Direct Numerical Simulation Dataset Research Articles

An improved Baldwin–Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

Effects of Pressure and Characteristic Scales on the Structural and Statistical Features of Methane/Air Turbulent Premixed Flames

AbstractIn this study, the highly nonlinear and multi-scale flame-turbulence interactions prevalent in turbulent premixed flames are examined by using direct numerical simulation (DNS) datasets to understand the effects of increase in pressure and changes in the characteristic scale ratios at high pressure. Such flames are characterized by length-scale ratio (ratio of integral length scale and laminar thermal flame thickness) and velocity-scale ratio (ratio of turbulence intensity and laminar flame speed). A canonical test configuration corresponding to an initially laminar methane/air lean premixed flame interacting with decaying isotropic turbulence is considered. We consider five cases with the initial Karlovitz number of 18, 37, 126, and 260 to examine the effects of an increase in pressure from 1 to 10 atm with fixed turbulence characteristics and at a fixed Karlovitz number, and the changes to characteristic scale ratios at the pressure of 10 atm. The increase in pressure for fixed turbulence characteristics leads to enhanced flame broadening and wrinkling due to an increase in the range of energetic scales of motion. This further manifests into affecting the spatial and state-space variation of thermo-chemical quantities, single point statistics, and the relationship of heat-release rate to the flame curvature and tangential strain rate. Although these results can be inferred in terms of an increase in Karlovitz number, the effect of an increase in pressure at a fixed Karlovitz number shows differences in the spatial and state-space variations of thermo-chemical quantities and the relationship of the heat release rate with the curvature and tangential strain rate. This is due to a higher turbulent kinetic energy associated with the wide range of scales of motion at atmospheric pressure. In particular, the magnitude of the correlation of the heat release rate with the curvature and the tangential strain rate tend to decrease and increase, respectively, with an increase in pressure. Furthermore, the statistics of the flame-turbulence interactions at high pressure also show sensitivity to the changes in the characteristic length- and velocity-scale ratios. The results from this study highlight the need to accurately account for the effects of pressure and characteristic scales for improved modeling of such flames.

Modified stochastic diffusion particle tracking model driven by skew Brownian motion: Analysis of sediment particle motion in turbulent flow under the effects of ejection and sweep.

Turbulent bursting events have been classified into outward interactions (Q1), ejections (Q2), inward interactions (Q3), and sweeps (Q4) in various studies. Ejections (Q2) and sweeps (Q4) have been identified as significant contributors to time consumption, momentum flux, and sediment flux. Additionally, research has shown that the distribution of these events varies nonuniformly at different bed elevations. Despite extensive investigations into the nonuniform distribution of turbulent bursting events, their impact on sediment transport has been rarely explored. In this work, we developed a modified stochastic diffusion particle tracking model (SD-PTM) driven by skew Brownian motion (SBM) using the stochastic Lagrangian approach to scrutinize sediment particle movement in turbulent flows. The model incorporates turbulent characteristics derived from a direct numerical simulation dataset, allowing for a comprehensive analysis of sediment particle dynamics. Moreover, the proposed model accounts for the nonuniform spatial distribution of ejection and sweep events, as well as the particle movement direction during these events. Numerical simulations of the model were conducted to trace sediment particle trajectories in the streamwise and vertical directions. The analysis of sediment transport involved calculating the variance of particle trajectories to examine anomalous diffusion. The model's performance was evaluated by comparing it with flow velocity and sediment concentration profiles obtained from measurements in previous studies. In conclusion, our study suggests that the motion of sediment particles in turbulent flow can be thoroughly investigated under extreme flow conditions using the modified SD-PTM driven by SBM.

A resolvent-based prediction framework for incompressible turbulent channel flow with limited measurements

A new resolvent-based method is developed to predict the space–time properties of the flow field. To overcome the deterioration of the prediction accuracy with increasing distance between the measurements and predictions in the resolvent-based estimation (RBE), the newly proposed method utilizes the RBE to estimate the relative energy distribution near the wall rather than the absolute energy directly estimated from the measurements. Using this extra information from RBE, the new method modifies the energy distribution of the spatially uniform and uncorrelated forcing that drives the flow system by minimizing the norm of the cross-spectral density tensor of the error matrix in the near-wall region in comparison with the RBE-estimated one, and therefore it is named as the resolvent-informed white-noise-based estimation (RWE) method. For validation, three time-resolved direct numerical simulation (DNS) datasets with the friction Reynolds numbers $Re_\tau = 180$ , 550 and 950 are generated, with various locations of measurements ranging from the near-wall region ( $y^+ = 40$ ) to the upper bound of the logarithmic region ( $y/h \approx 0.2$ , where h is the half-channel height) for the predictions. Besides the RWE, three existing methods, i.e. the RBE, the $\lambda$ -model and the white-noise-based estimation (WBE), are also included for the validation. The performance of the RBE and scale-dependent model ( $\lambda$ -model) in predicting the energy spectra shows a strong dependence on the measurement locations. The newly proposed RWE shows a low sensitivity on $Re_{\tau }$ and the measurement locations, which may range from the near-wall region to the upper bound of the logarithmic region, and has a high accuracy in predicting the energy spectra. The RWE also performs well in predicting the space–time properties in terms of the correlation magnitude and the convection velocity. We further utilize the new method to reconstruct the instantaneous large-scale structures with measurements from the logarithmic region. Both the RWE and RBE perform well in estimating the instantaneous large-scale structure, and the RWE has smaller errors in the estimations near the wall. The structural inclination angles around $15^\circ$ are predicted by the RWE and WBE, which generally recover the DNS results.

Insights into CFD Modelling of Water Hammer

A problem with 1-D water hammer modelling is in the application of accurate unsteady friction. Moreover, investigating the time response of fluid dynamics and unsteady turbulence structures during the water hammer is not possible with a 1-D model. This review article provides a summary of 1-D modelling using the recent finite volume approach and the discussion extends to a quasi-2-D model and historical developments as well as recent advancements in 3-D CFD simulations of water hammer. The eddy viscosity model is excellent in capturing pressure profiles but it is computationally intensive and requires more computational time. This article reviews 3-D CFD simulations with sliding mesh, an immersed solid approach, and dynamic mesh approaches for modelling valve closures. Despite prediction accuracy, a huge computational time and high computer resources are required to execute 3-D flow simulations with advanced valve modelling techniques. Experimental validation shows that a 3-D CFD simulation with a flow rate reduction curve as a boundary condition predicted accurate pressure variation results. Finally, a brief overview of the transient flow turbulence structures for a rapidly accelerated and decelerated pipe flow using DNS (Direct numerical simulation) data sets is presented. Overall, this paper summarises past developments and future scope in the field of water hammer modelling using CFD.

Decomposition of the drag force in steady and oscillatory flow through a hexagonal sphere pack

We investigate steady and oscillatory flow through a hexagonal close-packed arrangement of spheres in the framework of the volume-averaged momentum equation. We quantify the friction and pressure drag based on a direct numerical simulation dataset. Using the pressure decomposition of Graham (J. Fluid Mech., vol. 881, 2019), the pressure drag can be further split up into an accelerative, a viscous and a convective contribution. For the accelerative pressure, a closed-form expression can be given in terms of the potential flow solution. We investigate the contributions of the different drag components to the volume-averaged momentum budget and their Reynolds number scaling. For steady flow, we find that the friction and viscous pressure drag are proportional to $Re$ at low Reynolds numbers and scale with $Re^{1.4}$ for high Reynolds numbers. This is close to the steady laminar boundary layer scaling. For the convective pressure drag, we find a cubic scaling at low and a quadratic scaling at high Reynolds numbers. The Reynolds stresses have a minor contribution to the momentum budget. For oscillatory flow at low and medium Womersley numbers, the amplitudes of the drag components are similar to the steady cases at the same Reynolds number. At high Womersley numbers, the drag components behave quite differently and the friction and viscous pressure drag are relatively insignificant. The drag components are not in phase with the forcing and the superficial velocity; the phase lag increases with the Womersley number. This suggests that new models beyond the current quasisteady approaches need to be developed.

Entrainment, detrainment and enstrophy transport by small-scale vortex structures

The interaction of small-scale vortical structures with the surrounding fluid are studied using a fully resolved three-dimensional experimental data set of homogeneous turbulence measured at the centre of a von Kármán mixing flow facility and a direct numerical simulation (DNS) data set of forced isotropic turbulence. To identify the small-scale vortices and their boundaries, an objective observer-independent definition was implemented to avoid arbitrariness and is the first implementation applied to experimental measurements of small-scale turbulence. Volume-averaged and conditional statistics are presented to demonstrate consistency between the experimental and DNS data sets. To examine the interaction of the structures with the surrounding flow field, we examine the flow across the boundary of vortex structures by adopting a similar methodological approach to that used to investigate the local entrainment and detrainment across the turbulent–non-turbulent interface. The probability density function (p.d.f.) of entrainment velocity conditioned on the vortex boundary exhibited a non-Gaussian distribution that skewed slightly in favour of entrainment and is remarkably similar to the p.d.f.s of entrainment velocity observed in boundary layers and jets. We analyse the enstrophy transport equation conditioned on radial and axial coordinates of the vortices to quantify the inviscid and viscous components of the entrainment/detrainment process. A comparison with Burgers vortices is made and it is found that the Burgers vortex model captures the vortex structure average size and the mechanisms of enstrophy transport in the radial direction, but is unable to capture local statistics and describe the governing physics along the axes of the vortices.

A DNS evaluation of three MMC-like mixing models for transported PDF modelling of turbulent nonpremixed flames

Transported probability density function (TPDF) methods are suitable for modelling turbulent reactive flows. One of the main challenges is to accurately model the molecular mixing terms. In TPDF mixing models, it is desired that the principle of localness is satisfied so that the molecular mixing is performed locally in both physical and composition spaces. The multiple mapping conditioning (MMC) mixing model can ensure mixing localness without violating other desired principles. The present study examines three MMC-like mixing models, including the original MMC (OMMC) mixing model, shadow-position mixing model (SPMM) and a conceptually simplified multiple mapping conditioning (SMMC) mixing model. Three direct numerical simulation (DNS) datasets modelling turbulent nonpremixed ethylene flames with increasing levels of extinction are used for model evaluation. The DNS datasets are also used to provide both initial conditions and inputs needed over the course of TPDF runs to remove the uncertainties caused by turbulence closure, allowing the study to focus on the molecular mixing model. The mixing model coefficients are specified analytically by reference to a canonical mean scalar gradient (MSG) flow in order to achieve specifiable dissipation rate and user-controllable localness. The results show that the MMC-like mixing models yield similar prediction of flame extinction and reignition if the coefficients are properly specified. The MMC-like mixing models can also be tuned to achieve a desired level of localness. For conditional statistics, the MMC-like mixing models can yield correct level of conditional variances. By changing localness, the MMC-like models can yield solutions resembling the interaction by exchange with the mean (IEM) or Euclidean minimum spanning tree (EMST) mixing model for extreme parameter choices. The models differ in their abilities to specify unconditional dissipation rates, at least in the flow considered, and in their ease of implementation.

A pairwise mixing model with kernel constraint and its appraisal in transported PDF simulations of ethylene flames

Modeling micro-mixing remains a primary challenge for the transported probability density function (TPDF) method. In this study, the pairwise mixing with kernel constraint (KerM) model is proposed and evaluated in TPDF simulations of a turbulent non-premixed ethylene flame. The new model features controllable localness by selecting mixing particle pairs with a probability that depends on their distance in composition space, normalized by a characteristic kernel size. To evaluate the model in a controlled setting, TPDF simulations were carried out with the mean velocity, turbulent diffusivity and scalar mixing frequencies extracted from a direct numerical simulation (DNS) dataset. The predictions of the mean statistics and the conditional PDFs illustrate that the KerM model exhibits asymptotic behavior to the modified Curl (MC) and the Euclidean minimum spanning trees (EMST) model, respectively, depending on the kernel size. For the flame considered, results for KerM approach those for EMST when the kernel size is less than 0.01, while they approach those for MC when the kernel size is larger than 1.0. Given a kernel size of 0.1, KerM yields a notably better prediction of the overall combustion process than the conventional MC model. The predictions of the mean temperature and species mass fractions by KerM are similar to those by EMST, while KerM better predicts the conditional PDF of temperature than EMST that overdamps the conditional fluctuations. In addition, its complexity with the number of particles per cell is instead of O(Np2) for EMST. By incorporating different mixing timescales among species, the KerM-DD model better predicts the mean temperature field at the time instant close to local extinction than the KerM and EMST models. This work demonstrates that the KerM model, apart from being simple and robust in terms of implementation, features the advantages of being flexible in localness and being capable of incorporating differential diffusion.

A GPU-Accelerated Particle Advection Methodology for 3D Lagrangian Coherent Structures in High-Speed Turbulent Boundary Layers

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian coherent structures (LCS) in large-scale direct numerical simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains, requiring efficient search algorithms in large, structured domains. While this article focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence

Construction of efficient and generalizable reduced order models of developed turbulence is a formidable challenge. Bridging the gap between physics-based models and data-driven methods, we introduce a novel approach that involves constructing a hierarchy of learnable and parameterized reduced Lagrangian models based on Smoothed Particle Hydrodynamics (SPH) and machine learning. By training these models on high fidelity Direct Numerical Simulation data sets and comparing their generalizability, we demonstrate the effectiveness of SPH-informed models at predicting statistical and field-based quantities of turbulent flows across a range of resolutions, time scales, and turbulent Mach numbers.

Turbulent flame speed based on the mass flow rate: Theory and DNS

Starting with an integral formulation of average mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking Damköhler’s hypotheses. Major approximations and interim results are validated using a large Karlovitz number, unity Lewis number, Direct Numerical Simulation (DNS) dataset of n-heptane/air mixture, computed with reduced chemistry. A length scale quantifying the fluctuation distance of the isotherms within the premixed flame structure is analysed.

Auto-encoder-assisted analysis of amplitude and wavelength modulation of near-wall turbulence by outer large-scale structures in channel flow at friction Reynolds number of 5200

This paper reports a novel methodology that allows the intensity of, and the underlying mechanism for, the amplitude and length-scale modulation (amplification or attenuation) of turbulent stresses in the inner layer of a channel flow at Reτ≈5200 to be clarified. A unique aspect of the present framework is the use of an auto-encoder algorithm to separate full-volume extremely large direct numerical simulation (DNS) fields into large-scale and small-scale motions. This approach is adopted in preference to the empirical mode decomposition (EMD) previously used by the present authors at the lower Reynolds number, Reτ≈1000, because resource requirements posed by the EMD quickly become untenable due to the extremely large DNS dataset and the large solution box needed to capture the wide spectrum of scales at the present Reynolds number. A second original element is a formalism that derived the modulation, conditional on large-scale fluctuations, from continuous statistical quantities represented as multivariable-joint probability-density functions, thus obviating the need for any discrete representation or binning beyond that imposed by the discrete DNS solution. A third novel aspect is the use of the length-scale-wise derivative of the second-order structure function to quantify the modulation (increase or decrease) in the length scale, again conditional on large-scale structures. Apart from illuminating the modulation itself, the study examined the validity of the quasi-steady hypothesis that proposes that the near-wall turbulence is universal when scaled by the spatially and temporally varying large-scale wall shear stress rather than its time average.

Higher-Order Accurate Neural Network For Real-Time Fluid Velocimetry

In the present work, we introduce a novel lightweight neural network for fluid velocimetry called LIMA (Lightweight Image Matching Architecture) designed and optimized for PIV, which can potentially fit on low-cost computer hardware. We compare two versions of the network: LIMA-4, a 4-level architecture focused on fast reconstruction; and LIMA-6, a 6-level architecture focused on maximizing accuracy. We demonstrate the new approach provides more accurate prediction with fewer network parameters and faster inference speed. Furthermore, we quantified the disparity error using uncertainty quantification (UQ) by image matching to assess the prediction accuracy of the network. We assess the performance of a synthetic direct numerical simulation (DNS) dataset and a wind tunnel measurement dataset of flow past a cylinder. In all cases, we validate that the new network shows higher accuracy than the previous state-of-the-art neural network (PWCIRR) and also the classic particle image velocimetry (PIV) approach. In the future, we envision deploying the lightweight architecture on low-cost devices to provide affordable, real-time inference of the flow field during PIV measurements.

A mixing timescale model for differential mixing in transported probability density function simulations of turbulent non-premixed flames

The modeling of scalar mixing timescale remains a primary challenge in the transported probability density function (TPDF) method. The variation of scalar mixing timescale among species, i.e., differential mixing, results from the difference in molecular diffusivity and reaction-induced scalar gradient. Nevertheless, the vast majority of TPDF studies on turbulent non-premixed flames simply apply a single mixing timescale determined by the mixture fraction. In this work, a reaction-induced differential mixing timescale (RIDM) model for the mixing timescale of individual species in turbulent non-premixed flames is proposed. The key idea of the RIDM model is to approximate the relative magnitude of the species dissipation rates by using their values in laminar flamelets. A direct numerical simulation dataset of a temporally evolving non-premixed ethylene flame is employed to thoroughly evaluate the model performance via a priori and a posteriori tests. Results show that specifying a single mixing timescale for all species results in a poor prediction of the species dissipation rate and thus the failure to predict the overall combustion process. By accounting for the difference in molecular diffusivity, a slightly better prediction can be obtained, but the improvement is very limited, illustrating that simply modeling the difference due to molecular diffusivities for differential mixing is not sufficient. In comparison, the RIDM model exhibits superior performance in both a priori and a posteriori tests. Moreover, all the components of the RIDM model are readily available in the TPDF method, making the RIDM model a promising candidate employed in practice.

A priori assessment of flame surface density modelling for large-eddy simulation of sound generation by turbulent premixed flames

This paper presents an a priori assessment of flame surface density modelling in the context of large-eddy simulation (LES), with a focus on flame-generated sound. A direct numerical simulation (DNS) dataset of a stoichiometric premixed, methane-air, round jet flame in the thin reaction zones (TRZ) regime is used to perform this assessment. Models for different parts of the filtered flame front displacement term (ρSd)|∇c|¯ are studied, including those for the surface averaged density weighted displacement speed (ρSd)¯s and flame wrinkling factor models proposed by Charlette at al. (2002), Fureby (2005) and Muppala et al. (2005).In the first step, the wrinkling factor, the flame surface density and their conditional averages with the filtered progress variable are examined. Locally, large deviations of the modelled wrinkling factor from the DNS data are observed, especially near flame annihilation events. Nevertheless, the conditionally averaged flame surface density is predicted well by the Charlette and Fureby models.In the second step, Lighthill’s acoustic analogy is used to assess the models when the time derivative of the filtered flame front displacement term is used as a source. When the wrinkling factor is calculated with the models and (ρSd)¯s is obtained from the DNS, a reasonable agreement is achieved for the unsteady pressure and sound pressure level (SPL) of the generated noise. However, when the exact (ρSd)¯s is replaced with simple models, a significant underprediction of SPL is observed. These results suggest that flame surface density modelling requires significant improvement, particularly for (ρSd)¯s. Furthermore, special attention needs to be paid to flame annihilation events, which feature large variation of the wrinkling factor and flame displacement speed.

On the enhancement of boundary layer skin friction by turbulence: an angular momentum approach

Turbulence enhances the wall shear stress in boundary layers, significantly increasing the drag on streamlined bodies. Other flow features such as free stream pressure gradients and streamwise boundary layer growth also strongly influence the local skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them as torques that alter the shape of the mean velocity profile. This approach uniquely isolates the skin friction of a Blasius boundary layer in a single term that depends only on the Reynolds number most relevant to the flow's engineering context, so that other torques are interpreted as augmentations relative to the laminar case having the same Reynolds number. The AMI equation for external flows shares this key property with the so-called FIK relation for internal flows (Fukagata et al., Phys. Fluids, vol. 14, 2002, pp. L73–L76). Without a geometrically imposed boundary layer thickness, the length scale in the Reynolds number for the AMI equation may be chosen freely. After a brief demonstration using Falkner–Skan boundary layers, the AMI equation is applied as a diagnostic tool on four transitional and turbulent boundary layer direct numerical simulation datasets. Regions of negative wall-normal velocity are shown to play a key role in limiting the peak skin friction during the late stages of transition, and the relative strengths of terms in the AMI equation become independent of the transition mechanism a very short distance into the fully turbulent regime. The AMI equation establishes an intuitive, extensible framework for interpreting the impact of turbulence and flow control strategies on boundary layer skin friction.

Analysis of turbulent flow and thermal structures in low-Prandtl number buoyant flows using direct numerical simulations

A direct numerical simulation (DNS) database is presented for turbulent flow and heat transfer in a vertical channel for Reynolds number Reτ = 150 and 640, Prandtl number Pr = 0.004, 0.025 and 0.71, with and without buoyancy forcing (Ri = 0 and 0.15 or 0.21). The effects of Pr on mean and turbulent flow and thermal transport in mixed convective conditions are discussed. Aiding/opposing buoyant conditions result in acceleration/deceleration of mean flow and reduction/enhancement of turbulence. Flow turbulence is highly anisotropic and dominated by the streamwise component on the aiding side, and becomes two-dimensional on the opposing side with a decrease in Pr. Temperature distributions depend on the relative role of molecular and turbulent thermal transport. The former increases with decreasing Pr and the latter with increasing Re. Buoyancy affects thermal transport through augmentation of the wall-normal turbulent heat flux, v′θ′¯, which is more pronounced for higher Pr. A priori analysis of the DNS datasets shows that a variable formulation for turbulent Prandtl number in Reynolds-averaged Navier-Stokes simulations performs well for both high- and low-Pr flows without buoyancy and in stable convective regimes, but yields relatively high error in unstable convective regimes.

Interpretation and characterization of MILD combustion data using unsupervised clustering informed by physics-based, domain expertise

In this study we use an unsupervised clustering algorithm called Vector Quantization Principal Component Analysis (VQPCA) to characterize Moderate and Intense Low-oxygen Dilution (MILD) combustion. Two direct numerical simulation (DNS) datasets of non-premixed MILD combustion are used and they differ primarily in the oxygen (O2) dilution levels. Maximum volume fraction of O2 for Case-AZ1 is 3.5% (lower dilution) and for Case-BZ1 it is 2.0% (higher dilution). DNS grid points with thermo-chemical information are fed to VQPCA which partitions them into a few clusters. Qualitative and quantitative comparison between VQPCA clusters and structures of physical variables such as mixture-fraction, Z, and heat-release rate, HRR, are used to identify variable for system-level characterization. While qualitative comparison is based on visualization, quantitative comparison is newly developed in this study and is based on Boolean logic. Subsequently, a new physics-based method is proposed to rank important features (or variables) for each cluster. This is useful for a fine-grained characterization of the system. The method is based on calculating the Hellinger distance between the probability density functions (PDF) of each feature conditioned over a cluster and the region outside it. The outcome of physics-based feature ranking method is compared with several feature selection methods based on PCA. Finally, we also demonstrate that through careful selection of features we can tailor clustering outcomes in systems with high dilution, such as like BZ1, where initially no system-level variable was recognized.

Properties of the compressibility and transport motion in wall-bounded turbulent flows at Mach 8

The compressibility effect and transport motion in highspeed turbulent boundary layer (TBL) is a fundamental problem because they dominate the average and statistical characteristics. Using the statistical methods and flow visualization technology, flat-plate TBLs at [Formula: see text] with high- and low-wall temperatures, [Formula: see text] and 1.9, are investigated based on the direct numerical simulation (DNS) datasets. Compared with previous studies, this study considers relative higher Mach number and strong cold wall temperature condition at the same time. First, the turbulent Mach number and turbulent intensity show that the compressibility effects are enhanced by the cooling process. Second, the high-order statistical moments and structure parameters confirm cold wall that causes stronger compressibility and the corresponding increased intensities of local streamwise and wall-normal transport motions. Finally, for uncovering the relationship between the compressibility effect and turbulent transport, more in-depth visualization analyses of velocity streaks are performed. It is found that ‘knot-like’ structures are generated when cooling the wall, and they lead to stronger intermittent, which results in the rapid increase of local compressibility effect and the wall-normal transport motion. Our research sheds light on providing a theoretical basis for further understanding the compressibility effects of TBL at high Mach number.