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A spherical blast wave generated by a sudden release of a sphere of compressed gas is an important model problem to understand blast phenomena such as volcanic eruptions and explosive detonations. The resulting explosion flow physics, such as the instability at the gas contact discontinuity and the interaction between the shock wave and the gas contact, are dictated by the initial pressure and sound-speed ratios between the compressed gas and the ambience. Since the initial pressure and sound-speed ratios vary over a wide range in practical applications, it is of interest to investigate the scaling laws and similarity solutions formore » the spherical symmetric explosion flow. In the present study, numerical simulation of a spherical blast wave is performed. A long-term length scale that incorporates the initial charge radius and the initial pressure ratio is introduced. The trajectories of the main shock normalized by the long-term length scale for a wide range of parameters collapse after a short transition time, indicating an asymptotic similarity solution exists for the far field in the long term. With the assistance of this similarity solution, the full evolution of the main shock can be obtained semi-analytically. For near-field features, i.e. the gas contact and the secondary shock wave, only semi-similarity solutions are observed, which depend on the initial sound-speed ratio but not the initial pressure ratio. The gas contact and the secondary shock share the same scaling relations. Asymptotic analysis is performed to obtain the short-term dynamics of the gas contact, including the gas contact acceleration and the Atwood number, which are the key parameters determining the Rayleigh–Taylor instability development at the gas contact. The asymptotic contact radius as$$t\rightarrow \infty$$is also obtained, which is found to be well represented by the long-term length scale and thus only depends on the initial pressure ratio. A simple model of an oscillating bubble is employed to explain the scaling relation of the asymptotic gas contact radius.« less

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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 observedmore » 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. 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 performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. 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.« less

Here, the present paper addresses important fundamental issues of inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows through scaling analysis. In typical point-particle or two-fluid approaches, the fluid motion and convective heat transfer at the particle scale are not resolved and the momentum and energy coupling between fluid and particles are provided by proper closure models. By examining the kinetic energy transfer due to the coupling forces from the macroscale to microscale fluid motion, closure models are obtained for the contributions of the coupling forces to the energy coupling. Due to the inviscid origin of the added-massmore » force, its contribution to the microscale kinetic energy does not contribute to dissipative transfer to fluid internal energy as was done by the quasi-steady force. Time scale analysis shows that when the particle is larger than a critical diameter, the diffusive-unsteady kernel decays at a time scale that is smaller than the Kolmogorov time scale. As a result, the computationally costly Basset-like integral form of diffusive-unsteady heat transfer can be simplified to a non-integral form. Conventionally, the fluid-to-particle volumetric heat capacity ratio is used to evaluate the relative importance of the unsteady heat transfer to the energy balance of the particles. Therefore, for gas-particle flows, where the fluid-to-particle volumetric heat capacity ratio is small, unsteady heat transfer is usually ignored. However, the present scaling analysis shows that for small fluid-to-particle volumetric heat capacity ratio, the importance of the unsteady heat transfer actually depends on the ratio between the particle size and the Kolmogorov scale. Furthermore, the particle mass loading multiplied by the heat capacity ratio is usually used to estimate the importance of the thermal two-way coupling effect. Through scaling argument, improved estimates are established for the energy coupling parameters of each energy exchange mechanism between the phases.« less