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The influence of gravity on the Marangoni flow instability in half zone liquid bridges in the case of liquid metals is investigated by direct 3D and time‐dependent simulation of the problem. The computations are carried out for different heating conditions and environments (zero g conditions and on ground liquid zone heated from above or from below). The case of cylindrical shape (simplified model) and of melt/air interface deformed by the effect of gravity (real conditions) are considered. The comparison among these situations gives insight into the separate (gravity) effects of buoyancy forces and of the free surface deviation with respect to straight configuration. Body‐fitted curvilinear co‐ordinates are adopted to handle the non‐cylindrical problem. The liquid bridge exhibits different behaviours according to the allowed bridge shape. If the shape is forced to be cylindrical, the flow field is stabilized in the case of heating from above and destabilized if gravity is reversed. If the deformation is taken into account, gravity always stabilizes the Marangoni flow regardless of its direction (parallel or antiparallel to the axis) and the 3D flow structure is different according to the heating condition (from above or from below). In the latter case, the critical Marangoni number is larger and the critical wave number is smaller, compared with the opposite condition. In addition, for Pr=0.02 (Gallium), a surprising heretofore unseen behaviour arises. No steady bifurcation occurs and the flow becomes unstable directly to oscillatory disturbances. This phenomenon has never been reported before in the case of low Prandtl number liquids.

Describes the solution of the shallow water flow equations in strongly conservative form using a finite volume method. A SIMPLE‐like scheme is developed to treat the velocity depth coupling. The method is applied to flow in a sharply curved channel and the results compared with published data. An error analysis is included which indicates that the method proposed is suitable for solving two‐dimensional steady state problems in open channel flow.

A calculation procedure is proposed for heat and fluid flows in geometries with a time‐dependent boundary. The procedure incorporates a moving mesh arrangement with multi‐block iteration and has been developed to assist future simulations of heat and mass transfer with phase change. The solver for the basic equations is the SIMPLE algorithm with a non‐staggered grid arrangement. The space conservation law is invoked and applied for the explicit tracking of a moving boundary with a moving mesh. For mapping complex geometries a multi‐block iteration strategy is employed. A cubic spline interpolation allows the “uniqueness of zonal boundary” requirement to be met. An interpolation method is also developed for variables near the zone boundaries.The calculation procedure using multi‐block iteration and a moving mesh is applied to three benchmark‐testing problems. The numerical results are in very good general agreement with available experimental data.

The geometric conservation law (GCL) is an important concept for moving grid techniques because it directly regulates the treatments of the fluid flow and grid movement. With the grid movement at every time instant, the Jacobian, associated with the volume of each element in curvilinear co‐ordinates, needs to be updated in a conservative manner. In this study, alternative GCL schemes for evaluating the Jacobian have been investigated in the context of a pressure‐based Navier‐Stokes solver, utilizing moving grid and the first‐order implicit time stepping procedure as well as the PISO scheme. GCL‐based on first and second‐order, implicit as well as time‐averaged, time integration schemes were considered. Accuracy and conservative properties were tested on steady‐state, laminar flow inside a 2D channel and time dependent, turbulent flow around a 3D elastic wing; both treated with moving grid techniques. It seems that the formal order of accuracy is not a decisive indicator. Instead, the speed of grid movement and the interplay between the flow solver and the GCL treatments make a more noticeable impact.

In this paper the effects of choosing dependent variables and cell face velocities on convergence of the SIMPLE algorithm are discussed. Using different velocity components as either dependent variables or cell‐face velocities, both convergent rate and calculation accuracy of the algorithm are compared and studied. A novel method, named “cross‐correction”, is developed to improve the convergence of the algorithm of using non‐orthogonal grids. Cases with benchmark and analytical solutions are used for numerical experiments and validation. The results show that, although different velocity components are employed as either dependent variables or cell face velocities, there is no obvious difference in both the convergent rates and numerical solutions. Moreover, the “cross‐correction” method is validated by computations with several first‐order and high‐order convection schemes; and the generality of convergence improvement achieved by the method is shown in the paper.

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of block‐diagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard Beam‐Warming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars (λ±ξ and λ±η) for the respective split flux‐vectors (F± and G±) along the ξ− and η−directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, time‐step length and convergence criteria. This method is spatially second‐order accurate, fully conservative and implemented with general co‐ordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergence‐divergence nozzle and turbine cascade. Comparisons with other well‐documented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way.

Pulsatile flow of an incompressible, Newtonian fluid through a symmetric bifurcated rigid channel was numerically analysed by solving the three‐dimensional Navier‐Stokes equations. The upstream flow conditions were taken from an experimentally measured human arterial pulse cycle. The bifurcation was symmetrical with a branch angle of 60° and a daughter to mother area ratio of 2.0. The predicted velocity patterns were in qualitative agreement with experimental measurements available in the literature. The effect of unsteadiness on the various flow characteristics was studied. The most drastic effect observed was on the flow reversal regions. There was no flow reversal at the highest inlet Reynolds number in the pulse cycle, whereas in the case of steady flow at the same Reynolds number, the flow reversal region was the largest. The presence of secondary flow was observed at all times during the pulse cycle. Shear stress was calculated along the outer and inner walls and the low and high time averaged shear stress regions correspond to the clinically observed sites of formation of atherosclerotic plaque and lesions.

A combined experimental and numerical investigation into the fluid flow and heat transfer processes that take place in the spray deposition of tubular preforms is presented. The work is concerned principally with impingement mechanisms at jet diameter to target distances that are large in comparison with previous reported studies. The experimental investigation required the design of a novel heat transfer meter that was capable of resolving the heat transfer coefficient within 2.5 per cent. The experiments gave a new correlation for stagnation heat transfer, similar in form to correlations that have been published for small jet diameter to target distance values. The experiments also showed the presence of skewing of the heat transfer coefficient in the deposition zone due to its tapered nature. A finite volume based model of the deposition chamber was developed and run to compare with the experimental data. This model was found to yield trends similar to those measured experimentally, thus confirming its qualitative capability. However the absolute values of heat transfer coefficient that were computed were significantly lower than measured values. This points to the requirement to consider alternative computing schemes and to investigate the methods of representing the heat transfer mechanisms at the physical boundaries, particularly at the preform surface.

An algorithm is presented for the tracking of interior points in a shape evolving unstructured FE mesh. Evolution of the boundary shape may be associated with a governing equation, as in moving boundary problems, or may be prescribed, as in structural shape optimisation. In the latter SSO case the point tracking algorithm may be used in conjunction with a FD approximation to determine geometric sensitivities: in this case the boundary deformation is a small perturbation. For meshes undergoing gross deformations of the boundary an incremental method is used. Reversibility tests are undertaken to assess the robustness and accuracy of the algorithm and examples are given to illustrate the general utility of the method.

The buoyancy‐driven magnetohydrodynamic flow in a cubic enclosure was investigated by three‐dimensional numerical simulation. The enclosure was volumetrically heated by a uniform power density and cooled along two opposite vertical walls, all remaining walls being adiabatic. A uniform magnetic field was applied orthogonally to the gravity vector and to the temperature gradient. The Prandtl number was 0.0321 (characteristic of Pb–17Li at 300°C), the Rayleigh number was 10⁴, and the Hartmann number was made to vary between 0 and 2×10³. The steady‐state Navier–Stokes equations, in conjunction with a scalar transport equation for the fluid's enthalpy and with the Poisson equation for the electrical potential, were solved by a finite volume method using a purposely modified CFD code and a computational grid with 64³ nodes in the fluid. Emphasis was laid on the effects of increasing the Hartmann number on the complex three‐dimensional flow and current pattern.