We present well-resolved RANS simulations of two generic asymmetrically heated cooling channel configurations, a high aspect ratio cooling duct operated with liquid water at (Formula Presented) and a cryogenic transcritical channel operated with methane at (Formula Presented). The former setup serves to investigate the interaction of turbulence-induced secondary flow and heat transfer, and the latter to investigate the influence of strong non-linear thermodynamic property variations in the vicinity of the critical point on the flow field and heat transfer. To assess the accuracy of the RANS simulations for both setups, well-resolved implicit LES simulations using the adaptive local deconvolution method as subgrid-scale turbulence model serve as comparison databases. The investigation focuses on the prediction capabilities of RANS turbulence models for the flow as well as the temperature field and turbulent heat transfer with a special focus on the turbulent heat flux closure influence.

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We present well-resolved RANS simulations of a high-aspect-ratio generic cooling duct configuration consisting of an adiabatic straight feed line followed by a heated straight section ending with a 90° bend. The configuration is asymmetrically heated with a temperature difference of ∆T = 40 K. As fluid liquid water is used at a Reynolds number of Reb = 110 × 10 ³. The setup follows an experimental reference case, which has also been investigated using a well-resolved LES. The current investigation focuses on the prediction capabilities of different RANS turbulence closure models for the duct flow field, defined by the interaction of secondary flows and turbulent heat transfer. In the straight duct only turbulence-induced secondary flow is present, which becomes weaker along the heated duct due to the viscosity reduction, leading in turn to a reduced mixing. In the curved section, the stronger pressure-induced secondary flow superimposes the turbulence-induced one increasing the mixing of hot and cold fluid. A well-resolved LES serves as comparison database for the straight duct results.

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We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of Re_b = 110 × 10³ and an average Nusselt number of Nuxz = 371. The geometry and boundary conditions follow an experimental reference case and good agreement with the experimental results is achieved. The current investigation focuses on the influence of asymmetric wall heating on the duct flow field, specifically on the interaction of turbulence-induced secondary flow and turbulent heat transfer, and the associated spatial development of the thermal boundary layer and the inferred viscosity variation. The viscosity reduction towards the heated wall causes a decrease in turbulent mixing, turbulent length scales and turbulence anisotropy as well as a weakening of turbulent ejections. Overall, the secondary flow strength becomes increasingly less intense along the length of the spatially resolved heated duct as compared to an adiabatic duct. Furthermore, we show that the assumption of a constant turbulent Prandtl number is invalid for turbulent heat transfer in an asymmetrically heated duct.

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We present the results of well-resolved large-eddy simulations (LES) of an asymmetrically heated high aspect ratio cooling duct (HARCD) with an aspect ratio of AR = 4.3 for two different wall temperatures. The temperature difference with respect to the bulk flow is ∆T = 40 K, respectively ∆T = 60 K. The HARCD is operated with liquid water at a Reynolds number of Re_b = 110 ⋅ 10³ based on bulk velocity and hydraulic diameter. The generic HARCD setup follows a reference experiment. The main goal of the present study is the numerical investigation of the interaction of turbulent heat transfer and the turbulent duct flow, specifically the heating induced changes in mean flow and turbulent statistics with a spatially developing temperature boundary layer. Furthermore, we investigate the influence of asymmetric wall heating on streamwise vorticity and its dynamics as well as the turbulent Prandtl number and the effect of the secondary flow on its distribution.

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We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by. The Reynolds number based on the incoming boundary-layer thickness of is considerably higher than in previous LES studies. The very long integration time of allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

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We investigate a reacting shock–bubble interaction through three-dimensional numerical simulations with detailed chemistry. The convex shape of the bubble focuses the shock and generates regions of high pressure and temperature, which are sufficient to ignite the diluted stoichiometric H₂−O₂ gas mixture inside the bubble. We study the interaction between hydrodynamic instabilities and shock-induced reaction waves at a shock Mach number of Ma=2.83. The chosen shock strength ignites the gas mixture before the shock-focusing point, followed by a detonation wave, which propagates through the entire bubble gas. The reaction wave has a significant influence on the spatial and temporal evolution of the bubble. The misalignment of density and pressure gradients at the bubble interface, caused by the initial shock wave and the subsequent detonation wave, induces Richtmyer–Meshkov and Kelvin–Helmholtz instabilities. The growth of the instabilities is highly affected by the reaction wave, which significantly reduces mixing compared to an inert shock–bubble interaction. A comparison with two-dimensional simulations reveals the influence of three-dimensional effects on the bubble evolution, especially during the late stages. The numerical results reproduce experimental data in terms of ignition delay time, reaction wave speed and spatial expansion rate of the bubble gas. We observe only a slight divergence of the spatial expansion in the long-term evolution.

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We present well-resolved large-eddy-simulations (LES) of a straight, high-aspect-ratio cooling duct (HARCD) at a bulk Reynolds number of Re = 110 • 10³ and an average Nusselt number of Nu = 371. The geometry and boundary conditions have been defined together with Rochlitz et al. (2015), who conducted the experimental measurements for this case. Water was chosen as coolant. The current investigation focuses on the influence of asymmetrical wall heating on the flow field and specifically on the influence of the turbulence-induced secondary flow on turbulent heat transfer, the spatial development of the temperature boundary layer and the accompanying viscosity modulation. Due to the viscosity drop in the vicinity of the heated wall we observe a decrease in turbulent length scales and in turbulence anisotropy, resulting in a decrease of turbulent mixing and the secondary flow strength along the duct.

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We present LES results of temporally evolving cavitating shear layers. Cavitation is modeled by a homogeneous equilibrium mixture model whereas the effect of subgrid-scale turbulence is accounted for by the Adaptive Local Deconvolution Method (ALDM). We quantitatively compare LES results with experimental data available in the literature. In terms of computational performance, we present a strong scaling study of our MPI-parallelized in-house FORTRAN code INCA on Cray XE6 “Hermit” at the High Performance Computeing Center Stuttgart (HLRS).

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We present numerical simulations of a reacting shock-bubble interaction with detailed chemistry. The interaction of the Richtmyer-Meshkov instability (RMI) and shock-induced ignition of a stoichiometric H2-O2 gas mixture are investigated. Different initial pressures in the range of po = 0.25-0.75 atm at a constant shock wave Mach number of Ma = 2.30 trigger different reaction wave types (deflagration and detonation). Low pressure reactions are dominated by H, O, OH production and high pressure chemistry is driven by HO2 and H2O2. The reaction wave type is crucial for the spatial and temporal evolution of the bubble. The RMI and subsequent Kelvin Helmholtz instabilities show a high reaction sensitivity. Mixing is significantly reduced by both types of reaction waves, with detonation waves showing the strongest effect.@en

In this work our first objective is to study the spatial development of a laminar compressible mixing layer after a splitter plate at relatively high Reynolds number by using an implicit large-eddy simulation. A blowing and suction strip is used on the upper wall of the plate to promote the shear layer instability. In the perspective of flow control our second objective is to understand the effects of a strong thermal forcing to modify the spatial development. In the momentum-forcing case three distinct flow regions exists: a linear instability region, a mixing-transition region and a fully developed turbulent region, which has much different vorticity growth rate. In the fully developed region the distributions of mean velocity collapse into a self-similar profile. There is no spanwise roller observed near the trailing edge of the plate. When the thermal forcing is also applied, it introduces two-dimensional spanwise rollers. Two successive spanwise roller pairing are observed. The vorticity thickness and its growth rate are totaly different. At the end of the simulation domain the flow is not fully turbulent. Different Mach wave radiations are observed in the fast stream. Therefore, the thermal forcing can effectively to modify the spatial development of the mixing layer.@en

We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Wellresolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ~t^7/12 before re-shock and ~(t - t₀)^2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ~(t-t₀)^-10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit ≈ 0.85. The anisotropy measure.

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Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.

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We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a polynomial chaos expansion to propagate the initial-data uncertainties to the output quantities of interest. The initial flow configuration follows previous experimental and numerical works of the shock accelerated heavy-gas cylinder.We investigate three main initialdata uncertainties, (i) shock Mach number, (ii) contamination of SF₆ with acetone, and (iii) initial deviations of the heavy-gas region from a perfect cylindrical shape. The impact of initial-data uncertainties on the mixing process is examined. The results suggest that the mixing process is highly sensitive to input variations of shock Mach number and acetone contamination. Additionally, our results indicate that the measured shock Mach number in the experiment of Tomkins et al. ["An experimental investigation of mixing mechanisms in shock-accelerated flow," J. Fluid. Mech. 611, 131 (2008)] and the estimated contamination of the SF₆ region with acetone [S. K. Shankar, S. Kawai, and S. K. Lele, "Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder," Phys. Fluids 23, 024102 (2011)] exhibit deviations from those that lead to best agreement between our simulations and the experiment in terms of overall flow evolution.

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We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.

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In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by Ma=1.05,Ma=1.2, and Ma=1.5 shock waves interacting with a perturbed planar interface between air and SF6. At the lowest shock Mach number the fluids slowly mix due to viscous diffusion, whereas at the highest shock Mach number the mixing zone becomes turbulent. When a minimum critical Taylor microscale Reynolds number is exceeded, an inertial range spectrum emerges, providing further evidence of transition to turbulence. The scales of turbulent motion, i.e., the Kolmogorov length scale, the Taylor microscale, and the integral length, scale are presented. The separation of these scales is found to increase as the Reynolds number is increased. Turbulence statistics, i.e., the probability density functions of the velocity and its longitudinal and transverse derivatives, show a self-similar decay and thus that turbulence evolving from RMI is not fundamentally different from isotropic turbulence, though nominally being only isotropic and homogeneous in the transverse directions.

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Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a reference experiment. Details of the experiment, such as planar side walls, are taken into account, all wall boundary layers are well-resolved and no wall model is used. The Adaptive Local Deconvolution Method (ALDM) with shock sensor is employed for subgrid-scale turbulence modeling and shock capturing. The LES results are validated against experimental wall-pressure measurements and schlieren pictures. A detailed discussion of the complex flow phenomena of three-dimensional shock-wave-boundary-layer interaction, including corner vortices and recirculation zones, is presented. Limitations of RANS approaches are discussed with reference to the LES results.

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We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma_∞=2.3 and a Reynolds number based on the incoming boundary-layer thickness of Reδ0=60.5×103 by means of large-eddy simulation (LES). The compressible Navier-Stokes equations in conservative form are solved using the adaptive local deconvolution method (ALDM) for physically consistent subgrid scale modeling. Emphasis is placed on the correct description of turbulent inflow boundary conditions, which do not artificially force low-frequency periodic motion of the reflected shock. The control configuration combines suction inside the separation zone and blowing upstream of the interaction region by a pressure feedback through a duct embedded in the wall. We vary the suction location within the recirculation zone while the injection position is kept constant. Suction reduces the size of the separation zone with strongest effect when applied in the rear part of the separation bubble. The analysis of wall-pressure spectra reveals that all control configurations shift the high-energy low-frequency range to higher frequencies, while the energy level is significantly reduced only if suction acts in the rear part of the separated zone. In that case also turbulence production within the interaction region is significantly reduced as a consequence of mitigated reflected shock dynamics and near-wall flow acceleration.

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Industrially applied Computational Fluid Dynamics still faces a challenge when it comes to the accurate prediction of the complex flow over realistic highlift configurations. In this paper we demonstrate that the flow over the 3-element RA16SC1 highlift configuration can be effciently and accurately predicted with Implicit Large-Eddy Simulation (ILES) on Cartesian adaptive grids. In ILES the truncation error of the numerical discretization itself functions as an implicit Sub-Grid Scale (SGS) model. To prove and enable industrial application of ILES, the underlying Cartesian grid of this simulation has been automatically generated and refined for resolving the relevant flow features. The wall-boundary condition is applied with a second-order Conservative Immersed Interface Method (CIIM). Effciency is further increased by modeling near-wall turbulence based on the Thin-Boundary-Layer Equation (TBLE). The good agreement with the respective experimental results underlines the suitability of this CFD approach for industrial applications.@en