The subgrid-scale scalar variance under supercritical pressure conditions

To model the subgrid-scale (SGS) scalar variance under supercritical-pressure conditions, an equation is first derived for it. This equation is considerably more complex than its equivalent for atmospheric-pressure conditions. Using a previously created direct numerical simulation (DNS) database of transitional states obtained for binary-species systems in the context of temporal mixing layers, the activity of terms in this equation is evaluated, and it is found that some of these new terms have magnitude comparable to that of governing terms in the classical equation. Most prominent among these new terms are those expressing the variation of diffusivity with thermodynamic variables and Soret terms having dissipative effects. Since models are not available for these new terms that would enable solving the SGS scalar variance equation, the adopted strategy is to directly model the SGS scalar variance. Two models are investigated for this quantity, both developed in the context of compressible flows. The first one is based on an approximate deconvolution approach and the second one is a gradient-like model which relies on a dynamic procedure using the Leonard term expansion. Both models are successful in reproducing the SGS scalar variance extracted from the filtered DNS database, and moreover, when used in the framework of a probability density function (PDF) approach in conjunction with the β-PDF, they excellently reproduce a filtered quantity which is a function of the scalar. For the dynamic model, the proportionality coefficient spans a small range of values through the layer cross-stream coordinate, boding well for the stability of large eddy simulations using this model

The Jet Propulsion Laboratory Space Exploration – Past, Present and Future

The most recent scientific results from space exploration carried out by the Jet Propulsion Laboratory (JPL) are discussed. To understand these results, a brief background of JPL’s history is presented, followed by a description of the Deep Space Network, JPL’s system of antennas which communicates with spacecraft. The results from the missions of Voyager 1 and Voyager 2 are described. The atmosphere, rings, satellites and magnetospheres of Jupiter, Saturn, Uranus and Neptune are discussed with particular emphasis on novelty of the discoveries and the challenges encountered in explaining them. A brief discussion of the impact of spray research upon space exploration follows. This is because most recently launched missions used liquid fueled rockets to escape Earth’s gravity. A summary of future missions and the National Aeronautics and Space Administration’s new policies is presented in the conclusion

Dynamics and Thermodynamics of Dense and Dilute Clusters of Drops

Collective drop behavior is encountered in sprays produced for a variety of applications: fuel sprays produced for combusting devices, metal sprays produced for coating, paint sprays, printer sprays, atmospheric clouds, etc. There is experimental evidence that clusters of drops exist both in combusting [1], [2], [3], [4], [5], and non-combusting sprays for atomizers used in combusting devices [6], [3], [4]. Clusters of drops have also been observed in round jets laden with solid glass beads [7], although the glass beads (of 55p radius) did not behave entirely like liquid drops due to their large inertia. The existence of these clusters of drops indicates that the interaction among the drops is important in determining the dynamics of the drops because the drop proximity changes the flow around the individual drops in ways that affects the drag on each drop. Additionally, if there is a phase change between the liquid drops and the gaseous surroundings (either evaporation or condensation), this will also influence the flow around the individual drops; and phase change is also affected by the drop proximity. If evaporation occurs, it is the drop heat up that is affected by drop proximity and the build up of fuel vapor in the interstitial space among drops might lead to saturation of the gas, resulting in termination of evaporation. If condensation occurs, such as in atmospheric clouds, the rate of mass transfer to the hotter liquid drops from the colder gas results in the reduction of the temperature differential between phases and thus might terminate phase change; and the rate of mass transfer depends upon drop proximity

Detailed characteristics of drop-laden mixing layers: Large eddy simulation predictions compared to direct numerical simulation

Results are compared from direct numerical simulation (DNS) and large eddy simulation (LES) of a temporal mixing layer laden with evaporating drops to assess the ability of LES to reproduce detailed characteristics of DNS. The LES used computational drops, each of which represented eight physical drops, and a reduced flow field resolution using a grid spacing four times larger than that of the DNS. The LES also used models for the filtered source terms, which express the coupling of the drops with the flow, and for the unresolved subgrid-scale (SGS) fluxes of species mass, momentum, and enthalpy. The LESs were conducted using one of three different SGS-flux models: dynamic-coefficient gradient (GRD), dynamic-coefficient Smagorinsky (SMD), and constant-coefficient scale similarity (SSC). The comparison of the LES with the filtered-and-coarsened (FC) DNS considered detailed aspects of the flow that are of interest in ignition or full combustion. All LESs captured the largest-scale vortex, the global amount of vapor emanating from the drops, and the overall size distribution of the drops. All LESs tended to underpredict the global amount of irreversible entropy production (dissipation). The SMD model was found unable to capture either the global or local vorticity variation and had minimal small-scale activity in dynamic and thermodynamic variables compared to the FC-DNS. The SMD model was also deficient in predicting the spatial distribution of drops and of the dissipation. In contrast, the GRD and SSC models did mimic the small-scale activity of the FC-DNS and the spatial distribution of drops and of the dissipation. Therefore, the GRD and SSC models are recommended, while the SMD model seems inappropriate for combustion or other problems where the local activity must be predicted

On the Divergence of the Velocity Vector in Real-Gas Flow

A theoretical study was performed addressing the degree of applicability or inapplicability, to a real gas, of the occasionally stated belief that for an ideal gas, incompressibility is synonymous with a zero or very low Mach number. The measure of compressibility used in this study is the magnitude of the divergence of the flow velocity vector [V(bar) (raised dot) u (where u is the flow velocity)]. The study involves a mathematical derivation that begins with the governing equations of flow and involves consideration of equations of state, thermodynamics, and fluxes of heat, mass, and the affected molecular species. The derivation leads to an equation for the volume integral of (V(bar) (raised dot) u)(sup 2) that indicates contributions of several thermodynamic, hydrodynamic, and species-flux effects to compressibility and reveals differences between real and ideal gases. An analysis of the equation leads to the conclusion that for a real gas, incompressibility is not synonymous with zero or very small Mach number. Therefore, it is further concluded, the contributions to compressibility revealed by the derived equation should be taken into account in simulations of real-gas flows

Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation

Predictions from conventional large-eddy simulation (LES) are known to be grid-spacing and spatial-discretization-order dependent. In a previous article (Radhakrishnan & Bellan, J. Fluid Mech., vol. 697, 2012a, pp. 399–435), we reformulated LES for compressible single-phase flow by explicitly filtering the nonlinear terms in the governing equations so as to render the solution grid-spacing and discretization-order independent. Having shown in Radhakrishnan & Bellan (2012a) that the reformulated LES, which we call EFLES, yields grid-spacing-independent and discretization-order-independent solutions for compressible single-phase flow, we explore here the potential of EFLES for evaporating two-phase flow where the small scales have an additional origin compared to single-phase flow. Thus, we created a database through direct numerical simulation (DNS) that when filtered serves as a template for comparisons with both conventional LES and EFLES. Both conventional LES and EFLES are conducted with two gas-phase SGS models; the drop-field SGS model is the same in all these simulations. For EFLES, we also compared simulations performed with the same SGS model for the gas phase but two different drop-field SGS models. Moreover, to elucidate the influence of explicit filtering versus gas-phase SGS modelling, EFLES with two drop-field SGS models but no gas-phase SGS models were conducted. The results from all these simulations were 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. The absence of a gas-phase SGS model leads to build-up of energy near the filter cut-off indicating that while explicit filtering removes energy above the filter width, it does not provide the correct dissipation at the scales smaller than this width. A wider viewpoint leads to the conclusion that although the minimum filter-width to grid-spacing ratio necessary to obtain the unique grid-independent solution might be different for various discretization-order schemes, the grid-independent solution thus obtained is also discretization-order independent

A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions

A Direct Numerical Simulation (DNS) database was created representing mixing of species under high-pressure conditions. The configuration considered is that of a temporally evolving mixing layer. The database was examined and analyzed for the purpose of modeling some of the unclosed terms that appear in the Large Eddy Simulation (LES) equations. Several metrics are used to understand the LES modeling requirements. First, a statistical analysis of the DNS-database large-scale flow structures was performed to provide a metric for probing the accuracy of the proposed LES models as the flow fields obtained from accurate LESs should contain structures of morphology statistically similar to those observed in the filtered-and-coarsened DNS (FC-DNS) fields. To characterize the morphology of the large-scales structures, the Minkowski functionals of the iso-surfaces were evaluated for two different fields: the second-invariant of the rate of deformation tensor and the irreversible entropy production rate. To remove the presence of the small flow scales, both of these fields were computed using the FC-DNS solutions. It was found that the large-scale structures of the irreversible entropy production rate exhibit higher morphological complexity than those of the second invariant of the rate of deformation tensor, indicating that the burden of modeling will be on recovering the thermodynamic fields. Second, to evaluate the physical effects which must be modeled at the subfilter scale, an a priori analysis was conducted. This a priori analysis, conducted in the coarse-grid LES regime, revealed that standard closures for the filtered pressure, the filtered heat flux, and the filtered species mass fluxes, in which a filtered function of a variable is equal to the function of the filtered variable, may no longer be valid for the high-pressure flows considered in this study. The terms requiring modeling are the filtered pressure, the filtered heat flux, the filtered pressure work, and the filtered species mass fluxes. Improved models were developed based on a scale-similarity approach and were found to perform considerably better than the classical ones. These improved models were also assessed in an a posteriori study. Different combinations of the standard models and the improved ones were tested. At the relatively small Reynolds numbers achievable in DNS and at the relatively small filter widths used here, the standard models for the filtered pressure, the filtered heat flux, and the filtered species fluxes were found to yield accurate results for the morphology of the large-scale structures present in the flow. Analysis of the temporal evolution of several volume-averaged quantities representative of the mixing layer growth, and of the cross-stream variation of homogeneous-plane averages and second-order correlations, as well as of visualizations, indicated that the models performed equivalently for the conditions of the simulations. The expectation is that at the much larger Reynolds numbers and much larger filter widths used in practical applications, the improved models will have much more accurate performance than the standard one

Numerical Simulation of Jet Injection and Species Mixing under High-Pressure Conditions

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed of a round fluid jet entering a high-pressure chamber. The chemical compositions and temperatures of the jet and that of the fluid in the chamber are initially prescribed. The governing equations consist of the conservation equations for mass, momentum, species and energy, and are complemented by a real-gas equation of state. The fluxes of species and heat are written in the framework of fluctuation-dissipation theory and include Soret and Dufour effects. For more than two species, the full mass diffusion and thermal diffusion matrices are computed using high-pressure mixing rules which utilize as building blocks the corresponding binary diffusion coefficients. The mixture viscosity and thermal conductivity are computed using standard mixing rules and corresponding states theory. To evaluate the physical model and numerical method, LES is employed first to simulate a supercritical N_2 jet injected into N_2. Time averaged results show reasonable agreement with the experimental data. Then, DNS is conducted to study the spatial evolution of a supercritical N_2 jet injected into CO_2. Time averaged results are used to compute the length of the potential core and the species diffusion characteristics. Spectral analysis is then applied on a time series data obtained at several axial locations and a dominant frequency is observed inside the potential core