Ali Alhamaly

ME 537: Assignment1

Problem 2.1:

bmep is defined as :

(1)

The displacement volume can be written in terms of the engine volumetric capacity and the compression ratio as:

(2)

(3)

Naturally aspirated diesel engines have higher compression ratio than their naturally aspirated spark-ignition counterparts. For higher compression ratio the value is lower. This indicates that that bmep for same engine size decreases with the increase of the compression ratio. This is the reason why diesel engine has lower bmep than spark-ignition engine.

Maximum torque of the engine occurs at lower speed than the maximum brake power of the engine. At higher speed of the engine, frictional losses become higher as well. This leads to reduction in the brake power per cycle compared to lower speeds. From Eq. 1, we can see that a lower brake power per cycle leads to lower bmep. Bmep is higher at maximum torque because the brake power per cycle at maximum torque is higher compared with the brake power per cycle at maximum rated power of the engine.

Problem 2.3:

Engine in Fig 1-4:

Mean piston speed:

(4)

bmep:

(5)

Specific power:

(6)

Engine in Fig 1-9:

Mean piston speed:

(7)

bmep:

(8)

Specific power:

(9)

Engine in Fig 1-9:

Mean piston speed:

(10)

bmep:

(11)

Specific power:

(12)

Problem 2.9:

Part a)

The mass of the fuel is given by:

(13)

The mass of air is given by:

(14)

The volumetric efficiency can be approximated as:

is density of air at the inlet manifold (after the compressor)(15)

Preliminary gas dynamics analysis shows that

is the pressure after the compressor is the atmospheric pressure is the pressure ratio of the compressor is the isentropic efficiency of the compressor(16)

Using Eq. 16 the volumetric efficiency is:

(17)

Bmep can be given as:

(18)

Using Eq. 18 in Eq. 13 gives:

(19)

The fuel to air ratio is:

(20)

Substituting the value of the volumetric efficiency in Eq. 17 into Eq. 20 gives:

(21)

Eq. 21 is an equation relating the engine inlet pressure to the fuel to air ratio.

Part b)

(22)

Assuming square engine (bore equals the stroke):

(23)

Assuming an eight cylinder engine, then the bore is given by:

(24)

The maximum rated speed is:

(25)

Summary of the design values:

Number of cylinders: 8

Bore: .133 m

Stroke: .133 m

Maximum speed: 2700 RPM

Part c)

Parameter Assumed Value

bmep1200 kPa

.85

.6

.85

43.2 MJ/kg

1.2 kg/m3

2

1.4

Problem 3.5:

The stoichiometric combustion reaction of the fuel is:

(26)

The stoichiometric fuel to air ratio is given by:

y is the H/C ratio = 1.87

(27)

The actual fuel to air ratio is:

(28)

The equivalence ratio is:

(29)

The actual combustion reaction is given by:

(30)

Carbon balance:

(31)

Hydrogen balance:

(32)

Oxygen balance:

(33)

Total number of moles for the dry gas composition:

(34)

Molar fraction of in the dry exhaust mixture:

(35)

Molar fraction of in the dry exhaust mixture:

(36)

Equations (31, 32, 33, 35, and 36) have total of 5 unknowns (a, b, c, d, and ). These equations can be solve to get the value of which is the reciprocal of the equivalence ratio. These equations can be written in matrix form as follows:

(37)

, , (38)

Substituting the values of Eq. 38 into Eq. 37 gives:

(39)

Solution of Eq. 39 gives:

(40)

Problem 3.6:

a) The percentage of fuel chemical energy that becomes brake power:

(41)

b) The percentage of fuel chemical energy that becomes friction power:

(42)

c) The percentage of fuel chemical energy that becomes heat loss:

(43)

d) The percentage of fuel chemical energy that becomes exhaust chemical energy:

(44)

e) The percentage of fuel chemical energy that becomes exhaust chemical energy:

(45)

Problem 3.10:

Part a)

The chemical reaction is:

(46)

The total number of moles of the product can be found through the relations:

(47)

The H/C (y) ratio can be found through the relations:

H/C = 1.6(48)

Part b)

The equivalent ratio can be found through the relations:

(49)

The fuel to air ratio is:

y is the H/C ratio = 1.6

(50)

Part c)

The engine is a diesel engine because it is running at a very low value of equivalence ratio.

Part d)

At maximum load, the engine will run at equivalence ratio of 1. Since this is a diesel engine running at the same speed, then the air mass flow at low equivalence ratio and at stoichiometric condition will be the same. The percentage increase of the fuel flow rate will be then given as:

(51)

The equivalence ratio is limited by temperature and mechanical stresses concerns.

Problem 3.12:

Part a)

The chemical reaction can be written as a summation of three reactions:

+

+

=

=

(52)

The stoichiometric fuel to air ratio is:

(53)

Part b)

The higher heating value of the LPG per mole () is:

(54)

The higher heating value of the LPG per mole () is:

(55)

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