Numerical investigation on the flow resistance characteristics of balance block in the rotary compressor

With the increasing demand for energy saving, the air conditioner with variable frequency becomes the mainstream of the market, which leads to a high requirement for the dynamic balance characteristics of the rotary compressor at variable speed conditions. The balance block is the key part in the eccentric shaft system to balance the rotational inertia force brought by the eccentric wheel, and its flow resistance during rotating process has a large impact on the power consumption. In this paper, CFD simulations will be carried out to study the flow characteristics of several different compressor balance blocks and the results can provide reference for the optimization design of the balance block in the rotary compressor.


Introduction
As the main part of domestic electric appliance, especially in the hot climates, air conditioner accounts for the most of household power consumption.Moreover, the compressor takes up most of the power consumption of the household air conditioner system.[1,2] Rotary compressors are widely used in household air conditioners with their compact structure and excellent performance.[3,4] In past decades, many scholars would pay more attention to different types of leakage losses in the cylinder to enhance the thermal performance and improve the efficient of rotary compressor system.Cai et al. [5,6] and He et al. [7] conducted a theoretical method to calculate several kinds of leakage losses in rotary compressor and proposed the experimental investigation to compare the theoretical results with experimental results, which proved the validity of theoretical method.Pan et al. [8] presented a method to analyze leakage mass flow rate of six different leakage patterns, furthermore, verified the simulated results by monitoring the errors between the theoretical refrigerant mass flow rate and the experimental refrigerant mass flow rate.In fact, the flow resistance outside the compressor cylinder inside the housing of rotary compressor also has a notable effect on the power consumption of rotary compressor, which deserves more concerns.
Figure 1 shows the schematic diagram of rotary compressor and motor rotor.The pressure in the compression chamber increases as the volume changes due to the rotation of the eccentric rotor.With the high-speed rotation of eccentric rotor, large eccentric force will be generated and act on the crankshaft, which may cause noise and reduce the reliability of compressor.Therefore, it is necessary to equip with balance block on the top of the motor rotor.While the gas flows through the balance block, the flow resistance would lead to more power consumption.Liu et al. [9] proposed a CFD model to simulate the effect of balance block in scroll compressor under some different operation conditions and analyze the dynamic characteristics flow field and put forward a kind of balance block to reduce the flow resistance.
In this paper, a CFD model based on the housing of rotary compressor is established to simulate the flow resistance characteristics of balance block.Different shapes of balance block are proposed to figure out the effects of shapes of balance block on pressure distribution.To some extent, the simulated results can provide the effective guidance to the researchers who focus on further improving the efficiency of rotary compressor by the optimization design of the balance block.

Geometric model
According to the actual structure inside the housing of rotary compressor, the computational domain is built after simplifying partial structure.After being compressed, the refrigerant is discharged from the upper bearing on the cylinder with increased pressure, and then flows upward through the stator gap of the motor, finally flows out of the housing of rotary compressor from the discharge pipe on the top.The computational domain could be divided into the lower side of the motor, the stator gap of motor, the upper side of the motor where the balance block is in the top position of the motor rotor.Figure 2 displays the mesh of the computational domain.The computational domain model is established by unstructured grids, and the total number of grids is 255247.In order to simulate the moving parts of the balance block and the motor rotor, the sliding mesh is used in this part, and the static and dynamic parts transfer data through the interface.

Governing equations
The model is solved by using the commercial software ANSYS Fluent.The refrigerant flow in the fluid domain is governed by the classical thermodynamic principle, including the continuity equation, momentum conservation equation and energy conservation equation.These equations could be written as the following: Where ρ is the fluid density, t is the time, u is the fluid velocity vector, τ is the stress tensor and given by , e is total internal energy, λ is the thermal conductivity of fluid, T is the temperature, p is the pressure.

Boundary conditions
Table 1 shows operation conditions of the simulation.In the fluid domain, the working fluid is R32 and the operation speed is 3600r• min -1 .Figure 3 displays the velocity of inlet.It can be seen from figure 3 that the velocity of the refrigerant rises sharply when the refrigerant is discharged from rotary compressor, and then gets decreased due to the impact between valve plate and retainer.Subsequently, the velocity of gas gets increased again and decreases with the closing of discharge valve.The pressure in the end of discharge pipe is set as 3.25MPa and the housing of rotary compressor is set as nonslip and adiabatic.In order to realize the movement of motor, the balance block and motor rotor are set as moving wall.In addition, the turbulence model adopts RNG k-ε which is widely used and validated in compressor flow simulation, the governing equations are solved through second-order upwind scheme.

Results and discussion
During the movement of rotor, the pressure in the housing of rotary compressor changes with the rotation angle.Figure 4 displays the pressure variation in the housing of rotary compressor and θ refers the crank angle.As can be seen from the figure 4(a)-(d), the pressure in the housing of rotary compressor gradually increases with the discharge of gas from the cylinder, and then a circumferential stratification of the pressure can be noticed around the balance block.This is because that the movement of balance block would obstacle the movement of fluid and cause a tendency for the upward fluid to move with rotor.While the discharge valve fully opens and tends to close, the pressure is up to the maximum value and begins to reduce with the decrease of discharge volume flow rate from the cylinder.Finally, the pressure in the housing of rotary compressor would nearly return to the initial pressure.Figure 4.The pressure variation in the housing of rotary compressor.It's obvious that the balance block has a significant effect on the pressure distribution in the housing of rotary compressor during the discharge process.The front and back faces are perpendicular to the direction of rotation, and the flow resistance caused by the pressure difference between the front and back faces obstructs the rotation of the crankshaft.For the sake of investigating the effect of different shapes of balance block, this paper studies three different shapes of balance block, the common shape of balance block and two other shapes of balance blocks based on the modifications of common shape.The quality of the balancing blocks would have a direct effect on the dynamic balance of the crankshaft, and thus the quality of the balancing blocks should not be changed as much as possible.Figure 5 shows three different shapes of balance block.Shape A is the common shape, while shape B and shape C are based on it by adding rounded corners on one side each.The radius of the rounded corners is 10mm, the height of balance block is 15mm.Figure 6 shows the pressure distribution in shape A balance block at different moments.It can be seen from these figures that the pressure on the inside of the balance block is slightly lower than that on the outside and the pressure on the front side of the balance block is close to that on the back side in the early discharge process.And then the pressure on the front side of the balance block begins to increase and exceeds the back side with the rising pressure in the housing of rotary compressor.While the discharge valve has the tendency to close, the discharge volume rate gets lower and the velocity of gas gradually decreases, the gas still collects on in the front of balance block which causes the pressure difference between the front and back side.It is clear that the pressure of both sides would reduce with the end of discharge process and the existence of pressure difference between front side and back side would lead to more power consumption in the running of rotary compressor.
Figure 7 and figure 8 show the pressure distribution in shape B and shape C balance block at different moments respectively.As shown in these figures, there are some certain differences in the pressure distribution in balance block compared to each shape.Table 2 displays the average pressure on the front and back faces of balance blocks with different shapes.Compared to original model shape A, it can be found that the average pressure on the front face is lower and the average pressure on the back face is close while the rounded corner is on the back side of balance block.Therefore, the pressure difference is lower which means that flow resistance reduces.While the rounded corner is on the front side of balance block, both the average pressure on two faces are decreased, however, the pressure difference is clearly higher than other shapes and flow resistance increases, which has a negative effect on power consumption.
Table 2 Average pressure on the front and back faces of different balance blocks.

Conclusion
A CFD model for investigating the effect of balance block in the rotary compressor is developed.In this model, transient simulation of pressure distribution in the housing of rotary compressor and different shapes of balance block is obtained.The simulated results reveal the flow resistance caused by the balance block and that the shape of balance block can reduce the resistance caused by pressure difference between the front side and back side of balance block in a certain operation condition.

Figure 2 .
Figure 2. The computation domain of balance block in rotary compressor.

Figure 3 .
Figure 3.The velocity of inlet.

Figure 5 .
Figure 5. Three different shapes of balance block.

Figure 6 .Figure 7 .
Figure 6.The pressure distribution in balance block at different moments (Shape A).

Figure 8 .
Figure 8.The pressure distribution in balance block at different moments (Shape C).

Table 1
Operation conditions.