Calculation of flow of a viscous compressed Gas in the casing of low-flow centrifugal Compressor stages

Abstract

UDC 621.515.5:533.21.001.24 Calculations of the flow of three-dimensional viscous compressed gas in the casing of low-flow stages of centrifugal compressors (CC) are very laborious. Many problems, for example, determination of the turbulent viscosity of such flow, have not been solved sufficiently accurately and clearly. The complexity of the problem is also due to the nonstationary character of the flow itself. However, even approximate solutions make it possible to refine the physical and mathematical models of the flow and find ways of further improving the design of the casing. A method of calculating the flow with the method of finite differences in radial vaneless slots (vaneless diffusers (VLD), side pockets around the impeller (Im) disks, etc.) used for analyzing the flow in VLD was developed at SPSTU [I]. A comparison of the calculated and experimental data demonstrated the sufficiently high efficiency of the method for use as an algebraic model of turbulence, like the k---e model, and the possibility of taking into consideration the anisotropy of the roughness of the diffuser walls. The distribution of the values of the local loss factor by radius in VLD behind half-open Im for different angles ot 2 at the inlet with constant (5, 10, 15 ~ and also at variable (5-15 ~ and 15-5 ~ values along axis z is shown in Fig. 1. The first maximum is due to restructuring of the flow at the inlet to VLD behind Ira, and the second corresponds to local burbling zones. With a decrease in angle tx2, the values of the local loss factor increase as a result of an increase in the path length for a given Ar. The presence of flanges decreases the losses for small angles ct 2 around it and increases them for constant angle cr 2 or for higher values around it due to warping of the flow. Figure 2 shows the important effect of angle ct 2 and the ratio b 2 = b2/D 2 on the losses in VLD [ 1, 2]. We now propose investigating the flow in the side pockets around Im with the method developed. In the second stage, the analysis of the flow in the casing of a CC stage was conducted together with the Institute of Turbomachines at Hannover University (Germany) with Start CD software by the finite volumes method [3, 4]. The calculation was performed for a series of low-flow closed Ira, including Im of the "channel type," and immobile stage elements [VLD + reverse control apparatuses (RCA)]. The general shape of the region of the flow in the immobile elements is shown in Fig. 3. Note the reciprocal effect of the elements of the rotating elbow (RE) on flow in VLD. The existence of secondary flows is characteristic of RCA. For qb = 0.0188 (significantly lower than the calculated value) on the side of the vacuum, burbled flow arises again at the beginning of RCA and develops along its length due to secondary flows (Fig. 4). In tests of the SVD-6 low-flow "channel" impeller having qbop t -- 0.014, relatively high indexes and a wide zone of stable operation were obtained [4]. For modes close to the calculated mode, flow had a relatively stable character (Fig. 5a), while for low flow rates, developed burbled zones were observed in the channel (Fig. 5b). The third stage of the studies consisted of developing target software for calculating three-dimensional compressed viscous flow in the casing of a CC stage by the method of finite volumes based on the data on turbulent viscosity in [5]. A three-dimensional network sufficiently completely describes the geometry of the casing. The network is constructed with consideration of the effect of internal gas leaks and cross flows. The casing of the stage is divided into two parts: ultralow-flow Im with VLD and immobile elements (part of the VLD, RE, RCA, and ring confusor (RC). The stage casing is divided into two