DIFFERENTIAL QUADRATURE FOR AXISYMMETRIC GEOMETRICALLY NONLINEAR ANALYSIS OF CIRCULAR PLATES

New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.

Radiation and Exciting Forces of Axisymmetric Structures with a Moonpool in Waves

A highly efficient "hybrid integral-equation method" for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary.Eigenfunction representation of velocity potential is used in the outer domain;the three-dimensional potential in the inner domain is solved using a "two-dimensional" boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like structure.

Wall-modeled large eddy simulation for the flows around an axisymmetric body of revolution

The flow around an axisymmetric body of revolution(DARPA SUBOFF bare model)at Re=1.2×10^(7)is numerically investigated using the wall-modeled large eddy simulation(WMLES).To evaluate the capabilities of WMLES in such wall-bounded turbulent flows,the effects of the wall stress model and sampling distance are systematically studied.The numerical results of the non-equilibrium wall stress model with an appropriate sampling distance are in good agreement with the experiments in terms of pressure coefficient,skin-friction coefficient,and drag coefficient.On this basis,the thickening of the turbulent boundary layer and the expansion of the wake can be clearly observed through flow visualization,especially using the Liutex vortex identification method.

Wall-modeled large-eddy simulation of noise generated by turbulence around an appended axisymmetric body of revolution

The directivity of the noise generated by turbulent flows around an underwater vehicle(the fully appended SUBOFF body)is investigated numerically,where the turbulent flows are simulated by using the large eddy simulation(LES)with a non-equilibrium wall model and the noise is calculated by using the Ffowcs Williams and Hawking formulation.The wall-modeled LES reproduces the features of turbulent flows around SUBOFF,such as the attached boundary layers around the hull,separated vortices from appendages and the wrapped vortices in wakes.The coefficients and power spectral density of the wall pressures obtained are in agreement with the previous numerical results and experimental measurements.It is found that the constructive and destructive interferences of lift and side-force dipoles lead to the deviations of the directivities of instantaneous sound pressures from the lift directions.This is different from noise generated by flows around a circular cylinder,where lift dipoles dominate the radiated noise.

The inception cavitating flows over an axisymmetric body with a blunt headform

The inception cavitating flows around a blunt body are studied based on flow visualizations and velocity field measureme- nts. The main purpose of the present work is to study the incipient cavity evolution and the interplay between the inception cavitation and the local turbulent flows. A high-speed video camera is used to visualize the cavitating flow structures, and the particle image velocimetry （PIV） technique is used to measure the velocity field, the vorticity, and the Reynolds stresses under non-cavitating and inception cavitating flow conditions. It is found that the appearance of visible cavities is preceded by the formation of a cluster of micro-bubbles not attached to the body surface and in a hairpin-shaped vortex structure. During its evolution, the cavity moves downstream with a lower speed. The effect of the incipient cavity is significant on the local vortical structures but slight on the time- averaged velocity distribution. The mean Reynolds stress distributions in the turbulent shear flow can be substantially altered by the incipient cavities. The presence of the incipient cavities can lead to the production of turbulent fluctuations.

Numerical study of air layer drag reduction of an axisymmetric body in oscillatory motions

The air layer drag reduction(ALDR)of an axisymmetric body in oscillatory motions is investigated in this paper with open source toolbox OpenFOAM.The unsteady Reynolds-averaged Navier-Stokes(URANS)equations are used to determine the viscous flow and the volume of fluid(VOF)model is adopted to capture the interface of the air-water two-phase flow.The k-e turbulence model is adopted to simulate the turbulence.The dynamic mesh technique is applied to model the movement of the axisymmetric body.Firstly,the ALDR results are validated by the experimental data.Then,the effects of the movements of the body on the drag reduction during the ALDR state are investigated.Two representative kinds of movements are considered,namely,the pitch and the heave.The numerical results show that the drag reduction varies during the movements and the average drag reduction rates will be reduced.The variation of the drag reduction is related to the morphological change of the air layer.The heave motion is more likely to reduce the effects of the ALDR than the pitch motion.For both oscillatory motions,the large motion amplitude and the low motion period are not conductive to improving the effects of the ALDR.The effects of the oscillatory motion on the ALDR are more sensitive at high water speeds than at low water speeds.Besides,increasing the air flow ratio can be considered as one way to improve the effects of the ALDR.

NUMERICAL STUDY OF FLOW PAST AN AXISYMMETRIC BODY WITH A RING WING AT VARIOUS ATTACK ANGLES

The laminar and turbulent flows past an axi-symmetric body with a ring wingwere investigated numerically at various attack angles (0°-20°) for the Reynolds numbers rangingfrom 10~3 to 10~7. The DDM (Domain Decomposition Method) with the Schwarz iterative method based onfinite difference approximation was applied to simulate this problem. The primitive variableformulation was used for the solution of the incompressible Navier-Stoke equations. The velocityfield was calculated from the unsteady momentum equation by marching in time. The continuityequation was replaced by a Poisson-type equation for the pressure with the Neumann boundaryconditions. The Baldwin-Lomax model was adopted to simulate turbulence effect. The leap frogimplicit iterative method was used for the time difference approximations. The computed pressure atthe front stagnation point is found to have a small deviation, less than 10%, from the theoreticalvalue. The outlet flux has a loss about 5%. The lift coefficients increase linearly with the attackangle, but for attack angles greater than 15° the lift coefficients show mild decrease. Thefriction drag coefficients are insensitive to the attack angles, but the pressure drag coefficientsincrease markedly with the attack angles. In addition, complex flow patterns are revealed within thevicinity of the ring wing.

The high frequency acoustic radiation from the boundary layer of an axisymmetric body

The mechanism of acoustic radiation from the boundary layer of an axisymmetric body is analyzed, and its sound pressure spectrum is predicted. It is shown that the acoustic radiation results from the transition region and the turbulent boundary layer; and that the acoustic radiation from transition region is predominant at low frequencies; while the turbulent boundary layer has the decisive effect on acoustic radiation at high frequencies. The calculated values are in good agreement with the experimental data.

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.

A METHOD FOR THIRD ORDER FORCE ON AXISYMMETRIC BODIES

This paper develops a third order diffraction theory for the third order wave loads. Our method has been implemented for bodies of revolution with vertical axes, but the theory is also available for arbitrary bodies. Numerical tests were made to validate the numerical code by comparing the third order force with some published ones on a uniform cylinder. The method has also been used to compute the third order moments on a uniform cylinder and third order forces and moments on a truncated cylinder.