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At least 1,441 records · Page 80

The Application of the NFW Design Philosophy to the HSR Arrow Wing Configuration

The Natural Flow Wing design philosophy was developed for improving performance characteristics of highly-swept fighter aircraft at cruise and maneuvering conditions across the Mach number range (from Subsonic through Supersonic). The basic philosophy recognizes the flow characteristics that develop on highly swept wings and contours the surface to take advantage of those flow characteristics (e.g., forward facing surfaces in low pressure regions and aft facing surfaces in higher pressure regions for low drag). Because the wing leading edge and trailing edge have multiple sweep angles and because of shocks generated on nacelles and diverters, a viscous code was required to accurately define the surface pressure distributions on the wing. A method of generating the surface geometry to take advantage of those surface pressures (as well as not violating any structural constraints) was developed and the resulting geometries were analyzed and compared to a baseline configuration. This paper will include discussions of the basic Natural Flow Wing design philosophy, the application of the philosophy to an HSCT vehicle, and preliminary wind-tunnel assessment of the NFW HSCT vehicle.

Bauer, Steven X. S.↗

Pterodactyl: Aerodynamic and Aerothermal Modeling for a Symmetric Deployable Earth Entry Vehicle with Flaps

NASA’s Pterodactyl project has investigated a deployable atmospheric entry vehicle integrated with a flap control system that provides precision targeting during reentry. The control system consists of eight flaps mounted at the edge of a heatshield that can deflect in and out of the flow. An aerodynamic and aerothermodynamic analysis process was developed for preliminary vehicle design and aerodynamic database generation using engineering and CFD tools with varying levels of fidelity. The objective of this analysis was to: 1) understand the inherent aerodynamics, 2) provide an aerodynamics database for stability and control analysis, and 3) provide qualitative and quantitative aeroheating analysis for Thermal Protection System modeling of the flaps. A high fidelity Euler code, Cart3D, was used to resolve complex flow features such as secondary shocks and shock impingement. A wide range of supersonic (Mach 2) and hypersonic Mach numbers (up to Mach 40) were tested with an Earth atmosphere model. A process was developed to utilize the adaptive volume mesh generator utility of the perfect gas model of Cart3D to create meshes with high cell efficiency and numerical stability prior to running a 2nd order accurate solution with a real gas model. High-fidelity aerothermal CFD simulations were performed using US3D to further improve the aerothermal analysis on hypersonic flow around a complex entry vehicle shape including viscosity, chemical reactions of air species, vibrational energy, and catalytic surface reactions. In this process, it was found that the flap control system provided multi-axis control that can be utilized for entry precision targeting. Additionally, the Pterodactyl vehicle can achieve up to a trim L/D of 0.2. Finally, the increased fidelity of the aerothermal heating environments revealed that the shear stress contributes to increasing the heating on the flaps.

Deployable Entry Vehicle↗

Pterodactyl: Aerodynamic and Aerothermal Modeling for a Symmetric Deployable Earth Entry Vehicle with Flaps

NASA’s Pterodactyl project has investigated a deployable atmospheric entry vehicle integrated with a flap control system that provides precision targeting during reentry. The control system consists of eight flaps mounted at the edge of a heatshield that can deflect in and out of the flow. An aerodynamic and aerothermodynamic analysis process was developed for preliminary vehicle design and aerodynamic database generation using engineering and CFD tools with varying levels of fidelity. The objective of this analysis was to: 1) understand the inherent aerodynamics, 2) provide an aerodynamics database for stability and control analysis, and 3) provide qualitative and quantitative aeroheating analysis for Thermal Protection System modeling of the flaps. A high fidelity Euler code, Cart3D, was used to resolve complex flow features such as secondary shocks and shock impingement. A wide range of supersonic (Mach 2) and hypersonic Mach numbers (up to Mach 40) were tested with an Earth atmosphere model. A process was developed to utilize the adaptive volume mesh generator utility of the perfect gas model of Cart3D to create meshes with high cell efficiency and numerical stability prior to running a 2nd order accurate solution with a real gas model. High-fidelity aerothermal CFD simulations were performed using US3D to further improve the aerothermal analysis on hypersonic flow around a complex entry vehicle shape including viscosity, chemical reactions of air species, vibrational energy, and catalytic surface reactions. In this process, it was found that the flap control system provided multi-axis control that can be utilized for entry precision targeting. Additionally, the Pterodactyl vehicle can achieve up to a trim L/D of 0.2. Finally, the increased fidelity of the aerothermal heating environments revealed that the shear stress contributes to increasing the heating on the flaps.

Deployable Entry Vehicle↗

Anthropogenic influences on groundwater in the vicinity of a long-lived radioactive waste repository: Anthropogenic influences on groundwater

The groundwater flow system in the Culebra Dolomite Member (Culebra) of the Permian Rustler Formation is a potential radionuclide release pathway from the Waste Isolation Pilot Plant (WIPP), the only deep geological repository for transuranic waste in the United States. We did not expect that early conceptual models of the Culebra, groundwater levels would fluctuate markedly, except in response to long-term climatic changes, with response times on the order of hundreds to thousands of years. Recent groundwater pressures measured in monitoring wells record more than 25 m of drawdown. The fluctuations are attributed to pumping activities at a privately-owned well that may be associated with the demand of the Permian Basin hydrocarbon industry for water. Furthermore, the unprecedented magnitude of drawdown provides an opportunity to quantitatively assess the influence of unplanned anthropogenic forcings near the WIPP. Spatially variable realizations of Culebra saturated hydraulic conductivity and storativity were used to develop groundwater flow models to estimate a pumping rate for the private well and investigate its effect on advective transport. Simulated drawdown shows reasonable agreement with observations (average Model Efficiency coefficient = 0.7). Steepened hydraulic gradients associated with the pumping reduce estimates of conservative particle travel times across the domain by one-half and shift the intersection of the average particle track with the compliance boundary by more than two kilometers. Finally, the value of the transient simulations conducted for this study lie in their ability to (i) improve understanding of the Culebra groundwater flow system and (ii) challenge the notion of time-invariant land use in the vicinity of the WIPP.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Navier-Stokes, flight, and wind tunnel flow analysis for the F/A-18 aircraft

Computational analysis of flow over the F/A-18 aircraft is presented along with complementary data from both flight and wind tunnel experiments. The computational results are based on the three-dimensional thin-layer Navier-Stokes formulation and are obtained from an accurate surface representation of the fuselage, leading-edge extension (LEX), and the wing geometry. However, the constraints imposed by either the flow solver and/or the complexity associated with the flow-field grid generation required certain geometrical approximations to be implemented in the present numerical model. In particular, such constraints inspired the removal of the empennage and the blocking (fairing) of the inlet face. The results are computed for three different free-stream flow conditions and compared with flight test data of surface pressure coefficients, surface tuft flow, and off-surface vortical flow characteristics that included breakdown phenomena. Excellent surface pressure coefficient correlations, both in terms of magnitude and overall trend, are obtained on the forebody throughout the range of flow conditions. Reasonable pressure agreement was obtained over the LEX; the general correlation tends to improve at higher angles of attack. The surface tuft flow and the off-surface vortex flow structures compared qualitatively well with the flight test results. To evaluate the computational results, a wind tunnel investigation was conducted to determine the effects of existing configurational differences between the flight vehicle and the numerical model on aerodynamic characteristics. In most cases, the geometrical approximations made to the numerical model had very little effect on overall aerodynamic characteristics.

Ghaffari, Farhad↗

Turbulence Measurements on a Wing-Fuselage Junction Model for CFD Validation

Current turbulence models, such as those employed in Reynolds-averaged Navier-Stokes CFD, are unable to reliably predict the onset and extent of the three-dimensional separated flow that typically occurs in wing fuselage junctions. To critically assess, as well as to improve upon, existing turbulence models, experimental validation-quality flow field data in the junction region is needed. To that end, NASA has developed a CFD validation experiment for a generic full-span wing-fuselage junction model at subsonic conditions. In this paper, we present and discuss sample results from this effort, with a focus on turbulence measurements in the separated corner flow of the wing-fuselage junction that were obtained with an internally mounted laser Doppler velocimetry (LDV) system. In addition, sample comparisons between the flow field measurements and representative CFD of our test case are presented and here, we highlight some of the key discrepancies.

Kegerise, Michael↗

Using MODIS estimates of fractional snow cover area to improve streamflow forecasts in interior Alaska

Remotely sensed snow cover observations give an opportunity to improve operational snow melt and stream flow forecasting in remote regions. This is particularly true in Alaska, where remote basins and a spatially and temporally sparse gaging network plague efforts to understand and forecast the hydrology of subarctic boreal basins and where climate change is leading to rapid shifts in basin function. In this study,the operational framework employed by the United States (US) National Weather Service, including the Alaska Pacific River Forecast Center, is adapted to integrate Moderate Resolution Imaging Spectroradiometer (MODIS) remotely sensed observations of fractional snow cover area (fSCA) to determine if these data improve streamflow forecasts in interior Alaska river basins. Two versions of MODIS fSCA are tested against a base case extent of snow cover derived by aerial depletion curves: the MODIS 10A1(MOD10A1) and the MODIS Snow Cover Area and Grain size (MODSCAG) product over the period 2000–2010. Observed runoff is compared to simulated runoff to calibrate both iterations of the model. MODIS-forced simulations haveimproved snow depletion timing compared with snow telemetry sites in the basins, with discernable increases in skill for the streamflow simulations.The MODSCAG fSCA version provides moderate increases in skill but is similar to the MOD10A1 results. The basins with the largest improvement in streamflow simulations have the sparsest streamflow observations.Considering the numerous low-quality gages (discontinuous, short, or unreliable) and ungauged systems throughout the high-latitude regions of the globe, this result is valuable and indicates the utility of the MODIS fSCAdata in these regions. Additionally, while improvements in predicted discharge values are subtle, the snow model better represents the physical conditions of the snow pack and therefore provides more robust simulations,which are consistent with the US National Weather Service's move toward a physically based National Water Model. Physically based models may also be more capable of adapting to changing climates than statistical models corrected to past regimes. This work provides direction for both the Alaska Pacific River Forecast Center and other forecast centers across the US to implement remote-sensing observations within their operational framework, to refine the representation of snow, and to improve streamflow forecasting skill in basins with few or poor-quality observations.

54 ENVIRONMENTAL SCIENCES↗

Studies of Two-Phase Flow Dynamics and Heat Transfer at Reduced Gravity Conditions

The ability to predict gas-liquid flow patterns is crucial to the design and operation of two-phase flow systems in the microgravity environment. Flow pattern maps have been developed in this study which show the occurrence of flow patterns as a function of gas and liquid superficial velocities as well as tube diameter, liquid viscosity and surface tension. The results have demonstrated that the location of the bubble-slug transition is affected by the tube diameter for air-water systems and by surface tension, suggesting that turbulence-induced bubble fluctuations and coalescence mechanisms play a role in this transition. The location of the slug-annular transition on the flow pattern maps is largely unaffected by tube diameter, liquid viscosity or surface tension in the ranges tested. Void fraction-based transition criteria were developed which separate the flow patterns on the flow pattern maps with reasonable accuracy. Weber number transition criteria also show promise but further work is needed to improve these models. For annular gas-liquid flows of air-water and air- 50 percent glycerine under reduced gravity conditions, the pressure gradient agrees fairly well with a version of the Lockhart-Martinelli correlation but the measured film thickness deviates from published correlations at lower Reynolds numbers. Nusselt numbers, based on a film thickness obtained from standard normal-gravity correlations, follow the relation, Nu = A Re(sup n) Pr(exp l/3), but more experimental data in a reduced gravity environment are needed to increase the confidence in the estimated constants, A and n. In the slug flow regime, experimental pressure gradient does not correlate well with either the Lockhart-Martinelli or a homogeneous formulation, but does correlate nicely with a formulation based on a two-phase Reynolds number. Comparison with ground-based correlations implies that the heat transfer coefficients are lower at reduced gravity than at normal gravity under the same flow conditions. Nusselt numbers can be correlated in a fashion similar to Chu and Jones.

Witte, Larry C.↗

Ice Flow in the North East Greenland Ice Stream

Early observations with ERS-1 SAR image data revealed a large ice stream in North East Greenland (Fahnestock 1993). The ice stream has a number of the characteristics of the more closely studied ice streams in Antarctica, including its large size and gross geometry. The onset of rapid flow close to the ice divide and the evolution of its flow pattern, however, make this ice stream unique. These features can be seen in the balance velocities for the ice stream (Joughin 1997) and its outlets. The ice stream is identifiable for more than 700 km, making it much longer than any other flow feature in Greenland. Our research goals are to gain a greater understanding of the ice flow in the northeast Greenland ice stream and its outlet glaciers in order to assess their impact on the past, present, and future mass balance of the ice sheet. We will accomplish these goals using a combination of remotely sensed data and ice sheet models. We are using satellite radar interferometry data to produce a complete maps of velocity and topography over the entire ice stream. We are in the process of developing methods to use these data in conjunction with existing ice sheet models similar to those that have been used to improve understanding of the mechanics of flow in Antarctic ice streams.

Joughin, Ian↗

A Large Sample Volume Magic Angle Spinning Nuclear Magnetic Resonance Probe for In-Situ Investigations with Constant Flow of Reactants

A large-sample-volume constant-flow magic angle sample spinning (CF-MAS) NMR probe is reported for in-situ studies of the reaction dynamics, stable intermediates/transition states, and mechanisms of catalytic reactions. In our approach, the reactants are introduced into the catalyst bed using a fixed tube at one end of the MAS rotor while a second fixed tube, linked to a vacuum pump, is attached at the other end of the rotor. The pressure difference between both ends of the catalyst bed inside the sample cell space forces the reactants flowing through the catalyst bed, which improves the diffusion of the reactants and products. This design allows the use of a large sample volume for enhanced sensitivity and thus permitting in-situ 13C CF-MAS studies at natural abundance. As an example of application, we show that reactants, products and reaction transition states associated with the 2-butanol dehydration reaction over a mesoporous silicalite supported heteropoly acid catalyst (HPA/meso-silicalite-1) can all be detected in a single 13C CF-MAS NMR spectrum at natural abundance. Coke products can also be detected at natural 13C abundance and under the stopped flow condition. Furthermore, 1H CF-MAS NMR is used to identify the surface functional groups of HPA/meso-silicalite-1 under the condition of in-situ drying . We also show that the reaction dynamics of 2-butanol dehydration using HPA/meso-silicalite-1 as a catalyst can be explored using 1H CF-MAS NMR.

01 COAL, LIGNITE, AND PEAT↗

Contamination avoidance devices for poppettype shutoff valves

The determination of the cycle life is reported of the scal closure of a typical poppet-type shutoff valve in an uncontaminated GH2 environment and then compared this component performance with simulated operation with GN2 and LN2 containing controlled amounts of AL2O3 contaminant particles. The original valve design was tested for contamination damage tolerance characteristics under full-flow and cyclic-operating conditions, redesigned to improve the damage tolerance to contaminants, and then retested. The redesigned valve was found to have acceptable tolerance characteristics under all full-flow conditions and cyclic operation with small (25-75 microns) particulate contamination. The tolerance characteristics of the valve under cyclic conditions with large (75-250 microns) particulate contamination was improved but was not found to be completely satisfactory.

Endicott, D. L.↗

Development of the ANL Plant Dynamics Code and Control Strategies for the Supercritical Carbon Dioxide Brayton Cycle and Code Validation with Data from the Sandia Small-Scale Supercritical Carbon Dioxide Brayton Cycle Test Loop

Significant progress has been made in the ongoing development of the Argonne National Laboratory (ANL) Plant Dynamics Code (PDC), the ongoing investigation and development of control strategies, and the analysis of system transient behavior for supercritical carbon dioxide (S-CO 2 ) Brayton cycles. Several code modifications have been introduced during FY2011 to extend the range of applicability of the PDC and to improve its calculational stability and speed. A new and innovative approach was developed to couple the Plant Dynamics Code for S-CO 2 cycle calculations with SAS4A/SASSYS-1 Liquid Metal Reactor Code System calculations for the transient system level behavior on the reactor side of a Sodium-Cooled Fast Reactor (SFR) or Lead-Cooled Fast Reactor (LFR). The new code system allows use of the full capabilities of both codes such that whole-plant transients can now be simulated without additional user interaction. Several other code modifications, including the introduction of compressor surge control, a new approach for determining the solution time step for efficient computational speed, an updated treatment of S-CO 2 cycle flow mergers and splits, a modified enthalpy equation to improve the treatment of negative flow, and a revised solution of the reactor heat exchanger (RHX) equations coupling the S-CO 2 cycle to the reactor, were introduced to the PDC in FY2011. All of these modifications have improved the code computational stability and computational speed, while not significantly affecting the results of transient calculations. The improved PDC was used to continue the investigation of S-CO 2 cycle control and transient behavior. The coupled PDC-SAS4A/SASSYS-1 code capability was used to study the dynamic characteristics of a S-CO 2 cycle coupled to a SFR plant. Cycle control was investigated in terms of the ability of the cycle to respond to a linear reduction in the electrical grid demand from 100% to 0% at a rate of 5%/minute. It was determined that utilization of turbine throttling control below 50% load improves the cycle efficiency significantly. Consequently, the cycle control strategy has been updated to include turbine throttle valve control. The new control strategy still relies on inventory control in the 50%-90% load range and turbine bypass for fine and fast generator output adjustments, but it now also includes turbine throttling control in the 0%-50% load range. In an attempt to investigate the feasibility of using the S-CO 2 cycle for normal decay heat removal from the reactor, the cycle control study was extended beyond the investigation of normal load following. It was shown that such operation is possible with the extension of the inventory and the turbine throttling controls. However, the cycle operation in this range is calculated to be so inefficient that energy would need to be supplied from the electrical grid assuming that the generator could be capable of being operated in a motoring mode with an input electrical energy from the grid having a magnitude of about 20% of the nominal plant output electrical power level in order to maintain circulation of the CO 2 in the cycle. The work on investigation of cycle operation at low power level will be continued in the future. In addition to the cycle control study, the coupled PDC-SAS4A/SASSYS-1 code system was also used to simulate thermal transients in the sodium-to-CO 2 heat exchanger. Several possible conditions with the potential to introduce significant changes to the heat exchanger temperatures were identified and simulated. The conditions range from reactor scram and primary sodium pump failure or intermediate sodium pump failure on the reactor side to pipe breaks and valve malfunctions on the S-CO 2 side. It was found that the maximum possible rate of the heat exchanger wall temperature change for the particular heat exchanger design assumed is limited to ±7 C/s for less than 10 seconds. Modeling in the Plant Dynamics Code has been compared with available data from the Sandia National Laboratories (SNL) small-scale S-CO 2 Brayton cycle demonstration that is being assembled in a phased approach currently at Barber-Nichols Inc. and at SNL in the future. The available data was obtained with an earlier configuration of the S-CO 2 loop involving only a single-turbo-alternator-compressor (TAC) instead of two TACs, a single low temperature recuperator (LTR) instead of both a LTR and a high temperature recuperator (HTR), and fewer than the later to be installed full set of electric heaters. Due to the absence of the full heating capability as well as the lack of a high temperature recuperator providing additional recuperation, the temperature conditions obtained with the loop are too low for the loop conditions to be prototypical of the S-CO 2 cycle.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Optimal nodal point distribution for improved accuracy in computational fluid dynamics

In applying finite-difference techniques to flow field problems, the accuracy attained for a fixed number of node points can be improved using unequally-spaced node points. The distribution of these node points is chosen here by minimizing a measure of local truncation error with respect to the parameters which define a transformation between the computational space of equally-spaced node points and the physical space of unequally-spaced node points. The problem then becomes a nonlinear programming problem. Numerical results are presented for two one-dimensional test problems: the Blasius boundary layer problem and the inviscid Burgers' equation.

Pierson, B. L.↗

Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence

Particle-laden turbulent flows subject to radiative heating are relevant in many applications, for example concentrated solar power receivers. Efficient and accurate simulations provide valuable insights and enable optimization of such systems. However, as there are many uncertainties inherent in such flows, uncertainty quantification is fundamental to improve the predictive capabilities of the numerical simulations. For large-scale, multi-physics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as most strategies require a large number of high-fidelity solves. This requirement might result in an infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying high-dimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method exploits the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. Here, the application of this bi-fidelity approximation results in accurate estimates of the quantities of interest statistics, while requiring a small number of high-fidelity model evaluations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

First observation of currents induced by Alfven eigenmodes in a magnetic confinement device

Instabilities driven by energetic particles normally reduce fusion power but recent studies find Alfven eigenmode instabilities can drive ``zonal" flows and currents that reduce thermal transport, improving overall performance. Motional Stark effect (MSE) data from the DIII-D tokamak reveal changes in magnetic pitch angle during the phase when Alfven-eigenmode nonlinearity drives zonal flows, suppresses microturbulence, and increases the electron and ion temperatures. Finally, measured changes in safety factor of ∆q/q ≃ 5% occur in roughly 20 ms, consistent with a rough estimate based on the measured zonal flow.

Heidbrink, W. W. [Univ. of California, Irvine, CA ↗

Intermittency Model for Coupled CFD-Stability Transition Analysis in Hypersonic Flow

Accurate prediction of aerothermodynamic loads on hypersonic vehicles requires precise modeling of surface quantities across the boundary layer transition zone. The peak heating loads and total heat transfer are determined by parameters such as the transition zone length and the magnitude of potential overshoots in heat flux and skin friction beyond their respective values in fully turbulent flows. While previous studies on CFD integrated transition modeling using linear stability correlations have shown promise in modeling these features, they did not develop an intermittency model for hypersonic flows. This paper presents a data-driven approach to develop a model of this type by correlating experimental transition data with the relevant flow parameters. The resulting model demonstrates significant improvements over previous low-speed models in terms of predicting heat transfer distributions during the transition process associated with first and second mode instabilities in axisymmetric high-speed flows. Separate correlations for flight and ground test conditions are developed, and the potential to combine these correlations is discussed.

Transition↗

Discrete Element Method Analysis for Metal Powders Used in Additive Manufacturing, and DEM Simulation Tutorial Using LIGGGHTS-PUBLIC [PowerPoint and paper]

Discrete Element Method (DEM) is a method of analysis to evaluate the dynamic interactions between granular particles. This method has been used in the pharmaceutical industry to improve the powder compaction process for tablet manufacturing. There are also applications in agriculture, food industry, and manufacturing. Direct energy deposition is an additive manufacturing technique which uses metallic powders fed through a nozzle, melted using a directed laser, and transformed into a solid object layer by layer. One way of feeding metal particles into the system involves the use of a vibrating hopper. Given a specified amplitude and frequency input, the hopper will enable the powder to travel up a path, and inject through the system with assistance from a stream of gas. The mechanical properties of a printed object can vary, depending on the characteristics of the powder flow and the particles’ as-received properties. Improved understanding of dynamic interactions of flowing powders could enable additive manufacturing components with 2D or 3D variations in mechanical properties, e.g., density. This work uses DEM simulation software to investigate the effects of particle cohesion, friction, and density on the quality of the flow by performing an angle of repose simulation, which is often used as a metric to evaluate the flowability of powders.

36 MATERIALS SCIENCE↗

Near-wall variable-Prandtl-number turbulence model for compressible flows

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon (sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Sommer, T. P.↗