雷诺数和施密特数对激波-气泡相互作用中变密度混合的影响

Effects of Reynolds number and Schmidt number on variable density mixing in shock bubble interaction

惯性约束聚变、水动力空化侵蚀和微观尺度激波加速流动中的激波-气泡相互作用(SBI)构型处于高黏度(低雷诺数)或低扩散率(高施密特数)环境中,其混合性能尚不清楚.通过测定宽范围内的粘度和扩散系数,采用高分辨率数值模拟研究了雷诺数Re和施密特数Sc对SBI流动结构和混合行为的影响.次级斜压涡度(SBV)增长明显受雷诺数的影响,表现为斜压涡和黏性耗散之间的生长抑制涡度动力学平衡.混合速率受施密特数的影响,标度为χ^(∗)=β·Sc^(−α),其中系数β∼Re−0.2和标度指数α∼Re−0.385.混合标度表明,较高雷诺数下的SBV拉伸增强导致混合速率对施密特数的依赖性减弱,这可能为实际应用中的混合增强设计开辟新的途径.

Effects of Reynolds(Re)number and Schmidt(Sc)number on the flow structures and variable density mixing are numerically investigated through the canonical shock cylindrical bubble interaction.By determining the viscosity and diffusivity within a wide range,the controlling parameters,total vortex circulation,and compression rate,are conservative under a broad range of Re and Sc numbers(Re≈10^(3)-10^(5)and Sc≈0.1-5)in the same shock Mach(Ma)number condition(Ma=2.4).As for the Re number effect,the circulation of secondary baroclinic vorticity(SBV),induced by the main vortex centripetal acceleration,is observed to be higher in high Re number and vice versa.Based on the vorticity transport equation decomposition,a growth-inhibition vorticity dynamics balance mechanism is revealed:the vorticity viscous term grows synchronously with baroclinic production to inhibit SBV production in low Re number.By contrast,the viscous term terminates the baroclinic term with a time lag in high Re number,leading to the SBV production.Since the SBV reflects the local stretching enhancement based on the advection-diffusion equation,mixing is influenced by the Sc number in a different behavior if different Re numbers are considered.The time-averaged variable density mixing rate emerges a scaling law with Sc number asχ^(∗)=β·Sc^(−α),where the coefficientβ∼Re−0.2 and the scaling exponentα∼Re−0.385.The understanding of Re number and Sc number effect on variable density mixing provides an opportunity for mixing enhancement from the perspective of designing the viscosity and diffusivity of the fluid mixture.