Chapter 8

Diesel Power Plant

A Diesel power plant uses a Diesel engine. Of all types of standard prime movers of equivalent size, the Diesel engine has the highest thermal efficiency. Diesel engines are classified as two-stroke and four-stroke engines. The constant pressure process is observed in the Diesel cycle; the constant volume process is noted in the Otto cycle. The Diesel cycle can operate with a higher compression ratio than the Otto cycle. High-compression heat of air is the source of ignition energy in C.I. engines, while a spark plug provides ignition energy to S.I. engines. M.E.P. is defined as the mean pressure which, if imposed on the pistons uniformly, would produce the net work of the cycle. The ideal Diesel cycle follows four distinct processes, i.e., isentropic compression, constant pressure combustion, isentropic expansion, and constant volume cooling. The Otto cycle also comprises four processes, i.e., isentropic compression, constant volume combustion, isentropic expansion, and constant volume cooling.

Keywords

compression-ignition; spark-ignition; compression ratio; expansion ratio; cut-off ratio; M.E.P. supercharger

8.1 Introduction

In 1885, the English engineer Herbert Akroyd Stuart invented an engine using paraffin oil as the fuel. This was the first internal combustion engine to use a pressurized fuel injection system. This engine adopted a low-compression ratio, so the compressed air did not have adequate temperature in the combustion chamber to initiate ignition of fuel. Hence, the combustion of oil used to take place in a separate chamber called the “vaporizer” mounted on the cylinder head, which was heated externally by an oil lamp to raise the temperature of the chamber sufficient enough to ignite the oil. Compressed air from the cylinder is passed through a constricted passage into the vaporizer, where oil is then sprayed and ignited by the temperature of the vaporizer chamber for combustion. In 1892 Thomas Henry Barton built a high-compression internal combustion engine, thus eliminating the use of a separate vaporizer.

Credit for the invention of the modern diesel engine, however, goes to French engineer Rudolf Diesel. In 1892 Diesel adopted a high compression ratio in his engine, where air could be compressed so much that the temperature attained by air far exceeded the ignition temperature of the fuel, thereby ensuring appropriate combustion of the fuel gradually introduced into the combustion chamber. Diesel’s original 1897 designed engine is depicted in Figure 8.1.

image
Figure 8.1 Diesel’s original 1987 engine. Source: http://en.wikipedia.org/wiki/Diesel_engine.

A diesel power plant uses a diesel engine, similar to one developed by Rudolf Diesel, as the prime mover for the generation of electrical energy. This engine, also called a compression-ignition engine, is a reciprocating internal combustion engine. Unlike a spark-ignition engine, a diesel engine uses the heat of compression of air to initiate ignition and burning of the fuel in a combustion chamber.

Of all type of standard prime movers of equivalent size, whether internal or external combustion types, the diesel engine has the highest thermal efficiency (almost 52%) due to its very high compression ratio. Low-speed diesel engines can have a thermal efficiency greater than 50% [1].

A diesel power plant is generally compact. The largest unit at the time of writing is about 85 MW, which was put into service aboard a container ship. The world’s largest two-stroke diesel power-generating unit on land is of capacity 50 MW installed at GMR Vasavi power plant in Chennai, India.

Based on its requirement a diesel power plant may serve any one of the following three purposes [2]:

i. Base load station running continuously as sole source of power

ii. Standby station sometimes running continuously at rated load

iii. Emergency unit running for short time at rated load

The thermal efficiency of a diesel engine is inherently better than that of a steam or gas turbine. The efficiency of the engine could further be improved (to the extent of about 60% [1]) by recovering waste heat in exhaust gas in a heat recovery steam generator for generation of steam either to be used in a steam turbine to generate additional power or be used as process steam. In spite of its high efficiency a diesel power plant is generally used as emergency supply station because of high cost of diesel oil in most countries. As a smaller version a diesel power plant is a portable type that may be located in situ as and when there is an emergency demand. Diesel engine generators are attractive due to their long life. Today’s diesel engines emit less noise and generally do not require much maintenance.

Diesel engines are classified as two-stroke and four-stroke engines. While most diesel engines, particularly of domestic type, generally use the four-stroke one, larger engines are usually two-stroke type. Domestic diesel generator sets require single-phase power supply, whereas industrial or commercial application generators usually require three-phase power.

Most diesel engines have large pistons and therefore draw more air and fuel, which results in bigger and more powerful combustion. In internal-combustion engines, it is presumed that the combustion process occurs at either constant pressure or at constant volume or by a combination of these two processes. The constant-pressure process is observed in the slow-speed compression-ignition (C.I.) or Diesel cycle; the constant volume process is noted in the spark-ignition (S.I.) or Otto cycle; combination of these two processes, however, is called mixed or limited-pressure cycle and appears in high-speed compression-ignition engines.

Compression ratio (CR) of an internal combustion engine is defined as the ratio of “the volume between the piston and cylinder head before and after a compression stroke.” In the Diesel cycle mixing of air and fuel takes place near the end of compression, while in the Otto cycle mixing takes place before compression. In the diesel engine the heat of compression is used to initiate ignition to burn the fuel, while in the Otto cycle a spark is required to begin combustion of fuel. The Diesel cycle can operate with a higher compression ratio than the Otto cycle because only air is compressed in the Diesel cycle while a charge of fuel-air mixture is compressed in the Otto cycle. As a result there is no risk of auto-ignition of the fuel in the Diesel cycle.

In compression-ignition engines no separate source of ignition energy, like a spark plug, is required for igniting fuel. These engines use liquid fuels of low volatility. In the diesel engine the most common working fluid is air, which is introduced into the combustion chamber to burn fuel. The air is compressed with a compression ratio, typically between 11.5:1 and 22:1, resulting in a compression pressure ranging between 2.8 MPa and 4.8 MPa [3]. This high compression heats the air to 823 K, then fuel is injected directly into the compressed air in the combustion chamber. The fuel injector ensures that the fuel is broken down into small droplets, and is distributed as evenly as possible. The vapor is then ignited by the heat from the compressed air in the combustion chamber, where the droplets continue to vaporize from their surfaces and burn, getting smaller, until all the fuel in the droplets has been burnt. The start of vaporization causes a delay during ignition, resulting in an abrupt increase in pressure above the piston. The rapid expansion of combustion gases then drives the piston downward, supplying power to the crankshaft. The load and speed in this engine are controlled by varying the injected fuel flow.

Spark-ignition engines use high volatile liquids and gases as fuel and have compression ratios between 4:1 and 12:1. The compression pressure ranges from below 0.7 MPa to 2.0 MPa. S.I. engines use carburetors and fuel injection systems. Load and speed are usually controlled by throttling the charge [3].

The combustion process in an internal combustion engine is governed by the air-fuel ratio in the cylinder. In a typical compression-ignition engine burning hydrocarbon fuels the stoichiometric air-fuel ratio is 14.9. The limiting relative air-fuel ratio for combustion at full load ranges between 1.2 and 1.6 [4].

8.1.1 Advantages of diesel power plant over steam power plant

1. Simple design and layout of plant

2. Occupies less space and is compact

3. Can be started quickly and picks up load in a short time

4. Requires less water for cooling

5. Thermal efficiency (about 50% or more) is better than that of a steam power plant of same size

6. Overall cost is less than that of steam power plant of same size

7. Requires low operating staff

8. No stand-by losses

8.1.2 Disadvantages of diesel power plant over steam power plant

1. High running charges due to costly price of diesel

2. Plant does not work efficiently under prolonged overload conditions

3. Generates a comparatively small amount of power

4. Specific lubricating oil consumption and its costs are very high

5. Maintenance charges are generally high

8.1.3 Mean effective pressure (M.E.P.)

In a reciprocating engine it is difficult to isolate the positive and negative pressure in the cycle, since the processes are carried out in a single component. Hence, while comparing air-standard cycles of reciprocating engines a term mean effective pressure is usually referred to in lieu of the work ratio. Mean Effective Pressure, or in short M.E.P., is defined as the mean pressure that, if imposed on the pistons uniformly from the top to the bottom of each power stroke, would produce the net work of the cycle. A cycle operating with large M.E.P. will produce large work output per unit of swept volume. As a result size of an engine based on this cycle will be small for a given output.

For naturally aspirated four-stroke diesel engines, the maximum M.E.P. is in the range of 700 to 900 kPa. Two-stroke diesel engines have comparable values of M.E.P., while very large low speed diesel engines may have a M.E.P. up to 1900 kPa.

8.1.4 Four-stroke engine

A four-stroke engine comprises of the following:

i. Induction stroke: Air is drawn into the cylinder.

ii. Compression stroke: The air is compressed and just before the piston reaches the top dead center liquid fuel is sprayed into the cylinder. The temperature of the air at the end of compression is significantly high to vaporize the liquid droplets and ignite them.

iii. Expansion or working stroke: Combustion is almost completed at the start of the expansion stroke, where the product expands and pressure falls steadily. As the exhaust valve opens blow-down occurs and the pressure in the cylinder becomes slightly more than the atmospheric pressure.

iv. Exhaust stroke: The gases remaining in the cylinder at the end of the expansion stroke are displaced by the piston during the exhaust stroke.

8.1.5 Two-stroke engine

In a two-stroke engine the induction and exhaust strokes are eliminated and part of the compression and expansion strokes are used for exhaust and induction. At the end of the compression stroke the inlet port opens and air is admitted to the cylinder, while at the end of the expansion stroke the exhaust port is opened to allow blow-down of gases. Eventually the piston stroke of this engine is longer than that of a four-stroke engine of the same capacity.

The relative advantages/disadvantages of four-stroke and two-stroke engines are as follows:

8.1.6 Advantages of four-stroke engines

i. Better scavenging, hence higher M.E.P.

ii. More flexibility

iii. Low fuel and lubricating oil consumption

iv. Less noisy exhaust

v. Compression better maintained, since the engine runs cooler, and the average load on the piston rings is less

vi. Cylinder wears less than in some two strokes

8.1.7 Advantages of two-stroke engine

i. Larger power per cylinder

ii. Shorter crankshaft and more even torque reduces the risk of torsional oscillation

iii. Engine easily reversible

iv. Mechanically operated valves are eliminated

v. Few spares required

vi. Inferior fuel may be used

vii. Higher fuel consumption so greater output

Two-stroke engines have one major disadvantage – leakage of scavenge air through the exhaust ports accounts for a loss of air almost equal to 50% of the swept volume of the cylinder.

8.2 Thermodynamic Cycle

As discussed earlier a reciprocating internal-combustion engine may operate either on Diesel cycle or on Otto cycle. The following sections discuss these cycles in detail.

8.2.1 Diesel cycle

Figure 8.2 and Figure 8.3 depict the P-v and T-s diagrams for an ideal Diesel cycle, where P is the pressure and v is the specific volume. The ideal Diesel cycle follows four distinct processes: compression, combustion, expansion, and cooling. The cycle follows the numbers 1–4 in the clockwise direction.

• Process 1 to 2 is a isentropic compression process. The air is compressed isentropically through a volume ratio v1/v2. During this process work (Win) is done by the piston compressing the working fluid.

• Process 2 to 3 is a reversible constant-pressure heat addition process. Heat (Qin) is supplied by combustion of the fuel while the air expands at constant pressure to volume v3 during this process.

• Process 3 to 4 is an isentropic expansion process to the original volume v1. Work (Wout) is done by the working fluid expanding on to the piston, which produces usable torque.

• Process 4 to 1 is a reversible constant volume heat rejection (cooling) process. During this process heat (Qout) is rejected by exhausting air until the cycle is completed.

image
Figure 8.2 P-v Diagram of ideal Diesel cycle.
image
Figure 8.3 T-s Diagram of ideal Diesel cycle.

The stages of these four processes are discussed in the following. Note that theoretically each of the strokes of the cycle complete at either top dead center (TDC) or bottom dead center (BDC). However, due to delay in the opening and closing of the inlet and exhaust valves, the inertia of inlet air and exhaust gas, each of the strokes invariably begin and end beyond the TDC and BDC.

8.2.1.1 Compression

The cycle is started by drawing air at ambient conditions into the engine (Figure 8.4). This air is then compressed adiabatically by moving the piston upward in the cylinder from BDC to TDC (Figure 8.5). This compression raises the temperature of the air to a level where the fuel mixture, which is formed by injecting fuel once the air is compressed, spontaneously ignites. It is in this part of the cycle that work is applied to the air. This compression is considered to be isentropic.

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Figure 8.4 Induction of air into the cylinder in Diesel cycle. Source: http://image.slidesharecdn.com/asintroductionicengine.
image
Figure 8.5 Compression of air in Diesel cycle. Source: http://image.slidesharecdn.com/asintroductionicengine.

The ratio of the volume of the working fluid inducted into the cylinder before the compression process (v1) to its volume after the compression (v2) is defined as the volumetric compression ratio, rc (=v1/v2).

8.2.1.2 Combustion (Figure 8.6)

Next, the fuel is injected into the combustion chamber during the final stage of compression, thereby adding heat to the air by combustion of fuel. This process begins just as the piston leaves its TDC position. Because the piston is moving during this part of the cycle, the heat addition process is called isochoric (constant volume). The combustion process, however, takes place at constant pressure.

image
Figure 8.6 Combustionin in Diesel cycle. Source: http://image.slidesharecdn.com/asintroductionicengine.

8.2.1.3 Expansion (Figure 8.7)

In the Diesel cycle, fuel is burned to heat compressed air and as the rapidly burning mixture attempts to expand within the cylinder, it generates a high pressure that forces the piston downward from the TDC position to the BDC position in the cylinder. It is in this phase that the cycle contributes its useful work, rotating the engine crankshaft. This stage of an ideal Diesel cycle is considered as isentropic.

image
Figure 8.7 Expansion in Diesel cycle. Source: http://image.slidesharecdn.com/asintroductionicengine.

The ratio of the volume of the working fluid completing the expansion process (v4=v1) to its volume at the beginning of expansion (v3) is called the volumetric expansion ratio, re (=v1/v3).

The expanded mixture or gas is then ejected from the cylinder to the environment, which is replaced with a fresh supply of cold air from ambient conditions. Since this happens when the piston is at the TDC position in the cycle and is not moving, this process is isochoric (no change in volume). During actual operation there is a point in the cycle when both inlet and exhaust valves remain open simultaneously.

8.2.1.4 Thermal efficiency [5]

As explained above the compression and power strokes of an ideal Diesel cycle are adiabatic, hence the thermal efficiency of this ideal cycle can be calculated from the constant-pressure and constant-volume processes. Accordingly, the heat input (Qin), heat output (Qout), and thermal efficiency (ηth) can be calculated if the temperatures and specific heats of various end states are known. Assuming constant specific heats for the air and considering unit mass flow of the fluid, using Figure 8.3 we can write:

Qin=Cp(T3T2) (8.1)

image (8.1)

Qout=Cv(T1T4) (8.2)

image (8.2)

ηth=Qin+QoutQin (8.3)

image (8.3)

or,

ηth=1+QoutQin=1+Cv(T1T4)Cp(T3T2) (8.4)

image (8.4)

where

Cp=Specific heat at constant pressure

Cv=Specific heat at constant volume

T=Temperature at various end states of the cycle

From Figure 8.2 it can also be written that the compression ratio rc=v1/v2 and the expansion ratio re=v1/v3. Now, using the ideal gas law Pv=nRT and γ=Cp/Cv and for adiabatic condition Pvγ=constant, Eq. 8.4 can be written as

ηth=11γ(T4T1)(T3T2) (8.5)

image (8.5)

For adiabatic compression

T2T1=rc(γ1) (8.6)

image (8.6)

therefore

T1=T2rc(γ1) (8.7)

image (8.7)

For constant-pressure process

T3T2=v3v2=v3v1*v1v2=rcre (8.8)

image (8.8)

hence,

T3=T2rcre=T1rcγre (8.9)

image (8.9)

Again, for adiabatic expansion,

T3T4=re(γ1) (8.10)

image (8.10)

or,

T4=T3re(γ1)=T2rcre1re(γ1)=T2rcreγ=T1(rcre)γ (8.11)

image (8.11)

Substituting the values of T1, T3 and T4 from Eq. 8.7, Eq. 8.9, and Eq. 8.11, respectively, into Eq. 8.5 we arrive at

ηth=11γ(T2rcreγT2rc(γ1))(T2rcreT2)=11γ(rcreγ1rc(γ1))(rcre1)=11γ(1reγ1rcγ)(1re1rc)

image

or,

ηth=11γ(reγrcγ)(re1rc1) (8.12)

image (8.12)

Sometimes a “cut-off” ratio, as follows, is used to carry out various calculations:

rv=v3v2=v1v2*v3v1=rcre (8.13)

image (8.13)

Inputting the value of Eq. 8.13 into Eq. 8.12

ηth=11γrcγ{(rerc)γ1}rc1{(rerc)11}=1rc(1γ)γ{(1rv)γ1}(1rv)11=1rc(1γ)γ(rvγ1)(rv1) (8.14)

image (8.14)

Equations 8.12 and 8.14 give the ideal thermal efficiency of the Diesel cycle, which depends on the compression ratio as well as either the expansion ratio or the cut-off ratio, but not on the peak temperature T3. However, the thermal efficiency of actual Diesel cycle will be much lower than the ideal efficiency due to heat and friction losses, power absorbed by auxiliaries, e.g., lubricating oil pumps, cooling water pumps, fuel pumps, radiator fans, etc.

8.2.1.5 Mean effective pressure (M.E.P.)

As explained in Section 8.1.3 that M.E.P. is defined as the mean pressure, which, if imposed on the pistons uniformly from the top to the bottom of each power stroke, would produce the net work of the cycle.

In a cycle net work done=heat added – heat rejected.

Therefore,

W=Cp(T3T2)Cv(T4T1) (8.15)

image (8.15)

Again, a change in volume,

v1v2=v1(1v2v1)=RT1P1(11rc)=(CpCv)T1P1(rc1rc)=Cv(γ1)T1P1(rc1rc) (8.16)

image (8.16)

Using the values from Eq. 8.15 and Eq. 8.16,

M.E.P.=Wv1v2=Cp(T3T2)Cv(T4T1)Cv(γ1)T1P1(rc1rc)=P1rc(rc1)1(γ1){γ(T3T2)T1(T4T1)T1} (8.17)

image (8.17)

Inputting the values from Eq. 8.7, Eq. 8.9, and Eq. 8.11 into Eq. 8.17

M.E.P.=P1rc(rc1)1(γ1){γ(rcγrerc(γ1))(rcre)γ+1}

image

or,

M.E.P.=P1rc(rc1)(γ1){γrc(γ1)(rv1)(rvγ1)} (8.18)

image (8.18)

Example 8.1

1 kg of air at 298 K temperature and 101.3 kPa pressure is taken through the ideal Diesel cycle of Figure 8.1. The compression ratio, rc, of the cycle is 15 and the heat added is 1900 kJ. Find the ideal thermal efficiency and M.E.P. of this cycle.

(Assume R=0.287 kJ/(kg.K), Cp=1.005 kJ/kg/K, and γ=1.4 for air and conversion; factors: 1 kJ=102 m.kg and 1 kPa=102 kg/m2.)

Solution: For the unit mass flow the initial volume of the air is

v1=RT1P1=0.287*298101.3=0.844m3

image

After compression

T2=T1*rc(γ1)=298*150.4=880.34K

image

and

v2=0.84415=0.056m3

image

With heat added

Qin=Cp(T3T2)

image

or,

1900=1.005(T3880.34)

image

hence,

T3=2770.89K

image

The expansion ratio is

re=v4v3=v1v3=v1v2*v2v3=v1v2*T2T3=15*880.342770.89=4.766

image

hence,

T4=T31re(γ1)=2770.8914.7660.4=1483.74K

image

With heat rejected

Qout=Cv(T1T)4=1.0051.4(298.001483.74)=851.2kJ/kg

image

Net work

W=Qin+Qout=1900851.2=1048.8kJ/kg

image

Therefore, the ideal thermal efficiency is

ηth=1048.81900.0*100=55.2%

image

and

M.E.P.=1048.8(0.8440.056)=1330.96kPa=1.331MPa

image

An alternative solution of ηth using Eq. 8.12:

ηth=111.4(4.7661.4151.4)(4.7661151)=111.4(0.11240.0226)(0.20980.0667)=10.08980.2003=0.5518,i.e.55.18%

image

Example 8.2

Considering the unit mass flow of the fluid determine the thermal efficiency, the final temperature of fluid after expansion, and the compression ratio of an air-standard Diesel cycle, in which the inlet pressure and temperature are 100 kPa and 288 K, respectively. The heat addition to the cycle is 1045.9 kJ and the final temperature after heat addition is 2073 K. (Given Cp=1.005 kJ/kg/K, Cv=0.718 kJ/kg/K, and γ=1.4 for air.)

Solution: From Eq. 8.1, 1045.9=1.005(2073 – T2)

Hence, T2=1032.3 K

From Eq. 8.6, rc0.4=1032.3/288

Wherefrom, rc=24.32

From Eq. 8.8 and Eq. 8.13, the cut-off ratio is

rv=2073/1032.3=2.008

image

From Eq. 8.11

T4=288*2.0081.4=764.3K

image

Thus, from Eq. 8.14, the thermal efficiency of the air-standard Diesel cycle is

ηth={124.320.41.4(2.0081.412.0081)}*100=(115.0181.6541.008)*100=67.3%

image

8.2.2 Otto cycle

The Otto cycle was developed by German engineer Nikolaus Otto in 1876. This cycle is very similar to the Diesel cycle, except that the Otto cycle forms the basis of a spark-ignition (S.I.) engine, which requires a spark to begin combustion of fuel. Figure 8.8 represents a P-V diagram of an Otto cycle.

image
Figure 8.8 P-v Diagram of Otto cycle. Source: Fig. 12.14, Page 245, Gas Power Cycles, [6].

As in an ideal Diesel cycle four distinct processes are also followed in the Otto cycle: reversible adiabatic compression, addition of heat at constant volume, reversible adiabatic expansion, and rejection of heat at constant volume as follows:

i. Air enters the cycle at point 1 when compression starts and it ends at point 2. The air is compressed in an isentropic process through a volume ratio v1/v2, known as the compression ratio rc (the ratio of the volume of the working fluid before the compression process to its volume after).

ii. Heat addition starts at point 2 and ends at point 3. A quantity of heat Qin is added at constant volume, and the working fluid temperature rises.

iii. The isentropic expansion process starts at point 3 and it ends at point 4 to the original volume.

iv. The heat Qout is rejected at constant volume from point 4 to point 1. Air gets cooled and the working fluid temperature goes down at a constant volume until the cycle is completed.

Stages of above four processes are described below:

8.2.2.1 Compression

In this part of the cycle as the piston moves from the TDC to the BDC, the inlet valve is open and the exhaust valve is closed. A fresh charge of fuel-air mixture is drawn into the cylinder (Figure 8.9). As the inlet valve closes the piston moves from the BDC upward to the TDC, and in the process compresses the fuel-air mixture (Figure 8.10). In this stroke work is contributed to the air. In an ideal Otto cycle, this compression is considered to be isentropic.

image
Figure 8.9 Induction of air in Otto cycle. Source: http://enx.org/resources/beb.
image
Figure 8.10 Compression of air in Otto cycle. Source: http://enx.org/resources/beb.

8.2.2.2 Combustion (Figure 8.11)

In this stage heat is added to the fuel-air mixture by combustion of fuel when the piston is at the TDC position. Combustion is initiated by a spark with the help of a spark plug, which is the most important and fundamental difference between the Otto cycle and the Diesel cycle. The piston during heat addition remains at a standstill and hence the process of heat addition is known as isochoric (constant volume).

image
Figure 8.11 Combustion on Otto cycle. Source: http://enx.org/resources/beb.

8.2.2.3 Expansion (Figure 8.12)

While tending to expand, the rapidly burning fuel-air mixture generates high pressure thus forcing the piston to travel downward from the TDC to the BDC in the cylinder. It is in this stage that the cycle contributes its useful work, rotating the engine crankshaft. In an ideal Otto cycle this process is isentropic.

image
Figure 8.12 Expansion in Otto cycle. Source: http://enx.org/resources/beb.

In an engine, the cooling process involves exhausting the gas from the engine to the environment and replacing it with fresh air. Since this happens when the piston is at the TDC position in the cycle and remains immobile, this process is also isochoric (no change in volume).

8.2.2.4 Thermal efficiency [5]

The thermal efficiency of the Otto cycle can be expressed by dividing external work by heat input to the working fluid as follows:

ηth=Qin+QoutQin=1+QoutQin (8.19)

image (8.19)

Hence, considering the unit mass flow of the fluid and assuming constant specific heats for the air, for constant volume heating and cooling we can use

ηth=1+Cv(T1T4)Cv(T3T2)=1T4T1T3T2 (8.20)

image (8.20)

We know that for ideal gas Pv=nRT and γ=Cp/Cv and for adiabatic condition Pvγ=constant. Using Figure 8.8 v3=v2 and v4=v1. Hence,

T2T1=(P2P1)γ1γ=(v1v2)(γ1) (8.21)

image (8.21)

or,

T1=T2(v1v2)(γ1) (8.22)

image (8.22)

Again,

T4T3=(P4P3)γ1γ=(v3v4)(γ1) (8.23)

image (8.23)

or,

T4=T3(v2v1)(γ1)=T3(v1v2)(γ1) (8.24)

image (8.24)

Using the values of Eq. 8.22 and Eq. 8.24 in Eq. 8.20 and expressing the compression ratio as rc=v1/v2 the thermal efficiency of the Otto cycle changes to

ηth=11(v1v2)(γ1)=11rc(γ1) (8.25)

image (8.25)

where

ηth=Thermal efficiency

Qin=Heat added to the working fluid

Qout=Heat rejected from the working fluid

Cp=Specific heat at constant pressure

Cv=Specific heat at constant volume

Equation 8.25 shows that the thermal efficiency of the Otto cycle depends only on the compression ratio and not on the peak temperature T3.

Comparing Eqs. 8.12/8.14 and Eq. 8.25 it is noted that the formula for the thermal efficiency of the Diesel cycle is more complex than that of the Otto cycle. This is due to the fact that the heat addition in the Diesel cycle is at constant pressure and the heat rejection is at constant volume, while both heat addition and heat rejection in the Otto cycle take place at constant volume. For the same compression ratio the thermal efficiency of the Otto cycle is always greater than that of the Diesel cycle. In practice, however, the Diesel cycle yields higher thermal efficiency because it adopts higher compression ratios than those adopted by the Otto cycle, which is evident from Example 8.3.

Example 8.3

Determine the thermal efficiency, the final temperature after expansion, and the compression ratio of an air-standard Otto cycle for the same problem as given for Example 8.2.

Solution: From Eq. 8.19 and Eq. 8.20, 1045.9=0.718(2073 – T2)

Hence, T2=616.3 K

From Eq. 8.22, rc0.4image=616.3/288=2.14

Therefore, rc=6.7

From Eq. 8.24, T4=2073/6.70.4=968.7 K

From Eq. 8.25 ηth=(116.70.4)*100=53.3%image

Comparing the results of Example 8.2 and Example 8.3 it is clear that the thermal efficiency of the air-standard Diesel cycle (67.3%) is much higher than that of the Otto cycle. This is because the compression ratio of the Diesel cycle (24.3) greatly exceeds the compression ratio of the Otto-cycle, which is 6.7.

In practice many reciprocating engines adopt dual or mixed cycles as shown in Figure 8.13, where heat is added in part in the constant volume process and the rest in the constant-pressure process.

image
Figure 8.13 Dual or mixed cycle. Source: Fig. 12.17, Page 247, Gas Power Cycles, [6].

To find out the thermal efficiency of the dual cycle, as before, let us assume constant specific heats of air and consider unit mass flow of the fluid. If the compression ratio between point 2 and point 3 is expressed as rp=P3/P2 and as before the compression ratio between point 1 and point 2 as rc=v1/v2 and the cut-off ratio between point 4 and point 3 as rv=v4/v3, then the efficiency of this cycle could be expressed as follows:

ηth=1+QoutQin=1+Cv(T1T5)Cp(T4T3)+Cv(T3T2)=1+T1T5γ(T4T3)+(T3T2) (8.26)

image (8.26)

Converting Eq. 8.26 from temperature to compression-ratio, pressure-ratio, and cut-off ratio

ηth=11rc(γ1)rprvγ1(rp1)+γrp(rv1) (8.27)

image (8.27)

8.3 Design [2,4]

The fundamental decision regarding the design of a diesel-generating station starts with the desired power output. Once the power output is finalized the next step is to decide whether to select a two-stroke-cycle or a four-stroke-cycle diesel engine. Large, double-acting low-speed (80–200 rpm) power engines are the two-stroke type. A four-stroke-cycle should be preferred for lightweight, high-speed (1000–2500 rpm) engines. Medium-speed (200–1000 rpm) engines may operate on both cycles.

The individual parts of a low-speed, two-stroke engines are comparatively heavy, while the parts of four-stroke engines are much lighter. Two-stroke engines are equipped with fewer cylinders essentially there are less moving parts. Thus, maintenance cost of two-stroke engines is usually lower than that of medium or high speed engines. For the same output height of engine room of a four-stroke engine is lower than the height of engine room required by a two-stroke engine.

The lubrication of the piston rings in four-stroke engines is better than that in two-stroke engines. The specific lubricating oil consumption of a two-stroke engine instead is lower than that of a four-stroke engine.

Low-speed engines are generally built with horizontal cylinders. For higher speeds vertical cylinders are preferred.

The rotational speed of the engine must always match the frequency of the grid for the power-generating station in all respects. Hence, the speed of the engine shall be calculated as follows:

n=60f/p (8.28)

image (8.28)

where

n=Rotational speed, rpm

f=Frequency of the grid, Hz

p=Number of pair of poles

In a compression ignition engine the pressure of compression must be high enough, typically between 11.5:1 and 22:1, to ensure ignition at any conditions. The approximate compression pressure ranges from 2.8 MPa to 4.8 MPa. A higher compression ratio yields higher thermal efficiency or higher power output, but results in higher stress on working parts.

Another factor that influences the design is how many cylinders of the engine need to be considered. Once the number is known, the bore (d) and stroke (l) of the engine can be determined. The ratio of the stroke to the bore (l/d) generally varies between 0.9 and 1.9. Higher values of l/d up to as high as 2.5 or so may be chosen for opposed piston two-stroke engines.

Knowing all the data as explained above the expected power output of the designed unit may be determined using Eq. 8.29:

W=plan/333.5 (8.29)

image (8.29)

where

W=Power output, kW

p=Compression pressure, MPa

l=Stroke, m

a=Inner cross-sectional area of the cylinder, cm2

n=Rotational speed, rpm

Thereafter, it should be determined whether the expected output conforms to the desired output. (Note: 1 MPa=10.2 kg/cm2, 1 hp=0.746 kW=76.0 kg.m/s.)

8.4 Equipment and Accessories

Depending on its size, the engine of a Diesel-generating station comprises some or all of the following equipment and accessories:

i. Fuel injection equipment

ii. Piston

iii. Governor

iv. Starting system

v. Intake silencer

vi. Air filters

vii. Exhaust mufflers

viii. Supercharger

8.4.1 Fuel injection equipment

Correct functioning of the fuel injection equipment begets efficient combustion in a Diesel engine. Fuel is injected through nozzles at adequate pressure for proper atomization of fuel. The nozzle area should be small enough to allow fuel intake for complete vaporization without remaining in suspension as droplets. Depending on the size of the engine the atomizing pressure developed by the fuel injection pump/s may vary from 40 MPa to 100 MPa. The atomized fuel thus obtained mixes with pressurized air in the correct proportion in the combustion chamber so that complete combustion is ensured. This equipment ensures supply of metered quantity of fuel. The fuel injection equipment also controls fuel-air mixing rate according to the required power output. This equipment needs to be designed with high standards to limit gaseous emissions, noise, and smoke in compliance with the local environmental regulations.

8.4.2 Piston

In all internal combustion engines the design of a piston is very critical since it is the most vulnerable member. It is subjected to two prone attacks: one from the mechanical loading resulting from the maximum cylinder pressure and another thermal loading due to the heat of compression. Gas loads are transmitted to the crank shaft with the help of the piston. The design of a piston is influenced by the following parameters:

i. Engine rating

ii. Duty cycle

iii. Quality of fuel

iv. Maximum allowable weight, etc.

The sealing of gas and oil in a cylinder is provided by piston rings.

8.4.3 Governor

Like any rotary power-generating device every engine of a Diesel-generating plant is invariably provided with a governor to maintain the speed of the engine automatically by regulating the flow of fuel to meet the desired power output. A governor may be a hydro-mechanical or electronic type.

8.4.4 Starting system

To start a Diesel engine from standstill sufficient torque to the crankshaft has to be provided from the outside to rotate the engine at the desired speed, which is essentially done by a starting gear. The most common starting gear is the manual type, e.g., hand cranking or a rope and pulley system. It is simple, does not require an external source to break the starting torque, and its costs are low. The use of manual starting gear, however, is restricted to low-speed, small engines. The most commonly used starting gears for medium-speed and high-speed engines are electric. They consist of DC motors and battery packs to supply electric energy. In medium-speed and high-speed engines another starting gear that is widely used is pneumatic. An air motor or a power cylinder is supplied with pressurized air from an air compressor, which facilitates breaking the starting torque.

8.4.5 Intake silencer

When intake air from atmosphere rushes through the intake valve with high velocity it produces a hissing noise, which is intolerable to human ears. This noise is reduced by providing a silencer at the intake manifold.

8.4.6 Air filters

A filter is installed at the air intake to prevent wear of pistons, piston rings, cylinder, valves, etc., by airborne suspended impurities. An air filter also assists in the attenuation of intake noise.

8.4.7 Exhaust mufflers

When leaving the exhaust pipe exhaust gases produce an unbearable howling noise, which is much louder sound than intake noise. Hence, it is imperative to provide different means, e.g., expansion of exhaust gas, or change of direction of flow of gas, or cooling of gas with water, etc., at the exhaust system – for abatement of howling noise.

8.4.8 Supercharger

Supercharging of an engine can be defined as the artificial raising of the intake pressure of air above atmospheric pressure. The pressure is raised by the use of a compressor. If the compressor is driven by a turbine that operates on the exhaust gases from the engine it is called a turbocharger (Figure 8.14).

image
Figure 8.14 Turbocharging of an engine. Source: TURBOCHARGER, http://www.mechanicalengineeringblog.com/tag/turbo-lag/.

The objectives of supercharging are to:

1. Increase the power output of the engine

2. Maintain the power output regardless of the altitude

3. Increase the air-fuel ratio, and thereby improve the thermal efficiency of the engine

8.5 Diesel Engine Systems

For smooth trouble-free operation a Diesel engine is equipped with some or all of following systems. The necessity of each system is determined by the engine’s size, location of installation, and operating environment:

i. Fuel Oil System

ii. Lubricating Oil System

iii. Cooling Water System

iv. Compressed Air System

v. Firefighting System

8.5.1 Fuel oil system (Figure 8.15)

The fuel oil used in a Diesel engine should be completely free from water and mechanical impurities. Solid and liquid contaminants are cleaned before use to prevent damage to fuel pumps and engine components. A diesel engine is capable of burning a wide range of low-quality liquid. It should be ensured that heating of fuel to the required viscosity is carried out without developing thermal cracking. For start-up of a diesel engine either high-speed diesel (HSD) or light diesel oil (LDO) is used. For normal running, a heavier grade fuel oil, e.g., heavy fuel oil (HFO) or low sulphur heavy stock (LSHS), is generally used.

image
Figure 8.15 Fuel oil system.

The fuel oil system deals with oil receipt, storage, treatment, and forwarding of oil to the Diesel engine. Fuel oil may be delivered to a plant by road tankers or railway wagons or if the plant is located near a port through the pipeline from the port. Oil delivered by road tankers or railway wagons is unloaded with the help of unloading pumps equipped with suction strainers. Connection is made with the tankers or wagons through screwed hoses. Pressurized fuel oil from unloading pumps is supplied through the pipeline to bulk fuel oil storage tanks for storing. These storage tanks are usually vertical, cylindrical, cone-roof steel tanks. While storing heavy-grade fuel oil, the minimum temperature in bulk oil storage tanks should be maintained at around 353 K by electric or steam heating to ensure the fluidity of the oil. However, for ensuring the required viscosity of heavy-grade fuel oil at the engine end the minimum temperature should be maintained in the treated oil storage tank at around 393 K.

The fuel system of large diesel engines generally includes the following:

i. Fuel feed or lift pump

ii. Fine filters

iii. High-pressure fuel injection pumps

iv. Injectors

v. High-pressure pipes connecting the injection pumps to the injectors

vi. Low-pressure pipes

The fuel feed pump supplies fuel from the treated oil storage tank/s and delivers it through a fine filter to the high-pressure fuel injection pumps. These pumps transfer oil to the injectors located on each cylinder.

8.5.2 Lubricating oil system (Figure 8.16)

The lubricating oil system of a Diesel engine typically includes an external lube oil circuit. The primary function of this circuit is to filter and cool the circulating oil. It also serves to heat, prime, and scavenge the oil when preparing the diesel engine for starting. An internal lube oil circuit supplies oil to individual units and parts of the diesel engine. The pipelines of internal circuit are inside the engine.

image
Figure 8.16 Lubricating oil system.

The external lube oil circuit in turn is typically divided into two groups, i.e., the main lube oil circuit and the auxiliary lube oil circuit. The main lube oil is either delivered by road tankers with the help of lube oil unloading pumps or downloaded from drums containing lube oil to the Diesel engine main lube oil sump. A lube oil transfer pump delivers lube oil from the lube oil sump through a metal-in-oil detector, oil filter, and oil cooler into a circulating oil tank. When the pressure in the system exceeds the maximum limit a by-pass valve diverts part of the lube oil directly to the circulating tank. The temperature of the lube oil leaving the oil cooler is controlled by adjusting the flow of cooling water through the oil cooler automatically by a thermo-regulator.

The temperature of the lube oil in the circulating oil tank is maintained with the help of an oil pump provided with oil heater, which cuts-in automatically in the event that the oil temperature drops down to 313 K and cuts-out when the temperature rises above 323 K.

A lube oil separator is used to clean the oil circulating in the lubrication system. Oil is drawn by the separator pump, either from the system or from the tank, and after separation it is returned to the circulating tank. A temperature of 328 K or more, as recommended, is maintained in this circuit, if required, with the help of an oil heater.

Oil in the internal lube oil circuit is circulated with the help of an engine-driven internal lube oil pump. This pump draws oil from the circulating tank and delivers it to the engine through an oil filter. Prior to starting the Diesel engine it is primed with oil by the priming pump. The internal circuit is exclusively used for “piston cooling and lubrication of crosshead and crankpin bearing” and “lubrication of camshaft main bearings.” Oil is drained from the pistons and bearings into the Diesel engine sump, from which the scavenge pump takes its suction and delivers oil back to the circulating tank. Separate lube oil pipelines connect to various lubricating points of major and minor accessories, drives, and the turbo-charger.

8.5.3 Cooling water system (Figure 8.17)

The Diesel engine cooling system generally consists of two circuits: the internal cooling circuit, also known as jacket cooling system, and the external cooling circuit. The water circulating along the internal circuit cools the Diesel engine, while the water of the external circuit serves to cool the oil, the water of the internal cooling circuit and the air for supercharging. Distilled or de-mineralized water treated with a corrosion inhibitor is generally used in the inner circuit, while either raw water or filtered water is adopted in the external circuit.

image
Figure 8.17 Cooling water system.

The inner circuit cooling water pump takes water from the Diesel engine sump and circulates water through the engine jacket, jacket water cooler, and the turbo-compressor. From the supply manifolds, water also flows to cool the exhaust manifold sections and the working cylinders. The water from the working cylinders is drained to return manifolds, from which it is directed to the pump suction line, completing the cycle. An expansion tank is connected to the suction side of the pump to ensure initial priming, as well as to ensure reliable functioning of the closed system when the water volume changes due to heating or leakage. An independent water-circulating pump is provided with an electric heater to warm up the engine with hot water, particularly when the engine remains idle. The heater automatically cuts-in when the engine water outlet temperature falls below about 303 K and cuts-out when the temperature exceeds 323 K.

The external cooling circuit is equipped with an outer circuit cooling water pump. This pump draws water from an evaporative mechanical-draft cooling tower sump and directs it through the lube oil cooler and internal cooling circuit water cooler and then returns to the cooling tower with the help of a water transfer pump. Cooling water from this circuit is supplied to air coolers, generator-bearing cooler, and compressor cooling system as well. The amount of water passing through the lube oil cooler is usually determined by a thermo-regulator control unit, to maintain the operating temperature of the oil flowing out of the cooler.

For small capacity engines, the inner circuit cooling water may be cooled by supplying air to a radiator with cooling air fans.

8.5.4 Compressed air system

The starting air of a diesel engine is delivered by the air compressor. The pressurized air is stored in vertically mounted air receivers. During start-up, pressurized air enters the Diesel engine main starting pipeline through the main starting valves to serve bank of cylinders. From the main starting valves air gets into the air distributors as well as into working cylinder-starting valves. Once the diesel engine starts operating on fuel, the starting valve is closed to cut the supply of air.

From the starting air receivers control air is led off through pressure-reducing valve to the oil and water thermo-regulators. This air then regulates the flow of water through the cooler or heat-exchanger by opening or closing the valves.

8.5.5 Firefighting system

In a Diesel power station fire may start accidentally due to short circuiting, ignition of fuel and lubricants or of common combustible materials, e.g., paper, cotton waste, etc. As soon as minor fires are detected portable/semi-portable fire extinguishers are used to extinguish it.

Oil fire is best tackled by a foam-type extinguisher along with a spray water system. The foam provides a blanket over the oil surface and cuts off the oxygen supply, which is essential for supporting combustion.

As an alternative means, sand stored in the bins near the dyke walls of fuel storage tanks can also be used to prevent outbreak of minor fire. Sand is sprinkled evenly on the spillage surfaces using shovels/buckets. Small fires can be handled successfully using sand. Ordinary water is not generally suitable for fighting oil fire, since oil has a tendency to float and spread further.

Electrical fire is fought with carbon dioxide fire extinguishers. Wherever practical, the electric supply to the equipment on fire should be switched off before using the extinguisher. In general, fire due to combustible materials such as cotton waste, paper, timber, etc., is tackled either by soda-acid type fire extinguishers or with water stored in fire buckets. In the event of a big fire, portable/semi-portable extinguishers may not extinguish the fire effectively. In such an event, the central firefighting team should be called as soon as possible.

8.6 Problems

8.1 In an ideal air standard Diesel engine, 1 kg of air is taken from atmosphere at a pressure of 101.3 kPa and temperature of 288 K. Find the ideal thermal efficiency and M.E.P. of this engine and final pressure and temperature after compression.
(Assume γ=1.4, compression ratio rc=15 and expansion ratio re=5.)
Ans.: η=55.1%, M.E.P.=1.34 MPa, P2=4.49 MPa, and T2=851 K

8.2 Referring to Figure 8.6 determine the thermal efficiency of the ideal air standard Otto cycle, if 1 kg of air is taken from atmosphere at a pressure of 101.3 kPa and temperature 298 K. Also find the final pressure and temperature after compression.
(Assume compression ratio rc=10 and γ=1.4.)
(Ans.: η=60.19%, P2=2.54 MPa, and T2=749 K.)

8.3 In an ideal S.I. engine, a charge enters at a pressure of 100 kPa and temperature of 330 K. If the charge is compressed isentropically through a compression ratio of 7:1, determine the temperature and pressure at the end of compression, assuming charge to be (i) pure air and (ii) a mixture of air and fuel.
(Assume γair=1.4, γmixture=1.326.)
(Ans.: T2air=719 K, p2air=1.525 MPa, T2mixture=622 K, p2mixture=1.32 MPa)

8.4 Find the rotational speed of a two-stroke Diesel generator, if the number of poles of the generator is 120.
(Ans.: 25 rpm)

8.5 A Diesel engine is equipped with a cylinder having a bore of 20 cm and a stroke of 35 cm. For a compression pressure of 4.8 MPa, estimate the power output of the engine. The speed of the engine is 50 rpm.
(Ans.: 7.92 kW)

8.6 The bore of a Diesel engine cylinder is 28 cm and its stroke is 50 cm. The pressure and temperature at the end of admission are 101.3 kPa and 363 K, respectively. For a compression curve that follows PV1.34=constant find the pressure and temperature at the end of compression, if the clearance volume, i.e., the volume at the end of compression, is 9800 cm3.
(Ans.: 680.44 kPa and 588.56 K)

Bibliography

1. Wikipedia, Thermal Efficiency; Four-stroke Engine.

2. Lilly LCR. Diesel engine reference book Butterworth and Co. (Publishers) Ltd 1984.

3. Baumeister T, Marks LS. Mechanical engineers handbook sixth ed McGraw-Hill Book Company, Inc 1958.

4. Maleev VL. Internal combustion engine theory and design McGraw-Hill Book Company, Inc 1945.

5. Wrangham DA. Theory and Practice of Heat Engine. The English Language Book Society; 1962.

6. Rogers GFC, Mayhew YR. Engineering thermodynamics-work and heat transfer English Language Book Society and Longmans, Green and Co. Ltd 1967.

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