(230f) Numerical Investigation of Erosive Strength of Collapsing Cavitating Bubble in Cryogenic Environment Near Rigid Wall

Numerical investigation of erosive
strength of collapsing cavitating bubble in cryogenic environment near rigid
wall

¹Arpit Mishra^*, ¹Joydip
Mondal, ²Arnab Roy,³Rajaram Lakkaraju¹ and Parthasarathi
Ghosh

¹Cryogenic Engineering Centre, Indian Institute of Technology,
Kharagpur, India

²Department of Aerospace Engineering, Indian Institute of
Technology, Kharagpur, India

³Department of Mechanical Engineering, Indian Institute of
Technology, Kharagpur, India

Latent heat for cryogenic fluids is
considerably lower than that of water with a steeper slope of the
Clausius-Clapeyron curves^1,2, making it apt to vaporize with a
minimal amount of heat flux from the environments, forming a gas-liquid
two-phase flow. In many cryogenic fluid handling equipment, liquid-embedded
vapor cavities ensue due to localized pressure reduction below vapor pressure.
These cavities usually comprise number of vapor bubbles which might violently
collapse in high pressure regions of an accelerated flow. Impulsive force of
these collapsing cavitating bubbles in the vicinity of the rigid boundary can
lead to significant erosive damage. The high impact pressure resulting from jet
water hammer effect and collapsing shock waves near rigid geometries, due to
collapsing cavitating bubble has advantages in stone fragmentation, shock wave
lithotripsy and can erode hydrofoil altering the blade profile of any
turbo-machinery. Study of individual collapsing bubbles is still a cornerstone
to understanding the erosive damage process. To study the dynamically changing
interfacial structures due to the collapse of the cavitating bubble, and the
mechanism whereby forces large enough to cause damage are brought to bear
against a rigid wall is still somewhat obscure in cryogenic liquids.

Hancox & Brunton³ have
shown in experiments that collapse results in multiple jet impacts at a speed
of 90 m/sec that can even erode stainless steel. Plesset and Chapman⁴
reported that asymmetries triggered as a result of a solid wall could produce
cavitation damage by the impact of the liquid jet. Chahine⁵ observed
that violent processes take place in the collapse of bubbles revealing
themselves with the emission of shock, and it is not possible to define the
aggressiveness of cavitation erosion on a purely hydrodynamic basis. Tomita⁶
explained that jet and shock both carry damage potential, but the extent of
damage depend upon the non-dimensional stand-off distance from the rigid
boundaries. Although, it is not clear which one is the dominant mechanism of cavitation
induced erosion.

In this paper, single fluid
two-phase homogeneous mixture based VOF method has been used to simulate the
collapse of a spherical cavitating bubble (R max = 400 mm)
near a flat solid surface dipped in cryogenic fluid in a fully compressible
medium for different standoff distances (g=h/R _max). It has been
observed that due to the
collapse of torus bubble, microjets directed towards the rigid boundary can
produces an instantaneous water hammer pressure p _wh = 340 MPa (for g=0.7),  in case of water is more than the
yield strength of the material of the rigid surface, i.e. stainless steel (250
MPa), and can indent the surface.

Keywords: Bubble dynamics, Water hammer, Cryogenic,
Jets, Shock impact

References

[1]. 
Arpit M,
Rajaram L, Arnab R, Parthasarathi G. Influence of Thermophysical Properties of
Cryogenic Fluids on Growth and Collapse of Cavitating Bubbles

[2]. 
Arpit M, Arnab
R, Parthasarathi G. A computational study for characterizing cavitating flow in
hydrofoils operating at cryogenic conditions. 2017:6-12. doi: 10.18462/iir.cryo.2017.072

[3]. 
Hancox,
NL, Brunton, JH, (1966). A
Discussion on Deformation of Solids by the Impact of Liquids, and its Relation
to Rain Damage in Aircraft and Missiles, to Blade Erosion in Steam Turbines,
and to Cavitation Erosion. Phil. Trans. R. Soc. A. Vol. 260, No. 1110,
pp. 161-167.doi: 10.1098/rsta.1966.0036

[4]. 
Plesset, MS,
Chapman, RB, (1971). Collapse of an initially spherical vapour cavity in the
neighborhood of a solid boundary. J. Fluid Mech. 47 (2). pp. 283-290,
doi:10.1017/S0022112071001058.

[5]. 
Chahine, GL,
(2009). Numerical Simulation of Bubble Flow Interactions. J. Hydrodyn. Ser. B.
Vol. 21, Issue 3, pp. 316-332, doi:10.1016/S1001-6058(08)60152-3

[6]. 
Tomita Y, P.B.
Robinson, R.P. Tong, Growth and collapse of cavitation bubbles near a curved
rigid boundary, J. Fluid Mech., 466 (2002), pp. 259-283