Gupta Ronak, Alam Meheboob
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India.
Phys Rev E. 2017 Feb;95(2-1):022903. doi: 10.1103/PhysRevE.95.022903. Epub 2017 Feb 22.
Hydrodynamic fields, macroscopic boundary conditions, and non-Newtonian rheology of the acceleration-driven Poiseuille flow of a dilute granular gas are probed using "direct simulation Monte Carlo" method for a range of Knudsen numbers (Kn, the ratio between the mean free path and the macroscopic length), spanning the rarefied regime of slip and transitional flows. It is shown that the "dissipation-induced clustering" (for 1-e_{n}>0, where e_{n} is the restitution coefficient), leading to inhomogeneous density profiles along the transverse direction, competes with "rarefaction-induced declustering" (for Kn>0) phenomenon, leaving seemingly "anomalous" footprints on several hydrodynamic and rheological quantities; one example is the well-known rarefaction-induced temperature bimodality, which could also result from inelastic dissipation that dominates in the continuum limit (Kn→0) as found recently [Alam et al., J. Fluid Mech. 782, 99 (2015)JFLSA70022-112010.1017/jfm.2015.523]. The simulation data on the slip velocity and the temperature slip are contrasted with well-established boundary conditions for molecular gases. A modified Maxwell-Navier-type boundary condition is found to hold in granular Poiseuille flow, with the velocity slip length following a power-law relation with Knudsen number Kn^{δ}, with δ≈0.95, for Kn≤0.1. Transverse profiles of both first [N_{1}(y)] and second [N_{2}(y)] normal stress differences seem to correlate well with respective density profiles at small Kn; their centerline values [N_{1}(0) and N_{2}(0)] can be of "odd" sign with respect to their counterparts in molecular gases. The phase diagrams are constructed in the (Kn,1-e_{n}) plane that demarcates the regions of influence of inelasticity and rarefaction, which compete with each other resulting in the sign change of both N_{1}(0) and N_{2}(0). The results on normal stress differences are rationalized via a comparison with a Burnett-order theory [Sela and Goldhirsch, J. Fluid Mech. 361, 41 (1998)JFLSA70022-112010.1017/S0022112098008660], which is able to predict their correct behavior at small values of the Knudsen number. Lastly, the Knudsen paradox and its dependence on inelasticity are analyzed and contrasted with related recent works.
利用“直接模拟蒙特卡洛”方法，在一系列克努森数（Kn，平均自由程与宏观长度之比）范围内，对稀薄颗粒气体加速驱动的泊肃叶流的流体动力学场、宏观边界条件和非牛顿流变学进行了探究，涵盖了滑移和过渡流的稀薄区域。结果表明，“耗散诱导聚集”（对于1 - eₙ > 0，其中eₙ是恢复系数）导致沿横向方向的密度分布不均匀，这与“稀薄诱导解聚”（对于Kn > 0）现象相互竞争，在几个流体动力学和流变学量上留下看似“异常”的痕迹；一个例子是著名的稀薄诱导温度双峰性，这也可能由在连续介质极限（Kn→0）中占主导的非弹性耗散导致，如最近所发现的[阿拉姆等人，《流体力学杂志》782, 99 (2015)JFLSA70022 - 112010.1017/jfm.2015.523]。将滑移速度和温度滑移的模拟数据与分子气体已确立的边界条件进行了对比。发现一种修正的麦克斯韦 - 纳维型边界条件在颗粒泊肃叶流中成立，对于Kn≤0.1，速度滑移长度与克努森数Kn^δ遵循幂律关系，其中δ≈0.95。在小Kn时，第一法向应力差[N₁(y)]和第二法向应力差[N₂(y)]的横向分布似乎都与各自的密度分布有很好的相关性；它们的中心线值[N₁(0)和N₂(0)]相对于分子气体中的对应值可能具有“奇数”符号。在(Kn, 1 - eₙ)平面中构建了相图，该相图划分了非弹性和稀薄的影响区域，它们相互竞争导致N₁(0)和N₂(0)的符号变化。通过与伯内特阶理论[塞拉和戈德希尔施，《流体力学杂志》361, 41 (1998)JFLSA70022 - 112010.1017/S0022112098008660]进行比较，对法向应力差的结果进行了合理化分析，该理论能够预测在小克努森数下它们的正确行为。最后，分析了克努森悖论及其对非弹性的依赖性，并与近期相关工作进行了对比。
