Iskender Sahin

Application of a panel method to hydrodynamics of underwater vehicles

A low-order singularity panel method based on Greens formulation is used to predict the hydrodynamics characteristics of underwater vehicles. The low-order modeling employs constant strength sources and doublets, and the body surface is modeled by quadrilaterals. The method is first applied to predicting the force and moment coefficients of underwater vehicles for the body-alone and finned configurations. Hydrodynamic coefficients of added mass and added moment of inertia are also calculated by modifying the code. Results for several two and three-dimensional bodies show the usefulness of the method for predicting the added mass and added moment of inertia.

Added mass coefficients for submerged bodies by a low-order panel method

The added mass coefficients for two and three-dimensional submerged bodies were calculated using a low-order panel code. The source and dipole strengths, and the panel surface area for each panel, were used to compute the integrals needed for added mass in all six degrees of motions. Several applications of this method were used in comparing the results with the theoretical, when available, experimental or other numerical results. The method was found to be successful in predicting the added mass coefficients using relatively low numbers of panels.

Simulation of three-dimensional finite-depth wave phenomenon for moving pressure distributions

The flow field and the bottom pressure signatures due to an air cushion vehicle are calculated by analytical and computational means. The singularities in the integrals from the theoretical analyses are removed by using the Cauchy`s residue theorem and the resulting integrals are numerically evaluated by the adaptive quadrature routines of QUADPACK.

Three-dimensional flow around a submerged body in finite-depth water

Abstract The three-dimensional fluid flow around an axisymmetric body submerged in a finite-depth fluid is calculated by an analytical/numerical method based on a Greens function formulation. The flow around a submerged axisymmetric body, such as the infinite-fluid analogue of a Rankine body, can be constructed by superposition of a source and a sink along the axis of symmetry. Analytical evaluation is complicated because of the singular Cauchy-type principal-value integrals with infinite and semi-infinite limits. In this study these integrals are evaluated by using a set of adaptive numerical quadratures. This approach is direct, and it does not require an asymptotic expansion. The results for the three-dimensional flow calculations are applied for the evaluation of pressure signatures of several Rankine-type bodies with different Froude numbers. Streamlines were determined by a second-order finite-difference algorithm that follows a fluid particle by solving an appropriate initial-value problem. As expected, the shape distortion from the infinite-fluid Rankine body geometry was significant when the slenderness and the linearity (small-wave elevation and slope) approximations became inappropriate.

NUMERICAL CALCULATION FOR THE FLOW OF SUBMERGED BODIES UNDER A FREE SURFACE

Abstract The flow field generated by a Rankine body moving under a free surface in afinite-depth water is calculated by potential theory. Velocity field generated by a source located at the origin is calculated first by using highly efficient and adaptive quadratures of the QUADPACK library. This solution is used for generating the flow around a Rankine body by locating a source and an equal strength sink along the body axis. Results agree well with the existing literature.

Numerical Investigation of Fluid Flow in a Chandler Loop

The Chandler loop is an artificial circulatory platform for in vitro hemodynamic experiments. In most experiments, the working fluid is subjected to a strain rate field via rotation of the Chandler loop, which, in turn, induces biochemical responses of the suspended cells. For low rotation rates, the strain rate field can be approximated using laminar flow in a straight tube. However, as the rotation rate increases, the effect of the tube curvature causes significant deviation from the laminar straight tube approximation. In this manuscript, we investigate the flow and associated strain rate field of an incompressible Newtonian fluid in a Chandler loop as a function of the governing nondimensional parameters. Analytical estimates of the strain rate from a perturbation solution for pressure driven steady flow in a curved tube suggest that the strain rate should increase with Dean number, which is proportional to the tangential velocity of the rotating tube, and the radius to radius of curvature ratio of the loop. Parametrically varying the rotation rate, tube geometry, and fill ratio of the loop show that strain rate can actually decrease with Dean number. We show that this is due to the nonlinear relationship between the tube rotation rate and height difference between the two menisci in the rotating tube, which provides the driving pressure gradient. An alternative Dean number is presented to naturally incorporate the fill ratio and collapse the numerical data. Using this modified Dean number, we propose an empirical formula for predicting the average fluid strain rate magnitude that is valid over a much wider parameter range than the more restrictive straight tube-based prediction.

HYDRODYNAMIC LOADS ON VIBRATING CANTILEVERS UNDER A FREE SURFACE IN VISCOUS FLUIDS WITH SPH

Smoothed Particle Hydrodynamics (SPH) based simulations are implemented to study finite amplitude vibrations of a submerged cantilever beam in viscous fluids under a free surface. The cross section of a thin beam is modelled as a rectangular 2D oscillating rigid lamina, around which fluid field properties are computed. The study is carried out using non-dimensional frequency, amplitude of oscillations and depth of submergence. The total hydrodynamic force on the vibrating beam is extracted via SPH analysis, together with the contours of fluid field properties. Comparison is made between the results obtained with and without the free surface. We find that the presence of the free surface strongly influences the flow physics around the lamina, giving rise to non-harmonic velocity profiles and non-periodic force responses, coupled with phase lags and non-zero mean force during periodic oscillations.

A numerical method for the solution of a line source under a free surface

Abstract A modified source-and-dipole type singularity panel method is proposed to calculate the flow properties for an oscillating arbitrary body in the presence of a free surface. The technique is based on Greens identity whereby the boundary value problem is expressed as a boundary integral equation which is solved numerically. The free-space Green function is used in the integral equation. To demonstrate the feasibility of the method, the problem of a pulsating submerged line source under a free surface is treated and results are compared with the exact solution. An excellent agreement with the theory is obtained for panel density of about ten panels per wavelength and paneled water surface length of two wavelengths with very low computing times, indicating the feasibility of the method for unsteady water wave problems.

SEAFLOOR PRESSURE SIGNATURES OF A HIGH-SPEED BOAT IN SHALLOW WATER WITH SPH

Smoothed Particle Hydrodynamics (SPH) based simulations are implemented to evaluate the pressure-induced signatures on the ocean floor due to the passage of a high-speed boat in quiescent shallow water. Along with the standard WeaklyCompressible SPH (WCSPH) equations, the delta-SPH formulation is employed, which modifies the SPH continuity equation by incorporating numerical diffusion. This correction allows for a considerable reduction of the spurious oscillations characterizing pressure fields obtained with WCSPH algorithms. A simple computer model of a planing boat is developed for comparison with similar works in the literature. Simulations are performed using a parallel open-source SPH code on a high-end graphics processing unit (GPU). A convergence study on the size of the optimal computational domain is carried out, with a total number of particles per simulation ranging between 100,000 to 20,000,000. Part of the computational work is directed towards the investigation of the best set of SPH parameters to be employed in this specific study, with particular attention to the choice of a suitable kernel function, particle resolution and viscosity coefficients. Pressure contours and pressure plots at lateral locations at the seafloor are presented, showing good agreement with previous studies. It can be inferred that the SPH methodology is a suitable choice for free-surface problems, offering a good trade-off among the ease of implementation, computational efficiency and accuracy of the results. NOMENCLATURE B coefficient controlling density variations c speed of sound cs adjusted speed of sound d reference length 1.5 m Fr finite-depth Froude number u= p ghw g gravity h smoothing length hw undisturbed water depth m mass M Mach number u=c N total number of simulation particles

Motion analysis of floating structures by a surface singularity panel method

A singularity panel method based on Greens function integral equation is used to calculate the motion characteristics of ships and offshore structures. The free surface and the body surface are discretized by source-sink and dipole type singularity panels. This reduces the governing integral equation for the velocity potential to a system of algebraic equations which can easily be solved by a computer. The added mass and damping coefficients are computed by appropriate summations along the body surface. The approach is unique since it uses the free space Greens function instead of more complicated Greens function satisfying the free-surface boundary condition. The applications of the method are limited to linear, two-dimensional, incompressible free-surface problems. The extension to three-dimensional geometries is straightforward.