Supersonic Turbulent Channel Flow Research Articles

Direct numerical simulations of compressible turbulent channel flows with asymmetric thermal walls

This paper extends the work of Tamano & Morinishi (J. Fluid Mech., vol. 548, 2006, pp. 361–373) by simulating supersonic turbulent channel flow with asymmetric thermal walls using a larger computational domain and a finer mesh. Direct numerical simulation is carried out for four cases with different thermal wall boundaries at the top wall at fixed $Ma=1.5$ , $Re=6000$ and $Pr=0.72$ , while the bottom wall is maintained at a constant temperature of $T_L$ equal to the reference temperature. These cases are referred to as the adiabatic case TAd, where the top wall is adiabatic; the pseudo-adiabatic case T32, where the top wall is isothermal with temperature $T_{w,t}=T_A$ ; the sub-adiabatic case T25, with $T_{w,t}=0.77T_A$ ; and the super-adiabatic case T40, with $T_{w,t}=1.24T_A$ . Here, $T_A=3.234$ is the mean temperature at the adiabatic wall in the TAd case. The objective of this study is to compare and contrast the TAd case with its corresponding T32 case, and to investigate the effect of the wall temperature difference between the two isothermal walls. Comparisons of the basic turbulent statistics, the heat transfer between the Favre-averaged mean-flow kinetic energy, the Favre-averaged turbulent kinetic energy and the Favre-averaged mean internal energy, as well as the wall heat transfer properties, indicate that the TAd case and its corresponding T32 case are generally equivalent. The only discernible difference is in the region very close to the top wall for the temperature-fluctuation-related quantities. The analysis reveals that the asymmetry of the thermal walls causes asymmetry in the flow and thermal fields. In addition, the transfer of the heat generated by the pressure dilatation and the viscous stress is facilitated by the turbulent heat flux term and the mean molecular heat flux term.

Direct numerical simulations of high-enthalpy supersonic turbulent channel flows including finite-rate reactions

Direct numerical simulations of temporally evolving high-enthalpy supersonic turbulent channel flows are conducted at a Mach number of 3.0 and Reynolds number of 4880 under isothermal wall conditions. Air is assumed to behave as a five-species mixture, and chemical non-equilibrium and equilibrium assumptions are adopted to investigate the influence of finite-rate reactions on the turbulent statistics and large-scale structures. The two wall temperatures of 1733.2 and 3500 K are such that the mixture components undergo strong dissociation and recombination reactions along the channel. Investigation shows that the turbulent intensity is weakened and the mean and fluctuating temperatures are smaller when finite-rate reactions are considered. The mean dissociation degree is a quadratic function of the normal position, and its curvature under the chemical non-equilibrium assumption is greater than that under the chemical equilibrium assumption. The fluctuating mass fractions of the generated species seem to decrease slightly in the near-wall region, and their distributions are obviously different from those of the fluctuating velocity and fluctuating temperature. Finite-rate reactions increase the proportion of turbulent kinetic energy production in the skin friction decomposition, especially when the wall temperature is 3500 K. The large-scale structures visualized by the cross correlation between temperature and species mass fraction become stronger in the normal direction. The turbulent Schmidt number and several velocity–temperature correlations, including the recovery enthalpy and strong Reynolds analogy, are insensitive to the chemical reaction rate and wall temperature.

Turbulent drag reduction in compressible flows using streamwise traveling waves

Skin-friction drag reduction (DR) in supersonic turbulent channel flows using streamwise traveling waves of spanwise velocity (STWSV) has been studied using direct numerical simulations. In the present study, simulations are carried out for different phase speeds of the upstream and downstream traveling waves for a bulk Mach number Mab=1.5 and bulk Reynolds number Reb = 3000. The efficacy of the control has been investigated for other bulk Reynolds numbers as well. The Stokes layer generated by the control affects the near-wall statistics primarily by modifying the coherent structures, thereby either reducing or aggravating the skin-friction drag. For Reb = 3000 and Mab=1.5, a maximum drag reduction (DRmax) of 49% is achieved, primarily due to suppression of sweeps and ejections on application of control. The efficacy of skin-friction drag reduction varies in a small range when Reb is varied from 3000 to 6000; however, the maximum drag reduction is observed for Reb = 4000, owing to a drastic decrease in sweep events. Quadrant analysis reveals that for drag reduction (DR) cases, STWSV reduce magnitude of streamwise u′ and wall-normal w′ velocity fluctuations magnitude and stacks them around zero. In contrast, w′ is increased for drag increase (DI) cases. Skin-friction decomposition using Fukagata, Iwamoto and Kasagi (FIK) identity suggests that the control alters the turbulent component significantly. The behavior of the control is also studied at Mab = 0.3 and 2.5, and it is observed that the maximum drag reduction obtained decreases for high bulk Mach numbers.

Effects of Viscosity Law on High-Temperature Supersonic Turbulent Channel Flow for Chemical Equilibrium

Direct numerical simulations of temporally evolving high-temperature supersonic turbulent channel flow for chemical equilibrium were conducted with a Mach number of 3.0, a Reynolds number of 4880, and a wall temperature of 1733.2 K to investigate the influence of the viscosity law. The mean and fluctuating viscosity for the mixture rule is higher than that for Sutherland’s law, whereas an opposite trend is observed in the mean temperature, mean pressure, and dissociation degree. The Trettel and Larsson transformed mean velocity, the Reynolds shear stress, the turbulent kinetic energy budget, and the turbulent Prandtl number are insensitive to the viscosity law. The semilocal scaling that take into account local variation of fluid characteristics better collapses the turbulent kinetic energy budget. The modified strong Reynolds analogies provide reasonably good results for the mixture rule, which are better than those for Sutherland’s law. The streamwise and spanwise coherencies for the mixture rule are stronger and weaker than those for Sutherland’s law, respectively. The relationship between viscosity and species components can help to identify the traveling wave packet.

Effects of groove distributions on supersonic turbulent channel flows

This paper investigates the influences of the distribution of the grooves on the wall on the turbulent statistics, transport of turbulent kinetic energy, and flow structures in supersonic turbulent channel flows at the bulk Mach number of 3.0 by performing direct numerical simulations. It is found that the existence of the grooves leads to the enhancement of the turbulent kinetic energy close to the wall and the abatement thereof above the buffer layer. The density and temperature fluctuations are also enhanced, but only within the buffer layer, above which the influences of the grooves can be disregarded. The pressure fluctuations, however, are significantly increased, which is attributed to the radiated acoustic waves from the wall generated by the disturbances on the wall. Such inference is substantiated by the fact that the inclination angles of the phase averaged pressure are related to the Mach number. Nevertheless, the acoustic and dynamic processes seem to be decoupled, leading to insignificant pressure-dilatation terms in the transport of turbulent kinetic energy.

Linear response analysis of supersonic turbulent channel flows with a large parameter space

In this work, the linear responses of turbulent mean flow to both harmonic and stochastic forcing are investigated for supersonic channel flow. Well-established universal relations are utilized to obtain efficiently the mean profiles with a large parameter space, with the bulk Mach number up to 5 and the friction Reynolds number up to$10^4$, so a systematic parameter study is feasible. The most amplified structure takes the form of streamwise velocity and temperature streaks forced optimally by the streamwise vortices. The outer peak of the pre-multiplied energy amplification corresponds to the large-scale motion, whose spanwise wavelength ($\lambda _z^+$) is very insensitive to compressibility effects. In contrast, the classic inner peak representing small-scale near-wall motions disappears for the stochastic response with increasing Mach number. Meanwhile, the small-scale motions become much less coherent. A decomposition of the forcing identifies different effects of the incompressible counterpart and the thermodynamic components. Wall-cooling effects, arising with high Mach number, increase the spacing of the most amplified near-wall streaks; the spacing becomes nearly invariant with Mach number if expressed in semi-local units. Meanwhile, the coherence of stochastic response with$\lambda _z^+>90$is enhanced, but on the other hand, with$\lambda _z^+<90$it is decreased. The geometrical self-similarity of the response in the mid-$\lambda _z$range is still roughly satisfied, insensitive to Mach number. Finally, theoretical analyses of the perturbation equations are presented to help with understanding the scaling of energy amplification.

Wavelet-based adaptive large-eddy simulation of supersonic channel flow with different thermal boundary conditions

This work investigates the effect of different thermal wall boundary conditions on the wavelet-based adaptive large-eddy simulation of supersonic turbulent channel flow. The compressible flow governing equations are expressed in terms of wavelet-based Favre-filtered variables and are supplied with the anisotropic minimum dissipation closure model. Various computations are performed, where the resolved temperature field is constrained by either Dirichlet (isothermal) or Neumann (adiabatic) boundary conditions at the walls. The turbulence diagnostics include mean flow features and turbulent fluctuations statistics. The successful comparison with reference direct numerical simulations demonstrates the validity and the efficiency of the wavelet-based adaptive approach for wall-bounded turbulent compressible flow, regardless of the thermal boundary conditions that are imposed.

Supersonic turbulent flows over sinusoidal rough walls

Direct numerical simulations were performed to characterize fully developed supersonic turbulent channel flows over isothermal rough walls. The effect of roughness was incorporated using a level-set/volume-of-fluid immersed boundary method. Turbulence statistics of five channel flows are compared, including one reference case with both walls smooth and four cases with smooth top walls and bottom walls with two-dimensional (2-D) and three-dimensional (3-D) sinusoidal roughnesses. Results reveal a strong dependence of the turbulence on the roughness topography and the associated shock patterns. Specifically, the 2-D geometries generate strong oblique shock waves that propagate across the channel and are reflected back to the rough-wall side. These strong shocks are absent in the smooth-wall channel and are significantly weaker in cases with 3-D roughness geometries, replaced by weak shocklets. At the impingement locations of the shocks on the top wall in the 2-D roughness cases, localized augmentations of turbulence shear production are observed. Such regions of augmented production also exist for the 3-D cases, at a much weaker level. The oblique shock waves are thought to be responsible for a more significant entropy generation for cases with 2-D surfaces than those with 3-D ones, leading to a higher irreversible heat generation and consequently higher temperature values in 2-D roughness cases. In the present supersonic channels, the effects of roughness extend beyond the near-wall layer due to the shocks. This suggests that outer layer similarity may not fully apply to a rough-wall supersonic turbulent flow.

Modeling and simulation in supersonic three-temperature carbon dioxide turbulent channel flow

This paper pioneers the direct numerical simulation (DNS) and physical analysis in supersonic three-temperature carbon dioxide (CO2) turbulent channel flow. CO2 is a linear and symmetric triatomic molecular, with the thermal non-equilibrium three-temperature effects arising from the interactions among translational, rotational, and vibrational modes at room temperature. Thus, the rotational and vibrational modes of CO2 are addressed. The thermal non-equilibrium effect of CO2 has been modeled in an extended three-temperature kinetic model, with the calibrated translational, rotational, and vibrational relaxation time. To solve the extended kinetic equation accurately and robustly, non-equilibrium high-accuracy gas-kinetic scheme is proposed within the well-established two-stage fourth-order framework. Compared with the one-temperature supersonic turbulent channel flow, supersonic three-temperature CO2 turbulence enlarges the ensemble heat transfer of the wall by approximate 20% and slightly decreases the ensemble frictional force. The ensemble density and temperature fields are greatly affected, and there is little change in Van Driest transformation of streamwise velocity. The thermal non-equilibrium three-temperature effects of CO2 also suppress the peak of normalized root mean square of density and temperature, normalized turbulent intensities and Reynolds stress. The vibrational modes of CO2 behave quite differently with rotational and translational modes. Compared with the vibrational temperature fields, the rotational temperature fields have the higher similarity with translational temperature fields, especially in temperature amplitude. Current thermal non-equilibrium models, high-accuracy DNS and physical analysis in supersonic CO2 turbulent flow can act as the benchmark for the long-term applicability of compressible CO2 turbulence.

Investigation of low-dissipation low-dispersion schemes for incompressible and compressible flows in scale-resolving simulations

A comprehensive study is conducted on a second-order low-dissipation low-dispersion (LD2) scheme in scale-resolving simulations of both incompressible and compressible flows, using a node-based unstructured CFD solver. The scheme deploys a higher order central reconstruction of the face values (up to fourth-order on structured meshes) and a matrix dissipation formulation to reduce the dispersive and dissipative numerical errors. The LD2 scheme is examined for compressible flow cases involving shock discontinuities, LD2-Compressible (LD2C), and is verified in a classical shock-tube problem. The scheme is then further verified in Large-Eddy Simulations (LES) of decaying isotropic turbulence (DIT) in comparison with available experimental data. It is shown that in scale-resolving simulations, the LD2C scheme is able to significantly improve the prediction as compared to a conventional second-order central scheme. The scheme is then further assessed and verified in hybrid Reynolds-Averaged Navier–Stokes (RANS)-LES computations for the subsonic and supersonic turbulent channel flow, where excellent agreement with reference DNS and correlations are observed. Moreover, a supersonic base flow is simulated using hybrid RANS-LES, where improved predictions are observed. The LD2C scheme exploits a shock sensor incorporating vorticity and is shown to improve the prediction of the resolved shear stress in the shear layer of compression.

Direct numerical simulation of supersonic turbulent flows over rough surfaces

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers $M_b=0.3$ – $4$ , both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature–velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.

Supersonic turbulent channel flows over spanwise-oriented grooves

In the present study, we perform direct numerical simulations to study the influences of the spanwise-oriented grooves, which are emulated by the reasonably designed “relaxed” boundary conditions, on the kinetic and thermodynamic statistics in a supersonic turbulent channel flow at the Mach number of 1.5 and Reynolds number of 3000. The phase averaged flow fields show that the relaxed boundary induces compressive and expansive waves that travel across the whole channel and are reflected by the upper wall. These waves are isentropic in the average sense except in the viscous sublayer. In the near-wall region, vortices and streaks that constitute the self-sustaining cycles are less populated and less meandering, while in the outer region, especially near the channel center, the velocity divergence is as strong as the vorticity. The temperature, density, and pressure fluctuations are enhanced by these waves. The correlations between the velocity and temperature are altered, due to the counter effects caused by the vortical motions and isentropic waves.

Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls – ERRATUM

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Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

Abstract

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. The performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air. Program summaryProgram Title: Hypersonics Task-based Research solverProgram Files doi:http://dx.doi.org/10.17632/9zsxjtzfr7.1Licensing provisions: BSD 2-clauseProgramming language: RegentNature of problem: This code solves the Navier–Stokes equations at hypersonic Mach numbers including finite-rate chemistry for air dissociation along with multicomponent transport. The solver is designed for direct numerical simulations (DNS) of transitional and turbulent hypersonic turbulent flows at high enthalpies, and accounts for thermochemical effects such as vibrational excitation and chemical dissociation.Solution method: This code uses a low-dissipation sixth-order targeted essentially non-oscillatory (TENO) scheme for the spatial discretization of the conservation equations on Cartesian stretched grids. The time advancement is performed either with an explicit method, when the chemistry is slow and therefore does not introduce additional stiffness in the integration, or with an operator-splitting method that integrates the chemical production rates with an implicit discretization.Additional comments: The HTR solver builds on the runtime Legion [1] and is written in the programming language Regent [2] developed at Stanford University. Instructions for the installation of the components are provided in the README file enclosed with the HTR solver and in the Legion repository [1].

Velocity–temperature correlations in high-temperature supersonic turbulent channel flows for two gas models

Velocity–temperature correlations in a high-temperature supersonic turbulent channel flows, including thermally perfect gas (TPG) and calorically perfect gas (CPG), are investigated based on the direct numerical simulation database [Chen et al., J. Turbul. 19 (2018) 365] to study the gas model effects. The results show that in fully developed turbulent channel flow, the Reynolds analogy factor remains close to 1.2 for both gas models. The “recovery enthalpy” is better than Walz’s equation to connect the mean stream-wise velocity with mean static temperature because it is independent with gas models. The modified strong Reynolds analogy for TPG is more accurate scaling than that for CPG, and the turbulent Prandtl number is insensitive to gas models. In addition, the influence of gas model on the probability density functions of stream-wise velocity and static temperature concentrate on the corresponding right tails.

Effects of dimensional wall temperature on velocity-temperature correlations in supersonic turbulent channel flow of thermally perfect gas

Direct numerical simulations of temporally evolving supersonic turbulent channel flows of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 for various values of the dimensional wall temperature to study the influence of the latter on the velocity-temperature correlations. The results show that in a fully developed turbulent channel flow, as the dimensional wall temperature increases, there is little change in the mean velocity, but the mean temperature decreases. The mean temperature is found to be a quadratic function of the mean velocity, the curvature of which increases with increasing dimensional wall temperature. The concept of “recovery enthalpy” provides a connection between the mean velocity and the mean temperature, and is independent of dimensional wall temperature. The right tails of probability density function of the streamwise velocity fluctuation grows with increasing dimensional wall temperature. The dimensional wall temperature does not have a significant influence on the Reynolds analogy factor or strong Reynolds analogy (SRA). The modifications of SRA by Huang et al. and Zhang et al. provide reasonably good results, which are better than those of the modifications by Cebeci and Smith and by Rubesin.

Comparative study of Reynolds stress budgets of thermally and calorically perfect gases for high-temperature supersonic turbulent channel flow

To study the Reynolds stress budgets, direct numerical simulations of high-temperature supersonic turbulent channel flow for thermally perfect gas and calorically perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 combined with a dimensional wall temperature of 596.30 K. The reliability of the direct numerical simulation data is verified by comparison with previous results ( J Fluid Mech 1995, vol. 305, pp.159–183). The effects of variable specific heat are important because the vibrational energy excited degree exceeds 0.1. The viscous diffusion, pressure–velocity gradient correlation, and dissipation terms in the Reynolds stress budgets for TPG, except the streamwise component, are larger than those for calorically perfect gas close to the wall. Compressibility-related term decreases when thermally perfect gas is considered. The major difference for both gas models is mainly due to variations in mean flow properties. Inter-component transfer related to pressure–velocity gradient correlation term can be distinguished into inner and outer regions, whose critical position is approximately 16 for both gas models.

Direct numerical simulation of high–temperature supersonic turbulent channel flow of equilibrium air

Direct numerical simulations (DNS) of high–temperature supersonic turbulent channel flow of equilibrium air are conducted at constant dimensional wall temperature 1733.2 K. The Mach number based on the bulk velocity and the speed of sound at the isothermal wall is 3.0, and the Reynolds number based on the bulk density, bulk velocity, channel half–width, and viscosity at the isothermal wall is 4880. Bidirectional coupling (BC) and unidirectional influence (UI) conditions are investigated, conditions which take account, respectively, of the influence of turbulence on chemistry and the influence of chemistry on turbulence, and just the influence of turbulence on chemistry. The reliability of the DNS data for the UI condition is verified by comparison with the results of Coleman et al. [J. Fluid Mech. 305, 159–183 (1995)]. The results of present research show that the many turbulent statistics and instantaneous structures which hold for calorically perfect gas also hold for equilibrium air, even for the BC condition. The coupling condition has no significant influence on the van Driest transformed mean velocity and turbulent kinetic energy budget. The magnitudes of the mean and fluctuating specific heat and enthalpy for the BC condition are larger than those for the UI condition. An inverted trend is observed for the temperature and dissociation degree. Compared with the UI condition, the near–wall streaks for the BC condition are arranged in a more spanwise manner, owing mainly to the increase in anisotropy ratios. The large–scale structures become small, sharp, and chaotic for the BC condition.

Effects of dimensional wall temperature on Reynolds stress budgets in a supersonic turbulent channel flow with thermally perfect gas

ABSTRACTDirect numerical simulations of temporally evolving supersonic turbulent channel flow of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800, combined with constant dimensional wall temperatures from 149.075 to 1788.90 K to study the influence of dimensional wall temperature on the characteristics of Reynolds stress budgets. It is found that, as the dimensional wall temperature increases, the production, diffusion, pressure–velocity gradient correlation and dissipation terms increase, whereas the compressibility-related term decreases. This is mainly due to variations in mean flow properties. The mechanism of inter-component transfer (ICT) is insensitive to the dimensional wall temperature. The ICT relating to the pressure–velocity gradient correlation term can be divided into inner and outer regions, and the critical position separating these regions is at the semi-local scaling of approximately 16 irrespective of the different dimensional wall temperature.