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Numerical study of laminar, standing hydraulic jumps in a planar geometry

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Abstract

We solve the two-dimensional, planar Navier-Stokes equations to simulate a laminar, standing hydraulic jump using a Volume-of-Fluid method. The geometry downstream of the jump has been designed to be similar to experimental conditions by including a pit at the edge of the platform over which liquid film flows. We obtain jumps with and without separation. Increasing the inlet Froude number pushes the jump downstream and makes the slope of the jump weaker, consistent with experimental observations of circular jumps, and decreasing the Reynolds number brings the jump upstream while making it steeper. We study the effect of the length of the domain and that of a downstream obstacle on the structure and location of the jump. The transient flow which leads to a final steady jump is described for the first time to our knowledge. In the moderate Reynolds number regime, we obtain steady undular jumps with a separated bubble underneath the first few undulations. Interestingly, surface tension leads to shortening of wavelength of these undulations. We show that the undulations can be explained using the inviscid theory of Benjamin and Lighthill (Proc. R. Soc. London, Ser. A, 1954). We hope this new finding will motivate experimental verification.

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology, 400 076, Mumbai, India

    Ratul Dasgupta

  2. Department of Mechanical Engineering, Indian Institute of Science, 560 012, Bangalore, India

    Gaurav Tomar

  3. TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, 500 075, Narsingi, Hyderabad, India

    Rama Govindarajan

Authors
  1. Ratul Dasgupta
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  2. Gaurav Tomar
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  3. Rama Govindarajan
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Correspondence to Gaurav Tomar.

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Dasgupta, R., Tomar, G. & Govindarajan, R. Numerical study of laminar, standing hydraulic jumps in a planar geometry. Eur. Phys. J. E 38, 45 (2015). https://doi.org/10.1140/epje/i2015-15045-0

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  • DOI: https://doi.org/10.1140/epje/i2015-15045-0

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