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Register a new userSelf-similar solution of a supercritical two-phase laminar mixing layer
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Added by
Jordi Poblador Ibanez
Publication date
2020
fields
Physics
and research's language is
English
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Previous works for a liquid suddenly contacting a gas at a supercritical pressure show the coexistence of both phases and the generation of diffusion layers on both sides of the liquid-gas interface due to thermodynamic phase equilibrium. A related numerical study of a laminar mixing layer between the liquid and gas streams in the near field of the splitter plate suggests that mass, momentum and thermal diffusion layers evolve in a self-similar manner at very high pressures. In this paper, the high-pressure, two-phase, laminar mixing-layer equations are recast in terms of a similarity variable. A liquid hydrocarbon and gaseous oxygen are considered. Freestream conditions and proper matching conditions at the liquid-gas interface are applied. To solve the system of equations, a real-fluid thermodynamic model based on the Soave-Redlich-Kwong equation of state is selected. A comparison with results obtained by directly solving the laminar mixing-layer equations shows the validity of the similarity approach applied to non-ideal two-phase flows. Even when the gas is hotter than the liquid, condensation can occur at high pressures while heat conducts into the liquid. Finally, a generalized correlation is proposed to represent the evolution of the mixing layer thickness for different problem setups.
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Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product of density and viscosity in the gas phase showing a nearly constant result within the laminar flow region with no instabilities. Sufficiently thick diffusion layers form around the liquid-gas interface to support the case of continuum theory and phase equilibrium. While molecules are exchanged for both species at all pressures, net mass flux across the interface shifts as pressure is increased. Net vaporization occurs for low pressures while net condensation occurs at higher pressures. For a mixture of n-decane and oxygen, the transition occurs around 50 bar. The equilibrium values at the interface quickly reach their downstream asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). Validity of the boundary layer approximation and similarity are shown in both phases for Reynolds numbers greater than 239 at 150 bar. Results for other pressures are also taken at high Reynolds numbers. Thereby, the validity of the boundary layer approximation and similarity are expected. However, at very high pressures, the similar one-dimensional profiles vary for different problem constraints.
Three-dimensional laminar flow structures with mixing, chemical reaction, normal strain, and shear strain qualitatively representative of turbulent combustion at the small scales are analyzed. A mixing layer is subjected to counterflow in the transverse y- and z-directions. Both non-reactive and reactive flows are examined. Reduction of the three-dimensional boundary-layer equations to a one-dimensional similar form is obtained allowing for heat and mass diffusion with variations in density and properties. In steady configurations, a set of ODEs governs the three velocity components as well as the scalar-field variables. A flamelet model for individual diffusion flames with combined shear and normal strain is developed. Another model with solution in similar form is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. Results for the velocity and scalar fields are found for ranges of Damkohler number Da, normal strain rate due to the counterflow, streamwise-velocity ratio across the mixing layer, Prandtl number, and Mach number. For the flamelet model, a conserved scalar is cast as the independent variable to give an alternative description of the results. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. There is indication of diffusion control for partially premixed flames in the multi-branched flame situation. The enhancement of the mixing and combustion rates by imposed normal strain on a shear layer can be very substantial. Also, the imposition of shear strain and thereby vorticity on the counterflow can be substantial indicating the need for flamelet models with both shear strain and normal strain.
A two-phase, low-Mach-number flow solver is proposed for variable-density liquid and gas with phase change. The interface is captured using a split Volume-of-Fluid method, which solves the advection of the reference phase, generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass. A sharp interface is identified by using PLIC. Mass conservation is achieved in the limit of incompressible liquid, but not with the liquid compressibility and mass exchange. This is a relevant modeling choice for two-phase mixtures at near-critical and supercritical pressure conditions for the liquid but away from the mixture critical temperature. Under this thermodynamic environment, the dissolution of lighter gas species into the liquid phase is enhanced and vaporization or condensation can occur simultaneously at different interface locations. The numerical challenge of solving two-phase, supercritical-pressure flows is greater than simpler two-phase solvers because: a) local phase equilibrium is imposed at each interface cell to determine temperature, composition, or surface tension coefficient; b) a real-fluid thermodynamic model is used to obtain fluid properties; and c) necessary phase-wise values for certain variables are obtained via extrapolation techniques. To alleviate the increased numerical cost, the pressure Poisson equation (PPE) used to solve the low-Mach-number flow is split into a constant-coefficient implicit part and a variable-coefficient explicit part. Thus, a Fast Fourier Transform method can be used for the PPE. Various verification tests are performed to show the accuracy and viability of the present approach. The growth of surface instabilities in a binary system composed of liquid n-decane and gaseous oxygen at supercritical pressures for n-decane is analyzed. Other features of supercritical liquid injection are also shown.
The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas-liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. In order to investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been carried out. The turbulent dissipation is shown to be highly demanding on mesh resolution compared to other terms in TKE budget. The results obtained with the finest mesh are shown to be not far from converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.
Numerical work on shockwave/boundary-layer interactions (SBLIs) to date has largely focused on span-periodic quasi-2D configurations that neglect the influence lateral confinement has on the core flow. The present study is concerned with the effect of flow confinement on Mach 2 laminar SBLI in rectangular ducts. An oblique shock generated by a 2 degree wedge forms a conical swept SBLI with sidewall boundary layers before reflecting from the bottom wall of the domain. Multiple large regions of flow-reversal are observed on the sidewalls, bottom wall and at the corner intersection. The main interaction is found to be strongly three-dimensional and highly dependent on the geometry of the duct. Comparison to quasi-2D span-periodic simulations showed sidewalls strengthen the interaction by 31% for the baseline configuration with an aspect ratio of one. The length of the shock generator and subsequent trailing edge expansion fan position was shown to be a critical parameter in determining the central separation length. By shortening the length of the shock generator, control of the interaction and suppression of the central interaction is demonstrated. Parametric studies of shock strength and duct aspect ratio were performed to find limiting behaviours. For the largest aspect ratio of four, three-dimensionality was visible across 30% of the span width away from the wall. Topological features of the three-dimensional separation are identified and shown to be consistent with `owl-like separations of the first kind. The reflection of the initial conical swept SBLIs is found to be the most significant factor determining the flow structures downstream of the main interaction.
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