Pressure Effects from Direct Numerical Simulation of High-Pressure Multispecies Mixing

The focus of this study is the understanding of effects of pressure increase or Reynolds number increase in supercritical-pressure flows. To this effect, Direct Numerical Simulations are conducted for supercritical-pressure flows in which five species undergo mixing. The computation of multispecies mixing is based on a full mass-diffusion matrix, a full thermal-diffusion-factor matrix necessary to include Soret and Dufour effects, and both viscosity and thermal conductivity computed for the species mixture. The scaling of the physical viscosity, necessary for conducting DNS, induces a scaling of the other transport properties that respects the accurate values of the Schmidt (Sc) numbers and of the Prandtl (Pr) number. Computations are performed in the configuration of a temporal mixing layer and the results are analyzed to reveal the separate effect of pressure or Reynolds number increase on the flow. The analysis consists of examining vortical aspects of the flow, the fluxes and relevant thermodynamic properties. It is found that a larger pressure has an opposite effect to a larger Reynolds number, mainly by increasing the fluid density and making it more difficult to entrain and mix

Pressure Effects from Direct Numerical Simulation of High-Pressure Multispecies Mixing

The focus of this study is the understanding of effects of pressure increase or Reynolds number increase in supercritical-pressure flows. To this effect, Direct Numerical Simulations are conducted for supercritical-pressure flows in which five species undergo mixing. The computation of multispecies mixing is based on a full mass-diffusion matrix, a full thermal-diffusion-factor matrix necessary to include Soret and Dufour effects, and both viscosity and thermal conductivity computed for the species mixture. The scaling of the physical viscosity, necessary for conducting DNS, induces a scaling of the other transport properties that respects the accurate values of the Schmidt (Sc) numbers and of the Prandtl (Pr) number. Computations are performed in the configuration of a temporal mixing layer and the results are analyzed to reveal the separate effect of pressure or Reynolds number increase on the flow. The analysis consists of examining vortical aspects of the flow, the fluxes and relevant thermodynamic properties. It is found that a larger pressure has an opposite effect to a larger Reynolds number, mainly by increasing the fluid density and making it more difficult to entrain and mix

Small-Scale Dissipation in Supercritical, Transitional Mixing Layers

The dissipation and small-scale dissipation is calculated for transitional states obtained elsewhere from Direct Numerical Simulations (DNS) of temporal, supercritical mixing layers for two species systems, O₂/H₂ and C₇H₁₆/N₂, so as to understand their species-independent and species-dependent aspects. The effect of filter size on the results was also investigated, with filtering exclusively performed in the dissipation regime of the energy spectrum. Both domain-average dissipation and the small-scale dissipation were analyzed in terms of the three mode contributions to them due to the viscous, heat and species-mass fluxes. The species-mass flux originated contribution dominates both the dissipation and the small-scale dissipation for all simulations and its percentage of the total dissipation or of the small-scale dissipation varies in a very small range across the species system, the initial Reynolds number and the perturbation wavelength used to excite the layer. For a filter size that is four times the DNS grid size, the proportion of each small-scale dissipation mode in the total small-scale dissipation is similar to that obtained at the DNS scale, indicating a scale similarity. It was also found that the percentage of total small-scale dissipation in the total DNS dissipation is only species-system and filter size dependent but nearly independent of the initial conditions. With filter size increase, the increase in the small-scale dissipation portion of the DNS dissipation has similar functional variation for both species systems, although the fraction reached by C₇H₁₆/N₂ layers is much larger than for O₂/H₂ ones. Normalization by the results obtained at the smallest filter size led to highlighting several aspects that are only species-system dependent with increasing the filter size. Backscatter was shown to occur over a substantial percentage of the computational domain, and its magnitude was found to be a substantial fraction of the positive small-scale dissipation. A four fold increase in filter size decreased the spatial extent of backscatter by only at most 32%, 13% and 7.5% for the viscous, heat and species-mass flux originated modes. The implications or these results for Larger Eddy Simulation modeling are discussed

Entropy production of emerging turbulent scales in a temporal supercritical n-heptane/nitrogen three-dimensional mixing layer

A study of emerging turbulent scales entropy production was conducted for a supercritical shear layer as a precursor to the eventual modeling of subgrid scales (SGS: from a turbulent state) leading to large eddy simulations (LES). The entropy equation was first developed for a real, non-ideal fluid using a validated all-pressure fluid model, and the entropy flux and production terms were identified. Employing a direct numerical simulation (DNS) created database of a temporal three-dimensional supercritical shear layer using the fluid model, the different contributions to the irreversible entropy production term were evaluated. Both domain averaged and root mean square (RMS) terms were computed at three different stages of the DNS, representing the timewise ascending, culmination, and descending branches of the spatially averaged positive spanwise vorticity. The unifltered and filtered databases were compared to evaluate the relative importance of irreversible entropy production from viscous, Fourier heat diffusion, and molar fluxes terms. The results show that the average entropy production is dominated by the viscous terms at all stages of the evolution: however, the contribution to the RMS of the molar flux term for both the ascending and descending branches is non-negligible. This latter result was traced to the molar gradients tending to be smeared by emerging turbulent scales. Based on this finding a physical picture of the layer evolution was presented involving competition between large scales entraining heavy fluid from the lower stream and forming strong density and mass fraction gradients at spatially varying locations with time, and small-scale turbulent structures evolving but being damped by contact with the newly formed strong density gradient regions which act similar to material surfaces. Analysis of the results showed that the primary contribution to the molar flux dissipation for both the average and the RMS is the mixture non-ideality

Entropy production of emerging turbulent scales in a temporal supercritical n-heptane/nitrogen three-dimensional mixing layer

A study of emerging turbulent scales entropy production was conducted for a supercritical shear layer as a precursor to the eventual modeling of subgrid scales (SGS: from a turbulent state) leading to large eddy simulations (LES). The entropy equation was first developed for a real, non-ideal fluid using a validated all-pressure fluid model, and the entropy flux and production terms were identified. Employing a direct numerical simulation (DNS) created database of a temporal three-dimensional supercritical shear layer using the fluid model, the different contributions to the irreversible entropy production term were evaluated. Both domain averaged and root mean square (RMS) terms were computed at three different stages of the DNS, representing the timewise ascending, culmination, and descending branches of the spatially averaged positive spanwise vorticity. The unifltered and filtered databases were compared to evaluate the relative importance of irreversible entropy production from viscous, Fourier heat diffusion, and molar fluxes terms. The results show that the average entropy production is dominated by the viscous terms at all stages of the evolution: however, the contribution to the RMS of the molar flux term for both the ascending and descending branches is non-negligible. This latter result was traced to the molar gradients tending to be smeared by emerging turbulent scales. Based on this finding a physical picture of the layer evolution was presented involving competition between large scales entraining heavy fluid from the lower stream and forming strong density and mass fraction gradients at spatially varying locations with time, and small-scale turbulent structures evolving but being damped by contact with the newly formed strong density gradient regions which act similar to material surfaces. Analysis of the results showed that the primary contribution to the molar flux dissipation for both the average and the RMS is the mixture non-ideality

Explicitly Filtered LES of Single-Phase Compressible Flow

In Large Eddy Simulation (LES), it is often assumed that the filter width is equal to grid spacing. Predictions from such LES are grid-spacing dependent since any Subgrid Scale (SGS) model used in the LES equations is dependent on the resolved flow field which itself varies with grid spacing. Moreover, numerical errors affect the flow field, especially the smallest resolved scales. Thus, predictions using this approach are affected by both modeling and numerical choices. However, grid-spacing independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template. First, such a template is here created through Direct Numerical Simulation (DNS). Then, simulations are conducted using the conventional LES equations and also LES equations which are here reformulated so that the small-scale producing nonlinear terms in these equations are explicitly filtered (EF) to remove scales smaller than a fixed filter width; this formulation is called EFLES. The conventional LES solution is both grid-spacing and spatial discretization-order dependent, thus showing that both of these numerical aspects affect the flow prediction. The solution of the EFLES equations is grid independent for a high-order spatial discretization on all meshes tested. However, low order discretizations require a finer mesh to reach grid independence. With an eighth order discretization, a filter-width to grid-spacing ratio of two is sufficient to reach grid-independence, while a filter-width to grid-spacing ratio of four is needed to reach grid independence when a fourth or a sixth order discretization is employed. On a grid fine enough to be utilized in a DNS, the EFLES solution exhibits grid independence and does not converge to the DNS solution

Explicitly Filtered LES of Single-Phase Compressible Flow

In Large Eddy Simulation (LES), it is often assumed that the filter width is equal to grid spacing. Predictions from such LES are grid-spacing dependent since any Subgrid Scale (SGS) model used in the LES equations is dependent on the resolved flow field which itself varies with grid spacing. Moreover, numerical errors affect the flow field, especially the smallest resolved scales. Thus, predictions using this approach are affected by both modeling and numerical choices. However, grid-spacing independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template. First, such a template is here created through Direct Numerical Simulation (DNS). Then, simulations are conducted using the conventional LES equations and also LES equations which are here reformulated so that the small-scale producing nonlinear terms in these equations are explicitly filtered (EF) to remove scales smaller than a fixed filter width; this formulation is called EFLES. The conventional LES solution is both grid-spacing and spatial discretization-order dependent, thus showing that both of these numerical aspects affect the flow prediction. The solution of the EFLES equations is grid independent for a high-order spatial discretization on all meshes tested. However, low order discretizations require a finer mesh to reach grid independence. With an eighth order discretization, a filter-width to grid-spacing ratio of two is sufficient to reach grid-independence, while a filter-width to grid-spacing ratio of four is needed to reach grid independence when a fourth or a sixth order discretization is employed. On a grid fine enough to be utilized in a DNS, the EFLES solution exhibits grid independence and does not converge to the DNS solution

Explicitly Filtered LES of Two-Phase Flow with Evaporating Droplets

To investigate whether predictions from conventional Large Eddy Simulation (LES), which are known to be grid-spacing and spatial discretization-order dependent, can be rendered grid-spacing and discretization-order independent, we have reformulated LES by explicitly filtering the non-linear terms in the governing equations.1 The encouraging results we obtained1 for compressible single-phase flow motivated our present study in the context of evaporating two-phase flow. Thus, we created a database through Direct Numerical Simulation (DNS) to serve, when filtered, as a template for comparisons with both conventional LES and explicitly-filtered LES (EFLES). Conventional LES is conducted with the Smagorinsky model for the gas phase, and EFLES is also performed with Smagorinsky model; the drop-field SGS model is the same in all these simulations. The results from all these simulations are compared to those from DNS and from the filtered DNS (FDNS). Similar to the single-phase flow findings, the conventional LES method yields solutions which are both grid-spacing and spatial discretization-order dependent. The EFLES solutions are found to be grid-spacing independent for sufficiently large filter-width to grid-spacing ratio, although for the highest discretization order this ratio is larger in the two-phase flow compared to the single-phase flow. For a sufficiently fine grid, the results are also discretization-order independent