Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

The cumulative global capacity of organic Rankine cycle (ORC) power systems for the conversion of renewable and waste thermal energy is undergoing a rapid growth and is estimated to be approx. 2000 MWe considering only installations that went into operation after 1995. The potential for the conversion of the thermal power coming from liquid-dominated geothermal reservoirs, waste heat from primary engines or industrial processes, biomass combustion, and concentrated solar radiation into electricity is arguably enormous. ORC technology is possibly the most flexible in terms of capacity and temperature level and is currently often the only applicable technology for the conversion of external thermal energy sources. In addition, ORC power systems are suitable for the cogeneration of heating and/or cooling, another advantage in the framework of distributed power generation. Related research and development is therefore very lively. These considerations motivated the effort documented in this article, aimed at providing consistent information about the evolution, state, and future of this power conversion technology. First, basic theoretical elements on the thermodynamic cycle, working fluid, and design aspects are illustrated, together with an evaluation of the advantages and disadvantages in comparison to competing technologies. An overview of the long history of the development of ORC power systems follows, in order to place the more recent evolution into perspective. Then, a compendium of the many aspects of the state of the art is illustrated: the solutions currently adopted in commercial plants and the main-stream applications, including information about exemplary installations. A classification and terminology for ORC power plants are proposed. An outlook on the many research and development activities is provided, whereby information on new high-impact applications, such as automotive heat recovery is included. Possible directions of future developments are highlighted, ranging from efforts targeting volume-produced stationary and mobile mini-ORC systems with a power output of few kWe, up to large MWe base-load ORC plants.

/pdf/organic-rankine-cycle-power-systems-from-the-concept-to-10dpkniszb.pdf

Organic Rankine Cycle Power Systems: From the Concept to Current Technology, Applications, and an Outlook to the Future

乱流予混合火炎のDirect Numerical Simulation

Standard high order methods give rise to spurious oscillations near shocks which can be controlled by using localized artificial viscosity (AV) with high wavenumber bias. Using simulations of compressible isotropic turbulence with optimized high-order schemes at different resolutions we investigated the range of scales where artificial dissipation is active. We observed that the impact of AV was not limited to high wavenumbers. This is especially true for moderately high Mach number isotropic turbulence which spontaneously forms shocklets, for which the AV method is found to excessively damp the dilatational motions. We propose a modified form using a modified coefficient which activates AV only in the regions of strong compression, such as shocks, turning it completely off for turbulence and expansion waves. This is found to give improved statistics for all quantities, not just dilatation. This formulation reverts back to the traditional one for strong shocks, so that its shock capturing capability is not compromised (see Fig. 1).

/pdf/a-modified-artificial-viscosity-approach-for-compressible-u5n2euz178.pdf

A modified artificial viscosity approach for compressible turbulence simulations

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

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 thermophysics properties of which are described by using a fifth-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 non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, ie 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’s 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 (Phys Fluids, vol 27 (9), 2015, 095101) or Trettel & Larsson (Phys Fluids, vol 28 (2), 2016, 026102) 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 observations open the way to the development of suitable models for dense-gas turbulent flows

/pdf/direct-numerical-simulations-of-supersonic-turbulent-channel-2kcfswarzc.pdf

Direct numerical simulations of supersonic turbulent channel flows of dense gases

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

/pdf/small-scale-dynamics-of-dense-gas-compressible-homogeneous-57t5npfdt5.pdf

Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

A detailed numerical study of the influence of dense gas effects on the large-scale dynamics of decaying homogeneous isotropic turbulence is carried out by using the van der Waals gas model. More specifically, we focus on dense gases of the Bethe–Zel’dovich–Thompson type, which may exhibit non-classical nonlinearities in the transonic and supersonic flow regimes, under suitable thermodynamic conditions. The simulations are based on the inviscid conservation equations, solved by means of a ninth-order numerical scheme. The simulations rely on the numerical viscosity of the scheme to dissipate energy at the finest scales, while leaving the larger scales mostly unaffected. The results are systematically compared with those obtained for a perfect gas. Dense gas effects are found to have a significant influence on the time evolution of the average and root mean square (r.m.s.) of the thermodynamic properties for flows characterized by sufficiently high initial turbulent Mach numbers (above 0.5), whereas the influence on kinematic properties, such as the kinetic energy and the vorticity, are smaller. However, the flow dilatational behaviour is very different, due to the non-classical variation of the speed of sound in flow regions where the dense gas is characterized by a value of the fundamental derivative of the gas dynamics (a measure of the variation of the speed of sound in isentropic compressions) smaller than one or even negative. The most significant differences between the perfect and the dense gas case are found for the repartition of dilatation levels in the flow field. For the perfect gas, strong compressions occupy a much larger volume fraction than expansion regions, leading to probability distributions of the velocity divergence highly skewed toward negative values. For the dense gas, the volume fractions occupied by strong expansion and compression regions are much more balanced; moreover, strong expansion regions are characterized by sheet-like structures, unlike the perfect gas which exhibits tubular structures. In strong compression regions, where compression shocklets may occur, both the dense and the perfect gas exhibit sheet-like structures. This suggests the possibility that expansion eddy shocklets may appear in the dense gas. This hypothesis is also supported by the fact that, in dense gas, vorticity is created with equal probability in strong compression and expansion regions, whereas for a perfect gas, vorticity is more likely to be created in the strong compression ones.

/pdf/dense-gas-effects-in-inviscid-homogeneous-isotropic-3lt06nxfjc.pdf

Dense gas effects in inviscid homogeneous isotropic turbulence

Mixing of several species in high-pressure (high-p) turbulent flows is investigated to understand the influence of the number of species on the flow characteristics. Direct numerical simulations are conducted in the temporal mixing layer configuration at approximately the same value of the momentum ratio for all realizations. The simulations are performed with mixtures of two, three, five and seven species to address various compositions at fixed number of species, at three values of initial vorticity-thickness-based Reynolds number, Re_0, and two values of the free-stream pressure, p_0, which is supercritical for each species except water. The major species are C_7H_(16), O_2 and N_2, and the minor species are CO, CO_2, H_2 and H_2O. The extensive database thus obtained allows the study of the influence not only of Re_0 and p_0, but also of the initial density ratio and of the initial density difference between streams, Δρ. The results show that the layer growth is practically insensitive to all of the above parameters; however, global vortical aspects increase with Re_0, p_0 and the number of species; nevertheless, at the same Re_0, p_0 and density ratio, vorticity aspects are not influenced by the number of species. Species mixing produces strong density gradients which increase with p_0 and otherwise scale with Δρ but, when scaled by Δρ, are not affected by the number of species. Generalized Korteweg-type equations are developed for a multi-species mixture, and a priori estimates based on the largest density gradient show that the Korteweg stresses, which account for the influence of the density gradient, have negligible contribution in the momentum equation. The species-specific effective Schmidt number, Sc_(α,eff), is computed and it is found that negative values occur for all minor species – particularly for H_2 – thus indicating uphill diffusion, while the major species experience only regular diffusion. The probability density function (p.d.f.) of Sc_(α,eff) shows strong variation with p_0 but weak dependence on the number of species; however, the p.d.f. substantially varies with the identity of the species. In contrast, the p.d.f. of the effective Prandtl number indicates dependence on both p_0 and the number of species. Similar to Sc_(α,eff), the species-specific effective Lewis-number p.d.f. depends on the species, and for all species the mean is smaller than unity, thus invalidating one of the most popular assumptions in combustion modelling. Simplifying the mixture composition by reducing the number of minor species does not affect the crucial species–temperature relationship of the major species that, for accuracy, must be retained in combustion simulations, but this relationship is affected for the minor species and in regions of uphill diffusion, indicating that the reduction is nonlinear in nature.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BCF831EC7E413209E3C5F714077BDC6C/S0022112018009928a.pdf/div-class-title-the-influence-of-the-chemical-composition-representation-according-to-the-number-of-species-during-mixing-in-high-pressure-turbulent-flows-div.pdf

The influence of the chemical composition representation according to the number of species during mixing in high-pressure turbulent flows

/pdf/numerical-study-of-multistage-transcritical-organic-rankine-14gyum5469.pdf

Luca Sciacovelli

Papers

Direct numerical simulations of supersonic turbulent channel flows of dense gases

Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

Dense gas effects in inviscid homogeneous isotropic turbulence

The influence of the chemical composition representation according to the number of species during mixing in high-pressure turbulent flows

Numerical Study of Multistage Transcritical Organic Rankine Cycle Axial Turbines