Chapter 8 Production of Power from Heat

• Different sources of power, such as solar energy (from sun), kinetic energy

from atmospheric winds and potential energy from tides.

• The most important source of power is the chemical (molecular) energy of fuels and nuclear energy. [Fuel consumption = Heat Engines]

• Despite improvements in equipments design, the efficiency of the

conversion does not approach 100%. (as a consequence of 2-nd law). The efficiency of conventional fossil fuel steam power plants rarely exceeds 35%.

• Efficiency greater than 50% can be reached in combined cycle plants with

dual power generation: • From advanced – technology gas turbines. • From steam power cycles, operating on heat recovered from hot turbine exhaust gases.

• Two types of heat engines:

A. The steam power plant: A large scale heat engine in which: 1. The working fluid H2O, 2. in steady state flow, 3. through a pump, a boiler, a turbine and a condenser in a cyclic process, 4. The working fluid is separated from the heat source, and heat is

transferred a cross “physical boundary” (boiler tube walls).

B. The internal – combustion engine is another form of heat engine. High temperatures are attained by conversion of the chemical energy of a fuel directly into internal energy within the work production device (The combustion products serves as the working medium where heat transfer, like piston-cylinder arrangement). Example: Otto and diesel engines and gas turbines.

SEVERAL COMMON HEAT ENGINES WILL BE ANALYSED IN THIS CHAPTER.

8.1 The steam Power Plant

• The Carnot – engine cycle (sec. 5.2).

It is the most efficient way to produce a work from the flow of heat from high temperature TH to low temperature TC. “It operate reversibly”.

• It consists of two isothermal steps connected by two adiabatic steps. • At TH, heat is absorbed by the working fluid of the engine. • At TC, heat is discarded by the fluid. • The work produced is ⎜W⎜ = ⎜QH⎜ – ⎜QC⎜

• The thermal efficiency is η = 1 - ⎜QC⎟ / ⎜QH⎟ Then, η = 1 – TC / TH (5.8)

Simple steam power plant:

1. Steam is generated in a boiler. 2. Expands in an adiabatic turbine to produce work. 3. The discharge stream from the turbine passes to a condenser. 4. From which is pumped adiabatically back to the boiler.

The net power output = Rate of heat input in the boiler ⎜QH⎟ – Rate of heat rejection in the condenser ⎜QC⎟.

The most useful and easily understood way of comparing engine cycles with the Carnot cycle is the T-S diagram.

Step1-2: Vaporization process in the boiler. Where sat’d liquid water absorbs heat at

constant temperature TH. Step2-3: Reversible and adiabatic expansion of sat’d vapor into the two-phase region to

produce a mixture of sat’d liquid and vapor at TC. (Isentropic expansion represented by a vertical line).

Step3-4: Partial condensation process, where heat is rejected at TC. Step4-1: Takes a cycle back to its origin, producing sat’d liquid at point 1. (Isentropic

compression represented by a vertical line).

The Rankine Cycle Carnot cycle as a reversible cycle could serves as a standard of comparison for actual steam power plants. Practical mechanical problems attend the operation of equipment to carry out steps 2-3 and 4-1. 2-3 Turbines that takes sat’s steam produce an exhaust with high liquid content, which

causes sever erosion. 4-1 Pump that takes in a mixture of liquid and vapor (point 4) and discharges a sat’d

liquid (point 1) is even more difficult. For these reasons, an alternative model cycle is taken as the standard, it is called “Rankine Cycle “.

It is differ from the carnot cycle in: 1. Heating step 1-2, is carried well beyond vaporization to produce a super heated vapor.

(No mixtures, boiler with super heaters) 2. Cooling step 3-4, brings about complete condensation, yielding sat’d liquid to be

pumped to the boiler.

Fig. 8.3 called the Ideal (reversible) Rankine cycle.

Practical Cycle Power plants can be built to operate on a cycle very similar to Rankine cycle, but depart from it only in the irreversibility of the work-producing (2-3 step) and work-requiring (4-1 step).

Lines are no longer vertical but tend in the direction of increasing entropy. For boiler and condenser, ignoring kinetic and potential energy, result of Q = M ΔH (8.1) And Q = ΔH Turbine and pump calculation in details in sec. 7.2 and 7.3. Turbines: η = ΔH / (ΔH)s (7.16) (Range from 0.7-0.8) (ΔH)s = Ws = Rev. and adiabatic, maximum work can be obtained. Read Ex. 7.6. Pumps (Liquids): Ws = (ΔH)s = V (P2-P1) (7.24) Read Ex. 7.10.

Solve Ex. 8.1

8.2 Internal-Combustion Engine

• As we said earlier, in steam power plant the working fluid is separated from the heat source, as a result heat is transferred across “physical boundary” (Boiler tube walls).

• This is a disadvantage, because when heat transferred through walls, the ability of

the walls to stand high temperature and pressure imposes a limit on the temperature of heat absorption.

• On the other hand, in the internal-combustion engine, high temperature is

obtained by conversion of chemical energy of a fuel directly into internal energy with the work-producing device. (Fuel is burn within the engine itself, and the combustion products serves as the working medium, acting for example on a piston in cylinder).

The Otto Engine (The gasoline engine): The most common internal-combustion engine, because it is use in automobiles. It completes a cycle in four strokes of a piston.

0-1 Piston is moving outward draw a fuel/air mixture into a cylinder. 1-2 All valves are closed and fuel/air mixture is compressed.

(Adiabatic- rev. compression) Q = 0 , ⎜Win⎜ = -ΔU21 , ΔS = 0

2-3 The mixture is then ignited and combustion occurs so rapidly that the volume

remains nearly constant while the pressure and temperature rises. (heat addition at constant volume) ⎜Qin⎜ = CV (T3 – T2) , W = 0 , ΔS > 0 3-4 Work is produced. High P and T product of combustion expand.

(Adiabatic- rev. expansion) Q43 = 0 , ⎜Wout⎜ = -ΔU43 , ΔS = 0

4-1 Exhaust valve then opens and the pressure falls rapidly at nearly constant volume. (Heat removed).

1-0 Piston pushes the remaining combustion gases from the cylinder. ⎜Qout⎜ = CV (T4 – T1) , W = 0 , ΔS < 0

For idealized cycle “air-standard Otto cycle”, the thermal efficiency is:

η = ⎜Wnet⎟ / ⎜Qin⎟

η = 1 − r (1/r)γ = 1 − (1/r)γ−1 (8.6)

Where, r = Vc /VD And γ = Cp/CV

The Diesel Engine (The ideal diesel engine):

• In the gasoline engine the fuel/air mixture is compressed (explode) instantaneously on action of spark. The heat addition is instantaneous.

• In the diesel engine, air alone is compressed, then diesel fuel is introduced and

burns. This combustion is slower than for gasoline engine, so the piston moves out during combustion.

• Thus, diesel engine is higher compression ratio causing a higher pressure and

temperature.

• For the same compression ratio, the Otto engine has a higher efficiency than the diesel engine.

• However, the diesel engine can operate at much higher compression ratios than the

Otto engine, which make it more efficient. (pre-ignition limits the comp. ratio in Otto engine).

• With reference to example 8.3 and Fig. 8.10, the diesel engine efficiency:

(8.7)

e = VB /VA

Where, The compression ratio = r = Vc /VD The expansion ratio = r

η = 1 − 1/γ [(1/re)γ − (1/r)γ−1 / 1/re − 1/r]

The Gas - Turbine Engine

• Here, the advantages of internal combustion are combined with those of turbine.

• Turbine: is more efficient (in terms of friction) than the piston-cylinder engine.

• Air is compressed and burned with fuel in the combustion chamber. The higher

temperature of the combustion gases entering the turbine, the higher the efficiency of the unit (i.e, greater the work produced per unit of fuel burned).

• Referring to fig.8.12 the efficiency of this engine:

Where, PB/PA = Compression ratio.

• Metal turbine blades type determines the limiting temperature of the turbine. Now they are using Ceramic turbine blades to retain high temperature.

Read Ex. 8.4

η = 1 − (PA/PB )γ−1/γ