R.M.M. Mattheij

Numerical analysis of turbine blade cooling ducts

The cooling of turbine blades in turbines is enhanced by providing the cooling ducts with ribs, so-called turbulators. It is investigated how these ribs influence the heat transfer of the cooling air on the blades. A model is given to study this problem such that it lends itself to a numerical approach. A detailed discussion is given of the problem involved. It is shown how the ideas are implemented in a numerical code. The results of the simulations are assessed showing a practical way to test the quality of these cooling ducts.

Parallel stable compactification for ODEs with parameters and multipoint conditions

Many algorithms for solving ordinary differential equations with parameters and multipoint side conditions give rise to systems of linear algebraic equations in which the coefficient matrices have a bordered block diagonal structure. In this paper, we show how these problems can be solved by using parallel algorithms based on stabilized compactification.

Solidification of a two-dimensional high-Reynolds-number flow and its application to laser percussion drilling

The competition between inertia and solidification for the high-Reynolds-number flow of molten aluminium across a cool solid aluminium surface is investigated. A two-dimensional molten aluminium droplet is of finite extent and is surrounded by a passive gas. The droplet initially freezes due to rapid thermal conduction into the solid. Depending on the initial velocity of the molten aluminium, one of two situations may develop: (i) If the molten aluminium has a non-decreasing initial velocity profile, solidification continues until the passing of the trailing edge of the liquid/gas interface or the flow is engulfed; (ii) If the molten aluminium has a decreasing initial velocity profile, the droplet narrows and thickens resulting in a reduction in the heat flux and in the rate of solidification; this will eventually lead to fluid clumping and shock formation. The rate of solidification may also be reduced by increasing the ambient temperature. The results are interpreted in terms of the recast observed during the solidification phase of laser percussion drilling.

Stability and convergence of linear parabolic mixed initial-boundary value problems on nonuniform grids

Many problems in the physical sciences can be reduced to the solution of a system of time-dependent partial differential equations. Of particular interest to us are problems in combustion and heat and mass transfer, i.e., hydrocarbon ignition and catalytic combustion. The governing equations in these applications can be formulated as a system of parabolic mixed initial-boundary value problems. The numerical stiffness that results from solving these problems on a discrete mesh combined with the inherent stiffness of the disparate decay rates of the various chemical species necessitate the use of implicit time differencing methods. The problems also produce solutions that contain regions of high spatial activity, i.e., sharp peaks and steep fronts. Although an equispaced mesh could be used in the calculations, it is often more efficient to employ a nonuniform adaptive grid in the anticipation that the high activity regions will be better resolved. Important questions in such studies are the effects that adaptive time and space steps (both fixed and variable numbers of points) have on the stability and convergence of the parabolic solver. We investigate these issues in this paper for a class of linear mixed initial-boundary value problems.