A Novel Quasi 3-D Design Method for Centrifugal Compressor Meridional Plane

Abstract

This paper is concerned with a quasi-3D design method for centrifugal compressor impeller in the meridional plane. The method links up a novel inverse design algorithm, called Ball-Spine Algorithm (BSA), and a quasi-3D analysis code. The Euler equation is solved on the meridional plane for a numerical domain of which some unknown boundaries (hub and shroud) are iteratively modified under the BSA until a prescribed pressure distribution is reached. In BSA, the unknown walls are composed of a set of virtual balls that move freely along the specified directions called spines. The difference between target and current pressure distribution causes to deform flexible boundary at each modification step. In order to validate the quasi-3D analysis code, an existing compressor is investigated by some experiments in which several static pressure points on the shroud, the flow parameters at the compressor inlet and outlet are measured. Comparison of the quasi-3D analysis results with experimental results shows good agreement. Also, a full 3D Navier-Stokes code is used to analyze the existing and designed compressor numerically. The results show that the momentum decrease near the shroud wall in the existing compressor is removed by hub-shroud modification resulting an improvement in performance by 0.6 percent.

Inverse shape design via a new physical-based iterative solution strategy

“…Convergence histories of all three algorithms are shown in Figure 9. Note that each iteration in the direct design algorithm is basically a nonlinear iteration and corresponds to a solution of the equation set represented by Equation (19). In comparison, each iteration in the proposed and classical iterative algorithms corresponds to sequential calls to the grid generator, flow solver and the relevant shape updater.…”

“…Here, the basis for the determination of this parameter is not discussed and interested readers may consult. [19][20][21][22] The flow chart of this algorithm is shown in Figure 4(a). In this algorithm, after solving the governing equation on the initial grid and calculating V 0 t , the boundary node coordinates are updated separately using Equation (14).…”

“…Similar to the direct design method, the target velocity distribution is imposed through the implementation of boundary values of F ip according to Equation (19). Using the above expressions for F ip in the balance equations for the boundary control volumes, highlighted in Figure 4(b), and assembling all the corresponding algebraic equations for these control volumes, result in the following linear set of equations:…”

“…In the flexible string algorithm, proposed by Nili-Ahmadabadi et al [16][17][18], the boundary is considered as an elastic string that deforms under the force due to the pressure mismatch. In another method, called the ball-spine Algorithm, [19][20][21][22] hypothetical balls are distributed along the boundary. These balls are allowed to move along specified directions, called spines, under the pressure mismatch force.…”

Aerodynamic Design of S-Shaped Diffusers Using Ball–Spine Inverse Design Method

“…In the previous works of Nili-Ahmadabadi et al [11], 3D effects were not been taken into account. The BSA is applied to the upper and lower lines of the duct symmetric plane, and then, the 3D geometry is generated using elliptic cross-sectional profiles and a constrained width.…”