scholarly journals Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

2007 ◽  
Vol 593 ◽  
pp. 57-91 ◽  
Author(s):  
LAURENT C. SELLE ◽  
NORA A. OKONG'O ◽  
JOSETTE BELLAN ◽  
KENNETH G. HARSTAD
Keyword(s):  
Equation Of State ◽  
A Priori ◽  
Mixing Layer ◽  
Chemical Species ◽  
Additional Term ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Subgrid Scale ◽  
Filter Size ◽  
Energy Equations

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

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

2020 ◽  
Vol 105 (2) ◽  
pp. 377-392
Author(s):  
Lorenzo Sufrà ◽  
Helfried Steiner
Keyword(s):  
A Priori ◽  
Mixing Layer ◽  
Turbulent Pipe Flow ◽  
Numerical Error ◽  
Statistical Dependence ◽  
Special Focus ◽  
Subgrid Scale ◽  
Flux Divergence ◽  
Prandtl Numbers ◽  
The Individual

AbstractAn 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 $$Pr=10$$ P r = 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.

scholarly journals Generalization Capability of Convolutional Neural Networks for Progress Variable Variance and Reaction Rate Subgrid-Scale Modeling

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5096
Author(s):  
Victor Xing ◽  
Corentin Lapeyre ◽  
Thomas Jaravel ◽  
Thierry Poinsot
Keyword(s):  
Reaction Rate ◽  
A Priori ◽  
Turbulent Flame ◽  
Single Step ◽  
Subgrid Scale ◽  
Algebraic Models ◽  
Jet Flame ◽  
Progress Variable ◽  
Filter Size ◽  
Subgrid Scale Modeling

Deep learning has recently emerged as a successful approach to produce accurate subgrid-scale (SGS) models for Large Eddy Simulations (LES) in combustion. However, the ability of these models to generalize to configurations far from their training distribution is still mainly unexplored, thus impeding their application to practical configurations. In this work, a convolutional neural network (CNN) model for the progress-variable SGS variance field is trained on a canonical premixed turbulent flame and evaluated a priori on a significantly more complex slot burner jet flame. Despite the extensive differences between the two configurations, the CNN generalizes well and outperforms existing algebraic models. Conditions for this successful generalization are discussed, including the effect of the filter size and flame–turbulence interaction parameters. The CNN is then integrated into an analytical reaction rate closure relying on a single-step chemical source term formulation and a presumed beta PDF (probability density function) approach. The proposed closure is able to accurately recover filtered reaction rate values on both training and generalization flames.

Dynamic Structure SGS Models for Large Eddy Simulations

2004 ◽  
Author(s):  
Sergei Chumakov ◽  
Christopher J. Rutland
Keyword(s):  
Internal Combustion Engines ◽  
Isotropic Turbulence ◽  
A Priori ◽  
Mixing Layer ◽  
Dynamic Structure ◽  
Scalar Dissipation ◽  
Scalar Flux ◽  
New Family ◽  
Large Eddy ◽  
Separation Of Variable

Large Eddy Simulation (LES) is based on separation of variable of interest into two parts — resolved and unresolved, where resolved parts are obtained numerically using transport equations, and the effect of unresolved parts on resolved is modeled using subgrid-scale (SGS) models. This technique has been successfully applied to variety of problems including simulation of internal combustion engines. In this paper we present and discuss three new LES sub-grid scale (SGS) models for: • SGS scalar flux; • SGS scalar dissipation; • SGS energy dissipation. The proposed models belong to a new family of SGS models — Dynamic Structure (DS) models. The DS models take the structure of the model term from the corresponding Leonard-type term, and a particular form of a scaling factor is then used. The models are evaluated a priori using available DNS data for a non-reacting mixing layer and decaying isotropic turbulence. The evaluation results compare well with viscosity and similarity models. During the a priori tests, the DS models were found do be robust and perform better than dynamic viscosity and similarity models under variety of conditions including different test-to-base filter size ratios and non-symmetric filters. To evaluate the models a posteriori, they are implemented into a high-order finite-difference code and two LES simulations are conducted: an LES of decaying isotropic turbulence and an LES non-reacting incompressible mixing layer. The results from both runs are compared with data available from the literature and DNS simulations.

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

A time-dependent model for high-pressure discharges in narrow ablative capillaries

1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Time Dependent ◽  
Dimensional Model ◽  
Plasma Sources ◽  
One Dimensional ◽  
Space And Time ◽  
Dependent Model ◽  
Energy Equations ◽  
Time Dependent Model

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

A prioriassessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

2013 ◽  
Vol 14 (9) ◽  
pp. 43-61 ◽  
Author(s):  
N.S. Vaghefi ◽  
M.B. Nik ◽  
P.H. Pisciuneri ◽  
C.K. Madnia
Keyword(s):  
Compressible Turbulence ◽  
Scalar Dissipation ◽  
Subgrid Scale

Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method

2013 ◽  
Author(s):  
Scott Martin ◽  
Aleksandar Jemcov ◽  
Björn de Ruijter
Keyword(s):  
Turbulent Combustion ◽  
Large Scale ◽  
Reaction Rates ◽  
Moment Closure ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Conditional Moment ◽  
Progress Variable ◽  
Conditional Moment Closure ◽  
Scale Turbulence

Here the premixed Conditional Moment Closure (CMC) method is used to model the recent PIV and Raman turbulent, enclosed reacting methane jet data from DLR Stuttgart [1]. The experimental data has a rectangular test section at atmospheric pressure and temperature with a single inlet jet. A jet velocity of 90 m/s is used with an adiabatic flame temperature of 2,064 K. Contours of major species, temperature and velocities along with velocity rms values are provided. The conditional moment closure model has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes [2]. The simplified CMC model used here falls into the class of table lookup turbulent combustion models where the chemical kinetics are solved offline over a range of conditions and stored in a table that is accessed by the CFD code. Most table lookup models are based on the laminar 1-D flamelet equations, which assume the small scale turbulence does not affect the reaction rates, only the large scale turbulence has an effect on the reaction rates. The CMC model is derived from first principles to account for the effects of small scale turbulence on the reaction rates, as well as the effects of the large scale mixing, making it more versatile than other models. This is accomplished by conditioning the scalars with the reaction progress variable. By conditioning the scalars and accounting for the small scale mixing, the effects of turbulent fluctuations of the temperature on the reaction rates are more accurately modeled. The scalar dissipation is used to account for the effects of the small scale mixing on the reaction rates. The original premixed CMC model used a constant value of scalar dissipation, here the scalar dissipation is conditioned by the reaction progress variable. The steady RANS 3-D version of the open source CFD code OpenFOAM is used. Velocity, temperature and species are compared to the experimental data. Once validated, this CFD turbulent combustion model will have great utility for designing lean premixed gas turbine combustors.

scholarly journals Chaotic period doubling

2009 ◽  
Vol 29 (2) ◽  
pp. 381-418 ◽  
Author(s):  
V. V. M. S. CHANDRAMOULI ◽  
M. MARTENS ◽  
W. DE MELO ◽  
C. P. TRESSER
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Chaotic Dynamics ◽  
A Priori ◽  
Period Doubling ◽  
Small Scale ◽  
Unimodal Maps ◽  
One Dimensional ◽  
Renormalization Operator ◽  
Renormalization Theory

AbstractThe period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend on the choice of the map under rather mild smoothness conditions. The existence of a unique renormalization fixed point that is also hyperbolic among generic smooth-enough maps plays a crucial role in the corresponding renormalization theory. The uniqueness and hyperbolicity of the renormalization fixed point were first shown in the holomorphic context, by means that generalize to other renormalization operators. It was then proved that, in the space ofC2+αunimodal maps, forα>0, the period doubling renormalization fixed point is hyperbolic as well. In this paper we study what happens when one approaches from below the minimal smoothness thresholds for the uniqueness and for the hyperbolicity of the period doubling renormalization generic fixed point. Indeed, our main result states that in the space ofC2unimodal maps the analytic fixed point is not hyperbolic and that the same remains true when adding enough smoothness to geta prioribounds. In this smoother class, calledC2+∣⋅∣, the failure of hyperbolicity is tamer than inC2. Things get much worse with just a bit less smoothness thanC2, as then even the uniqueness is lost and other asymptotic behavior becomes possible. We show that the period doubling renormalization operator acting on the space ofC1+Lipunimodal maps has infinite topological entropy.

A priori analysis of subgrid-scale terms in compressible transcritical real gas flows

2021 ◽  
Vol 33 (8) ◽  
pp. 085126
Author(s):  
Alexis Giauque ◽  
Aurélien Vadrot ◽  
Paolo Errante ◽  
Christophe Corre
Keyword(s):  
A Priori ◽  
Gas Flows ◽  
Subgrid Scale ◽  
Real Gas ◽  
A Priori Analysis

Stable and accurate a posteriori LES of 2D turbulence with convolutional neural networks: Backscatter analysis and generalization via transfer learning

2021 ◽  
Author(s):  
Yifei Guan ◽  
Ashesh Chattopadhyay ◽  
Adam Subel ◽  
Pedram Hassanzadeh
Keyword(s):  
Neural Network ◽  
Transfer Learning ◽  
Network Architecture ◽  
Turbulence Modeling ◽  
Scale Effects ◽  
A Priori ◽  
A Posteriori ◽  
Subgrid Scale ◽  
Artificial Neural Network Ann ◽  
Short Term Prediction

<p>In large eddy simulations (LES), the subgrid-scale effects are modeled by physics-based or data-driven methods. This work develops a convolutional neural network (CNN) to model the subgrid-scale effects of a two-dimensional turbulent flow. The model is able to capture both the inter-scale forward energy transfer and backscatter in both a priori and a posteriori analyses. The LES-CNN model outperforms the physics-based eddy-viscosity models and the previous proposed local artificial neural network (ANN) models in both short-term prediction and long-term statistics. Transfer learning is implemented to generalize the method for turbulence modeling at higher Reynolds numbers. Encoder-decoder network architecture is proposed to generalize the model to a higher computational grid resolution.</p>

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