This research is directed towards the development and application of numerical techniques for practical problems involving fluid flow, heat transfer, turbulence, and related processes. The use of the supercomputers has made it possible to apply the techniques to more difficult problems, to obtain highly accurate solutions, and to devise new algorithms. Many individual projects have been undertaken in this research.
Computational techniques for flows in irregular geometries are being developed in one of these projects. These techniques are based on the use of curvilinear nonorthogonal coordinates. The novelty in the technique is the absence of complication that normally occurs in the mathematical treatment of the equations. Cartesian velocity components are used to obtain the proper body forces and curvature terms in the momentum equations. Tests are being run to compare formulations with covariant and contravariant velocity components.
Additional work is being done on the multigrid technique. It is well known that the convergence rate of an iterative technique decreases as the grid becomes finer. By a suitable interplay of the original fine grid and a set of superimposed coarse grids, an efficient iterative technique can be treated. The development of such a technique for complex fluid flow is currently undertaken. Initial explorations show that speed-up facotrs of ten or twenty are easily achievable; even larger factors are possible for three-dimensional flows.
Saleh H. Abudayyeh, Graduate Student Researcher
Aiman Alshare, Graduate Student Researcher
Mulugeta Berhe, Graduate Student Researcher
Kailash C. Karki, Innovative Research Inc., Minneapolis, Minnesota
Momose Kazunari, Mechanical Engineering Department, University of Minnesota, Minneapolis, Minnesota
Kanchan M. Kelkar, Innovative Research Inc., Minneapolis, Minnesota
Kazunari Momose, Mechanical Engineering Department, University of Minnesota, Minneapolis, Minnesota
Girija Parthasarathy, Graduate Student Researcher
Amir Radmehr, Graduate Student Researcher
Tom VanOverbeke, Graduate Student Researcher
Another project is dealing with the radiation model. Thermal radiation is the most complex mechanism for heat transfer. Its exact distribution is governed by integro-differential equations. The radiation intensity depends not only on position but also on the angle. Numerical solution methods need to discretize the angular dimension as well as the space coordinates. A further complication is introduced by the absorption, emission, and scattering caused by the medium. Often, the radiation characteristics of the medium depend on the wavelength. When all the physical details are included, the computation becomes very intensive. Methods are being developed for an accurate and economical computation of radiation heat transfer. Practical applications are in furnaces, gas turbine combusion chambers, and metallurgical operations.
A class of interesting flow problems consists of solid particles or liquid droplets moving through a liquid or gas flow. The particles follow different trajectories depending on their size and density. In some situations, the presence of the particles has a significant effect on the underlying fluid flow. Novel techniques are being developed for the prediction of such flows. There are a number of possible industrial applications of this methodology.
Liquid flows often have a free surface of unknown geometry. In unsteady situations, the shape of the free surface may continuously change. A method is being developed for determining the shape of the free surface in a fixed computational mesh. The available methods in this area rely on explicit time-marching schemes and therefore become computationally time-consuming. Implicit methods often do not preserve the sharpness of the interface between the liquid and gas. The proposed method would retain the efficiency of implicit schemes and still try to produce sharp interfaces.
The calculation of film cooling on turbine blades presents two challenges. First, the entire flow in the film-cooling hole (as affected by the upstream plenum) needs to be included in the calculation. Second, the film-cooling jets produce an anisotropic turbulence pattern, which is not predicted by standard turbulence model. Work is planned to introduce appropriate anisotropy in the turbulence model.
The flow and heat transfer in structured porous materials is calculated from first principles by solving the governing differential equations for the flow and temperature. From these computations, the effective properties of the porous material are obtained as a function of different parameters characterizing the material.
The level of turbulence in a natural convection flow depends on the kind and degree of stratification. With stable stratification, turbulence is damped; unstable stratification leads to enhanced turbulence. Appropriate modifications to standard turbulence models are being investigated so that the behavior of turbulence in natural convection is correctly predicted.
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