Submerged laminar jet impingement on a plane

Abstract

Submerged laminar jet impingement on a plane is studied using computation. Steady-state Navier-Stokes equations for the axisymmetric case are solved numerically. The extent of the infinite flow is approximated by applying the boundary conditions at a finite but sufficiently large distance. The tube-exit velocity profile is assumed to be either a fully developed parabolic profile or a flat profile. For the former case, two different nozzle heights from the target plane are considered. The presence of a toroid-shaped eddy at low values of Reynolds number, Re, leads to some interesting observations such as the manner in which the wall shear stress depends on Re. An increase in the height of the nozzle exit from the target plane decreases the wall shear stress, more so at lower values of Re. A change from the parabolic exit velocity profile to the flat profile leads to a decrease in wall shear stress due to decreased momentum flux. The study was motivated by experiments designed to measure the yield shear strength of the vascular endothelium wherein a small saline jet was used to erode the tissue by normal impingement.

Wall shear stress from jetting cavitation bubbles

“…The high speed recorded images with pixel size of 20 µm are used to validate the gas phase dynamics and thus the flow field in the numerical simulations. For the validation of the wall shear stress from the simulations, we benchmarked the model with earlier simulations of a submerged steady wall jet impinging on a surface Deshpande & Vaishnav (1982), see Appendix. We also compare the simulation result with experiments Dijkink & Ohl (2008) of cavitation bubble induced wall shear stress.…”

“…Historically, the shear stress generated from steady impinging jets on solid walls has been solved by Glauert (1956), and confirmed through simulations (Deshpande & Vaishnav 1982;Phares et al 2000), and experiments (Narayanan et al 2004;Visser et al 2015). However, the shear stress produced by transient jets from near wall cavitation has recently received more attention, in particular for its importance for surface cleaning (Ohl et al 2006a;Kim et al 2009;Gonzalez-Avila et al 2011) and cell membrane poration cells (Ohl et al 2006b;Le Gac et al 2007).…”

“…To validate the calculation by equation 3.1, we perform a simulation of the steady submerged wall jet simulation and compare the results with Glauert (1956)'s analytical solution and the classical simulation simulation from Deshpande & Vaishnav (1982), see Appendix. The comparisons indicate that the calculation of the wall shear stress with the present model is reliable once the region with constant shear rate within the boundary layer is resolved.…”

Surfactant Adsorption Kinetics by Total Internal Reflection Raman Spectroscopy. 1. Pure Surfactants on Silica

“…Most modeling has been done on flow systems comprising a hole in a plate rather than a nozzle, in order to minimize the formation of vortices either side of the nozzle. 27 However, Melville et al 28 showed that the flux at the surface was only ∼ 2% greater for a submerged nozzle compared to a hole in a plate, and so the difference in flux can be neglected in all but the most precise work. Unless otherwise specified the surfactant solutions were injected at a rate of 0.5 mL min −1 corresponding to a mean flow rate in the inlet pipe of 0.27 mm s −1 .…”

The wall shear stress produced by the normal impingement of a jet on a flat surface

“…Recently, a few applications that utilize the shear imposed at the surface by impinging jets have been discussed in the literature. Deshpande & Vaishnav (1982) used submerged impinging saline jets to probe the shear strength of the endothelial surface of a vascular tissue. The structure of this delicate layer of cells can be visibly altered by excessive applied shear.…”