Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “turbulence simulation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Development of a data-driven neural network model for electron thermal transport in NSTX

A data-driven electron thermal transport neural network (ETT-NN) model, trained on TRANSP interpretative analysis results of National Spherical Torus Experiment (NSTX), was developed to enable faster and more accurate ETT computation for spherical tokamaks (STs). The model incorporates both convolutional NNs and recurrent NNs, allowing it to simultaneously account for the spatial and temporal non-localities and multi-scale features of turbulent transport, which have been considered only in a limited manner in conventional models. The model was validated through interpretative analysis and predictive simulations using Tokamak Reactor Integrated Automated Suite for Simulation and Computation, demonstrating relatively high accuracy. Additionally, parameter scans were performed on test discharges known to exhibit specific turbulent modes, such as microtearing mode, trapped electron mode, kinetic ballooning mode, and electron temperature gradient mode. The scanning results revealed that the ETT-NN model exhibits the same trends as those observed in conventional gyrokinetic simulations or theories, while also capturing the global nature of turbulent transport, indicating that the data-driven model accurately reflects the underlying physical characteristics. Furthermore, due to the dimensionless nature of the model, we can feasibly expand its applicability by incorporating data from other devices and uncovering the characteristics of ETT in STs in the future.

NSTX↗
DOE OSTI2025

Molecular fluctuations inhibit intermittency in compressible turbulence

In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.

compressible turbulence↗
DOE OSTI2024

Numerical Mixing Suppresses Submesoscale Baroclinic Instabilities Over Sloping Bathymetry

Abstract The impacts of spurious numerical salinity mixing on the larger‐scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas‐Louisiana shelf and features oscillatory near‐inertial wind forcing. can exceed the physical mixing from the turbulence closure in frontal zones and within the mixed layer. This suggests that simulated mixing processes in frontal zones are driven largely by . Near‐inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of to in simulations with no prescribed horizontal mixing. We then test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated using the volume‐integrated eddy kinetic energy and available potential energy . While all schemes have similar total mixing, the HSIMT simulations have over double the volume‐integrated and 20% less relative to other schemes, which suppresses the release of and reduces the by roughly 25%. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced suppresses instability growth. Differences in and between the MPDATA and U3HC4 simulations are marginal. However, the U3HC4 simulations have 25% more . Experiments with variable horizontal viscosity and diffusivity coefficients show that small amounts of prescribed horizontal mixing improve the representation of the ocean state for all advection schemes by reducing the and increasing the .

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Effects of turbulent diffusion and back-reaction on the dust distribution around two resonant planets

In evolved and dusty circumstellar discs, two planets with masses comparable to Jupiter and Saturn that migrate outwards while maintaining an orbital resonance can produce distinctive features in the dust distribution. Dust accumulates at the outer edge of the common gas gap, which behaves as a dust trap, where the local dust concentration is significantly enhanced by the planets’ outward motion. Concurrently, an expanding cavity forms in the dust distribution inside the planets’ orbits, because dust does not filter through the common gaseous gap and grain depletion in the region continues via inward drifting. There is no cavity in the gas distribution because gas can filter through the gap, although ongoing gas accretion on the planets can reduce the gas density in the inner disc. Such behaviour was demonstrated by means of simulations neglecting the effects of dust diffusion due to turbulence and of dust backreaction on the gas. Both effects may alter the formation of the dust peak at the gap outer edge and of the inner dust cavity, by letting grains filter through the dust trap. We performed high-resolution hydrodynamical simulations of the coupled evolution of gas and dust species, the latter treated as pressureless fluids, in the presence of two giant planets. We show that diffusion and backreaction can change some morphological aspects of the dust distribution but do not alter some main features, such as the outer peak and the expanding inner cavity. Furthermore, these findings are confirmed for different parametrizations of gas viscosity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Large-eddy simulation of non-vaporizing sprays using the spectral-element method

Predictive simulations of high-pressure sprays require accurate representation of the turbulent gaseous flow field generated by liquid jet. Typically, the accuracy that can be obtained with low-order numerical methods (e.g. finite volume, finite element) is limited by stability issues in fine grids and the order of convergence of the method. In this work, we resolve the turbulent flow field in an Eulerian manner using the high-order spectral element method, coupled with a Lagrangian parcels approach to model the atomizing liquid jet. Large eddy simulations of single-hole sprays under non-evaporative conditions were conducted and compared against experimental data from Margot et al. (2008) and Spray A data from the Engine Combustion Network. The sensitivity of liquid penetration and droplet sizes to different breakup model parameters was studied. The effect of different numerical parameters, such as polynomial order of the solution (grid resolution), on liquid penetration was also analyzed. The method achieved grid-independent results using p-refinement, achieving finer resolution (by a factor of x 1.7 - x 3.5) in the gas-phase solution than in state-of-the-art simulations using the finite-volume method. Here the results showed good agreement with experimental data, demonstrating the ability of the current method to accurately capture liquid penetration and the shape of the spray.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas , vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci. , vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Physics↗
DOE OSTI2021

Bursty magnetic reconnection at the Earth's magnetopause triggered by high-speed jets

The impact of high-speed jets—dynamic pressure enhancements in the magnetosheath—on the Earth's magnetopause has been observed to trigger local magnetic reconnection. We perform a three-dimensional hybrid simulation to study the magnetosheath and magnetopause under turbulent conditions using a quasi-radial southward interplanetary magnetic field (IMF). In contrast to quasi-steady reconnection with a strong southward IMF, we show that after the impact of a jet on the magnetopause, the magnetopause moves inward, the current sheet is compressed and intensified and signatures of local magnetic reconnection are observed, showing similarities to spacecraft measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Reduced models for ETG transport in the tokamak pedestal

This paper reports on the development of reduced models for electron temperature gradient (ETG) driven transport in the pedestal. Model development is enabled by a set of 61 nonlinear gyrokinetic simulations with input parameters taken from pedestals in a broad range of experimental scenarios. The simulation data have been consolidated in a new database for gyrokinetic simulation data, the multiscale gyrokinetic database (MGKDB), facilitating the analysis. The modeling approach may be considered a generalization of the standard quasilinear mixing length procedure. The parameter η, the ratio of the density to temperature gradient scale length, emerges as the key parameter for formulating an effective saturation rule. With a single order-unity fitting coefficient, the model achieves an error of 15%. A similar model for ETG particle flux is also described. We also present simple algebraic expressions for the transport informed by an algorithm for symbolic regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Review and Analysis of Heat Transfer Correlations For Horizontal Pseudocritical CO 2 Heat Exchanger Applications

There is significant interest in the development of supercritical carbon dioxide (sCO 2 ) power cycles because of the potential for smaller and more energy efficient systems than a steam Rankine cycle. Heat exchanger designs typically use empirical correlations, but the applicability of these correlations near the CO 2 critical point is a potential issue. Though numerous correlations have been proposed in the literature, there are some disagreements when it comes to the accuracy. The current work recognizes the role of thermophysical properties, and its impacts on the heat transfer correlations and cycle efficiency. Heat transfer correlations proposed for horizontal flow inside circular pipes were analyzed with the help of numerical simulations. Steady state RANS simulations were performed using SST k-w turbulence model to evaluate the Nusselt number empirical correlations. It was found that the most of correlations (except Yoon) produced a Nusselt number that differed significantly with the one predicted numerically. Some of the correlations were developed for pure forced convection regime and as mentioned in Lin et al. do not account for mixed convection or free convection effects. Based on the limited observation, it appears that Yoon et al. predictions match well with the numerically predicted Nusselt Numbers. However, further analysis is required understand the applicability of various correlations and is contingent on accurate measurements or predictions of wall temperature profiles in the axial and the circumferential directions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Flow friction in a wide rectangular duct with a beveled inlet: Informal Notes of Fundamental Fluid Physics Studies

Fundamental streamwise pressure distributions were measured at Idaho State University to address a primary objective of obtaining insight into the apparent evolution of air flow regimes at moderate Reynolds numbers in thin, wide rectangular ducts with converging inlets. Ducts of 3.030 and 4.077 mm spacings s (called three and four mm), having non-dimensional lengths of (L/s) ≈ 500.8 and 372.2 and widths (W/s) ≈ 114.6 and 83.2, respectively, were compared. Flow rates ranged from Reynolds numbers based on hydraulic diameter (Re Dh ) of about 980 to 10,000 and corresponding non-dimensional downstream pressure gradient parameters (-K p ) covered the range 0.038 to 0.0061, respectively.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Interaction of radio frequency waves with cylindrical density filaments -- scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Hard Synchrotron Spectra from Magnetically Dominated Plasma Turbulence

Synchrotron emission from astrophysical nonthermal sources usually assumes that the emitting particles are isotropic. By means of large-scale two- and three-dimensional particle-in-cell simulations, we demonstrate that the dissipation of magnetically dominated (${\sigma }_{0}\gg 1$) turbulence in pair plasmas leads to strongly anisotropic particle distributions. At Lorentz factors $\sim {\sigma }_{0}{\gamma }_{\mathrm{th}0}$ (here, ${\gamma }_{\mathrm{th}0}$ is the initial Lorentz factor), the particle velocity is preferentially aligned with the local magnetic field; instead, the highest energy particles are preferentially oriented in the plane perpendicular to the field. This energy-dependent anisotropy leads to a synchrotron spectral flux $\nu {F}_{\nu }\propto {\nu }^{s}$ that is much harder than for isotropic particles. Remarkably, for ${\sigma }_{0}\gg 1$ we find that the angle-integrated spectral slope in the slow cooling regime is $s\sim 0.5-0.7$ for a wide range of turbulence fluctuations, $0.25\lesssim \delta {B}_{\mathrm{rms}0}^{2}/{B}_{0}^{2}\lesssim 4$, despite significant variations in the power-law energy spectrum of nonthermal particles. This is because weaker turbulence levels imprint a stronger degree of anisotropy, thereby counteracting the effect of the steeper particle spectrum. The synchrotron spectral slope may be even harder, $s\gtrsim 0.7$, if the observer is in the plane perpendicular to the mean magnetic field. Our results are independent of domain size and dimensionality. Further, our findings may help explain the origin of hard synchrotron spectra of astrophysical nonthermal sources, most notably the radio spectrum of pulsar wind nebulae.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Relativistic Alfvén Turbulence at Kinetic Scales

Abstract In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close to k −3 or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Numerical study of multi-component flow and mixing in a scaled fission product venting system

Numerical simulation of isothermal multi-component gas flow was conducted to study fluid flow and mixing in a scaled low-pressure, low-temperature test facility for the fission product venting system (FPVS) of a gas cooled fast reactor (GFR). The geometry of FPVS test facility was an open loop including gradual expansion coupling and two 90°pipe elbows. First, the validation of large eddy simulation (LES) wall-adapting local eddy-viscosity (WALE) turbulent model was performed for transitional flow in a circular pipe with gradual expansion. The reactingFOAM solver in OpenFOAM v8 was employed. By introducing appropriate turbulence disturbance at the flow inlet, such as turbulence intensity, the numerical results showed good agreement in (1) the velocity profile downstream of the pipe expansion measured by particle image velocimetry (PIV) in this study, and (2) the reattachment length reported in the literature. Using this validated model, the numerical simulation of flow and component mixing was performed for the FPVS with an inlet flowrate corresponding to a Reynolds number of 2,400 to investigate the flow behavior and component mixing. Standard deviation of the mass fraction of component, referred to as absolute mixing index (AMI), was calculated to quantify the mixing of components, showing that the component mixing length determined by AMI is related to the reattachment length downstream of the expansion. Additionally, this study was able to identify the best location in the FPVS test facility to measure the velocity and concentration profies where multicomponent flow is well mixed.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Development of a Time-Height Profile Assimilation Technique for Large-Eddy Simulation

Mesoscale-to-microscale coupling (MMC) aims to address the limited scope of traditional large-eddy simulations by driving the microscale flow with information concerning large-scale weather patterns provided by mesoscale models. We present a new offline MMC technique for horizontally homogeneous microscale flow conditions, in which internal forcing terms are computed based on mesoscale time–height profiles of mean-flow quantities. The advantage of such an approach is that it can be used to drive a microscale simulation with either mesoscale or observational data, and that it does not rely on specific terms in the mesoscale budget equations, which are typically not part of the default output of a mesoscale solver. The performance of the proposed profile assimilation technique is assessed based on the simulation of a typical diurnal cycle over the Scaled Wind Farm Technology site in west Texas. Results indicate that simple data assimilation techniques lead to unphysically high levels of shear and turbulence caused by the algorithm’s inability to cope with inaccuracies in the mesoscale time–height profiles. Modifying the algorithm to account for vertical coherence in the mesoscale source terms gives the microscale solver a greater ability to correct the provided mesoscale time–height profiles, leading to improved predictions of shear and turbulence statistics. The resulting turbulence statistics are in good agreement with meteorological tower observations and simulation results obtained with state-of-the-art coupling techniques using mesoscale budget components.

data assimilation↗
DOE OSTI2021

Multiresolution classification of turbulence features in image data through machine learning

During large-scale simulations, intermediate data products such as image databases have become popular due to their low relative storage cost and fast in-situ analysis. Serving as a form of data reduction, these image databases have become more acceptable to perform data analysis on. In this work, we present an image-space detection and classification system for extracting vortices at multiple scales through wavelet-based filtering. A custom image-space descriptor is used to encode a large variety of vortex-types and a machine learning system is trained for fast classification of vortex regions. By combining a radial-based histogram descriptor, a bag of visual words feature descriptor, and a support vector machine, our results show that we are able to detect and classify vortex features at various sizes at multiple scales. Once trained, our framework enables the fast extraction of vortices on new, unknown image datasets for flow analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Structure of iso-density sets in supersonic isothermal turbulence

Context: The gas density structure of the cold molecular phase of the interstellar medium is the main controller of star formation. Aims: A theoretical framework is proposed to describe the structural content of the density field in isothermal supersonic turbulence. Methods: It makes use of correlation and structure functions of the phase indicator field defined for different iso-density values. The relations between these two-point statistics and the geometrical features of iso-density sets such as the volume fraction, the surface density, the curvature, and fractal characteristics are provided. An exact scale-by-scale budget equation is further derived revealing the role of the turbulent cascade and dilation on the structural evolution of the density field. Although applicable to many flow situations, this tool is here first invoked for characterising supersonic isothermal turbulence, using data from the currently best-resolved numerical simulation. Results: We show that iso-density sets are surface fractals rather than mass fractals, with dimensions that markedly differ between dilute, neutral, and dense regions. The surface–size relation is established for different iso-density values. We further find that the turbulent cascade of iso-density sets is directed from large towards smaller scales, in agreement with the classical picture that turbulence acts to concentrate more surface into smaller volumes. Intriguingly, there is no range of scales that complies with a constant transfer rate in the cascade, challenging our fundamental understanding of interstellar turbulence. Finally, we recast the virial theorem in a new formulation drawing an explicit relation between the aforementioned geometrical measures and the dynamics of iso-density sets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A direct numerical simulation study for confined non-isothermal jet impingement at moderate nozzle-to-plate distances: Capturing jet-to-ambient density effects

A direct numerical simulation (DNS) campaign is deployed for a series of confined downward oriented, non-isothermal turbulent impinging jet configurations. A baseline Reynolds number of 9960 is obtained through a precursor DNS pipe flow simulation (Re τ = 505). Three jet temperature configurations (confinement height to nozzle diameter of three) enter a cylindrical domain that share ambient and impingement plate temperatures (298.15 K). The range of jet temperatures are crafted such that the ratio of inlet to ambient density varies from unity to 0.52, showcasing the effect of density disparity on flow characteristics such as core collapse, radial mixing of momentum and energy, near-wall stagnation behavior, wall-jet profiles, and large-scale vortical structures. Surface quantities provided include mean radial heat flux and wall-shear stress profiles, and heat flux histograms at select radial stations. Results showcase increased radial normal stresses for higher temperature jets that support increased mixing, resulting in large-scale recirculation structures that are smaller, while retaining similar normalized radial wall profiles for shear stress, heat flux and pressure. Furthermore, radial plots for wall shear stress and Nusselt number showcase strong radial decay as compared to previous configurations that share similar jet and ambient temperatures. For the 373.15 K case, a Gaussian-like histogram for heat fluxes at the impingement plate transitions to a log-normal profile as radial distances increase. In contrast, the 573.15 K configuration displays a bi-modal heat flux characteristic at the impingement plate, and in similar manner to the moderate temperature counterpart, transitions to a log-normal profile at larger radial distances.

33 ADVANCED PROPULSION SYSTEMS↗