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Of interest to the research community dealing with real gas flows, this study analyzes the influence of the physical complexity of real gases on the amplitude of subgrid-scale (SGS) terms present in the filtered Navier–Stokes equations to be solved in large eddy simulations. The direct numerical simulation results of three academic configurations (homogeneous isotropic turbulence, mixing layer, and channel flow) are filtered from the largest scale in the domain down to the Kolmogorov length scale. The analysis of the filtered flow variables consistently shows that the SGS turbulent stress and the SGS pressure cannot be neglected in the momentum equation. In the total energy equation, SGS pressure work and SGS internal and kinetic fluxes are found to be significant in the inertial zone of the turbulent kinetic energy spectrum. Since in the inertial zone, which corresponds to large filter sizes, specific models have not yet been designed for some of these terms, this study calls for such a modeling effort that will benefit the real gas and organic Rankine cycles research communities.

Content uploaded by Alexis Giauque

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All content in this area was uploaded by Alexis Giauque on Aug 18, 2021

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... Therefore, LES has a wide range of applications. [8][9][10] The rise of machine learning has injected new vitality into the study of LES modeling. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Gamahara and Hattori developed a data-driven SGS model using DNS data of channel turbulence, based on an artificial neural network (ANN). ...

Density-unweighted methods in large-eddy simulations (LES) of turbulence have received little attention, and the modeling of unclosed terms using density-unweighted methods even less. We investigate the density-unweighted subgrid-scale (SGS) closure problem for LES of decaying compressible isotropic turbulence at initial turbulent Mach numbers 0.4 and 0.8. Compared to the LES with Favre (density-weighted) filtering, there are more unclosed SGS terms for density-unweighted LES, which can be reconstructed using different SGS models, including the gradient model (GM), approximate deconvolution model (ADM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the dynamic iterative approximate deconvolution (DIAD) models proposed by Yuan et al. “Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence,” Phys. Fluids 33, 085125 (2021). We derive GM models suitable for density-unweighted methods. We also, for the first time, apply the DIAD model to investigate compressible turbulence. In the a priori tests, the correlation coefficients of the GM, ADM, and DIAD models are larger than 0.9. Particularly, the correlation coefficients of DIAD models exceed 0.98 and the relative errors are below 0.2, which is superior to that in other SGS models. In the a posteriori tests of the density-unweighted LES, the DIAD model shows great advantages over other SGS models (including GM, ADM, DSM, and DMM models) in predicting the various statistics and structures of compressible turbulence, including the velocity spectrum, probability density functions (PDFs) of SGS fluxes
and the instantaneous spatial structures of SGS heat flux, SGS kinetic energy flux, and vorticity.

... Because the equation of state of ideal gas cannot properly describe the thermal properties of dense gas, we employ a more accurate model: the Martin-Hou model, 13 which has been widely used in previous studies of dense gas. 1,15,39,50 The Martin-Hou equation, including five viral terms, can be written as ...

The small-scale statistics and local flow topology of compressible homogeneous isotropic turbulence of dense gas are numerically investigated with the turbulent Mach number and Taylor Reynolds number, respectively, nearly equaling 1.0 and 153.0. The initial state of the flow field is in the inversion zone, where the fundamental derivative of gas dynamics is negative. After reaching the stationary state, the flow field includes three different gas regions: a Bethe–Zel'dovich–Thompson (BZT) region, a classical dense gas (CDG) region, and a usual gas region. In the present study, the effects of different gas regions on the statistical properties of the enstrophy production term are investigated. Based on Helmholtz decomposition, it is found that the enstrophy production mainly comes from its solenoidal component. The dense gas effect reduces the production of enstrophy in the compression region and weakens the loss of enstrophy in the expansion region. Furthermore, the properties of flow topology based on the three invariants of the velocity gradient tensor are studied. The expansion region is mainly occupied by the BZT and CDG regions. In the expansion region, the dense gas effect significantly reduces the expansive vortex structure and weakens the contribution of this structure to the enstrophy loss.

... Moreover, this IDFTM theory could be exploited for parameterizing sub-grid scales of numerical models of large-scale geophysical regimes (ocean, atmosphere), since it provides a means of orthogonalization of the sub-grid, vertical turbulent processes, given that the fluid parcel scale considered is much smaller than the sub-grid scale. Subgrid scale modeling research is rather crucial, since it is widely accepted that the microscale processes play an important role in the dissipation of energy and mixing of climate sensitive parameters such as temperature, thereby crucially regulating the climate change, but also in industrial flows [David et al. (2021); Giauguea et al. (2021); Inagaki and Kabuyasi (2020); Yao et al. (2020);Yu et al. (2017)]. ...

The present article investigates the effects of a BZT (Bethe-Zel'dovich-Thompson) dense gas (FC-70) on the development of turbulent compressible mixing layers at three different convective Mach numbers Mc = 0,1; 1,1 and 2,2. This study extends previous analysis conducted at Mc = 1,1 (Vadrot et al. 2020). Several 3D direct numerical simulation (DNS) of compressible mixing layers are performed with FC-70 using the fifth order Martin-Hou thermodynamic equation of state (EoS) and air using the perfect gas (PG) EoS. After having carefully defined self-similar periods using the temporal evolution of the integrated streamwise production term, the evolutions of the mixing layer growth rate as a function of the convective Mach number are compared between perfect gas and dense gas flows. Results show major differences for the momentum thickness growth rate at Mc = 2:2. The well-known compressibility-related decrease of the momentum thickness growth rate is reduced in the dense gas. Fluctuating thermodynamics quantities are strongly modified. In particular, temperature variations are suppressed leading to an almost isothermal evolution. The small scales dynamics is also influenced by dense gas effects, which calls for a specific sub-grid scale modelling when computing dense gas flows using large eddy simulation (LES). Additional dense gas DNS are performed at three others initial thermodynamic operating points. DNS performed outside and inside the BZT inversion region do not show major differences. BZT effects themselves therefore only have a small impact on the mixing layer growth.

Transonic flows of a molecularly complex organic fluid through a stator cascade are investigated by means of Large Eddy Simulations (LES). The selected configuration is considered as representative of the high-pressure stages of high-temperature Organic Rankine Cycle (ORC) axial turbines, which may exhibit significant non ideal gas effects.
A heavy fluorocarbon, the perhydrophenanthrene (PP11), is selected as the working fluid to exacerbate deviations from the ideal-flow behavior.
The LES are carried out at various operating conditions (pressure ratio and total conditions at inlet), and their influence on compressibility and viscous effects is discussed. The complex thermodynamic behavior of the fluid generates highly non-ideal shock systems at the blade trailing edge. These are shown to undergo complex interactions with the transitional viscous boundary layers and wakes, with an impact on the loss mechanisms and predicted loss coefficients compared to lower fidelity models relying on the Reynolds-Averaged Navier--Stokes (RANS) equations.

Analysis of turbulence characteristics in a temporal dense gas compressible mixing layer using direct numerical simulation - Volume 893 - Aurélien Vadrot, Alexis Giauque, Christophe Corre

Direct Numerical Simulations (DNS) of forced homogeneous isotropic turbulence in a dense gas (FC-70), accurately described by a complex EoS, are computed for a turbulent Mach number of 0.8. In a numerical experiment, results are compared to the ones obtained when considering the fluid as a perfect gas. It is found that the dense gas displays a deeply modified shocklets' structure. The amplitude of compression shocklets jumps in pressure, density and entropy is divided by an order of magnitude with respect to the perfect gas. Moreover, expansion shocklets are found in the dense gas flow, also associated with small jumps in pressure, density and entropy. Comparing TKE spectra, the same inertial range is found regardless of the EoS. Results confirm previous findings on the limited effect of the dense gas thermodynamic properties on the kinematic properties of the flow. By comparing the terms of the filtered TKE equation for the dense and perfect gas EoS, it is found that for FC-70 and the present turbulent Mach and Taylor Reynolds numbers, the SGS deformation work is the only significant term in the inertial regime and does not significantly change with the EoS. A preliminary analysis of the flux terms responsible for the total energy conservation shows that the viscous term has the same symmetrical PDF regardless of the EoS. The pressure term PDF is however significantly modified by the thermodynamic properties of the fluid.

Liquid rocket, Diesel or aircraft engines may operate in the transcritical regime. In such thermodynamic conditions, the classical phase change that occurs at subcritical pressure disappears and the mixing layer between the dense and cold jet and the outer gaseous stream is characterized by large variations of density and thermodynamic properties. Fluids show strong departure from a perfect gas behavior and a real-gas formulation is needed to model the fluid state. The extension of the unstructured AVBP solver, jointly developed by CERFACS and IFPEN, to handle high-pressure thermodynamics is presented in details. It is then validated on the experimental coaxial injectors studied with the Mascotte test rig from ONERA that operate in the transcritical range, namely the LOx/GH2 cases A60 and C60 and the LOx/GCH4 configuration G2. The flame pattern observed in experiments is properly recovered, hence validating the numerical strategy. Numerical results are then discussed focusing on the role of the momentum flux ratio on the development of transcritical flames.

The influence of dense gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermo-physics properties of which are described by using a 5th-order virial equation of state and advanced models for the transport properties. In the dense gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the nonstandard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin' hypothesis is well respected at any Mach number considered in the study. The preceding features make high-Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patel et al. (2015) or Trettel & Larsson (2016), is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the van Driest transformation also performs reasonably well. The present observation open the way to the development of suitable models for dense-gas turbulent flows.

The study and understanding of transcritical and supercritical jet flow are critical in liquid rockets, gas turbines, and diesel engines, as high-pressure atmospheres in these devices’ mixing chambers drastically modify the morphology of their jets. In the transcritical jet, new elongated entities called finger-like structures appear and characterize the fluid flow phenomenon. This study examines these entities by simulating two classical cases based on Mayer’s experiments. The turbulence is described by the Large-eddy simulation technique with a sub-grid scale model known as the selective structures-function model. Real-gas behavior is evaluated by the Soave-Redlich-Kwong equation, and the transport properties are estimated by Chung’s methods. From the results, a longitudinal modulation which triggers an azimuthal modulation is observed. Then, bulges are formed on the jet surface. Cross-sectional views reveal pairs of streamwise vortices with inverted rotational directions, which are located on either side of the bulges (on the outer edge of the dense core). These transversal, turbulent movements seem to be engaged with the elongation of the bulges and the subsequent formation of finger-like structures. The existence of the counter-rotating vortices is related with the baroclinic vorticity. Then, since one may refer to the Rayleigh-Taylor instability when it is baroclinically generated, this instability could give an explanation of the origin of the finger-like structures. Transcritical parcels emitted at the end of the dense core are bounded by a thermal-shield. Finger-like structures are not observed in the supercritical case. The thermal-shield is absent from the supercritical parcels.