Extension of the Integral Boundary Layer Method to Thin Film Flow Created by Vertical Cylindrical Jet Dispense

  • Kebinger, Simon (Graz University of Technology)
  • Steiner, Helfried (Graz University of Technology)

Please login to view abstract download link

The present work applies the classical Kármán-Pohlhausen-based Integral Boundary Layer (IBL) method for computationally investigating thin film flow generated by a circular liquid jet impinging on a moving, wet surface. The work extends the previous work of Liu et al. [1], who considered spatially one- dimensional shallow water flow created by the impingement of a planar slot jet, to the more challeng- ing spatially two-dimensional counterpart met with circular jet impingement. The governing system of hyperbolic partial differential equations is solved using an (in-house) approximate Riemann (Harten- Lax-Leer) solver, essentially following the concept presented by LeVeque [2]. Volume-of-Fluid based three-dimensional high-fidelity CFD simulations were performed as well, providing accurate reference data for comprehensive validation. The comparison against the CFD results proved the developed IBL model is capable of describing the complex flow field around the impingement fairly accurately, as- sessing in particular the predicted geometry of the emerging bow-shaped hydraulic jump as well as the obtained spatial variation of wall shear stress along the moving substrate. Underneath the impinging jet and some limited distance further downstream both, 3D CFD and 2D IBL are also shown to be in good agreement with an analytical self-similarity solution developed by Libby [3]. Upstream towards the bow wave, the similarity solution increasingly deviates. The validation of the IBL predictions further clearly revealed the shortcomings of commonly used assumptions for the dependence of velocity profiles on the vertical distance to the wall, which often leads to underestimated wall shear stresses. Gaussian shape based profiles are tested as promising alternatives to the popular choices of parabolic or quartic polynomials, which have been mostly used in spatially one-dimensional shallow water flow [1, 4]. References [1] Xiaohe Liu et al. “Flow of a shallow film over a moving surface”. In: Physics of Fluids 34.8 (Aug. 2022), p. 083602. ISSN: 1070-6631. DOI: 10.1063/5.0099587. [2] Randall J LeVeque. Finite volume methods for hyperbolic problems. Reprinted. Cambridge: Cam- bridge Univ. Press, 2007, p. 558. ISBN: 9780521009249. [3] PAUL A. LIBBY. “Wall Shear at a Three-Dimensional Stagnation Point with a Moving Wall”. In: AIAA Journal 12.3 (Mar. 1974), pp. 408–409. ISSN: 0001-1452. DOI: 10.2514/3.49255. [4] S. Kebinger, G. Brenn, and H. Steiner. “Thin film flow on spinning