Large Eddy Simulation Formulation Research Articles

Alya toward exascale: algorithmic scalability using PSCToolkit

In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier–Stokes equations. We developed a software module in the Alya’s kernel to interface the libraries included in the current version of PSCToolkit, a framework for the iterative solution of sparse linear systems, on parallel distributed-memory computers, by Krylov methods coupled to Algebraic MultiGrid preconditioners. The Toolkit has undergone various extensions within the EoCoE-II project with the primary goal of facing the exascale challenge. Results on a realistic benchmark for airflow simulations in wind farm applications show that the PSCToolkit solvers significantly outperform the original versions of the Conjugate Gradient method available in the Alya’s kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code toward exascale.

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

Mathematical formulation of large eddy simulation using hybrid finite difference methods and poisson equations

This study uses the hybrid finite-difference method (HFDM), which combines the finite-difference and spectral approaches, to describe the Magnetohydrodynamic (MHD) turbulence decay. By using a finite-difference approach in conjunction with a cyclic Penta-diagonal matrix, the numerical algorithm of the hybrid method solves the Navier-Stokes equations and the magnetic field equation with the fourth order's precision in space and second order in time. The spectral approach is used to solve the pressure Poisson equation. The time-dependent turbulence features of this flow were in excellent agreement with the appropriate analytical solution, which is valid for short timeframes, for the classical issue of the 3-D Taylor and Green vortex flow without taking the magnetic field into account. We also show how the effective numerical approach may be utilised to model the decline of magnetohydrodynamic turbulence at various magnetic Reynolds numbers.

Modeling of spray flame in gas turbine combustors with LES and FGM

A large eddy simulation formulation was proposed for spray combustion in gas turbine combustion chambers, using a FGM combustion model coupled with detailed chemical reaction mechanisms. The solver was developed using the open-source toolkit—OpenFOAM. The two-way coupling between spray particles and gas field was modeled by a Eulerian–Lagrangian method. The enthalpy loss resulting from spray evaporation was also considered in the FGM combustion model. The solver was first validated against the experimental data of a model combustion chamber. The predictions of mean and fluctuation velocities were in good agreement with the experimental values for both cold and reacting flows, and the flame shapes were also nicely reproduced. It was revealed that there existed local extinctions at the swirler exit, leading to a lift-off flame. The validated solver was then applied to a realistic combustor of an aeroengine. It was found that different from the diffusive nature of the flame in the model combustor, the spray combustion in the realistic combustor is of partially premixed nature. The predicted pressure loss and the exit temperature profile agreed rather well with the measurements, demonstrating the capability of the present solver to simulate realistic combustors with complex geometries.

2D/3D RANS and LES Calculations of Natural Convection in a Laterally-Heated Cylindrical Enclosure Using Boussinesq and Temperature-Dependent Formulations

This article presents an investigation of fluid flow and natural convection heat transfer in a cylindrical enclosure heated laterally. Two-dimensional (2D) Reynolds-averaged Navier–Stokes (RANS) equations and three-dimensional (3D) Large Eddy Simulation (LES) calculations are conducted using commercial computational fluid dynamics (CFD) software, ANSYS FLUENT. The Rayleigh number (Ra) = 2E+7 is constant in all of the simulations and is based on a length scale that is equal to the ratio of volume to the lateral area of the reactor, i.e., R/2, where R is the radius of the reactor. The validity of the Boussinesq approximation is analyzed by comparing calculations using both the Boussinesq approximation and temperature-dependent properties (non-Boussinesq approach) using 2D RANS and 3D LES (Dynamic Smagorinsky) formulations. Moreover, 2D axisymmetric k-ω SST RANS model will be implemented to investigate whether the 2D axisymmetric model can give results that are comparable to those of the 3D LES (Dynamic Smagorinsky) model when the corresponding longitudinal or azimuthal cross section are compared. In other words, the validity of using a 2D model instead of a 3D model for the current geometry, flow regime and thermal boundary conditions will be discussed. The flow and temperature contours of these two types of simulations are analyzed, compared to determine the various aspects of each case and discussed for deeper physical insight.

Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.

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.

On the scalability of CFD tool for supersonic jet flow configurations

New regulations are imposing noise emissions limitations for the aviation industry which are pushing researchers and engineers to invest efforts in studying the aeroacoustics phenomena. Following this trend, an in-house computational fluid dynamics tool is build to reproduce high fidelity results of supersonic jet flows for aeroacoustic analogy applications. The solver is written using the large eddy simulation formulation that is discretized using a finite difference approach and an explicit time integration. Numerical simulations of supersonic jet flows are very expensive and demand efficient high-performance computing. Therefore, non-blocking message passage interface protocols and parallel Input/Output features are implemented into the code in order to perform simulations which demand up to one billion grid points. The present work addresses the evaluation of code improvements along with the computational performance of the solver running on a computer with maximum theoretical peak of 2.727 PFlops. Different mesh configurations, whose size varies from a few hundred thousand to approximately one billion grid points, are evaluated in the present paper. Calculations are performed using different workloads in order to assess the strong and weak scalability of the parallel computational tool. Moreover, validation results of a realistic flow condition are also presented in the current work.

A Priori Assessment of Subgrid-Scale Models and Numerical Error in Forced Convective Flow at High Prandtl Numbers

An extensive a priori analysis has been carried out on data from Direct numerical simulation of fully developed heated turbulent pipe flow at high molecular Prandtl numbers Pr=10/20, testing three popular modelling candidates for subgrid-scale closure in Large-Eddy simulation (LES). Aside from assessing the models’ capabilities to describe quantitatively the unresolved turbulent fluxes, a special focus is also put on the role of the numerical error, which arises from the discretization of the filtered advective fluxes on a coarse LES grid. The present analysis extends here previous studies on subgrid-scale momentum transport in a isothermal mixing layer and channel flow carried out by Brandt (J Numer Methods Fluids 51: 635–657, 2006) and Vreman et al. (J Eng Math 29: 299–327, 1995), respectively, to the subgrid-scale transport of heat at high Prandtl numbers. The statistical dependence between the individual contributions (resolved, subgrid-scale, numerical discretization error) constituting the filtered advective flux divergence in the LES formulation is investigated as well, in terms of corresponding cross-correlations. The sensitivity of the tested sgs-models to a grid refinement is further examined performing also a posteriori LES, where the basically more sophisticated candidates turn out to be more demanding in terms of required grid resolution.

Impact of burner plenum acoustics on the sound emission of a turbulent lean premixed open flame

The acoustic field of a turbulent lean cpremixed open flame is numerically investigated by a hybrid method solving the Navier-Stokes equations in a large-eddy simulation formulation and the acoustic perturbation equations. The interaction of acoustic modes of a burner plenum and the turbulent flame is analyzed with respect to the sound emission of the flame. It is investigated if a simplified computation yields a good broadband agreement of the sound pressure spectrum with experimental measurements. The results of two numerical setups, i.e., the first configuration consists of the burner plus the plenum geometry while in the second configuration the plenum is neglected, which is often done in technical applications due to computational efficiency reasons, are compared with experimental findings. It can be concluded that the plenum has a pronounced impact on the dynamics and combustion noise of the open flame. To be more precise, the comparative juxtaposition of the numerical and experimental results shows a good agreement only for the full burner-plenum computation since the interaction of the acoustic quarter-wave modes of the burner plenum with the jet flow has to be captured. The interaction of these quarter-wave modes with the flow is analyzed and the acoustic response to heat release fluctuations of the flame of the full burner-plenum computation is compared to that of the simplified burner computation, in which the plenum acoustics is neglected. Due to the excitation by the plenum acoustics, the jet flow of the full burner plenum contains higher turbulent kinetic energy and the flame is excited at several additional frequencies which result in distinct peaks in the acoustic spectrum and a higher overall sound pressure level.

Strong scaling of numerical solver for supersonic jet flow configurations

Acoustics loads are rocket design constraints which push researches and engineers to invest efforts in the aeroacoustics phenomena which is present on launch vehicles. Therefore, an in-house computational fluid dynamics tool is developed in order to reproduce high-fidelity results of supersonic jet flows for aeroacoustic analogy applications. The solver is written using the large eddy simulation formulation that is discretized using a finite-difference approach and an explicit time integration. Numerical simulations of supersonic jet flows are very expensive and demand efficient high-performance computing. Therefore, non-blocking message passage interface protocols and parallel input/output features are implemented into the code in order to perform simulations which demand up to one billion degrees of freedom. The present work evaluates the parallel efficiency of the solver when running on a supercomputer with a maximum theoretical peak of 127.4 TFLOPS. Speedup curves are generated using nine different workloads. Moreover, the validation results of a realistic flow condition are also presented in the current work.

Deep neural networks for data-driven LES closure models

In this work, we present a novel data-based approach to turbulence modeling for Large Eddy Simulation (LES) by artificial neural networks. We define the perfect LES formulation including the discretization operators and derive the associated perfect closure terms. We then generate training data for these terms from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local convolution filters to predict the underlying unknown non-linear mapping from the coarse grid quantities to the closure terms without a priori assumptions. We show that selecting both the coarse grid primitive variables as well as the coarse grid LES operator as input features significantly improves training results. All investigated networks are able to generalize from the data and learn approximations with a cross correlation of up to 47% and even 73% for the inner elements, demonstrating that the perfect closure can indeed be learned from the provided coarse grid data. Since the learned closure terms are approximate, a direct application leads to stability issues. We show how to employ the artificial neural network output to construct stable and accurate models. The best results have been achieved with a data-informed, temporally and spatially adaptive eddy viscosity closure. While further investigations into the generalizability of the approach is warranted, this work thus represents a starting point for further research into data-driven, optimal turbulence models.

Large eddy simulation of impinging flames: Unsteady ignition and flame propagation

The dynamic processes of ignition and turbulent flame development in a turbulent impinging flame are studied using large eddy simulation (LES). The Dynamic Thickened Flame (DTF) model is extended to incorporate realistic chemical mechanisms to simulate the partially premixed flames due to flame impingement on a solid wall. A new chemical mechanism with 22 species 66 steps is developed for propane. This LES formulation correctly reproduces the different ignition and turbulent flame dynamics under three different ignition conditions corresponding to experiments. Combustion modes formed by the impinging propane flame are investigated using the flame indicator and chemical explosive modes analysis, which reveals the existence of both turbulent premixed and diffusion flames. The extent and strength of premixed and diffusion flame modes, respectively, are strongly influenced by the ignition location relative to the wall. The corresponding thermal expansion leads to different flow and mixing processes, which in turn affects the subsequent flame development. The variation of the overall heat release with time is different for the three ignition locations, reflecting different contributions from the premixed and diffusion flames, respectively.

A regularized deconvolution method for turbulent closure modeling in implicitly filtered large-eddy simulation

Turbulence closure models that are based on a regularized deconvolution method (RDM) are proposed for application to implicitly filtered Large-Eddy Simulation (LES). This method reconstructs sub-grid scale contributions by approximately recovering filtered quantities through an optimization approach. Physical principles on the boundedness and conservation of reconstructed quantities are preserved by constraining the optimization problem. To account for effects of scales that are not resolved in implicitly filtered LES, a reconstruction method is proposed that combines sub-grid projection and energy-similarity to enrich unresolved scales. With this method, closure models are developed for turbulent scalar fluxes and turbulence–chemistry interaction that are intrinsically consistent with the LES formulation. These closure models are evaluated in application to a piloted turbulent jet flame with inhomogeneous inlet composition, in which combustion is represented by a two-scalar manifold model. The RDM-formulation is benchmarked against simulations obtained using a presumed PDF method and eddy diffusivity closure model. In partially-premixed flame regions, it is observed that RDM improves the prediction of turbulent mixing, and faster grid convergence is observed for results with RDM compared to simulations employing a presumed PDF method.

Investigation on turbulence in the vicinity of liquid-liquid interfaces – Large eddy simulation and PIV experiment

In this work, the turbulence in the vicinity of the liquid-liquid interfaces in an incompressible interfacial flow is investigated numerically and experimentally. A new large eddy simulation formulation is employed where all the subgrid scale (SGS) terms appearing in the filtered governing equations are closed by a volume of fluid-based Approximate Deconvolution Model (ADM-VOF) (Saeedipour et al., 2018). In this structural turbulence modelling approach, the SGS terms of stress tensor and surface tension in the Navier-Stokes equations, as well as the interface dynamics in the VOF transport equation, are mathematically reconstructed from the resolved scales. An oil-water benchmark experiment was designed for validation purposes where an oil layer is poured on the top of the water into which a submerged turbulent jet is injected and interacts with the oil–water interface. The interactions of the turbulence with the liquid-liquid interfaces are then studied by shadowgraphy visualization and time-resolved PIV measurement. Two sets of LES were performed using the ADM-VOF and a conventional LES model based on eddy-viscosity approach. The statistics of interfacial turbulence including velocity fluctuations and interface dynamics are analyzed and compared with the ones obtained from the experiment. The results reveal that in the interface vicinity the ADM-VOF approach, which reconstructs more turbulent scales and includes the SGS terms of turbulence-interface interactions, is of superior performance in predicting the energy spectra and statistics of turbulence. Far from the interface no particular difference between the LES models was observed. In addition, the temporal average of the interface motion as well as the evolution of the interfacial area is studied. While both models predict the averaged temporal evolution of the interface similarly, the ADM-VOF revealed its potentials for high fluctuating regions as it accounts for the effect of SGS term interface dynamics. This study provides a perspective for connecting the interfacial turbulence to metallurgical aspects of the continuous casting process.

Prediction of Noise and Acoustical Spectrum of Counter-Rotating Propellers

The acoustical performance of a counter-rotating marine propeller system is computed using the Ffowcs, Williams and Hawkings (FWH) algorithm. The solution procedures, where finite volume computational fluid dynamics calculations were exploited, was validated with a conventional propeller having experimental results (namely David Taylor Model Basin [DTMB] 4119). The large eddy simulation formulation and the sliding mesh technique are employed to build thrust and torque curves. Mesh dependency, turbulence model, and discretization schemes were all assessed to have repeatable and accurate results. Because the application under consideration involved inhomogeneous flow and blade interactions, DTMB 3684 and 3685 counterrotating propeller (CRP) models were used for comparisons. In terms of validation of numerical acoustics, the acoustical model evaluation study was first performed on a flow over a cylinder and a rain gutter model. The FWH approach produced good results for the spectrum at near-field and far-field locations. The performance of an inclined propeller, namely VP1304, in a noncavitating condition was investigated and the results were compared with the experiments conducted at the Potsdam Model Basin. Pressure pulses of this propeller in the cavitation tunnel were also attained and compared with experimental results. The amplitudes of the pressure fluctuations were in good agreement with the experimental data except for the weak third harmonics. Last, the generic form of the CRP system attached to an underwater vehicle body was considered to investigate the acoustic spectrum in terms of blade passing frequencies, interacted harmonics and radiated noise. 1. Introduction Propellers are used to drive marine systems including underwater vehicles. To boost their performance and fuel efficiency, they were designed mainly by experimentations. Recent studies (Denny 1968; Liu & Hong 2011), however, show that useful information about the characteristics of different conventional propellers can be extracted with the computational fluid dynamics (CFD) methodology which generally produces results supporting the experimental findings. As, for example, Subhas et al. (2012) succeeded to reproduce the blade characteristics of the INSEAN E779a propeller-designed and manufactured by Marine Technology Research Institute in the field of naval architecture and marine engineering in Italy-using the CFD. Similar finite volume calculations (Güngör & Özdemir 2015b) of the performance of propeller P4382 agreed well with the available experimental data. Embedding a model (Xia et al. 2012) for cavitation occurring on blade surfaces has been shown to improve the numerical performance in comparison with the calculations that neglect the cavitation effects. In the present analyses, we take into account the single-phase nature of the flow, and the cavitation effects are neglected with the emphasis placed in the noncavitating regions where reliable test results are available. Thus, to produce meaningful results, propeller hydrodynamics needs be considered especially under inhomogeneous flow conditions. Experiments (Potsdam Experimental Team 2015) on propellers subjected to the inhomogeneous flow reveal a variable wake in front of the propeller, which can be conveniently modeled numerically although unsteady interactions make the convergence difficult. On the other hand, the counter-rotating propeller (CRP) tests might be necessary to understand the interactions between the blades and hubs. To observe the axial distance effect, the CRP tests were handled in a cavitation tunnel (Hecker & McDonald 1960) where thrust and torque comparison assists in validations of numerical computing for each propeller's performance.

Noise investigation of a cavitating orifice: use of cfd simulation and ffowcs williams–hawkings (fw-h) formulation to gain insight into acoustics condition

In piping systems, hydrodynamic cavitation is well known for its destructive capabilities such as generation of intense noise. The investigation of the effect of the cavitation on acoustic pressure fluctuations and resonance frequencies provides much information about the geometry of the cavitation area, the propagation and the damping characteristics of the cavitation medium. The acoustical effects of cavitation caused by a water flow through a single-hole orifice have been investigated by using Computational Fluid Dynamics (CFD) and Ffowcs Williams–Hawkings (FW-H) formulation. The fluid zone downstream of the orifice where the cavitation happens considered as acoustic source. Time-accurate solutions of the flow-field variables are obtained from large eddy simulation (LES). Two cavitation regimes are investigated and for each regime, the sound pressure signals far downstream of the orifices are computed by applying the Ffowcs Williams–Hawkings (FW-H) formulation. From the results, it can be concluded that the spectral characteristics of the sound pressure fluctuations are influences by the cavitation condition. The super cavitation condition generates significantly more noise than the developed cavitation condition. Moreover, the results demonstrate that a combination of LES and FW-H formulation is a promising tool for acoustical study of cavitating orifices.

Detailed SGS atomization model and its implementation to two-phase flow LES

A novel turbulent atomization model, which is physically closed itself and free of case-by-case parameter tuning using experimental data, has been formulated and demonstrated in the framework of turbulent spray combustion large-eddy simulation (LES). Based on our accumulated research findings that elementary droplet/ligament generation is a deterministic phenomenon, not something random as considered in the conventional understanding, the model describes two dominant modes of turbulent atomization, i.e. the turbulent resonant mode and the Rayleigh–Taylor (RT) mode, in a physically straightforward manner. Extending the baseline theory proposed in Umemura (2016), to a hybrid turbulent spray LES formulation which includes both an Eulerian liquid jet core and Lagrangian droplets, the subgrid-scale (SGS) atomization characteristics are completely detailed in this study. Using the LES-resolved turbulent Weber and Bond numbers on the liquid core surface, the atomization mode and the SGS atomization characteristics such as droplet size, number, ejection velocity and core regression velocity are all identified locally, and the information is transferred back to the LES code as input information. Test cases of Diesel fuel jets demonstrate that the present formulation well reproduces the turbulent spray behavior. Thanks to the obtained detailed data, the spray formation process can be tracked both temporally and spatially, from the initial head formation with edge atomization to the later core atomization and spray spreading. It is essentially featured that the present turbulent atomization model works well without ambiguous user input, contrary to the conventional way of spray simulation. This is a significant breakthrough to urge paradigm shift in spray simulation, from unclosed/unpredictable to closed/predictable, which enables drastic improvement in the accuracy of spray simulation and may exert a large impact on both research studies and industrial applications.

Compliance of combustion models for turbulent reacting flow simulations

The utilization of low-dimensional manifold combustion models for large-eddy simulation (LES) of turbulent reactive flows introduces model simplifications that represent sources of uncertainties in addition to those arising from turbulent closure models and numerical discretization. The ability to quantitatively assess these uncertainties in the absence of measurements or reference results is vital for reliable and predictive simulations of practical combustion devices. This paper is concerned with the extension of the manifold drift term to LES to examine the compliance of a particular combustion model in describing a quantity of interest (QoI) with respect to the underlying flow-field representation. This drift term was previously introduced as a key component of the Pareto-efficient combustion (PEC) framework. The behavior of the drift term is examined in a series of test cases. To this end, large-eddy simulations of a partially-premixed turbulent pilot flame with inhomogeneous inlet streams are performed, in which the non-premixed flamelet/progress-variable (FPV) model and the premixed filtered tabulated chemistry LES (F-TACLES) formulation are employed. The drift term is shown to be capable of identifying chemically sensitive regions with respect to user-specific QoIs. With this, a species-specific combustion regime indicator is derived by computing the relative magnitude of the drift terms for different combustion models. Comparisons with commonly employed flame indicators suggests that the flame index and other indicators that are solely based on major species and flame topology are insufficient in describing complex physical processes in multi-regime combustion.

Numerical validation of the conjecture of a subglacial lake at Amundsenisen, Svalbard

The likelihood of a subglacial lake beneath Amundsenisen Plateau at Southern Spitzbergen, Svalbard, pointed out by the flat signal within the Ground Penetrating Radar (GPR) remote survey of the area, is justified, here, via numerical simulation.This investigation has been developed under the assumption that the icefield thickness does not change on average, as it is confirmed by recently published physical measurements taken over the past 40 years. As a consequence, we have considered admissible to assume the temperature and density in-depth profiles, snow and firn layers included, to be stationary. The upper icefield surface and the rocky bed surface are known in detail.The mathematical numerical model is based on an unsteady Stokes formulation of the ice flow and on a Large Eddy Simulation formulation of the lake water flow. Following the numerical sensitivity results that we presented on a recent issue of this journal, we have, here, upgraded the model by improving the description of critical aspects of icefield thermo-mechanics, such as the local water release within temperate ice as a strain heating effect and ice sliding on the bedrock. The first issue impacts on ice texture, i.e. its constitutive equation, while the second one drives icefield surging. Actually, we have obtained 13% enhancement of the numerical value of the ice top surface velocity versus measured one, and physically consistent numerical ice sliding velocity values at the rocky bottom.Adopting a new physically sound initial subglacial lake water temperature and velocity fields, we present the numerical simulation of the whole system, icefield and conjectured subglacial lake, within a time slot of 20,000d (physical time), when its evolution trend was clearly captured. By then, although the maximum value of water temperature keeps rather low, metastability appears to be overcome on more than half of the conjectured basin, with a progressive trend in time in support to the subglacial lake existence. We stress that the numerical subglacial lake surface converges to the GPR flat signal spot with tolerance equal to the GPR measuring error.Finally, we observe that the numerical simulation results meet quantitatively and qualitatively the fundamental aspects of the conjecture, so that further on-site investigations on the subglacial lake (e.g. drilling operations) appear fully justified.