Numerical investigation and performance enhancement of roots pumps operating with gas-liquid mixtures

Highlights

• Flow characteristics of Roots pumps operating with gas-liquid mixtures are analyzed.

• The pressure difference caused by the backflow is identified as the main reason to lower pump efficiency.

• Increasing gaps between the rotor and casing fails to increase the pump efficiency to a satisfactory value.

• The gradually varied gaps near the outlet can increase flow efficiency and maintain a roughly constant volumetric efficiency.

Abstract

The suitability of Roots pumps operating with gas-liquid mixture is investigated. The computational fluid dynamics method is employed and validated against experimental results. To highlight flow characteristics of Roots pumps operating with gas-liquid mixtures, the Roots pumps operating with pure gas and liquid are included as the reference case. A pump efficiency of 48% is attained for the gas-liquid mixture at the volume ratio of 4:1, while the efficiency of 59% for gas and 80% for liquid are achieved, respectively. The reduced pre-compression effects and the resulting high-pressure difference between the outlet and the working chamber are found to be reason for low efficiency. To enhance performance, increasing the gap between the rotor and casing is utilized. It is demonstrated that the flow efficiency is increased, while the volumetric efficiency cannot be maintained due to the increased leakage through the gap between two rotors. Alternatively, the configuration with the gradually varied gap near the pump outlet is employed. The pump efficiency is significantly enhanced due to increased pre-compression effects, while the high volumetric efficiency can also be maintained. The work provides the insight into flow characteristics of Roots pump operating with gas-liquid mixture.

Introduction

The power supply is vital to the operation of Unmanned Underwater Vehicles (UUVs). The primary or secondary batteries are currently limited by its low energy density and are also not cost-effective. In addition, the open-cycle thermal power system is not independent of operating depth, since the back-pressure increases with the operating depth, degrading engine performance significantly [1]. One of viable solutions is to use the semi-closed cycle thermal power system [2]. Effectively, the exhaust gas is condensed and dissolved, forming gas-liquid mixture. The gas-liquid mixture is then pumped out [3]. For underwater applications, the key is that the gas-liquid mixture needs to be pressurized properly. The pump can be operated in different depths and rotational speeds, presenting following requirements:

• 1. The pump must operate efficiently at multiple pressure ratios and volume fractions.

• 2. The pump structure should be compact, due to the sizing constraint for UUV application.

Pumping gas-liquid mixture is usually required in petroleum transportations and cooling of power plants [4,5]. The centrifugal pump was widely considered in literature. Minemura and Murakami [6] derived the equations of bubble motion in centrifugal pumps. They concluded that the drag force caused by the slip velocity between phases and the force due to the pressure gradient around the bubble are the main factors that controls the bubble motion. Otherwise, the bubble has the tendency to deviate from the liquid streamlines. Lea and Bearden [7] researched the performances of different centrifugal pumps at several operating conditions. They found that the flow rate, suction pressure and gas fraction are the main parameters affecting the pump performance. Cirilo [8] attributed the reduction of pump head to the accumulation of gas in the impeller. Cappelino et al. [9] experimentally studied the method of improving the performance of the gas-liquid mixture centrifugal pump. Even a centrifugal pump can handle higher inlet gas volume fraction at design point, the pump head drops sharply at off-design conditions. Sato et al. [10] concluded that the drop of pump head is attributed to the phase separation and the gas accumulation in the impeller due to the Coriolis force. Caridad et al. [5] simulated the conditions of electrical submersible pump conveying gas-liquid mixture.

Other pumps that are frequently used to compress gas-liquid mixture are twin-screw pump and twin-screw compressor [11]. Wietstock [12] conducted experimental study on the performance of various multiphase pumps and found that the multiphase positive displacement pumps are suitable. Egashira et al. [13] studied the performance of a twin-screw pump with the focus of pump backflow and scale-up parameters. An analytical model was built and used to predict the backflow on relatively broad conditions. Prang et al. [14] established a prediction method of the flow in twin-screw pump and verified the accuracy by comparing against test data over a wide range of fluid viscosity and inlet gas volume fraction from 0 to 100%. Rausch et al. [15] studied the performance of multiphase twin screw pump theoretically and experimentally. Cao et al. [16] drew a conclusion by experiments and theoretical analysis that the pressure change curve during a discharge process of a twin-screw multiphase compressor becomes higher when the condition has a lower gas volume fraction, higher discharge pressure, higher rotational speed and higher inlet pressure. Yin et al. [17] established the thermal deformation and force deformation models of the rotors of a twin-screw multiphase pump and studied the effect of rotor deformation on volumetric efficiency.

Other pumps are also considered. Hong and Son [18] simulated the internal flow field of the vane vacuum pump with the check valve and groove, where the clearance and the contamination due to oil leakage were both considered. The results show that the check valve and the groove can significantly reduce the required power of the pump. Yang et al. [19] performed theoretical and experimental studies to investigate the pumping behavior of a synchronal rotary multiphase pump at the inlet gas volume fraction up to 98%. The pump exhibits low pump efficiency of 10% at the high inlet gas volume fraction (98%). Yu et al. [20] conducted unsteady simulations of the gas-liquid mixture flow in a multiphase pump by assuming tiny bubbly flows. It is found that the two-fluid model can accurately capture the transport process. Serena and Bakken [21] described the design and construction of an advanced laboratory setup, allowing the study of a multiphase pump model.

The work in literature shows that the centrifugal pump and multiphase twin-screw pump are candidate choices for pressurizing gas-liquid mixture. The centrifugal pump encounters a sharp decrease of pump head when the gas void fraction is high, since the gas is separated from the water and gathered in the pump. The proper designed centrifugal pump can certainly handle high inlet gas void fraction. However, its performance becomes extremely poor at off-design conditions. Consequently, the centrifugal pump is not a suitable choice for UUV thermal power system, where the exhaust gas void fraction changes over a wide range (the gas volume fraction at design point is approximately 80%). For the multiphase twin-screw pump, the ratio between the fluid crossing section and the pump section is small, leading to a relatively large size. In addition, to balance the axial force, the twin-screw pump often uses a double-suction configuration. This further increases the structure complexity. The large size and complex structure prevent the application of multiphase twin-screw pumps in UUV. The twin-screw compressor also can pump gas-liquid mixture. Nevertheless, the exhaust pressure will change by almost ten-folds for UUV working conditions. The internal pressure ratio of the multiphase twin-screw compressor might deviate significantly from the external pressure ratio. The internal volume ratio regulating mechanism cannot be fitted in a narrow hatch of UUVs. Moreover, the change of the UUV working conditions may cause a sudden change of the intake gas void fraction (from 0 to 100%), resulting in a pressure surge, or even a liquid slugging in the compressor, which seriously affects the operation of twin-screw compressor. Therefore, the twin-screw compressor is not suitable for the working conditions of UUV.

As an alternative solution, the Roots pump, which is taken as isometric compression approximately. The working fluid condition does not adversely affect the performance. It has the potential to pressurize the gas-liquid mixture. Previous investigations of Roots pumps focus on the optimization of rotor profiles. Laczik et al. [22] proposed a novel method to design the gear teeth profile. Hsieh [23] also proposed a new mathematical model to design rotary lobe pumps. The results show that a smaller elliptical axial ratio can enhance discharge efficiency. He and Zhou [24] compared the performance of cylindrical and screw type Roots pumps. The results show that the cylindrical type has a higher average flow rate while the pulsation of screw type is low. Cai et al. [25,26] presented rotor tooth profiles with the Assur-group-associated virtual linkage method. The feasibility is validated against experiment results. In addition, the Roots pump with a gradually expanding outlet is proposed. The impact of the backflow and the noise level are significantly reduced [27]. Wang et al. [28] proposed an elliptical rotor profile with elliptical arc and its conjugate curve and established the mathematical model. The results showed the area efficiency of the new type rotor increases in comparison to the conventional circular rotor.

To investigate pumping performance, the CFD method is usually employed. Vizgalv et al. [29] simulated a Roots pump connecting with an ejector and found that the volumetric and adiabatic efficiency are both increased. Hsieh and Deng [30] studied the method to improve the flow characteristics of multistage Roots pumps. The results show that a parallel connection and varied phase angle multistage Roots pumps vacuum system shows a better performance. Liu et al. [31] performed three-dimensional (3D) unsteady simulations of a three lobe Roots pump with the spiral inlet and outlet. The spiral inlet and outlet can significantly reduce the pulsation of the flow. Huang et al. [32] used the 3D dynamic mesh to simulate flow for three typical rotating pumps. Sun et al. [33,34] compared the pump performance using simple pipes and smaller-diameter pipes. Good agreement is achieved for the case with smaller-diameter pipes in comparison to experimental results. They [35] further investigated the performance of Roots pump with a backflow design. The results show that the backflow design can reduce the pressure pulsation and power consumption. Li et al. [36] presented a Roots pump with gradually varied gap. This structure can effectively mitigate the pulsation of radial force.

However, previous studies on Roots pumps are limited to pure gas or liquid. The suitability of Roots pumps for pressurizing gas-liquid mixtures has not yet been proven. This paper aims to fill this gap by investigating flow characteristics of Roots pump operating with gas-liquid mixtures. The reminder of this paper is organized as follows: a gas-liquid mixture Roots pump is designed by referring to the conventional gas Roots pump in Section 2 and key parameters to evaluate pump performance are also proposed. In Section 3, the computational model is proposed, and the model validation and grid independence study are described in Section 4. Section 5 presents comparative results of Roots pumps for pressurizing gas, liquid and mixture. The structure of gas-liquid mixture Roots pump with gradually varied gap is proposed for performance enhancement.