Mississippi State University
CACHE Modules on Energy in the Curriculum
Hydrogen as a Fuel
Module Title: Theoretical Fuel Consumption and Power
Module Author: Dr. Daniel A. Crowl
Author Affiliation: Michigan Technological University
Course: Stoichiometry, process design
Text Reference: Felder and Rousseau, Elementary Principles of Chemical Processes, 3rd ed., New York: John Wiley and Sons, 2005.
Concepts: Fuel consumption
Problem Motivation:
The cylinders in an internal combustion engine have a displacement that is the total volume of all cylinders when they are at maximum volume. The displacement is measured in liters, with typical values from 4 to 12 L.
During the operation of the combustion engine, air and fuel are either drawn into the engine through a carburetor or mixed in the cylinder by fuel injection. If we know the total volumetric flow rate of air and the concentration of the fuel, we can calculate the fuel consumption. The volumetric flow rate can be calculated from the RPM of the engine and the engine displacement. Finally, knowing the enthalpy of combustion of the fuel, and the fuel flow rate, we can calculate the theoretical power.
These numbers provide a quick screening method to look at different fuels and their performance. This evaluation does not consider the burning rate of the fuel nor the maximum pressure generated by the combustion. This varies from fuel to fuel and would have an effect on the engine performance.
This calculation also assumes that all the thermal energy generated by the combustion is available to do mechanical work. In reality, the 2nd Law of Thermodynamics applies and reduces the efficiency of conversion of the thermal energy to mechanical energy. There are also losses due to friction in the mechanical parts.
Basic Definitions:
▪ Theoretical Fuel Consumption
Fuel consumption based entirely on volumetric air flow through the combustion engine and stoichiometric combustion.
▪ Theoretical Power
The power delivered based entirely on the theoretical fuel consumption.
Problem Information
Example Problem Statement:
An internal combustion engine with a displacement volume of 4 L has a rotational speed of 1500 rpm.
a. If hydrogen is used as a fuel, calculate the theoretical hydrogen consumption rate at this rpm. Remember that each cylinder fires once every two revolutions. Assume that the combustion occurs stoichiometrically. Assume that the air – fuel mixture enters the engine at 300 K and 1 atm.
b. If the heat of combustion for the hydrogen is 241 kJ/mole, what is the theoretical power delivered by this engine, in HP?
Example Problem Solution:
a. First, let’s calculate the volumetric flow of the air – fuel mixture. The engine operates at 1,500 rpm, but the cylinders only fire every other rotation. Thus, the volumetric flow is:
[pic]
The stoichiometry of the combustion is as follows:
BASIS: 1 mole of hydrogen combusting
The hydrogen in pure oxygen combusts according to the following reaction:
H2 + ½ O2( H2O
With air the following can be written”
H2 + ½ O2+(1/2) [pic]N2 ( H2O + 1.88 N2
We then have the following mixture, from which we can calculate the mole fractions and the volumetric consumption of each species.
Volumetric
Consumption
Species Moles Mole Fraction (Liters/min)
H2 1 0.295 885 = (0.295)(3000 L/min)
O2 0.5 0.148 444
N2 1.88 0.556 1,668
3.38 0.999 2,997
At 300 K and 1 atm the molar volume is
[pic]
The molar flow of hydrogen is
[pic]
The hydrogen consumption rate is then
[pic]
b. The power rate is the energy release rate from the combustion reaction
[pic]
Home Problem Statement:
An internal combustion engine with a displacement volume of 4 L has a rotational speed of 1500 rpm.
a. If propane is used as a fuel, calculate the theoretical propane consumption rate at this rpm. Remember that each cylinder fires once every two revolutions. Assume that the combustion occurs stoichiometrically. Assume that the air – fuel mixture enters the engine at 300 K and 1 atm.
b. If the heat of combustion for the propane is 2043 kJ/mole, what is the theoretical power delivered by this engine, in HP?
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