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A review of some approximate methods used in aerodynamic heating analyses

It is pointed out that preliminary design and optimization studies for new aerospace vehicles require techniques which can calculate aerodynamic heating rates accurately and efficiently. The method employed to calculate the flow field depends to a large extent on the shape of the vehicle, Mach number, Reynolds number, and Knudsen number. In the case of the aero-assisted orbital transfer vehicle (AOTV), a substantial portion of the flight will be in the transitional regime between continuum and free molecule flow. The present paper discusses some approximate methods which have been used to calculate heating rates on high-speed vehicles. Attention is given to the stagnation point and leading edges, the downstream region, the axisymmetric analog, laminar and turbulent heating rates, transition heating rates, gas models, and three-dimensional applications.

Dejarnette, F. R.↗

Hypersonic research at Stanford University

The status of the hypersonic research program at Stanford University is discussed and recent results are highlighted. The main areas of interest in the program are the numerical simulation of radiating, reacting and thermally excited flows, the investigation and numerical solution of hypersonic shock wave physics, the extension of the continuum fluid dynamic equations to the transition regime between continuum and free-molecule flow, and the development of novel numerical algorithms for efficient particulate simulations of flowfields.

Candler, Graham↗

High-Subsonic Performance Characteristics and Boundary-Layer Investigations of a 12 10-Inch-Inlet-Diameter Conical Diffuser

Performance and boundary-layer data were taken in a 12 degree 10-inch inlet-diameter conical diffuser of 2:1 exit- to inlet-area ratio. These data were taken for two inlet-boundary-layer conditions. The first condition was that of a thinner inlet boundary later (boundary-layer displacement thickness, delta* approximately equal to 0.034) produced by an inlet section approximately 1 inlet diameter in length between the entrance bell and the diffuser. The second condition was a thicker inlet boundary layer (delta* approximately equal to 0.120) produced by an additional inlet section length of approximately 6 diameters. Longitudinal static-pressure distributions were measured fro wall static orifices. Transverse total- and static-pressure surveys were made at the inlet and exit stations. Boundary-layer velocity distributions were measured at seven stations between the inlet and exit. These data were obtained for a Reynolds number (based on inlet diameter) range of 1 x 10(exp 6) to 3.9 x 10(exp 6). The corresponding Mach number range was from M = 0.2 to choking. At the maximum-power-available condition supersonic flow was obtained as far as 4.5 inches downstream from the diffuser inlet with a maximum Mach number of M approximately equal to 1.5. The total-pressure loss through the diffuser in percentage of inlet dynamic pressure was approximately 2.5 percent for the thinner inlet boundary later and 5.5 percent for the thicker inlet boundary later over the lower subsonic range. These valued increased with increasing flow rate- the values for the thicker inlet boundary later more than those for the thinner inlet boundary layer. The diffuser effectiveness, expressed as the ratio of the actual static-pressure rise to the ideal static-pressure rise, was about 85 percent for the thinner inlet boundary layer and about 67 percent for the thicker inlet boundary later in the lower subsonic range. These values decrease with increasing flow rate. Separated flow was observed for both inlet-boundary-layer conditions in the region of adverse pressure gradient just downstream of the transition curvature from inlet section to diffuser. The flow for the thinner-inlet-boundary-layer condition did not fully re-establish itself along the diffuser walls. The thicker inlet-boundary-layer flow, while not completely re-establishing the normal flow pattern downstream of the separated region, did re-establish more successfully than the thinner inlet boundary layer.

Little, B. H., Jr.↗

Modeling heat pipe startup and noncondensable gases in Sockeye

For this work, a one-dimensional gas mixture flow model was developed and implemented in the heat pipe code Sockeye to model the effects of noncondensable gases. Additionally, a startup model based on the dusty gas model was implemented to model the transition from rarefied gas dynamics to continuum flow, which occurs during the frozen startup of high-temperature heat pipes. Multiple startup and noncondensable gas models were tested against experimental data for sodium heat pipes, showing excellent agreement. Additionally, the newly developed gas mixture model for modeling noncondensable gas is further tested with a theoretical case study with arbitrary heating configurations. Finally, several recommendations and conclusions are made from the studies in this work to guide future heat pipe modeling efforts.

97 - MATHEMATICS AND COMPUTING↗

A Study of Grid Resolution, Transition and Turbulence Model Using the Transonic Simple Straked Delta Wing

Three-dimensional transonic flow over a delta wing is investigated using several turbulence models. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition aft of the leading edge or are fully turbulent are performed. These computations show that grid resolution, transition location and turbulence model significantly affect the 3D flowfield.

Bartels, Robert E.↗

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗

Significance of turbulence and transition location on radiative heating with ablation injection

This paper presents forebody flowfield solutions for Jupiter entry conditions where the ablation injection rate is coupled with the surface heating rate. The calculations are made with a time-dependent viscous-shock-layer analysis where the flow is assumed to be in chemical equilibrium. Both laminar and turbulent solutions are presented to describe the impact of turbulence on surface mass loss rates for flow conditions where the heating is due primarily to radiation. Results are also presented where the transition location to turbulent flow is arbitrarily varied. Results show that the radiative heating rate values based on several downstream transition locations adjust quickly to the corresponding values based on transition near the stagnation point.

Moss, J. N.↗

A linear analysis of the transition curve for the baroclinic annulus

A primitive equation linear model is shown to be capable of quantitatively predicting the neutral curve for a baroclinic annulus. Flows unstable to small nonaxisymmetric perturbations are assumed to lie on the nonaxisymmetric side of a transition curve, while the stable flows are on the axisymmetric side. The stability in the presence of perturbations is tested with linearized hydrostatic primitive equations. Attention is given to the fastest growing eigenmodes, demonstrating that the linear and nonlinear wave have similar structures at a particular point in the nonaxisymmetric regime. All the waves are similar to the Eddy wave except at the extreme to the transition curve, where the waves maintain little structure with height. The eddy kinetic energy is baroclinic with a potential energy suppresed by the large static stability of the basic state. Eddy dissipation is noted to be significant near all boundaries.

Miller, T. L.↗

Development of the Glenn Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

Ameri, Ali↗

Development of the Glenn-HT Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.

infrared↗

Development of the Glenn-Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

heat transfer↗

Renewable Energy Transitions: Risk and Opportunities

This presentation summarizes historical and modeled data of the energy transition, including energy generation sources, energy jobs, and global materials flow. It concludes with discussion points about potential risks and opportunities of the energy transition.

ENERGY PLANNING, POLICY, AND ECONOMY,ENVIRONMENTAL↗

Shape fluctuations and optical transition of He 2 * excimer tracers in superfluid He 4

Metastable He$_{2}^{*}$ excimer molecules have been utilized as tracer particles of the normal component in superfluid $^4$He (He II) which can be imaged via laser-induced fluorescence. These excimer molecules form tiny bubbles in He II and can bind to quantized vortices at sufficiently low temperatures, thereby allowing for direct visualization of vortex dynamics in an inviscid superfluid. However, the $a^{3}\Sigma^+_{u}$${\rightarrow}$$c^{3}\Sigma^+_{g}$ optical absorption line, which is responsible for the fluorescence imaging of the He$_{2}^{*}$ molecules, is controlled by fluctuations on the bubble shape, and its exact line profile is not known at low temperatures. In this paper, we present a bubble model for evaluating the surface fluctuation eigenmodes of the excimers in He II. The line profile of the $a^{3}\Sigma^+_{u}{\rightarrow}c^{3}\Sigma^+_{g}$ transition is calculated at different temperatures by considering both the zero-point and thermal fluctuations on the bubble shape. We show that, as the temperature drops from 2~K to 20 mK, the peak absorption strength is enhanced by a factor of about five, accompanying a blueshift of the peak location by about 2 nm. A double-peak line profile due to the rotational levels of the molecular core can be resolved. This bubble model also allows us to evaluate the stiffness of the He$_{2}^{*}$ bubbles and hence their diffusion constant in He II due to scattering off thermal phonons. Our results will aid the design of future experiments on imaging quantized vortices in He II using He$_{2}^{*}$ tracers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A Transport Equation Approach to Modeling the Influence of Surface Roughness on Boundary Layer Transition

A computational investigation has been performed to better understand the impact of surface roughness on the flow over a contaminated surface. This report highlights the implementation and development of the roughness amplication model in the flow solver OVER FLOW-2. The model, originally proposed by Dassler, Kozulovic, and Fiala, introduces an additional scalar field roughness amplification quantity. This value is explicitly set at rough wall boundaries using surface roughness parameters and local flow quantities. The additional transport equation allows non-local effects of surface roughness to be accounted for downstream of rough sections. This roughness amplification variable is coupled with the Langtry-Menter model and used to modify the criteria for transition. Results from at plate test cases show good agreement with experimental transition behavior on the flow over varyings and grain roughness heights. Additional validation studies were performed on a NACA 0012 airfoil with leading edge roughness. The computationally predicted boundary layer development demonstrates good agreement with experimental results. New tests using varying roughness configurations have been carried out at the Texas A&M Oran W. Nicks Low Speed Wind Tunnel to provide further calibration of the roughness amplification method. An overview and preliminary results are provided of this concurrent experimental investigation.

17 WIND ENERGY↗

Remapping HELENA to incompressible plasma rotation parallel to the magnetic field

Plasma rotation in connection to both zonal and mean (equilibrium) flows can play a role in the transitions to the advanced confinement regimes in tokamaks, as the L-H transition and the formation of internal transport barriers (ITBs). For incompressible rotation, the equilibrium is governed by a generalised Grad-Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the pressure. For parallel flow, the GGS equation can be transformed to one identical in form with the usual Grad-Shafranov equation. In the present study on the basis of the latter equation, we have extended HELENA, an equilibrium fixed boundary solver. The extended code solves the GGS equation for a variety of the two free-surface-function terms involved for arbitrary Alfvén Mach number and density functions. We have constructed diverted-boundary equilibria pertinent to ITER and examined their characteristics, in particular, as concerns the impact of rotation on certain equilibrium quantities. It turns out that the rotation and its shear affect noticeably the pressure and toroidal current density with the impact on the current density being stronger in the parallel direction than in the toroidal one.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An analytic model for limiting high density LH transition by the onset of the tertiary instability

We perform an analytic study of the tertiary instability driven by a strong excitation of zonal flows during high density low to high (LH) mode transition. The drift resistive ballooning mode is assumed to be a dominant edge turbulence driver. The analysis reproduces main qualitative features of early computational results [Rogers and Drake, Phys. Rev. Lett. 81, 4396 (1998); Guzdar et al., Phys. Plasmas 14, 020701 (2007)], as well as new characteristics of the maximum edge density due to the onset of the tertiary instability. An analytical scaling indicates that the density scaling of LH transition power may be determined by the onset condition of the tertiary instability when the operating density approaches to the Greenwald density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling Heat Pipe Startup And Noncondensable Gases In Sockeye

A one-dimensional gas mixture flow model was developed and implemented in the heat pipe code Sockeye to model the effects of non-condensable gases. Additionally a startup model based on the dusty gas model was implemented to model the transition from rarefied gas dynamics to continuum flow, which occurs during the frozen startup of high-temperature heat pipes. Multiple startup models and non-condensable gas models were tested against experimental data for sodium heat pipes, showing excellent agreement. Additionally, the newly developed gas mixture model for modeling non-condensable gas is further tested with a theoretical case study with arbitrary heating configurations. Finally, several recommendations and conclusions are made from the studies in this work to guide future heat pipe modeling efforts.

97 - MATHEMATICS AND COMPUTING↗

Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability

The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number $A_{t}$ from 0.035 to 0.159, with varying amounts of shear and $\unicode[STIX]{x0394}U/U$ ranging from 0 to 0.48, where $\unicode[STIX]{x0394}U$ is the speed difference between the two flow streams being investigated and $U$ is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.

Mechanics↗

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