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## A pplied Thermodynamics

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**3. GAS TURBINES AND JET PROPULSION**Introduction: Gas turbines are prime movers producing mechanical power from the heat generated by the combustion of fuels. They are used in aircraft, some automobile units, industrial installations and small – sized electrical power generating units. A schematic diagram of a simple gas turbine power plant is shown below. This is the open cycle gas turbine plant.**Working:**Air from atmosphere is compressed adiabatically (idealized) in a compressor (usually rotary) i.e., Process 1–2. This compressed air enters the combustion chamber, where fuel is injected and undergoes combustion at constant pressure in process 2–3. The hot products of combustion expand in the turbine to the ambient pressure in process 3–4 and the used up exhaust gases are let out into the surroundings.**The compressor is usually coupled to the turbine, so that**the work input required by the compressor comes from the turbine. The turbine produces more work than what is required by the compressor, so that there is net work output available from the turbine. Since the products of combustion cannot be re–used, real gas turbines work essentially in open cycles. The p–v and T–s diagrams of such a plant are shown above.**The compressor is usually coupled to the turbine, so that**the work input required by the compressor comes from the turbine. The turbine produces more work than what is required by the compressor, so that there is net work output available from the turbine. Since the products of combustion cannot be re–used, real gas turbines work essentially in open cycles. The p–v and T–s diagrams of such a plant are shown above.**Brayton Cycle:**This is the air–standard cycle for the gas turbine plant. It consists of two reversible adiabatic processes and two reversible isobars (constant pressure processes). The p–v and T–s diagrams of a Brayton Cycle are as shown.**Process 1 - 2: Reversible adiabatic compression.**2 – 3: Reversible constant pressure heat addition. 3 – 4: Reversible adiabatic expansion. 4 – 1: Reversible constant pressure heat rejection. A schematic flow diagram of this somewhat hypothetical gas turbine plant is shown below.**Though this plant works on a closed cycle, each of the four**devices in the plant is a steady–flow device, in the sense that there is a continuous flow of the working fluid (air) through each device. Hence, the steady–flow energy equation is the basis for analysis, and can be applied to each of the four processes. Neglecting changes in kinetic and potential energies, the steady flow energy equation takes the from Q – W = ∆h = Cp.∆T (Since air is assumed to be an ideal gas) Process 1 – 2 is reversible adiabatic, hence Q1-2 = 0 W1-2 = - Cp.∆T = - Cp (T2 – T1): - ve, work input Work of compression Wc = |W1 – 2| = Cp (T2-T1)**Process 2–3 is a constant pressure process**Heat added, Process 3-4 is again reversible adiabatic, +ve work output.**Process 4-1 is also a constant pressure process**: -ve, i.e., heat is rejected Heat rejected, Q2 = |Q4-1| = Cp (T4-T1) Therefore the cycle efficiency,**Therefore the cycle efficiency,**For isentropic process 1-2, & for process 3-4,**Since p3 = p2 and p4 = p1**Compression ratio,**Therefore,**Pressure ratio, Thus it can be seen that, for the same compression ratio, A closed cycle turbine plant is used in a gas–cooled nuclear reactor plant, where the source is a high temperature gas cooled reactor supplying heat from nuclear fission directly to the working fluid (gas/air).**Comparison between Brayton Cycle and Otto cycle:-**For the same compression ratio, and nearly same net work output (represented by the area inside the p–v diagram), the Brayton cycle handles larger range of volume and smaller range of pressure than does the Otto cycle.**A Brayton cycle is not suitable as the basis for**the working of reciprocating type of devices (Piston–Cylinder arrangements). A reciprocating engine cannot efficiently handle a large volume flow of low pressure gas. The engine (Cylinder) size becomes very large and friction losses become excessive. Otto cycle therefore is more suitable in reciprocating engines.**However, a Brayton cycle is more suitable than an Otto**cycle, as a basis for a turbine plant. An I.C. engine is exposed to the highest temperature only intermittently (for short way during each cycle), so that there is time enough for it to cool. On the other hand, a gas turbine, being a steady flow device, is continuously exposed to the highest temperature.**Metallurgical considerations, therefore limit the**maximum temperature that can be used. Moreover, in steady flow machines, it is easier to transfer heat at constant pressure than at constant volume. Besides, turbines can be efficiently handle large volume of gas flow. In view of all these, the Brayton cycle more suitable as the basis for the working of gas turbine plants.**Effect of irreversibility’sin turbine/compressor:**In the ideal Brayton cycle, compression and expansion of air are assumed to be reversible and adiabatic. In reality, however, irreversibility’s do exist in the machine operations, even though they may be adiabatic. Hence the compression and expansion processes are not really constant entropy processes. Entropy tends to be increase (as per the principle of increase of entropy).**Effect of irreversibility’sin turbine/compressor:**The T–s diagram of a Brayton cycle subject to irreversibility’s will be as shown. Irreversibility’s result in a reduction in turbine output by (h4-h4S) and in an increase in the compressor input by (h2 – h2S). Hence the output reduces by the amount (h4–h4S )+ (h2–h2s). Though heat input is also reduced by (h2-h2s), the cycle efficiency is less than that of an ideal cycle. The extent of losses due to irreversibility’s can be expressed in terms of the turbine and compressor efficiencies.**Turbine efficiency,**Compressor efficiency,**Methods of improving the efficiency of Brayton cycle:**Use of regeneration: The efficiency of the Brayton cycle can be increased by utilizing part of the energy of exhaust air from the turbine to preheat the air leaving the compressor, in a heat exchanger called regenerator. This reduces the amount of heat supplied Q1from an external source, and also the amount of heat rejected Q2 to an external sink, by an equal amount. Since Wnet = Q1 - Q2 and both Q1 and Q2 reduce by equal amounts, there will be no change in the work output of the cycle.**Heat added Q1 = h3 –h2’ = Cp (T3 – T2’)**Heat rejected Q2 = h4’ – h1 = Cp (T4’ – T1) Turbine output WT = h3 – h4 = Cp (T3 – T4) Compressor input WC = h2 – h1 = Cp (T2 – T1) Regeneration can be used only if the temperature of air leaving the turbine at 4 is greater than that of air leaving the compressor at 2. In the regenerator, heat is transferred from air leaving the turbine to air leaving the compressor, thereby raising the temperature of the latter. The maximum temperature to which compressed air at 2 can be heated is equal to the temperature of turbine exhaust at 4.**This, however, is possible only in an ideal regenerator.**In reality, T2’<T4. The ratio of the actual temperature rise of compressed air to the maximum possible rise is called effectiveness of the regenerator.**With a regenerator, since Wnet remains unchanged, but Q1**reduces, efficiency η = Wnet/Q1 increases. This is also evident from the fact that the mean temperature of heat addition increases and the mean temperature of heat rejection reduces with the use of the regenerator, and efficiency is also given by**With regenerator,**In the regenerator, Heat lost by hot air = Heat gained by cold air i.e., With an ideal regenerator,**, the cycle**efficiency decreases with increasing pressure ratio. In practice, a regenerator is expensive, heavy and bulky and causes pressure losses, which may even decrease the cycle efficiency, instead of increasing it. For a fixed ratio**In this arrangement, compression of air**is carried out in two or more stages with cooling of the air in between the stages. The cooling takes place in a heat exchanger using some external cooling medium (water, air etc). Shown above is a schematic flow diagram of a gas turbine plant with two-stage compression with inter cooling.**1-2: first stage compression (isentropic)**2-3: inter cooling (heat rejection at constant pressure) 3-4: second stage compression (isentropic) 4-3: constant pressure heat addition 5-6: isentropic expansion 6-1: constant pressure heat rejection.**Air, after the first stage compression is cooled before it**enters the second stage compressor. If air is cooled to a temperature equal to the initial temperature (i.e., if T3=T1), inter cooling is said to be perfect. In practice, usually T3 is greater than T1. Multistage compressor with inter cooling actually decreases the cycle efficiency. This is because the average temperature of heat addition Tadd is less for this cycle 1-2-3-4-5-6 as compared to the simple Brayton cycle 1-4’-5-6 with the initial state 1. (referfig). Average temperature of heat rejection Trej also reduces, but only marginally.**Hence efficiency is less for the modified cycle. However, if**a regenerator is also used the heat added at lower temperaturerange (4 to 4’) comes from exhaust gases from the turbine. So there may be an increase in efficiency (compared to a simple Brayton cycle) when multi–stage compression with inter cooling is used in conjunction with a regenerator. For a gas turbine plant using 2–stage compression without a generator, Q1 = h5 - h4 = Cp(T5 - T4) WT = h5 - h6 = Cp(T5-T6) WC = (h2 - h1) + (h4 - h3) = Cp [(T2 - T1) + (T4 - T3)]**WC = (h2 - h1) + (h4 - h3) = Cp [(T2 - T1) + (T4 - T3)]**Wnet = WT – WC = Cp [(T5 - T6) – {(T 2- T1) + (T4 - T3)}]**Here expansion of working fluid (air) is carried out in 2 or**more stages with heating (called reheating) in between stages. The reheating is done in heat exchangers called Reheaters. In an idealized cycle, the air is reheated, after each stage of expansion, to the temperature at the beginning of expansion. The schematic flow diagram as well as T-s diagram for a gas turbine plant where in expansion takes place in two turbine stages, with reheating in between, are shown. Multi-Stage expansion with reheating, by itself, does not lead to any improvement in cycle efficiency. In fact, it only reduces.**However, this modification together with regeneration**may result in an increase in cycle efficiency. It can be seen from the T-s diagram that the turbine exhaust temperature is much higher when multi stage expansion with reheating is used, as compared to a simple Brayton cycle. This makes the use of a regenerator more effective and may lead to a higher efficiency. Heat added Q1 = (h3 - h2) + (h5 - h4) = Cp(T3 - T2) + Cp(T5 - T4) Turbine output WT = (h3 - h4) + (h5 - h6) = Cp(T3 - T4) + Cp(T5 - T6) Compressor input WC = h2 - h1 = Cp(T2 - T1)**Ideal Regenerative cycle with inter cooling and reheat:**Considerable improvement in efficiency is possible by incorporating all the three modifications simultaneously. Let us consider a regenerative gas turbine cycle with two stage compression and a single reheat. The flow diagram and T-S diagram of such an arrangement is shown. Idealized Regenerative Brayton cycle with two stage compression with inter cooling and also two stage expansion with reheating – ideal regenerator, equal pressure ratios for stages, no irreversibilities, perfect inter cooling and reheating.**Heat added Q1 = Cp(T5 - T4’) + Cp(T7 - T6)**Turbine output WT = Cp(T5 - T6) + Cp(T7 - T8) Compressor input WC = Cp(T2 - T1) + Cp(T4 - T3) If perfect inter cooling, no irreversibilities, equal pressure ratios for stages and ideal regenerator are assumed, T1=T3, T2=T4=T8’, T5=T7 and T6=T8=T4’**Then, Q1 = Cp(T5 - T4’) + Cp(T7 – T6)**= Cp (T5 - T6) + Cp(T5 - T6) = (T5 - T6) Q2 = Cp(T8’ - T1) + Cp(T2 - T3) = Cp(T2 - T1) + Cp(T2 - T1) =2 Cp(T2 - T1)**It can be seen from this expression that the efficiency**decreases with increasing pressure ratio rp.**Effect of pressure Ratio rp on simple Brayton Cycle:-**That means, the more the pressure ratio, the more will be the efficiency. Temperature T1 (=Tmin) is dependent on the temperature of surroundings. Temperature T3 (=Tmax) is limited by metallurgical considerations and heat resistant characteristics of the turbine blade material. For fixed values of Tmin and Tmax, the variation in net work output, heat added and efficiency with increasing pressure ratio rp can be explained with the help of a T-s diagram as shown.**For low pressure ratio, the net work output is small and the**efficiency is also small (Cycle 1 – 2 – 3 - 4). In the limit, as rp tends 1, efficiency tends to zero (net work output is zero, but heat added is not zero). As the pressure ratio increases, the work output increases and so does the efficiency. However, there is an upper limit for rp when the compression ends at Tmax. As rp approaches this upper limit (rp)max, both net work output and heat added approach zero values. However, it can be seen that the mean temperature heat addition Tadd approaches Tmax, while the mean temperature of heat rejection approaches Tmin, as rp comes close to (rp)max.**Hence cycle efficiency, given by**approaches the Carnot efficiency i.e., rp - (rp)max When the compression ends at Tmax i.e., when state point 2 is at Tmax. When rp=rpmax,**The variation of net work output Wnet with pressure ratio rp**is shown below. As rp increases from 1 to (rp)max, Wnet increases from zero, reaches a maximum at an optimum value of rp i.e., (rp)opt and with further increase in rp, it reduces and becomes zero when rp = rpmax**Pressure Ratio for maximum net work output:-**Wnet= Cp[(T3 - T4) - (T2 - T1)] T3 = Tmax & T1= Tmin**Condition for maximum Wnet is**i.e., It can be seen that,**Maximum net work output**Corresponding to rp = (rp)opt i.e., when Wnet is maximum, cycle efficiency is**Open Cycle Gas Turbine Plants:**In practice, a gas turbine plant works on an open cycle. Air from atmosphere is first compressed to a higher pressure in a rotary compressor, which is usually run by the turbine itself, before it enters the combustion chamber. Fuel is injected into the combustion chamber where it undergoes combustion. The heat released is absorbed by the products of combustion and the resulting high temperature; high pressure products expand in the turbine producing work output.