Simulations Of Compressible Isotropic Turbulence Research Articles

Spatially multi-scale artificial neural network model for large eddy simulation of compressible isotropic turbulence

In this work, subgrid-scale (SGS) stress and SGS heat flux of compressible isotropic turbulence are reconstructed by a spatially multi-scale artificial neural network (SMSANN). The input features of the SMSANN model are based on the first order derivatives of the primary and secondary filtered variables at different spatial locations. The SMSANN model performs much better than the gradient model in the a priori test, including the correlation coefficients and relative errors. Specifically, the correlation coefficients of the SGS stress and SGS heat flux can be larger than 0.997 and the relative errors of the SGS stress and SGS heat flux can be smaller than 0.08 for the SMSANN model. In an a posteriori analysis, the performance of the SMSANN model has been evaluated by a detailed comparison of the results of the SMSANN model and the dynamic mixed model (DMM) at a grid resolution of 643 with the Taylor Reynolds number Reλ ranging from 180 to 250. The SMSANN model shows an advantage over the DMM in the prediction of the spectra of velocity and temperature. Besides, the SMSANN model can accurately reconstruct the statistical properties of velocity and temperature and the instantaneous flow structures. An artificial neural network with consideration of spatial multiscale can deepen our understanding of large eddy simulation modeling.

Detonation initiation by compressible turbulence thermodynamic fluctuations

Theory and computations have established that thermodynamic gradients created by hot spots in reactive gas mixtures can lead to spontaneous detonation initiation. However, the current laminar theory of the temperature-gradient mechanism for detonation initiation is restricted to idealized physical configurations. Thus, it only predicts conditions for the onset of detonations in quiescent gases, where an isolated hot spot is formed on a timescale shorter than the chemical and acoustic timescales of the gas. In this work, we extend the laminar temperature-gradient mechanism into a statistical model for predicting the detonability of an autoignitive gas experiencing compressible isotropic turbulence fluctuations. Compressible turbulence forms non-monotonic temperature fields with tightly-spaced local minima and maxima that evolve over a range of timescales, including those much larger than chemical and acoustic timescales. We examine the utility of the adapted statistical model through direct numerical simulations of compressible isotropic turbulence in premixed hydrogen-air reactants for a range of conditions. We find strong, but not conclusive, evidence that the model can predict the degree of detonability in an autoignitive gas due to turbulence-induced thermodynamic gradients.

Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence

In this work, the subgrid-scale (SGS) stress and the SGS heat flux of compressible isotropic turbulence are modeled by an artificial neural network (ANN) mixed model (ANNMM), which maintains both functional and structural performances. The functional form of the mixed model combining the gradient model and the Smagorinsky’s eddy viscosity model is imposed, and the ANN is used to calculate the model coefficients of the SGS anisotropy stress, SGS energy, and SGS heat flux. It is shown that the ANNMM can reconstruct the SGS terms more accurately than the gradient model in the a priori test. Specifically, the ANNMM almost recovers the average values of the SGS energy flux and SGS energy flux conditioned on the normalized filtered velocity divergence. In an a posteriori analysis, the ANNMM shows advantage over the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the spectra of velocity and temperature, which almost overlap with the filtered direct numerical simulation data, while the DSM and DMM suffer from the problem of the typical tilted spectral distribution. Besides, the ANNMM predicts the probability density functions of SGS energy flux much better than DSM and DMM. ANN with functional model forms can enlighten and deepen our understanding of large eddy simulation modeling.

Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence.

A subgrid-scale (SGS) model for large-eddy simulation (LES) of compressible isotropic turbulence is constructed by using a data-driven framework. An artificial neural network (ANN) based on local stencil geometry is employed to predict the unclosed SGS terms. The input features are based on the first-order and second-order derivatives of filtered velocity and temperature which appear in the second-order Taylor approximation of the SGS stress and heat flux. It is shown that the proposed ANN-7 model performs better than the gradient model in the a priori test. The correlation coefficient is larger and the relative error is smaller for ANN-7 model as compared to those of the gradient model in the a priori test. In an a posteriori analysis, the performance of ANN-7 model shows advantage over the dynamic Smagorinsky model and dynamic mixed model in the prediction of spectra and structure functions of velocity and temperature, and instantaneous flow structures. Artificial neural network is a promising tool for understanding the physical fundamentals of SGS unclosed terms with further improvement.

A Hybrid Numerical Simulation of Supersonic Isotropic Turbulence

This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still utilizes an 8th-order compact scheme with built-in hyperviscosity for smooth regions and a 7th-order WENO scheme for highly compressive regions, but now both in their conservation formulations and for the latter with the Roe type characteristic-wise reconstruction. To enhance the robustness of the WENO scheme without compromising its high-resolution and accuracy, the recursive-order-reduction procedure is adopted, where a new type of reconstruction-failure-detection criterion is constructed. To capture the upwind direction properly in extreme conditions, the global Lax-Friedrichs numerical flux is used. In addition, a new form of cooling function is proposed, which is proved to be positivity-preserving. With these techniques, the new scheme not only inherits the good properties of the original one but also extends largely the computable range of turbulent Mach number, which has been further confirmed by numerical results.

1401 一様等方性圧縮性乱流における音源項の統計的性質

The characteristics of sound sources are analyzed by Lighthill equation based on the direct numerical simulations of compressible isotropic turbulence to investigate the physical mechanisms of the noise from fine scale turbulence and their interactions with shocklets. We study mainly on the compressibility effects on the sound source terms in Lighthill equation by comparing various turbulent Mach numbers (M_<t0> = 0.1 to M_<t0> = 1.0), where the sound source terms are decomposed into the Reynolds stress, entropy, and viscous term. We show that the Reynolds stress term is the most contributer to the overall sound sources for all Mach number cases, on the other hand, the sound level of viscosity term is very small. Also the characteristics of sound sources are changed due to the generation of shocklets for high Mach number cases. For low Mach number flows, the Reynolds stress term and entropy term has positive correlation so that the overall sound level is intensified. However, for high Mach number flows, the overall sound level is weakened because the negative correlation between the Reynolds stress term and entropy term becomes stronger and they partially cancels out each other.

Temporal decorrelations in compressible isotropic turbulence

Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components, while the classic random sweeping model is proposed for solenoidal components. The swept-wave model shows that the temporal decorrelations in dilatational fluctuations are dominated by two physical processes: random sweeping and wave propagation. These models are supported by the direct numerical simulation of compressible isotropic turbulence, in the sense that all curves of normalized time correlations for different wave numbers collapse into a single one using the normalized time separations. The swept-wave model is further extended to account for a constant mean velocity.

Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers ∼0.1 … 1. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wave number of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that C ≈ 1.7. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover, we discuss length scales related to the dissipation, in particular, an effective numerical length scale Δ eff, which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.

Higher entropy conservation and numerical stability of compressible turbulence simulations

We present a numerical formulation for the treatment of nonlinear instabilities in shock-free compressible turbulence simulations. The formulation is high order and contains no artificial dissipation. Numerical stability is enhanced through semi-discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation. The numerical implementation is achieved using a conservative skew-symmetric splitting of the nonlinear terms. The robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high Reynolds number. Results show the scheme is capable of capturing the statistical equilibrium of low Mach number compressible turbulent fluctuations at infinite Reynolds number. Comparisons with the entropy splitting technique [J. Comput. Phys. 162 (2000) 33; J. Comput. Phys. 178 (2002) 307], staggered method [J. Comput. Phys. 191(2) (2003) 392], and skew-symmetric like schemes [J. Comput. Phys. 161 (2000) 114] confirm the superiority of the current approach. We also discuss a flaw in the skew-symmetric splitting implemented in the literature. Very good results are obtained based on the proper splitting.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure–dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Toward the large-eddy simulation of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a963grid using Fourier collocation methods. Extensive comparisons between the direct and modelled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence – conducted on a coarse323grid – is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

The subgrid-scale modeling of compressible turbulence

A subgrid-scale model recently derived by Yoshizawa [Phys. Fluids 29, 2152 (1986)] for use in the large-eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is only applicable to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre-filtered fields, is suggested which appears to reduce these limitations.