Thermodynamics and Heat Engine4 (3+1)

LESSON - 42 GAS POWER CYCLES, AIR STANDARD CYCLES, THE AIR-STANDARD CARNOT CYCLE: THE IDEAL CYCLE FOR IC ENGINE

42.1. GAS POWE CYCLES 

Internal combustion (IC) engines like spark-ignition internal combustion engine (petrol engine) and compression-ignition internal combustion engine (diesel engine) as shown in Fig. 42.1 are the examples of heat engines that operate on the gas power cycles.

In IC engines, combustion chamber takes in air or air+fuel, compress it to a high pressure, and cause it to burn in combustion chamber liberating heat energy. The product of combustion at high pressure and temperature expand and do work and then the exhaust gas (product of combustion of air and fuel) leaves the engine. This way the IC engine operates on gas power cycle which uses only gas as a working fluid. Such IC engines are said to operate on the open gas power cycle as the working fluid in IC engine after undergoing a series of processes is not restored back to its initial state at the end of the gas power cycle.

Fig. 42.1. Internal Combustion Engine

Why we need ideal cycle in the analysis of gas power cycle

In order to study the performance of IC engines, it is important to analyse the open gas power cycle encountered in IC engines. However, analysis of actual open gas power cycle is difficult due to its following complexities.

a)      Mass of air in the cycle does not remain fixed due to introduction of fuel into an IC engines.

b)      IC engines operate in open cycle.

c)      The processes of the actual cycle are irreversible due to friction, pressure differences, and turbulence, etc.

d)     In I.C. engine we have combustion inside for heat addition and removal of exhaust gases for heat rejection.

e)      The mass, specific heats and state of working fluid are all variable during the cycle.

f)       The working fluid is not air throughout the entire cycle due to product of combustion.

To make this analysis feasible, it is advantageous to device an idealized cycles known as Air-Standard cycles that closely approximate the actual open gas cycle of actual IC engines and then analyze the performance of these idealized cycles. For example, the spark-ignition internal combustion engine (petrol engine) is usually approximated by the Otto cycle and compression-ignition internal combustion engine (diesel engine) is usually approximated by the Diesel cycle.

The following assumptions are used in ideal cycle Air-Standard cycles, which provide considerable simplification in the analysis without significant deviation from the actual cycles.

a) The mass of air in the cycle remains fixed throughout the entire cycle.

b) The engine is imagined to operate in a closed cycle so that working fluid is restored to its initial state at the end of each cycle. Thus, there are no intake and exhaust processes.

c) Each process is carried out reversibly.

d) The combustion process and exhaust process are replaced by addition and rejection of heat due to processes of heat transfer from external heat reservoir alone.

e) Specific heat of air remains constant and its values are determined at room temperature (25°C).

f) The working fluid is air throughout the entire cycle and always behaves as the perfect gas.

It is apparent from the above assumptions that the results obtained from the analysis of air standard cycle will differ from their actual engine. However, certain generalization can be arrived at from this analysis which enables us to study qualitatively the influence of major parameters on the performance of the actual engines. 

42.2. BASIC COMPONENT AND TERMS USED IN IC ENGINE

Before we start with Air-Standard cycles (idealized gas power cycle) for IC engines, it is necessary to know the basic components of IC engines along with commonlyused terms in conjunction with IC engines.

I.C. engines like spark-ignition (petrol) engine and compression-ignition (diesel) engine make use of the piston-cylinder arrangement. The basic componentsof IC engine are shown in Fig. 42.1 and 42.2.

	Where,       d  = cylinder diameter (or bore),       L  = piston stroke (stroke),      Vc = clearance volume,      Vs = swept /stroke volume
Fig. 42.2. Simplified Piston-cylinder Arrangement of IC engine

Clearance volume, V_c: The minimum volume formed in the cylinder when the piston is at TDC.

 Swept volume or displacement volume or stroke volume, V_s: The volume displaced by the piston as it moves between TDC and BDC.

V_s = (π/4) .d² . L

 Full cylinder volume (Cylinder volume) V:    

V = V_c +V_s

Compression ratio, r: The ratio of the full cylinder volume to the minimum (clearance) volume.

r_v = 

Clearance ratio, c: The ratio of the clearance volume to the stroke volume. 

c =           (typical value = 5-10%)

Efficiency Ratio or relative efficiency  = 

Work ratio = 

Specific fuel consumption: It is mass of fuel consumed per unit energy (power output x time) produced by engine

Metallurgical limit     

It is maximum possible temperature of the working fluid which can be achieved during the cycle keeping in view the life (function of material it is made of) span of highly stressed parts of the I.C. engine.

Highly stressed parts:  piston & cylinder in I. C. engine

Metallurgical limits:  2750^oC

42.3. INDICATOR DIAGRAM We can plot indicated p-v diagram of a cycle of an internal combustion engine with the help of Indicator. The function of an indicator is to draw a pressure–volume (p-V) diagram on a piece of paper showing the variation of pressure and volume inside the engine cylinder. This p-V diagram is called Indicator diagram. A typical actual indicator diagram of engine is shown in the Figure 42.3.   Shaded area of loop = Net work output of engine per cycle, Wnet   Similar to steam engines, the theoretical indicator diagram of the IC engines differs much from the actual indicator diagram.

Figure 42.3. Indicator diagram

42.4. MEAN EFFECTIVE PRESSURE (MEP), P_M

Similar to reciprocating steam engines as discussed in lesson 35, the mean effective pressure of IC engine can be determined with the help of an indicator diagram.

It can be seen from the indicated diagram in Fig 42.3 that the effective pressure does not remain constant during the whole cycle. So an average or mean effective pressure (mep) is required for the calculation of net work done per cycle.

Mean Effective Pressure is that imaginary constant pressure as shown in Fig. 42.4 which acting on a piston through one stroke would do the same amount of work as is done by varying pressure during one cycle.

Fig. 42.4. Mean effective pressure on p-v diagram

W_net = mep x swept volume = P_m x V_s                                                                                                         ……(42.1)

or           Mean effective pressure, p_m =

Therefore, Mean effective pressure can be defined as a measure of work output per cycle per unit cylinder size.

So with increase in p_m, the cylinder size required to develop certain power decreases and vice-versa.

The mean effective pressure can be used as a parameter to compare the performances of reciprocating engines of equal size. The engine with large value of mean effective pressure delivers more net work per cycle and thus performs better.

If the mean effective pressure (mep) is determined from the actual indicator diagram taken by indicator, it is known as actual mean effective pressure (imep), p_am.But if it is calculated from the area of a theoretical pressure-volume diagram, it will be the theoretical mean effective pressure, p_t,m.

42.5. CARNOT GAS CYCLE: THE IDEAL CYCLE FOR IC ENGINE

In Lesson 16, it was observed that the engine run on Carnot cycle has maximum efficiency compared to the engine run on other cycles.  Thus it is natural to first take the Carnot cycle as a prospective ideal cycle for IC engines.

The Carnot gas cycle is represented on p-v and T-s diagram is shown in Figure 42.5.

Fig. 42.5. Carnot cycle p-v and T-s diagram

Process 1-2        → Isentropic (Reversible adiabatic) expansion

Process 2-3        → Isothermal (constant temperature) heat rejection

Process 3-4       → Isentropic (Reversible adiabatic) compression

Process 4-1       → Isothermal (constant temperature) heat addition

The thermal efficiency of Carnot cycle is given by the relation

            

Even though we know the IC engines operating on Carnot cycle is more efficient, however, Carnot cycle is not possible in practice for IC engines because of the following problems.

Problems with Carnot Cycle as an ideal cycle for IC engine

1. In Carnot cycle, heat supply and heat rejection take place at constant temperature.  However, for gas as working fluid, it is much more convenient to heat and cool gas at constant pressure  or constant volume under some finite temperature difference. 

2. It has low work ratio i.e. its net work output (area 1-2-3-4 in pV diagram) is small as compared to positive work obtained in expansion process.

For work to be positive,  

The normal temperatures encountered in actual engine are T₄ = 2000^oC, T₃ =15^oC; and  pressure of sink P₂ = 1 bar

> 7.9^3.5 > 1380 bar   (in actual engine pressure rarely exceed 100 bar.)

 Also  we have

   (in actual engine volume ratio rarely exceed 20.) It means that stroke should be too large & p_m will be very low.

So, to get some work output of engine operating on Carnot cycle, very high pressures and volumes are involved. Besides p_m is also very low. But in actual engine it is very rare.

Even Carnot Cycle as an ideal cycle for IC engine is not possible in practice. Still the analysis of Carnot cycle permits the designer to arrive at the maximum possible efficiency that can be obtained in any engine under given conditions.