Paper Submission
ETC2019 17th European Turbulence Conference





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10:45   Compressible Flows 1
10:45
15 mins

#179
Self-similar compressible turbulent boundary layers with pressure gradients - Part 1: DNS of sub- and supersonic flow
Christoph Wenzel, Tobias Gibis, Markus Kloker, Ulrich Rist
Abstract: A direct-numerical-simulation (DNS) study of approximately self-similar compressible flat-plate turbulent boundary-layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth, pure PGs both for favorable and adverse PG distributions (FPG, APG) and thus are comparable to experiments using a reflected-wave set-up. The resulting flow fields are characterized by long regions of almost constant Rotta-Clauser parameters \beta_K which was found to still predict the approximated state of local self-similarity/equilibrium in the compressible regime, see "Self-similar compressible turbulent boundary layers with pressure gradients -- Part2: Self-similarity analysis of the outer layer". The equilibrium character makes a systematical comparability between sub- and supersonic cases reasonable, allowing the isolation of pure PG effects and thus the evaluation of the validity of common compressibility transformations for compressible PGTBLs. Whereas the subsonic APG cases show the well-known incompressible trends, the interpretation of the supersonic PG cases is complex. The boundary layer consists of both sub- and supersonic regions counteracting in their spatial evolution. The boundary-layer thickness \delta_{99} as well as the skin-friction coefficient c_f for instance are in a comparable range for all compressible APG cases, see figure 1. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behavior both for sub- and supersonic cases characterized by comparable kinematic Rotta-Clauser parameters \beta_K, which approximately validates Morkovin's scaling/hypothesis also for compressible equilibrium PG\,TBLs. Also the local non-dimensionalized distributions of the mean-flow pressure and the pressure-fluctuations compare, respectively, and thus are almost invariant to the local Mach number for same \beta_K-cases. In the inner layer, the van-Driest transformation almost perfectly collapses compressible mean-flow data of the streamwise velocity component into their nearly incompressible counterparts with same \beta_K. However, depending on the strength of the PG, noticeable differences can be observed in the wake area. Both for sub- and supersonic cases, the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but stays almost constant in regions of approximated equilibrium.
11:00
15 mins

#180
Self-similar compressible turbulent boundary layers with pressure gradients -- Part 2: Self-similarity analysis of the outer layer
Tobias Gibis, Christoph Wenzel, Markus Kloker, Ulrich Rist
Abstract: The concept of equilibrium boundary layers introduced by Clauser is one of the most successful approaches to understand and characterize boundary layers (BL) with pressure gradients in incompressible flows. Equilibrium BLs are a special class minimizing history effects and thus allowing for a correlation between the pressure gradient and the reaction of the BL. For compressible flows, however, the problem of self-similarity becomes more intricate as a pressure gradient causes a varying Mach number in the streamwise direction and thus couples pressure and compressibility effects. Supersonic BLs additionally consist of both subsonic and supersonic parts, which are expanded and compressed oppositely to each other in case of pressure gradients. The growth of the compressible BL is therefore strongly depending on local conditions and often differs from intuition based on subsonics. From a literature point of view, it is not clear what the properties of compressible equilibrium BLs are or if they are even possible. The aim of this study is to discuss the properties of canonical compressible turbulent self-similar BLs and to evaluate the findings with carefully conducted simulations, see "Self-similar compressible turbulent BLs with pressure gradients -- Part 1: DNS of sub- and supersonic flow". Specific issues to be evaluated are: Does a compressible self-similar theory exist analogously to the incompressible one? What are the properties, relevant parameters/scales and conditions to obtain a (near-) equilibrium state? Based on the Favre-averaged turbulent BL equations a self-similarity analysis after George & Castillo and Maciel et al. has been performed. This analysis allows to study the existence and properties of compressible equilibrium layers with pressure gradients. The results are then used to analyze nearly self-similar flows obtained by DNS. The analysis returns the form of generalized scalings for all quantities and conditions which have to be fulfilled approximately, if self-similarity of the momentum and energy BLs ought to be obtained. In the analysis of the energy equation no obvious inconsistencies were revealed, meaning that the state of (approximated) self-similarity also can be obtained by the energy BL.
11:15
15 mins

#485
Detached-eddy simulation of transverse hydrogen injection into supersonic crossflow
Alexey Troshin, Vladimir Vlasenko, Vladimir Sabelnikov
Abstract: Simulations of a transverse hydrogen jet injection into supersonic air flow with self-ignition are presented. In the experiment, a flat plate with round orifice of diameter d_j = 2 mm was mounted in hot air flow at Mach number 3.38. From the orifice, a sonic hydrogen stream was injected perpendicular to the flow with relative momentum flux J = 1.4. The test reproduces a common fuel supply scheme used in aircraft engines. This research serve as validation of the presented scale resolving technology. It is considered a necessary step towards combustion chamber simulations. The problem was solved using zFlare in-house solver (TsAGI). Explicit finite volume WENO5 scheme with fractional time stepping was employed. The scheme is implemented on multiblock hexahedral meshes. There are hybrid SST-DDES and SST-IDDES models in the code with SLA subgrid length scale. The computational region had the form of a rectangular box, Fig. 1, left. The computational mesh contained 22 million cells. Hybrid SST-IDDES model was employed. 256 CPU cores of an HPC cluster were used. Several computational runs of this problem were carried out on the "Lomonosov" supercomputer. In Fig. 1, center, vortex structure of the flow is shown by means of a Q-criterion isosurface. Horseshoe vortices are visible which are attached to the plate, as well as strong vorticity layer at the leeward side of the mixing layer. There is no strong vorticity at the mixing layer windward side, which may be attributed to the bow shock inhibiting the vortex development. Instantaneous temperature field in longitudinal plane is depicted in Fig. 1, right. Separation bubble characteristics are also analyzed and hydrogen flow penetration depth is estimated. At least qualitative correspondence to the experiment is observed, and for certain flow characteristics, quantitative improvement is obtained compared to the data available in the literature. Stable operation of the computational program is demonstrated as well as the possibility of its parallelization on 10^2 - 10^3 CPU cores. It is concluded that the program is ready for solving the simulation problems concerning the different combustion regimes in aircraft combustors. The research was supported by the Ministry of Education and Science of Russian Federation ("megagrant", agreement No. 14.G39.31.0001).
11:30
15 mins

#538
Identification of Lagrangian Coherent Structures (LCS) in a flat-plate turbulent boundary layer with adverse pressure gradient
Matthias Weinschenk, Christoph Wenzel, Ulrich Rist
Abstract: Turbulent flow fields contain small- and large-scale patterns, cf. Figure 1(a). In this work we tried to compute the phase speed of these patterns by correlating finite-size interrogation windows between consecutive time steps, which is common practice in Particle-Image Velocimetry (PIV). The underlying DNS data has been computed by Christoph Wenzel et al. [3] for an inflow Mach number Ma=0.5 and an adverse pressure gradient with constant Rotta-Clauser parameter \beta_K = 1.0. The correlation technique is based on Pearson's correlation coefficient, see [2]. A 35 x 35-size interrogation window has been used for computing the maximal streamwise correlation \Delta x_{maxcor} for each of the 900 x 512 (x x z) input data points of two consecutive snapshots. Dividing this by the timestep, the instantaneous, local convection velocity is obtained: c_i=\Delta x_{maxcor}/{\Delta t}, where the index i stands for any of the flow variables (u,v,w,\rho,p,T). Applying this technique to all available snapshots (100 in the present case) of the selected flow variable the average convection speed \overline{c}_i is obtained after an additional local average in spanwise direction. Subtracting the average from the instantaneous convection velocity yields high- and low-speed streaks as spatially connected patterns with either positive or negative c'_i=c_i-\overline{c}_i, see Figure 1(b) showing an example for the outcome of this procedure applied to the density \rho' snapshot in Figure 1(a). Interestingly, all flow variables i contain very similar patterns in their respective c'_i. In addition, these patterns correspond to the well-known high- and low-speed streaks in the streamwise velocity component u. Furthermore, the averaged convection velocity \overline{c}_i varies strongly with the wall distance and comes close to the averaged streamwise velocity \overline{u} in the logarithmic part of the mean flow profile, see Figure 2. Obviously, all instantaneous patterns existing in this flow are bound to the underlying material transport in streamwise direction by the streamwise velocity component u. Only \overline{c}_p from the pressure p behaves different. However, this can be explained by the fact that pressure is governed by a Poisson equation which means that it decays at a much lower rate compared to other variables with distance from a source. This means in the present context, that the convection speed of the dominant structures around y^+~ 100 would be detectable as a pressure-wave at the wall that runs over the fluid with the speed of the coherent structures further away. The observation that all patterns (apart from pressure) travel with the local streamwise velocity means that these structures are bound to material, i.e., they are structures in the Lagrangian sense, presumably related to so-called Lagrangian Coherent Structures (LCS) {1}.
11:45
15 mins

#234
Investigation of an unsteady shock wave in a Mach 2 boundary layer
Rio Baidya, Sven Scharnowski, Matthew Bross, Christian Kähler
Abstract: In this work, shock wave - boundary layer interaction is examined with an aim to investigate the influence of turbulent structures on the interaction processes. In this regard, a multi-camera planar particle image velocimetry (PIV) technique is utilised to simultaneously capture the instantaneous shock front locations and the turbulent structures residing within the boundary layer. Preliminary results suggest that the unsteadiness of the reflected shock location is related to the local thickness of boundary layer where the incident shock impinges. Since locally thinning or thickening of the boundary layer is typically accompanied by enhanced momentum transfer, we postulate that this leads to modification of adverse pressure region at the shock foot, thereby influencing the initiation point of the reflection shock at the wall.
12:00
15 mins

#491
EFFECT OF RAREFACTION ON TEMPORALLY DEVELOPING COMPRESSIBLE MIXING LAYER
Vishnu Mohan, Sameen A., Balaji Srinivasan
Abstract: Compressible mixing layer have been studied to better understand the development of free-shear layers such as those seen in supersonic jets. In the present study, we investigate the effect of rarefaction on compressible mixing layer. Such situations arise in rarefied plumes, observed in satellite nozzles and rocket exhaust at high-altitudes. A deterministic finite volume method based solver for the BGK-Boltzmann equation is used. The scheme [Xu and Huang, 2010] used in the present work takes into account intermolecular collisions during the flux calculation, thereby studying flows in the continuum regime is computationally inexpensive. In the present study, the convective Mach number and the Knudsen number are varied in order to understand its effect on the development of a 2D temporally developing compressible mixing layer. The convective Mach numbers employed in this study are M c = 0.2, 0.4 and 0.6. The Knudsen numbers selected are such that both the continuum regime (Kn is O(10 −3 )) as well as the slip-flow regime (Kn = 10 −2 ) are analyzed. Figure 1 shows the variation of the normalised vorticity thickness against time, for different convective Mach numbers and Knudsen numbers. It is seen that on changing the Knudsen number for a given Mach number, there is significant variation in the development of the mixing layer. However, the flow structures seen in continuum, such the formation of the vortices and their merging still persist in the slip-flow regime. Changes to the flow field are the result of the increased dissipation of vorticity due to reduced molecular collisions. Nonetheless, for a substantial period of time (t ∈ [10, 30]) the vorticity thickness in both continuum and slip-regime follow similar trends. We find that the flow is undergoing two competing processes– the growth of the initial perturbation provided to the system and the diffusion of vorticity due to decreased intermolecular collisions. During the initial development, the vorticity gets diffused due to the latter. However, between time t ∈ [10, 30] the growth of the perturbations take over, which is why the vorticity thickness in both continuum and rarefied case follow the same trend. We show that in both continuum and slip-flow regime as the convective Mach number of the mixing layer increases the growth rate of the pertubation decreases; which was previously shown by Sandham (1994) for the continuum case.
12:15
15 mins

#342
Scale energetics in baroclinic-torque-driven turbulent mixing
Sidharth GS, Graham Candler
Abstract: Turbulent mixing in the presence of baroclinic-torque-generated vorticity, particularly shock-deposited vorticity is of relevance to flow regimes encountered in high speed combustion and inertial confinement fusion. Baroclinic torque is generated by pressure gradient across the shock and non-aligned density gradients in the fluid. The presence of this torque causes departure from conventional vorticity dynamics observed in constant-density or barotropic turbulent flows. The work of Sidharth and Candler (2018) shows that while density variations do not have a pronounced effect on the bulk energy, they significantly alter the statistics associated with velocity-gradient quantities, implying that the small velocity scales are primarily affected. The role played by baroclinic vorticity in the interscale dynamics of turbulence is important to understand from a subgrid-scale modeling perspective. We carry out direct numerical simulations of a varicose heavy gas curtain that is shocked twice, the second time from a reflected shock. The problem setup is inspired by the experiments of Balakumar et al. (2008). The post-reshock dynamics involves rapid breakdown of the vortices resulting from the passage of the first shock. Eventually, a fully turbulent flow is observed. The Fourier energy spectrum evolves in two stages. Post reshock, there is a rapid buildup of energy in the small scales over a long time period relative to the shock passage time. This is the first stage, and involves an energy cascade that is out of dynamic equilibrium. The second stage is marked by spectral smoothing and decay. For the analysis, we can scale decompose the energy and express the large-scale energy in terms of moments under the filter. We work with the Reynolds-filtered first moments as their dynamics does not involve the third moment, unlike in the Favre-filtered case. By explicitly filtering the DNS data, we observe that the subgrid pressure acceleration is dynamically important after the reshock and can cause counter-gradient diffusion of first moment energy. The transport equation of the specific stress subgrid term is also analyzed and contrasted with its dynamics in constant-density turbulence. A comprehensive understanding of scale energetics in this flow allows for building physically accurate subgrid models for turbulent flows with strong variable-density effects.
12:30
15 mins

#367
ENERGY TRANSFER IN COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE FOR SELF GRAVITATING FLUIDS
Supratik Banerjee, Alexei G. Kritsuk
Abstract: Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016); J. Phys. A: Math. Theor. 50, 015501 (2017)], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.