HEAT TRANSFER

Thermal design problems related to turbomachinery components and propulsive systems are here concerned. We are interested mainly in the thermal design of coated turbine blades, a design problem that is approached here by an inverse method.
Other unsteady heat transfer problems are also investigated numerically by FEM analysis. For example, the analysis of an automotive wheel + brake system during the fading test case is illustrated.

Thermal Inverse Problem on a Coated Cylinder with internal heating

The solution of the thermal field in a coated hollow cylinder with prescribed outer boundary temperature, and heat convection rates at the inner flow passage can be derived analitically. This fundamental solution is often used to test accuracy of numerical methods. In our case, we builded up a test case to validate our thermal design procedure based on an inverse method. The procedure aims to derive the shape of the coolant/heating channel that realizes, for instance, a prescribed temperature distribution on the outer boundary of the solid domain. Once the inverse problem is solved numerically, both the channel geometry and the thermal field can be compared to this simple analitical solution to check the accuracy.
An initial geometry of the channel in the solid domain is guessed. As visible in Figure 1, we selected a very small circular hole in a non-symmetric position. The numerical results converged to the analitic solution, with a perfectly radially symmetric thermal field

FIGURE 1. The initial grid and the thermal field in the cylinder.

FIGURE 2. Solution of the inverse problem. The final gometry and thermal field in the cylinder.

Inverse Problem on the MARK-II Turbine Blade.

The inverse procedure has been validated against a more severe test based on experimental results about the MARK-II turbine blade. Now were are ten cooling channel of circular shape. The test-case working conditions have been imposed at the boundaries, on the initial guess of the coolant channels position and dimension. At convergence, the inverse procedure was able to find the correct location and dimension of the coolant holes.

FIGURE 3: Solution of inverse problem on the MARK II cooled turbine: (a) Initial and (b) final geometry, (c) initial and (d) final temperature field.

Inverse Problem on a Multi-holed Coated Turbine Blade.

The same approach is applied to teh design of a more realistic configuration of a modern coated and cooled turbine blade. The Thermal design of the multi-holed turbine reqiires a different parametric formulation of the inverse problem. The test follows the same guidelines of previous example.

FIGURE 4: Solution of the inverse problem on a multi-holed coated turbine blade. (a) Initial and (b) final blade geometry and temperature field.

Unsteady Heat Transfer Problems: Brake Disc Thermal Analysis

The FEM core of the solver developed for the inverse procedure of thermal design is also able to compute the unsteady thermal field on domain of complex shape. As example, the temperature field evolution and the performances of the system wheel + disc brake + calliper during a standard fading test are proposed. Fluid dynamics related parameters have been derived by CFD simulation of the wheel aerodynamics.

FIGURE 5:
(a) Temperature field evolution of the system [wheel + disc brake + calliper] during the fading test.

(b) 3D flowfield around a wheel.

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