Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Operator‐splitting method for the analysis of cavitation in liquid‐lubricated herringbone grooved journal bearings

This paper presents an operator‐splitting method (OSM) for the solution of the universal Reynolds equation. Jakobsson–Floberg–Olsson (JFO) pressure conditions are used to study cavitation in liquid‐lubricated journal bearings. The shear flow component of the oil film is first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component is computed by the Galerkin finite element method. Present OSM solutions for slider bearings are in good agreement with available analytical and experimental results. OSM is then applied to herringbone grooved journal bearings. The film pressure, cavitation areas, load capacity and attitude angle are obtained with JFO pressure conditions. The calculated load capacities are in agreement with available experimental data. However, a detailed comparison of the present results with those predicted using Reynolds pressure conditions shows some differences. The numerical results showed that the load capacity and the critical mass of the journal (linear stability indicator) are higher and the attitude angle is lower than those predicted by Reynolds pressure conditions for cases of high eccentricities. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐2: Time‐dependent computations

The interfacial dynamics‐based cavitation model, developed in Part‐1, is further employed for unsteady flow computations. The pressure‐based operator‐splitting algorithm (PISO) is extended to handle the time‐dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water–vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto‐oscillation or quasi‐steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time‐dependent computations. Copyright © 2004 John Wiley & Sons, Ltd.     

Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.