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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. [ABSTRACT FROM AUTHOR]

Current research conducts the quantitative comparisons between implicit large eddy simulation (iLES) and explicit eddy-viscosity large eddy simulation (eLES). iLES and eLES in a compressible Taylor–Green vortex problem are implemented with a fourth-order finite-volume gas kinetic scheme. Compared with the key statistical quantities of direct numerical simulation, iLES outweighs eLES on the exactly same unresolved grids. With DNS solution, a priori analysis of compressible filtered subgrid-scale (SGS) turbulent kinetic energy ρ ¯ K sgs f is performed. Forward and backward filtered SGS turbulent kinetic energy transfer coexists. The ensemble turbulent kinetic energy Ek is on the order of o (10 4) to o (10 2) of ensemble filtered SGS turbulent kinetic energy K sgs f . The ensemble dominant physical dissipation rate ε 1 is approximately 20 times larger than the ensemble filtered SGS dissipation rate − τ i j f S ̃ i j f . Then, for iLES and eLES, the total dissipation rate is decomposed into the resolved physical dissipation rate ε phy , modeling SGS dissipation rate ε sgs mod , and numerical SGS dissipation rate ε sgs num . Quantitative comparisons on the modeling SGS dissipation rate and numerical SGS dissipation rate in iLES and eLES are evaluated. The numerical dissipation in iLES can be treated as the built-in SGS dissipation, which accounts for the reasonable performance of iLES. While the explicit modeling SGS dissipation in eLES pollutes the resolved turbulent structures in such low-Reynolds number turbulence. The next generation of large eddy simulation on unresolved grids must take into account both the built-in numerical SGS dissipation and its competition explicit modeling SGS dissipation. [ABSTRACT FROM AUTHOR]

In this study, the high-order gas kinetic scheme (GKS) is employed for explicit large eddy simulation (hereafter referred to simply as "LES") and implicit large eddy simulation (iLES) of turbulent channel flows. The main objective is to compare the performance of iLES and LES in the high-order finite volume framework, and study which is most suitable for turbulence simulation. The prediction abilities of different explicit LES models and iLES method on various statistics and flow structures are compared. Most results from both iLES and explicit LES are very close to those of direct numerical simulation. Moreover, iLES is generally superior to explicit LES in predicting several important flow properties, including the mean velocity profiles, Reynolds stress, and Q-criterion iso-surfaces. This superior performance of iLES may arise that the numerical dissipation of the high-order scheme is enough to replace the subgrid dissipation needed in large eddy simulation of turbulence. If the explicit LES model is further adopted, the dissipation will increase, so the results degrade. The overall satisfactory results show that the high-order GKS can provide appropriate numerical dissipation and is suitable for iLES of turbulence. [ABSTRACT FROM AUTHOR]

For simulation of hypersonic turbulent and transitional flows at high Reynolds numbers, a gas-kinetic scheme (GKS) strongly coupled with the turbulent kinetic energy equation in shear stress transport (SST) k−ω turbulence model is developed. To extend the current method to transitional flows, Langtry-Menter γ − R e θ transition model is added together with SST k−ω turbulence model. Comparisons among the numerical solutions from current GKS method coupled with turbulent kinetic energy equation, GKS method uncoupled with turbulent kinetic energy equation, Reynolds-Averaged Navier-Stokes (RANS) solutions with turbulence/transition models, and experimental data are conducted. It is concluded that the current method can significantly improve the accuracy of numerical results. [ABSTRACT FROM AUTHOR]

For increasingly non-equilibrium flowfields, the Navier-Stokes equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook equation coupled with the Landau-Teller-Jeans relaxation model has been proposed for two-dimensional hypersonic non-equilibrium multi-temperature flow computation. In a recent study, a two-stage fourth-order gas-kinetic scheme (GKS) has been developed for equilibrium flows, which achieves a fourth-order accuracy in space and time as well as high efficiency and robustness. In this paper, targeting for accurate and efficient simulation of multi-temperature non-equilibrium flows, a high-order three-dimensional multi-temperature GKS is constructed under the two-stage fourth-order framework, with the fourth-order Simpson interpolation rule for the newly emerged source term. Simulations on decaying homogeneous isotropic turbulence, low-density nozzle flow, rarefied hypersonic flow over a flat plate, and type IV shock-shock interaction are used to validate the multi-temperature model through the comparison with experimental measurements. The unified gas kinetic scheme (UGKS) results and the Direct Simulation Monte Carlo (DSMC) solutions will be used as well in some cases for validation. Computational results not only confirm the high-order accuracy and quite robustness of this scheme but also show the significant improvement on computational efficiency compared with UGKS and DSMC, especially for the flow in the near continuum regime. [ABSTRACT FROM AUTHOR]