A Study of the Unsteady Flow Field and Turbine Vibration Characteristic of the Supersonic Partial Admission Turbine for a Rocket Engine

Turbines used in upper stage engine for a rocket are sometimes designed as a supersonic turbine with partial admission. A turbine with partial admission nozzle causes strong unsteadiness in the flow field due to the existence of the closed nozzle passages. Although there are a number of published numerical studies on steam turbines employing partial admission nozzle, three dimensional CFD analysis of a supersonic partial admission turbine are rarely dealt with in those studies. In this study, a three dimensional unsteady CFD analysis of the supersonic partial admission turbine has been conducted in order to gain knowledge of three dimensional flow patterns, unsteady pressure variation and aerodynamic forces on the rotor blade. The result shows strong three dimensional flow pattern, such as large separation zone, in the region between closed nozzle passages and rotor blades. Furthermore, large unsteady aerodynamic forces appear on the rotor blade with the largest harmonic EO (Engine Order) component occurring at the nozzle closed sector passing frequency. This study also conducts one-way fluid-structural interaction (FSI) analysis in order to investigate turbine vibration response and cyclic stress. The unsteady pressure data on each grid points on the rotor blades obtained by the CFD analysis are transferred to the FEM model and unsteady nodal forces on each FEM nodes are calculated. FFT operations of these unsteady nodal forces are conducted and characteristic unsteady components, 3EO, 36EO and 45EO, are extracted on each FEM nodes. The 3EO force component is the largest one and corresponds to nozzle closed sector passing frequency component. The others are force components which cross 1 or 2 eigenfrequency curves of a rotor blade mode shapes around turbine design rotation speed on a Campbell diagram. Frequency response analyses of a rotor blade model and a turbine full angular model are conducted using those force components as nodal force conditions. The frequency response analyses of a rotor blade model indicate that 36EO and 45 EO force components excite 1 and 2 mode shapes. However, 3EO force component, the largest force component, does not excite these mode shapes because the force frequency is enough far from the eigenfrequencies of a rotor blade mode shapes. The result of frequency response analysis of a turbine full angular model shows that 3EO force component excites 3ND mode shape if the force frequency close to the eigenfrequency of that mode shape. However, 1ND or 2ND mode shapes are not excited even if the force frequency is close to eigenfrequencies of these mode shapes. INTRODUCTION Turbines for a rocket engine are used for driving turbopump systems. The turbines used for lower stage engine, for example LE-7A, the first stage engine of the H-2A and H-2B rocket in japan, are usually required to produce large output power. Thus, the turbines are supplied with working gas at flow rate sufficient for a full admission configuration. On the other hand, the output power required for upper stage turbines, for example LE-5B, the second stage engine of the H-2A and H-2B rocket, is not as large. So, if the working gas has enough energy, the turbines must be driven with small flow rate [1]. Thus, a turbine with a full admission configuration would result in turbine blades with extremely low blade height or the diameter must be much smaller to avoid extremely low blade height. The former design causes the increase in some kind of losses, for example passage vortices or tip leakage flow and friction etc., and the latter causes the decrease in velocity ratio. So, both designs result in a decrease of turbine efficiency. In order to prevent these undesirable features, a partial admission configuration can be employed [1]. In the partial admission configuration, several groups or sectors of nozzle inlets are completely closed and because of this the blade height and turbine diameter can be kept at a reasonable value. This configuration is actually used in LE-5B and considered in the next generation rocket engine as well. However, the existence of the closed nozzle sector creates additional losses such as windage loss, end off sector loss and expansion loss [2]. Furthermore, the rotor blades experience very unsteady aerodynamic force because they pass through open and closed nozzle passages periodically and this may cause high cycle fatigue (HCF) or fatal turbine vibration. The partial admission turbine is also used in steam turbine control stages in order to control output power. Numerous studies focusing on aerodynamic performance, both experimentally and numerically, have been conducted in the past. Sakai, et al. [3] compared quasi-three-dimensional CFD analysis with experimental results. Three-dimensional unsteady CFD simulations are also conducted in recent years. Hushmandi, et al. [4] presented unsteady aerodynamic force on the rotor blades. Kalkkuhl, et al. [5] showed detailed flow patterns in a steam turbine control stage. Yoshida, et al. [6] compared unsteady pressure fluctuation on a rotor blade predicted by numerical approach including disk cavity domain model with unsteady data measured by experimental approach and the results showed good agreement with each other. Apart from aerodynamic point of view, a forced response analysis based on experimental approach of a partial admission turbine was conducted by Fridh, et al. [7]. In contrast, there are few cases treating supersonic turbine for a rocket. Aerodynamic experimental researches were conducted in Ref. [8,9] in 1970s and showed the influence of the number of the closed nozzle sector to the turbine efficiency. The authors conducted CFD analyses, in Ref. [10,11], to understand basic unsteady flow patterns in recent years. However, these numerical studies dealt with two-dimensional analysis. Thus, very few three-dimensional unsteady flow patterns through the supersonic partial admission turbine stage for rocket have been presented. Although the partial admission configuration for rocket turbine can keep the blade height within a reasonable value comProceedings of International Gas Turbine Congress 2015 Tokyo November 15-20, 2015, Tokyo, Japan 962 ISBN978-4-89111-008-6 Copyright© 2015 Gas Turbine Society of Japan pared to full admission case, the blade height often becomes less than 10mm. Therefore, three-dimensional flow phenomena may have a great impact on the flow fields and investigating these flow fields in detail is very important to design a turbine with higher aerodynamic performance. In contrast to the aerodynamic research, to the author’s best knowledge, no studies dealing with the influence of the unsteady aerodynamic force caused by the partial admission configuration to the turbine vibration response has been published in the past. However, understanding how unsteady force components excite which and how turbine vibration mode shapes is very important in avoiding turbine resonance or HCF problems during the design phase. In this study, three-dimensional unsteady CFD simulation is conducted in order to investigate the three-dimensionality of the unsteady flow field in the supersonic partial admission turbine. Furthermore, this study conducts one-way fluid-structural interaction (FSI) analysis to research the turbine response to the unsteady aerodynamic force. Frequency response analyses of a turbine blade and a turbine full anular model are performed by FEM procedure. The simulations of a turbine blade model are performed to focus on the blade response with reasonable computational cost and the simulations dealing with the full anular model are conducted to research the turbine disk response. The unsteady nodal forces on each FEM nodes on the rotor blade surfaces are interpolated from the CFD result. Then, the unsteady forces are transformed into frequency domain by FFT procedure and the characteristic force components are extracted and used as nodal force conditions of the frequency response analysis. SIMULATED TURBINE STAGE The turbine studied in this study is a scaled model of the FTP turbine for NASA M-1 engine [9]. This turbine is a two-stage supersonic turbine with partial admission having three closed nozzle sectors. Three-dimensional partial admission CFD simulation needs large computational resources. The previous study [11], dealing with two-dimensional two-stage CFD simulation, indicated that the most complex characteristic and influential flow events caused by the nozzle closed sector, such as strong shock waves due to the flow acceleration, appeared in the first stage. Thus, only the first stage is treated in this study to reduce the computational cost. There are 44 nozzle passages and 24 nozzle passages are used as admitted sector and 20 nozzle passages are closed. The 1 stage rotor consists of 94 blades. The turbine blade profiles and characteristics are shown in Figure 1 and Table 1, respectively. In the simulation, blade scaling procedure is employed to reduce CFD simulation cost by using the periodic boundary condition as in Ref. [11]. So, the number of the each nozzle and rotor blade used in the calculation is changed to 45 from 44 and changed to 93 from 94, respectively. As a result of the scaling, one third of full passages are simulated, that is, 8 admitted and 7 closed passages for the nozzle and 31 passages for the 1 stage rotor, respectively, as shown in Figure 2. Detailed information about the scaling procedure is described in Ref. [11]. CFD PROCEDURE URANS simulation is performed by ANSYS CFX 13 in this study. Temporal discretization is the second-order backward Euler method and the convective terms are discretized by a high resolution TVD scheme. The shear stress transport (SST) model is used as turbulence model, however, as mentioned later, wall-function treatment is applied globally near the wall. Simulated conditions correspond to the experimental conditions in Ref. [10] and total pressure, total temperatur