Numerical Simulation of Cushioning Problem for Blunt Bodies Using Boundary Element Method

Abstract

Induced air pressure and resulting free surface profile due to air cushioning layer is studied. The study is mainly focused on 2D blunt circular bodies with constant downward speed. The problem is first solved for the air flow between the body and the free surface of the water. Then the results are employed to solve the problem for the water problem, numerically. Both air and water problem are assumed to be governed by Laplace potential equation. Depending on the induced pressure and velocity of the escaping air flow from cushioning layer, compressibility of the air is also included in the modeling. Gravitational acceleration is also included in the model. An iterative boundary element method is used for numerical solution of both air and water problems. Instantaneous pressure distribution and free surface profile are evaluated for different bodies. The results of calculation for large blunt bodies show that inviscid potential method can fairly approximate the problem for large blunt bodies. Additionally, the behavior of the air pressure for the very blunt body is impulsive and the magnitude of the peak pressure is in order of impact pressure of water entry. The obtained results are compared with analytical method. The comparison shows that as the bluntness of a body increases, the better agreement is concluded.

Air-cushioning effect and Kelvin-Helmholtz instability before the slamming of a disk on water

“…In this paper we will address this question, and show how the water surface is affected in the very last stages before impact, when the air is squeezed out from the gap between the liquid and the disk at increasing speeds. We will experimentally demonstrate that the resulting surface deformation is quite different for this case, supporting and substantiating prior speculations based on qualitative grounds [20][21][22][23], and on numerical [24,25] and theoretical arguments [23,[26][27][28]. Here, we combine high-speed imaging with a novel deflectometric technique which allows us to measure the vertical movements of the water surface just before the impact of a flat disk with micron precision, and succeed for the first time to experimentally characterize the motion of the free surface.…”

Air-cushioning effect and Kelvin-Helmholtz instability before the slamming of a disk on water

“…In this paper we will address this question and show how the water surface is affected in the very last stages before impact, when the air is squeezed out from the gap between the liquid and the disk at increasing speeds. We will experimentally demonstrate that the resulting surface deformation is quite different for this case, supporting and substantiating prior speculations based on qualitative grounds [20][21][22][23], and on numerical [24,25] and theoretical arguments [23,[26][27][28]. Here we combine high-speed imaging with a novel deflectometric technique which allows us to measure the vertical movements of the water surface just before the impact of a flat disk with micron precision and succeed to experimentally characterize the motion of the free surface.…”

“…To better understand this, we now focus on the liquid suction phenomenon, which has been reported in boundary-integral simulations [24,25] but never measured experimentally. As visible in Fig.…”

Slamming Liquid Impact and the Mediating Role of Air

“…We anticipate that in later stages before impact, the growth of h max may also interfere with the growth of h min . The upwards suction has been reported in boundary-integral simulations before [92,94] but not measured using experiments. In the present experiments, growth of h max was found to start at a much later stage than h min .…”

“…However, many phenomena depend crucially on what happens immediately before the moment of impact, when the ambient fluid (usually air) plays an important role. In the impact of a flat plate, ambient fluid flow, and how it might affect the interface before impact have been studied before using analytical and numerical techniques [89,90,91,92,93,94], but the dynamics at free-surface have not been precisely measured using experiments [23,24,95]. In this chapter, we address exactly this topic of experimentally measuring the free surface deflections caused due to the action of a rapidly escaping air layer before the water impact of a flat disc.…”