Mechpb21044relerpr__unit 3 First Part Ic Engine Study Material.pdf.pdf

IC ENGINES

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1. Introduction Heat engine (Thermal engine) is a machine for converting heat, developed by burning fuel into useful work. It can be said that heat engine is equipment which generates thermal energy and transforms it into mechanical energy. Heat engines can be broadly classified into two categories

(i) External combustion engine: An engine in which combustion of fuel takes place outside the engine cylinder is called external combustion engine. These engines are generally called EC engines. Ex: Steam engines, steam turbines, closed cycle gas turbine etc. (ii) Internal combustion engine: An engine in which combustion of fuel takes

place inside the engine cylinder is called internal combustion engine. These engines are generally called IC engines. Ex: Petrol engine, diesel engine, gas engine etc.

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Advantages of I.C Engines over E.C Engines •

High efficiency

•

Simplicity

•

Compactness

•

Light Weight

•

Easy Starting

•

Comparatively Lower Cost

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2. Classification of I.C. Engines (i) According to the type of fuel used: •

Petrol engines: In this type of engines, the fuel used is petrol.

•

Diesel engines: In this type of engines, the fuel used is diesel.

•

Gas engines: In this type of engines, the gaseous fuels like natural gas, biogas, LPG is used.

•

Bi-fuel engines (Bio-fuel): These engines use a mixture of two fuels. Examples: Mixtures of Diesel and Natural gas, Mixture of Diesel and Neem oil.

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4- Stroke Engine

2-Stroke Engine

(ii) According to the number of strokes per cycle: • 4-stroke

engine: In this type of engines, the working cycle is completed in four different strokes.

• 2-stroke

engine: In this type of engines, the working cycle is completed in two different strokes.

(iii)According to the method of ignition: • Spark

ignition engine (S.I. Engine): In this type of engines, fuel is ignited by an electric spark generated by a spark plug.

• Compression

ignition engine (C.I. Engine): In this type of engines, the fuel gets ignited as it comes in contact with the hot compressed air.

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(iv) According to the cycle of combustion: • Otto

cycle engine: In this type of engines, combustion of fuel takes place at constant volume.

• Diesel

cycle engine: In this type of engines, combustion of fuel takes place at constant pressure.

• Duel

combustion engine: In this type of engines, combustion of fuel first takes place at constant volume and then at constant pressure.

(v) According to the number of cylinders: • Single

cylinder engine: This type of engines consists of only one cylinder.

• Multi

cylinder engine: This type of engines consists of 2, 3, 4, 6 or 8 cylinders.

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(vi) According to the arrangement of cylinders • Vertical

engine: In this type of engines, the cylinder is arranged in a vertical position.

• Horizontal

engine: In this type of engines, cylinder is arranged in horizontal position.

• Inline

engine: In this type of engines, cylinders are arranged in-line.

• Radial

engine: In this type of engines, cylinders are arranged along the circumference of a circle.

• V-engine:

In this type of engines, combination of two inline engines equally set an angle.

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Radial Engine

V Engine

Inline Engine

(vii) According to the method of cooling: • Air

cooled engine: In this type of engines, the heated cylinder walls are cooled by continuous flow of air.

• Water

cooled engine: In this type of engines, water is used for cooling the heated cylinder walls.

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3. Parts of I.C. Engine

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(i) Cylinder: A cylindrical vessel in which the fuel is burnt and the power is developed. It is considered as heart of the engine. The primary functions of cylinder is •

To contain the working fluid under pressure.

•

To guide the piston while reciprocating inside the cylinder.

ii) Cylinder head: The top end of the cylinder is closed by a removable component called cylinder head. The cylinder head consists of two valves inlet valve and exhaust valve, or the other components like sparkplug, or fuel injector. (iii) Piston: A cylindrical shaped component that fits perfectly inside the engine cylinder. The primary functions of piston include, •

To compress the charge (fuel) during the compression stroke.

•

To receive the force impulse produced by the combustion of fuel, and to transmit this force to the crankshaft through the connecting rod.

•

Act as a guide (supporting member) for the upper end of the connecting rod.

•

Serves as carrier of the piston rings that are used to seal the combustion chamber from the crankcase.

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(iv) Piston Rings: The rings placed in the grooves cut towards top of the piston are called Piston Rings. The piston rings are of two types; compression rings and oil rings.  Compression rings: The compression rings press hard with the cylinder walls forming a tight seal between the piston and the cylinder. This prevents escaping of the high pressure gases into the crankcase.  Oil rings: The function of oil rings is to extract the lubricating oil from the cylinder walls and send it back to oil sump through the holes provided on the piston.

(v) Connecting rod: The connecting rod is a link that connects the piston and the crankshaft. Its function is to convert the reciprocating motion of the piston into rotary motion of the crankshaft. (vi) Crank: The crank is a lever with one of its end connected to the connecting rod by a pin joint with other end connected rigidly to the crankshaft. The power required for any useful purpose is taken from the crankshaft. (vii) Crank case: It encloses the crankshaft and serves as a sump for the lubricating oil.

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(viii) Valves: The valves are control devices that allow the air/fuel to enter into the cylinder and also to discharge the burnt gases to atmosphere. There are two valves. (a) Inlet valve

(b) Exhaust valve

(a) Inlet valve is the one through which fresh charge (air and fuel or air) enters into the cylinder. (b) Exhaust valve through which the burnt gases are discharged out of the cylinder. These valves are actuated by means of cams driven by the crankshaft. (ix) Cams: It is an element designed to control the movement of both the inlet and exhaust valves. (x) Flywheel: It is a heavy mass of rotating wheel or large disc mounted on the crankshaft and is used as an energy storing device. The flywheel stores energy received during the power stroke and supplies the same during other strokes.

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4. I.C. Engine Terminology

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(i) Bore: The inside diameter of the cylinder is called Bore.

(ii) Top dead center (TDC): The extreme position of the piston near to the cylinder head is called top dead center or TDC. (iii) Bottom dead center (BDC): The extreme position of the piston nearer to the crankshaft is called bottom dead center or BDC. (iv) Stroke: It is the linear distance travelled by the piston from the TDC to BDC or to TDC.

BDC

(v) Clearance volume (𝑽𝑪 ): It is the volume of cylinder above the top of the piston, when the piston is at the TDC.

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(vi) Swe pt volume or Stroke volume (𝑽𝑺 ): It is the volume swept by the piston as it moves from BDC to TDC or TDC to

BDC.

(vii) Compression ratio(𝑹𝑪): The ratio of the total cylinder volume to the clearance volume is called Compression ratio. Total cylinder volume = Stroke volume (𝑉𝑆) + Clearance volume (𝑉𝐶 )

𝑉𝑆 + 𝑉𝐶 𝑅𝐶 = 𝑉𝐶

(viii) Piston Speed: The average speed of the piston is called piston speed. Piston speed = 2*L*N Where; L = Stroke length in m. N = Speed of engine in RPM.

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Four-Stroke Petrol Engines • In

Four-stroke engines, piston performs four different strokes to complete all the operations of the working cycle. The four different strokes performed are; Suction stroke Compression stroke

Power stroke / Expansion stroke / Working stroke Exhaust stroke • Each

stroke is completed when the crankshaft rotates by 180°. Hence in a 4-stroke engine, four different strokes are completed through 720° of the crankshaft rotation or 2 revolutions of the crankshaft based on the type of fuel used.

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Note: In Four-stroke engines, opening and closing of valves during different strokes with respect to piston position and the rotation of crank is given in the table below.

Position of the Stroke

Piston Initia l

Inlet

Exhaust

Crank

valve

valve

rotation

Final

TDC

BDC

Open

Close

00 - 1800

BDC

TDC

Close

Close

1800 - 3600

Power/ Working

TDC

BDC

Close

Close

3600 - 5400

Exhaust

BDC

TDC

Close

Open

5400 - 7200

Suction Compressio n

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(a) Suction stroke: • This

stroke starts when the piston is at TDC and about to move downwards.

• During

this cycle inlet valve remains open and exhaust valve remains closed.

• Due

to low pressure created by the downward moving piston, the charge (air-fuel mixture) is drawn into the cylinder.

• At

the end of this stroke the inlet valve closes.

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(b) Compression Stroke

•

During this stroke the compression of fresh drawn charge takes place by the return stroke (BDC to TDC) of piston.

•

During this stroke both inlet and exhaust valves are closed.

•

As the piston moves upwards, the air -petrol mixture in the cylinder is compressed adiabatically. The pressure and temperature of the charge increases.

•

When the piston reaches the TDC (or) just before the completion of compression stroke, the spark plug ignites the charge. The compression ratio in petrol engines ranges from 7:1 to 11:1.

Adiabatic Process: It is process in which there is no heat transfer from the system to the surroundings or vice versa.

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(c) Expansion/Power/working Stroke

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• At

the beginning of the stroke, piston is in TDC and during the stroke piston moves from TDC to BDC. During this stroke both inlet and exhaust valves remain closed.

• The

combustion of fuel liberates gases and these gases start expanding. Due to expansion, the hot gases exert a large force on the piston and as a result the piston is pushed from TDC to BDC.

• The

power impulse is transmitted down through the piston to the crank shaft through the connecting rod. This causes crankshaft to rotate at high speeds. Thus work is obtained in this stroke. Hence, this stroke is also called working stroke. Also gas expands and does work on the piston so this stroke is also called an expansion stroke.

• As the piston reaches the

BDC, the exhaust valve opens. A part of the burnt gases escape through the exhaust valve out of the cylinder due to their own expansion.

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(d) Exhaust stroke: • At

the beginning of the stroke piston is in BDC and during the stroke the piston moves from BDC to TDC.

• During

this stroke inlet valve is closed and exhaust valve is opened.

• As

the piston moves upward, it forces the remaining burnt gases out of the cylinder to the atmosphere through the exhaust valve

• When

the piston reaches the TDC, the exhaust valve closes and this completes the cycle.

• In

the next cycle the piston which is at TDC moves to BDC thereby allowing fresh charge to enter the cylinder and the process continues.

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P-V Diagram

1. 2. 3. 4.

Suction Stroke(A-B) compression Stroke (B-C) Expansion stroke (D-E) Exhaust stroke (E-B & B-A)

7. Four-Stroke Diesel Engine The working principle of a Four-stroke diesel engine is based on theoretical diesel cycle. Hence it is also called diesel cycle engine.

A Four-stroke diesel engine performs four different strokes to complete one cycle. The working of each stroke is shown in the Figure 2.5 and its details are discussed below.

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(a) Suction stroke: • At

the beginning of the stroke piston is in TDC and during the stroke, piston moves from TDC to BDC.

• During

this stroke the inlet valve opens and the exhaust valve will be

closed. • The

downward movement of the piston creates suction in the cylinder and as a result, fresh air is drawn into the cylinder through the inlet valve.

• When

the piston reaches the BDC, the suction stroke completes and this is represented by the line AB on P-V diagram as shown in the figure 2.6

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(b) Compression stroke : • At

the beginning of the stroke piston is in BDC and during the stroke piston moves from BDC to TDC.

• During

this stroke both inlet and the exhaust valves are closed.

• As

the piston moves upwards, air in the cylinder is compressed to a high pressure and temperature. The compression process is adiabatic in nature and is shown by the curve BC in P-V diagram.

•

At the end of the stroke, the fuel (diesel) is sprayed into the cylinder by fuel injector. As the fuel comes in contact with the hot compressed air, it gets ignited and undergoes combustion at constant pressure. This process is shown by the line CD on PV diagram. At the point D fuel supply is cutoff.

• The

compression ratio ranges from 16:1 to 20:1.

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(c) Power stroke / Expansion stroke/ Working stroke : • At

the beginning of this stroke, piston is in TDC and during the stroke, piston moves from TDC to BDC.

• During

this stroke both inlet and the exhaust valve remain closed.

• As

combustion of fuel takes place, the burnt gases expand and exert a large force on the piston. Due to this, piston is pushed from TDC the BDC. The power impulse is transmitted down through the piston to the crank shaft through the connecting rod. This causes the crankshaft to rotate at high speeds. Thus work is obtained in this stroke.

• The

expansion of gases is adiabatic in nature and this is shown by the curve DE on P- V diagram. When the piston reaches the BDC, the exhaust valve opens. A part of burnt gases escapes through the exhaust valve out of the cylinder due to self expansion. The drop in pressure at constant volume is shown by the line EB on P-V diagram.

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(d) Exhaust stroke: • At

the beginning of the stroke piston is in BDC and during this stroke, piston moves from BDC to TDC.

• During

this stroke the inlet valve is closed and the exhaust valve is

opened. • As

the piston moves upward, it forces the remaining burnt gases out of the cylinder through the exhaust valve. This is shown by the line BA on P- V diagram. When the piston reaches the TDC the exhaust valve closes. This completes the cycle.

In the next cycle the piston which is at the TDC moves to BDC thereby allowing fresh air to enter into the cylinder and the process continues.

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10.Petrol Engine Vs Diesel Engine

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8. Two-Stroke Engines In a 2-stroke engine, ports are present in the cylinder in place of valves. The ports are the openings in the cylinder opened and closed by the movement of piston within the cylinder. There are three ports, namely

• • •

Inlet port: Through which admitting of charge into the crankcase takes place. Transfer port: Through which the charge is transferred from the crankcase to the cylinder.

Exhaust port: Through which the burnt gases are discharged out of the cylinder.

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In a Two-stroke engine, piston performs two different strokes or crankshaft completes one revolution to complete all the operations of the working cycle. In these engines there are no suction and exhaust strokes, instead they are performed while the compression and power strokes are in progress. Based on the type of fuel used, Two-stroke engines are classified as; 1. Two- stroke petrol engine. 2. Two- stroke diesel engine.

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11. Two stroke Vs Four stroke I.C. Engine

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TWO-STROKE ENGINES In a 2-stroke engine, ports are present in the cylinder in place of valves. The ports are

the openings in the cylinder opened and closed by the movement of piston within the cylinder. There are three ports, namely  Inlet port: Through which admitting of charge into the crankcase takes place.  Transfer port: Through which the charge is transferred from the crankcase to the

cylinder.  Exhaust port: Through which the burnt gases are discharged out of the cylinder.

In a Two-stroke engine, piston performs two different strokes or crankshaft completes one revolution to complete all the operations of the working cycle. In these engines there are no suction and exhaust strokes, instead they are performed while the compression and power strokes are in progress. Based on the type of fuel used, Two-stroke engines are classified as; 1. Two- stroke petrol engine. 2. Two- stroke diesel engine.

Two- Stroke Petrol Engine 2-Stroke petrol engine works on the principle of theoretical Otto cycle. The two different strokes performed are first stroke (downward stroke) and second stroke (upward stroke). Position of the

Inlet port

Exhaust port

Transfer port

In TDC

Opens

Closes

Closes

In BDC

Closes

Opens

Opens

piston

a) First Stroke (Downward Stroke) •

At the beginning of this stroke, the piston is in the TDC. At this position, inlet port is opened and hence fresh air petrol mixture enters into the crank case. At this position, compressed air-petrol mixture present in the cylinder in the previous cycle is ignited by the spark generated by the spark plug. The combustion of fuel releases hot gases which increases the pressure in the cylinder. The high pressure gases exert a pressure on the piston and hence the piston moves from TDC to BDC. Thus piston performs power stroke. The power impulse is transmitted from the piston to the crankshaft through the connecting rod. This causes the crankshaft to rotate at high speeds. Thus work is obtained in this stroke.

• As the piston moves downwards, it uncovers the exhaust port and hence burnt gases escape out of the cylinder. As piston moves downwards further, opens the transfer port and the charge in the crank case is compressed by the underside of the piston. The compressed charge from the crankcase rushes into the cylinder through the transfer port. The charge entering the cylinder drives away the remaining exhaust gases through the exhaust port. •

The process of removing the exhaust gases with the help of fresh charge is known as scavenging. The piston is provided with a projection at its top known as 'deflector'. The purpose of providing a deflector is to deflect the fresh charge coming through the transfer port to move towards the top end of the cylinder. By doing this, the fresh charge will be able to drive the entire burnt gases out of the cylinder.

b) Second Stroke (Upward Stroke) •

At the beginning of the stroke, piston is in BDC and it covers the inlet port and stops the flow of fresh charge into the crankcase. During the stroke, piston ascends and move towards TDC. As the piston moves upwards, it closes the transfer port, there by stopping the flow of fresh charge into the cylinder.

•

Further upward movement of the piston closes the exhaust port and actual compression of the charge begins. In the mean time, the inlet port is opened and the upward movement of piston creates suction in the crankcase. Fresh charge enters into the crankcase through the inlet port. The compression of the charge in the cylinder continues till the piston reaches the TDC. This completes the cycle.

Simple calculations in I.C. Engines 1. Indicated Mean Effective Pressure (Pm): It is the mean or average pressure acting on the piston during the power stroke. The indicated mean effective pressure of an engine is obtained from the indicator diagram. The indicated diagram on the P-V diagram, for one cycle at that load, drawn with the help of an indicator fitted on the engine. Indicated mean effective pressure is given by

𝑷𝒎 =

Spring value of the spring used in the indicator S in 𝐛𝐚𝐫/𝐦 Length of the indicator diagram 𝑙 in 𝐦

Net area of the indicator ∗ diagram 𝑎 in 𝐦𝟐 𝑷𝒎 =

𝑺𝒂 bar 𝒍

2. Indicated Power (IP): The total power developed inside the engine cylinder is called indicated power. It is denoted by IP and is expressed in kW (Kilowatts) 𝟏𝟎 𝐤𝐖 𝟔 Where, n = Number of cylinders. Pm = Indicated mean effective pressure in Bar L = Stroke length in m A = Cross-sectional area of the cylinder in m2

𝑰𝑷 = 𝒏𝑷𝒎𝑳𝑨𝑵𝑲

𝝅𝒅𝟐 , 𝟒

𝑨= where d= diameter of cylinder in m N = Speed of crankshaft in rpm K=

.

𝟏 𝟐

for 4-stroke engine

K = 𝟏 for 2-stroke engine

3) Brake Power (BP): The net power available at the crankshaft is called Brake Power. The power available at the crankshaft is measured by applying the brake and is called brake power. 𝟐𝝅𝑵𝑻 𝑩𝑷 = 𝐤𝐖 𝟔𝟎 ∗ 𝟏𝟎𝟎𝟎 Where, N = Speed of engine in R.P.M. T = Torque in Nm Torque is measured by using either belt or rope brake dynamometer. (a) Belt dynamometer Torque (T) = Force * distance 𝑻 = 𝑻𝟏 − 𝑻𝟐 ∗ 𝑹

𝐍𝐦

Where, 𝑻𝟏 = Tension in tight side of the belt in N 𝑻𝟐= Tension in slack side in N 𝑹 = Radius of pulley in m

(b) Rope brake dynamometer Torque (T) = Force * distance T = Effective brake load * drum radius 𝑻 = 𝑾−𝑺 𝑹 Where, 𝑾 = Suspended weight in N 𝑺 = Spring balance reading in N 𝑹 = Radius of the pulley measured to the center of the rope in m 𝑫+𝒅

𝑹= 𝟐 D = Diameter of pulley in m d = Diameter of the rope in m

Note: The brake power developed is always less than the indicated power. This is because the power developed inside the cylinder is transmitted to the crankshaft through the piston, connecting rod, crank etc. hence a fraction of the indicated power developed is lost due to friction of these moving parts.

4) Friction Power (FP): The amount of power lost due to friction of the moving parts inside the engine cylinder is called friction power. Friction power is the difference between indicated power and brake power. It is denoted by FP and expressed in kW. FP = IP –BP kW Where, IP = Indicated Power BP = Brake Power 5) Mechanical Efficiency (𝜼𝒎𝒆𝒄𝒉 ): It is defined as the ratio of Brake power to the Indicated power. 𝜼𝒎𝒆𝒄𝒉 =

𝑩𝑷 *100 𝑰𝑷

6) Thermal efficiency (𝜼𝒕𝒉 ): It is defined as the ratio of power output to the heat supplied by combustion of fuel. 𝜼𝒕𝒉 =

𝑷𝒐𝒘𝒆𝒓 𝒐𝒖𝒕𝒑𝒖𝒕 *100 𝑯𝒆𝒂𝒕 𝒔𝒖𝒑𝒑𝒍𝒊𝒆𝒅

Heat supplied = mf * CV in kJ/sec Where, mf = Mass of fuel in kg/sec CV = calorific value of fuel in kJ/kg

The power output may be indicated power (IP) or Brake power (BP). (a) Indicated Thermal efficiency(𝜼𝑰𝒕𝒉 ): It is defined as the ratio of indicated power to the heat supplied by combustion of fuel. 𝑰𝑷 𝜼𝑰𝒕𝒉 = ∗ 𝟏𝟎𝟎 𝒎𝒇 ∗ 𝑪𝑽

(b) Brake Thermal efficiency(𝜼𝑩𝒕𝒉 ):

It is defined as the ratio of brake power to the heat supplied by combustion of fuel. 𝑩𝑷 𝜼𝑩𝒕𝒉 = ∗ 𝟏𝟎𝟎 𝒎𝒇 ∗ 𝑪𝑽 (7) Brake Specific Fuel Consumption (BSFC):

It is defined as the mass of the fuel consumed in one hour by an engine in developing 1 kW of brake power. This can be expressed as 𝑴𝒂𝒔𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒇𝒖𝒆𝒍 𝒄𝒐𝒏𝒔𝒖𝒎𝒆𝒅 𝒊𝒏 𝒌𝒈/𝒉𝒓 𝑩𝑺𝑭𝑪 = 𝑩𝒓𝒂𝒌𝒆 𝒑𝒐𝒘𝒆𝒓 𝒅𝒆𝒗𝒆𝒍𝒐𝒑𝒆𝒅 𝒊𝒏 𝒌𝑾

𝐤𝐠 / 𝐤𝐖 − 𝐡𝐫

Problems 1. A 4-stroke engine has a piston diameter 250mm and stroke 400mm. The mean effective pressure is 4 bar and speed is 500 rpm. The diameter of the brake drum is 1000mm and the effective brake load is 400N. Find the indicated power, brake power and friction power. Solution: πd2

= 0.049m2;

Area, A=

Stroke, L = 400mm = 0.4m; Speed, N = 500 rpm;

Mean effective pressure, Pm = 4 bar;

Radius of brake drum, R = 0.5m;

Effective brake load, (W - S) = 400N;

Assuming single cylinder engine, n = 1;

For 4-stroke engine K=1/2

4

=

π(0.25)2

Diameter of piston d= 250mm = 0.25m;

4

Diameter of the brake drum, D = 1000mm = 1m;

(a) Indicated power We know that,

10

IP = nPm LANK � 6 � kW

1 10 IP = 1 ∗ 4 ∗ 0.4 ∗ 0.049 ∗ 500 ∗ � � kW 2 6 𝐈𝐈𝐈𝐈 = 𝟑𝟑𝟑𝟑. 𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤

(b) Brake power

BP =

2πNT 60 ∗ 1000

kW

T = (W − S)R = 400*0.5 = 200 Nm BP =

(c) Friction power

2π ∗ 500 ∗ 200 60 ∗ 1000

𝐁𝐁𝐁𝐁 = 𝟏𝟏𝟏𝟏. 𝟒𝟒𝟒𝟒 𝐤𝐤𝐤𝐤

FP = IP – BP FP = 32.67 – 10.47 FP = 22.20 kW ***************************************************************************** 2. The following details refer to a 4-stroke engine. Cylinder diameter = 200mm, Stroke = 300mm, Speed = 300 rpm, effective brake load = 500kg, mean circumference of the brake drum = 400 mm, Mean effective pressure = 6 bar. Calculate (i) Indicated power (ii) Brake power (iii) Mechanical efficiency

Solution: Diameter of piston, d= 200mm = 0.2m;

Area, A =

πd2 4

=

π(0.2)2 4

Mean effective pressure, Pm = 6 bar;

Stroke, L=300mm=0.3m;

=0.0314m2; Speed, N = 300 rpm;

Mean circumference of the brake drum, 2πR = 400 mm; R = 200/π = 0.2/π = 0.06366 m Mean effective load, (W-S) = 500*9.81 = 4905 N; Assuming single cylinder engine, n=1;

For 4-stroke engine K=1/2

(a) Indicated power 10

IP = nPm LANK � 6 � kW

We know that,

1 10 IP = 1 ∗ 6 ∗ 0.3 ∗ 0.0314 ∗ 300 ∗ � � kW 2 6 𝐈𝐈𝐈𝐈 = 𝟏𝟏𝟏𝟏. 𝟏𝟏𝟏𝟏 𝐤𝐤𝐤𝐤

(b) Brake power

BP =

2πNT 60 ∗ 1000

kW

T = (W − S)R = 4905*0.06366 = 312.5 Nm BP =

(c) Mechanical efficiency

2π ∗ 300 ∗ 312.5 60 ∗ 1000

𝐁𝐁𝐁𝐁 = 𝟗𝟗. 𝟖𝟖 𝐤𝐤𝐤𝐤 ηmech =

BP IP

*100

9.8

ηmech = 14.13*100 𝛈𝛈𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦 =69.35%

***************************************************************************** 3) A 4-stroke IC engine running at 450 rpm as bore diameter 100 mm and stroke length 120 mm. The details of the indicator diagram are as follows: Area of the indicator diagram = 4cm2, length of the indicator diagram = 6.5 cm and spring value of the spring used = 10 bar/cm. calculate the indicated power of the engine. Solution: Assuming single cylinder engine, n=1; Bore diameter, d = 100mm = 0.1m;

For a 4-stroke engine, K = 1/2 Area, A=

πd2 4

=

π(0.1)2 4

= 7.85*10-3 m2;

Stroke length = L= 120mm = 0.12m;

S = 10 bar/cm; Area of the indicator diagram, a =

4cm2; length of the indicator diagram, l = 6.5cm Mean effective pressure, Pm =

𝑆𝑆𝑆𝑆

Indicated power

𝑙𝑙

=

10∗4 6.5

= 6.15 bar; N = 450 rpm

10

IP = nPm LANK � 6 � kW

1 10 IP = 1 ∗ 6.15 ∗ 0.12 ∗ 7.85 ∗ 10−3 ∗ 450 ∗ � � kW 2 6 𝐈𝐈𝐈𝐈 = 𝟐𝟐. 𝟏𝟏𝟏𝟏 𝐤𝐤𝐤𝐤

***************************************************************************** 4) A 2-stroke internal combustion engine has a stroke length of 150mm and cylinder diameter 100mm. Its mean effective pressure is 5.4*105 N/m2 and crankshaft speed is 1000 rpm. Find IP. Solution: Assuming single cylinder engine, n=1; L = 150 mm = 0.15m;

For a 2-stroke engine, K = 1

d = 100 mm = 0.1m;

Area, A=

Pm = 5.4*105 N/m2 = 5.4 bar (1 bar = 105 N/m2);

πd2 4

=

π(0.1)2 4

= 7.85*10-3 m2;

N = 1000 rpm;

Indicated power 10

IP = nPm LANK � 6 � kW

10 IP = 1 ∗ 5.4 ∗ 0.15 ∗ 7.85 ∗ 10−3 ∗ 1000 ∗ 1 � � kW 6 𝐈𝐈𝐈𝐈 = 𝟏𝟏𝟏𝟏. 𝟔𝟔 𝐤𝐤𝐤𝐤

***************************************************************************** 5) A single cylinder 4-stroke engine runs at 1000 rpm and has a bore of 115mm and a stroke of 140mm. The brake load is 60N at 600mm radius and 𝛈𝛈𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦 = 𝟖𝟖𝟖𝟖%. Calculate brake

power and mean effective pressure. Solution: For single cylinder engine, n=1; For a 4-stroke engine, K = 1/2; N = 1000 rpm;

d= 115mm = 0.115m;

L = 140mm = 0.14m; Brake load, (W – S) = 60N;

Area, A=

πd2 4

=

π(0.115)2 4

= 0.0103m2;

R = 600mm = 0.6m; ηmech = 80%

(a) Brake power BP =

2πNT 60 ∗ 1000

kW

T = (W − S)R = 60*0.6 = 36 Nm BP =

(b) Mean effective pressure

2π ∗ 1000 ∗ 36 60 ∗ 1000

𝐁𝐁𝐁𝐁 = 𝟑𝟑. 𝟕𝟕𝟕𝟕 𝐤𝐤𝐤𝐤 ηmech = 80 =

BP IP

*100

3.76

*100

IP

𝐈𝐈𝐈𝐈 = 4.7 kW

10 IP = nPm LANK � � kW 6 1 10 4.7 = 1 ∗ Pm ∗ 0.14 ∗ 0.0103 ∗ 1000 ∗ � � kW 2 6 𝐏𝐏𝐦𝐦 = 𝟑𝟑. 𝟗𝟗𝟗𝟗 𝐛𝐛𝐛𝐛𝐛𝐛

***************************************************************************** 6) A 4 cylinder 2-stroke engine develops 26 kW brake power at 2200 rpm. The mean effective pressure is 7 bar and 𝛈𝛈𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦 = 𝟖𝟖𝟖𝟖%. Determine the bore diameter and stroke of the engine, if the stroke length is 1.5 times the bore. Solution: n = 4; Pm = 7 bar; We know that;

K = 1; ηmech= 87%;

BP = 26 kW;

N = 2200 rpm;

L = 1.5d ηmech =

87 =

BP *100 IP

26 IP

*100

𝐈𝐈𝐈𝐈 = 29.88 kW

10 IP = nPm LANK � � kW 6

29.88 = 4 ∗ 7 ∗ 1.5d ∗

πd2 10 ∗ 2200 ∗ 1 ∗ � � kW 4 6

d = 0.0627m

d = 62.74 mm

L = 1.5d = 1.5*62.74 L = 94.11 mm ***************************************************************************** 7) A single cylinder 4-stroke IC engine has a bore of 180mm, stroke of 200mm and a rated speed of 300 rpm. Torque on the brake drum is 200Nm and mean effective pressure is 6 bar. It consumes 4 kg of fuel in one hour. The calorific value of the fuel is 42000 kJ/kg. Determine (i) Brake power (ii) Indicated power (iii) Brake thermal efficiency (iv) Mechanical efficiency. Solution: For single cylinder engine, n=1; For a 4-stroke engine, K = 1/2; πd2 4

π(0.18)2 4

= 0.0254m2;

d = 180mm = 0.18m;

A=

L = 200mm = 0.2m;

N = 300 rpm; Torque, T = 200Nm;

=

Pm = 6 bar; 4

mf = 4kg/hr = 60∗60 = 1.11*10-3 kg/sec;

CV = 42000 kJ/kg

(i) Brake power

2πNT

BP = 60∗1000

BP =

kW

2π ∗ 300 ∗ 200 60 ∗ 1000

𝐁𝐁𝐁𝐁 = 𝟔𝟔. 𝟐𝟐𝟐𝟐 𝐤𝐤𝐤𝐤

(ii) Indicated power

10 IP = nPm LANK � � kW 6 1 10 IP = 1 ∗ 6 ∗ 0.2 ∗ 0.0254 ∗ 300 ∗ � � kW 2 6 (iii) Brake thermal efficiency

ηBth = (iv) Mechanical efficiency

𝐈𝐈𝐈𝐈 = 𝟕𝟕. 𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤

ηBth =

BP ∗ 100 mf ∗ CV

6.28 ∗ 100 1.11 ∗ 10−3 ∗ 42000 𝛈𝛈𝐁𝐁𝐭𝐭𝐭𝐭 = 𝟏𝟏𝟏𝟏. 𝟒𝟒𝟒𝟒%

ηmech =

BP IP

*100

6.28

ηmech = 7.63*100 𝛈𝛈𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦 =82.3%

***************************************************************************** 8. Calculate the brake power output of a single cylinder 4-stroke petrol engine for the following given data. Diameter of brake wheel = 600mm.Brake rope diameter = 30mm. Dead weight = 24kg. Spring balance reading = 4kg, RPM =450. Solution: Diameter of brake wheel, D = 600mm = 0.6m Brake rope diameter, d = 30mm = 0.03m Effective radius, R =

𝐷𝐷 + 𝑑𝑑 2

=

0.6+0.03 2

= 0.315m

Dead weight = 24kg = 24*9.81 = 235.44N Spring balance reading = 4kg = 4*9.81 = 39.24N Speed, N = 450rpm Torque, T = (W – S) * R T = (235.44 – 39.24) * 0.315 T = 61.803 Nm We know that, 2πNT

BP = 60∗1000

BP =

kW

2π ∗ 450 ∗ 61.803 60 ∗ 1000

𝐁𝐁𝐁𝐁 = 𝟐𝟐. 𝟗𝟗𝟗𝟗 𝐤𝐤𝐤𝐤

***************************************************************************** 9. A 4-stroke engine has a piston diameter of 150mm and the average piston speed is 3.5m/sec. Its mean effective pressure is 0.796MPa; find the indicated power of the engine. Solution: Assuming single cylinder engine, n=1; For a 4-stroke engine, K = 1/2; d = 150mm = 0.15m;

A=

πd2 4

=

π(0.15)2 4

= 0.0176m2;

Pm = 0.796 MPa = 0.796 N/mm2 = 0.796*106 N/m2 = 7.96*105 N/m2 = 7.96 bar Average piston speed = 3.5 m/sec

=

3.5 1 60

( )

m/min

Average piston speed = 210 m/min Average piston speed = 2LN m/min 2LN = 210 m/min LN = 105 m/min 10 IP = nPm LANK � � kW 6 1 10 IP = 1 ∗ 7.96 ∗ 105 ∗ 0.0176 ∗ � � kW 2 6 𝐈𝐈𝐈𝐈 = 𝟏𝟏𝟏𝟏. 𝟐𝟐𝟐𝟐 𝐤𝐤𝐤𝐤

***************************************************************************** 10. A 4-stroke petrol engine is running at 2500 rpm. The stroke of the piston is 1.5 times the bore. If the mean effective pressure is 0.915 MPa and the diameter of the piston is 140mm. Find the indicated power of the engine. If the frictional power is 13kW, find the brake power output and the mechanical efficiency. Solution: Assuming single cylinder engine, n=1;

For a 4-stroke engine, K = 1/2;

N = 2500 rpm;

L = 1.5d = 1.5 * 140 = 210mm = 0.21m;

Pm = 0.915 MPa = 0.915*106 N/m2 = 9.15*105 N/m2 = 9.15 bar d = 140mm = 0.14m;

A=

πd2

FP = 13kW

4

=

π(0.14)2 4

= 0.0154m2;

(i) Brake power 10 IP = nPm LANK � � kW 6

1 10 IP = 1 ∗ 9.15 ∗ 0.21 ∗ 0.0154 ∗ 2500 ∗ � � kW 2 6 𝐈𝐈𝐈𝐈 = 𝟔𝟔𝟔𝟔. 𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤 FP = IP – BP

13 = 61.62 – BP BP = 48.62 kW (ii) Mechanical efficiency

ηmech =

BP IP

*100

48.62

ηmech = 61.62*100 𝛈𝛈𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦 =78.9%

***************************************************************************** 11. A 4 cylinder 4-stroke engine running at 1000rpm develops an indicated power of 15 kW. The mean effective pressure is 5*105 N/m2. Find the diameter of the cylinder and the stroke of the piston when the ratio of diameter to stroke is 0.8. Solution: For a 4-stroke engine, K = 1/2;

Number of cylinders, n = 4

Pm = 5*105 N/m2 = 5 bar;

N = 1000rpm

Diameter

L = 0.8 = 1.25d

Stroke

d

= L = 0.8;

d

10 IP = nPm LANK � � kW 6

15 = 4 ∗ 5 ∗ 1.25d ∗

π𝑑𝑑 2 1 10 ∗ 1000 ∗ � � kW 4 2 6

d = 0.09714m d = 97.14mm L = 1.25d

L = 1.25*97.14 L = 121.42mm ***************************************************************************** 12. A 4-stroke petrol engine of 100mm bore and 150mm stroke consumes 1 kg of fuel per hour. The mean effective pressure is 7 bar and its indicated thermal efficiency is 30%. The calorific value of the fuel is 40*103 kJ/kg. Find the crankshaft speed. Solution: Assuming single cylinder engine, n=1;

For a 4-stroke engine, K = 1/2;

d = 100mm = 0.1m;

A=

L = 150mm =0.15m;

Pm = 7 bar;

mf = 1 kg/hr = (1/3600) = 2.77*10-4 kg/sec;

ηIth = 30%;

ηIth =

πd2 4

IP ∗ 100 mf ∗ CV

=

π(0.1)2 4

= 7.85*10-3m2;

CV = 40*103 kJ/kg

30 =

2.77 ∗

IP ∗ 100 ∗ 40 ∗ 103

10−4

IP = 3.324 kW

10 IP = nPm LANK � � kW 6

1 10 3.324 = 1 ∗ 7 ∗ 0.15 ∗ 7.85 ∗ 10−3 ∗ N ∗ � � kW 2 6 N = 483 rpm

*****************************************************************************

Note: Conversion factors / relations 1. Pressure 1Pa = 1N/m2 105N/m2 = 1bar 1MPa = 1*106Pa = 10*105N/m2 = 10bar 1kPa = 1*103Pa = 103N/m2 = 0.01bar 1bar = 105 N/m2 = 105Pa = 0.1MPa

2. Volume 1m3 = 1000 litres 1 litre = 10-3 m3