**Chapter 8.**

**Chapter 8.**

**Production of Power from Heat**

**Production of Power from Heat**

**Introduction**

**Introduction**

### **Production of Power **

### **Energy from the sun : Photovoltaic cells **

### **Kinetic Energy from atmospheric wind : windmills **

### **Fossil fuels, atomic fuels **

- Chemical Energy Heat Power (Electrical Work) - Efficiencies are low (35 – 50 %)

### **Fuel cell**

- Chemical Energy Power (Electrical Work) - Greater efficiency (85 %)

**Use of Fossil Fuels**

**Use of Fossil Fuels**

### **Steam Power Plant : Fossil fuel and nuclear**

### **Internal combustion engines **

### **Otto engines**

### **Diesel engines**

### **Gas turbine**

### **Jet engines**

**8.1 Steam Power Plant**

**8.1 Steam Power Plant**

### Simple steam power plant

**Diagram of a real power plant**

**Diagram of a real power plant**

**Steam Plant…**

**Steam Plant…**

**Carnot cycle**

**Carnot cycle**

*H*
*C*

*H*

*T*

*T* *Q*

*W*

### 1 1

### Efficiency increases as

### T

_{H}

### increases T

_{C}

### decreases

### T

### S

**1** **2**

**4** **3** **T**

_{H}**T**

_{C}**Vaporization process in the boiler** **Reversible, adiabatic expansion of **

**saturated vapor into two-phase ** **(turbine) **

**Condensation (condenser)**

**Isentropic compression (pump)**

**Rankine Cycle**

**Rankine Cycle**

### **In a Carnot cycle, several steps are almost impossible ** **for practical reasons**

### **23 : Steams with liquid content causes erosion problems in ** **turbine blades**

### **41 : Pumping of gas-liquid mixture is difficult**

**Carnot vs. Rankine Cycles**

**Carnot vs. Rankine Cycles**

### **Two major differences**

### **Heating step 12 : Heating beyond vaporization**

### **Cooling step 34 : Complete Condensation**

**Rankine Cycle : alternative standard for power plant**

**Rankine Cycle : alternative standard for power plant**

### **Two modification from Carnot cycle**

### **12 : Heating beyond vaporization**

### **34 : Complete Condensation**

### T

### S

**2**

**1**

**3** **4**

**Heating of **
**subcooled liquid **

**(const P)**

**Vaporization at const T **
**and P**

**Superheating of vapor **
**well above the **

**saturation T**

**(Reversible, adiabatic)**
**Expansion **

**(reduced moisture **
**contents)**

**Condensation**
**(Const P, const T)**
**Pumping of sat. **

**liquid to boiler **
**temperature**

Real path due to irreversibility

**Steam Power Plant**

**Steam Power Plant**

### **Turbine (Ch.7)**

### **Pump (Ch.7)**

### **Boiler and Condenser**

**Heat transfer process**

S s

s

### ) H (

### H )

### isentropic (

### W

### W

###

###

###

###

### ) H H

### ( H

### W

_{s}

###

_{3}

###

_{2}

### H ) H ( W

### ) isentropic (

### W

_{S}

s s

###

###

###

###

### ) H H

### ( H

### W

_{s}

###

_{1}

###

_{4}

### H Q

### , H m

### Q

**Example 8.1**

**Example 8.1**

### **Steam generated in a power plant at a pressure of 8,600 kPa and a ** **temperature of 500 **

^{o}**C is fed to a turbine. Exhaust from the turbine ** **enters a condenser at 10 kPa, where it is condensed to saturated liquid, ** **which is then pumped to the boiler.**

**(a) The thermal efficiency of a Rankine cycle**

**(b) The thermal efficiency of a practical cycle if the turbine efficiency **

**and pump efficiency are both 0.75**

**Example 8.1**

**Example 8.1**

**(a)**

8,600 kPa
500 ^{o}C

H_{2} = 3391.6 kJ/kg

10 kPa

H_{3} = 2117.4 kJ/kg
10 kPa

T^{sat}= 45.83 ^{o}C
H_{4} = 191.8 kJ/kg
Isentropic pumping
(process 4 1)

(H)_{S} = 8.7 kJ/kg (Ex 7.10)
H_{1} = H_{4} + (H)_{S} = 200.5 kJ/kg

the turbine operate under the same condition as Ex. 7.6

### H

_{S}

### 1 , 274 . 2 kJ / kg

### 3966 .

### 1 0 . 191 , 3

### 5 . 1265 )

### boiler (

### Q

### ) Rankine (

### W

### kg / kJ 5 . 265 , 1 6

### . 925 , 1 1 . 191 , 3 )

### condenser (

### Q ) boiler (

### Q )

### Rankine (

### W or

### kg / kJ 5 . 265 , 1 7

### . 8 2 . 1274 )

### pump (

### W ) turbine (

### W ) Rankine (

### W

### kg / kJ 1 . 191 , 3 5 . 200 6

### . 391 , 3 H H

### ) boiler (

### Q

### kg / kJ 6 . 925 , 1 4

### . 117 , 2 8 . 191 H

### H ) condenser (

### Q

S S S

1 2

3 4

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

**Example 8.1**

**Example 8.1**

**(b)** ^{ } ^{} ^{} ^{}

###

2961 .

2 0 . 188 , 3

0 . 944 )

boiler (

Q

) Rankine (

W

kg / kJ 2 . 188 , 3 4 . 203 6

. 391 , 3 H H

) boiler (

Q

kg / kJ 4 . 203 6

. 11 8 . 191 H

H H

kg / kJ 0 . 944 75

. 11 6 . 955 )

pump (

W ) turbine (

W ) Rankine (

W

kg / kJ 75 . 75 11

. 0

676 . ) 8 pump (

H W H

, 10 . 7 Ex From

kg / kJ 0 . 436 , 2 6 . 955 6

. 391 , 3 H H

H

kg / kJ 6 . 955 2

. 274 , 1 75 . 0 ) turbine (

W H

H , 6 . 7 Ex From

S

1 2 4

1

S S

S

S S

2 3

S S

**The Regenerative Cycles**

**The Regenerative Cycles**

### **Higher efficiencies**

**Increased Boiler Temperature Increased Boiler Pressure ** **Increased cost **
**for construction**

**Lower condenser temperature Lower condenser pressure ** **practical **
**condensation controlled by ambient temp**

### **Most modern power plants operate on a modification of the Rankine cycle ** **that incorporates feed water heaters**

**Water from the condenser is first heated by steam extracted from the turbine**

**In Rankine cycle, water from the condenser is pumped directly back to the **
**boiler**

**The Regenerative Cycles**

**The Regenerative Cycles**

### **Stagewise preheating the feed water can improve efficiencies**

**Simple steam power plant**

**steam power plant by regenerative cycle**

**Example 8.2**

**Example 8.2**

### **Determine the thermal efficiency of the power plant in **

**Figure, assuming turbine and pump efficiency of 0.75.**

**Example 8.2 – Section I**

**Example 8.2 – Section I**

**From energy**
**balance**

###

kg / kJ 4 . 240 )

5 . 320 (

75 . 0

H H

W_{S} _{S}

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

H ) liq . sat ( H H

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

kg / kJ 5 . 971 )

liq . sat ( H

H ) liq . sat ( H H

kg / kJ 2 . 151 , 3

4 . 240 6

. 391 , 3 H

balance Energy

**Basis**

**Example 8.2 – Section II**

**Example 8.2 – Section II**

**From energy**
**balance**

###

_{S}

S H H

W

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

H ) liq . sat ( H H

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

kg / kJ 5 . 971 )

liq . sat ( H

H ) liq . sat ( H H

###

H_{S}2

. 151 , 3 H

balance Energy

**Example 8.2**

**Example 8.2**

### To get the thermal efficiency of whole process,

### Complete the calculation on turbine (section I – V)

###

### 3276 .

### 6 0 . 418 , 2

### 4 . 792 )

### boiler (

### Q

### ) Rankine (

### W

### kJ 6 . 418 , 2 0 . 973 6

### . 391 , 3 H )

### boiler (

### Q

### kJ 4 . 792 6

### . 11 0

### . 804 )

### pump (

### W )

### turbine (

### W )

### Rankine (

### W

### kg / kJ 6 . 75 11

### . 0

### 676 . ) 8 pump (

### H W H

### , 10 . 7 Ex From

### ) V I tion (sec turbine

### for kJ 0 . 804 W

S

S S

S

S S

S

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

**8.2 Internal – Combustion Engines**

**8.2 Internal – Combustion Engines**

### **Characteristics of Steam Power Plant**

### **Steam is an inert medium heat is transferred from a burning fuel**

### **Large heat transfer surfaces **

- Absorption of heat by the steam at a high T in the boiler, and rejection of heat from the steam at a relatively low T in the condenser

- Thick walls to withstand high T, P impose a limit on heat absorption.

### **Complicated structure**

### **Characteristics of Internal-Combustion Engines**

### **Combustion are carried out within engine**

- The combustion products serve as the working medium, acting on a piston in a cylinder - High temperatures are internal, and do not involve heat-transfer surfaces

### **Complex thermodynamic analysis **

### **No working fluid undergoes a cyclic process**

**The Otto Engine**

**The Otto Engine**

### **No working fluid undergoes cyclic process**

### **An imaginary cyclic engine with air as working fluid**

- The combustion step is replaced by the addition to the air of an equivalent amount of heat

### **Equivalent in performance to actual internal-combustion engine**

### **The most common internal-combustion engine **

** The Otto engine**

- Used in automobiles

**Otto Engine Cycle**

**Otto Engine Cycle**

**Air / fuel mixture fed **
**into the engine**
**Air / fuel mixture are **

**compressed by the **
**piston**

**Combustion of fuel **
**: So rapid so that the **
**volume remains const. **

**Adiabatic expansion**

**Valve opened and **
**exhaust gas vented**

**Piston pushes **
**remaining exhaust **

**gases**

**Idealized Otto Cycle**

**Idealized Otto Cycle**

**Increasing the compression ratio is to increase the efficiency of engine. (Proof ?)**

**Using idealized Otto engine**

**Two adiabatic & two const V steps**

**The working fluid is air (ideal gas with constant C**_{p}**)**

**Reversible adiabatic **
**compression**
**Sufficient heat is **
**absorbed by the air at **

**constant volume**
**(P and T increase)**

**Reversible adiabatic **
**expansion**

**Cooling at constant **
**volume**

**Thermodynamic Analysis of Otto Engine**

**Thermodynamic Analysis of Otto Engine**

### **Increasing the compression ratio is to increase the efficiency of ** **engine. (Proof ?)**

### **Using idealized Otto engine**

### ) (

_{A}

_{D}*V*

*DA*

*C* *T* *T*

*Q*

### ) T T

### ( C

### Q

_{BC}

###

_{V}

_{C}

###

_{B}

###

###

D A

C B

D A

V

B C

V D

A V

DA BC DA

DA net

### T T

### T 1 T

### T T

### C

### T T

### C T

### T C

### Q Q Q

### Q W

###

###

###

###

###

###

###

###

###

###

**Otto Engine - Analysis**

**Otto Engine - Analysis**

### **The Compression ratio, r ≡ V**

_{C}**/V**

_{D} **r increases : efficiency increases**

### **The thermal efficiency increases rapidly at low value of r, but more slowly ** **at higher value of r**

##

## ^{T} ^{T}

^{T}

^{T}

^{C}

_{A}^{} ^{} ^{T} ^{T}

^{T}

^{T}

_{D}

^{B}##

###

### 1

*nRT* *PV *

*const* *PV *

^{}

### 1

1### 1

###

###

###

###

###

### *r*

###

###

###

###

*D*
*C*

*V* *r* *V*

**Derive yourself! (Page 304)**

**Diesel Engine**

**Diesel Engine**

### **Difference from Otto Engine**

### **Compression is high, combustion is initiated spontaneously**

### **High compression ratio, high efficiency**

**Efficiency in Diesel – Example 8.3**

**Efficiency in Diesel – Example 8.3**

### **The thermal efficiency of Diesel cycle**

### **The compression ratio, r (≡ V**

_{C}**/V**

_{D}**)**

### **The expansion ratio, r**

_{e}**(≡ V**

_{B}**/V**

_{A}**)**

### ) T T

### ( C

### Q

_{DA}

###

_{P}

_{A}

###

_{D}

### ) T T

### ( C

### Q

_{BC}

###

_{V}

_{C}

###

_{B}

###

### ^{} ^{} ^{} ^{} ^{} ^{} _{} ^{} ^{} ^{} ^{} _{} ^{}

###

###

###

###

###

###

D A

C B

D A

P

B C

V

DA BC DA

BC DA

### T T

### T T

### 1 1 T

### T C

### T T

### 1 C

### Q 1 Q Q

### Q Q

### RT PV

### V / V r

### V / V r

### V T V

### T

### V T V

### T

A B e

D C

1 C C 1

D D

1 B B 1

A A

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

### r / 1 r / 1

### ) r / 1 ( ) r / 1 ( 1 1

### r / r 1

### ) r / 1 )(

### r / r ( )

### r / 1 ( 1 1

e e

e

1 e

1 e

**Derive yourself! **

**(Page 306)**

**The Gas-Turbine Engine**

**The Gas-Turbine Engine**

### **Otto & Diesel engines**

**Direct use of the energy of high T and P gases, acting on a piston within a cylinder**

**However, turbines are more efficient than reciprocating engines**

### **Gas Turbine Engine**

**Advantage of high T and P for internal combustion engine**

**Advantage of using turbine rather than reciprocating engine**

**Gas-Turbine Engine**

**Gas-Turbine Engine**

### **The gas turbine is driven by high-T gases from a combustion chamber**

**The entering air is compressed before combustion**

**The centrifugal compressor operates on the same shaft as the turbine**

**Part of the work of the turbine serves to drive the compressor**

**Brayton Cycle**

**Brayton Cycle**

### **Brayton cycle**

**The idealization of the gas-turbine engine**

**The working fluid is taken as air, ideal gas with const C**_{p}

**Reversible adiabatic **
**compression**
**Heat Q**_{BC}**is added at **

**constant P**

**(replacing combustion)** **Reversible adiabatic **

**expansion (Isentropic)**

**Cooling at constant **
**pressure**

**Thermodynamic Analysis of Brayton Engine**

**Thermodynamic Analysis of Brayton Engine**

### ) T T

### ( C

### Q

_{BC}

###

_{P}

_{C}

###

_{B}

### ) T T

### ( C H

### H

### W

_{AB}

###

_{B}

###

_{A}

###

_{P}

_{B}

###

_{A}

B C

A D

BC AB CD

BC net

### T T

### T 1 T

### Q W W

### Q W

###

###

###

###

###

###

### ) T T

### ( C

### Q

_{DA}

###

_{P}

_{A}

###

_{D}

### ) T T

### ( C

### W

_{CD}

###

_{P}

_{C}

###

_{D}

/ ) 1 (

A B /

) 1 (

C D C

D

/ ) 1 (

A B A

B

P P P

P T

T

P and P T

T

###

###

###

###

###

###

/ ) 1 (

B A

### P

### 1 P

**8.3 Jet Engines, Rocket Engines**

**8.3 Jet Engines, Rocket Engines**

### **Previous power cycles**

**High T, P gas expands in a turbine (steam power plant or gas turbine) or in the **
**cylinders with reciprocating pistons (Otto or Diesel engine)**

** The power become available through a rotating shaft!**

### **Turbojet (or jet) engine**

**A nozzle for expanding the hot gases**

**The power is available as kinetic energy in the jet of exhaust gases leaving the nozzle**

**Turbojet engine (or jet engine)**

**Turbojet engine (or jet engine)**

### **Turbojet engine (or jet engine)**

### **Compression by an axial-flow compressor**

### **Combustion of the fuel with air**

### **The hot gases pass through a turbine**

- The expansion provides enough power to drive the compressor - The remainder of the expansion accomplished in the nozzle

- The velocity of exhaust gases increases Provide a force on the engine in the forward direction

### **For adiabatic and reversible compression and expansion**

- The jet engine cycle is identical to the ideal gas turbine cycle (Brayton cycle)

**Rocket engine**

**Rocket engine**

### **Rocket engine**

### **Difference from a jet engine The oxidizing agent is carried with the ** **engine (not surrounding air for burning the fuel)**

### **Can operate in a vacuum such as in outer space**

### **The combustion and expansion steps**

- Same as an ideal jet engine

**Homework**

**Homework**