Pressurization process and performance analysis of gear-claw hydrogen circulating pump used in PEMFC system

Owing to the structure of the gear-claw rotor, working chambers of claw pumps are divided into small multi-chambers by a pair of intermeshing claw rotors in the mixing process, and the transient flow in multi-chambers is complicated, which results in the increase of the pump consumption. Hence, it is necessary to study the transient flow and working process of gear-claw hydrogen circulating pumps to optimize the pump performance. In this study, the meshing model of a high-order curve and its conjugate curve was proposed, and the profile composition of the gear-claw rotor was introduced. The influence of the radius ratio of claw addendum arc on the performance including relative carryover, built-in volume ratio and volume utilization was analyzed. The flow field of gear-claw hydrogen circulating pump including pressure and velocity field was analyzed by using numerical simulations. Furthermore, the p-V diagram of pumps was obtained. It is found that the gas in the compression chamber is mixed with the gas in the carryover, and the initial pressure in the compression chamber is 130.78kPa, which increases by 29.07% compared to the original initial pressure in the compression chamber. Therefore, an overcompression phenomenon at the end of the compression process (at the beginning of the discharge process) occurs.


Introduction
Proton exchange membrane fuel cell (PEMFC), an efficient and clean power generation device, is an effective way to solve the shortage of fossil fuels and the environmental pollution [1][2][3].In this system, in order to improve hydrogen utilization, unreacted hydrogen is transported from the anodic discharge port to the inlet of fuel cell stacks by means of a hydrogen circulating pump.Therefore, the oil-free hydrogen circulating pump is the key equipment in the PEMFC.The claw pump [4], which is a new type of hydrogen circulating pump, shows significant advantages in terms of simple manufacturing, oilfree and high reliability over other hydrogen circulating pumps.Therefore, the claw pump is well-suited for the PEMFC system.
With regard to the claw rotor profile research, Hsieh [5] established an analytical model of a claw rotor, and discussed the performance including volume utilization and the volume of carryover.Giuffrida [6] proposed a geometric model of a claw rotor, in which the straight line, circular arc were adopted to modify unsmooth points at addendum and dedendum arcs of rotor profiles in claw rotors.Wang [7] adopted a circular arc and an equidistant curve of a cycloid to modify non-smooth connection points of claw rotor.With regard to numerical simulations of claw pumps.Voorde [8] discussed the transient flow at gaps including the pressure field and flow field in the vacuum pump by using numerical simulations.Gu [9] analyzed the transient flow at the axial clearance and the radial clearance of a doubleclaw pump in the hydrogen circulating system, and obtained the pressure variation varying with the volume of the working chamber of hydrogen circulating pumps.Dong [10] established a mathematical model of a double-claw hydrogen circulating pump, and discussed the influence of suction pressure, rotational speed and radial clearance on the volumetric efficiency and pump efficiency of the claw pump by using numerical simulations.Zhao [11] discussed the effects of axial clearance and contents of water vapor and nitrogen on the performance of the claw hydrogen circulating pump.Concerning the aforementioned research, it is found that the claw hydrogen circulating pump has received more and more interest.However, due to the structure of gear-claw rotors, a carryover is formed by two intermeshing gear-claw rotors at the end of the discharge process, and therefore a special mixing process in the gear-claw hydrogen circulating pump is generated, which results in the increase of the pump consumption.Hence, it is necessary to study the transient flow and working process of gear-claw hydrogen circulating pumps to optimize the pump performance.In this study, the meshing model of a high-order curve and its conjugate curve was proposed, and rotor profiles of gear-claw rotors were introduced.The influence of the radius ratio of claw addendum arc on the pump performance was analyzed.The transient flow of gear-claw hydrogen circulating pump was analyzed by using numerical simulations.Furthermore, the p-V diagram of pumps was obtained.The results of this study are important to improve the performance of the claw hydrogen circulating pump and the PEMFC system.

The structure of the gear-claw hydrogen circulating pump
The hydrogen circulating pump consists of gear-claw rotors, shafts, gears, motors and bearings, etc.A pair of intermeshing gear-claw rotors are installed on parallel shafts, and clearances between the rotor and the cylinder, or between two gear-claw rotors exist to meet the dry oil-free requirement of the hydrogen circulating pump.A special twisting clearance between two gear-claw rotors was constructed [12], as shown in Figure 1.The working medium flows through this twisting clearance under pressure difference, and the working medium stream pinches, which significantly reduces the gas leakage between two gear-claw rotors.Gears with a transmission ratio of 1:1 in the gearbox are mounted on parallel shafts.The gear-claw rotors are driven by gears to complete the hydrogen delivery in the working process.

An analytical model of gear-claw rotors
Rotor profiles of gear-claw rotors are shown in Figure 2. The composition and parameter equation of rotor profiles of two gear-claw rotors are displayed in reference [12].The design procedure of the highorder curve and its conjugate curve is as follows.

Construction of a high-order curve.
The generation process of the high-order curve is illustrated in Figure 3.The radii of circles I, II and III are R1, R2 and R3, respectively.A high-order curve B1C1 is used to smoothly connect to the circular arcs A1B1 and C1D1.In order to ensure the curve continuity and smoothness at each intersection, it is necessary for both function values and first derivatives of the highorder curve B1C1, circular arc A1B1 and C1D1 to be equal at intersections B1 and C1.
where R4 is the radius of the circular arc A1B1; R2 is the radius of pitch circle II; t is angular parameter; θ is the central angle.
Circular arc C1D1 can be represented as where β is rotational angle.High-order curve B1C1 can be represented as where b0, b1, b2, b3 are coefficients of the high-order curve.
The continuity and smoothness conditions of the circular arc A1B1 and high-order curve B1C1 at point B1 are derived by where the coordinate of The continuity and smoothness conditions of the circular arc C1D1 and high-order curve B1C1 at point C1 can be derived by Coordinates of B1C1 at point C1 can be obtained as The first derivative of high-order curve B1C1 at point C1 can be expressed as Coefficients are obtained by combining equation (4) and equation ( 5), and then the equation of the high-order curve is obtained.

Conjugate curve of the high-order curve.
The static coordinate systems X1O1Y1, X2O2Y2 and the rotational coordinate systems x1O1y1, x2O2y2 are demonstrated in Figure 4.The high-order curve B1C1 is fixedly located in x1O1y1, and the conjugate curve b1c1 of the high-order curve B1C1 is fixedly located in x2O2y2.x1O1y1 is rotated with an angle φ relative to X1O1Y1, and x2O2y2 is also rotated with an angle φ relative to X2O2Y2.The conjugate cluster rb1c1 of B1C1 can be represented as where M21 is the transformation matrix, and it can be represented as The curve b1c1 of B1C1 can be obtained by combining equation ( 8) and equation (10).

The mixing process
Owing to the specific structure of gear-claw rotors, a carryover V1 is formed by two intermeshing gearclaw rotors at the end of the discharge process, and therefore a special mixing process in the gear-claw hydrogen circulating pump is generated, as shown in Figure 5.
Figure 5.The mixing process.In this mixing process, working chambers are divided into small multi-chambers by a pair of intermeshing claw rotors, and the working medium in the carryover is mixed with the working medium in suction chamber in the previous working cycle, which increases irreversible energy loss and power consumption of the claw hydrogen circulating pump.Hence, the carryover should be reduced as much as possible without reducing the performance including volume utilization and built-in volume of the hydrogen circulating pump.

Effects of radius ratio of claw addendum arc.
The radius ratio of claw addendum arc μ is an important geometric parameter of the claw compressor, which determines the volume of the carryover.The radius ratio of claw addendum arc μ can be defined as where R5 is radius of claw addendum circular arc; R6 is pitch circle radius.
The variation of the claw arm length and the occupied area of the gear-claw rotor II is same as that of the gear-claw rotor I. Hence, the gear-claw rotor I is selected as the research object.The gear-claw rotor I is generated varying with different μ, as shown in Figure 6.As can be seen, the arm length of the gear-claw rotor L linearly increased with the increase of μ.When μ increases from 1.29 to 1.96, L exhibits a growth of 498.90 mm.The occupied area of the gear-claw rotor is reduced by 13.08% with the increase of μ.As μ increases, the mechanical property of the gear-claw rotor I reduces; while the volume of the carryover increases.

Analysis of relative carryover.
The relative carryover η is an indicator for evaluating the magnitude of the carryover, and it can be expressed as Cmax S 100% V V   (12) where VCmax is the maximum carryover volume; VS is the suction chamber volume.
The η varying with μ is shown in Figure 7.The relative carryover volume η and suction volume Vs increase with the increase of μ.As μ increases from 1.29 to 1.96, η and Vs increase by 77.84% and 73.67%, respectively.The length of the epicycloid curve is the key factor to determine the carryover volume.The longer the epicycloid, the larger the carryover volume.Therefore, the length of the epicycloid and the value of η should be reduced as much as possible.

Analysis of built-in volume ratio. The built-in volume ratio  can be presented as
where VA is the available volume; VR is the rotor volume; Vd is the maximum discharge volume.
The built-in volume ratio  varying with  is shown in Figure 8.When  increases from 1.29 to 1.96,  decreases by 21.94%.The thickness of the claw rotor arm decreases with the increase of , and therefore the mechanical property of rotors decreases.The distance between the pitch circle and the dedendum arc increases, as  increases, which is conducive to opening a larger suction and discharge port.

Analysis of volume utilization. The volume utilization λ can be expressed as
The λ varying with  is shown in Figure 9.As  increases from 1.29 to 1.96, λ increases from 34.95% to 66.65%.The significant increase of λ indicates that λ is very sensitive to .The increase of volume utilization effectively enhances the suction volume.

Fluid domains of gear-claw hydrogen circulating pumps
The entire fluid domains of gear-claw hydrogen circulating pump are composed of five domains including the suction port, working chamber, end face I and II, discharge port.Main design parameters of gear-claw hydrogen circulating pump are displayed in Table 1 [12].

Grid generation
The grid of gear-claw hydrogen circulating pumps is shown in Figure 10.The grid of fluid domains is generated by using software Mesh.With the aim to reduce the calculation time and improve computational efficiency, the chamber fluid domain is remeshing subdomain, and other domains are non-remeshing subdomains.For ensuring the accuracy of calculation, the tetrahedral grids are used to the remeshing subdomain, and hexahedral grids are used to non-remeshing subdomains.The maximum grid of entire fluid domains is 0.6mm.Grid dynamic elements of the gear-claw hydrogen circulating pump are set as 1353298.

Boundary conditions
The pressure distribution and transient flow of the gear-claw hydrogen circulating pump were analyzed by using software Fluent.The RNG k-ε turbulence model, which considers the vortex and flow curvature, is set as the turbulence model in the simulation.The working medium is the hydrogen with the density of 0.0899 kg/m 3 .The inlet pressure and inlet temperature is 0.101MPa and 293.15 K, respectively.The outlet pressure and outlet temperature is 0.21 MPa and 362.18K, respectively.The rotational speeds of two claw rotors are both 3000 r/min.

Analyses of pressure distributions
Pressure distributions of gear-claw hydrogen circulating pumps are shown in Figure 11.In the mixing process, working chambers are divided into small multi-chambers by two gear-claw rotors, and the pressure variation in multi-chambers is complicated.Due to the decrease of the volume of the carryover, the pressure in the carryover firstly increases.Then the pressure in the carryover decreases, due to the gas leakage from the carryover to the suction chamber.Furthermore, the gas leakage in the mixing process also enhances the pressure in the suction chamber, and therefore the initial pressure in the compression chamber is 130.78kPa, which increases by 29.07%compared to the original initial pressure in the compression chamber.Due to the increase of the initial pressure in the compression chamber, an overcompression phenomenon at the end of the compression process (at the beginning of the discharge process) occurs, which increases the power consumption.Figure 13.The volume variation of the gear-claw hydrogen circulating pump.In the mixing process I, the volume variation of the carryover is complicated.The carryover V1 with the value of 3609.39 mm 3 is formed, when the discharge process ends.Subsequently, V1 is divided into V2 and V3 at the rotational angle of 14°, and the volume of V2 and V3 decreases from 961.35 mm 3 and 268.14 mm 3 to 0. In the process of the information of a new working chamber, a new working chamber V4 is instantaneously formed with the volume of 3759.48 mm 3 .At the next moment, V4 is connected with the suction chamber of the previous cycle.Then, V5, V6 and V7 are formed.V5, V6 and V7 are combine, and a new working chamber V8 with the volume of 1535.18 mm 3 is formed.
In the suction process, V8 significantly increases from 3609.39 mm 3 to 61255.98 mm 3 varying with the rotational angle.In the mixing process II, the volume of V8 increases from 63186.29 mm 3 to 66544.31mm 3 and then suddenly decreases to 66405.88 mm 3 , which is caused by the increase of the carryover of the previous cycle.Subsequently, the carryover of the previous working cycle is assimilated by V8, and the volume of V8 reaches the maximum value of 66831.63 mm 3 .A new instantaneous working chamber V9 is formed at the rotational angle of 371°, which reduces the volume of V8.At the next moment, V8 and V9 are combined, and a novel working chamber V10 is formed.The volume of V10 slowly increases and then rapidly decreases.In the compression process, V10 is significantly reduced from 63222.27 mm 3 to 49823.31mm 3 .In the discharge process, V10 gradually decreases from 49823.31 mm 3 to 3609.39 mm 3 .

p-V diagram.
The pressure varying with the volume of the working chamber is shown in Figure 14.The suction process is shown in curve AB.In the suction process, the gas rapidly flows into the suction chamber, and the pressure stabilizes at 101.33 kPa.The mixing process II is shown in curve BC.Due to the gas leakage from the carryover in the previous working cycle to the suction chamber by clearances, the pressure in the suction chamber increases from 101.325 kPa to 130.78 kPa.Therefore, the initial pressure in the compression process(as shown in curve CD) is higher than 101.33 kPa, and overcompression occurs at the end of the compression process, which increases the power consumption.The discharge process is shown in curve DE.As the discharge process begins and the discharge port area remains small, the volume of the discharge chamber still decreases, and therefore the pressure in the discharge chamber increases.As the area of the discharge port increases, the pressure in the discharge chamber gradually stabilizes at the discharge pressure with the value of 210.00 kPa.As the discharge port closes, the pressure in the discharge chamber increases to 252.86 kPa.The mixing process I is shown in curve EFA.In the mixing process, the pressure in the carryover is firstly increased and then decreased.A new working chamber is formed at point F, as the volume of the new working chamber decreases, the pressure in this chamber increases, and then the pressure decreases due to the gas leakage.

Conclusion
With the aim of studying the transient flow and working process of gear-claw hydrogen circulating pumps, the meshing model of a high-order curve and its conjugate curve was proposed, and rotor profiles of gear-claw rotors were introduced.The influence of the radius ratio of the claw addendum arc on the performance was analyzed.As radius ratio of claw addendum arc μ increases from 1.29 to 1.96, the relative carryover, suction volume and volume utilization increases by 77.84%, 73.67% and 47.56%, respectively.As μ increases from 1.29 to 1.96, the built-in volume ratio decreases by 21.94%.With the increase of μ, power consumption increases, and the mechanical property of rotors decreases; while the area of the suction and discharge port is large, and the volume utilization improves.
The streamline and leakage flow of the gear-claw hydrogen circulating pump are analyzed.The gas in the carryover rushes into the suction chamber by gas leakage clearance, and breaks the gas balance in the suction chamber.Therefore, vortices are formed, and the flow separation occurred near the wall of the working chamber.The gas flow in the working chamber of the claw pump is changed by vortex, which leads to the occurrence of flow loss and increases energy loss of the claw pump.
The pressure distribution and p-V diagram of the gear-claw hydrogen circulating pump are obtained.In the special mixing process, due to the gas leakage from the carryover to the suction chamber, the gas leakage in the mixing process also enhances the pressure in the suction chamber, and therefore the initial pressure in the compression chamber is 130.78kPa.The increase of the initial pressure in the compression chamber, an overcompression phenomenon at the end of the compression process (at the beginning of the discharge process) occurs, which increases the power consumption.

Figure 1 .
Figure 1.The structure of the hydrogen circulating gear-claw pump.

Figure 3 .
Figure 3. Generation of the high-order curve.Circular arc A1B1 can be represented as

Figure 4 .
Figure 4. Conjugate curve of a high-order curve.The conjugate cluster rb1c1 of B1C1 can be represented as

Figure 7 .
Figure 7.The relationship of the  and η.

Figure 8 .
Figure 8.The relationship of the  and η.

Figure 9 .
Figure 9.The variation of λ with .

Figure 10 .
Figure 10.The grid of fluid domains of the gear-claw hydrogen circulating pump.

Figure 11 .Figure 12 .
Figure 11.Pressure distributions of the gear-claw hydrogen circulating pump.5.2 Analyses of streamline and leakage flowStreamline distributions of the gear-claw hydrogen circulating pump in the mixing process are shown in Figure12.The gas in the carryover rushes into the suction chamber by gas leakage clearance, and breaks the gas balance in the suction chamber.Therefore, multiple vortices are formed at positions I, II, III and IV, and the flow separation occurred near the wall of the working chamber.The two circular vortices formed at position I have a significant impact on the surrounding flow.The vortex generates the entrainment effect, which sucks the surrounding gas.The gas flow in the working chamber of the