Computational study of Reynolds number effect on the typical first stage of a high-pressure compressor
At present methods of blade machines characteristics are widely used by many scientists all over the world. However, the applied methods of problem setting while flow modeling suppose the boundary layer to be fully turbulent in all regions, and do not reflect transient effects actually in the flow in effect. For the flows with low Reynolds numbers the problem setting with no account for laminar-turbulent transition might lead to significant disagreement between experimental and computational results. The article presents the results of the computational study of Reynolds number effect on the first stage of high pressure K-8B compressor with the low aspect ratio of the rotor wheel blades (RW) (0.729). The stage has the following key geometry and gas-dynamic parameters: - the hull diameter above the rotor wheel D<sub>t_r</sub>= 306.5 mm - relative hub diameter at the inlet `d<sub>1</sub>=0.742mm - relative hub diameter at the outlet `d<sub>2 </sub>= 0.853 mm - adiabatic efficiency h<sup>*</sup><sub>ad</sub> = 0.86 - total pressure ratio p<sup>*</sup> = 2.0. The values of corrected specific mass flow rate through the stage are related to the values at the design point. The compressor stage regulation allows vary the setting angles of the inlet control assembly (ICA) and distributor, though at the rotor rotation frequencies under consideration (100% and 95%) zero angles were set. The ICA row, RW row and distributor row contain 46, 35 and 76 blades respectively. The gaps at theperiphery and hub of guiding devices were assumed as 0.4 mm and 0.6 mm correspondingly in the stage model. The rotor row gap was assumed as 0.5 mm. The value of the total temperature at the input boundary conditionis 288.15 K. For Reynolds number decrease modeling the values of total pressure were assumed as P<sub>in</sub> = P<sub>0</sub>, P<sub>in</sub> = 0,72P<sub>0</sub>, P<sub>in</sub> = 0,29P<sub>0</sub>, P<sub>in</sub> = 0,21P<sub>0</sub>, where P<sub>0</sub> = 101325 Pa is the standard atmosphere. The values of static pressure at the periphery were fixed on the outlet boundary condition. Simulation of 3D viscous flow in blade channel of the stage was performed with ANSYS CFX SOLVER MANAGER in the setting of 3D averaged Navier-Stokes equations (3D RANS). The computational mesh was created with integrated automatic mesh generator ANSYS TURBOGRID and contains 3643432 elements. The solution for the setting with fully turbulent flow was obtained by Menter SST turbulence model. The calculations accounting for laminar-turbulent transitionwere also performed. For this purpose the Menter SST turbulence model supplemented with γ - R<sub>eθ</sub> transition model by Langtry and Menter was applied. For solution concordance, “stage” or in other words “Mixing planes” option was used at the rotor-stator interfaces. According to the calculation results the stage characteristics degradation between maximum and minimum Reynolds numbers was as follows: adiabatic efficiency h<sup>*</sup><sub>ad</sub> (4%), pressure ratio (p<sup>*</sup>) at the points of max h<sup>*</sup><sub>ad</sub> (2.8%), corrected specific air flow rate (1.52%) at rotor rotation frequency n = 100%, and ∆max h<sup>*</sup><sub>ad</sub> = 5%, ∆p<sup>*</sup> = 4.3%, ∆G<sub>cor</sub>= 2.3% for n = 95%. Thus, the shift of characteristics corresponding to lower Reynolds numbers occurs to the area of reduced flow of h<sup>*</sup><sub>ad</sub> and p<sup>*</sup>. The transitional model addition affects these differences as follows: ∆max h<sup>*</sup><sub>ad</sub> = 3.9%, ∆p<sup>*</sup> =2.2%, ∆G<sub>cor</sub>= 1.6% for n = 100% and ∆max h<sup>*</sup><sub>ad</sub>=3.7%, ∆p<sup>*</sup>=2%, ∆G<sub>cor</sub>= 1.6% for n = 95%. Comparing to the experimental results, obtained for n = 95%, application of transitional model of turbulence increases significantly the accuracy of the numerical study. Namely, deviations between experimental data and calculations with transitional model by values of max h<sup>*</sup><sub>ad</sub> pressure ratio at the points max h<sup>*</sup><sub>ad</sub> is less than 1%, while for standard SST model these deviations are of about 2% for maximum Re number, and 3.5% for minimum Re. Comparing the fields relative to Mach numbers for two models (SST and SST γ - Re<sub>θ</sub>), the basic difference in the flow while laminar-turbulent transition modeling consists in qualitatively true modeling of the processes occurring in the boundary layer. In this case, laminar boundary layer near the front edge of the blades, laminar separation and attachment really exist. Turbulization at the rotor wheel blades occurs at the shock wave location, after which the boundary layer already has turbulent structure for the most part with preservation of a very thin laminar layer. Besides, the changes in flow through the radial clearance in the rotor wheel are being present. For γ - Re<sub>θ</sub> “bubble” flow-over while Re number reduction slightly reduces its size. The separation near the back edge herewith becomes more intensive.