Direct Numerical Simulation Data Research Articles

Effects of Fuel Lewis Number on Wall Heat Transfer During Oblique Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The influence of fuel Lewis number {mathrm{Le}}_{F} on the statistical behaviour of wall heat flux and flame quenching distance has been analysed using direct numerical simulation (DNS) data for the turbulent V-shaped flame-wall interaction in a channel flow configuration corresponding to a friction velocity-based Reynolds number of 110 for fuel Lewis number, {mathrm{Le}}_{F}, ranging from 0.6 to 1.4. It has been found that the maximum wall heat flux magnitude in turbulent V-shaped flame-wall interaction increases with decreasing {mathrm{Le}}_{F} but just the opposite trend was observed for 2D laminar V-shaped flame-wall interaction and 1D laminar head-on quenching cases. This behaviour has been explained in terms of the correlation of temperature and fuel reaction rate magnitude with local flame surface curvature for turbulent flames due to the thermo-diffusive effects induced by the non-unity Lewis number. The wall heat flux magnitude and wall shear stress magnitude are found to be negatively correlated for all cases considered here. Moreover, their mean variations in the streamwise direction are qualitatively different irrespective of {mathrm{Le}}_{F}, although the magnitudes of wall heat flux and wall shear stress increase with decreasing {mathrm{Le}}_{F}. Furthermore, the flame alignment relative to the wall also affects the wall heat flux and it has been found that local occurrences of head-on quenching can lead to higher magnitudes of wall heat flux magnitude. It has been found that {mathrm{Le}}_{F} also affects the evolution of the flame quenching distance in the streamwise direction with the progress of flame quenching for different flame normal orientations with respect to the wall. This analysis shows that the effects of fuel Lewis number on flame orientation, correlations of reaction rate and temperature with local flame curvature and coherent flow structures within the turbulent boundary layer ultimately affect the wall heat transfer and flame quenching distance. Thus, the thermo-diffusive effects arising from the non-unity Lewis number need to be taken into account for accurate modelling of wall heat transfer during flame-wall interaction in turbulent boundary layers.

Super-resolution reconstruction for the three-dimensional turbulence flows with a back-projection network

Recent attempts to employ deep learning technology for the super-resolution (SR) reconstruction of turbulence have focused chiefly on reconstructing two-dimensional (2D) slices of the three-dimensional (3D) flow fields. However, tomographic particle image velocimetry (Tomo-PIV) measurements yield 3D velocity fields. The resolutions of 3D velocity field data along three directions cannot be simultaneously enhanced using a 2D SR reconstruction model. Additionally, a 3D velocity flow field structure cannot be accurately reconstructed using a 2D model. Therefore, we present a 3D flow field SR reconstruction method (FSR-3D) based on a back-projection network. The FSR-3D model incorporates a multiscale convolutional residual block and an up-and-down projection module and establishes the mapping relationship between low-resolution features and high-resolution (HR) features through an iterative mechanism. The proposed model is validated using two experiments. First, the original velocity field is reconstructed from downsampled forced isotropic turbulence data. Second, the downsampled direct numerical simulation (DNS) data of a turbulent channel flow are used to reconstruct the HR flow field to verify the reconstruction capability of the FSR-3D model with respect to the flow field of the boundary layer. Third, Tomo-PIV measurements of the wake flow behind a circular cylinder are used to further verify the generalization ability of the model and the reconstruction effect of the measured data. The experimental results demonstrate that the proposed FSR-3D model can accurately reconstruct the HR 3D velocity field. At the same time, the properties of the reconstruction results, such as their vortex structure, kinetic energy spectrum, and Reynolds stress, are closer to the DNS results than those of the 2D model. The reconstruction results of the Tomo-PIV measurement data show that the FSR-3D model has good generalization ability.

A priori assessment of nonlocal data-driven wall modeling in large eddy simulation

In the present study, a priori assessment is performed on the ability of the convolutional neural network (CNN) for wall-modeling in large eddy simulation. The data used for the training process are provided by the direct numerical simulation (DNS) of the turbulent channel flow. Initially, a study is carried out on the input choices of CNN, and the effect of different flow parameters on establishing a wall model is investigated. Then, the influence of the wall-normal distance on the established data-driven wall model is studied by choosing the CNN input data from two regions of the inner layer (y+>10,y/δ<0.1) and the logarithmic layer. The performance of the obtained CNN wall models based on the inputs from the two regions is further investigated by feeding the network with the data outside the training range. In the next step, the models are tested under various conditions, including a different grid size and a higher Reynolds number. The results show that the models using the inner layer (excluding y+≤10) data as the CNN input have better accuracy in establishing a wall model compared to the models based on the input data in the logarithmic layer, especially when implemented outside the training range. After optimizing the hyperparameters of CNN, a high correlation coefficient of 0.9324 is achieved between the wall shear stress calculated using the filtered DNS data and predicted by the best CNN wall model, which is trained using the data in the inner layer, excluding y+≤10. The performance of the CNN wall model is also compared with the existing wall-stress models, and it is shown that the CNN wall model has better accuracy in establishing a wall model. Additionally, the CNN wall model is shown to have good performance when applied to a different grid size or a higher Reynolds number.

Influence of small-scale turbulence on internal flamelet structure

Direct numerical simulation data obtained from a highly turbulent (Kolmogorov length scale is less than a laminar flame thickness by a factor of about 20) lean hydrogen–air complex chemistry flame are processed, with the focus of the study being placed on flame and flow characteristics conditioned to instantaneous local values cFx,t of the fuel-based combustion progress variable. By analyzing such conditioned quantities, the following two trends are documented. On the one hand, magnitudes of fluctuations of various local flame characteristics decrease with increasing the combustion progress variable, thus implying that the influence of small-scale (when compared to the laminar flame thickness) turbulence on internal flamelet structure is reduced as the flow advance from unburned reactants to combustion products. On the other hand, neither local turbulence characteristics (conditioned rms velocities, total strain, and enstrophy) nor local characteristics of flame–turbulence interaction (flame strain rate) decrease substantially from the reactant side to the product side. To reconcile these two apparently inconsistent trends, the former is hypothesized to be caused by the following purely kinematic mechanism: residence time of turbulence within a large part of a local flamelet is significantly shortened due to combustion-induced acceleration of the local flow in the direction normal to the flamelet. This residence-time reduction with increasing cF is especially strong in the preheat zone (cF<0.3) and the residence time is very short for 0.3<cF<0.8. Therefore, small-scale turbulence penetrating the latter zone is unable to significantly perturb its local structure. Finally, numerical results that indirectly support this hypothesis are discussed.

A wall model learned from the periodic hill data and the law of the wall

Toward data-driven wall-modeled large-eddy simulations of different wall-bounded turbulent flows, a wall model is learned in this work using the wall-resolved large-eddy simulation (WRLES) data of the flow over periodic hills (PH) and the law of the wall (LoW). The feedforward neural network (FNN) is employed to construct the model. The obtained FNN_PH-LoW model is successfully tested using the direct numerical simulation data of turbulent channel flows and the WRLES data of PH cases, and applied to turbulent channel flows for a wide range of Reynolds numbers.

Direct numerical simulation of flow and heat transport in a closely-spaced bare rod bundle

Direct Numerical Simulation (DNS) of fully-developed flow and heat transfer is performed for a bare rod bundle with a low pitch-to-diameter ratio using the highly-scalabale spectral element code Nek5000. The simulation is performed at a Reynolds number, Reh, based on the bulk velocity and hydraulic diameter, of 9800, with iso-temperature and iso-flux thermal boundary conditions and Prandtl numbers 0.025, 1.0 and 2.0. The mean velocity and temperature statistics are first validated against the experimental measurements of Hooper et al. (1983) and complementary DNS results of Lai et al. (2019) which are reported in the literature at a higher Reh of 22,600. The mean flow and temperature are demonstrated a similar behaviour at the present low Renolds number and the higher Reynolds number of Lai et al. (2019), indicating the Reynolds number scaling of the mean flow. The anisotropy of the flow is illustrated using distribution of normal and Reynolds stresses, and the Lumley invariant map. It is shown that the turbulence in the subchannel region is characteristic of wall-bounded turbulent flows such as channel flows. In the narrow gap, however, turbulence is suppressed, only enhanced in the streamwise direction due to flow pulsations. Further, temperature statistics with both thermal boundary conditions are presented, demonstrating the effect of the Prandtl number on the mean and fluctuating quantities. The temperature statistics with iso-temperature wall boundary conditions, not reported in literature before, are shown to behave differently in the interstitial subchannel region and the narrow gap between two rods. The distribution of turbulent heat flux is also presented. The streamwise component of turbulent heat flux is again shown to be enhanced, in comparison to the same in the subchannel. The pulsating motion of flow across the narrow gap is discussed further. A frequency analysis of the velocity in the narrow gap elucidates the frequency of flow pulsations. Unlike mean flow statistics, the flow pulsations are shown to exhibit a low Reynolds number effect. The reference DNS data presented in the present work, complementary to that of Lai et al. (2019), serves as a benchmark against which lower order turbulence models may be further developed or improved. In particular, the newly presented anisotropy data and the turbulence heat flux data are essential for further development, improvement and validation of turbulent heat transfer models at different Prandtl numbers.

Post-shock turbulence recovery in oblique-shock/turbulent boundary layer interaction flows

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.

Displacement speed, flame surface density and burning rate in highly turbulent premixed flames characterized by low Lewis numbers

Direct numerical simulation data obtained from four pairs of turbulent, lean hydrogen–air, complex-chemistry flames are analysed to explore the influence of molecular diffusion on flame surface density, displacement speed $S_d$ and the flame surface density transport equation terms. Each pair involves (i) a flame where mixture-averaged molecular diffusivities are adopted and Lewis number $Le$ is significantly less than unity and (ii) an equidiffusive flame where all molecular diffusivities are set equal to molecular heat diffusivity of the mixture and $Le=1$ , with other things being equal. Reported results show that significantly higher turbulent burning rates simulated in the former flames result mainly from an increase in the local fuel consumption rate, whereas an increase in flame surface area plays a secondary role, especially in more intense turbulence. The rate increase stems from (i) an increase in the peak local fuel consumption rate and (ii) an increase in a width of a zone where the rate is significant. The latter phenomenon is of more importance in richer flames and both phenomena are most pronounced in the vicinity of the flame leading edges, thus indicating a crucial role played by the leading edge of a premixed turbulent flame in its propagation. Moreover, mean displacement speed differs significantly from the laminar flame speed even in the equidiffusive flames, varies substantially across flame brush and may be negative at the leading edges of highly turbulent flames.

Turbulence control in plane Couette flow using low-dimensional neural ODE-based models and deep reinforcement learning

The high dimensionality and complex dynamics of turbulent flows remain an obstacle to the discovery and implementation of control strategies. Deep reinforcement learning (RL) is a promising avenue for overcoming these obstacles, but requires a training phase in which the RL agent iteratively interacts with the flow environment to learn a control policy, which can be prohibitively expensive when the environment involves slow experiments or large-scale simulations. We overcome this challenge using a framework we call “DManD-RL” (data-driven manifold dynamics-RL), which generates a data-driven low-dimensional model of our system that we use for RL training. With this approach, we seek to minimize drag in a direct numerical simulation (DNS) of a turbulent minimal flow unit of plane Couette flow at Re=400 using two slot jets on one wall. We obtain, from DNS data with O(105) degrees of freedom, a 25-dimensional DManD model of the dynamics by combining an autoencoder and neural ordinary differential equation. Using this model as the environment, we train an RL control agent, yielding a 440-fold speedup over training on the DNS, with equivalent control performance. The agent learns a policy that laminarizes 84% of unseen DNS test trajectories within 900 time units, significantly outperforming classical opposition control (58%), despite the actuation authority being much more restricted. The agent often achieves laminarization through a counterintuitive strategy that drives the formation of two low-speed streaks, with a spanwise wavelength that is too small to be self-sustaining. The agent demonstrates the same performance when we limit observations to wall shear rate.

Backscatter of scalar variance in turbulent premixed flames

To explore the direction of inter-scale transfer of scalar variance between subgrid scale (SGS) and resolved scalar fields, direct numerical simulation data obtained earlier from two complex-chemistry lean hydrogen–air flames are analysed by applying Helmholtz–Hodge decomposition (HHD) to the simulated velocity fields. Computed results show backscatter of scalar (combustion progress variable$c$) variance, i.e. its transfer from SGS to resolved scales, even in a highly turbulent flame characterized by a unity-order Damköhler number and a ratio of Kolmogorov length scale to thermal laminar flame thickness as low as 0.05. Analysis of scalar fluxes associated with the solenoidal and potential velocity fields yielded by HHD shows that the documented backscatter stems primarily from the potential velocity perturbations generated due to dilatation in instantaneous local flames, with the backscatter being substantially promoted by a close alignment of the spatial gradient of mean scalar progress variable and the potential-velocity contribution to the local SGS scalar flux. The alignment is associated with the fact that combustion-induced thermal expansion increases local velocity in the direction of$\boldsymbol {\nabla } c$. These results call for development of SGS models capable of predicting backscatter of scalar variance in turbulent flames in large eddy simulations.

Investigation of the mixing inside the confined impinging jet mixer using the Fokker–Planck mixing model

Confined Impinging Jet Mixers (CIJMs) are widely used due to their small-scale-mixing efficiency. This property makes them especially useful for nanoprecipitation. The CIJM process parameters are computationally expensive to predict when using direct-numerical simulation (DNS) and large-eddy simulation (LES). In this work, binary nonreactive mixing of a CIJM is studied using a CFD approach with less computational cost than DNS and LES. The flow field is modelled using Reynolds-averaged Navier–Stokes (RANS) equations and molecular mixing is studied using the Fokker–Planck (FP) molecular-mixing model. The extended quadrature method of moments and generalized quadrature method of moments approaches with β kernel density functions are used to approximate the solution to the evolution of the univariate composition. The results of the flow simulation are compared to experimental and DNS data reported in the literature at various inlet flow rates. Multiple closure models for RANS simulation were investigated in this study. The model that produced the most favorable results was the Launder–Reece–Rodi (LRR) turbulence model due to its ability to handle flow separation and complex vortical structures. The FP mixing model was then employed to resolve the probability density function of a univariate composition to determine the efficacy of mixing at the molecular level for different inlet flow rates. The model used in this study is less computationally expensive than DNS and LES and is shown to be sufficient to accurately capture nanoparticle mixing. Thus, the present work provides a framework for industrial improvement to nanoparticle mixing processes using numerical analysis.

A Note on Friction Velocity and Viscous Effect for Idealized Urban Canopy Flows

Friction velocity is one of the important scaling parameters in atmospheric boundary layer studies. However, several definitions of friction velocity exist in the literature: e.g. estimated from the total drag force or used only pressure drag, etc. In this study, a series of large-eddy simulation (LES) calculations were carried out to evaluate the impact of various definitions on the friction velocity for idealized urban geometries, i.e. staggered array of cubes with different packing densities and wind directions. We first compared the normalized velocity fields with the literature data for the case with a packing density of $$25\%$$ . The results show that the LES data normalized by the friction velocity derived from the Reynolds stress using the extrinsic spatial average is more consistent with the direct numerical simulation data. Furthermore, when varying the wind direction, the distribution of Reynolds stress and pressure drag show significant change in streamwise and spanwise directions. We further found that for packing density of $$44.44\%$$ , the frictional drag accounts for more than a quarter of the total drag, and even higher than the pressure drag in parallel wind direction. This leads to the deviation of friction velocity estimated from the pressure drag and that calculated from the total drag force up to 33%. Such characteristic of viscous effect challenges the assumption widely used in wind tunnel experiments and urban canopy parameterizations that the contribution of viscous force is negligible, especially for ultra-dense arrays.

On the origin of spanwise vortex deformations during the secondary instability stage in compressible mixing layers

The three-dimensionality of turbulence initiates with spanwise vortex deformations associated with the amplification of three-dimensional disturbance modes. However, the origin of spanwise vortex deformations is still not well understood. In this paper, compressible mixing layers are performed via direct numerical simulation (DNS). Two typical types of secondary instabilities producing spanwise vortex deformations are of consideration: fundamental instability and subharmonic instability. Based on the fast Fourier transform and DNS data, a low-rank velocity model v0 is obtained to demonstrate that spanwise vortex deformations are originated from a linear superposition of fundamental norm mode, a pair of fundamental or subharmonic oblique modes, and the mean mode. Through observing flow structures of the above norm and oblique modes, a striking feature is found that the velocity model v0 containing deformed spanwise vortices can be decomposed into three new velocity models v1, v2, and v3 containing relatively simplified counterparts (spanwise or oblique vortices). Then, the instability mechanism of the latter vortices is explored by analyzing the position relationship between the function of the generalized inflection points and cores of relatively simplified vortices. We find that an inviscid inflectional instability mechanism is responsible for the formation of spanwise and oblique vortices. Based on the above findings, a view is first proposed that spanwise vortex deformations with aligned and staggered patterns are a joint result of the parametric resonant mechanism and the inviscid inflectional instability mechanism.

A Wavenumber–Frequency Spectrum Model for Sheared Convective Atmospheric Boundary Layer Flows

Abstract Parameterizing turbulence in the atmospheric boundary layer as a function of space and time is essential for weather and climate models. Here, we explore a model for wavenumber–frequency spectra based on a linear random advection approach to characterize sheared convective atmospheric boundary layer flows. Building on previous works, we obtain the wavenumber–frequency spectrum as a product of the wavenumber spectrum and a Gaussian frequency distribution, whose mean and variance are given by the mean advection and random sweeping velocities, respectively. The applicability of the model is tested with direct numerical simulation data in the mixed layer and the entrainment zone for the streamwise and vertical velocity components and buoyancy. To obtain a fully analytical model, we propose using a von Kármán wavenumber spectrum parameterized by the characteristic variances and integral length scales. These parameters are height dependent and vary considerably with the relative balance of buoyancy and shear forces. The introduced analytical model relies on fitting parameters obtained from numerical data in the relevant range of scales. The comparison of the von Kármán–based spectra for velocity and buoyancy to simulation results shows that the main features of the measured spectra are captured by the model.

An integral method to determine mean skin friction in turbulent boundary layers

This study is concerned with accurately determining the mean skin friction in a zero-pressure-gradient turbulent boundary layer. By assuming a linear relation for the weighted total shear stress in the near-wall region, an integral method to evaluate the skin friction is proposed. The method requires the wall-normal profiles of the mean streamwise velocity and Reynolds shear stress within the range of y/δ≤0.4 at only one streamwise location, where δ is the boundary layer thickness. A number of direct numerical simulation and experimental data available in the literature are employed to validate the accuracy of the method over a wide range of Reynolds numbers. The skin friction coefficient obtained using the proposed method is found to be within ±4% in agreement with the published values in both the smooth- and rough-wall turbulent boundary layers. A comparison of the present approach with several existing methods is presented, showing that the proposed skin friction relation is robust and accurate.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Numerical prediction of turbulent flow and heat transfer in buoyancy-affected liquid metal flows

The present paper investigates the capabilities of some selected Reynolds-Averaged Navier Stokes (RANS) based turbulence models in reproducing liquid metals thermal hydraulics Direct Numerical Simulation (DNS) data. For this purpose, forced and mixed convection conditions, both addressing buoyancy-aided and buoyancy-opposed flow, are considered. The paper mainly focuses on velocity and temperature fields estimation, providing a comparison between the RANS and DNS computations. The capabilities of the turbulence models are discussed with the aim to highlight which ones provide the best predictions.In particular, attention is paid to the approach adopted for the calculation of the turbulent heat flux contributions. Together with models assuming the commonly adopted Simple Gradient Diffusion Hypothesis (SGDH) approach and the Reynolds analogy, a model including the Algebraic Heat Flux Model (AHFM) approach is considered. While being a practical and robust approach to deal with turbulent heat fluxes, the SGDH approach shows intrinsic limitation in dealing with liquid metal thermal hydraulics, mainly because of their low-Prandtl number. The adoption of a more advanced AHFM method may instead relevantly improve the quality of the obtained predictions.The obtained results show that the selected model adopting the AHFM method provides definitively better predictions of the addressed phenomena with respect to the ones considering the SGDH approach. While some discrepancies are still observed for the velocity fields, the temperature fields are captured very well, suggesting a clear superiority of the AHFM model. The present paper thus provides further validation and supports the use of AHFM as a valuable tool to predict turbulent heat fluxes.

Direct numerical simulation of one-sided forced thermal convection in plane channels

We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to ${Re}_{\tau } \approx 2000$ are considered, and Prandtl numbers from ${Pr}=0.025$ to ${Pr} = 4$ , the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be $k_{\theta } = 0.459$ . Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately $20\,\%$ at unit Prandtl number; however, it can become much more significant at low Prandtl number.

Modeling of Turbulent Convective Heat-Transfer Characteristics in a Concentric Annular Channel

Turbulent convective heat-transfer characteristics in a concentric annular channel with both walls heated are theoretically modeled and numerically computed in this article. Generalized algebraic predictive models and equations for heating over a single wall are first reviewed by summarizing the well-known methods in the literature. These methods are then scrutinized according to the most recent investigations such that new viewpoints and corrections are introduced accordingly. Moreover, the application of superposition in temperature is used in the current work instead of the Nusselt number as seen in the literature. The numerical integration method is applied to the generalized equations to obtain the solutions, which are found to be in decent agreement with the direct numerical simulation (DNS) data in the literature. The results in this work also indicate that the wall heat flux density ratio and the annular radius ratio are two key factors that have a great influence on the heat-transfer characteristics of the case with both walls heated.

Flamelet LES of a turbulent non-premixed cool flame

Turbulence, low-temperature reactivity, and their couplings as turbulent cool flames are crucial to modern engine designing and low-carbon fuel development. While the flamelet method is a promising solution to turbulent combustion, its applicability and accuracy to cool flames have not been thoroughly comprehended. The objective of the present study is to explore the capability of the steady flamelet method in large eddy simulation (LES) of turbulent cool flames. A laminar counterflow non-premixed cool flame configuration is first simulated on a 2-dimensional grid, showing the good validity of flamelet library setup and table interpolation of the method. Then the application to full-scale turbulent cases of cool combustion is presented with the comparison to the experimental measurements and the referenced direct numerical simulation (DNS) data. This is the first LES of a turbulent cool flame, and the result demonstrates the ability of the method in capturing the mean and variance trends for the temperature, mixture fraction and formaldehyde with good quantitative agreement. Meanwhile, conditional result analysis also shows that this approach in a two-stream flamelet form can describe the three-stream experimental system reasonably well. On this basis, three well-documented reaction mechanisms are employed to examine their performances in flamelet LES of turbulent cool flames. The result reveals that the choice of the chemistry scheme does alter the time-averaged prediction of temperature and formaldehyde, whereas the variance profiles of formaldehyde and mixture fraction are not significantly influenced.