Tadashi Tanuma

Numerical Prediction of Unsteady Flows through Whole Nozzle-Rotor Cascade Channels with Partial Admission

Abstract This paper presents a numerical study for unsteady flows in a high-pressure steam turbine with a partial admission stage. Compressible Navier-Stokes equations are solved by the high-order high-resolution finite-difference method based on the fourth-order compact MUSCL TVD scheme, Roes approximate Riemann solver, and the LU-SGS scheme. The SST-model is also solved for evaluating the eddy-viscosity. The unsteady two-dimensional flows through whole nozzle-rotor cascade channels considering a partial admission are numerically investigated. 108 nozzle passages with two blockages and 60 rotor passages are simultaneously calculated. The influence of the flange in the nozzle box to the lift of rotors is predicted. Also the efficiency of the partial admission stage changing the number of blockages and the number of nozzles is parametrically predicted. Keywords: Numerical Study, Steam Turbine, Unsteady Flow, Partial Admission, Nozzle-rotor Cascade Channels 1. Introduction Steam turbines are used in most of the thermal power plants and the nuclear power plants. The improvement of the steam-turbine performance certainly results in the reduction of the greenhouse gas. Large-scale steam turbines with a nozzle governing system have separated nozzle-blade groups (usually four groups with inlet control valves respectively) for the high pressure first stage (admission stage). For the design condition, valves of the three groups are almost fully opened and one valve of the remaining nozzle group is nearly closed to control the mass flow rate of the turbine system. Also super-critical pressure steam turbines, which were introduced into a number of current coal-fired power generation plants, require a high stiffness design for their admission stage nozzles (nozzle box structure). In these nozzles, some nozzle-blade spacings especially near the horizontal joint flanges are blocked to reinforce their structural stiffness against high pressure and high temperature steam conditions. In these admission stages, since the nozzle-blade spacings are partially opened, the flows into the rotor cascade channels are fluctuated in the circumstantial direction. Generally, internal flows through this kind of partially-opened admission stages cause the loss of the performance. It is also known that this structure causes unsteady and disturbed flows affecting the following rotor blades. The rotor cascade channels occasionally lose flows due to the blocking of the flow at the flange and it results in a relatively lower performance at the admission stage. This loss is called the partial admission loss. Although the prediction of the loss is important, the experimental studies are hard to conduct because of the difficulty of the measurement in actual steam conditions. Therefore, the numerical prediction is quite valuable. But it is suggested that the whole flow fields including nozzles, rotors, and the blocks of the flange and the closed nozzle group should be calculated simultaneously to predict the actual performance. Only a few numerical studies for this flow problem have been reported, because they also require a large-scale computation. A performance prediction for a partial admission has been presented by Cho[1]. He [2] and Sakai [3] have reported the numerical studies solving the quasi three-dimensional Navier-Stokes equations and compared with the experimental r esults. However, no massive computations such assuming whole noz zle-rotor cascade channels have been reported yet. Recently our research group has developed computational codes for unsteady flows of wet-steam through 2-D and 3-D multi-stage cascade channels in a steam turbine using the high-order high-resolution finite-difference method [4][5]. In this paper, the 2-D code is applied to unsteady flows in whole nozzle-rotor cascade channels of a partial admission stage. As numerical examples, the unsteady 2-D flows with a partial admission stage in a middle class coal-fired steam turbine are calculated assuming 108 nozzle passages with two blockages and 60 rotor passages. The effect of the blockage to the unsteady force of rotors is numerically predicted. The performance affected by the change of the number of blockages and the number of nozzles is also parametrically predicted.

Numerical Analysis and Steam-Tunnel Tests of Transonic Flows throught a SteamTurbine Cascade.

An implicit time-marching finite-difference method for solving two-dimensional compressible Navier-Stokes equations is applied to the numerical analysis of transonic viscous flows through a steam turbine cascade. The distinctive feature of this method is its use of the momentum equations of contravariant velocity components. A high-order accurate difference scheme modified from the Chakravarthy-Osher TVD scheme is used in order to clearly capture shock waves which occur at the blade trailing edges. Steam-tunnel tests to measure losses of a linear cascade of transonic steam turbine blades are carried out in order to verify the effectiveness of the numerical method. Computed shock wave structures agree well with Schlieren photographs of the cascade tests. The agreement between the computed results and the measurements of total pressure loss coefficients and those of total pressure profiles in the blade wakes is also found to be reasonable.