Water entry of an expanding wedge/plate with flow detachment

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to π. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions

Liquid impact on a permeable solid body

All rights reserved.The free surface flow and the hydrodynamic loads generated by impact between a liquid wedge and a permeable solid body are investigated. The study is carried out within the framework of self-similar solution, which is realistic for this kind of configuration and over the short period of impact. We study the effect of liquid penetration through the porous/perforated solid surface on the pressure distribution and flow pattern. An integral hodograph method is employed to convert the differential equation in the fluid domain into integral equations along the axes of a parameter plane, from which the problem corresponding to the impermeable solid surface is a special case. The system of integral equations are solved numerically using the method of successive approximations. Results are presented for streamline patterns and pressure distribution along the solid surface of permeable wedges

Free-surface gravity flow due to a submerged body in uniform current

The hydrodynamic problem of a body submerged beneath a free surface in a current is considered. The mathematical model used is based on the velocity potential theory with fully nonlinear boundary conditions. The integral hodograph method used previously in a simply connected domain is extended for the present problem to a doubly connected domain. Analytical expressions for the complex velocity and for the complex potential are derived in a rectangular region in a parameter plane, involving the theta functions. The boundary-value problem is transformed into a system of two integral equations for the velocity modulus on the free surface and for the slope of the submerged body surface in the parameter plane, which are solved through the successive approximation method. Case studies are undertaken both for a smooth body and for a hydrofoil with a sharp edge. Results for the free surface shape, pressure distribution as well as resistance and lift are presented for a wide range of Froude numbers and depths of submergence. It further confirms that at each submergence below a critical value there is a range of Froude numbers within which steady solution may not exist. This range increases as the submergence decreases. This applies to both a smooth body and a hydrofoil. At the same time it is found that at any Froude number beyond a critical value the wave amplitude and the resistance decrease as the body approaches the free surface. In these cases nonlinear effects become more pronounced

Local flow at plate edge during water entry

The local flow near the edge of a horizontal plate impacting a flat liquid surface is investigated through velocity potential flow theory. The inner solution is matched with the outer solution. The far field of the inner solution is assumed to be far away from the other edge of the plate, and thus, its effect can be neglected. The effects of surface tension, viscous friction, and gravity are accounted for in the fully nonlinear dynamic boundary condition on the free surface. When one of these effects is dominant and the other two can be ignored, it is then possible to use self-similar variables to describe the local flow if the entry speed varies with time in a corresponding manner. Detailed results for various self-similar solutions are provided, and the relative importance of the Weber number, Reynolds number, and Froude number is investigated. Simulations are also undertaken for general non-similar flow, and the comparison with the experimental data is also made

Boundary shear flow past a cylinder near a wall

An investigation on boundary shear flow past a circular cylinder near a wall is numerically performed via a stabilized finite element method. The main focus is to uncover its major difference with the flows corresponding to the symmetry boundary, and to two identical circular cylinders in a side-by-side arrangement. In particular at Reynolds number extensive simulations are made for different gaps between the cylinder and wall. It is noted that in the wake of the cylinder the vortex contour lines shift upwards. At the flow behind a cylinder near the wall may be time dependent. With a reduction of the gap spacing to a magnitude in (0.75,1), the vortex shedding nearly vanishes. For the flow behind two identical circular cylinders side and side, the flow may change from periodic flow to totally irregular one. The drag force CD, lift force CL,rms and Strouhal number St of the circular cylinder near the wall vary differently with the gap, compared with those in the other two cases. When the cylinder is located in the boundary layer, the boundary shear flow has strong effect on the hydrodynamic quantities. Extensive simulations are also made for 400, 600 and 800. It is found that the Reynolds number has strong effect on the flow and force on the cylinder, not only through the variation of Re itself but also the boundary layer of the wall. Withe Re increasing, strong vortex shedding from the near-wall cylinder at starts above a Re in (200, 300)

Hydrodynamic force on a ship floating on the water surface near a semi-infinite ice sheet

The hydrodynamic problem of wave interaction with a ship floating on the water surface near a semi-infinite ice sheet is considered based on the linearized velocity potential theory for fluid flow and the thin elastic plate model for ice sheet deflection. The properties of an ice sheet are assumed to be uniform, and zero bending moment and shear force conditions are enforced at the ice edge. The Green function is first derived, which satisfies both boundary conditions on the ice sheet and free surface, as well as all other conditions apart from that on the ship surface. Through the Green function, the differential equation for the velocity potential is converted into a boundary integral equation over the ship surface only. An extended surface, which is the waterplane of the ship, is introduced into the integral equation to remove the effect of irregular wave frequencies. The asymptotic formula of the Green function is derived and its behaviors are discussed, through which an approximate and efficient solution procedure for the coupled ship/wave/ice sheet interactions is developed. Extensive numerical results through the added mass, damping coefficient and wave exciting force are provided for an icebreaker of modern design. It is found that the approximate method can provide accurate results even when the ship is near the ice edge, through which some insight into the complex ship/ice sheet interaction is investigated. Extensive results are provided for the ship at different positions, for different ice sheet thicknesses and incident wave angles, and their physical implications are discussed

Effect of Reynolds number on amplitude branches of vortex-induced vibration of a cylinder

The effect of Reynolds number on curves of the transverse-only motion amplitude of a circular cylinder with the body mass m∗=0.935 and the damping ratio ζ=0.00502 in the turbulent flow range is investigated systematically using a two-dimensional in-house code developed based on lattice Boltzmann method. Large eddy simulation is chosen as the turbulence model to describe viscous, incompressible and Newtonian fluid and the immersed boundary method is used to impose the boundary condition on the moving cylinder surface. Multi-block model is adopted to improve the accuracy and the computational efficiency. It is well established that when the variation of Reynolds number changes with the reduced velocity, there are three branches in the motion amplitude curve of a low mass cylinder, including initial, upper and lower branches connected by two jumps. However, in the present work, Reynolds number and reduced velocity are considered as independent parameters. Detailed results are provided for thevariationsofmotionamplitude,motionfrequencyandliftcoefficientagainstthereducedvelocity in the lock-in region at different fixed Reynolds numbers. The results show that at a fixed Reynolds number the motion amplitude curve has two branches. At lower range of Reynolds number calculated, there are only initial and upper branches, and at higher range, there are only upper and lower branches. Also, the motion amplitude against the Reynolds number near the jumps is studied when the reduced velocity is fixed. It shows that the values of amplitude near the jumps are very sensitive to Reynolds number

Splash jet generated by collision of two liquid wedges

A complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined