Characteristics of transitional multicomponent gaseous and drop-laden mixing layers from direct numerical simulation: Composition effects

Abstract

Transitional states are obtained by exercising a model of multicomponent-liquid ͑MC-liquid͒ drop evaporation in a three-dimensional mixing layer at larger Reynolds numbers, Re, than in a previous study. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete dynamic and thermodynamic coupling between phases is included. The liquid composition, initially specified as a single-Gamma ͑SG͒ probability distribution function ͑PDF͒ depending on the molar mass, is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF ͑DGPDF͒. The compositions of liquid and vapor emanating from the drops are calculated through four moments of their PDFs, 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, resulting into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions, and the effects 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 Re is investigated in the direct-numerical-simulation-accessible regime. The results encompass examination of the global layer characteristics, flow visualizations, and homogeneous-plane statistics at transition. Comparisons are performed with previous pretransitional MC-liquid simulations and with transitional single-component ͑SC͒ liquid-drop-laden mixing layer studies. Contrasting to pretransitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF. Unlike in pretransitional situations, regions of large composition standard deviation no longer necessarily coincide with those of large mean molar mass. The rotational and composition characteristics are all liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The classical energy cascade is found to be of similar strength, but the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation for MC flows. The kinetic energy and dissipation are liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from, a SGPDF. Eulerian and Lagrangian statistics of gas-phase quantities show that the different observation framework may affect the perception of the flow.

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

“…The number of drops precipitously declines away from Q = 0, and more on the Q > 0 side corresponding to regions of high vorticity than the Q < 0 side corresponding to regions of high strain; this effect has been experimentally observed by Fessler, Kulick & Eaton (1994) and numerically identified in many studies (e.g. Selle & Bellan 2007). The results show that all medium-grid LES calculations closely follow the corresponding FDNS, whereas the coarse-grid LES calculations follow the corresponding FDNS everywhere except for Q < 0, where they underestimate N. It thus appears that over the Q (δ ω,0 / U 0 ) 2 range shown in figure 4(a), predicting the number of drops at those flow locations can …”

Large Eddy Simulation composition equations for single-phase and two-phase fully multicomponent flows

“…The DNS governing equations for mixing and evaporation have been presented in [5,6] and transitional states have been created and analyzed in depth in [7]. Summarizing, the DNS equations consist of two sets of coupled governing equations, one for gas, the other for the drops.…”

“…is the vapor mass fraction with m being the molar mass of the gas (vapor and air), and S n vn ; S mole and S mass are evaporative sources of n vn , moles and mass, respectively, for which mathematical expressions have been given elsewhere [5][6][7]. The diffusion and diffusion-like term of Eq.…”

“…For reactive flows, the equation formulation of [5,7] can be enlarged by adding source terms: the molar reaction rate of vapor (gaseous fuel), _…”

“…When attempting to reduce the complexity of large elementary-reaction mechanisms, lumping of species has been proposed based on 'similar' species (like isomers) [1] and when modeling flames, bundling for modeling diffusivities has also been recommended [2]. In the same framework, a formulation has been proposed [3][4][5][6][7] for modeling SP and TP MC flows using statistical concepts that lump species according to their molar mass, m, a quantity strongly related to the diffusivity. DNS performed with this formulation has unraveled many fundamental aspects of MC flows.…”