A gas turbine for an automobile is designed with a...

A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. The compressor pressure ratio is $8,$ the maximum cycle temperature is $800^{\circ} \mathrm{C},$ and the cold airstream leaves the regenerator $10^{\circ} \mathrm{C}$ cooler than the hot airstream at the inlet of the regenerator. The cycle produces $150 \mathrm{~kW}$. The compressor isentropic efficiency is 87 percent, and the turbine isentropic efficiency is 93 percent. Determine the exergy destruction for each of the processes of the cycle. The temperature of the hot reservoir is the same as the maximum cycle temperature, and the temperature of the cold reservoir is the same as the minimum cycle temperature. Use constant specific heats at room temperature.

Key Concepts

Constant Specific Heats Assumption

Assuming constant specific heats (cp and cv) at a reference temperature simplifies the analysis of thermodynamic processes, especially when dealing with air or ideal gases. This approximation allows for direct application of energy balance equations and efficiency calculations without the complexities of temperature-dependent property variations, making it a common approach in preliminary design and analysis of cycles like gas turbines.

Gas Turbine Cycle

The gas turbine cycle is a thermodynamic cycle that converts fuel energy into mechanical work through a series of processes including compression, heat addition, and expansion. It involves a compressor that pressurizes the air, a combustor where fuel is added and burned, and a turbine that extracts work, making it a fundamental concept in power generation and propulsion, especially in systems where high power-to-weight ratios are important.

Regenerator

A regenerator is a heat exchanger used in a gas turbine cycle to transfer heat between the exhaust (hot stream) and the incoming air (cold stream). This recovery of thermal energy improves the overall cycle efficiency by preheating the compressed air, thereby reducing the amount of additional fuel required for reaching the required high cycle temperatures. It exemplifies how waste heat recovery can enhance system performance.

Exergy Destruction

Exergy destruction refers to the loss of useful work potential due to irreversibilities in a process, such as friction, heat transfer across finite temperature differences, and non-ideal fluid dynamics. In thermodynamic analysis, quantifying exergy destruction in each component of the cycle helps identify inefficiencies and areas for improvement, as it provides insight into how far a process is from the ideal reversible state.

Isentropic Efficiency

Isentropic efficiency is a measure of how closely the performance of a real process (such as compression or expansion in turbines) approaches that of an ideal isentropic process, which is both reversible and adiabatic. For compressors and turbines, the isentropic efficiency indicates how effectively work is consumed or converted, which is crucial for accurate performance prediction and for diagnosing energy losses in the cycle.

Transcript

00:01 Another question is a gas turbine for an automobile is designed with a regenerator.

00:03 A air enters the compressor of this engine at 100 khal pressure with a compression ratio with a compressor pressure ratio is 8.

00:21 The maximum cycle temperature is at temperature is 20 degrees centigrade and the maximum cycle temperature is 800 degrees centigrade and the core air string leaves that regenerated 10 degree centigrade cooler than a hot stream of the inlet of the regenerate.

00:37 The cycle produces 150 kilowatt of power.

00:41 Compressor isotropic efficiency is 87 % and power is 150 kilowatt.

01:02 The compressor ionotropic efficiency is 97 % and the turbine efficiency is 93%.

01:10 Determine the exorgy destruction for each of the compresses of the cycle.

01:14 The temperature of the hot reservoir is same as the maximum cycle and the temperature of the the cold is the same as the minimum cycle temperature use constant specific heat at room temperature now first properties of air at room temperature are also given that is cp is equals to 1 .005 kilojou per kg .k and k is equal to 1 .4 now first we will draw the t in s diagram this is 6 3 5 s heat added heat output heat this is 293 kelvin and this is 107 3 kelvin.

02:52 Now for the compression expansion processes we have an expansion processes.

03:17 We have k2s is equals to t1 rp power k minus 1 divided by k is equals to 293 into 8 power 0 .4 divided by 1 .4.

03:41 Is equals to 530 .8.

03:51 Cp is equals to t2s minus t1 cp into t2 minus t1 that is t2 is equal to t1 plus t2s minus t1 divided by efficiency of a compressor that is 293 plus 530 .8 minus 293 divided by 0 .8 7 answer would be 560 6 .3 kelvin.

04:34 Now t5 s is equals to t4 into 1 divided by rp power k minus 1 divided by k that is 1073 divided by 1 by 8 power 0 .4 divided by 1 .4 answer would be 592 .3 fecency would be t 4 minus t 5 divided by cp into t 4 minus t 5 s so from here t 4 is equals to t 4 minus efficiency of a turbine into t 4 minus t 5s that is equals to one 0 7 3 minus 0 .93 into 107 3 minus 5 92 .3 answer would be 625 .9 when the first clause applied to the heat exchanger to heat exchanger it gives t3 minus t2 is equals to t5 minus t6 while the regenerator temperature specification gives t3 is equals to t5 minus 110 minus 10 is equals to 620 minus 10 is equals to 615 .9 10.

07:14 And the simultaneous solution of these two results give.

07:23 And the simultaneous solution results give t6 is equals to t5 minus t3 minus t2 that is 625 .9 minus 6 .1.

07:58 Minus 566 .3 answer to 3...

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