FLOW SEPARATION AT THE INITIAL STAGE OF THE OBLIQUE WATER ENTRY OF A WEDGE B.S. Yoon and Y.A. Semenov School of Naval Architecture and Ocean Engineering University of Ulsan, Republic of Korea E-mail: bsyoon@ulsan.ac.kr , semenov@a-teleport.com ABSTRACT The limit combination of the initial parameters corresponding to flow separation from the wedge vertex during the initial stage of the oblique impact of a wedge on a liquid half-space is investigated on the basis of an analytical solution of the problem. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is two-dimensional and potential. The analysis revealed a limit combination of the initial parameters at which the pressure along the whole length of one side of the wedge becomes less than the atmospheric pressure. Such a pressure distribution results in the ventilation of the wedge side, which starts from the contact point on the free surface and extends suddenly along the whole length of the wedge side, thus leading to flow separation from the wedge vertex. I. INTRODUCTION The problem of body penetration into fluids is topical in applications concerned with high-speed planing boats, seaplanes, half-submerged propellers, ships and offshore platforms designed to operate in a heavy sea [1]. Various initial parameters such as the direction of the entry velocity and the body orientation with respect to the free surface may correspond to different types of the flow morphology depending on a particular combination of these initial parameters. The present study is focused on one aspect of the water impact of wedge-shaped bodies, namely, on the onset of flow separation at the wedge vertex, which may occur due to an arbitrary wedge orientation and the horizontal component of the entry velocity. The present study is focused on the effect that the horizontal component of the velocity exerts on the flow parameters during the initial stage of the water impact. The fluid is assumed to be ideal, weightless and with negligible surface tension effects. Two types of the flow depending on the position of flow separation are possible. For the first type studied in the present work, it is assumed that there is no flow separation at the wedge vertex, and therefore the velocity magnitude and pressure become infinite at the wedge vertex. Although infinite velocities in real flows do not occur, flow separation at the wedge vertex due to cavitation requires some physical conditions for the growth of cavitation nuclei contained in the real liquid. The dynamics of the cavitation nuclei is governed by the negative external pressure in the flow field and the time, and therefore the occurrence of cavitation at the wedge vertex depends on the pressure distribution along the wedge side and the flow velocity. It should also be noted that real wedge-shaped bodies have rounded edges. Even a small radius of the edge prevents the velocity from becoming infinite while affecting other flow parameters only slightly. In this study we assume that cavitation at the wedge vertex does not occur and flow separation depends on the flow characteristics enabling the ventilation of one wedge side. Such a type of the flow morphology is confirmed by experiments [2]. 2. ANALYSIS OF THE FLOW PARAMETERS AT THE ONSET OF FLOW SEPARATION An analytical solution for the asymmetric/oblique water entry of a wedge which does not assume flow separation from the wedge vertex has been derived in [3] by using an advanced hodograph method. A sketch of the flow and the definitions of the geometric parameters are shown in Fig. 1. Figure 1. Sketch of water entry of a wedge The pressure coefficient ) 5 . 0 /( ) ( 2 y a V P P p ρ − = along the wedge sides is defined in terms of the vertical component y V of the entry velocity. The force coefficients on the right and left wedge sides, nR C and nL C , are evaluated by integrating the pressure along the wedge sides { } { } ∫ = } , { 0 , 2 , ) ( 2 B O S L R y nL nR dS S P H V C ρ where th V H y = , ] cot [cot sin L R v h β β γ + = ∞ ∞ , ∞ v and ∞ γ are the magnitude and angle of the entry velocity; R β and