# UFR 2-06 Description

# Flow around (airfoils and) blades (transonic)

Underlying Flow Regime 2-06 © copyright ERCOFTAC 2004

# Description

## Preface

The transonic flow through blade cascades is crucial problem for many turbomachinery applications. Blade cascades represent the basic element for the energy transformation in turbines and compressors as well. The demand for increasing of performance, efficiency and reliability of all types of turbomachines leads to the demand for further improvement of the design methods, especially methods based on CFD codes.

Turbomachinery internal flows belong to the most complex ones in practical applications of fluid dynamics. It follows from complicated geometry of flow passages, three-dimensional flow character with substantial effects of secondary flows, effects of laminar-turbulent transition, heat transfer, rotation, shock-wave/boundary-layer interaction and effect of further parameters. Due to this complexity, there is a noticable need for careful validation of CFD codes used and for their continuous improvement.

During last twenty years due to the progress of computational techniques, the use of CFD for turbomachinery applications is continuously increasing. A lot of commercial and in-house software codes have been produced during these years. There are many papers (publications) dealing with numerical simulations of flow though blade cascades starting with inviscid models up to sophisticated models of viscous turbulent flows, see e.g. Novak et al. (1992), Chen and Leschziner (1999). Reviews of CFD methods for turbomachinery flows and their validations were given by Hirsch (1994), Couaillier (1995), and by Casey and Wintergerste (2000).

The commercial packages enable on one hand solving of complex three-dimensional viscous flows in boundary conditions typical for turbomachinery internal flows but on the other hand they are too general and do not allow to solve some specific phenomena as laminar/turbulent transition and/or non-reflecting boundary conditions at the exit of the cascade.

Therefore, there is still need for suitable relevant test cases allowing verification and validation of the numerical codes from the viewpoint of their reliability. The transonic flow through blade cascade represents such a flow regime involving the most important features of transonic flow in turbomachinery, especially shock-wave/boundary-layer interaction with possible separation and laminar-turbulent transition.

## Introduction

Transonic flows are becoming the most typical flows of modern turbomachinery, in power generation (turbines of large output - tip sections of last stages, first stages in the high pressure side), in air-breathing engines (transonic fans, inlet guide vanes and diffusers of radial flow compressors), or in refrigeration technology (expansion turbines, compressors). From the aerodynamics point of view, there are several phenomena typical of transonic cascades, like

- aerodynamic choking and the existence of a critical cross section (the narrowest effective cross section);

- secondary flows due to the channel curvature and area constriction, as well as due to corner boundary layers, and are the most important reason for the three-dimensional character of internal transonic flows;

- strong viscous/inviscid interaction with very specific aspects of flow separation, and transition from supersonic to subsonic velocities (pseudoshock waves);

- upstream effect of downstream conditions on the development of transonic phenomena is very important. Due to strong viscosity effects, there always exists a non-negligible subsonic region near the walls, representing a way for upstream propagation of the downstream flow conditions. It is a fertile field for transonic instability and for various unsteady phenomena*.*

Because of the complexity of transonic flow in the three-dimensional cascades, the attention is concentrated to the two-dimensional transonic flow through the blade cascade. The 2D analysis of blade cascades is still interesting both from experimental and from numerical point of view. The interest is motivated by the need for profiles with increasing load and high efficiency.

As the underlying flow regime was chosen the two-dimensional transonic flow through the turbine rotor blade cascade where the most important phenomena that should be adequately modelled are as follows:

- stagnation point flow;

- laminar/turbulent transition;

- shock-wave/boundary-layer interaction with possible flow separation.

The shock-wave/boundary-layer interaction seems to be the most important phenomenon and its adequate capture in numerical simulations is crucial for the description of the flow field and for the determination of energy losses.

Besides UFR considered here, further Underlying Flow Regimes are important for the selected case of transonic flow in blade cascades, especially laminar-turbulent boundary-layer transition (UFR3-04), shock/boundary-layer interaction (UFR3-05), 2D boundary layers with pressure gradients (UFR3-03) and stagnation point flow (UFR3-12).

## Review of UFR studies and choice of test case

There are numerous experimental data on flow through turbine blade cascades used as test cases for validation of CFD methods in various databases, e.g. VKI turbine cascade. Studies on the selected test case chosen as the UFR — transonic flow in blade cascades — are given by Šťastný, Šafařík (1990, 1992) and by Šafařík (1996). The chosen steam turbine rotor cascade(called SE 1050) was designed for the last stage of a SKODA steam turbine with the blade length 1085 mm and a nominal speed of 3000 rpm. The SE 1050 profile is a section of a rotor blade at the distance 320 mm from the root. This cascade operated in the transonic regime was chosen as an etalon blade cascade suitable for testing of numerical methods and experimental techniques as well. The experimental investigation of the SE 1050 blade cascade includes experimental test data based on interferometric pictures of fluid flow and pressure measurement of boundary layers and wakes behind the cascade*.*

The basic series of measurements was made at the inlet angle β_{1} = 70.7 deg for the exit Reynolds number based on the chord length Re = 1.48 x 10^{6} with the exit isentropic Mach number changed in the range M_{2is} ∈ (0.489; 1.387). Some additional experiments were carried out for extreme values of incidence covering the range from very small loading to overloading conditions. The measurement for the inlet angle β_{1} = 70.7 deg and the exit isentropic Mach numbers 1.198 corresponding to design conditions was chosen for the underlying flow regime.

Numerical simulations of transonic flow through the blade cascade SE 1050 were carried out using models of inviscid flow (in-home software) and of viscous flow (in-home software and FLUENT code). The algebraic Baldwin-Lomax model, the one-equation Spalart-Almaras model (Dobeš *et al.*, 2003), and the two-equation Menter SST model (Louda *et al.*, 2003) were used for modelling of turbulent flow in in-home codes while the RNG k-eps model, the one-equation Spalart-Almaras model (Matas *et al.*, 2001 and Fialová *et al.*, 2000) and the RSM model (Šafařík *et al.*, 2003) were used in the FLUENT code.Simulations by FLUENT code were made not only for the nearly design condition i.e. for the Mach number M_{2is} = 1.189 but in a wide range of exit velocities from subsonic (M_{2is} = 0.489) to low supersonic ones (M_{2is} = 1.313).

The test case considered is however dominated by inviscid effects, so that it is more suitable for testing numerical schemes rather than turbulence models.

© copyright ERCOFTAC 2004

Contributors: Jaromir Prihoda; Karel Kozel - Czech Academy of Sciences