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Use of transpiration for reduction of resistance to relative movement of parallel plates

Longyin Jiao1,* and J. M. Floryan2,†

  • 1School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China
  • 2Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9

  • *Visiting graduate student.
  • †floryan@uwo.ca
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Phys. Rev. Fluids 6, 014101 – Published 11 January, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.014101

Abstract

An analysis of the effects of transpiration on the forces required to maintain the relative movement of parallel plates has been carried out using a two-dimensional model problem. Transpiration was placed either at the stationary or at the moving plates. In both cases its spatial distribution was made of periodic components, but the explicit results are provided only for the commensurable systems. It is shown that the force required to maintain plate movement is affected by the reduction of the effective spacing between the plates caused by formation of a cushion made of the transpiration “bubbles,” by the elimination of the direct contact between the fluid in the slot and the plate with transpiration, and by nonlinear streaming generated by the transpiration. It is possible to reduce the pulling force through the proper selection of the transpiration pattern. The transpiration wave number resulting in the largest reduction corresponds to the maximization of the nonlinear streaming. The largest reduction of resistance is achieved by concentrating transpiration at a single transpiration wave number and avoiding commensurability effects. An analysis of finite-slot transpiration demonstrates the existence of the reduced distribution model, i.e., the performance of such systems can be well approximated using just a few leading modes from the Fourier expansions describing such transpirations. The analysis of energy costs shows that the overall energy cost of the modified flow is higher than the cost of the unmodified flow. Conditions leading to the minimization of this cost have been identified. These conditions describe the most effective use of transpiration as a propulsion augmentation system. Transfer of transpiration to the moving plate does not affect the reduction of resistance and does not change the energy cost associated with transpiration.

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Phys. Rev. Fluids 6, 014101– Published 11 January, 2021
  • Received 5 July 2020
  • Accepted 26 October 2020
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