Direct Numerical Simulation Data Research Articles

A conceptual generalization of Taylor microscales with applications to isotropic and wall turbulence

Two new concepts of the Taylor microscale matrix (TMM) and Taylor microscale tensor (TMT) are proposed to extend the classical concept of Taylor microscale of isotropic turbulence to the general scenario of anisotropic turbulence. The first concept TMM is derived from the classical definition of two-point auto-correlation function, which has shortcomings for not being a tensor. The second concept TMT is proposed based on a new correlation function that rigorously maintains tensor properties. The three eigenvalues of TMM or TMT represent the general Taylor microscales (GTMs). When these three new general concepts, TMM, TMT, and GTM, are applied to homogeneous and isotropic turbulence, the classical Taylor microscale is automatically recovered. The proposed concepts can also be used for characterizing anisotropic turbulence. To demonstrate, direct numerical simulations (DNSs) of turbulent plane-channel flows of three Reynolds numbers are performed. The asymptotic near-wall behaviors of GTM are derived analytically and validated using DNS data. In the current literature, it is popular to study the orientation of turbulent flow structures qualitatively based on the isopleths of a two-point auto-correlation function. As a new advancement, a rigorous explanation of this popular approach is obtained based on the concept of GTM such that the characteristic inclination angle of flow structures (such as the mean angle of hairpin packets) can be precisely defined and computed. It is interesting to observe that in the outer layer, the mean streamwise spacing between two successive hairpin vortices in a hairpin packet is approximately twice the proposed GTM λT1(1).

Evaluation of Subfilter Model Performance for Large-Eddy Simulations of Supercritical Fluids

Abstract The accuracy of three large-eddy simulations (LES) is assessed using a reference dataset obtained via direct numerical simulation (DNS). All of the LES simulations employ the dynamic Smagorinsky model to close the momentum equation and a dynamic gradient model to close the total energy equation. The LES data are obtained on three grids with resolutions spanning from the wall-resolved LES limit to two successive levels coarser in the spatial and temporal domains. The configuration employed for the study is a three-dimensional spatially evolving turbulent shear layer. The working fluid is pure carbon dioxide. The system is maintained at a supercritical state near the critical point such that the field is dominated by strongly nonlinear thermophysics. This allows the analysis to occur under conditions where the subfilter closures are significantly strained by the thermodynamics. Results explore characteristics of the turbulence from both a modeling and fundamental perspective. First, mixing layer growth rates are quantified. Discrepancies are found between the reference DNS data and the LES data. Energy spectra, turbulent transport coefficients, and Reynolds stress anisotropy results are presented to explore the origins of this mismatch.

Energy thickness in turbulent boundary layer flows

In this study, we investigate the properties of energy thickness $\delta _3$ in turbulent boundary layer (TBL) flows, a parameter derived solely from the mean streamwise velocity ( $U$ ) profile. Through an analysis of the energy integral equation for zero pressure gradient TBLs, we establish a close relationship between turbulent kinetic energy (TKE) production and $\delta _3$ , offering a practical method to estimate TKE production, which is particularly useful in physical experiments where direct measurements are challenging. The significance of $\delta _3$ becomes even more pronounced in TBLs under pressure gradient. Through extensive analysis of numerical and experimental data, we show that the ratio between $\delta _3$ and the momentum thickness $\delta _2$ is a promising criterion for predicting flow separation. Moreover, we derive a new energy integral equation for TBLs under arbitrary pressure gradients, and provide approximations for TKE productions terms by $R_{uv}\,\partial U/\partial y$ and $R_{uu}\,\partial U/\partial x$ , and dissipation term by the mean shear. Here, $x, y$ represent the streamwise and wall-normal directions, respectively, and $R_{uu}$ and $R_{uv}$ are the Reynolds normal and shear stresses. The accuracy and robustness of the new energy integral equation and the approximation equations are validated using direct numerical simulations data. Our results show that the TKE production by $R_{uv}\,\partial U/\partial y$ and the overall productions consistently remain positive, reflecting a continuous conversion of mean kinetic energy into TKE across all TBLs. However, under strong favourable pressure gradients, TKE production by $R_{uu}\,\partial U/\partial x$ becomes negative, indicating a reverse energy transfer from TKE to mean kinetic energy.

A Data-Driven Approach to Refine the Partially Stirred Reactor Closure for Turbulent Premixed Flames

AbstractAccurately predicting turbulent combustion processes is fundamental for optimizing efficiency, reducing pollutant emissions, and ensuring operational safety in combustion systems. To this purpose, computational fluid dynamics (CFD) simulations are widely employed. In particular, large eddy simulations (LES) balance prediction accuracy with computational efficiency by resolving only the most energy-containing scales of turbulence and rely on modeling the turbulence-chemistry interactions (TCI) occurring at the smallest scales. Among the existing closures, the partially stirred reactor (PaSR) model incorporates finite-rate chemistry and estimates a cell reacting fraction based on the local Damköhler number to account for the subfilter-scale TCI. Although widely validated in CFD computations, the PaSR model was found limited by the way it computes the cell reacting fraction. To tackle this point, our study proposes a machine learning (ML) enhanced partially stirred reactor model for LES. A fully connected neural network is trained on direct numerical simulation (DNS) data of turbulent premixed jet flames to compute a correction coefficient for the cell reacting fraction. Maintaining the original model shape, this ML-enhanced closure aims at bridging the gap between physics-based models and advanced data-driven techniques. The proposed formulation not only improves the prediction accuracy of quantities of interest such as the heat release rate but also features computational feasibility and generalisation capabilities over a large range of LES grid refinement. This demonstrates the significant potential of ML-aided TCI closures in future applications of combustion engineering.

Assessment of algebraic anisotropic turbulent heat flux models using Reynolds stress modeling for simulating film cooling flows

This study evaluates the performance of various algebraic turbulent heat flux models in predicting film cooling flows using different Reynolds stress turbulence models. a priori analysis using direct numerical simulation data was used to assess the models' performance. Additionally, Reynolds-averaged Navier–Stokes (RANS) simulations based on Reynolds stress turbulence models were performed to investigate the models' practical application in film cooling. Results demonstrate that the enhanced explicit algebraic turbulent heat flux model significantly outperforms existing models. It accurately predicts both streamwise and wall-normal turbulent heat fluxes based on direct numerical simulation data in a channel flow, and exhibits superior performance in film cooling simulations respect to known turbulent heat flux models. The recommended turbulent heat flux model decreased the error norm more than 90% in channel flow. Furthermore, the study highlights the importance of selecting appropriate Reynolds stress models in conjunction with turbulent heat flux models for accurate film cooling predictions. The right choice of Reynolds stress model according to the turbulent heat flux model can significantly influence the overall accuracy of the RANS simulation.

Friction and heat transfer in forced air convection with variable physical properties

We establish a theoretical framework for predicting friction and heat transfer coefficients in variable-property forced air convection. Drawing from concepts in high-speed wall turbulence, which also involves significant temperature, viscosity and density variations, we utilize the mean momentum balance and mean thermal balance equations to develop integral transformations that account for the impact of variable fluid properties. These transformations are then applied inversely to predict the friction and heat transfer coefficients, leveraging the universality of passive scalars transport theory. Our proposed approach is validated using a comprehensive dataset from direct numerical simulations (DNS), covering both heating and cooling conditions up to a friction Reynolds number $\textit {Re}_\tau \approx 3200$ . The predicted friction and heat transfer coefficients closely match the DNS data with accuracy margin 1–2 %, representing a significant improvement over the current state of the art.

Modeling of vibrational nonequilibrium effects on pressure Hessian tensor using physics-assisted deep neural networks

This study focuses on modeling the effect of vibrational nonequilibrium on the pressure Hessian tensor. The pressure Hessian tensor is one of the unclosed processes involved in the velocity gradient evolution equation. Accessing the velocity gradient tensor following a fluid particle is needed to understand the physics of various nonlinear turbulent processes. Our modeling strategy employs a combination of two different deep neural networks (DNNs) to model the magnitude and the directional aspects of the vibrational nonequilibrium tensor separately. Both the DNNs are optimized using two appropriate physics-assisted custom loss functions, comparing the desired features of the DNN predictions against the exact behavior observed in the direct numerical simulation (DNS) database. A detailed investigation of four different DNS databases of vibrationally excited decaying compressible turbulence with different initial Reynolds numbers, Mach numbers, and vibrational Damköhler numbers is performed to identify the appropriate normalized forms of input and output quantities for the two neural networks. The training of both the DNNs is done using the DNS data of merely one simulation. The trained models are then subjected to extensive evaluation against different DNS databases. Indeed, the new model captures many DNS features quite well. Such an extensive evaluation of the new model proves the generalizability of the model, at least in the range of parameters involved in our study.

Modulation of large-scale motions on turbulent/non-turbulent interface in spatially developing compressible mixing layer

Direct numerical simulations (DNSs) are conducted to investigate the modulations of large-scale motions (LSMs) on the turbulent/non-turbulent interfaces (TNTIs) in spatially developing compressible mixing layers with convective Mach numbers (Mc) of 0.4 and 0.8. Turbulent statistics, including velocity profiles, turbulent Mach number, normalized growth rate, Reynolds stress, and velocity spectrum, are analyzed to validate the DNS data. At the shear layer center, large-scale high- and low-speed structures are observed, with spanwise rollers being suppressed as the Mach number increases. At the upper layer, the TNTI elevates above the low-speed (negative fluctuating streamwise velocity) large-scale motions (nLSMs) and sinks above the high-speed (positive fluctuating streamwise velocity) large-scale motions (pLSMs). The conditional averages based on LSMs reveal the modulations of LSMs on TNTIs. Across the upper TNTI, nLSMs stimulate positive (upward) transverse velocity and pLSMs stimulate negative (downward) transverse velocity. Under the influence of nLSMs, the jumps in velocity, turbulent kinetic energy (TKE), and vorticity magnitude are larger, as compared to pLSMs. As the convective Mach number increases, small-scale variables are suppressed, while the modulations of LSMs on TNTIs become more pronounced. The lower TNTI exhibits opposite behaviors. It is less affected by LSMs, with less shear and less intense rotation. The jumps of temperature and density increase with increasing convective Mach number. The effect of LSMs on the temperature and density jumps is significant at Mc=0.8.

On the accuracy of compressibility transformations

This study highlights the importance of satisfying the eddy viscosity equivalence below the logarithmic layer, to deriving accurate compressibility transformations. First, we analyze the ability of known transformations to satisfy the eddy viscosity equivalence and show that the accuracy of these transformations is strongly dependent on this ability. Second, in a step-by-step manner, we devise new transformations that satisfy this hypothesis. An approach based on curve fitting of the incompressible Direct Numerical Simulation data for eddy viscosity profiles below the logarithmic layer provides an extremely accurate transformation, which motivates self-contained methods, making use of mixing length formulas in the inner region. It is shown that the accuracy of existing transformations can be significantly improved by applying these ideas, below the logarithmic layer. Motivated by the effectiveness of the formulations derived from eddy viscosity equivalence, we introduce a new integral transformation based on Reynolds number equivalence between compressible and incompressible flows. This approach is based on defining a new compressible velocity scale, which affects the accuracy of transformations. Several choices for the velocity scale are tested, and in each attempt, it is shown that the eddy viscosity equivalence plays a very important role for the accuracy of compressibility transformations.

Keplerian turbulence in Taylor–Couette flow of dilute polymeric solutions

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ( $Re$ ) ranging from $10^2$ to $10^4$ . The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$ ; the angular momentum transport scales as $Re^{0.42}$ ; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$ , respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach

Physics-informed neural networks (PINNs) have emerged as a promising approach for simulating nonlinear physical systems, particularly in the field of fluid dynamics and turbulence modelling. Traditional turbulence models often rely on simplifying assumptions or closed numerical models, which simplify the flow, leading to inaccurate flow predictions or long solve times. This study examines solver constraints in a PINNs solver, aiming to generate an understanding of an optimal PINNs solver with reduced constraints compared with the numerically closed models used in traditional computational fluid dynamics (CFD). PINNs were implemented in a periodic hill flow case and compared with a simple data-driven approach to neural network modelling to show the limitations of a data-driven model on a small dataset (as is common in engineering design). A standard full equation PINNs model with predicted first-order stress terms was compared against reduced-boundary models and reduced-order models, with different levels of assumptions made about the flow to monitor the effect on the flow field predictions. The results in all cases showed good agreement against direct numerical simulation (DNS) data, with only boundary conditions provided for training as in numerical modelling. The efficacy of reduced-order models was shown using a continuity only model to accurately predict the flow fields within 0.147 and 2.6 percentage errors for streamwise and transverse velocities, respectively, and a modified mixing length model was used to show the effect of poor assumptions on the model, including poor convergence at the flow boundaries, despite a reduced solve time compared with a numerically closed equation set. The results agree with contemporary literature, indicating that physics-informed neural networks are a significant improvement in solve time compared with a data-driven approach, with a novel proposition of numerically derived unclosed equation sets being a good representation of a turbulent system. In conclusion, it is shown that numerically unclosed systems can be efficiently solved using reduced-order equation sets, potentially leading to a reduced compute requirement compared with traditional solver methods.

Localization of internal gravity waves in stratified channel flow

Linear and nonlinear contributions to the localization and dynamics of internal gravity waves in a stably stratified turbulent channel flow are investigated using data from direct numerical simulations (DNS). The classification into linear and nonlinear mechanisms is based on the resolvent formulation of the Navier–Stokes equations, which interprets velocity and temperature fluctuations (flow response) as the result of a linear operator (resolvent) acting on the nonlinear advection terms (forcing). Spatial and spatio-temporal power spectral densities computed from DNS data demonstrate that the stratified flow response is localized in spectral space and in the channel core, while the nonlinear forcing is broadband and spans up to the entire channel height. The localization of the velocity and temperature fluctuations in wavenumber and frequency is captured by the leading singular value of the resolvent operator. The wall-normal localization on the other hand results from a combination of linear dynamics and nonlinear forcing, and the latter is further examined using the cross-spectral density (CSD) tensor. Wall-normal subsets of the forcing CSD lead to flow responses that reveal a three-layer structure. The middle one hosts the critical layer of the gravity wave, and is termed the outer layer since it is flanked by an inner layer at the wall and the core region at the channel centre. Forcing within this outer layer generates the majority of the flow response in the channel core. Furthermore, a decomposition of the forcing CSD into velocity and temperature demonstrates that each imprints distinct phase relations on their associated responses, which lead to destructive interference and localization of the gravity waves in the channel core.

Local precursors to anomalous dissipation in Navier-Stokes turbulence: Burgers vortex-type models and simulation analysis

Anomalous dissipation is a mechanism to dissipate kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to Reynolds number Re, the dimensionless parameter that characterizes the strength of turbulence, given that Re≫1. The present study aims at bridging this statistical behavior of high-Reynolds-number turbulence to one specific structural building block of fluid turbulence—local vortex stretching configurations which take in the simplest case the form of Burgers's classical vortex stretching model from 1948. We discuss the anomalous dissipation in the framework of Duchon and Robert for this analytical solution of the Navier-Stokes equations, apply the same analysis subsequently to a generalized model of randomly oriented Burgers vortices by Kambe and Hatakeyama, and analyze finally direct numerical simulation data of three-dimensional homogeneous, isotropic box turbulence in this respect. We identify local high-vorticity events in fully developed Navier-Stokes turbulence that approximate the analytical models of strong vortex stretching well. They correspond to precursors of enhanced anomalous dissipation. Published by the American Physical Society 2024

Modelling of filtered drag force for clustered particle-laden flows based on interface-resolved simulation data

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

Tailor-Designed Models for the Turbulent Velocity Gradient through Normalizing Flow.

Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for nonlocal pressure and viscous contributions. The fidelity of the resulting models depends on the accuracy of the underlying modeling assumptions. Here, we discuss an alternative data-driven approach leveraging machine learning to derive a velocity gradient model which captures its statistics by construction. We use a normalizing flow to learn the velocity gradient probability density function (PDF) from direct numerical simulation (DNS) of incompressible turbulence. Then, by using the equation for the single-time PDF of the velocity gradient, we construct a deterministic, yet chaotic, dynamical system featuring the learned steady-state PDF by design. Finally, utilizing gauge terms for the velocity gradient single-time statistics, we optimize the time correlations as obtained from our model against the DNS data. As a result, the model time realizations resemble the time series from DNS statistically closely.

A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows

Super-resolution reconstruction of turbulent flows using deep learning has gained significant attention, yet challenges remain in accurately capturing physical small-scale structures. This study introduces the Conditional Enhanced Super-Resolution Generative Adversarial Network (CESRGAN) for reconstructing high-resolution turbulent velocity fields from low-resolution inputs. CESRGAN consists of a conditional discriminator and a conditional generator, the latter being called CoGEN. CoGEN incorporates subgrid-scale (SGS) turbulence kinetic energy as conditional information, improving the recovery of small-scale turbulent structures with the desired level of energy. By being aware of SGS turbulence kinetic energy, CoGEN is relatively insensitive to the degree of detail in the input. As shown in the paper, its advantages become more pronounced when the model is applied to heavily filtered input. We evaluate the model using direct numerical simulation (DNS) data of forced homogeneous isotropic turbulence. The analysis of Q-criterion isosurfaces, energy spectra, and probability density functions shows that the proposed CoGEN reconstructs fine-scale vortical structures more precisely and captures turbulent intermittency better compared to the traditional generator. Particle-pair dispersion simulations validate the physical fidelity of CoGEN-reconstructed fields, closely matching DNS results across various Stokes numbers and filtering levels. This paper demonstrates how incorporating available physical information enhances super-resolution models for turbulent flows.

Anisotropy of Reynolds Stresses and Their Dissipation Rates in Lean H2-Air Premixed Flames in Different Combustion Regimes

The interrelation between Reynolds stresses and their dissipation rate tensors for different Karlovitz number values was analysed using a direct numerical simulation (DNS) database of turbulent statistically planar premixed H2-air flames with an equivalence ratio of 0.7. It was found that a significant enhancement of Reynolds stresses and dissipation rates takes place as a result of turbulence generation due to thermal expansion for small and moderate Karlovitz number values. However, both Reynolds stresses and dissipation rates decrease monotonically within the flame brush for large Karlovitz number values, as the flame-generated turbulence becomes overridden by the strong isotropic turbulence. Although there are similarities between the anisotropies of Reynolds stress and its dissipation rate tensors within the flame brush, the anisotropy tensors of these quantities are found to be non-linearly related. The predictions of three different models for the dissipation rate tensor were compared to the results computed from DNS data. It was found that the model relying upon isotropy and a linear dependence between the Reynolds stress and its dissipation rates does not correctly capture the turbulence characteristics within the flame brush for small and moderate Karlovitz number values. In contrast, the models that incorporate the dependence of the invariants of the anisotropy tensor of Reynolds stresses were found to capture the components of dissipation rate tensor for all Karlovitz number conditions.

Data-Guided Low-Reynolds-Number Corrections for Two-Equation Models

Abstract The baseline Launder–Spalding k−ε model cannot be integrated to the wall. This paper seeks to incorporate the entire law of the wall into the model while preserving the original k−ε framework structure. Our approach involves modifying the unclosed dissipation terms in the k and ε equations specifically within the wall layer according to direct numerical simulation (DNS) data. The resulting model effectively captures the mean flow characteristics in both the buffer layer and the logarithmic layer, resulting in robust predictions of skin friction for zero-pressure-gradient (ZPG) flat-plate boundary layers and plane channels. To further validate our formulation, we apply our model to boundary layers under varying pressure gradients, channels experiencing sudden deceleration, and flow over periodic hills, with highly favorable results. Although not the focus of this study, the methodology here applies equally to the k–ω formulation and yields improved predictions of the mean flow in the viscous sublayer and buffer layer.

Estimation of Turbulent Mixing Factor and Study of Turbulent Flow Structures in Pressurized Water Reactor Sub Channel by Direct Numerical Simulation

Abstract Subchannel analysis codes are presently a requirement for design and safety analysis of nuclear reactors. Among the crucial inputs for these codes, the turbulent mixing factor holds particular significance. However, acquiring this factor through experimental means proves to be a challenging endeavor, primarily due to the necessity for precise pressure equilibrium between subchannels. Consequently, this requirement leads to the undertaking of expensive and intricate experiments for each new reactor or in cases where there are modifications in fuel bundle design. The need for direct numerical simulation (DNS) stems from the challenges and costs involved in experimental techniques, and the uncertainties due to empiricism in computational fluid dynamics (CFD) models. In this study, DNS has been conducted across six Reynolds numbers, ranging from 17,640 to 1.176 × 105, in the geometry of a pressurized water reactor (PWR) subchannel. The resulting turbulent flow structures have been computed and their dynamics are examined. Furthermore, this paper presents a methodology for directly calculating the turbulent mixing factor from the fluctuating velocity field obtained from DNS data. The turbulent mixing process has been scrutinized in-depth, and a correlation for the turbulent mixing factor is developed. It is noted that most of the mixing occurs in the near-wall region. The study suggests different mixing factors for mass and momentum mixing. This paper aims to provide a comprehensive insight into the turbulent mixing phenomenon.

Multiscale analysis of Reynolds stresses and its dissipation rates for premixed flame–wall interaction

Direct numerical simulation (DNS) data of flame–wall interaction (FWI) has been utilized to analyze the multiscale nature of turbulent Reynolds stresses and dissipation rate tensor anisotropies within turbulent reacting flow boundary layers across a broad range of scales. The DNS data of head-on quenching of premixed flames propagating through turbulent boundary layers, representative of friction Reynolds numbers Reτ of 110 and 180, has been explicitly filtered using both two- and three-dimensional Gaussian filter kernels for the purpose of multiscale analysis. The low-pass filter results demonstrate the transition from a 2-component limit to a 1-component limit near the wall with increasing filter width, accompanied by a decrease in isotropy, suggesting a significant alteration in dominant flow patterns and a diminishing tendency toward isotropy. The high-pass filter results indicate a progressive increase in anisotropy with the progress of FWI at the channel center, emphasizing the anisotropy of the large scales with the progress of FWI. Furthermore, behaviors of the second and third invariants of the Reynolds stress tensor remain qualitatively similar to that of the dissipation rate tensor at all stages of FWI, suggesting a link between viscous dissipation and Reynolds stress distributions; notably, there is a stronger isotropic tendency in the dissipation rate tensor when the flame is away from the wall, intensifying with an increase in Reynolds numbers. However, as FWI progresses, the shift in the trend toward the 1-component limit indicates an increase in anisotropy within the turbulent reacting flow for the region near the center of the channel.