Experimental techniques and results of gas turbine-related heat transfer were discussed in previous chapters. It can be seen that experimental heat transfer covers more than half a century of research, and it developed signicant new design improvements to increase efciency and durability of turbine components that are exposed to high operating temperatures. Numerical model development by Crawford (STAN series) and Patankar (SIMPLE velocity and pressure interlinkage method) opened new avenues for numerical ow and heat-transfer research. Numerical predictions provide the details that are difcult to obtain by experimental means. Moreover, the increase in computation power in desktop computers has made it economical to optimize the design parameters based on numerical analyses. Turbulence models developed by Launder, Spalding, Satyanarayana, Rodi, Speziale, and others improved the quality of the numerical prediction signicantly. In this chapter, different aspects of turbine heat-transfer prediction-namely, heat transfer in airfoil, endwall, and tip gap-are discussed. Like experimental heat-transfer analysis, predictions have two broad classications: the external and internal cooling arrangements. Most external heat-transfer predictions are done with the time-averaged turbulence model of Baldwin-Lomax and two equation models, e.g., k-ε and k-ω turbulence models, whereas internal cooling arrangements are simulated with more computation-intensive turbulence models. Details of these models are discussed in turbulence-and ow-modeling texts (Wilcox, 1993; Tannehill et al., 1997). A brief description of these models is given here. Several numerical models are used to capture the turbulence effects in a gas turbine. Based on the number of equations to be solved, turbulence modeling approaches can be broadly classied as one-equation, two-equation, and second-moment closure models. Most common models are based on a two-equation turbulence model, namely, k-ε model, low Reynolds number k-ε model, two-layer k-ε model, and k-ε model. Other popular models are

Baldwin-Lomax model, algebraic closure model, and second-moment closure model. The basic equations solved in these models are given here.