Annular Newtonian Poiseuille flow with pressure-dependent wall slip

Kostas D. Housiadas, Evgenios Gryparis, Georgios C. Georgiou
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Abstract

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier's slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.
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随压力变化的壁面滑移的环状牛顿泊伊流
我们利用纳维耳滑移定律和随压力呈指数变化的滑移参数,研究了随压力变化的壁面滑移对稳定的牛顿环形波瓦耶流的影响。通过实施一种以小的无量纲压力相关滑移参数为条件的常规扰动方案,对无量纲控制方程和伴随的辅助条件进行了最高二阶的解析求解。此外,还得出了保持恒定容积流量所需的平均压降的明确公式。通过采用收敛加速技术对其进行适当的后处理,以提高原始扰动序列的精度。当壁面滑移较弱时,与压力相关的壁面滑移效应更为明显。结果表明,在雷诺数变得足够大之前,平均压降实际上保持不变。值得注意的是,随着环形间隙的减小,所有与压力相关的壁面滑移现象都会被放大。
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