Direct Numerical Simulation Data Research Articles

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. These observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

A priori tests of eddy viscosity models in square duct flow

We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number {text {Re}}_tau =1055. We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components a_{ij} responsible for turbulent secondary flows, namely the normal stress a_{22} and the secondary shear stress a_{23}. A priori tests on constitutive relations for a_{ij} are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of a_{ij}. We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data {widetilde{C}}_{ij}, which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress a_{12} ({widetilde{C}}_{12}>0.99), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress ({widetilde{C}}_{22}=0.911, {widetilde{C}}_{23}=0.743). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k–varepsilon and v^2–f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the v^2–f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.

DNS analysis of boundary layer flashback in turbulent flow with wall-normal pressure gradient

The presence of swirl in combustion systems produces a marked change in their boundary layer flashback behaviour. Two aspects of swirling flow are investigated in this study: the effect of the swirl-generated wall-normal pressure gradient, and the effect of misalignment between the mean flow direction and the direction of flame propagation. The analysis employs Direct Numerical Simulation (DNS) of fuel-lean premixed hydrogen-air flames in turbulent planar channel flow with friction Reynolds number of 180. The effect of swirl on the flashback process is investigated by imposing a wall-normal pressure gradient profile. Analysis of the DNS data shows how the resulting differences in flow field and flame topology contribute to the differences in the overall flashback speed. Misalignment of the flow and propagation directions leads to asymmetry in the flame shape statistics as streaks of high velocity fluid in the boundary layer cleave into the flame front at an angle, yielding an increase in flame surface density away from the wall. Swirl has a stabilising effect on the turbulent flame front during flashback along the centre-body of a swirling annular flow due to the density stratification across the flame front, and produces a reduction in turbulent consumption speed. However the swirl also sets up a hydrostatic pressure difference that drives the flame forward, and the net effect is that the flashback speed is increased. The dominance of hydrostatic effects motivates development of relatively simple modelling for the effect of swirl on flashback speed. A model accounting for the inviscid momentum balance and for confinement effects is presented which adequately describes the effect of swirl on flashback speed observed in previous experimental studies.

Front propagation formulation for large eddy simulation of turbulent premixed flames

The front propagation formulation (FPF) for large eddy simulation (LES) of turbulent premixed flames is presented and discussed. The FPF method adopts a regularized Dirac delta function to minimize the spurious propagation of under-resolved filtered flame fronts in LES, while reproducing the reaction characteristics of premixed flame fronts. The extension of the FPF method to LES and the relation to existing sub-filter combustion models are discussed. An algebraic model for the regularized Dirac delta function is presented and validated using direct numerical simulation (DNS) data for statistically planar premixed flames propagating in homogeneous isotropic turbulence. A posteriori validation for a filtered 1-D planar laminar flame is performed to demonstrate the characteristics of FPF in reproducing the propagation speed and the thickness of the under-resolved flame front. LES of a turbulent Bunsen flame is also performed to demonstrate the performance of the proposed method.

Transitions in overstable rotating magnetoconvection.

The classical Rayleigh-Bénard convection (RBC) system is known to exhibit either subcritical or supercritical transition to convection in the presence or absence of rotation and/or magnetic field. However, the simultaneous exhibition of subcritical and supercritical branches of convection in plane layer RBC depending on the initial conditions, to the best of our knowledge, has not been reported so far. Here, we report the phenomenon of simultaneous occurrence of subcritical and supercritical branches of convection in overstable RBC of electrically conducting low Prandtl number fluids (liquid metals) in the presence of an external uniform horizontal magnetic field and rotation about the vertical axis. Extensive three-dimensional (3D) direct numerical simulations (DNS) and low-dimensional modeling of the system, performed in the ranges 750≤Ta≤3000 and 0<Q≤1000 of the Taylor number (Ta, strength of the Coriolis force) and the Chandrasekhar number (Q, strength of the Lorenz force), respectively, establish the phenomenon convincingly. Detailed bifurcation analysis of a simple 3D model derived from the DNS data reveals that a supercritical Hopf bifurcation and a subcritical pitchfork bifurcation of the conduction state are responsible for this. The effect of Prandtl number on these transitions is also explored in detail.

Direct numerical simulations of turbulent viscoelastic jets

Direct numerical simulations (DNS) of spatially evolving turbulent planar jets of viscoelastic fluids described by the FENE-P model, such as those consisting of a Newtonian fluid solvent carrying long chain polymer molecules, are carried out in order to develop a theory for the far field of turbulent jets of viscoelastic fluids. New evolution relations for the jet shear-layer thickness , centreline velocity and maximum polymer stresses are derived and validated by the new DNS data, yielding , , and , respectively, where is the coordinate in the streamwise direction. It is shown that, compared with a classical (Newtonian) turbulent jet, the effect of the polymers is to reduce the spreading rate, centreline velocity decay, Reynolds stresses and viscous dissipation rate. The self-preserving character of the flow is analysed and it is shown that profiles of mean velocity, Reynolds stresses and polymer stresses are self-similar provided the proper scales are used in the normalisation of these quantities. A fundamental difference from the Newtonian jet in this regard is the necessity for two, instead of only one, different velocity and length scales to properly characterise the evolution of the turbulent flow. These extra velocity and length scales are directly related to a time scale associated with the characteristic fading memory property of viscoelastic fluids.

Large Eddy Simulation of soot evolution in turbulent reacting flows: Strain-Sensitive Transport Approach for Polycyclic Aromatic Hydrocarbons

Polycyclic Aromatic Hydrocarbons (PAH) are confined to spatially intermittent regions of low scalar dissipation rates due to their slow formation chemistry. The length scales of these regions are on the order of the Kolmogorov scale or smaller, where molecular diffusion dominates over turbulent mixing irrespective of the large-scale turbulent Reynolds number. A strain-sensitivity parameter is proposed to identify such species. A Strain-Sensitive Transport Approach (SSTA) is then developed to model this differential transport in the nonpremixed flamelet equations. Specifically, the strain-sensitive species are modeled with their non-unity molecular effective Lewis numbers, while the remaining species are modeled with unity effective Lewis numbers. An a priori analysis of nonpremixed flamelet solutions reveals that the flame temperature and strain-insensitive species (e.g., major products of combustion, acetylene, etc.) profiles from the proposed SSTA closely match those from the unity effective Lewis number approach, but the mass fractions of strain-sensitive species (e.g., naphthalene) are significantly modified compared to the unity effective Lewis number approach and are consistent with Direct Numerical Simulation (DNS) data. This new SSTA model is implemented within a Large Eddy Simulation (LES) framework, applied to a series of laboratory-scale turbulent nonpremixed sooting jet flames, and validated via comparisons with experimental measurements of temperature and soot volume fraction. Both the unity effective Lewis number approach and SSTA model provide temperature predictions in good agreement with the experimental data, but the non-unity molecular effective Lewis number approach overpredicts the flame length. Compared to the unity effective Lewis number approach, the spatial distribution of soot volume fraction predicted by SSTA is in better agreement with the experimental measurements in terms of the upstream growth of the soot volume fraction and the location of its peak value along the centerline, both of which strongly depend on accurate predictions of the PAH mass fraction. The maximum soot volume fraction is minimally influenced and in good agreement with the experimental measurements. Finally, with this new SSTA model, the influence of global strain rate on turbulent nonpremixed sooting jet flames is analyzed to find that, even though PAH is inversely proportional to the global strain rate, the soot volume fraction may not be inversely proportional to the global strain rate due to an increase in the acetylene surface growth rate coefficient with global strain rate.

Evaluation of mean species mass fractions in premixed turbulent flames: A DNS study

Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent burning are analyzed (by adapting five alternative definitions of combustion progress variable c) in order to examine three different models that (i) are based on the flamelet paradigm and (ii) aim at evaluating mean concentrations of various species in applied CFD research into turbulent combustion. Mean mole fractions of all considered species and mean density are predicted if the laminar-flame profiles of species mole fractions and density, respectively, are directly averaged using a Probability Density Function (PDF) P(c). The best predictions are obtained by extracting P(c) from the DNS data and defining c based on hydrogen mass fraction. These predictions suggest that mean mole fractions of various species in a premixed turbulent flame can be evaluated at a post-processing stage of a CFD study by adopting P(c), obtained at the major stage of the simulations, to average a flamelet library. When applied in such a way, the flamelet paradigm is useful even for lean hydrogen-air flames and even at Karlovitz number as large as 13. If the same PDF is applied to average reaction rates from the same flamelet library, the mean rates of production/consumption of species n are poorly predicted, e.g. for radicals H, O, OH, HO2, and H2O2 if c is defined using hydrogen mass fraction. A hypothesis that conditioned rates 〈Wn|c〉 can be predicted using conditioned mole fractions 〈Xn|c〉, temperature 〈T|c〉, and density 〈ρ|c〉 is not supported either, e.g. for radicals O and OH. These differences between predictive capabilities of the first approach (directly averaging concentration profiles) and two other approaches (averaging reaction rates) are attributed to weakly (highly) non-linear dependencies of the concentrations (rates, respectively) on c.

A New Mathematical Framework for Describing Thin-Reaction-Zone Regime of Turbulent Reacting Flows at Low Damköhler Number

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent flow in the case of a low Damköhler number. In the cited paper, the theory is also supported by Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent premixed combustion is argued. The present work aims at complementing the theory with a new mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c ( x , t ) is considered to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c ( x , t ) &lt; 1 , where molecular transport plays an important role, and (ii) equilibrium products, c ( x , t ) = 1 . The two zones are separated by an infinitely thin reaction sheet, where c ( x , t ) = 1 and | ∇ c | is fixed in order for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable, its second moment, and instantaneous characteristic functions. Averaging of these equations yields exact, unclosed transport equations for the conditioned reaction-progress-variable moments and Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet. The closure problem for the derived equations is beyond the scope of the paper.

Analysis of wall-pressure fluctuation sources from direct numerical simulation of turbulent channel flow

The sources of wall-pressure fluctuations in turbulent channel flow are studied using a novel framework. The wall-pressure power spectral density (PSD) $(\phi_{pp}(\omega))$ is expressed as an integrated contribution from all wall-parallel plane pairs, $\phi_{pp}(\omega)=\int_{-\delta}^{+\delta}\int_{-\delta}^{+\delta}\Gamma(r,s,\omega)\,\mathrm{dr}\,\mathrm{ds}$, using the Green's function. Here, $\Gamma(r,s,\omega)$ is termed the net source cross spectral density (CSD) between two wall-parallel planes, $y=r$ and $y=s$ and $\delta$ is the half channel height. Direct Numerical Simulation (DNS) data at friction Reynolds number of $180$ and $400$ are used to compute $\Gamma(r,s,\omega)$. Analysis of the net source CSD, $\Gamma(r,s,\omega)$ reveals that the location of dominant sources responsible for the premultiplied peak in the power spectra at $\omega^+\approx 0.35$ and the wavenumber spectra at $\lambda^+\approx 200$ is in the buffer layer at $y^+\approx 16.5$ and $18.4$ for $Re_{\tau}=180$ and $400$, respectively. The contribution from a wall-parallel plane (located at distance $y^+$ from the wall) to wall-pressure PSD is log-normal in $y^+$ for $\omega^+>0.35$. A dominant inner-overlap region interaction of the sources is observed at low frequencies. Further, the decorrelated features of the wall-pressure fluctuation sources are analyzed using spectral Proper Orthogonal Decomposition (POD). We require the modes to be orthogonal in an inner product with a symmetric positive definite kernel. Spectral POD supports the case that the net source is composed of two decorrelated components - active (dominant mode) and inactive (remaining modes). The structure represented by the dominant POD mode at the premultiplied wall-pressure PSD peak inclines in the downstream direction. At the low-frequency linear PSD peak, the dominant mode resembles a large scale vertical pattern.

A Numerical Investigation of the Minimum Ignition Energy Requirement for Forced Ignition of Turbulent Droplet-laden Mixtures

ABSTRACT The effects of droplet diameter, overall (i.e. liquid and gaseous phases) equivalence ratio, and turbulence intensity on the variation of the Minimum Ignition Energy (MIE) for localized forced ignition of uniformly dispersed mono-sized n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on Direct Numerical Simulation (DNS) data. The MIE was evaluated just for (i) obtaining thermal runway irrespective of the fate of the resulting flame kernel, and (ii) also for a successful self-sustained flame propagation without the assistance of an external energy source following the energy deposition by the ignitor. It has been found that the MIE requirement increases with increasing turbulence intensity and this trend for the MIE increase is especially significant for large values of turbulence intensity. The MIE requirement increases with increasing initial droplet diameter and with decreasing overall equivalence ratio. The MIE requirements for droplet-laden mixtures have been found to be greater than the corresponding value for homogeneous mixture with the same nominal values of initial turbulence intensity and equivalence ratio for the parameter range considered here. This behavior arises due to the deposited energy being partially utilized to supply the latent heat of evaporation and also due to the predominantly fuel-lean composition of the gaseous flammable mixture. This tendency of obtaining fuel-lean mixture strengthens with increasing (decreasing) initial droplet diameter (overall equivalence ratio). It has also been demonstrated that combustion takes place predominantly in the fuel-lean premixed mode although there is a finite probability of having non-premixed combustion in all cases. Moreover, there is a small probability of fuel-rich combustion occurring for small droplets, especially under fuel-rich overall equivalence ratios. The stochastic nature of the ignition event has been demonstrated by considering different realizations of statistically similar turbulent flow fields. The conditions giving rise to a successful thermal runaway/self-sustained flame propagation have been identified by a detailed analysis of the energy budget.

Improved Law-of-the-Wall Model for Turbulent Boundary Layer in Engineering

Accurate prediction of mean velocity in turbulent boundary layer is an important topic from the standpoints of both physics and engineering. In the current study, a unified form of law of the wall is proposed for the mean streamwise velocity in the turbulent boundary layer with zero pressure gradient. From the physical perspective, the improved form of the law is capable of reflecting the actual weight variations between the molecular viscosity and the turbulence-eddy viscosity in the viscous, transition, and logarithmic sublayers. In the viscous sublayer, a variety of direct numerical simulation (DNS) data, including 19 groups, are used to examine the proposed law. In the transition and logarithmic sublayers, 19 groups of canonical DNS velocity profiles and 14 groups of reliable experimental data are used to confirm the applicability and accuracy of the present formula under a wider ranges of Reynolds numbers. The local and maximum relative errors are given and analyzed in detail. The results show that the improved form of the law is sufficiently accurate to represent the mean streamwise velocities in the viscous, transition, and logarithmic sublayers. The present work is helpful for prediction of mean velocity behaviors in engineering.

Statistical Analysis and Verification of a New Premixed Combustion Model with DNS Data

ABSTRACT In this paper, a new analytical premixed flamelet pdf model based on a surrogate reaction source term, is verified with a planar laminar flame and validated using explicitly filtered direct numerical simulation (DNS) data of statistically planar turbulent premixed flames with single-step irreversible Arrhenius chemistry at two different Karlovitz numbers. It is shown that the modeled filtered reaction source term is in excellent agreement with the one using the Arrhenius source term for the planar laminar flame over a wide range of filter widths. The model performs also very well on the filtered turbulent DNS data provided that a flame normalized isosurface area is incorporated. Interestingly, the model performance improves with increasing filter widths. This makes it an ideal candidate for high-pressure premixed combustion where usually the filter widths are much larger than the flame’s thermal reaction zone thickness .

Reduced-order modelling of radiative transfer effects on Rayleigh–Bénard convection in a cubic cell

This paper presents a reduced-order modelling strategy for Rayleigh-Benard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh-Benard cell is performed for an air/H 2 O/CO 2 mixture at room temperature and at a Rayleigh number of 10 7. It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary-layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of π/2 of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an a priori model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.

Evaluation of a Neural Network-Based Closure for the Unresolved Stresses in Turbulent Premixed V-Flames

Data-driven modelling in fluid mechanics is a promising alternative given the continuous increase of computational power and data-storage capabilities. Highly non-linear flows which include turbulence and reaction are challenging to model, and accurate algebraic closures for the unresolved terms in large eddy simulations of such flows are difficult to obtain. In this study, an artificial neural network is developed in order to directly model an important unclosed term namely the unresolved stress tensor. The performance of this approach is evaluated a priori using direct numerical simulation data of a highly demanding flow configuration, a turbulent premixed V-flame, and compared against the predictions of eight other classic models in the literature which include both static and dynamic formulations.

DNS of turbulent flat-plate flow with transpiration cooling

Transpiration cooling in a turbulent boundary layer on a flat plate is investigated using direct numerical simulations (DNS). The simulations are performed by solving the compressible Navier-Stokes equations at low Mach number conditions (M∞=0.3). Both the coolant and the hot gas are air, with isothermal walls and coolant at a temperature of Tw/T∞=0.5, while the blowing ratio and boundary conditions have been varied. These simulations elucidate the turbulence and heat-flux alterations due to the interaction of the coolant with the hot-gas boundary layer. By increasing the blowing ratio, the peak turbulent kinetic energy moves away from the wall to a region of shear between the low-momentum coolant and high-momentum hot gas. The reduction of the wall heat transfer is caused by the combined effects of heat advection due to the non-zero wall-normal velocity at the wall, and the reduction of the average boundary-layer temperature due to the accumulation of coolant. A new model for the latter effect is proposed which is physically realistic in the limit cases. The proposed combined model accounts for both heat advection and film accumulation and shows good agreement with the DNS data. An increase in turbulent transport of heat with increasing blowing rate is caused by the production of vortices between the coolant and hot gas. This causes a reduction in the cooling effectiveness, and can be seen near the leading edge of the transpiration region. In order to investigate wall modelling effects, simulations with uniform coolant injection have been compared to simulations with injection via many small strips. It is observed that as the strips get smaller (at fixed total mass flow rate and fixed wall porosity), the results trend towards the uniform injection case. Therefore, it is hypothesized that for small pore sizes, neglecting the effects of the individual pores in the wall boundary condition is physically justifiable.

Data-driven surrogate modeling of multiphase flows using machine learning techniques

This study focuses on the development of a theoretical framework and corresponding algorithms to establish spatio-temporal surrogate models for multiphase flow processes using Gaussian process (GP) based machine learning technique trained by direct numerical simulation (DNS) data. The training (and testing) datasets are obtained by solving the incompressible form of the Navier Stokes equations with surface tension in an Eulerian reference frame. The liquid-gas interfacial evolution is resolved using a volume-of-fluid (VOF) interface capturing method. The overall framework proceeds in four steps: 1) design of experiments study to identify the training and testing points and generation of corresponding datasets using DNS calculations; 2) dimensionality reduction using proper orthogonal decomposition; 3) Gaussian process regression (supervised training) over the reduced training dataset over the entire range of operating conditions under consideration; and 4) Galerkin reconstruction and error quantification by comparing the emulated flowfields (at test conditions) with the testing dataset. The machine learning framework predicts both the spatial basis-functions and the time-coefficients, thus, predicting the entire flowfield in time and space. The capabilities of the algorithm are demonstrated for two canonical flow configurations: 1) flow over a circular cylinder for a range of Reynolds numbers from 10 to 200; and 2) diesel jet injected into a quiescent nitrogen environment at chamber pressure of 30 atm and room temperature conditions, and injection velocities from 10 to 55 m/s, corresponding to a range of gas-based Weber numbers from 11.5 to 348. The emulations from the learned GP algorithm show excellent agreement with high-fidelity numerical data for test conditions; average error (in both space and time) at the testing point of Re = 185 for the flow over cylinder case is 4.4%, and for the diesel jet injection configuration at a testing point corresponding to velovity of 22.5 m/s is found to be 15.5%. The tip penetration location of the diesel jet is predicted within 2.5% of the DNS calculations. Corresponding to these two representative test points, speedup of 256 and 8000 is achieved for flow over cylinder and diesel jet atomization configurations, respectively. This paper represents the first effort of its kind on the development of a general machine learning framework to predict multiphase flows.

Lewis Number Effects on Flame Speed Statistics in Spherical Turbulent Premixed Flames

The influences of characteristic Lewis number hbox{Le} on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for hbox{Le} = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing hbox{Le} , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on hbox{Le} , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the hbox{Le} = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the hbox{Le} = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

Effect of Pulsation and Acceleration of Liquid Metal Turbulent Flow Through a Horizontal Channel by Large Eddy Simulation

Abstract Pulsation and acceleration of liquid metal turbulent flow through a horizontal channel has been numerically studied using a large eddy simulation (LES) technique. The effect of inlet pulsation and acceleration on flow and heat transfer characteristics of low Prandtl number liquid metal flow have been investigated and reported here. Results have been presented for different Reynolds numbers, different amplitudes, and frequency with constant bottom wall thickness. The flow field is modeled as unsteady-state two-dimensional incompressible turbulent-forced convection flow. Turbulence is modeled using a LES technique. Two-dimensional unsteady-state heat conduction equation is solved to know the temperature distribution in the solid region. Finite difference method solver is developed for solving the governing equations using sixth-order accuracy of compact schemes. The average Nusselt number shows cyclic variation with respect to time in pulsation flows. The enhancement of heat transfer with pulsation at amplitude 0.4 and frequency 100 Hz is 6.51%. The rate of heat transfer increases in pulsation flow compared to quasi-steady flow. The inlet acceleration shows a significant effect on flow characteristics. The present results are compared with direct numerical simulation (DNS) results available in the literature and matching well with DNS data.