Direct Numerical Simulation Data Research Articles

Direct numerical simulation of turbulence over systematically varied irregular rough surfaces

Lattice Boltzmann direct numerical simulation of turbulent open-channel flows over randomly distributed hemispheres at $Re_{\unicode[STIX]{x1D70F}}=600$ is carried out to reveal the influence of roughness parameters related to a probability density function of rough-surface elevation on turbulence by analysing the spatial and Reynolds- (double-) averaged Navier–Stokes equation. This study specifically concentrates on the influence of the root-mean-square roughness and the skewness, and profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as a wall-normal integrated plane porosity. The effective distance can completely collapse the total shear stress outside the roughness sublayer, and thus the similarity of the streamwise mean velocity is clearer by introducing the effective distance. In order to examine the influence of the root-mean-square roughness and the skewness on dynamical effects that contribute to an increase in the skin friction coefficient, the triple-integrated double-averaged Navier–Stokes equation is analysed. The main contributors to the skin friction coefficient are found to be turbulence and drag force. The turbulence contribution increases with the root-mean-square roughness and/or the skewness. The drag force contribution, on the other hand, increases in particular with the root-mean-square roughness whereas an increase in the skewness does not increase the drag force contribution because it does not necessarily increase the surface area of the roughness elements. The contribution of the mean velocity dispersion induced by spatial inhomogeneity of the rough surfaces substantially increases with the root-mean-square roughness. A linear correlation is confirmed between the root-mean-square roughness and the equivalent roughness while the equivalent roughness monotonically increases with the skewness. A new correlation function based on the root-mean-square roughness and the skewness is developed with the available experimental and direct numerical simulation data, and it is confirmed that the developed correlation reasonably predicts the equivalent roughness of various types of real rough surfaces.

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

To address the hitherto unknown mechanism of boundary-layer transition on blunt reentry capsules, the role of roughness-induced disturbance growth on a spherical-section forebody is assessed via optimal transient growth theory and direct numerical simulations (DNS). Optimal transient-growth studies have been performed for the blunt capsule experiments at Mach 5.9 in the Hypersonic Ludwieg tube at the Technische Universität Braunschweig (HLB), which included measurements behind a patch of controlled, distributed micron-sized surface roughness. Transient-growth results for the HLB capsule indicate similar trends as the corresponding numerical data for a Mach 6 experiment in the Actively Controlled Expansion (ACE) facility of the Texas A&M University (TAMU) at a lower Reynolds number. Both configurations indicate a similar dependence on surface temperature ratio and, more important, rather low values of maximum energy gain. DNS are performed for the conditions of the HLB experiment to understand the generation of stationary disturbances by the roughness patch and the accompanying evolution of unsteady perturbations. However, no evidence of either modal or nonmodal disturbance growth in the wake of the roughness patch is found in the DNS data; thus, the physical mechanism underlying the observed onset of transition still remains unknown.

Assessment of a transport equation for mean reaction rate using DNS data obtained from highly unsteady premixed turbulent flames

Recently, a transport equation for the mean rate of product creation in a premixed turbulent flame was derived and a joint closure relation for dominant terms in that equation was developed and validated against Direct Numerical Simulation (DNS) data obtained from weakly turbulent flames. Present communication reports results of further DNS tests of this newly introduced approach, performed using recent data computed under substantially different turbulent conditions. In particular, the ability of the approach to predict significant oscillations of the turbulent burning velocity with time is shown under conditions associated with not only the flamelet but also the thin-reaction-zone regimes of premixed turbulent burning. While such oscillations are documented in the present and other DNS studies, capabilities of other models of premixed turbulent combustion to reproduce this challenging phenomenon have not yet been demonstrated in the literature.

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73–L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650. Journal of Fluid Mechanics, 743, 202–248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics, 774, 395–415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

A modification of the k-kL-ω turbulence model for simulation of short and long separation bubbles

The prediction of separation bubbles is highly important due to the controlling effects that they have on the airfoils performance. In the present study, a two-dimensional numerical simulation of the incompressible transitional flow around the NACA 0012 and Eppler 387 airfoils is studied. In order to examine the capability of the turbulence models for predicting the separation bubbles, several modified versions of the three-equation k-kL-ω turbulence model presented in previous research studies and the original four-equation SST k-ω turbulence model are compared with the experimental and Direct Numerical Simulation (DNS) data. A new modification based on the previous modified versions of the k-kL-ω model is also proposed. The Reynolds number based on the airfoil chord length is between 3 × 104 and 1.3 × 105. Simulation of the flow-field is performed by the solution of the Reynolds-averaged Navier–Stokes equations using a pressure-velocity coupling algorithm so-called RK-SIMPLER. An explicit method of second-order accuracy in time and space is used to integrate the momentum conservation equations. The results from this study indicate that the new proposed modification presents the better prediction for the separation bubbles than the previous versions, especially in the long separation bubbles. An excellent result is also obtained for the lift coefficients.

Autoignition and flame propagation in non-premixed MILD combustion

Direct Numerical Simulation (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed to gather insights on autoignition and flame propagation in MILD combustion. Unlike in conventional combustion, the chemical reactions occur over a large portion of the computational domain. The presence of ignition and flame propagation and their coexistence are studied through spatial and statistical analyses of the convective, diffusive and chemical effects in the species transport equations. Autoignition is observed in regions with lean mixtures because of their low ignition delay times and these events propagate into richer mixtures either as a flame or ignition. This is found to be highly dependent on the mixture fraction length scale, ℓZ, and autoignition is favoured when ℓZ is small.

Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method

A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system one at a time and calculating the responses using long-time averaged Direct Numerical Simulations (DNS), the system's Linear Response Function (LRF) has been computed. Another matrix, called the Eddy Flux Matrix (EFM), that relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, has also been calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings, and that the LRF can well predict the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigen/singular vectors are compared with the leading Proper Orthogonal Decomposition (POD) modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square-root of Rayleigh number, they perform equally well for flows at other $\mathrm{Ra}$, at least in the investigated range of $ 5 \times 10^5 \le \mathrm{Ra} \le 1.25 \times 10^6$. The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system.

Analysis of heat transfer of supercritical water by direct numerical simulation of heated upward pipe flows

Direct numerical simulation (DNS) was performed to investigate the turbulent heat transfer of supercritical water in an upward pipe with and without buoyancy. The heat transfer deterioration mechanisms were comprehensively studied by analyzing the effects of large thermophysical property variations, flow acceleration and buoyancy. It is shown that the large property variations near the wall severely impair the heat transfer in supercritical water especially for forced convection. The flow acceleration induced by thermal expansion shows an obvious suppression on turbulence but does not affect the heat transfer significantly due to the quick developing of thermal boundary layer. A small buoyancy first impairs the heat transfer and then improves the heat transfer due to the turbulence attenuation and recovery. With buoyancy increasing, the turbulence recovery gets earlier and stronger, and the wall temperature is significantly reduced due to the large buoyancy production of turbulent kinetic energy (TKE) in supercritical water flows. The instantaneous vortical structures based on Q criterion also clearly show the process of turbulence attenuation and recovery. In addition, the simulation using two eddy-viscosity turbulent models is compared to DNS data. The results show that the failed prediction of wall temperature and Nusselt number by those turbulent models is possibly due to the bad results of TKE, production of TKE and turbulent Prandtl number (Prt).

On the minimum ignition energy and its transition in the localised forced ignition of turbulent homogeneous mixtures

The minimum energy requirements for ensuring (i) just successful ignition and (ii) successful self-sustained flame propagation without the assistance of an external energy source following a successful ignition event have been analysed for the forced ignition of a homogeneous stoichiometric methane–air mixture under a wide range of turbulence intensities using three-dimensional Direct Numerical Simulation (DNS) data. It has been found that the minimum energy needed for successful ignition is also sufficient to ensure self-sustained flame propagation for small turbulence intensities. However, for large turbulence intensities, the minimum energy for ensuring self-sustained flame propagation can be considerably greater than the minimum energy needed just to successfully ignite the mixture. At low turbulence intensities, the thermal runaway has been obtained for the minimum ignition energy after the end of the energy deposition indicating an autoignition. For larger energy inputs and turbulence intensity, the thermal runaway was obtained during the energy deposition period. It has been found that the minimum energy requirements for ignition and self-sustained flame propagation increase with increasing turbulence intensity but a transition in this behaviour has been observed. There is a critical turbulence intensity such that the increase in the energy demand is significantly more rapid above the critical value than that for turbulence intensities smaller than the critical value. This has been found to be qualitatively consistent with previous experimental findings. The stochastic nature of the ignition event has been demonstrated by considering different realisations of statistically similar turbulent flow fields. The conditions giving rise to a successful ignition have been identified by a detailed analysis of the energy budget. A scaling analysis has been performed for the critical condition for ensuring self-sustained flame propagation and the insights gained from this analysis have been utilised to explain the physical mechanisms behind the transition of the minimum ignition energy.

Three-dimensional nonadiabatic electron- optical gyrotron systems with inhomogeneous current density

The results of a numerical study of the effect of threedimensional perturbations of the space charge density distribution in a nonadiabatic electron-optic systems of gyrotrons are presented. Data of direct numerical simulation using the 3-D program CST Studio Suite are described.

Machine learning methods for turbulence modeling in subsonic flows around airfoils

In recent years, the data-driven turbulence model has attracted widespread concern in fluid mechanics. The existing approaches modify or supplement the original turbulence model by machine learning based on the experimental/numerical data, in order to augment the capability of the present turbulence models. Different from the previous researches, this paper directly reconstructs a mapping function between the turbulent eddy viscosity and the mean flow variables by neural networks and completely replaces the original partial differential equation model. On the other hand, compared with the machine learning models for the low Reynolds (Re) number flows based on direct numerical simulation data, high Reynolds number flows around airfoils present the apparent scaling effects and strong anisotropy, which induce large challenges in accuracy and generalization capability for the machine learning algorithm. We mainly concentrate on the high Reynolds number turbulent flows around the airfoils and take the results calculated by the computational fluid dynamics solver with the Spallart-Allmaras (SA) model as training data to construct a high-dimensional data-driven network model based on machine learning. The radial basis function neural network and the auxiliary optimization methods are adopted, and the individual models are built separately for the flow fields of the near-wall region, wake region, and far-field region. The training data in this paper is extracted from only three subsonic flow fields of NACA0012 airfoil. The data-driven turbulence model can be applied to various airfoils and flow states, and the predicted eddy viscosity, lift/drag coefficients, and skin friction distributions are all in good agreement with the results of the original SA model. This research demonstrates the promising prospect of machine learning methods in future studies about turbulence modeling.

Effects of Rotation on Turbulence Production

Direct numerical simulations (DNS) of non-rotating and rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations was used to investigate the prominent coherent structures involved in the turbulence generation cycle. Predictions from three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. Quadrant analysis was used to determine a phase shift between the fluctuating streamwise and wall-normal velocities as a characteristic of turbulence production in the suction region at a low rotation number.

Improved Five- and Six-Point Targeted Essentially Nonoscillatory Schemes with Adaptive Dissipation

This Paper proposes an improvement of the five- and six-point targeted essentially nonoscillatory (TENO5 and TENO6) schemes by introducing an adaptive dissipation-control strategy. Nonlinear numerical dissipation is controlled by dynamically adjusting the cutoff parameter in the TENO weighting strategy according to the first-order smoothness measure of the local flow scales. For the five-point reconstruction, the dissipation bandwidth of the underlying linear scheme is delayed by introducing slight antidissipation at low wave numbers with small dispersion errors. A new sixth-order scale-separation parameter is derived, and the modified TENO5-A scheme is third-order accurate. For the six-point reconstruction, the dispersion and dissipation errors are optimized separately, resulting in a modified fourth-order TENO6-A scheme. All necessary parameters are determined by spectral analyses and are shown to be problem independent by numerical experiments. A set of benchmark cases, including highly compressible gas dynamics and nearly incompressible and compressible turbulence decay, is considered. Numerical experiments demonstrate that both the proposed TENO5-A and TENO6-A schemes show excellent performance for shocks and broadband turbulence. The turbulence statistics obtained with TENO6-A at coarse resolution are comparable to those from the state-of-the-art implicit large-eddy simulation model and agree well with direct numerical simulation data.

Integral properties of temperature variance production in a turbulent channel flow with passive scalar transport

This paper investigates the integral properties of the mean temperature dissipation α(∂Θ/∂y)2 and the temperature variance production Pθ=Rvθ(∂Θ/∂y) in fully developed turbulent channel flow, and in particular the effects of Prandtl number Pr=ν/α and Reynolds number Reτ=δuτ/ν (and/or Peclet number Peτ=ReτPr). Here Θ is the mean temperature and Rvθ is the wall-normal turbulent heat flux. y is the wall-normal direction and δ is the channel half-height. ν and α are the fluid viscosity and thermal diffusivity, respectively. uτ is the friction velocity. The main findings of the present work include: (1) Identities are derived from the mean thermal energy equation for the global integral of the mean temperature dissipation and temperature variance production for four heating conditions: constant heat source (CHS), constant wall heat flux (CHF), constant temperature difference (CTD), and constant wall temperature (CTD). Identities for the CHS and CHF conditions are consistent with those derived by Pirozzoli et al. (2016) and Abe and Antonia (2017). The identities are verified using publicly available direct numerical simulation (DNS) data under three heating conditions CHS, CHF, and CTD. (2) The global integral of the mean temperature dissipation is found to depend strongly on the fluid Prandtl number, but it is largely independent of the Reynolds number of the flow. In inner-scaling, this global integral can be approximated as(1/Pr)∫0δ+(∂Θ+/∂y+)2dy+≈9.13Pr1-n where Θ+=Θ/θτ is the inner-scaled mean temperature and θτ is the friction temperature. y+=yuτ/ν is the inner-scaled wall-normal distance. n≈1/2 for Pr≲1 and n≈1/3 for Pr≳1. The strong dependence of (1/Pr)∫0δ+(∂Θ+/∂y+)2dy+ on the Prandtl number is directly rooted in the molecular thermal diffusion sub-layer. (3) The global integral of temperature variance production is found to strongly depend on both Prandtl number and Reynolds number. (3.1) At sufficiently high Reynolds number and Peclet number, the integral of temperature variance production is found to exhibit a logarithmic-like layer similar to that of the mean temperature profile. (3.2) The effect of Prandtl number is mainly caused by the molecular thermal diffusion sub-layer and buffer layer. (3.3) Between the peak wall-normal turbulent heat flux Rvθ location, ymt, and the channel centerline, δ, the integral of temperature variance production increases with Peclet number in a logarithmic-like fashion. (3.4) At low Prandtl number Pr≲1, the integral of temperature variance production is found to be equally partitioned around ymt.

Large eddy simulation of turbulent channel flow using differential equation wall model

A large eddy simulation (LES) of a plane turbulent channel flow is performed at a Reynolds number Re? = 590 based on the channel half width, ? and wall shear velocity, u? by approximating the near wall region using differential equation wall model (DEWM). The simulation is performed in a computational domain of 2?? x 2? x ??. The computational domain is discretized by staggered grid system with 32 x 30 x 32 grid points. In this domain the governing equations of LES are discretized spatially by second order finite difference formulation, and for temporal discretization the third order low-storage Runge-Kutta method is used. Essential turbulence statistics of the computed flow field based on this LES approach are calculated and compared with the available Direct Numerical Simulation (DNS) and LES data where no wall model was used. Comparing the results throughout the calculation domain we have found that the LES results based on DEWM show closer agreement with the DNS data, especially at the near wall region. That is, the LES approach based on DEWM can capture the effects of near wall structures more accurately. Flow structures in the computed flow field in the 3D turbulent channel have also been discussed and compared with LES data using no wall model.

On negative turbulence production phenomena in the shear layer of separating and reattaching flows

The analysis of Direct Numerical Simulation data of the separating and reattaching flow over a blunt bluff body with sharp edges, reveals the presence of negative turbulence production mechanisms in the leading-edge shear layer. Contrary to what is commonly observed in fully developed turbulent flows, this phenomenon represents flow reversal of energy from the fluctuating field to the mean flow. The detailed study of the data reveals that at the origin of such mechanisms is a statistically positive relation between Reynolds shear stresses and vertical shear. We argue that such a positive relation is a result of large-scale interactions of the fluctuating field with the streamwise inhomogeneity. The analysis of time cospectra confirms this picture by highlighting the presence of a net separation of scales consisting in a range of small scales positively contributing to turbulence production in opposition to a range of large scales giving to a reversal of flow energy from the fluctuating to the mean field. By means of a reduced description of the interactions of the fluctuating field with the mean field given by a generalized mixing length hypothesis, we finally also provide conceptual arguments for the modelling of turbulence production in the transitional shear layer. A model for the mixing length is also proposed which is found to work nicely in shear flows. The simplicity of the formulation supports its use especially in experiments of wall-bounded turbulence.

On the Reynolds number dependence of velocity-gradient structure and dynamics

We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ($Re_{\unicode[STIX]{x1D706}}$). The analysis factorizes the velocity gradient ($\unicode[STIX]{x1D608}_{ij}$) into the magnitude ($A^{2}$) and normalized-gradient tensor ($\unicode[STIX]{x1D623}_{ij}\equiv \unicode[STIX]{x1D608}_{ij}/\sqrt{A^{2}}$). The focus is on bounded $\unicode[STIX]{x1D623}_{ij}$ as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of $\unicode[STIX]{x1D623}_{ij}$ and its scalar invariants are shown to attain $Re_{\unicode[STIX]{x1D706}}$ independence. The critical values beyond which each feature attains $Re_{\unicode[STIX]{x1D706}}$ independence are established. We proceed to characterize the $Re_{\unicode[STIX]{x1D706}}$ dependence of $\unicode[STIX]{x1D623}_{ij}$-conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.

Anisotropic minimum-dissipation (AMD) subgrid-scale model implemented in OpenFOAM: Verification and assessment in single-phase and multi-phase flows

Minimum-dissipation sub-grid models represent simple alternatives to the Smagorinsky-type approaches to the implementation of sub-grid scales’ (SGS) effects in the large-eddy simulation (LES) approach. Recently, the anisotropic minimum-dissipation (AMD) model has been introduced, which is a static type of eddy-viscosity SGS model and is a new addition to this family. This model is easy to implement; furthermore, not only can it consider the effect of various directions in computing sub-grid stress, it can also operate transitional flows from laminar to turbulent. For the first time, we implemented AMD in the open source package OpenFOAM. Foremost, we verified the OpenFOAM implementation of the AMD model for the prediction of isotropic decaying turbulence, a temporal mixing layer and an internal channel flow. To achieve this, decaying turbulence was considered for the isotropic turbulence produced by a grid with a mesh size of 5.08 × 10–2 m in a flow of mean velocity of 10 m/s. The temporal mixing layer was simulated at a Reynolds number based on half the initial vorticity thickness of 105. Channel flow was investigated at the three frictional Reynolds numbers of 180, 395 and 590. The verification results revealed that the implemented AMD model in OpenFOAM offered satisfactory accuracy to capture decaying turbulence and temporal mixing layer and calculate boundary layer velocity profiles and first and second-order turbulent parameters in the channel flow on anisotropic grids. Following this, for the first time, we evaluated AMD's performance in predicting external non-cavitating and cavitating flows over a 3D sphere. Non-cavitating and cavitating flow over the sphere were considered at Re = 2 × 104 and Re = 1.5 × 106, respectively. The AMD results were then compared with the direct numerical simulation (DNS) data and the numerical results obtained from the established SGS models such as dynamic Smagorinsky (DS), one equation eddy viscosity model (OEEVM), detached eddy simulation (DES), and delayed detached eddy simulation (DDES), where applicable. In treating sphere flow, in spite of the use of a coarse grid rather than the alternative SGS models, the AMD model predicted accurate results for pressure coefficient, shear stress, and separation point location over the sphere as well as the velocity profile in the wake region. It was detected that the simulation time of the AMD model was lower than that of DS in all the considered test cases by approximately 10–16%.

Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data

Recently, the methodology of deep learning is used to improve the calculation accuracy of the Reynolds-averaged Navier-Stokes (RANS) model. In this paper, a neural network is designed to predict the Reynolds stress of a channel flow of different Reynolds numbers. The rationality and the high efficiency of the neural network is validated by comparing with the results of the direct numerical simulation (DNS), the large eddy simulation (LES), and the deep neural network (DNN) of other studies. To further enhance the prediction accuracy, three methods are developed by using several algorithms and simplified models in the neural network. In the method 1, the regularization is introduced and it is found that the oscillation and the overfitting of the results are effectively prevented. In the method 2, y+ is embedded in the input variable while the combination of the invariants is simplified in the method 3. From the predicted results, it can be seen that by using the first two methods, the errors are reduced. Moreover, the method 3 shows considerable advantages in the DNS trend and the smoothness of a curve. Consequently, it is concluded that the DNNs can predict effectively the anisotropic Reynolds stress and is a promising technique of the computational fluid dynamics.

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.