Pressure Drop in a Metal Foam Centrifugal Breather: A Simulation Approach

Abstract

One of the main issues faced in the operation of a metal foam centrifugal breather is the high pressure drop. This study investigates the pressure drop of a metal foam centrifugal breather. The numerical simulation research method is adopted. The DPM model is used to calculate the two-phase flow field of the metal foam breather, and the porous medium model is used to replace the metal foam at the breather. The resistance caused by the metal foam is replaced by a distributed resistance added to the fluid. The effects of flow rate, rotational speed, porosity, PPI (pores per inch), and temperature on the pressure drop of the breather are analyzed. The results indicate that rotational speed, flow rate, porosity, and PPI significantly influence the resistance of the metal foam centrifugal breather. The resistance of the breather is directly proportional to the rotational speed, flow rate, temperature, and metal foam pore density, and inversely proportional to the porosity. Temperature has a minor impact on the resistance of the metal foam centrifugal breather. Therefore, the metal foam centrifugal breather is more suitable for low-speed operating conditions.

1. Introduction

Currently, aeroengines widely use mechanical transmission as the main power transfer mode, and its effectiveness and reliability primarily depend on the lubrication system, while modern advanced aeroengines require higher speeds, loads, and temperatures, thus placing higher demands on the design of lubrication systems for aeroengines. The ventilation system, as a subsystem of the lubrication system, primarily functions to discharge a portion of the high-pressure sealing gas from the oil tank and bearing chambers. This ensures that the pressure within each lubrication chamber remains within the normal operating range, thereby preventing excessively high pressure that could adversely affect sealing integrity as well as oil supply and return performance. During the work process, the gas from the lubricating oil chamber will inevitably mix with part of the lubricating oil. If the oil–gas mixture is directly discharged into the atmosphere, it will not only result in lubricant consumption but also pollute the atmosphere. Therefore, the installation of a breather to separate and recover lubricants from the oil–gas mixture in the lubricating oil chambers is necessary to reduce lubricant consumption.

The centrifugal breather is one of the common aeroengine breathers at present. Different from other breathers, the centrifugal breather is installed as an independent accessory within the engine nacelle, with a dedicated drive mechanism to rotate it [1]. When the oil–gas mixture from each lubricating oil chamber enters the centrifugal breather, the high-speed rotating impeller and other components drive the oil and gas to rotate. Due to the centrifugal force, the lubricating oil is thrown to the wall of the breather shell and then returns to the oil tank. The clean air is discharged from the outlet of the hollow shaft of the breather. The centrifugal breather is also a kind of oil and gas separator, but unlike the oil–gas separator, the oil–gas mixture entering the breather contains less lubricating oil, and the size of oil droplets is small. Therefore, the oil droplets in the breather follow the flow very strongly, which requires the breather to have a higher separation capacity [2].

A metal foam centrifugal breather adds metal foam to the centrifugal breather to improve separation efficiency. The schematic of a metal foam centrifugal breather is shown in Figure 1. Metal foam is a kind of porous medium material with low density, a large specific surface area, and high porosity [3]. Its main materials are aluminum, copper, nickel, and ceramics [4]. When the oil and gas mixture enters the metal foam centrifugal breather, in addition to the centrifugal separation effect, the porous structure of the metal foam can effectively perform secondary separation of oil droplets, thereby significantly improving the separation efficiency of the breather without increasing the rotational speed, size, or weight of the breather [5].

However, the addition of metal foam may also have a large impact on the pressure drop of the breather. The pressure drop of the breather is one of the key parameters of the ventilation system. The pressure drop affects the reliability of the ventilation system. If the pressure drop is too high, it will affect the normal working pressure of each lubricating oil chamber, while if the pressure drop is too low, it will increase the consumption of lubricating oil.

Research on metal foam commenced early, with researchers initiating studies on them as early as 1856. Over time, research on metal foam has progressively advanced and deepened. Ergun et al. [6], based on the pebble bed porous media test, on the basis of the Forchheimer–Darcy porous media flow equation, added the porous media structure parameters of porosity and sphere diameter. M.D.M [7] designed the metal foam resistance test to obtain the Ergun equation. Ricardson et al. [8] obtained the relationship between the porosity and PPI of the metal foam through experiments. Moreira et al. [9] fitted the flow resistance relationship inside the metal foam. Simon, M. et al. [10] obtained the metal foam resistance correlation. To date, research on metal foam has developed to a high level of maturity. The research on metal foam in the current public literature mainly focuses on its heat transfer and heat storage properties, manufacturing process, mechanical properties, flow properties, etc. [11,12,13,14]. In recent years, research on breathers has focused on both separation efficiency and pressure drop loss. Willenborg, K. [15] conducted experimental research on oil–gas separators, focusing on the separation of small liquid droplets with diameters less than 10 μm. The study also analyzed the impact of rotational speed and flow rate on pressure drop. Laura Cordes et al. [16] conducted experimental research on the effects of air mass flow rate, rotational speed, and water droplet diameter on the pressure drop of a rotating aeroengine oil separator using three different separator configurations. Eastwick et al. [17] used a two-phase coupling method to calculate the two-phase flow field of the breather, and the results indicate that increasing the rotation speed significantly enhances the separation efficiency of the breather, while simultaneously increasing the resistance of the breather. Zhengwei Nie et al. [18] employed the Lagrangian method to investigate the flow of dispersed oil phase in open-cell foams. The results indicate that metal foams exhibit a favorable separation efficiency for oil droplets, and this efficiency improves with decreasing porosity and increasing pore density of the metal foam. Zhang, X.B. et al. [19] conducted a numerical study on the separation efficiency and resistance of the impeller-type breather, using the DPM model to calculate the oil droplet phase and obtain the breather separation efficiency; using the RNG turbulence model, the ventilation resistance was calculated, and finally the mathematical relationship between the separation efficiency and ventilation resistance was obtained.

However, the factors influencing the pressure drop of breathers are diverse, including the impact of metal foam structural parameters and operating conditions. This study conducted a comprehensive analysis of the pressure drop of a metal foam centrifugal breather, obtaining the effects of different factors on the pressure drop of the breather, which can provide essential reference information for metal foam centrifugal breather design.

2. Metal Foam Centrifugal Breather

The breather in this paper is a metal foam centrifugal breather. The metal foam is installed with a shell on the outside, which has uniformly distributed oil outlets for discharging the recovered lubricating oil from the metal foam and centrifugal action.

Each piece of metal foam has an inner diameter of 56 mm, an outer diameter of 93 mm, and a thickness of about 15 mm. The structure of the breather is shown in Figure 2.

3. Numerical Method

3.1. Computational Domain and Mesh

The computational model requires specified inlet boundary conditions. However, it is challenging to determine these conditions for the breather. Arbitrarily specifying these conditions may introduce significant errors. Therefore, an external flow domain is established outside the inlet of the breather, with the inlet of the external flow domain located far from the inlet of the breather. The inlet of the breather is completely within the calculated flow field, thereby minimizing the influence of inappropriate boundary conditions on the computational results. The established geometry model is shown in Figure 3. Taking the experimental conditions as a reference, the inlet boundary condition is set as the mass flow boundary, and the outlet is the pressure outlet.

A hybrid mesh is used, i.e., the metal foam region is divided with a structured mesh (hexahedral mesh), and the rest of the region is divided with an unstructured mesh (tetrahedral). The unstructured mesh needs to be dense near the wall to control the mesh generation, and the generated mesh is shown in Figure 4.

3.2. Boundary Conditions

For air, the inlet boundary is given as a mass flow rate and the outlet as a pressure outlet boundary. Due to the rotating components of the impeller, struts, metal foam, and outlet duct, the MRF model is used for calculation. The metal foam is treated as a porous medium, and its drag coefficient and inertial resistance coefficient are obtained from numerical experiments.

3.3. Grid Independence

In order to ensure the reliability, accuracy, and repeatability of numerical calculation results, it is important to minimize the impact of grid density on the computational results. Therefore, grid independence validation should be conducted prior to formal calculations.

Three grid quantities, namely 2.08 million, 3.23 million, and 4.11 million, were selected for calculation, and the grid details are shown in Figure 5. The pressure drop of the breather is shown in Figure 6.

The computational results indicate that the case with 2.08 million grids exhibits a slightly larger deviation, while the cases with 3.23 million and 4.11 million grids demonstrate virtually identical results. Consequently, the case with 3.23 million grids was selected for the next research.

3.4. Determination of Working Fluid for Calculations

The working fluid in the breather is a two-phase flow of oil and gas, and in order to simplify the calculations, this section constructs a model of the metal foam and compares the pressure drop of the two-phase and single-phase flow after passing through the metal foam.

Porosity and PPI are frequently utilized as fundamental structural parameters in the construction of metal foam models for numerical simulations [20,21,22,23].

PPI means pores per inch, and porosity $e$ is defined as follows:

$$e={\displaystyle \frac{V_e}{V_t}}$$

(1)

where e is the porosity, $V_e$ is the volume of the internal voids within the metal foam, and $V_t$ is the total volume of the metal foam.

In this paper, the Kelvin structure with a 30° cut angle is used as the metal foam structure model, with a porosity of 92% and a PPI of 25, as shown in Figure 7. The cut angle $\theta$ is the angle between the inlet surface of the metal foam model and the upper end surface of the cut model. The main view of the metal foam model at $\theta =30°$ is shown in Figure 8.

After the construction of the metal foam model, numerical experiments were conducted using a simplified model (the computational domain and grid are shown in Figure 9) to obtain the drag coefficient and inertial resistance coefficient of the metal foam. For specific methods, please refer to reference [24].

Single-phase flow and two-phase flow are used to calculate the model shown in Figure 10. The DPM model is employed for the calculation of liquid phase, with the oil droplet particle distribution following an R-R distribution. The average diameter of the oil droplets is 25 μm, with a maximum diameter of 70 μm and a minimum diameter of 3 μm. Prior to reaching the breather, the oil droplets and air undergo significant momentum exchange in the ventilation duct, resulting in negligible velocity differences between the oil droplets and air. Therefore, the inlet velocity of the particles is the same as that of the air entering the airflow field. The wall boundary is set as “reflect”, which allows discrete phase particles to fully exchange momentum with the continuous phase in the flow field, thus effectively reflecting the impact of the discrete phase on the air phase.

The pressure drop between two-phase flow calculation and single-phase flow calculation are compared, as shown in Figure 10. The pressure drop calculated using two-phase flow is approximately 0.8% higher than that calculated using single-phase flow, which is almost negligible. Therefore, it can be considered that the pressure drop of the metal foam inside the breather can be calculated using single-phase flow instead of two-phase flow.

4. Validation

4.1. Experimental Apparatus

In this paper, an experimental study is conducted on the pressure drop of a high-speed metal foam breather. The overall experimental setup is depicted in Figure 11.

The breather is driven by a high-speed motor, and the shafts are connected by a coupling. The exterior of the breather is equipped with a cubic chamber, with slotted holes on the upper and lower ends. The hole on the upper end serves as the air inlet, while the lower end serves as the oil outlet. Inside the chamber, a pressure sensor is installed at the top of the impeller, measuring the pressure at the inlet of the breather. Similarly, a pressure sensor is also installed at the exhaust port of the axial ventilation duct, measuring the pressure at the outlet. The difference in inlet and outlet pressures can effectively characterize the pressure drop of the breather.

During the experiment, the oil–gas mixture was supplied by the oil–gas generator, and the mass fraction of oil in the oil–gas mixture typically ranged from 6 to 9%.

4.2. Validation Case

A metal foam model with a porosity of 92% and a PPI of 25 using the Kelvin structure are constructed in this section. The viscous resistance coefficient and inertia resistance coefficient are calculated and incorporated into the porous media model to simulate the airflow field of the breather. The pressure drop is determined and compared with experimental data to validate the numerical calculation method for the breather.

Upon calculation, the viscous resistance coefficient of the Kelvin structure metal foam with a porosity of 92% and a PPI of 25 is $6.669\times {10}^7$, and the inertia resistance coefficient is 3147. Figure 12 shows the comparison between the calculated and experimental data of the resistance of a metal foam centrifugal breather with a porosity of 92% and a PPI of 25 at different rotational speeds with a flow rate of 20 g/s.

As shown in Figure 12, when the rotational speed is below 22,000 rpm, the calculated values are slightly lower than the experimental data, indicating that the computed resistance coefficient for the metal foam is somewhat underestimated at this range. Conversely, when the rotational speed exceeds 22,000 rpm, the calculated resistance coefficient is higher, resulting in a slightly increased pressure drop. Notably, at a rotational speed of 22,000 rpm, the calculated results align very well with the experimental data. Overall, the trend of the pressure drop calculated numerically is consistent with the experimental data as a function of the rotational speed. The average error of the pressure drop is 11.436%. Therefore, it can be considered that the metal foam construction method and the numerical calculation method of the breather adopted in this paper have a certain reliability and can meet the requirements for studying the pressure drop of the metal foam centrifugal breather.

5. Results Discussion

5.1. The Influence of Rotational Speed on Pressure Drop

This section will conduct a thorough examination of the flow field and resistance characteristics of the breather at different rotational speeds.

In order to investigate the flow field of the breather with the addition of metal foam at different rotational speeds, a comparative analysis will be conducted between the flow fields of the breather without the metal foam and the breather with the metal foam.

Taking the example of a metal foam centrifugal breather with a porosity of 92% and a PPI of 25 and a breather without metal foam installed, a qualitative analysis of the pressure field of the breather at 0 rpm and 16,000 rpm speed and a flow rate of 16 g/s is conducted.

Figure 13 and Figure 14 illustrate the pressure contour of the cross-section, with the cross-section location (purple plane) as depicted in Figure 15.

From Figure 14, it can be observed that for the breather without the metal foam, at 0 rpm, the area where the metal foam was originally installed exhibits a uniform pressure distribution. Pressure gradually decreases along the axial direction, which is caused by local losses resulting from changes in the flow path shape. At 16,000 rpm, the flow field experience radial pressure gradients due to centrifugal forces, resulting in higher pressure near the outer wall.

From Figure 15, it can be observed that for the breather with the metal foam, at 0 rpm, the area with the metal foam exhibits a significant pressure drop, which is the primary pressure drop compared to the losses caused by changes in the flow path shape. At 16,000 rpm, compared to the breather without the metal foam, both the axial and radial pressure drop increase.

To quantitatively analyze the pressure distribution at various key positions, key cross-sections were selected in the computational domain, as shown in Figure 16. Section 1 represents the inlet surface of the computational domain, Section 2 represents the inlet of the metal foam, Section 3 represents the outlet of the metal foam, Section 3.5 represents the center position of the pipe where the outlet of the metal foam is located, and Section 4 represents the outlet of the computational domain.

The centrifugal breather with a metal foam installed, featuring a porosity of 92% and a pore density (PPI) of 25, was compared with the centrifugal breather without metal foam under operating conditions of a flow rate of 20 g/s and speeds of 16,000 rpm, 18,000 rpm, 22,000 rpm, and 27,000 rpm. Pressure data at key locations were extracted, and the results are presented in Figure 17.

From Figure 17a, it can be seen that for the breather without the installation of metal foam, the pressure drop changes are smaller at 1–2 and 2–3, significant at 3–3.5, and slightly increased at 3.5–4. As the rotational speed increases, the overall resistance of the breather increases. Specifically, the pressure increases significantly at 1–2 and 2–3 as the rotational speed increases. As shown in Figure 17b, it can be observed that for the breather with metal foam, an increase in rotational speed results in a significant rise in pressure. The pressure drop at 1–2 remains relatively stable, while the pressure drop changes significantly at 2–3, and there is also a significant pressure drop change at 3–3.5. A slight pressure increase is observed at 3.5–4. The increase in pressure drop at 2–3 is attributed to the installation of the metal foam. It is noteworthy that whether the breather is equipped with or without a metal foam, the pressure drop at 3–3.5 under different rotational speeds accounts for over 50% of the total pressure drop, making it the primary pressure drop in the breather. Subsequently, the pressure drop generated by the metal foam accounts for approximately 44% to 46% of the total pressure drop at different rotational speeds.

The reason for the above phenomenon is that for the breather without a metal foam, the main sources of flow loss are the friction loss generated by high-speed rotating airflow and the wall surface, the loss generated by shear action between airflow, and the local loss generated by changes in the airflow channel.

The greater the flow loss, the greater the energy dissipation, resulting in the need for the gas to have more momentum to reach the next location. Therefore, the incoming air needs to have a higher total pressure (with a lower inlet velocity, the total pressure is close to the static pressure). With the outlet pressure remaining constant, this results in an overall increase in pressure drop for the breather.

Figure 18 shows three-dimensional flow line of the breather without metal foam installed at different speeds. It can be observed that an increase in the rotational speed of the breather results in an increase in the circumferential velocity of the airflow, as well as an increase in the radial velocity gradient of the airflow. This leads to an increase in frictional and shear losses. However, due to the work done by the impeller on the airflow at positions 1–2, the total pressure of the gas inside the breather increases, resulting in a small pressure difference at this location. The channel from position 2 to position 3 is short and has a large flow area, resulting in a relatively small pressure change. However, at high speeds, the pressure drop is also large at this location. This is because local losses increase with an increase in velocity. The passage from position 3 to position 3.5 requires passing through a slot-shaped outlet, resulting in significant local losses and therefore a large pressure drop. From position 3.5 to position 4, there is a slight increase in pressure as the flow stabilizes.

After the addition of the metal foam, there is a significant increase in the overall pressure drop of the breather. From the streamline in Figure 19, it can be observed that the distribution of streamlines at the metal foam (position 2–3) is significantly different from that in Figure 18. When airflow enters the metal foam, it inevitably encounters collisions and friction with the skeletal structure of the numerous small cells that comprise the metal foam. As the airflow passes through these cells, localized losses occur due to the interactions with the skeletal framework, resulting in a significant increase in pressure drop at position 2–3 within the medium.

5.2. Influence of Ventilation Flow Rate on the Pressure Drop of the Breather

A detailed study will be conducted in this section to analyze the variations in airflow and pressure drop characteristics of the breather when using different ventilation flow rates.

Figure 20 shows the pressure of the breather at different positions under different flow rates with a speed of 27,000 rpm, with and without the installation of metal foam. It can be seen that the impact of flow rate of the pressure drop of the breather is significant, regardless of whether the metal foam is installed or not.

As the flow rate increases, the proportion of pressure drop caused by the metal foam within the breather increases. At a flow rate of 20 g/s, the pressure drop caused by the metal foam accounts for approximately 46% of the total pressure drop, while at 50 g/s, it accounts for approximately 52%.

From the streamline in Figure 21 and Figure 22, it can be observed that, at the same rotational speed, the axial flow velocity of the breather airflow significantly increases at high flow rates, while the circumferential velocity changes relatively little. This is because as the ventilation flow rate increases, and the flow area remains constant, the axial flow velocity of the breather must necessarily increase. Meanwhile, the tangential flow velocity is primarily determined by the rotational speed of the impeller and other rotating components. Therefore, with the increase in flow rate, the axial velocity of the airflow significantly increases. The increase in axial velocity will result in an increase in frictional losses and local losses, leading to an increase in the resistance of the flow passage.

Based on the above analysis, it can be concluded that the fundamental factors affecting the pressure drop of the metal foam centrifugal breather by speed and flow rate are the changes in the circumferential velocity and axial velocity of the fluid, which are caused by their combined effects. The circumferential velocity is related to airflow shear loss and wall friction loss, with higher circumferential velocity resulting in greater friction loss and larger velocity gradients along the radial direction inside the breather, leading to greater shear loss between airflow. The axial velocity is related to friction loss and pressure drop caused by the metal foam and is also proportional to the aforementioned losses. This is similar to the research results of Laura Cordes [16] and others on the resistance of similar structured metal foam breathers, indicating that the circumferential velocity of the fluid and the axial velocity at the inlet of the metal foam are the main influencing factors affecting the pressure drop of the metal foam centrifugal breather.

5.3. Influence of Structural Parameters on the Pressure Drop Characteristics of the Breather

This section explores the influence of different porosities and PPIs on the pressure drop characteristics of metal foam centrifugal breathers.

(1)

The effect of porosity on the pressure drop of the metal foam centrifugal breather.

Figure 23 and Figure 24 display the calculations for metal foam breathers with a PPI of 25 and different porosities.

As can be seen from Figure 23, after adding the metal foam, the overall resistance of the breather is increased. When the porosity of the metal foam in the breather changes, the pressure difference in the rest of the parts changes very little, and only the pressure difference at the import and export of the metal foam has a large change, which is the main part of the resistance change.

From Figure 24a, it can be observed that at different rotational speeds, with the increase in porosity, the overall pressure drop of the breather decreases. This is because the larger the porosity, the less space occupied by the skeletal structure, and the lower the flow resistance of the airflow. Therefore, the corresponding pressure drop also decreases.

The overall pressure drop of the breather decreases with the increase in porosity at different flow rates, as shown in Figure 24b. Moreover, with the increase in flow rate, the change in pressure drop becomes larger. This is because the increase in flow rate significantly increases the axial flow velocity at the entrance of the metal foam. The greater the change in the entrance axial velocity, the greater the change in pressure drop.

(2)

The influence of PPI on the pressure drop of the metal foam centrifugal breather.

For a metal foam centrifugal breather with a porosity of 0.92, calculations were conducted for different PPI values, and the results are shown in Figure 25 and Figure 26.

Figure 25 shows the pressure at different positions of metal foam centrifugal breathers with different PPI values at a rotational speed of 27,000 rpm and a flow rate of 20 g/s. It can be observed that the variation in PPI of the metal foam only affects the pressure at the location of the metal foam, with minimal impact on the pressure at other positions.

From Figure 26, it can be observed that as the PPI of the metal foam increases, the pressure drop of the metal foam centrifugal breather at different rotational speeds and flow rates also increases. This is because an increase in the PPI leads to an increase in the number of cells per unit length of the metal foam, resulting in an increase in flow resistance. When the flow rate increases, the axial velocity also increases, leading to a rapid increase in pressure drop.

In conclusion, it can be seen that the addition of metal foam significantly increases the pressure drop of the breather. The pressure drop of the breather is greater with higher PPI, lower porosity, higher speed, and larger flow rate.

5.4. Influence of Temperature on the Pressure Drop of the Breather

This section investigates the pressure drop of a metal foam centrifugal breather with a porosity of 92% and a PPI of 25, operating at flow rates of 18 g/s and rotational speeds of 16,000 rpm, 18,000 rpm, and 22,000 rpm, as well as temperatures of 300 K, 320 K, 340 K, and 360 K.

From Figure 27, it can be observed that with the increase in temperature, the pressure drop across the breather gradually increases. At a rotational speed of 16,000 rpm, a temperature increase of 60 °C results in an increase of approximately 0.4 kPa in breather pressure drop, representing a relative increase of about 6%. At 18,000 rpm, a temperature increase of 60 °C leads to an increase of approximately 0.5 kPa in breather resistance, representing a relative increase of around 5%. At 22,000 rpm, a temperature increase of 60 °C results in an increase of approximately 0.55 kPa in breather resistance, representing a relative increase of about 5%.

The main reason for the above results is that, at the same mass flow rate, an increase in temperature leads to a decrease in air density and an increase in air flow velocity. This causes an increase in fluid losses within the breather, resulting in an overall increase in pressure drop. Although the temperature variation within the breather is relatively small, the impact of temperature changes on the pressure drop of the breather can still reach 5% or more. Therefore, the influence of temperature on the pressure drop of the breather cannot be ignored.

6. Conclusions

In this paper, a numerical study on the pressure drop of metal foam centrifugal breathers has been carried out, and the main conclusions obtained are as follows:

(1)

In the breather calculation, the single-phase flow can be used to calculate the pressure drop to improve the efficiency of the calculation.

(2)

More than 95% of the pressure drop in a metal foam centrifugal breather is caused by the metal foam and the breather shaft exhaust pipe from the metal foam outlet to the breather outlet.

(3)

Higher rotational speeds result in greater fluid circumferential velocities with relatively small changes in axial velocity. Higher flow rates lead to greater fluid axial velocities with relatively small changes in circumferential velocity. The circumferential velocity has a greater effect on the pressure drop at the breather shaft pipe and a smaller effect on the pressure drop at the metal foam; the axial velocity not only affects the pressure drop at the metal foam but also has some effect on the pressure drop at the breather shaft pipe.

(4)

An increase in porosity leads to a decrease in the overall pressure drop across the breather, whereas an increase in the PPI results in an increase in the overall pressure drop across the breather.

(5)

As the temperature of the breather increases, its pressure drop also increases. In some operating conditions, the impact of pressure drop exceeds 5%.