Abstract
Static characteristics and leakage flow rates of liquid annular seals have great influences on the hydraulic efficiency of turbomachinery. In this paper, a two-dimensional (2D) mathematical model for predicting the leakage flow rates and static characteristics of liquid seal is established, based on the lattice Boltzmann method (LBM) combined with the D2G9 velocity model for incompressible fluid and large eddy simulation (LES) turbulence model, in which the transformation equation of reference pressure is developed with the Bernoulli equation. Moreover, the proposed model is validated by comparing with the experimental results, calculation results based on the finite volume method (FVM), and the results based on the empirical method of three seals under different operating conditions. The comparisons show that the maximum deviation in leakage prediction of the calculating model based on 2D LBM is 4%, and this calculating model will effectively improve the leakage prediction accuracy of the seals compared with the FVM and theoretical method.
Highlights
In turbomachinery, there exist several sets of liquid annular seals, including neck-ring seals, interstage seals, and balancepiston seals. ese seals prevent leakage flow while increasing the volumetric efficiency of the machinery
Experimental results are conducted by Darden et al [32], and the calculation results which are calculated by the three methods for leakage flow rates of Model 2 are shown in Figure 7 and Table 5
It is observed that the leakage rates based on empirical formulas were under-predicted with an error of more than 10% compared to the experimental results. e prediction error of the leakage rate based on finite volume method (FVM) is 2.85% under the pressure difference of 9.29 MPa but with error of more than 5% under the other two operating conditions
Summary
There exist several sets of liquid annular seals, including neck-ring seals, interstage seals, and balancepiston seals. ese seals prevent leakage flow while increasing the volumetric efficiency of the machinery. There are mainly three methods to investigate the static and dynamic characteristics of these seals, including empirical formulas, bulk-flow method, and computational fluid dynamics (CFD) method. These three methods are all based on the hypothesis of continuous media, which means that the methods are all developed from a point of macroscopic view. Many researchers have analyzed the static and dynamic characteristics of sliding bearings, which are structurally similar to liquid annular seals based on LBM. Kucinschi and Afjeh [1] analyzed the internal flow characteristics and the fluid-film lubrication details within model sliding bearings based on 2D LBM. Kim et al [2] have used LBM to study the flow conditions in a nano-sized air bearing, and Ramirez et al [3] used this method to analyze the switching flow characteristics between different channels in a micron-sized air bearing. e simulation results showed that LBM has high accuracy in simulating the fluid flow of the sliding bearing with mini clearance
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