NAZARIN B. NORDIN

What you will learn: First law of thermodynamics Isothermal process, adiabatic process, combustion process for petrol/diesel engines Volumetric Efficiency; spark ignition/ compression ignition; ignition process and tests

First Law of Thermodynamics Conservation of Energy for Thermal Systems

Joule Equivalent of Heat James Joule showed that mechanical energy could be converted to heat and arrived at the conclusion that heat was another form of energy. He showed that 1 calorie of heat was equivalent to J of work. 1 cal = J

Energy Mechanical Energy: KE, PE, E Work is done by energy transfer. Heat is another form of energy. Need to expand the conservation of energy principle to accommodate thermal systems.

1 st Law of Thermodynamics Consider an example system of a piston and cylinder with an enclosed dilute gas characterized by P,V,T & n.

1 st Law of Thermodynamics What happens to the gas if the piston is moved inwards?

1 st Law of Thermodynamics If the container is insulated the temperature will rise, the atoms move faster and the pressure rises. Is there more internal energy in the gas?

1 st Law of Thermodynamics External agent did work in pushing the piston inward. W = Fd =(PA)  x W =P  V xx

1 st Law of Thermodynamics Work done on the gas equals the change in the gases internal energy, W =  U xx

1 st Law of TD Let’s change the situation: Keep the piston fixed at its original location. Place the cylinder on a hot plate. What happens to gas?

Heat flows into the gas. Atoms move faster, internal energy increases. Q = heat in Joules  U = change in internal energy in Joules. Q =  U

1 st Law of TD What if we added heat and pushed the piston in at the same time? F

1 st Law of TD Work is done on the gas, heat is added to the gas and the internal energy of the gas increases! Q = W +  U F

1 st Law of TD Some conventions: For the gases perspective: heat added is positive, heat removed is negative. Work done on the gas is positive, work done by the gas is negative. Temperature increase means internal energy change is positive.

1 st Law of TD Example: 25 L of gas is enclosed in a cylinder/piston apparatus at 2 atm of pressure and 300 K. If 100 kg of mass is placed on the piston causing the gas to compress to 20 L at constant pressure. This is done by allowing heat to flow out of the gas. What is the work done on the gas? What is the change in internal energy of the gas? How much heat flowed out of the gas?

P o = 202,600 Pa, V o = m 3, T o = 300 K, P f = 202,600 Pa, V f =0.020 m 3, T f = n = PV/RT. W = -P  V  U = 3/2 nR  T Q = W +  U W =-P  V = -202,600 Pa (0.020 – 0.025)m 3 =1013 J energy added to the gas.  U =3/2 nR  T=1.5(2.03)(8.31)(-60)=-1518 J Q = W +  U = 1013 – 1518 = -505 J heat out

Performance Factors Volumetric Efficiency

1a. Indicated Power. Indicated Power (IP) : Power obtained at the cylinder. Obtained from the indicator diagram. Given by: IP = P i LANn/60x in Watts where P i is the indicated mean effective pressure, in N/m 2, L is the stroke length, in m A is the area of cross section of the piston, m 2, N is the engine speed in rev/min, n is the number of cylinders and x =1 for 2 stroke and 2 for 4 stroke engine.

1b. Brake Power Brake Power (BP) : Power obtained at the shaft. Obtained from the engine dynamometer. Given by: BP = 2  NT/60 in Watts where T is the brake torque, in Nm, given by T = W.L where W is the load applied on the shaft by the dynamometer, in N and L is the length of the arm where the load is applied, in m N is the engine speed, in rev/min

1c. Friction Power Friction Power (FP) : Power dissipated as friction. Obtained by various methods like Morse test for multi-cylinder engine, Willan’s line method for a diesel engine, and Retardation test and Motoring test for all types of engines. Given in terms of IP and BP by: FP = IP – BP in Watts

2. Mean Effective Pressure. Indicated Mean Effective Pressure (IMEP). This is also denoted by P i and is given by P i = (Net work of cycle)/Swept Volume in N/m 2 The net work of cycle is the area under the P-V diagram. Brake Mean Effective Pressure (BMEP). This is also denoted by P b and is given by P b = 60.BPx/(LANn) N/m 2 This is also the brake power per unit swept volume of the engine. Friction Mean Effective Pressure (FMEP). This is also denoted by P f and is given by P f = P i - P b N/m 2

3. Efficiencies. Indicated Thermal Efficiency (  i ) given by  i = IP/(m f. Q cv ) m f is the mass of fuel taken into the engine in kg/s Q cv is the calorific value of the fuel in J/kg Brake Thermal Efficiency (  b ) given by  b = BP/(m f. Q cv ) Indicated Relative Efficiency (  i,r ) given by  i,r =  i /ASE ASE is the efficiency of the corresponding air standard cycle Brake Relative Efficiency (  b,r ) given by  b,r =  b /ASE Mechanical Efficiency (  m ) given by  m = BP/IP = P b /P i =  b /  i =  b,r /  I,r

Specific Fuel Consumption (sfc or SFC) This is the fuel consumed per unit power. Brake Specific Fuel Consumption (bsfc). This is given by bsfc = m f /BP kg/J if BP is in W and m f is in kg/s bsfc is usually quoted in kg/kWh. This is possible if BP is in kW and m f is in kg/h. Indicated Specific Fuel Consumption (isfc). This is given by isfc = m f /IP kg/J if IP is in W and m f is in kg/s isfc is also usually quoted in kg/kWh. This is possible if IP is in kW and m f is in kg/h. Mechanical Efficiency in terms of the sfc values is given by  m = isfc/bsfc

Specific Energy Consumption (sec or SEC). This is the energy consumed per unit power. Brake Specific Energy Consumption (bsec). This is given by bsec = bsfc.Q cv We can similarly define indicated specific energy consumption (isec) and based on the two quantities also we can define mechanical efficiency.

Air Capacity of Four-stroke cycle Engines The power, P, developed by an engine is given by Power will depend on air capacity if the quantity in the bracket is maximized. Plot of power versus air flow rate is normally a straight line.

Volumetric Efficiency Indicates air capacity of a 4 stroke engine. Given by Mi is the mass flow rate of fresh mixture. N is the engine speed in rev/unit time. V s is the piston displacement (swept volume). ρ i is the inlet density.

Volumetric Efficiency Can be measured: At the inlet port Intake of the engine Any suitable location in the intake manifold If measured at the intake of the engine, it is also called the overall volumetric efficiency.

Volumetric Efficiency Based on Dry Air Since there is a linear relationship between indicated output (power) and air capacity (airflow rate), it is more appropriate to express volumetric efficiency in terms of airflow rate (which is the mass of dry air per unit time). Since fuel, air and water vapor occupy the same volume V a = V f = V w = V i Thus we have:

Here ρ a is the density of dry air or the mass of dry air per unit volume of fresh mixture. Thus, since

Also V d = A p L s = 2LN L is the piston stroke and s is the piston speed.

Measurement of Volumetric Efficiency in Engines The volumetric efficiency of an engine can be evaluated at any given set of operating conditions provided and ρ a can be accurately measured. Measurement of Air Flow Airflow into the engine can be measured with the help of a suitable airflow meter. The fluctuations in the airflow can be reduced with the help of surge tanks placed between the engine and the airflow meter.

Measurement of Inlet Air Density By Dalton’s Law of partial pressures: p i = p a + p f + p w In this case p i is the total pressure of the fresh mixture, p a is the partial pressure of air in the mixture, p f is the partial pressure of fuel in the mixture, p w is the partial pressure of water vapor in the air. Since each constituent is assumed to behave as a perfect gas, we can write

M indicates mass of the substance, 29 is the molecular weight of air, m f is the molecular weight of the fuel, and 18 is the molecular weight of water vapor.

F i is the ratio of mass of fuel vapor to that of dry air and h is the ratio of mass of water vapor to that of dry air at the point where p i and T i are measured. This indicates that the density of air in the mixture is equal to the density of air at p i and T i multiplied by a correction factor, that is, the quantity in the parentheses.

The value of h depends on the humidity ratio of the air and is obtained from psychrometric charts. For conventional hydrocarbon fuels, the correction factor is usually around 0.98, which is within experimental error. For diesel engines and GDI engines, F i is zero. In practice, with spark ignition engines using gasoline and with diesel engines the volumetric efficiency, neglecting the terms in the parentheses, is given by

If we do not neglect the terms in the parentheses we get the following relation for volumetric efficiency: If the humidity is high or a low molecular weight fuel is used in a carbureted engine, the correction factor cannot be ignored. For example, with methanol at stoichiometric conditions and h = 0.02, the correction factor is 0.85.

Volumetric Efficiency, Power and Mean Effective Pressure Since and

For an engine, the mean effective pressure, mep, is given by

Ways to increase power and mep The mean effective pressure may be indicated or brake, depending on whether η is indicated or brake thermal efficiency. Thus, the mean effective pressure is proportional to the product of the inlet density and volumetric efficiency when the product of the thermal efficiency, the fuel-air ratio, and the heat of combustion of the fuel is constant. From the preceding two expressions we can figure out ways to increase the power and mep of an engine.

OTTO CYCLE-THE IDEAL CYCLE FOR SPARK-IGNITION ENGINES The Otto cycle is the ideal cycle for spark-ignition reciprocating engines. It is namedafter Nikolaus A. Otto, who built a successful four-stroke engine in 1876 in Germany using the cycle proposed by Frenchman Beau de Rochas in In most spark-ignition engines, the piston executes four complete strokes (two mechanical cycles) within the cylinder, and the crankshaft completes 2 revolutions for each thermodynamic cycle. These engines are called FOUR-STROKE internal combustion engines.