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Numerical Simulation of Gas-Liquid Two-Phase Flow Driven by a Rotating Object

Gas-liquid two-phase flows are often found in industrial applications for the purpose of lubrication and cooling and improvement of its efficiency is required from the point of view of the environmental concerns. Detailed analysis of the two-phase flow phenomena makes it possible to optimize industrial machine design and minimize energy loss.

 In the gas-liquid two-phase flow driven by a rotating object such as a gear, the gas-liquid interface repeats breakups and coalescence with large deformations of the interface and the distribution of the liquid phase varies significantly in time and space. It has been a big challenge to simulate and investigate the detailed flow field due to the complexity of the physical phenomena. We decided to solve the Navier-Stokes equation described on a rotating coordinate system. The Coriolis and centrifugal forces, which are unique in the rotating motion, are also considered. One-field model formulation in which the physical properties are switched between the gas and liquid phase is employed to model the two-phase flow. Although a sparse matrix by the pressure Poisson’s equation needs to be solved, it is well known that the iterative solver sometimes has a difficulty to get a converged solution due to the large density ratio, which is up to 1:1000, between the phases. Utilization of a matrix solver library (MG-BiCGStab) by the Mizuho Research Institute Inc. makes it possible to get stable and fast convergence of the large-scale sparse matrix.

 The CLSVOF (Coupled Level Set and Volume of Fluid) method is used for the interface capturing. The gas-liquid interface is modeled to have finite transition thickness due to the numerical stability although the interface is considered as discontinuous for the length scale we are investigating. The numerical diffusion, which is inevitable even if a high order discretization scheme is applied, is prevented and the thickness of the interface is kept constant by applying a reconstruction procedure of the VOF function [1]. The unit normal vector of the interface is computed from a smooth singed distance function (Level Set function) instead of VOF function that has steep gradient.

The numerical simulation of the two-phase flow driven by a rotating object is executed on TSUBAME2.0 with 128 CPU cores and the numerical results are compared with the experimental results provided by Nissan Motors Co., Ltd. Fig.1 shows that the numerical simulation describes the gas-liquid interface profile very well [2].


Fig.1 Comparison of the gas-liquid interface profile between the numerical and experimental results.

 

Fig.2 illustrates that the frictional moment acting on the object agrees well between the numerical and experimental results, too.


Fig.2 Comparison of the frictional moment between the numerical and experimental results.

In addition, the simulation makes it possible to understand the detailed phenomena by analyzing the pressure and shear stress acting on the object as in Fig.3. As a result, Fig.4 reveals fluctuation of the frictional moment due to the pressure and the shear stress. The instant A to D corresponds between Fig.3 and 4. While the large pressure on the teeth face leads to the maximum frictional moment at the moment when the teeth goes into the oil, little time fluctuation is observed in the frictional moment due to the shear stress. Although the total frictional moment is able to be measured by the experiments, the contribution of the shear stress and pressure to the frictional moment is able to be revealed only by the numerical simulation. The numerical code will be a promising technology to improve the operational efficiency of the machines in the industry.


Fig.3 Distribution of the pressure and shear stress acting on the rotating object.


Fig.4 Fluctuation of the frictional moment due to the pressure and shear stress.

References

[1] E. Olsson and G. Kreiss: A conservative level set method for two phase flow, Journal of Computational Physics, 210, 225-246, (2005).
[2] N. Tan and T. Aoki: Numerical simulation of gas-liquid two-phase flow driven by a rotating object, Journal of Japanese Society of Mechanical Engineers Series B, Vol.77, No.781, 1699-1714 (2011). (In Japanese)

 

 

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