Film Cooling Calculations With an Iterative Conjugate Heat Transfer Approach Using Empirical Heat Transfer Coefficient Corrections

Abstract

An iterative conjugate heat transfer technique has been developed to predict the temperatures on film cooled surfaces such as flat plates and turbine blades. Conventional approaches using a constant wall temperature to calculate heat transfer coefficient and applying it to solid as a boundary condition can result in errors around 14% in uncooled blade temperatures. This indicates a need for conjugate heat transfer calculation techniques. However, full conjugate calculations also suffer from inability to correctly predict heat transfer coefficients in the near field of film cooling holes and require high computational cost making them impractical for component design in industrial applications. Iterative conjugate heat transfer (ICHT) analysis is a compromise between these two techniques where the external flow convection and internal blade conduction are loosely coupled. The solution obtained from solving one domain is used as boundary condition for the other. This process is iterated until convergence. Flow and heat transfer over a film cooled blade is not solved directly and instead convective heat transfer coefficients resulting from external convection on a similar blade without film cooling and under the same flow conditions are corrected by use of experimental data to incorporate the effect of film cooling in the heat transfer coefficients. The effect of conjugate heat transfer is taken into account by using this iterative technique. Unlike full conjugate heat transfer (CHT) the ICHT analysis doesn’t require solving a large number of linear algebraic equations at once. It uses two separate meshes for external convection and blade conduction and thus problem can be solved in lesser time using less computational resources. A demonstration of this technique using a commercial CFD solver FLUENT is presented for simulations of film cooling on flat plates. Results are presented in form of film cooling heat transfer coefficients and surface temperature distribution which are compared with results obtained from conventional approach. For uncooled surfaces, the deviations were as high as 3.5% between conjugate and conventional technique results for the wall temperature. For film cooling simulations on a flat plate using the ICHT approach showed deviations up to 10% in surface temperature compared to constant wall temperature technique for a high temperature difference case and 3% for a low temperature difference case, since surface temperature is not constant over the surface when conjugate heat transfer is considered. Results show that conjugate heat transfer effect is significant for film cooling flows involving high temperature differences for the current blade materials and application of film cooling correction obtained from experimental data is very useful in obtaining realistic blade temperatures.