OCTANE AND CETANE NUMBERS

Self ignition temperature (SIT) of a fuel is the temperature at which the fuel ignites on its own without spark. If large amount of mixture in an engine cylinder auto ignites, there will be a rapid rise in pressure causing direct blow on engine structure accompanied by thudding sound. This causes vibrations in the engine. The phenomenon is called knocking.

If however, a small pocket of fuel-air mixture auto ignites, pressure waves are generated which travel with the speed of sound across the cylinder. These pressure waves are of such small duration that indicator diagram mechanism fails to record them. These waves interact within themselves and with the cylinder walls, creating characteristics ping sound. The phenomenon is called pinking.

The engine runs rough, overheats and loses efficiency due to knocking and pinking.

The processes of knocking and pinking are related to the nature of the fuel and relative merits of the fuel are decided on the basis of their anti-pinking and anti-knock property. The merit is measured by octane number such that a fuel of high octane number will be liable to less pink or knock as compared to a fuel of low octane number in the same engine. It is important to note that the same fuel will show same tendency to pink or knock in all engines.

Commonly used fuel in SI engines is a mixture of iso-octane and n-heptane. Iso-octane has minimum tendency to knock and this fuel is arbitrarily assigned an octane number of 100 (ON = 100) where as n-heptane has maximum knocking tendency with ON = 0. The octane number of a given fuel is percentage of iso-octane in the mixture of iso-octane and n-heptane. Thus a fuel other than mixture of iso-octane and n-heptane if assigned an ON of 80, it means, it will knock under standard operating condition similar to the mixture of 80% iso-octane and 20% n-heptane.

The tendency to knock in an engine increases with the increase in compression ratio. The highest compression upto which no knocking occurs in a given engine is called highest useful compression ratio (HUCR).

Certain chemical compounds when added to the fuel successfully suppress the knocking tendency. Tetra-ethyl lead [Pb(C₂ H₅)₄] also commonly called TEL and tetra-methyl lead [Pb(CH₃)₄] also referred to as TML are effective dopes in the automobile fuel to check knocking. They are called as anti-knocking agents. However, because of lead poisoning effects TEL and TML are not being used now-a-days. In stead, some organic auto knocking agents have been developed to check the undesirable effects like knocking.

In CI engine air alone is compressed to a compression ratio of 15 to 20 (commonly). The fuel is injected under a pressure of 120 to 210 bars about 20° to 35° before TDC. As the fuel in the engine starts to evaporate the pressure in the cylinder drops and it delays the ignition process by a small amount. The time between beginning of injection and the beginning of combustion is known as the delay period which consists of time for atomization, vapourization and mixing along with time of chemical reaction prior to auto-ignition. The combustion of fuel continues in the expansion and is called after burning. Increased delay period causes accumulation of atomized fuel in the combustion chamber and as the pressure and temperature continue to rise at one instant, the bulk of fuel auto-ignites. This would result in high forces on the structure of the engine causing vibration and rough running.

The CI engine fuel rating is based on ignition delay and is measured in terms of cetane number. Cetane fuel [C₁₆ H₃₄] has very low delay period and is arbitrarily assigned a cetane number of 100. Another fuel a α-methyl-napthalene [C₁₁ H₁₀] has poor ignition quality and is assigned zero cetane number. The volume percentage of cetane in a mixture of cetane and a-methyl naphthalene is the cetane number of the fuel that produces same delay period as the mixture under specified test conditions. Additives such as methyl nitrate, ethyl thio-nitrate and amyl nitrate increase cetane number of a fuel respectively by 13.5%, 10% and 9% if added to the extent of 0.5%.

MOCK CLASS TEST: THERMODYNAMICS Sub: Code: EME-303; Mahamaya Technical University

Time: 2 hrs                                                                                                   Maximum Marks: 50 

Attempt all the questions: 

SECTION A: 

1) Attempt the following questions:                                                                        (5 x 2 = 10) 

a) Define system, surroundings and universe. 

b) Distinguish between Heat pump and Refrigerator. 

c) What is Exergy and Anergy? 

d) Explain the law of degradation of energy. 

e) What is triple point of water? 

SECTION B: 

2) Attempt any three questions:                                                                               (3 x 5 = 15) 

a) Distinguish between macroscopic and microscopic approaches of thermodynamics. 

b) Discuss the neccessity of 2nd law of thermodynamics. 

c) 2 kg of a gas at 10 bar expands adiabatically and reversibly till its pressure drops to 5 bar. During the process 120 kJ of non-flow work is done by the system and the temperature drops from 377°C centigrade to 257°C. Calculate the value of the index of expansion and the characteristics gas constants. 

d) Steam at a pressure of 4 bar absolute and having dryness fraction 0.8, is heated at constant volume to a pressure of 8 bar absolute. Find the final temperature of the steam. Also, find the total heat absorbed by 1 kg of steam. 

e) 2 kg of air at NTP is heated at constant volume untill the pressure becomes 6 bar. Find the change of entropy of the system. 

SECTION C: 

Attempt part (a) or part (b) of the following questions                                                 (5 x 5 = 25) 

3) (a) Explain the thermodynamic equilibrium and quasi-static process. 

(b) Prove the equivalence of Kelvin-Planck statement and Clausius statement. 

4) (a) A steam turbine developing 110 kW is supplied steam at 17.5 bar with an internal energy of 2600 kJ/min, specific volume = 15.5 m³/kg and velocity of 275 m/s. Heat loss from the steam turbine  37.6 kJ/kg. Neglecting the changes in potential energy, determine the steam flow rate in kg/hr. 

(b) A reversible engine takes 2400 kJ/min from a reservoir at 750 K develops 400 kJ/min of work during cycle. The engine rejects heat at two reservoir at 650 K and 550 K. Find the heat rejected to each sink. 

5) (a) Explain the causes of internal and external irreversibility. 

(b) Explain the importance of Gibb's function and Gibb's free energy. 

6) (a) 5 kg steam at pressure 8 bar and temperature 300°C is adiabatically mixed with 4 kg steam at 6 bar and 250°C. Find the final condition of the mixture. Also find the change in entropy. 

(b) Hot steam is flowing through a perfectly adiabatic pipe. At point A the temperature of the steam is 250°C and pressure is 4 bar, while at the point B, its temperature is 275°C and pressure is 3.5 bar. Find the direction of the flow. 

7) (a) 5 kg of Oxygen is enclosed within a vessel of 0.05 m³ at a temperature 200°C, is being supplied 120 kJ of energy through heating. Find the final pressure and temperature. 

(b) One kg of an ideal gas is heated from 18.3°C to 93.4°C. Assuming R = 287 J/kg-K and  γ  = 1.18 for the gas. Find out (i) specific heats, (ii) change in internal energy, and (iii) change in enthalpy and entropy.

Steam Turbine and Power Plants

Steam turbine

A steam turbine is a device that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Sir Charles Parsons in 1884.

Because the turbine generates rotary motion, it is particularly suited to be used to drive an electrical generator – about 90% of all electricity generation in the United States (1996) is by use of steam turbines. The steam turbine is a form of heat engine that derives much of its improvement in thermodynamic efficiency through the use of multiple stages in the expansion of the steam, which results in a closer approach to the ideal reversible process.

Back Pressure Steam Turbine

Steam turbines are the prime movers in generating electricity. Back pressure steam turbines are a type of steam turbine that is used in connection with industrial processes where there is a need for low or medium pressure steam.

The high pressure steam enters the back pressure steam turbine and while the steam expands – part of its thermal energy is converted into mechanical energy. The mechanical energy is used to run an electric generator or mechanical equipment, such as pumps, fans, compressors etc.

The outlet steam leaves the back pressure steam turbine at “overpressure” and then the steam returns to the plant for process steam application such as heating or drying purposes.

Steam Turbine Power Plants:

Steam turbine power plants operate on a Rankine cycle. The steam is created by a boiler, where pure water passes through a series of tubes to capture heat from the firebox and then boils under high pressure to become superheated steam. The heat in the firebox is normally provided by burning fossil fuel (e.g. coal, fuel oil or natural gas). However, the heat can also be provided by biomass, solar energy or nuclear fuel. The superheated steam leaving the boiler then enters the steam turbine throttle, where it powers the turbine and connected generator to make electricity. After the steam expands through the turbine, it exits the back end of the turbine, where it is cooled and condensed back to water in the surface condenser. This condensate is then returned to the boiler through high-pressure feedpumps for reuse. Heat from the condensing steam is normally rejected from the condenser to a body of water, such as a river or cooling tower.

Steam turbine plants generally have a history of achieving up to 95% availability and can operate for more than a year between shutdowns for maintenance and inspections. Their unplanned or forced outage rates are typically less than 2% or less than one week per year.

Modern large steam turbine plants (over 500 MW) have efficiencies approaching 40-45%. These plants have installed costs between $800 and$2000/kW, depending on environmental permitting requirements.

Combustion (Gas) Turbines:

Combustion turbine plants operate on the Brayton cycle. They use a compressor to compress the inlet air upstream of a combustion chamber. Then the fuel is introduced and ignited to produce a high temperature, high-pressure gas that enters and expands through the turbine section. The turbine section powers both the generator and compressor. Combustion turbines are also able to burn a wide range of liquid and gaseous fuels from crude oil to natural gas.

The combustion turbine’s energy conversion typically ranges between 25% to 35% efficiency as a simple cycle. The simple cycle efficiency can be increased by installing a recuperator or waste heat boiler onto the turbine’s exhaust. A recuperator captures waste heat in the turbine exhaust stream to preheat the compressor discharge air before it enters the combustion chamber. A waste heat boiler generates steam by capturing heat form the turbine exhaust. These boilers are known as heat recovery steam generators (HRSG). They can provide steam for heating or industrial processes, which is called cogeneration. High-pressure steam from these boilers can also generate power with steam turbines, which is called a combined cycle (steam and combustion turbine operation). Recuperators and HRSGs can increase the combustion turbine’s overall energy cycle efficiency up to 80%.



Combustion (natural gas) turbine development increased in the 1930’s as a means of jet aircraft propulsion. In the early 1980’s, the efficiency and reliability of gas turbines had progressed sufficiently to be widely adopted for stationary power applications. Gas turbines range in size from 30 kW (micro-turbines) to 250 MW (industrial frames). Industrial gas turbines have efficiencies approaching 40% and 60% for simple and combined cycles respectively.

The gas turbine share of the world power generation market has climbed from 20 % to 40 % of capacity additions over the past 20 years with this technology seeing increased use for base load power generation. Much of this growth can be accredited to large (>500 MW) combined cycle power plants that exhibit low capital cost (less than $550/kW) and high thermal efficiency.

Introduction To the Combustion of Fuels

Combustion:

Principle of Combustion:

Combustion is the conversion of a substance called a fuel into chemical compounds
known as products of combustion by combination with an oxidizer. The combustion
process is an exothermic chemical reaction, i.e., a reaction that releases energy as it
occurs.

Thus combustion may be represented symbolically by:
Fuel + Oxidizer = Products of combustion + Energy

Here the fuel and the oxidizer are reactants, i.e., the substances present before the
reaction takes place. This relation indicates that the reactants produce combustion
products and energy. Either the chemical energy released is transferred to the
surroundings as it is produced, or it remains in the combustion products in the form of
elevated internal energy (temperature), or some combination thereof.

Fuels are evaluated, in part, based on the amount of energy or heat that they
release per unit mass or per mole during combustion of the fuel. Such a quantity is
known as the fuel’s heat of reaction or heating value.

Heats of reaction may be measured in a calorimeter, a device in which chemical
energy release is determined by transferring the released heat to a surrounding fluid.
The amount of heat transferred to the fluid in returning the products of combustion to
their initial temperature yields the heat of reaction.

In combustion processes the oxidizer is usually air but could be pure oxygen, an
oxygen mixture, or a substance involving some other oxidizing element such as
fluorine. Here we will limit our attention to combustion of a fuel with air or pure
oxygen.

Chemical fuels exist in gaseous, liquid, or solid form. Natural gas, gasoline, and
coal, perhaps the most widely used examples of these three forms, are each a complex
mixture of reacting and inert compounds. We will consider each more closely later in
the chapter. First let’s review some important fundamentals of mixtures of gases, such
as those involved in combustion reactions.

Therefore, combustion refers to the rapid oxidation of fuel accompanied by the production of heat, or heat and light. Complete combustion of a fuel is possible only in the presence of an adequate supply of oxygen.

Oxygen (O₂) is one of the most common elements on earth making up 20.9% of our air. Rapid fuel oxidation results in large amounts of heat. Solid or liquid fuels must be changed to a gas before they will burn. Usually heat is required to change liquids or solids into gases. Fuel gases will burn in their normal state if enough air is present.

Most of the 79% of air (that is not oxygen) is nitrogen, with traces of other elements. Nitrogen is considered to be a temperature reducing dilutant that must be present to obtain the oxygen required for combustion.

Nitrogen reduces combustion efficiency by absorbing heat from the combustion of fuels and diluting the flue gases. This reduces the heat available for transfer through the heat exchange surfaces. It also increases the volume of combustion by-products, which then have to travel through the heat exchanger and up the stack faster to allow the introduction of additional fuel air mixture.

This nitrogen also can combine with oxygen (particularly at high flame temperatures) to produce oxides of nitrogen (NO_x), which are toxic pollutants.

Carbon, hydrogen and sulphur in the fuel combine with oxygen in the air to form carbon dioxide, water vapour and sulphur dioxide, releasing 8084 kcals, 28922 kcals & 2224 kcals of heat respectively.

Under certain conditions, Carbon may also combine with Oxygen to form Carbon Monoxide, which results in the release of a smaller quantity of heat (2430 kcals/kg of carbon) Carbon burned to CO2 will produce more heat per pound of fuel than when CO or smoke are produced.

C + O₂ → CO₂ + 8084 kCals/kg of Carbon

2C + O₂ → 2 CO + 2430 kCals/kg of Carbon

2H₂ + O₂ → 2H₂O + 28,922 kCals/kg of Hydrogen

S + O₂ → SO₂ + 2,224 kCals/kg of Sulphur

3 T’s of Combustion:

The objective of good combustion is to release all of the heat in the fuel. This is accomplished by controlling the "three T's" of combustion which are

1. Temperature high enough to ignite and maintain ignition of the fuel,
2. Turbulence or intimate mixing of the fuel and oxygen, and
3. Time sufficient for complete combustion.

Commonly used fuels like natural gas and propane generally consist of carbon and hydrogen. Water vapor is a by-product of burning hydrogen. This robs heat from the flue gases, which would otherwise be available for more heat transfer.

Natural gas contains more hydrogen and less carbon per kg than fuel oils and as such produces more water vapor. Consequently, more heat will be carried away by exhaust while firing natural gas.

Too much, or too little fuel with the available combustion air may potentially result in unburned fuel and carbon monoxide generation. A very specific amount of O2 is needed for perfect combustion and some additional (excess) air is required for ensuring complete combustion. However, too much excess air will result in heat and efficiency losses.

Not all of the heat in the fuel are converted to heat and absorbed by the steam generation equipment. Usually all of the hydrogen in the fuel is burned and most boiler fuels, allowable with today's air pollution standards, contain little or no sulfur. So the main challenge in combustion efficiency is directed toward unburned carbon (in the ash or incompletely burned gas), which forms CO instead of CO₂.

                                                                                                                             Subhankar Karmakar

MOCK QUESTION PAPER: APPLIED THERMODYNAMICS (2 units only)

                                                                   Paper Code: EME-402

B.  Tech - ME

(SEM.IV) Sessional Examination, 2011 – 12

Applied Thermodynamics

Time:   3hrs                        Total Marks:  100

    Note:   (1)           Attempt all questions.

         (2)  Be precise in your answer.

SECTION-A:

Q.1: Answer the following questions as per the instructions.           

2X10=30

 (i) What is the importance of feed pump in steam engine?

(ii) What is reversible adiabatic process?

(iii) Explain the term isothermal compressibility?

(iv) What is missing quantity?

(v) What is Work Ratio in Carnot vapour cycle?

(vi) Explain the term “Specific steam consumption.”

(vii) What is thermal efficiency of a steam engine?

(viii) What is indicated power?

(ix) What is mean effective pressure of a steam engine?

(x) What is inversion temperature?

SECTION-B:

Q.2: Answer any three parts of the followings:     

                                                                                                               3X10=30

a) Derive the Tds equations.

b) Derive the expressions of mass discharge of steam through a Nozzle.

c) A single cylinder double acting steam engine is supplied with dry and saturated steam at 11.5 bar and exhaust occur at 1.1 bar. The cut-off occurs at 40% of the stroke. If the stroke equals 1.25 times the cylinder bore and engine develops 60 kW at 90 rev/min. Determine the bore and the stroke of the engine. (Assume hyperbolic expansion and diagram factor of 0.79.)

Also calculate the theoretical steam consumption

d) Dry saturated steam enters a steam nozzle at a pressure of 12 bar and is discharged at a pressure of 1.5 bar. If the dryness factor of the discharged steam is 0.95, what would be the final velocity of the steam? Neglect initial velocity of steam.

If 12% heat drop is lost in friction, find the % reduction in the final velocity.

SECTION C:
Q.3: Answer any two parts of the following: 

                                                                                         5X2=10

a) Explain the term “Joule-Thomson coefficient.”

b) With proper diagrams explain the term nozzle efficiency.

c) Explain the Clausius Clapeyron equation. Also write their field of application.

Q.4: Answer any one part of the following:   

                                                                                           1X10=10

a) Explain the effect of velocity and pressure in the flow of a nozzle. What is a choked flow? Also explain the concept of critical pressure in isentropic flow through nozzle.

b) Steam at a pressure of 20 bar, 250°C expands in a convergent-divergent nozzle up to the exit pressure of 2 bar. Assuming a nozzle efficiency of 0.94 for supersaturated flow up to the throat and nozzle efficiency as 90%, find (i) velocity at throat, (ii) mass flow rate if the throat diameter is 1 cm and (iii) velocity and diameter of the nozzle.

Q.5: Answer any three questions: 

                                                                         3X10=30

a) Derive the Maxwell’s Equations

b) Prove that C_p - C_V = -T(∂V/∂T)_p²(∂p/∂V)_T.

c) Steam at a pressure of 10 bar, dry saturated enters the nozzle when exit pressure is 0.3 bar. The nozzle efficiency for the convergent position is 96% and that of the divergent portion is 92%. The throat diameter for each nozzle is 6 mm. Find the mass flow rate of steam and the exit diameter required.

d) Air enters a nozzle at 5 bar, 350°C and comes out at 0.95 bar. The efficiency of expansion through the nozzle is 92%. If the mass flow rate of air is 1.5 kg/s, determine the exit diameter of the nozzle and velocity of air at exit.

TEST PAPER: EME- EME-303: THERMODYNAMICS

Section A:

      (1)           Attempt All The Questions:                                             5x2 = 10

a)     Define system & surroundings.

b)    What is heat pump & refrigerator?

c)     What is availability?

d)    What is Entropy?

e)  What is triple point of water?

Section B:

    (2)          Attempt any three questions                                                          3x5 = 15

    

(a)    Distinguish between microscopic & macroscopic approaches of thermodynamics.

(b)   What are the limitations of First law of thermodynamics? Explain the statements of Second law of thermodynamics.

(c)    2 kg of a gas at 10 bar expands adiabatically and reversibly till the pressure drops to 5 bar. During the process 120 kJ of non-flow work is done by the system, and the temperature falls from 377° centigrade to 257°C. Calculate the value of the index of expansion and the characteristics gas constants.

Let the equation of expansion be P1-γ.Tγ = constant Hence, P1(1-γ)T1γ = P2(1-γ)T2γ

(d)   Derive the Tds equations.

(e)    Steam at a pressure of 4 bar absolute and having dryness fraction of 0.75 is heated at constant volume to a pressure of 5 bar absolute. Find the final condition of the steam and the heat absorbed by 1 kg of steam.

Section C:

Attempt part (a) or part (b) of the following questions                           5x5=25

(3) (a) Explain thermodynamic equilibrium and quasi-static process.

     (b) A steam turbine developing 110 kW is supplied steam at 17.5 bar with an internal energy of 2600 kJ/min and specific volume of 0.155 m³/kg and velocity of 100 m/s. exhaust from turbine is at 0.1 bar with internal energy of 2093 kJ/min and sp. Volume = 15.5 m³/kg and velocity of 275 m/s. heat loss from the steam turbine 37.6 kJ/kg neglecting potential energy changes, determine steam flow rate in kg/hr.

(4)(a) Prove the equivalence of Kelvin-Planck statement & Clausius statement.

     (b) A reversible engine takes 2400 kJ/min from a reservoir at 750 K develops 400 kJ/min of work during the cycle. The engine rejects heat to two reservoirs at 650 K & 550 K. Find the heat rejected to each sink.

(5)(a) Explain the principle of entropy increase.

    (b) Explain the Gibbs Function & Gibbs free energy

           

(6)(a) Distinguish between Universal gas constant and characteristics gas constant with proper example.

    (b) Explain the causes of internal and external irreversibility.

(7)(a) A gas having a moleculer mass of 28 occupies 0.13 m³ at a pressure of 1.5 bar and a temperature 21°C. Find the mass of gas and the volume as well as the density at 0°C and 1 bar pressure.

(b)    One kg of an ideal gas is heated from 18.3°C to 93.4°C. Assuming R=287 J/kg-K and

 γ = 1.18 for the gas. Find out (i) specific heats, (ii) change in internal energy and

(iii) change in enthalpy

ASSIGNMENT ON THERMODYNAMICS

Numericals on Thermodynamics:

1.     Mass enters an open system with one inlet and one exit at a constant rate of 50 kg/min. At the exit, the mass flow rate is 60 kg/min. If the system initially contains 1000 kg of working fluid, determine the time when the system mass becomes 500 kg.

2.     Mass leaves an open system with a mass flow rate of c*m, where c is a constant and m is the system mass. If the mass of the system at t = 0 is m₀, derive an expression for the mass of the system at time t.

3.     Water enters a vertical cylindrical tank of cross-sectional area 0.01 m² at a constant mass flow rate of 5 kg/s. It leaves the tank through an exit near the base with a mass flow rate given by the formula 0.2h kg/s, where h is the instantaneous height in m. If the tank is empty initially, develop an expression for the liquid height h as a function of time t. Assume density of water to remain constant at 1000 kg/m³.

4.     A conical tank of base diameter D and height H is suspended in an inverted position to hold water. A leak at the apex of the cone causes water to leave with a mass flow rate of c*sqrt(h), where c is a constant and h is the height of the water level from the leak at the bottom. (a) Determine the rate of change of height h. (b) Express h as a function of time t and other known constants, rho (constant density of water), D, H, and c if the tank was completely full at t=0.

5.     Steam enters a mixing chamber at 100 kPa, 20 m/s, with a specific volume of 0.4 m³/kg. Liquid water at 100 kPa and 25^oC enters the chamber through a separate duct with a flow rate of 50 kg/s and a velocity of 5 m/s. If liquid water leaves the chamber at 100 kPa and 43oC with a volumetric flow rate of 3.357 m³/min and a velocity of 5.58 m/s, determine the port areas at the inlets and exit. Assume liquid water density to be 1000 kg/m³ and steady state operation.

6.     Air is pumped into and withdrawn from a 10 m³ rigid tank as shown in the accompanying figure. The inlet and exit conditions are as follows. Inlet: v₁= 2 m³/kg, V₁= 10 m/s, A₁= 0.01 m²; Exit: v₂= 5 m³/kg, V₂= 5m/s, A₂= 0.015 m². Assuming the tank to be uniform at all time with the specific volume and pressure related through p*v=9.0 (kPa.m³), determine the rate of change of pressure in the tank.

7.     A gas flows steadily through a circular duct of varying cross-section area with a mass flow rate of 10 kg/s. The inlet and exit conditions are as follows. Inlet: V₁= 400 m/s, A₁= 179.36 cm²; Exit: V₂= 584 m/s, v₂= 1.1827 m/kg. (a) Determine the exit area. (b) Do you find the increase in velocity of the gas accompanied by an increase in flow area counter intuitive? Why?

8.     Steam enters a turbine with a mass flow rate of 10 kg/s at 10 MPa, 600^oC, 30 m/s, it exits the turbine at 45 kPa, 30 m/s with a quality of 0.9. Assuming steady-state operation, determine (a) the inlet area, and (b) the exit area. 

Answers: (a) 0.01279 m² (b) 1.075 m²