Effects of Tip Endwall Contouring on the Three Dimensional Flow Field in an Annular Turbine Nozzle Guide Vane: Part 2 — Numerical Investigation

Abstract

This paper describes the numerical investigation of the three dimensional flow through a low speed, low aspect ratio, high turning annular turbine nozzle guide vane with meridional tip endwall contouring. This rotational flow field has been simulated using a finite volume discretization and a time marching technique to solve the three dimensional, time dependent Euler equations expressed in a cylindrical coordinates system. The results are presented under the form of contour plots, spanwise pitch-averaged distributions and blade static pressure distributions. Detailed comparisons with the measurements described in part I of the paper are also provided.

A numerical solution of 3D inviscid rotational flow in turbines and ducts

“…This test case has already been investigated by several researchers [6][7][8]. Comparison with experiments and other calculations illustrate the capabilities of the present code.…”

“…At the pressure side, the horse-shoe vortex leg rotates in the same direction as the passage vortex and therefore, both have coalesced (Figure 13(a) and (b)). These two separate, but interacting, secondary flow mechanisms have also been the focus of different researchers: Boletis et al [4] investigated skewed inlet boundary layer type flow profiles through the VKI turbine nozzle, while highly three-dimensional blade passage loading has been addressed by Arts [6], who considered a tip endwall contoured VKI annular turbine nozzle guide vane.…”

“…The value of the hub pressure corresponds to an isentropic outlet Mach number of 0.3. This Mach number, higher than the experimental value by one order, was chosen to enhance convergence as suggested by Arts [6] and Novak et al [8]. The spanwise distribution of the pitchwise averaged static pressure coefficient at the exit is obtained using the radial momentum equation.…”

A numerical solution of 3D inviscid rotational flow in turbines and ducts

“…The other test case which reports the 3D flow results of the nozzle guide vane of the VKI is also well documented [3 -5]. This test case has already been investigated by several researchers [6][7][8]. Comparison with experiments and other calculations illustrate the capabilities of the present code.…”

“…where DE ( ( = DFib +DGjb +DHkb . Integration of Equation (1) using Equation (6) and divergence theorem gives: The first integral in Equation (8) is evaluated around the cell in Figure 1(c) as follows:…”