Hydrogen has a wide flammability range (4.0% - 75% compared to 1.4% - 7.6% by volume in air for gasoline). This is of utmost importance for safe handling of hydrogen. However, this leads to the suitability for use in lean burn mixture engine. Lean mixture allows for better complete combustion and better thermal efficiency i.e. better economy. This in turn permits for lower for lower maximum combustion temperature that leads to lower nitrogen oxides (NO_x) [3] [5] .

Hydrogen has a small quenching distance of 0.6 mm compared to 2.0 mm for gasoline. This is the distance from the cylinder wall where flame front extinguishes. This means it is more difficult to extinguish the hydrogen flame and implies more susceptibility of the engine to backfire since the hydrogen-air mixture flame more easily passes through valves than the gasoline-air mixture flame [3] [6] .

Hydrogen burns with high flame front speed. This allows hydrogen engines to thermodynamically more closely approach the constant volume heat addition ideal cycle. This resemblance is adequate for stoichiometric mixture, when hydrogen engine runs lean to improve fuel economy and reduce nitrogen oxides, the flame speed slows down. However, it is still very much higher than the gasoline-air mixture flame speed [3] [6] . Flame speed and maximum combustion temperature are of prime concern for thermal efficiency and emissions.

Self-ignition temperature of hydrogen is high as 585˚C. This makes it difficult to ignite the hydrogen-air mixture without an external ignition source. Table 1 shows this temperature compared to gasoline and diesel fuels. The table also summarizes the other important properties. The auto-ignition temperature is an important property in determining the maximum compression ratio (Higher Useful Compression Ratio) that an engine can operate at [7] .

The minimum ignition energy required to ignite the fuel-air mixture by an ignition source such as a spark plug for hydrogen is about an order of magnitude lower than gasoline-air mixture i.e. 0.02 mJ compared to 0.24 mJ for gasoline. The low ignition energy means that hot gases and hot spots on cylinder serve as sources of ignition creating premature ignition and flashback [3] [6] .

The stoichiometric combustion equation for hydrogen in air is:

Stoichiometric air/fuel ratio is = 8/0.23 = 35

The excess air factor

MOLS of air/MOL of hydrogen for complete combustion = 2.38.

This corresponds to stoichiometric volume percent of hydrogen in air-fuel mixture = 29.5.

For gasoline the volume percent of fuel in stoichiometric fuel-air mixture is only 1.76, with (A/F)_st = 14.6.

Despite the lower calorific value of hydrogen is 120 mJ/kg compared to the gasoline as 44 mJ/kg, the energy content per m³ of gas fuel-air mixture under standard atmospheric conditions is lower [8] . Based on flammability range by volume in air, the flammability limits of hydrogen vary from equivalence ratio φ from 0.1 to 7.1. This enables the engine to run well into the lean mixture and prompts ignition and hence higher thermal efficiency [9] . Table 1 compares the properties of hydrogen and gasoline and diesel fuels.

Without significance compression or conversion to liquid hydrogen, a very large volume may be necessary to store enough hydrogen to provide adequate drive range. It also implies the fuel-air mixture has low energy per unit mixture volume which reduces the engine output for carburetor or inlet port fuel induction. Thus, when hydrogen engine run lean issues of inadequate power arise [3] .

In spark ignition engine, hydrogen can be used as fuel almost similar to SI gasoline engine. There are now many companies start marketing hydrogen ICE engine vehicles e.g. Ford and BMW [9] . The fuel induction modes are carburetion, inlet manifold and inlet port injection and direct cylinder injection [10] [11] . Hydrogen cannot be used as a sole fuel in CI engine due to the high self-ignition temperature of hydrogen. Hydrogen fueling of diesel engine must have spark plug in addition to hydrogen injector [12] .

The working fluid in this cycle is assumed as air with constant specific heats with no fuel combustion but with equivalent amount of heat transferred through the cylinder wall. The specific heat ratio is taken as 1.4 and the compression ratio is 8. Assuming T1 = 400˚ K, P1 = 1 bar.

The indicated thermal efficiciencyand the indicated mean effective pressure are obtained from Equations (5) and (6) and results in Table 3.

.

The equation for combustion of H₂ with excess air factor λ can be written as:

- Number of moles before combustion is given by:

- Number of moles after combustion is given by:

The calorific value is then L.C.V. = 120 MJ/kg hydrogen

The following table shows (Table 4) for different values of (λ).

The products of combustion are shown in Table 5:

The molar specific heat of each constitutes of the combustion gases as function of temperature (T) [8] . This is based on polynomial curve fit to thermodynamic data assuming that the unburned mixture is frozen in composition and the burned mixture is in equillibrium. This is based on the equilibrium NASA program [12] .

Similar terms for, and as function of temperature.

As: (11)

These specific heats of products of combustion are also function of (λ), the combustion gases molar specific heats at every temperature can be obtained in KJ/Kmol_cg.˚K as:

If the reference state for internal energy and enthalpy is taken as, at T₀ = 0˚ K

The internal energy and enthalpy can be obtained at different temperatures and different excess air factor λ as:

The entropy at any given temperature and excess air factor λ also can be obtained if the reference state point is taken as:

at P₀ = 1 bar, T₀ = 300˚ K and, so that,

MATLAB is used in programmed mode to construct the temperature-entropy chart with constant pressure lines and constant specific volume lines, for different excess air factors λ, s. The temperature-internal energy lines and the temperature-enthalpy lines are also constructed on the chart for different excess air factors λ, s. All properties are given per mole combustion gases for reactants and products of combustion. The constructed temperature-entropy chart is shown in Figure 2 with some selected pressure and specific volumes lines and selected excess air factors.

In this analysis, the actual fuel-air working fluid is used and the combustion is assumed to occur instantaneous at TDC. The change of specific heat of the reactants and products of combustion is taken into the analysis. The change of the number of molecules and dissociation effects are taken into account. However, as the mixture excess air factor is 1.5 or more, the effects of dissociation are minimal. As a demonstration to the numerical procedure, the hydrogen SI four stroke engine cycles is applied to the generated chart. The engine is four stroke, water cooled engine having compression ratio r of 8 with hydrogen mixture excess air factor λ of 1.5. The in cylinder gases condition at start of compression stroke is taken as P₁ = 1 bar and T₁ = 400˚ K. The isentropic compression from the known state point (1) to state point (2) with the known specific volume from the specified engine compression ratio, is iterated using Equation (15) for an excess air factor λ = ∞ and initial guess of T₂. The temperature T₂ is incremented until. At state (2) combustion carried out instantaneous and the working fluid changes into products of combustion at λ = 1.5. The lower calorific value is =

. Assuming the cooling water percent loss as 34%, As distinct from gasoline or

diesel fuel/air cycles , all heat of combustion is added at constant volume due excessively high flame speed.

The internal energy of combustion gases is obtained from. The maximum cycle temperature is determined from and the internal energy vector of combustion gases at different temperatures for λ = 1.5 generated from Equation (13). For the constant specific volume line and known temperature determine the specific entropy per mole combustion gases at state (3). Isentropic expansion from state (3) to state (4) with known specific volume is iterated using Equation (15) for excess air factor λ = 1.5 and an initial guess lower than T₄ lower than T₃. With the temperature T₄ progressively decreased until. The properties of gases at state (4) is determined to obtain the exhaust gas loss, from which then, the indicated work done per cycle is determined. Engine sizing and performance parameters are predicted.

The hydrogen/air cycle numerical representation is shown in the Figure 2 for engine compression ratio of 8 and λ = 1.5. The procedure is summerized as follows:

Point (1)

P₁ =1bar, T₁=400˚ K,

Point (2) Compression is isentroic from state (1) to (2) where

P₂ = 13.75 bar, T₂ = 767˚ K, Then,

T₃ = 1883˚ K

Heat lost in exhaust = 35,238 ? 8572 = 26,666 kJ/mol_cg

IWD = 38,919 ? 26,666 = 12,253 kJ/mol_cg

The indicated thermal efficiency:

, , the indicated mean effective pressure

, brake mean effective pressure.

bmep = 421.1 * 0.87 = 366.33 kpa, where η_mechanical = 0.87

brake specific fuel consumption (bsfc) =

If the engine develops 50 kW @ N = 5000 rpm, L/D = 1 bmep =, Vs = 3.27 liters with L = D =

10.1 cm. P_b/liters = 15.3 (which is low compared to modern gasoline engines).

The fuel/air cycle analysis of performance predictions compares very well with the actual engine cycles for petrol and diesel engine using hydrocarbon fuels [8] . The results obtained in the present work for hydrogen/air cycle analysis show a good estimate of engine sizing power developed and bsfc compared to that of actual engine. Also peak pressures and exhaust temperatures that affect engine structure and design can be closely predicted. The effect of many variables on hydrogen engine performance can also be understood.

For a certain engine configuration, CFD code Fluent which include the turbulence and detailed combustion processes that are modeled with sufficient generality to include delay period, chemical kinetics and flame propagation is then required. This simulation will give good understanding of in cylinder gas motion with detailed combustion process that are essential to improve performance and reduce emissions without sacrificing fuel economy and to study the effects of using different hydrogen fuel induction methods [13] .