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In order to find the total energy needed for the voyage, the time and average shaft power are multiplied. πΈπΈππππππππππ ππππππππππππ ππππππ ππππππππππππ [ππππh] = π΄π΄π΄π΄ππππππππππ ππhππππππ ππππππππππ [ππππ] Γ ππππππππ [hππ] At this point, the steps are different for batteries and fuel cells and the calculations continue from Equation 3.3 in the next two sections. 3.1.1. Fuel Cell and Hydrogen System Mass and Volume Equation 3.3: Step 3 For hydrogen fuel cell systems the calculation picks up from Equation 3.3 to calculate the amount of hydrogen to be stored in the containers of LH2 or 5000 psi hydrogen. Since the FC is not 100% efficient, the loss of energy due to thermal inefficiency needs to be accounted for. Assuming the efficiency of FCs is 45%, the required energy of hydrogen can be calculated by dividing the energy needed for voyage by the efficiency (0.45).23 Equation 3.4: Step 4A πΈπΈππππππππππ π»π» [kWh] = πΈπΈππππππππππ ππππππππππππ ππππππ ππππππππππππ [ππππh] 2 0.45 Next, convert from kWh to kg by using the conversion of kWh to MJ and lower heating value of hydrogen (LHV) to find the mass of the required hydrogen. ππππ Equation 3.5: Step 5 ππππππππ ππππ π»π» [kg] = πΈπΈππππππππππ π»π» [kWh] Γ 3.6 οΏ½ππππh 2 2 119.96 πππποΏ½ππππ Now that the mass of H2 is calculated, the mass and volume of the tanks of LH2 and 5000 psi hydrogen can be easily calculated using the values in Table 2.3 and the formulas below: Equation 3.6ππππππππ ππππ ππππππππ [ππππ] = ππππππππ ππππ π»π»2 [ππππ] Γ πΊπΊπππππ΄π΄ππππππππππππππ ππππππππ [ππππ ππππππππ] ππππ π»π»2 (The total mass of the fuel and tank is then found by summing the tank mass and the fuel mass.) Equation 3.7 ππππππππππππ ππππ ππππππππ [πΏπΏ] = ππππππππ ππππ π»π»2 [ππππ] Γ ππππππππππππππππππππ ππππππππ [πΏπΏ ππππππππ] ππππ π»π»2 23 The assumed efficiency of the hydrogen fuel cell is 45%. Even though the max efficiency is about 53%, the fuel cell will not always operate at its highest efficiency point. This may be somewhat conservative and overpredict the amount of hydrogen needed. 32PDF Image | Regenerative Fuel Cell
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