Thermodynamics Principles

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Thermodynamics Principles

Specific internal energy

It is the energy stored in the substance due to molecular motion as well as intermolecular forces.

The SI unit is kJ/kg.

Specific enthalpy (h)

It is the sum of the specific internal energy and the product of pressure P versus specific volume,

v. The SI unit is kJ/kg.

Thermal power (Q)

It is the form of energy rate transferred to or from the machine due to a difference of

temperatures between the machine and the surroundings, the higher temperature to the lower

one.

Specific heat at constant pressure (Cp)

Cp = dhdT

Specific heat at constant volume (CV)

CV= du/dT

For an ideal gas, there is a very useful relationship between these two specific heats given by

CpCV = R

First Law of Thermodynamics Analysis for Control Volumes

Thermal machines convert chemical energy in shaft work by burning fuel (heat) in a combustion

chamber. In doing so, mass fluxes of air and fuel enter the machine and combustion products exit

it. In a working machine, energy in its several forms is presented in the conversion process, such

as heat, shaft work, enthalpy, and chemical energy. Even though energy is transformed from one

form into another, the overall amount of energy must be conserved as stated by the First Law of

Thermodynamics. In order to establish the First Law consider the schematics in Fig. 2 showing a

control volume around a thermal machine

Energy balance for the control volume in Fig. 2 results in


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(dE )CV = mi [ hi+ V2+ Zi]- m0[ ho + V

2 + Zo] + QW

dt 2 2

Second Law of Thermodynamics Analysis for Control Volumes

The rate of entropy generated in a control volume (Fig. 2) can be written according to Eq. 17

(dS )CV misi- M0s0+ QCV/ T

dt

Where, S is the total instantaneous entropy of the control volume, Siand so are the specific

entropy associated with the inlet and outlet mass fluxes, T is the control volume surface

temperature where heat is exchanged with the surrounding environment at a given rate, Q cv

RANKINE CURVE

Process 1-2: The working fluid is pumped from low to high pressure, as the fluid is a liquid at

this stage the pump requires little input energy.

Process 2-3: The high pressure liquid enters a boiler where it is heated at constant pressure by an

external heat source to become a dry saturated vapor.

Process 3-4: The dry saturated vapor expands through aturbine,generating power. This

decreases the temperature and pressure of the vapor

Process 4-1: The wet vapor then enters acondenserwhere it is condensed at a constant

temperature to become asaturated liquid.
http://en.wikipedia.org/wiki/Turbinehttp://en.wikipedia.org/wiki/Turbinehttp://en.wikipedia.org/wiki/Turbinehttp://en.wikipedia.org/wiki/Surface_condenserhttp://en.wikipedia.org/wiki/Surface_condenserhttp://en.wikipedia.org/wiki/Surface_condenserhttp://en.wikipedia.org/wiki/Boiling_pointhttp://en.wikipedia.org/wiki/Boiling_pointhttp://en.wikipedia.org/wiki/Boiling_pointhttp://en.wikipedia.org/wiki/Boiling_pointhttp://en.wikipedia.org/wiki/Surface_condenserhttp://en.wikipedia.org/wiki/Turbine


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Thermal Efficiency of Rankine Cycle:

Heat Input = Q23 = H3H2

Heat Rejected = Q41 = H4H1

Work Output = W34 = H3H4

Work done by Pump = W12 = H2H1

Work outputPump work W34W12 Heat Input Q23

1.1 FUEL POWER F.P.)Fuel power is the thermal power released by burning fuel inside the engine.

F.P. = mass of fuel burned per second x calorific value of the fuel.

F.P. = mf x C.V.All engines burn fuel to produce heat that is then partially converted into mechanical

power. The chemistry of combustion is not dealt with here. The things you need to

learn at this stage follow.

1.1.1 AIR FUEL RATIOThis is the ratio of the mass of air used to the mass of fuel burned.

Air Fuel Ratio = ma/mf


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CALORIFIC VALUEThis is the heat released by burning 1 kg of fuel. There is a higher and lower value for

fuels containing hydrogen. The lower value is normally used because water vapour

formed during combustion passes out of the system and takes with it the latent energy.

We can now define the fuel power.

FUEL POWER = Mass of fuel/s x Calorific Value

COMBINED-CYCLE THERMODYNAMICS

A gas turbine cycle is depicted symbolically in Fig. 1. By definition, the efficiency of the gas

turbine is given by

gt = Wgt / QH

where _Qh is the energy input rate from the high-temperature source at temperature Th, and

_Wgt is the power output delivered to an electric generator. By energy conservation, the rate of

energy transfer to the lower-temperature reservoir at the exhaust temperature Tex is

QEX= Qh - Wgt

The gas-turbine cycle is based upon the reversible JouleBrayton cycle . The JouleBrayton

cycle models not only gas turbine power plants but also the familiar gas turbines of jet

engines.19Because they can burn relatively clean fuel, have relatively low capital costs, and can

be started and stopped quickly, gas turbines have become popular for electricity peaking and

emergency power generation, as well as for base load operations (providing minimum power


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requirements).16 Stationary gas turbines have the flexibility to burn not only methane but also

distillate oil, which though less clean than natural gas, is often preferable to coal for power

plants. The basic operation in Fig. 2 entails compression of air (12), providing the high pressure

needed to drive the turbine Then combustion of a fuel, typically methane (23), increases the

temperature and energy of the gas stream. Segment 34 represents the combustion gases

expanding as they drive the rotating turbine, and 41 cools and exhausts the hot gases at constant

atmospheric pressure, thereby dumping wasted energy to the environment. Advances in

metallurgy and cooling technology during recent years have enabled ever higher combustion and

exhaust temperatures. Modern gas turbines with ultra-high combustion temperatures have

efficiencies of about 0.4, roughly the same as the most advanced coal-burning plants. However,

they not only have the advantage of much higher inlet temperatures than steam turbines but also

characteristically have the disadvantage of much higher exhaust temperatures, T4 _ Tex in Fig.

2. Thus, a gas turbine cycle can dump substantial amounts of wasted energy to the environment,

which limits its efficiency. For high-efficiency operation, one generally wants a high inlet

(maximum) temperature, which gas turbines have, but also a low exhaust temperature, near that

of the environment, which gas turbines lack. Bejan cites various sources of irreversibility that

plague gas turbines and explains how clever engineering designs, entailing regenerative heat

exchangers, reheaters, and intercoolers, can bring higher efficiencies.20 However, even greater

efficiency gains are possible for electricity generation by using the high-temperature exhaust of

the gas turbine to power a steam cycle, which inherently has a much lower exhaust temperature.

For example, a gas turbine with inlet and exhaust temperatures 1673K and 873K, respectively,

might use the exhaust gases to heat a steam turbine that has exit temperature 350K, achieving the

overall temperature range, 1673 K ! 350 K. A single gas turbine cycle cannot match this. In this

regard, Bejan writes,gas-turbine cycles are better suited for efficient operation at high

temperatures than steam-turbine cycles. On the other hand, the steam-turbine cycle is more

attractive from the point of view of minimizing the temperature gap between the cold end of the

cycle and the low-temperature reservoir The engineering challenge that remains is to mesh

optimally the two cycles along that seam of intermediate temperatures where the upper (warmer)

cycle must act as a heat source for the lower one. The bottom line is that existing combined

cycles are more efficient than any currently achievable single cycle. In the simplest combined-

cycle design, the gas turbine drives one electric generator and the steam turbine runs another, as


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illustrated in Figs. 3 and 4. Ignoring losses in the heat exchanger, the inlet temperature to the

steam turbine is Tex. Combining Eqs. (3) and (4), the waste energy rate,

QEX= Qh - gt QH

In the exhaust gases becomes the input power for the steamturbine cycle, whose efficiency we

call

st =Wst / Qex

Thus,the power output delivered by the steam turbine is

Wst = st Qex = st (QH - gt Qh

Combining Eqs. (3) & (6), the total power delivered by the bgas and steam turbine combination

is

Wtot = Wgt + Wst = gt + st (1- gt) Qhand the combined-cycle efficiency is,

cc = Wtot / Qh = gt + stgtst

Simple Brayton Cycle

In an actual gas turbine, the working fluid changes from atmospheric air to combustion products thatexhaust back to the atmosphere, as illustrated in Fig. 5a. However, in order to evaluate the machine fromthe thermodynamic point-of-view, some assumptions are needed. Firstly, the working fluid is assumed tobe plain air, without any chemical transformation due to the combustion. In doing so, the airfuelcombustion process is replaced by a heat addition process at a constant pressure. Secondly, the exhaustand admission processes are replaced by a heat transfer process to the environment, which makes the


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air to flow continuously in a closed loop as indicated in Fig. 5b. In the closed cycle, air at environment pressureand temperature is first compressed, next it receives heat QH and it is followed by an expansion process in the

turbine section to, finally, reject heat QL at constant pressure. This is the Air-Standard Brayton Cycle. Having the

cycle of Fig. 5b in mind along with the ideal gas behavior and constant thermodynamic properties one may obtain

the working equations from an energy balance (Eq. 16) for each cycle component:

Heat addition:qH = h3 - h2 = CP(T3 - T2 )

Heat rejection:qL = h4 - h1 = CP(T4_ T1)

Compression work:wcomp = h2 - h1 = CP(T2_ T1 )

Turbine work:Wtur = h3 - h4 = CP(T3 - T4)

The thermal efficiency, gth; of a cycle is defined as the ratio between the cycle net work and heat added, as given byEq. 35. By applying the First Law for the whole cycle, one easy can show that w = qH- qL. Therefore, one obtains:

th = 1qL / qH

By examining the temperature-entropy diagram in Fig. 6a, one can easily notice that T3 is the maximum cycle

temperature, also known as the firing temperature, while T 1 is the minimum one (usually the environmenttemperature).

By using isentropic ideal gas relationships between pressure and temperature Eq. 34), it is straightforward to show

that


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Thermodynamics Principles