Full-Annulus Simulations of Airfoil Clocking in a 1-1/2 Stage Axial Compressor

Abstract

Axial compressors have inherently unsteady flow fields because of relative motion between rotor and stator airfoils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead to progressively more complex wake/wake and wake/airfoil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. In addition, as the Mach number increases the interaction between blade rows can be intensified due to potential effects.It has been shown, both experimentally and computationally, that airfoil clocking can be used to improve the efficiency and reduce the unsteadiness in multiple-stage axial turbomachines with equal blade counts in alternate blade rows. While previous investigations have provided an improved understanding of the physics associated with airfoil clocking, more research is needed to determine if airfoil clocking is viable for use in modern gas-turbine compressors. This paper presents the results of a combined experimental/computational research effort to study the physics of airfoil clocking in a high-speed axial compressor. Computational simulations have been performed for eight different clocking positions of the stator airfoils in a 1-1/2 stage high-speed compressor. To accurately model the experimental compressor, full-annulus simulations were conducted using 34 IGV, 35 rotor and 34 stator airfoils. It is common practice to modify blade counts to reduce the computational work required to perform turbomachinery simulations, and this approximation has been made in all computational clocking studies performed to date. A simulation was also performed in the present study with 1 inlet guide vane, 1 rotor airfoil, and 1 stator airfoil to model blade rows with 34 airfoils each in order to examine the effects of this approximation. Time-averaged and unsteady data (including performance and boundary layer quantities) were examined. The predicted results indicate that simulating the full annulus gives better qualitative agreement with the experimental data, as well as more accurately modeling the interaction between adjacent blade rows.

Hydrodynamic interaction of axial turbomachine cascades

“…Some experimental data confirming the character of dependence of unsteady loadings on N 1 /N 2 are presented in [20]. Results of numerical modeling are presented in [12].…”

“…In connection with the use of formulas (12) and (13), it is necessary to notice that integral (13) diverges in case of a smooth trailing edge, where V 0 (τ ) ∼ τ near τ = 0. Therefore, in calculations it is necessary to assume the trailing edge to be angular with an internal corner < π.…”

“…The functions J 1 (z 0 , t) and J 2 (z, t) in (15) are determined by the equalities (13) and according to (12) depend linearly on the circulation of the relative flow velocity on airfoils of cascades 1 and 2. The values J and J 1 in the expression for V 2rel are specified by the equalities (11) and (14) and, therefore, are determined by a profile loss factor ζ * for cascade 1 and by circulation of the relative flow velocity on its airfoils.…”

“…was carried out by means of the theory of potential-vortical interaction of cascades in the quasi-stationary problem formulation. The cascade geometry is shown in Figure 7 for gaps between the cascades equal to 12 = 0·84h 1 and 23 = 0·27h 3 . The coefficients of the profile losses of the cascades 1 and 2 were taken equal to ζ * = 0·023, and the relation h 3 /h 1 was varied: h 3 /h 1 = 1 (curve 1); 1/2 (curve 2), and 33/34 (curve 3).…”

“…Similar experiments and a numerical analysis have been executed for turbine stages in [7][8][9]. Further experimental and numerical studies were performed for a subsonic model stage of the axial compressor 1 [10][11][12][13]. The practical importance of this problem has led to a continuation of the investigations devoted to the clocking effect (see, for example, [14,15]).…”