more rapidly at higher fuel pressure with thinner ligaments being rapidly shredded. The high-viscosity fuel is qualitatively observed to have markedly longer, thicker ligaments and larger droplet diameters after the primary breakup than the normal viscosity fuel. Using an image processing and droplet quantification strategy, the mean droplet velocity magnitudes were found to decrease with decreasing fuel pressure and fuel-flow rate. The increase in preheat temperature from 323 to 370 K results in an increase in the mean droplet velocity magnitude and a decrease in numerical average and Sauter mean diameter, indicating improved atomization. The high-viscosity fuel was found to have larger average droplet diameters at each condition than the normal viscosity fuel. The increased preheat is found to enhance the combustion efficiency, which is hypothesized to couple with the improved atomization due to the higher combustion temperatures. This indicates the importance of examining spray atomization and breakup under realistic combusting conditions for relevant fuels as the heat release directly couples with the atomization process.

42 ENGINEERING↗

Supersonic jet noise reduction by coaxial rectangular nozzles

A physical understanding of noise reduction mechanisms in supersonic, single, and coaxial rectangular jets is quantified and obtained, with emphasis on shock noise reduction. For all conditions, corresponding acoustic measurements for an equivalent round jet are also obtained so that the noise characteristics of the two types of jets can be compared directly to quantify the noise reductions. Comparisons are thus provided for a single rectangular nozzle vs a single equivalent round nozzle, and a coaxial rectangular nozzle vs an equivalent round nozzle. It is shown that different operating conditions and nozzle arrangements for the same thrust, total exit area, and mass flow rate can produce different noise levels. With at least one stream operated supersonically, the coaxial rectangular nozzle operated in the inverted-velocity profile is always quieter than in the normal velocity profile mode for the same thrust, exit area, and mass flow rate. In general, the coaxial rectangular nozzle is shown to be quieter than an equivalent circular nozzle only for those conditions for which both nozzles are operated supersonically.

Ahuja, K. K.↗

A Mechanistic Study of Nucleate Boiling Under Microgravity Conditions

The overall objective of this work is to study nucleate boiling heat transfer under microgravity conditions in such a way that while providing basic knowledge of the phenomena, it also leads to development of simulation models and correlations that can be used as design tools for a wide range of gravity levels. In the study a building block type of approach is used and both pool and low velocity flow boiling are investigated. Starting with experiments using a single bubble, the complexity of the experiments is increased to two or three inline bubbles, to five bubbles placed on a two-dimensional grid. Finally, experiments are conducted where a large number of prescribed cavities nucleate on the heater and when a commercial surface is used. So far experiments have been conducted at earth normal gravity and in the reduced gravity environment of the KC-135 aircraft whereas experiments on the space station are planned. Modeling/complete numerical simulation of the boiling process is an integral part of the total effort. Experiments conducted with single bubbles formed on a nucleation site microfabricated on a polished silicon wafer show that for gravity levels (g) varying from 1.5g(sub e) to 0.01g(sub e), the bubble diameter at departure varies approximately as (g(sub e)/g)(exp 1/2) and the growth period as (g(sub e)/g). When bubbles merge either inline or in a plane, the bubble diameter at departure is found to be smaller than that obtained for a single bubble and shows a weaker dependence on the level of gravity. The possible reason is that as the bubbles merge they create fluid circulation around the bubbles, which in turn induces a lift force that is responsible for the earlier departure of the bubbles. The verification of this proposition is being sought through numerical simulations. There is a merger of two inline, three inline, and several bubbles in a plane in the low gravity environment of the KC-135 aircraft. After merger and before departure, a mushroom type of bubble with several stems attached to the heater surface is clearly evident. Local heat fluxes during growth and departure of a single bubble were also measured. It was found that during most of the growth period of the bubble, generally the wall heat flux decreased with time because of the increased dry area under the bubble. However, the heat flux increased rapidly just prior to departure of the bubble because of the transient conduction into the cold liquid rushing to fill the space vacated by the bubble as the bubble base shrinks. The measured heat fluxes at various radial locations are found to be in qualitative agreement with the numerical predictions. Single bubble studies at earth normal gravity have also been performed on surfaces oriented at different angles to the gravitational acceleration with flow parallel to the surface. It is found that in all cases the bubbles slide along the surface before lift-off from the surface. The lift force generated as a result of the relative motion between the sliding bubbles and the imposed flow is found to play an important role when the normal force due to buoyancy is reduced. An experimental apparatus for the study of the bubble behavior with imposed flow under reduced gravity conditions has been developed and will soon be employed for experiments in the KC-135 aircraft.

Dhir, V. K.↗

Effects of water immersion on renal hemodynamics in normal man

The present study was undertaken to delineate the effects of water immersion to the neck (NI) on renal plasma flow and glomerular filtration rate as assessed by the clearance of p-aminohippuric acid (PAH) and inulin, respectively. Nine normal male subjects were studied on two occasions, control and NI. The conditions of seated posture and time of day were identical. Immersion did not alter either clearance at a time when sodium excretion was increasing markedly. The constancy of PAH clearance during NI suggests that renal blood flow is unaltered and that the natriuresis of NI is mediated independently of alterations in overall renal perfusion. The sluggish decline of a natriuresis during recovery is consistent with the presence of a humoral factor contributing to the encountered natriuresis.

Epstein, M.↗

Refining a Novel Process Monitoring Method to Safeguard Continuously Cycling Designs Using Isotopic Ratios

In advanced reactor (AR) designs, a common feature is continuous chemical processing and circulation of the nuclear material. This work bridges a significant measurement gap in safeguarding reactors with circulating fuel or continuous refueling by leveraging and building on the isotope ratio method first developed by our team under an FY21 Advanced Reactors International Safeguards Engagement (ARISE) project (Uribe et al. 2021). In circulating fuel designs, the radioisotope inventory changes from traditional effects (e.g., radioactive decay, fission) but also includes material transport due to pressure and temperature gradients. Such designs may also require regular or continuous additions or removals during operation, which significantly increases the rate of inventory change compared to traditional pressurized water reactor (PWR)s. Thus, directly tracking the nuclear inventory is ineffective since the isotopes are continuously added and removed. The isotope ratio method instead focuses on detecting changes to the input and output flows of radioisotopes. Previous work showed that for well-chosen pairs of isotopes, the isotopic ratio provides a sensitive and lasting indicator of deviation from normal conditions (e.g., startup, shutdown, diversion). The isotope ratio method is a process monitoring method with potential for application in for forward-looking approaches to International Atomic Energy Agency (IAEA) safeguards. The original process monitoring method was developed for a specific case—the decay tank of a thorium-fueled molten salt breeder reactor. In this expanded work, we explored other types of reactors and processes with nonstationary (e.g., flowing) nuclear material, which are difficult to safeguard with traditional methods because of the transient nature of the systems. The goal of the present work is to generalize the isotope ratio method for use in processes with continuously flowing nuclear material. All continuous processes have an average time for isotopes to be replaced in the system. The isotope ratio method works by choosing radioisotopes with half-lives both above and below the processing time. The present work seeks to explore which isotopes are suitable for the method by simulating the nuclear inventory, radioisotope emissions, and detector responses for several classes of advanced reactors. While the method can in principle be applied to other processes (e.g., enrichment or reprocessing facilities), the present work limits scope to ARs with continuously flowing fuel. Section 2 details the mathematics supporting the isotope ratio method, and Section 3 introduces the representative ARs selected for this work. Section 4 discusses how each reactor was analyzed, and Section 5 showcases the results for each representative reactor. Finally, Section 6 provides concluding remarks and suggests pathways for further analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

A finite difference treatment of Stokes-type flows: Preliminary report

The equations Laplacian operator omega = 0, (1.1a) and omega = Laplacian operator Chi, (1.1b) describe, in suitable units, 2-D Stokes flow of an incompressible fluid occupying a domain D in which omega is the vorticity and Chi is the stream function. The flow is uniquely determined by specifying the velocity on the boundary B of D, a condition which leads to specifying the stream function Chi and its normal derivative Chi sub n on B. A mathematically similar problem arises in describing the equilibrium of a flat plate in structural mechanics where a related 1-D problem by finite difference or finite element methods is to introduce effective methods for imposing the boundary conditions through which (1.1a) is coupled to (1.1b). These models thus provide a simple starting point for examining the general treatment of boundary conditions for more general time dependent Navier-Stokes incompressible flows. For the purpose of discussion it is assumed that D is a square domain. A standard finite difference method to solve (1.1) is to introduce a uniform grid and then use standard five point finite difference operators to express each equation in (1.1). At any point on the boundary B a value of Chi is specified by the boundary conditions but a value of omega at the same boundary mesh point will also be required to complete the computation. Methods are discussed which overcome the difficulty in solving these problems.

Rose, M. E.↗

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for unsteady and steady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux-vector-splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flows results are made as well as with experimental data where available.

Anderson, W. Kyle↗

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for steady and unsteady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux vector splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flow results are made, as well as with experimental data where available.

Anderson, W. Kyle↗

Synthesis of zinc ultrafine powders via the Guen–Miller flow-levitation method

Zinc ultrafine powders (UFPs) with the average particle size of 0.175 to 1.24 μm are synthesized via the flow-levitation method. The peculiarities of the formation of zinc UFPs are considered with respect to the carrier gas properties (heat capacity, thermal conductivity, and diffusion coefficient), as well as the gas flow parameters (pressure and flow rate). The obtained zinc particles are studied via scanning electron microscopy and X-ray diffraction. The factors determining the crystal structure of zinc particles and their size distribution are discussed as well. The data on oxidation of zinc stored in unsealed containers under normal conditions are also presented.

36 MATERIALS SCIENCE↗

Shock shapes on blunt bodies in hypersonic-hypervelocity helium, air, and CO2 flows, and calibration results in Langley 6-inch expansion tube

Shock shape results for flat-faced cylinders, spheres, and spherically blunted cones in various test gases, along with preliminary results from a calibration study performed in the Langley 6-inch expansion tube are presented. Free-stream velocities from 5 to 7 km/sec are generated at hypersonic conditions with helium, air, and CO2, resulting in normal shock density ratios from 4 to 19. Ideal-gas shock shape predictions, in which an effective ratio of specific heats is used as input, are compared with the measured results. The effect of model diameter is examined to provide insight to the thermochemical state of the flow in the shock layer. The regime for which equilibrium exists in the shock layer for the present air and CO2 test conditions is defined. Test core flow quality, test repeatability, and comparison of measured and predicted expansion-tube flow quantities are discussed.

Miller, C. G., III↗

Linear Disturbance Amplification Over Blunted Flat Plates in High-Speed Flows

Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.

Boundary layer transition↗

Linear Disturbance Amplification Over Blunted Flat Plates in High-Speed Flows

Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.

Boundary layer transition↗

Redox Reactions of Reduced Flavin Mononucleotide (FMN), Riboflavin (RBF), and Anthraquinone-2,6-disulfonate (AQDS) with Ferrihydrite and Lepidocrocite

Flavins are secreted by the dissimilatory iron-reducing bacterium Shewanella and can function as endogenous electron transfer mediators (ETM). In order to assess the potential importance of flavins in Fe(III) bioreduction, we investigated the redox reaction kinetics of reduced flavins (FMNH2 and RBFH2) with ferrihydrite and lepidocrocite. The organic reductants rapidly reduced and dissolved ferrihydrite and lepidocrocite in the pH range 4-8. The rate constant k for 2-line ferrihydrite reductive dissolution by FMNH2 was 87.5 ± 3.5 M-1∙s-1 at pH 7.0 in batch reactors, and the k was similar for RBFH2. For lepidocrocite, the k was 500 ± 61 M-1∙s-1 for FMNH2, and 236 ± 22 M-1∙s-1 for RBFH2. The surface area normalized initial reaction rates (ra) were between 0.08 and 77 μmoles∙m-2∙s-1 for various conditions in stopped-flow experiments. Initial rates (ro) were first-order with respect to Fe(III) oxide concentration, and ra increased with decreasing pH. Poorly crystalline 2-line ferrihydrite yielded the highest ra, followed by more crystalline 6-line ferrihydrite, and crystalline lepidocrocite. Compared to a previous whole-cell study with Shewanella oneidensis strain MR-1, our findings suggest that ETM reduction by the Mtr pathway coupled to lactate oxidation are rate limiting, rather than heterogeneous electron transfer to the Fe(III) oxide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

VSC-HVDC Interties for Urban Power Grid Enhancement

Urban power grids are facing many operational and expansion challenges to meet further demand growth and increased reliability requirements. Advanced transmission technologies have been considered by the electric utilities to effectively increase the utilization of existing infrastructure and operational flexibility. The focus of this paper is on VSC-HVDC technologies for urban power grid enhancement and modernization. First, a potential technical scheme is proposed for converting an existing AC circuit to DC operation, which could boost the power transfer capability of the critical transmission corridor and increase network operational flexibility. Second, this paper proposes three operation modes for the VSC-HVDC interties in urban power grids corresponding to normal, emergency and island operating conditions, respectively. An integrated, adaptive emergency control strategy (AEC) is proposed that can enable adaptive power flow responses of the VSC-HVDC intertie under varying system operating conditions and critical contingencies. The flexibility and effectiveness of the proposed operational principles of urban VSC-HVDC intertie and the corresponding control strategies are verified in PSCAD/EMTDC using a realistic urban power grid in China.

24 POWER TRANSMISSION AND DISTRIBUTION↗

On convergence of computation of chemically reacting flows

The computational problems associated with high-temperature flows undergoing finite-rate ionization reactions is investigated. The conservation equations governing chemical species and vibrational and electron energies are solved simultaneously with those for overall mass, momentum, and energy for a one-dimensional subsonic flow, through a constant-area duct, originating behind a normal shock wave, using an implicit time-marching technique. Boundary conditions are imposed in the form of characteristic wave variables accounting for the effects of chemical reactions on the speed of sound. Converging solutions are obtained for cases in which chemical reactions are weak, but difficulty is encountered in other cases. The cause of the difficulty is investigated and shown to be the sharp pressure disturbances produced by such reactions.

Park, C.↗