EE 3278Engineering Thermodynamics

Chapter 1: Gas Power Cycles

Introduction and basic considerations

Introduction and basic considerations

• Devices or systems used to produce a net power output engines

• Actual cycle vs. Ideal cycle– Actual cycles are difficult to

analyze– Friction, insufficient time for

equilibrium conditions, i.e. irreversibilities

The Carnot Cycle

The Carnot Cycle

• The most efficient cycle that can be executed between a heat source at temperature TH and a sink temperature TL

• Can be executed in closed systems (a piston-cylinder device) or steady-flow systems(utilizing turbines and compressors)

• Working fluid can be gas or vapour

The Carnot Cycle

The Carnot Cycle

• 12: isothermal heat addition• 23: isentropic expansion• 34: isothermal heat rejection• 41: isentropic compression• Thermal efficiency for Carnot cycle

ηth = 1 −

The Carnot Cycle

Example

Show that the thermal efficiency of a Carnot cycle operating between the temperature limits of TH and TL is solely a function of these two temperatures.

Reciprocating Engines

Reciprocating Engines

Nomenclature for reciprocating enginesDisplacement and clearance volumes of a reciprocating engine.

Reciprocating Engines

Compression ratio, r

푟 =푉푉 =

푉푉

Reciprocating Engines

Mean effective pressure, MEP

MEP used as a parameter to compare the performances of reciprocating engines of equal size; larger value of MEP delivers more net work per cycle and thus performs better

MEP =푊

푉 − 푉=

푤푣 − 푣

The Otto Cycle

Reciprocating Engines: Otto Cycle• The ideal cycle for spark-ignition reciprocating

engines• Named after Nikolaus A. Otto who built a

successful four-stroke engine in 1876

Reciprocating Engines: Otto Cycle

1-2: Isentropic compression2-3: Constant-volume heat addition3-4: Isentropic expansion4-1: Constant-volume heat rejection

First law analysis on Otto Cycle (closed cycle):- Energy balance:

also,

- Thermal efficiency

Processes 1-2 and 3-4 are isentropic, and 푣 = 푣 and 푣 = 푣 . Thus,푇푇

=푣푣

=푣푣

=푇푇

푞 − 푞 + 푤 − 푤 = ∆푢

푞 = 푢 − 푢 = 푐 푇 − 푇 and 푞 = 푢 − 푢 = 푐 푇 − 푇

휂 , =푤푞

= 1 −푞푞

= 1 −푇 − 푇푇 − 푇

= 1 −푇 푇

푇 − 1

푇 푇푇 − 1

∴ 휂 , = 1 − where 푟 = = = and 푘 =

Reciprocating Engines: Otto Cycle

Reciprocating Engines: Otto CycleExample

An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 100 kPaand 17 °C, and 800 kJ/kg of heat is transferred to air during the constant-volume heat-addition process. Utilizing the cold-air standard assumptions, determine (a) the maximum temperature and pressure that occur during the cycle, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. Take 푐 = 0.718kJ/kgK.

The Diesel Cycle

Reciprocating Engines: Diesel Cycle• The ideal cycle for CI reciprocating engines• CI engine: first proposed by Rudolph Diesel in

the 1890s

Reciprocating Engines: Diesel Cycle

Reciprocating Engines: Diesel CycleFirst law analysis of Diesel cycle (closed system)

and

Therefore, the thermal efficiency;

Defining cutoff ratio, 푟 = = ;

푞 − 푤 , = 푢 − 푢 →푞 = 푃 푣 − 푣 + 푢 − 푢= ℎ − ℎ = 푐 푇 − 푇

−푞 = 푢 − 푢 → 푞 = 푢 − 푢 = 푐 푇 − 푇

휂 , =푤푞

= 1 −푞푞

= 1 −푇 − 푇

푘 푇 − 푇= 1 −

푇 푇푇 − 1

푘푇 푇푇 − 1

휂 , = 1 −1

푟푟 − 1푘 푟 − 1

Reciprocating Engines: Diesel CycleExample

An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and 27 °C. Utilizing the cold-air-standard assumptions, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure

ReferencesCengel, Y. A. & Boles, M. A. (2011). Thermodynamics: An Engineering Approach, 7th edition, New York: McGraw-Hill

Eastop, T. D. & McConkey, A. (1993). Applied Thermodynamics for Engineering Technologists, 5th edition, Harlow: Pearson Education Limited.