Home

Library

Media Documents

Hydrogen Ejector Design

Hydrogen Ejector Design: Determining the Adiabatic Index

Fan Weijun

In a hydrogen fuel cell, the hydrogen ejector is responsible for supplying hydrogen and recovering hydrogen from the tail gas. With advantages such as no electrical energy consumption, hydrogen recovery and no moving-fault components, the hydrogen ejector has established its own position.

The design of a hydrogen ejector involves many physical parameters. The adiabatic index is one of them.

The process of high-pressure hydrogen jetting can be regarded as an adiabatic process, and calculation of many state parameters must rely on determining the adiabatic index. For mixtures of multiple gases, such as recirculated tail gas, the adiabatic index also needs to be calculated according to the actual composition.

According to the definition of the adiabatic index, the ratio of the constant-pressure heat capacity to the constant-volume heat capacity of an ideal gas is its adiabatic index, also called the heat-capacity ratio. That is:

k = Cp / Cv

The adiabatic equation of state of an ideal gas is:

P / ρk = Constant

Combined with the general equation of state of an ideal gas, the density, specific volume, temperature, pressure and other parameters under subcritical flow rate, critical flow rate and supercritical flow rate can be determined.

To determine the adiabatic index, we also need to know an important formula: the Mayer equation.

The Mayer equation states that under the same temperature conditions, the constant-pressure heat capacity of any ideal gas must be greater than its constant-volume heat capacity, and the difference between the two is always equal to a constant. The Mayer equation is one of the important formulas for studying the thermophysical properties of ideal gases. Its expression is as follows:

Cp − Cv = R

That is, at a given temperature, the difference between the constant-pressure heat capacity and constant-volume heat capacity of an ideal gas is the gas constant.

In this way, once the constant-pressure heat capacity of a gas at a certain temperature is known, the adiabatic index at the corresponding temperature can be calculated.

For a mixed gas, the molar constant-pressure heat capacity of the mixture can be calculated from the mole fraction of each component, and then its adiabatic index can be obtained.

The recirculated gas in a hydrogen fuel cell is a mixed gas of hydrogen, nitrogen, water vapor and other components, so its adiabatic index can be calculated by the method above.

For the adiabatic index that does not change much in the common temperature range, it can also be used according to the lookup table value. The following table shows the adiabatic indices of common gases.

Table 2-86 Mass heat capacity ratio Cp/Cv of some organic and inorganic gases at 1.01325×10⁵ Pa (1atm)
chemical formula Chinese name English name t/℃ Heat capacity ratio k=Cp/Cv chemical formula Chinese name English name t/℃ Heat capacity ratio k=Cp/Cv
C2H4O Acetaldehyde acetaldehyde 30 1.14 HCN hydrogen cyanide hydrogen cyanide 65 1.31
C2H4O2 Acetic acid acetic acid 136 1.15 HCN hydrogen cyanide hydrogen cyanide 140 1.28
C2H2 Acetylene acetylene 15 1.26 HCN hydrogen cyanide hydrogen cyanide 210 1.24
C2H2 Acetylene acetylene −71 1.31 HI hydrogen iodide hydrogen iodide 20～100 1.40
Air air 925 1.36 H2S hydrogen sulfide hydrogen sulfide 15 1.32
Air air 17 1.403 H2S hydrogen sulfide hydrogen sulfide −45 1.30
Air air −78 1.408 H2S hydrogen sulfide hydrogen sulfide −57 1.29
Air air −118 1.415 I2 iodine iodine 185 1.30
NH3 ammonia ammonia 15 1.310 C4H10 Isobutane Isobutane 15 1.11
Ar Argon argon 15 1.668 Kr krypton krypton 19 1.68
Ar Argon argon −180 1.76 Hg mercury mercury 360 1.67
Ar Argon argon 0～100 1.67 CH4 Methane methane 600 1.113
C6H6 benzene benzene 90 1.10 CH4 Methane methane 300 1.16
Br2 bromine bromine 20～350 1.32 CH4 Methane methane 15 1.31
CO2 carbon dioxide carbon dioxide 15 1.304 CH4 Methane methane −80 1.34
CO2 carbon dioxide carbon dioxide −75 1.37 CH4 Methane methane −115 1.41
CS2 carbon disulfide disulfide 100 1.21 C3H6O2 Methyl acetate methyl acetate 15 1.14
CO carbon monoxide monoxide 15 1.404 CH4O Methanol alcohol 77 1.203
CO carbon monoxide monoxide −180 1.41 C2H6O Methyl ether ether 6～30 1.11
Cl2 chlorine chlorine 15 1.355 C3H8O2 Dimethoxymethane (commonly known as methylal) methylal 13 1.06
CHCl3 Chloroform chloroform 100 1.15 C3H8O2 Dimethoxymethane (commonly known as methylal) methylal 40 1.09
(CN)2 cyanide cyanogen 15 1.256 Ne neon neon 19 1.64
C6H12 cyclohexane cyclohexane 80 1.08 NO Nitrogen oxide nitric oxide 15 1.400
CCl2F2 Dichlorodifluoromethane dichlorodifluoromethane 25 1.139 NO Nitrogen oxide nitric oxide −45 1.39
C2H6 Ethane Ethane 100 1.19 NO Nitrogen oxide nitric oxide −80 1.35
C2H6 Ethane Ethane 15 1.22 N2 nitrogen nitrogen 15 1.404
C2H6 Ethane Ethane −82 1.28 N2 nitrogen nitrogen −181 1.47
C2H6O ethanol ethyl alcohol 90 1.13 N2O nitrous oxide nitrous oxide 100 1.28
C4H10O Ether ether 35 1.08 N2O nitrous oxide nitrous oxide 15 1.303
C4H10O Ether ether 80 1.086 N2O nitrous oxide nitrous oxide −30 1.31
C2H4 Ethylene ethylene 100 1.18 N2O nitrous oxide nitrous oxide −70 1.34
C2H4 Ethylene ethylene 15 1.255 O2 oxygen oxygen 15 1.401
C2H4 Ethylene ethylene −91 1.35 O2 oxygen oxygen −76 1.415
He helium helium −180 1.660 O2 oxygen oxygen −181 1.45
C6H14 n-Hexane hexane (n-) 80 1.08 C5H12 Pentane pentane (n-) 86 1.086
H2 hydrogen hydrogen 15 1.410 P phosphorus phosphorus 300 1.17
H2 hydrogen hydrogen −76 1.453 K Potassium potassium 850 1.77
H2 hydrogen hydrogen −181 1.597 Na sodium sodium 750～920 1.68
HBr hydrogen bromide hydrogen bromide 20 1.42 SO2 sulfur dioxide sulfur dioxide 15 1.29
HCl hydrogen chloride hydrogen chloride 15 1.41 Xe xenon xenon 19 1.66
HCl hydrogen chloride hydrogen chloride 100 1.40

For the adiabatic index of actual gases, different equations need to be followed, which will be introduced in another article.

Home