Ice Lecture 2

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

TERMODYNAMIC AND CYCLING 1. First Law Analysis of Engine Cycle-Energy Balance System boundary

Fuel in Air in

Work out

Engine

Exhaust

Qt

a). Indicated thermal efficiency (η t ). Indicated thermal efficiency is the ratio of energy in the indicated horse power to fuel energy.

ηt = =

ihp fuel hp ihp x 4500 mass of fuel/min x calorific value

b). Mechanical efficiency (η m ) Mechanical efficiency is the ratio of brake horse power (delivered power) to the indicated horse power (power provided to the piston) friction

bhp ηm = ihp

ihp

Engine

bhp

bhp

ihp

Energy in fuel

and fhp = ihp − bhp

Energy lost in exhaust, coolant, radiation etc Energy loss in fiction, pumping etc

7

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

c). Brake thermal efficiency (η tb ). Brake thermal efficiency is ratio of energy in brake horse power to the fuel energy. η tb = =

bhp fuel hp bhp x 4500 mass of fuel/min x calorific value

The brake thermal equals the product of the indicated thermal efficiency ηt and the mechanical efficiency ηm . η tb = η t x η m d). Volumetric efficiency (η V ) ηV =

mass of charge actually indicated mass of charge represented by cylinder volume at intake temperature and pressure condition

e). Specific fuel consumption. The fuel consumption characteristics of an engine are generally expressed in terms of specific fuel consumption in grams per horsepower-hour. Brake specific fuel consumption and indicated specific fuel consumption, abbreviated as bsfc and isfc, are the specific fuel consumptions on the basis of bhp and ihp, respectively. f). Fuel-air (F/A) or air-fuel (A/F) ratio. The relative proportions of the fuel and air in the engine are very important from the standpoint of combustion and efficiency of engine. This expressed either as the ratio of the mass of the fuel to that of the air. Fr =

actual fuel − air ratio stoichiometric fuel − air ratio

Stoichiometric = a chemically correct is mixture that contains just enough air for complete combustion of all fuel. 2. Useful Thermodynamic Relations The following are the useful thermodynamic relations used in the analysis of air standard cycles. a). For ideal gas cycle the working fluid is a perfect gas which follows the law pV = mRT , or pv = RT where p is the pressure, V volume, v specific volume, m mass, R gas constant and T absolute temperature (0Kelvin). 8

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

b). For perfect gas cP − cV =

R J

where cP (= 0,24) is the specific heat at constant pressure and cV (= 0.17) is the specific heat at constant volume. The ratio γ =

cp cV

= 1.4 will be designated by the symbol γ .

c). From the perfect gas law, it can be seen that an isothermal process will follow the relationship

pv = cons tan t d). It is readily shown that for perfect gas the reversible adiabatic or isentropic process will follow the relationship

pv γ = cons tan t e). The definition of enthalpy h is given by the expression

h = u + pv

u + pv u

which for a perfect gas, becomes

h = u + RT f). For a perfect gas internal energy u and enthalpy h are functions of temperature only T2

T2

∆u = ∫ c v dT

∆h = ∫ c p dT T1

T1

g). In a compression process, if p1, V1, and T1 represent the initial conditions p2, V2, and T2 the final conditions are given by

T2  V1   = T1  V2 

n −1

p =  2  p1

  

( n −1) / n

where n is the index of compression. For reversible adiabatic or isentropic compression n = γ. h). For isothermal process of a perfect gas, the change in u and h is zero. Therefore, for both flow and non-flow process

Q = Wisothermal = mRT log

v2 v1

where Q is the heat interchange and W the work done i). The work done in a non-flow polytrophic process is given by

W=

p1 V1 − p 2 V2 mR ( T1 − T2 ) = n −1 n −1 9

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

where m = mass of gas The work transfer during flow process is given by

W=nx

mR ( T1 − T2 ) n −1

j). The heat transfer to any fluid can be evaluated from

Q rev = ∫ Tds = ∫ c n dT where cn = specific heat of the fluid in which subscript n refers to the property which remains constant during the process. k). For any general process, according to the first law of thermodynamics, for non-flow process Q − W = ∆U and for flow process Q − W = ∆H l). For any cycling process

ΣW = ΣQ = Q added − Q rejected = η t x Q added Where the symbol Σ refers to over the cycle and η t is the thermal efficiency. ∴η t =

ΣW Q added THE CARNOT CYCLE (Carnot is a French Engineer)

10

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

During the isentropic process bc and da the heat transfer form or to the working substance is zero. Therefore, heat transfer takes place during isothermal process ab and cd only. Let r = ratio of expansion Vb/Va during process ab = ratio of compression Vc/Vd during process cd If the ratio of expansion and compression are not equal it would be a closed cycle. Now, consider 1 kg of working substance: Heat supplied during process ab, q c − p a v a log e r = RT1 log e r Heat rejected during process cd, q d − p c v c log e r = RT2 log e r Work done = heat supplied – heat rejected = RT1 log e r − RT2 log e r ∴ Thermal efficiency of the Carnot cycle,

ηcarnot =

workdone heat sup plied

=

RT1 log e r − RT2 log e r RT1 log e r

=

T1 − T2 T = 1− 2 T1 T1

=

ΔT Higher temperatur

Carnot cycle on T-s diagram. On T-s diagram the two isothermal processes ab and cd are represented by horizontal lines and two isentropic processes bc and ad by vertical lines. The heat supplied during the isothermal process ab is given by

q 1 = area a b s1 s 2 = T1 (s 2 − s1 ) Similarly, the heat rejected during the isothermal process cd is given by

q 2 = area c d s1 s 2 = T2 (s 2 − s1 ) Hence we have thermal efficiency of Carnot cycle

η carnot = =

T1 ( s 2 −s1 ) − T2 ( s 2 − s1 ) T1 ( s 2 − s1 ) T1 − T2 T = 1− 2 T1 T1 11

Ir. TRI TJAHJONO, MT/INTERNAL COMBUSTION ENGINE

Net work output = (T1 – T2)(s2 – s1) Gross work of expansion = work done during process ab + work done during process bc. For isothermal process Q = W i.e., Wab = Qab = area under line ab on T-s diagram = T1(s2-s1) For isentropic process from b and c Wbc = ub - uc Therefore, for a perfect gas Wbc = c v ( T1 − T2 ) ∴ Work ratio =

( T1 − T2 )( s 2 − s1 ) T1 ( s 2 − s1 ) + c v ( T1 − T2 )

Relative work outputs of various piston engine cycles is given by mean effective pressure (mep or pm), which is defined as the constant pressure producing the same net work output whilst causing the piston to move through the same swept volume as in the actual cycle Let pm = mean effective pressure Vs = swept volume W = net work output per cycle

Then, p m = = Also, p m =

work done per cycle stroke volume W ∫ pdV = Vs Vs area of the indicator diagram length of the diagram

12