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A model of a temporal three-dimensional mixing layer laden with a multitude of drops of a fuel containing a large number of species is derived.
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A model of multicomponent-liquid (MC-liquid) drop evaporation in a three-dimensional mixing layer is here exercised at larger Reynolds numbers than in a previous study, and transitional states are obtained. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete coupling between phases is included with source terms in the gas conservation equations accounting for the drop/flow interaction in terms of drop drag, drop heating and species evaporation. The liquid composition, initially specified as a single-Gamma (SG) probability distribution function (PDF) depending on the molar mass is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of the DGPDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions and the effect of the initial mass loading and initial free-stream gas temperature are explored. For reference, Simulations are also performed for gaseous multicomponent mixing layers for which the effect of Reynolds number is investigated. The results encompass examination of the global layer characteristics, flow visualizations and homogeneous-plane statistics at transition. Comparisons are performed with previous pre-transitional MC-liquid simulations and with transitional single-component (SC) liquid studies. It is found that MCC flows at transition, the classical energy cascade is of similar strength, but that the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation in the former case. Contrasting to pre-transitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to the drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF; such a correlation only exists for the magnitude of the mean but not for that of the standard deviation. Unlike in pre-transitional situations, regions of large composition standard deviation no longer necessarily coincide with regions of large mean molar mass. The kinetic energy, rotational and composition characteristics, and dissipation are liquid specific and the variation among liquids is amplified with increasing free-stream gas temperature. Eulerian and Lagrangian statistics of gas-phase quantities show that the different. Observation framework may affect the perception of the flow characteristics. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from a SGPDF. The PDF of the scalar dissipation rate is calculated for drop-laden layers and is shown to depart more significantly from the typically assumed Gaussian in gaseous flows than experimentally measured gaseous scalar dissipation rates, this being attributed to the increased heterogeneity due to drop/flow interactions.
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The near-wall scaling of mean velocity U(yw) is addressed for the case of zero skin friction on one wall of a fully turbulent channel flow. The present DNS results can be added to the evidence in support of the conjecture that U is proportional to the square root of yw in the region just above the wall at which the mean shear dU=dy = 0.
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The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.
The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.
The three-dimensional time-dependent turbulent flow in a neutrally stratified Ekman layer over a smooth flat surface was numerically simulated by directly solving the Navier-Stokes equations. Issues addressed using the direct numerical simulation (DNS) fields include the presence or absence of large-scale coherent structures ('longitudinal' or 'roll' vortices) in neutrally stratified Ekman-layer turbulence, the effects of the horizontal component of the angular velocity vector (i.e., latitude), and implications for models of the PBL. Experimental and DNS profiles are compared.
Direct numerical simulations of two-dimensional temporally growing compressible mixing layers are presented. The Kelvin-Helmholtz instability is initially excited by a white-noise perturbation superimposed onto a hyperbolic tangent meanflow profile. The linear regime is studied at low resolution in the case of two flows of equal temperatures, for convective Mach numbers from 0.1 to 1 and for different values of the Reynolds number. At higher resolution, the complete evolution of a two-eddy mixing layer between two flows of different temperatures is simulated at moderate Reynolds number. Similarities and differences between flows of equal convective Mach numbers are discussed.
A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth.