Assessing the Sensitivity of Turbine Cascade Flow to Inflow Disturbances Using Direct Numerical Simulation

Direct numerical simulations (DNS) are conducted of flow through a linear low-pressure turbine cascade with T106 blade sections at Re=60,000, based on chord and isentropic exit velocity. A highly efficient in-house compressible Navier-Stokes solver was adapted for turbine cascade simulations and applied to investigate the effect of inflow disturbances on transition behaviour and blade profile losses. It was found that in compressible DNS the attenuation of acoustic reflections at the inflow boundary are essential as the wake loss, unlike the pressure coefficient on the blade, is sensitive to upstream acoustic perturbations. The results of DNS without inflow turbulence are compared with experimental data and show excellent agreement for both pressure coefficient on the blade and for the wake loss. Additional DNS with inflow turbulence level Tu=1% and Tu=3.8% were conducted. In all cases a laminar boundary-layer separation on the suction side was observed, however, the separation bubble size varies with turbulence level. It is found that with increasing turbulence level the peak amplitude of the wake loss reduces and the peak location is shifted towards the pressure side, and that the separation point of the suction side boundary layer moves downstream. INTRODUCTION To reduce specific fuel consumption and cost of jet engines, it is desirable to decrease the number of blades. This results in the individual blades of modern low-pressure turbines (LPT) being subjected to more severe pressure gradients, which affect the boundary layers. The profile losses of a linear turbine cascade depend strongly on the state of the boundary layers on the blades. Due to high pressure ratios and moderate Mach and Reynolds numbers in LPTs, the boundary layers are prone to laminar separation. Modern turbine blades actually allow for small separation bubbles on the blade surface by design. Both separation bubbles and the type/location of laminar-turbulent transition type of a boundary layer are known to be sensitive to upstream disturbances. In particular incoming wakes have a profound effect on laminar separation bubbles and boundary layer mechanisms. In an experimental study, Engber and Fottner [1] investigated the effect of incoming wakes on boundary layer transition of a highly loaded turbine cascade and provided data to improve empirical correlations for the calculation of transition in boundary layers. A later experiment showed a variation of the pressure loss coefficient for different clocking positions of the incoming wakes [2]. The first incompressible direct numerical simulation (DNS) of a turbine cascade was performed by Wu and Durbin [3] and found evidence that incoming wakes are responsible for longitudinal structures forming on the pressure side. Additional numerical studies, also using incompressible DNS and largeeddy simulations (LES) have contributed further to the understanding of the effect of incoming wakes on the pressure and suction side boundary layers [4,5]. In these studies both LES and DNS of the same configuration were compared and it was concluded that good overall agreement with DNS could be obtained with well resolved LES. Ravery et al. [6] conducted compressible LES without incoming background turbulence level and reported on the coupling of the separation bubble and vortex shedding at the trailing edge. Matsuura and Kato [7] performed compressible LES with different inflow background turbulence levels and found that the vortex-shedding separation-bubble coupling was negligible at higher inflow turbulence levels. Sarkar [8] performed incompressible LES focusing on wakes with different eddy structure size and showed that the structure of the incoming wakes, i.e. level of three dimensionality, strongly affects blade performance and wake losses. In a recent contribution, Medic and Sharma [9] performed compressible LES at various Reynolds number and found significantly improved results compared to URANS. However, despite capturing most trends observed in experiments with LES, at lower Reynolds number the losses were under predicted for clean inflow cases. In addition, in contrast to available experimental data no significant reduction in wake loss could be found for 4% free stream turbulence level and the boundary layer separation points obtained by LES appeared insensitive to changing freestream levels. One of the main objectives of the current work is therefore to assess whether better agreement with experimental results can be obtained by eliminating the uncertainties introduced by subgrid scales models, i.e. performing fully resolved DNS. Further, to date most studies have either focused on the influence of background turbulence level [7] or the disturbances caused by incoming wakes. The influence of both effects has been shown to be important in the context of loss prediction. In a real engine environment both background turbulence and wake disturbances coexist with varying respective strengths and so it would be of interest to thoroughly investigate the combined effect, as suggested by Coull and Hodson [10]. In the present paper, a first step towards this goal is made by testing a numerical setup that allows for compressible DNS of a linear LPT cascade with inlet background turbulence using a novel Navier-Stokes code. In this initial step, this setup is used to investigate the influence of inflow turbulence on the blade performance and wake losses. In order to resolve the incoming turbulence, a fine mesh upstream of the blade profile and in the passage is required and therefore no large savings in computational cost using large-eddy simulation over DNS can be expected. The main objectives of the current paper are: i. validate the numerical setup, i.e. compressible DNS with novel code, against experiments ii. investigate the effect of inlet turbulence on transition and wake iii. generate a database of the turbulent kinetic energy transport equation budget for future model improvement DESCRIPTION OF TEST CASE The turbine blade geometry considered in the current work is the T106 profile experimentally investigated by Stadtmüller [11]. The measurements were obtained in a low-pressure linear turbine test rig with seven aft-loaded blades with an aspect ratio of 1.76, implying that the flow at the midspan can be considered to be statistically two-dimensional. Therefore, the use of spanwise periodic boundary conditions would appear to be a reasonable assumption. In the experiments, the pitch-to-chord ratio, stagger angle , the inlet flow angle 1 and the exit flow angle 2 are 0.799, 30.7°, 37.7° and 63.2°, respectively. However, as explained in Michelassi et al. [12], there is some uncertainty about the actual inlet conditions, both in terms of total pressure and inlet flow angle. RANS simulations by Stadtmüller [11] and DNS and LES by Michelassi et al. [12] suggest an inlet angle of 45.5°. A variable density system in the test rig allowed measurements at a relatively low Reynolds number of 5.18 ×10 4 and an isentropic exit Mach number of 0.4. In the current study, the resulting Reynolds number and outlet Mach number were 59,634 and 0.405, respectively. The ratio of specific heats is specified as γ = 1.4 and the Prandtl number as Pr = 0.72. The spanwise width of the computational domain was chosen as 0.2 chord lengths, which is deemed to be sufficient to capture transition in a possibly separated blade boundary layer based on previous experience gained with separation bubbles on low-Reynolds number aerofoils [13]. Furthermore, previous studies of linear turbine cascades found a spanwise width based on axial chord of 0.2 [14, 15] or even 0.15 [3] to be