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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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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Development and Validation of a Multidisciplinary Tool for Accurate and Efficient Rotorcraft Noise Prediction (MUTE)

A physics-based, systematically coupled, multidisciplinary prediction tool (MUTE) for rotorcraft noise was developed and validated with a wide range of flight configurations and conditions. MUTE is an aggregation of multidisciplinary computational tools that accurately and efficiently model the physics of the source of rotorcraft noise, and predict the noise at far-field observer locations. It uses systematic coupling approaches among multiple disciplines including Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD), and high fidelity acoustics. Within MUTE, advanced high-order CFD tools are used around the rotor blade to predict the transonic flow (shock wave) effects, which generate the high-speed impulsive noise. Predictions of the blade-vortex interaction noise in low speed flight are also improved by using the Particle Vortex Transport Method (PVTM), which preserves the wake flow details required for blade/wake and fuselage/wake interactions. The accuracy of the source noise prediction is further improved by utilizing a coupling approach between CFD and CSD, so that the effects of key structural dynamics, elastic blade deformations, and trim solutions are correctly represented in the analysis. The blade loading information and/or the flow field parameters around the rotor blade predicted by the CFD/CSD coupling approach are used to predict the acoustic signatures at far-field observer locations with a high-fidelity noise propagation code (WOPWOP3). The predicted results from the MUTE tool for rotor blade aerodynamic loading and far-field acoustic signatures are compared and validated with a variation of experimental data sets, such as UH60-A data, DNW test data and HART II test data.

Liu, Yi↗
DOE OSTI2020

An Overview of Wind Energy Production Prediction Bias, Losses, and Uncertainties

The financing of a wind farm directly relates to the preconstruction energy yield assessments which estimate the annual energy production for the farm. The accuracy and the precision of the preconstruction energy estimates can dictate the profitability of the wind project. Historically, the wind industry tended to overpredict the annual energy production of wind farms. Experts have been dedicated to eliminating such prediction errors in the past decade, and recently the industry is recording near-zero average energy prediction bias. Herein, we present an overview of the energy yield assessment errors across the global wind energy industry. We identify a long-term trend of reduction in the overprediction bias, whereas the uncertainty associated with the prediction error is prominent. We also summarize the recent advancements of the wind resource assessment process that justify the bias reduction, including the improvements in modeling and measurement techniques. Additionally, because the energy losses and uncertainties substantially influence the prediction error, we document and examine the estimated and observed loss and uncertainty values from the literature, according to the proposed framework in the International Electrotechnical Commission 61400-15 wind resource assessment standard. From our findings, we highlight the opportunities for the industry to move forward, such as the validation and reduction of prediction uncertainty, and the prevention of energy losses caused by wake effect and environmental events. Overall, this study provides a summary on how the wind energy industry has been quantifying and reducing prediction errors, energy losses, and production uncertainties. Finally, for this work to be as reproducible as possible, we include all of the data used in the analysis in appendices to the manuscript.

literature review↗
NASA NTRS1991

The computation and validation of hovering rotor performance

Recent experience with the HELIX-I code is presented, and its ability to predict the flow and performance of both conventional rotors and the unconventional anhedral parabolic tip rotor utilized on the Super Puma MK2 is described. HELIX-I is a standard full-potential rotor code having the ability to efficiently predict the detailed flow on a rotor blade, including 3D, transonic, and weak viscous effects (using appropriate boundary layer analyses). The resulting code is the first full-potential CFD code with the ability to model free wake convection and the first CFD code of any type to predict hover performance.

Mba, M. N.↗
DOE OSTI2021

Spatially and Temporally Resolved Velocimetry for Hypersonic Flows

The development of new hypersonic flight vehicles is limited by the physical understanding that may be obtained from ground test facilities. This has motivated the present development of a temporally and spatially resolved velocimetry measurement for Sandia National Laboratories (SNL) Hypersonic Wind Tunnel (HWT) using Femtosecond Laser Electronic Excitation Tagging (FLEET). First, a multi-line FLEET technique has been created for the first time and tested in a supersonic jet, allowing simultaneous measurements of velocities along multiple profiles in a flow. Secondly, two different approaches have been demonstrated for generating dotted FLEET lines. One employs a slit mask pattern focused into points to yield a dotted line, allowing for two- or three-component velocity measurements free of contamination between components. The other dotted-line approach is based upon an optical wedge array and yields a grid of points rather than a dotted line. Two successful FLEET measurement campaigns have been conducted in SNL’s HWT. The first effort established optimal diagnostic configurations in the hypersonic environment based on earlier benchtop reproductions, including validation of the use of a 267 nm beam to boost the measurement signal-to-noise ratio (SNR) with minimal risk of perturbing the flow and greater simplicity than a comparable resonant technique at 202 nm. The same FLEET system subsequently was reconstituted to demonstrate the ability to make velocimetry measurements of hypersonic turbulence in a realistic flow field. Mean velocity profiles and turbulence intensity profiles of the shear layer in the wake of a hypersonic cone model were measured at several different downstream stations, proving the viability of FLEET as a hypersonic diagnostic.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons

Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.

17 WIND ENERGY↗
DOE OSTI2020

Dispersion Validation for Flow Involving a Large Structure Revisited: 45 Degree Rotation

The atmospheric dispersion of contaminants in the wake of a large urban structure is a challenging fluid mechanics problem of interest to the scientific and engineering communities. Magnetic Resonance Velocimetry (MRV) and Magnetic Resonance Concentration (MRC) are relatively new techniques that leverage diagnostic equipment used primarily by the medical field to make 3D engineering measurements of flow and contaminant dispersal. SIERRA/Fuego, a computational fluid dynamics (CFD) code at Sandia National Labs is employed to make detailed comparisons to the dataset to evaluate the quantitative and qualitative accuracy of the model. This work is the second in a series of scenarios. In the prior work, a single large building in an array of similar buildings was considered with the wind perpendicular to a building face. In this work, the geometry is rotated by 45 degrees and improved studies are performed for simulation credibility. The comparison exercise shows conditionally good comparisons between the model and experiment. Model uncertainties are assessed through parametric variations. Various methods of quantifying the accuracy between experiments and data are examined Three-dimensional analysis of accuracy is performed. The effort helped identify deficiencies in the techniques used to make these comparisons, and further methods development therefore becomes one of the main recommendations for follow-on work.

42 ENGINEERING↗
NASA NTRSDate not supplied

Fundamental Test of a Hovering Rotor: Comprehensive Measurements for CFD Validation

A model-scale hover test of a 4-bladed, 11.08-ft diameter rotor was recently completed inside the National Full-Scale Aerodynamics Complex 80- by 120-Foot Wind Tunnel test section. The primary objective of the test was to acquire key experimental data for a hovering rotor of sufficient quality and quantity to allow validation of state-of-the-art analysis codes. A comprehensive measurement set has been acquired, including rotor performance, blade airloads, flow transition locations, blade deflections, and wake geometry for a range of tip Mach numbers and collective settings. The present paper provides an overview of the test, including detailed descriptions of the hardware, instrumentation, and measurement systems. In addition, the specific test objectives, approach, and sample results are presented. The full test database, as well as detailed rotor geometry information, will ultimately be shared openly on a NASA-sponsored website to serve as a benchmark validation dataset.

Hover↗
NASA NTRS2008

Deconvoluting the Friction Stir Weld Process for Optimizing Welds

In the friction stir welding process, the rotating surfaces of the pin and shoulder contact the weld metal and force a rotational flow within the weld metal. Heat, generated by the metal deformation as well as frictional slippage with the contact surface, softens the metal and makes it easier to deform. As in any thermo-mechanical processing of metal, the flow conditions are critical to the quality of the weld. For example, extrusion of metal from under the shoulder of an excessively hot weld may relax local pressure and result in wormhole defects. The trace of the weld joint in the wake of the weld may vary geometrically depending upon the flow streamlines around the tool with some geometry more vulnerable to loss of strength from joint contamination than others. The material flow path around the tool cannot be seen in real time during the weld. By using analytical "tools" based upon the principles of mathematics and physics, a weld model can be created to compute features that can be observed. By comparing the computed observations with actual data, the weld model can be validated or adjusted to get better agreement. Inputs to the model to predict weld structures and properties include: hot working properties ofthe metal, pin tool geometry, travel rate, rotation and plunge force. Since metals record their prior hot working history, the hot working conditions imparted during FSW can be quantified by interpreting the final microstructure. Variations in texture and grain size result from variations in the strain accommodated at a given strain rate and temperature. Microstructural data from a variety of FSWs has been correlated with prior marker studies to contribute to our understanding of the FSW process. Once this stage is reached, the weld modeling process can save significant development costs by reducing costly trial-and-error approaches to obtaining quality welds.

Schneider, Judy↗
DOE OSTI2026

Wind Conditions for Solar Energy Facility Design Based on Field Measurements at Nevada Solar One

This study characterises near-surface wind conditions at the Nevada Solar One (NSO) concentrated solar power plant using two years of measurements from a 15-m mast located 30 m west of the solar arrays. The surrounding terrain is fairly flat within 3 km, but nearby solar photovoltaic (PV) and concentrated solar power (CSP) installations introduce strong directional wind inhomogeneity, which motivates a sector-based analysis that distinguishes undisturbed inflow from waked flow. The analysis uses data from three sonic anemometers to assess whether turbulence in the surface layer can be represented as Gaussian and whether standard surface-layer scaling remains valid below 10 m height. The roughness length and displacement height are estimated for twelve directional sectors under near-neutral wind conditions, and all three velocity components show departures from Gaussian behaviour. Spectral analysis indicates that the turbulence contains low-frequency fluctuations with amplitudes higher than those predicted by standard models such as the Kaimal model or the Simiu and Scanlan model. The study introduces a new turbulence spectral model based on the eddy-surface-layer framework to better represent near-surface wind turbulence. The analysis further quantifies the influence of the surrounding power plants on mean wind profiles, one-point spectra, and vertical coherence for all velocity components. The solar collector arrays located 30 m east of the mast significantly modify the turbulence structure, whereas PV installations situated a few hundred metres away have only a limited influence on the turbulence measured at the mast. These findings highlight the limitations of conventional turbulence models for near-surface wind over solar infrastructure and provide improved parameterisations to support the structural design. The implications for the structural response of parabolic troughs and PV modules to such turbulence remain uncertain and require further investigation.

14 SOLAR ENERGY↗
DOE OSTI2023

Comparison of three DWM-based wake models at above-rated wind speeds

In this study we investigate three mid-fidelity wind turbine wake models based on the dynamic wake meandering (DWM) model principle, and compare their performance with a reference dataset, produced with large-eddy simulations using the actuator line model. The models are compared with respect to flow field, power, and loads on a row of four 5MW reference turbines experiencing above-rated wind conditions. In general, the DWM models show fairly good agreement with large-eddy simulation for the time-averaged flow fields, blade forces and power, with increasing differences along the turbine row. Also when comparing fatigue loads of blade root moments, the differences between the models increase further into the row, with deviations up to 25 % of the reference case. However, while the development in blade root moment fatigue along the turbine row is predominantly driven by the energy content at the frequency corresponding to the turbine's rotational period (1 P ) for the DWM models, the large-eddy simulation results suggest that the key drivers for the blade root and tower loads are the increase in meandering and energy at higher frequencies (> 1 P ) deeper into the turbine row. For the tower loads, the DWM models highly underestimate the fatigue for the waked turbines. From these results, we suggest priorities for future model developments so that robust model implementations can be used in wind farm design and operation.

17 WIND ENERGY↗
DOE OSTI2024

Going beyond BEM with BEM: an insight into dynamic inflow effects on floating wind turbines

Blade element momentum (BEM) theory is the backbone of many industry-standard wind turbine aerodynamic models. To be applied to a broader set of engineering problems, BEM models have been extended since their inception and now include several empirical corrections. These models have benefitted from decades of development and refinement and have been extensively used and validated, proving their adequacy in predicting aerodynamic forces of horizontal-axis wind turbine rotors in most scenarios. However, the analysis of floating offshore wind turbines (FOWTs) introduces new sets of challenges, especially if new-generation large and flexible machines are considered. In fact, due to the combined action of wind and waves and their interaction with the turbine structure and control system, these machines are subject to unsteady motion and thus unsteady inflow on the wind turbine's blades, which could put BEM models to the test. Consensus has not been reached on the accuracy limits of BEM in these conditions. This study contributes to the ongoing research on the topic by systematically comparing four different aerodynamic models, ranging from BEM to computational fluid dynamics, in an attempt to shed light on the unsteady aerodynamic phenomena that are at stake in FOWTs and whether BEM is able to model them appropriately. Simulations are performed on the UNAFLOW 1:75 scale rotor during imposed harmonic surge and pitch motion. Experimental results are available for these conditions and are used for baseline validation. The rotor is analyzed in both rated operating conditions and low wind speeds, where unsteady aerodynamic effects are expected to be more pronounced. Results show that BEM, despite its simplicity, can adequately model the aerodynamics of FOWTs in most conditions if augmented with a dynamic inflow model.

17 WIND ENERGY↗
NASA NTRS2017

CFD Simulations of the Supersonic Inflatable Aerodynamic Decelerator (SIAD) Ballistic Range Tests

A series of ballistic range tests were performed on a scaled model of the Supersonic Flight Demonstration Test (SFDT) intended to test the Supersonic Inflatable Aerodynamic Decelerator (SIAD) geometry. The purpose of these experiments were to provide aerodynamic coefficients of the vehicle to aid in mission and vehicle design. The experimental data spans the moderate Mach number range, $3.8-2.0$, with a total angle of attack ($alpha_T$) range, $10o-20o$. These conditions are intended to span the Mach-$alpha$ space for the majority of the SFDT experiment. In an effort to validate the predictive capabilities of Computational Fluid Dynamics (CFD) for free-flight aerodynamic behavior, numerical simulations of the ballistic range experiment are performed using the unstructured finite volume Navier-Stokes solver, US3D. Comparisons to raw vehicle attitude, and post-processed aerodynamic coefficients are made between simulated results and experimental data. The resulting comparisons for both raw model attitude and derived aerodynamic coefficients show good agreement with experimental results. Additionally, near body pressure field values for each trajectory simulated are investigated. Extracted surface and wake pressure data gives further insights into dynamic flow coupling leading to a potential mechanism for dynamic instability.

CFD modeling↗
NASA NTRS1989

A defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, compressible boundary layer is examined. A law of the wall/law of the wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer region is arbitrary. The modified Crocco temperature-velocity relationship is used as a simplification of the differential energy equation. Formulations for both equilibrium and nonequilibrium boundary layers are presented including a constrained zero-order form which significantly reduces the computational workload while retaining the significant physics of the flow. A formulation for primitive variables is also presented. Results are given for the constrained zero-order and second-order equilibrium formulations and are compared with experimental data. A compressible wake function valid near the wall has been developed from the present results.

Barnwell, Richard W.↗
DOE OSTI2023

Terrain-Influenced Winds and Fire-Fire Interactions in Wildland Fire Simulations [Dissertation]

Ensemble-based approaches to prescribed fire planning cannot be supported by computational fluid dynamics based models like FIRETEC and the Wildland-Urban Interface Fire Dynamics Simulator (WFDS) because they are too computationally expensive and cannot leverage large eddy simulation approaches like CAWFE and WRF-SFIRE because they have too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, that is typical for instance in the Western United States. This dissertation describes a variety of improvements made to QUIC-Fire and its various incorporated algorithms in an effort to make it a viable tool in simulating wildland and prescribed fires on terrain. The modifications made to QUIC-Fire are described in three chapters. The first chapter describes the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. The terraininfluenced winds it generates are analyzed and compared. In particular, this chapter presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captures the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. The model agrees well with measurements on the upwind side of the peak, but overestimates speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field is obtained in 6 s, making the solver appealing for coupled fire-atmosphere simulations. The Socorro Mountain is highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect is addressed in this work). In the second chapter the implementation of the terrain-following version of QUIC-URB into QUIC-Fire, and the necessary changes needed to include terrain are described. No changes to the underlying fire spread algorithm are made other than what is required to correctly account for the inclusion of terrain. Previously published FIRETEC results that use five different topographies that share the same centerline profile are compared to simulation results from the modified QUIC-Fire that use the same topographies and fuels. QUIC-Fire results show overall similar behaviors in terms of how the topographies affect fire shapes and trends in spread rates. Due to the terrain-following version of QUIC-URB being unable to generate flow separations at the crest of hills, fire spread rates in these regions across all topographies are over-predicted when compared to FIRETEC. Lateral fire growth shows similar trends with FIRETEC between topographies but does not capture the increase in spread due to a diagonal interface between grassland and forested fuel region of the domain. These results suggest that there are three algorithms within QUIC-Fire that could use improvement: how flame tilt angle is accounted for, the incorporation of non-local drag effects, and the inclusion of the wake-eddy parameterizations that are used in QUIC-URB. Lastly, the third chapter describes a modification to the initial guess used for the calculation of the QUIC-URB mass-conserved wind solution during fire simulations. The modification is aimed at improving fire-fire interactions in QUIC-Fire simulations. The modification consists of using the solution from the previous timestep as the starting point for the calculation of the solution for the next timestep. Fire-fire interactions is greatly improved by the change but a new source of error is introduced. Due to how plumes are modelled in QUIC-Fire the new solution contains errors where gaps in the plume structure are present. However, these errors are mostly limited to the upper atmosphere, where they do not affect fire behavior at the surface, and their magnitude isn’t significant enough to discount the amount of new fire phenomenology now captured in QUIC-Fire with the change.

58 GEOSCIENCES↗
NASA NTRS1976

Aerodynamic characteristics of a powered tilt-proprotor wind tunnel model

An investigation was conducted in the Langley V/STOL tunnel to determine the performance, stability and control, and rotor-wake interaction effects of a powered tilt-proprotor aircraft model with gimbal-hub rotors. Tests were conducted at representative flight conditions for hover, helicopter, transition, and airplane flight. Force and moment data were obtained for the complete model and for each of the two rotors. In addition to wind-speed variation, the angle of attack, angle of sideslip, rotor speed, rotor collective pitch, longitudinal cyclic pitch, rotor pylon angle, and configuration geometry were varied. The results, presented in graphical form, are available in tabular form to facilitate the validation of analytical methods of defining the aerodynamic characteristics of tilt-proprotor configurations.

Wilson, J. C.↗
DOE OSTI2022

QUIC-URB and QUIC-fire extension to complex terrain: Development of a terrain-following coordinate system

Ensemble-based approaches to prescribed fire planning cannot be supported by CFD-based models like FIRETEC and WFDS because they are too computationally expensive and cannot leverage LES approaches like CAWFE and WRF-SFIRE because too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, typical for instance of the Western United States. In this paper, we describe the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. In particular, the paper presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captured the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. We report the model agreed well with measurements on the upwind side of the peak, but overestimated speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field was obtained in 6 s, making the solver appealing for coupled fire–atmosphere simulations. The Socorro Mountain was highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect was addressed in this work). Results highlight that future work should focus on the implementation of parameterizations of wake-eddies, similar to QUIC-URB’s building parameterizations, and on thermodynamic-driven flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

How accurate is a machine learning-based wind speed extrapolation under a round-robin approach?

As the size of commercial wind turbines keeps increasing, having accurate ways to vertically extrapolate wind speed is essential to obtain a precise characterization of the wind resource for wind energy production. Recently, machine learning has been proposed and applied to extrapolate wind speed to hub heights. However, previous studies trained and tested the machine learning methods at the same site, giving them an unfair advantage over the conventional extrapolation techniques, which are instead more universal. Here, we use data from four sites in Oklahoma to test a round-robin validation approach for machine learning, under which we train a random forest at a site, and test it at a different site, where the model has no prior knowledge of the wind resource. We quantify how the accuracy of this technique varies with distance from the training site, and we find that it outperforms conventional techniques for wind extrapolation at all the considered spatial separations. We then assess how the accuracy of the machine-learning based approach varies when it is used to predict wind speed in a wind farm far wake. Finally, we explore as case study the performance of the random forest in extrapolating winds during a low-level jet event.

17 WIND ENERGY↗
NASA NTRS1973

Radiative coupled viscous flow with massive blowing

An analysis of the fully-coupled viscous, radiating flow past an ablating blunt body at hyperbolic entry conditions is presented. A detailed thermodynamics computation, as well as a realistic radiation transport model, is included. A locally nonsimilar approach is employed to solve the conservation equations away from the stagnation point. The validity of the locally nonsimilar approach is demonstrated for some nonablating cases. Sample calculations are made for the typical flight condition of a Jovian entry probe. The effects of the downstream injection of the ablation products of a carbon heat shield on the flux distribution around the body are discussed in detail. It is found that most of the radiative energy is absorbed by the injected carbon gas and dumped into the wake.

Chou, Y. S.↗