Saad A. Ragab

Linear instabilities in two‐dimensional compressible mixing layers

Linear instability waves in supersonic shear layers are analyzed. Both viscous and inviscid disturbances are considered. The basic state is obtained by solving the compressible laminar boundary‐layer equations or is specified by the hyperbolic tangent profile. The effects of the velocity ratio and temperature ratio are determined. The numerical results show that the maximum growth rate depends nonlinearly on the velocity ratio. The results also substantiate the convective Mach number as a compressibility parameter for mixing layers.

Numerical simulation of vortices with axial velocity deficits

Axial velocity deficit is a source of instability in vortices that may otherwise be stable. Temporal large‐eddy simulation is performed to study the response of vortices with axial velocity deficits to random and controlled disturbances at high Reynolds numbers. The q vortex [Batchelor, J. Fluid Mech. 20, 321 (1964)] is used as a model of such vortices. When the vortex is linearly unstable, the disturbances grow and result in the appearance of large‐scale helical sheets of vorticity. Later, these large‐scale helical structures break up into small‐scale filaments. Associated with the formation of the large‐scale structures is a redistribution of both angular and axial momentum between the core and the surroundings. The redistribution weakens the axial velocity deficit in the core while strengthens the rigid‐body‐like rotation of the core. The emerging mean velocity profiles drive the vortex core to a stable configuration. The vortex eventually returns to a laminar state, with an insignificant decay in the ...

Effect of bulges on the stability of boundary layers

The instability of flows around hump and dip imperfections is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for viscous/inviscid interaction and separation bubbles. Then, the two‐dimensional linear stability of this flow is analyzed, and the amplification factors are computed. Results are obtained for several height/width ratios and locations. The theoretical results have been used to correlate the experimental results of Walker and Greening (British Aeronautical Research Council 5950, 1942). The observed transition locations are found to correspond to amplification factors varying between 7.4 and 10.0, consistent with previous results for flat plates. The method accounts for both viscous and shear‐layer instabilities. Separation is found to increase significantly the amplification factor.

Large eddy simulation of longitudinal stationary vortices

The response of longitudinal stationary vortices when subjected to random perturbations is investigated using temporal large‐eddy simulation. Simulations are obtained for high Reynolds numbers and at a low subsonic Mach number. The subgrid‐scale stress tensor is modeled using the dynamic eddy‐viscosity model. The generation of large‐scale structures due to centrifugal instability and their subsequent breakdown to turbulence is studied. The following events are observed. Initially, ring‐shaped structures appear around the vortex core. These structures are counter‐rotating vortices similar to the donut‐shaped structures observed in a Taylor–Couette flow between rotating cylinders. These structures subsequently interact with the vortex core resulting in a rapid decay of the vortex. The turbulent kinetic energy increases rapidly until saturation, and then a period of slow decay prevails. During the period of maximum turbulent kinetic energy, the normalized mean circulation profile exhibits a logarithmic region, in agreement with the universal inner profile of Hoffman and Joubert [J. Fluid Mech. 16, 395 (1963)].

Roll stabilization by anti-roll passive tanks

Since the most severe roll motion occurs at resonance (known as synchronous rolling), the best way of reducing it is to increase the damping. The most common means of doing so is by the installation of bilge keels. If more control is required, both anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. The use of tanks with liquid free surfaces for reducing roll motion of ships is an old idea. Many researchers have studied the design of anti-roll tanks. However, most of the past effort has concentrated on studying the performance of anti-roll tanks in damping the roll motion of the ship. Little attention has been paid to the fluid motion inside the tank itself. Another important issue is the tank tuning. Proper tuning of the anti-roll tank, to match the ships natural frequency, is very important in reducing the roll motion. This paper concentrates on the most familiar type, which is the U-tube passive tank as a mechanical absorber of roll motion. A detailed study, covering tank damping, mass, location relative to the ship CG, and tuning, is presented. New suggestions and observations are stated concerning tank damping and tuning.

The nonlinear development of supersonic instability waves in a mixing layer

The nonlinear development of two‐dimensional supersonic instability waves in a mixing layer is investigated by solving the full unsteady Navier–Stokes equations. A finite‐difference predictor–corrector explicit method is used. The method is second‐order accurate in time and fourth‐order accurate in space. The results have also been checked using a fourth‐order central‐difference scheme with a Runge–Kutta time marching. Both confined and unconfined shear layers are simulated. For a fast or a slow mode of instability, in which the flow relative to the wave is subsonic on one side of the shear layer and supersonic on the other side, rolled up vortical structures are observed on the subsonic side only. The development of these structures is enhanced by confining the layer between parallel walls. Contours of a passive scalar show that the core of the rolled up vortex contains fluid predominantly from the subsonic side. Oblique shock waves develop in the side where the relative flow is supersonic. In the unconf...

Interaction of spanwise vortices with a boundary layer

The interaction of a spanwise vortex with a boundary layer has been numerically simulated using a fractional‐step method. The incompressible Navier‐Stokes equations are solved to accurately predict the strong viscous–inviscid interaction between a vortex either near or embedded within a boundary layer of comparable size. A strong vortex induces an eruption and the production of a secondary vortex. The secondary vortex causes the primary vortex to rebound, a response observed in many previous experiments and numerical simulations. However, weaker vortices as well do not follow the inviscid trajectory despite the absence of a secondary vortex. Rather than creating vorticity at the wall, a weaker vortex mainly redistributes the vorticity of the boundary layer, pulling it away from the wall. The redistributed vorticity alters the path of the vortex. In the laminar cases studied the decay of the vortex is not significantly altered by the boundary layer.

The three-dimensional interaction of a vortex pair with a wall

The interaction of vortices passing near a solid surface has been examined using direct numerical simulation. The configuration studied is a counter-rotating vortex pair approaching a wall in an otherwise quiescent fluid. The focus of these simulations is on the three-dimensional effects, of which little is known. To the authors’ knowledge, this is the first three-dimensional simulation that lends support to the short-wavelength instability of the secondary vortex. It has been shown how this Crow-type instability leads to three dimensionality after the rebound of a vortex pair. The growth of the instability of the secondary vortex in the presence of the stronger primary vortex leads to the turning and intense stretching of the secondary vortex. As the instability grows the secondary vortex is bent, stretched, and wrapped around the stronger primary. During this process reconnection was observed between the two secondary vortices. Reconnection also begins between the primary and secondary vortices but the ...

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

Abstract The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.

Effect of a bulge on the subharmonic instability of boundary layers

The influence of a two‐dimensional hump on the three‐dimensional (3‐D) subharmonic secondary instability on a flat plate is investigated. The mean flow is calculated by using interacting boundary layers, thereby accounting for the viscid/inviscid interaction. The primary wave is taken in the form of a two‐dimensional (2‐D) Tollmien–Schlichting (T–S) wave. The secondary wave is taken in the form of a 3‐D subharmonic wave. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation.