Naoaki Shibashita

A Numerical Method for Turbulent Flows in Highly Staggered and Low Solidity Supersonic Turbine Cascades

Two main problems are associated with conventional numerical methods for simulating turbulent flows in high-reaction-type supersonic turbine cascades near the tip of the last stage blade in a steam turbine: the large skewness of computational grids and treatments of boundary conditions when the shock waves hit boundaries. This paper presents a numerical method to deal with these issues. A grid generation technique which uses five-block structured grids has been developed. The orthogonality of the grid is good even for highly staggered and low solidity cascades. In addition, the grids are completely continuous at the boundary between the blocks and at the periodic boundaries. Both the gradient of the grid lines and the change rate of the grid widths connected smoothly. As a result, shock waves can be captured accurately and stably. The inflow and outflow boundary conditions based on the two-dimensional characteristic theory have been applied and diminished the spurious reflections and fluctuations of shock waves at both the inlet and outlet boundaries. Therefore the non-physical reflection does not affect the flow in the cascades. A low Reynolds number k-e turbulent model has been proposed. Distance from a wall is not used as the characteristic length of turbulent flows so that the turbulent model can be applied to a wake and a separation flow. The validity of the numerical method was verified by comparisons of the pressure distributions on the blade, the loss coefficients, and flow angles with linear cascade experiments of transonic compressor cascades.Copyright

Three-Dimensional Design Method for Long Blades of Steam Turbines Using Fourth-Degree NURBS Surface

A new blade design method for steam turbines using the fourth-degree NURBS surface was developed. The method enables engineers to easily generate three-dimensional complex blade shapes that have inherently good aerodynamic performance and constraint satisfaction. The developed design method has three steps. First, 2D aerofoils are independently generated at each design height. The convergent or convergent-divergent aerofoils are selected on the basis of the outlet Mach number. The convergent flow path is defined by a fourth-degree NURBS curve to preserve the continuity of the slope of the curvature. The divergent flow path for supersonic flow is generated by the method of characteristic curves to avoid strong shock waves. The inlet and outlet angles are constrained to coincide with the flow angle of the velocity triangle. The design parameters, such as chord length, stagger angle and control points of NURBS are automatically decided using an evolutionary optimization technique NSGA-II to minimize the loss by computational fluid dynamics. Therefore, fewer man-hours are needed for design work and better proficiency is not a significant requirement. Second, the number of control points and knot vectors are equalized for all aerofoils by inserting or removing knots and fitting the divergent part by the fourth-degree NURBS curve. Finally, all aerofoils are stacked radially, for example, along the centroid axis, and the fourth-degree NURBS surface is generated by interpolating the control points of the NURBS curves of all the aerofoils. This design method can easily generate long blades of the last stage for steam turbines. The blade has a surface with continuity of the slope of curvature in all directions and good aerodynamic performance under constraints.© 2010 ASME

Computations for Unsteady Compressible Flows in a Multi-Stage Steam Turbine With Steam Properties at Low Load Operations

A computational technique for compressive fluid in multistage steam turbines which can allow for thermodynamic properties of steam is presented. The understanding and prediction of flow field not only at design conditions but also at off-design conditions are important for realizing high-performance and high-reliability steam turbines. Computational fluid dynamics is useful for estimations of flows. However, current three-dimensional multi-stage calculations for unsteady flows have two main problems. One is the long computation time and the other is how to include the thermodynamic properties of steam. Properties of the ideal gas, such as equations of state and enthalpy formula, are assumed in most computational techniques for compressible flows. In order to shorten the computation time, a quasi-three-dimensional flow calculation technique is developed. In the analysis, system equations of conservation laws for compressible fluid in axisymmetric cylindrical coordinates are solved by using a finite volume method based on an approximate Riemann solver. Blade forces are calculated from the camber and lean angles of blades using momentum equations. The axisymmetric assumption and the blade force model enable the effective calculation for multi-stage flows, even when the flow is strongly unsteady under off-design conditions. In order to take into account steam properties including effects of the gas-liquid phase change and two-phase flow, a flux-splitting procedure of compressible flow is generalized for real fluid. Density and internal energy per unit volume are selected as independent thermodynamic variables. Pressure and temperature in a superheated region or wetness mass fraction in a wet region are calculated by using a steam table. To improve computational efficiency, a discretized steam table matrix is made in which the density and specific internal energy are independent variables. For accuracy and continuity of steam properties, the second order Taylor expansion and linear interpolation are introduced. The computed results of last four-stage low-pressure steam turbine at low load conditions show that there is a reverse flow near the hub region of the last (fourth stage bucket and the flow concentrates in the tip region due to the centrifugal force. At a very low load condition, the reverse flow region extends to the former (i.e. the first to third) stages and the unsteadiness of flow gets larger due to many vortices. Four-stage low pressure steam turbine tests are also carried out at low load or even zero load. The radial distributions of flow direction downstream from each stage are measured by traversing pneumatic probes. Additionally pressure transducers are installed in the side wall to measure the unsteady pressure. The regions of reverse flow are compared between computations and experiments at different load conditions, and their agreement is good. Further, the computation can follow the trends of standard deviation of unsteady pressure on the wall to volumetric flow rate of experiments. The validity of the analysis method is verified.Copyright