The gas-turbine cycle of a combined gas-steam power plant...

The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of $12 .$ Air enters the compressor at $310 \mathrm{K}$ and the turbine at $1400 \mathrm{K}$. The combustion gases leaving the gas turbine are used to heat the steam at $12.5 \mathrm{MPa}$ to $500^{\circ} \mathrm{C}$ in a heat exchanger. The combustion gases leave the heat exchanger at $247^{\circ} \mathrm{C}$. Steam expands in a high-pressure turbine to a pressure of $2.5 \mathrm{MPa}$ and is reheated in the combustion chamber to $550^{\circ} \mathrm{C}$ before it expands in a low-pressure turbine to $10 \mathrm{kPa} .$ The mass flow rate of steam is $12 \mathrm{kg} / \mathrm{s}$. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate of air in the gas-turbine cycle, ( $b$ ) the rate of total heat input, and ( $c$ ) the thermal efficiency of the combined cycle.

The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of $12 .$ Air enters the compressor at $310 \mathrm{K}$ and the turbine at $1400 \mathrm{K}$. The combustion gases leaving the gas turbine are used to heat the steam at $12.5 \mathrm{MPa}$ to $500^{\circ} \mathrm{C}$ in a heat exchanger. The combustion gases leave the heat exchanger at $247^{\circ} \mathrm{C}$. Steam expands in a high-pressure turbine to a pressure of $2.5 \mathrm{MPa}$ and is reheated in the combustion chamber to $550^{\circ} \mathrm{C}$ before it expands in a low-pressure turbine to $10 \mathrm{kPa} .$ The mass flow rate of steam is $12 \mathrm{kg} / \mathrm{s}$. Assuming all the compression and expansion processes to be isentropic, determine
(a) the mass flow rate of air in the gas-turbine cycle, ( $b$ ) the rate of total heat input, and ( $c$ ) the thermal efficiency of the combined cycle.

Key Concepts

Heat Exchanger

A heat exchanger is a device designed to efficiently transfer heat from one fluid to another without mixing them. In combined cycle power plants, heat exchangers are crucial as they extract residual thermal energy from the exhaust gases of the gas turbine to generate high-pressure steam for the steam turbine cycle, thereby boosting overall efficiency.

Steam Cycle

The steam cycle, often implemented as a Rankine cycle in power plants, involves converting water into steam using heat (from a boiler or heat exchanger), expanding the steam in a turbine to produce work, and then condensing the steam to be reused in the cycle. Reheating and multi-stage expansion processes can be incorporated to improve cycle efficiency and work output.

Isentropic Process

An isentropic process is a thermodynamic process that occurs without any entropy change, implying that it is both adiabatic (no heat transfer) and reversible. In ideal analyses, compression and expansion processes in turbines and compressors are assumed to be isentropic to simplify calculations and understand maximum theoretical performance, even though practical processes involve inefficiencies.

Mass Flow Rate

Mass flow rate is a measure of the mass of fluid moving through a system per unit time. In power cycles, it is a critical parameter as it directly relates to the energy content and flow of working fluids, impacting the size, efficiency, and performance of components such as turbines, compressors, and heat exchangers.

Combined Cycle Power Plant

A combined cycle power plant integrates both a gas turbine cycle and a steam turbine cycle to enhance the overall efficiency of power generation. In such plants, the high-temperature exhaust gases from the gas turbine, which would normally be wasted, are used to generate steam in a heat recovery boiler or heat exchanger. This steam then drives a steam turbine, thus providing additional power output from the same fuel source and resulting in improved fuel utilization and reduced emissions.

Gas Turbine Cycle

A gas turbine cycle is a thermodynamic cycle in which air is compressed, mixed with fuel and burn in a combustion chamber, and the high-temperature, high-pressure gas is then expanded through a turbine to produce work. This cycle is characterized by high power-to-weight ratios and is commonly used in power generation and aviation due to its simplicity and efficiency in converting fuel energy into mechanical energy.

Pressure Ratio

Pressure ratio is the ratio of the pressure at the compressor discharge to the pressure at the compressor inlet in a turbine engine. It is a key parameter that influences the thermal efficiency and performance of the system, as higher pressure ratios typically lead to increased work output and better fuel efficiency, albeit at the cost of increased mechanical and thermal stresses on the components.

Thermal Efficiency

Thermal efficiency is defined as the ratio of the work output (or net power generated) by a thermodynamic system to the total heat input. It describes how effectively a system converts heat energy into useful work, serving as a vital metric in evaluating the performance and energy conversion capabilities of thermal power plants.

Transcript

00:01 So we have a gas steam combined turbine, combined cycle here.

00:10 So in this case, we have a little bit of an interesting feature in that we're sending some of the steam out of the steam turbine into the combustion chamber for reheating, which is an interesting little way, interesting way to do things.

00:31 So it turns out that the temperature coming in out of here is 550 degrees c and well, it's coming in here is 550, coming in here is 550.

00:42 So we're actually getting a higher temperature.

00:47 Basically we reheated to a higher temperature.

00:53 Now we can, i mean, we could have obviously done a reheat cycle through the heat exchanger too, but we actually ran it through the combustion chamber.

01:03 Which is an interesting choice, because actually we'll basically then taking some of the energy out that would be then flowing into the gas turbine.

01:13 So i'm not sure exactly if that's a good thing to do or not.

01:18 But you could obviously do an analysis of that.

01:23 So let's see here.

01:24 We have a pressure ratio in the compressor of, we have 12 times the pressure here as we do here, and then 12 times the pressure here as we do here.

01:34 So this is all at atmospheric pressure here.

01:39 Let's see here.

01:40 What else do we know? coming in, we have 310 kelvin into the compressor.

01:46 Into the gas turbine, we have 1 ,400 kelvin.

01:51 These are degree c.

01:52 High pressure side of the steam cycle, we have 12 .5 megapascals.

01:59 The reheat pressure is 2 .5 megapascals, and the condenser pressure is 10 kilopepar pascal's, we're given a mass flow rate of steam of 12 kilograms per second.

02:13 So that's, i think, everything we can go talk about there.

02:18 And so we have, let's see here, we have an analysis to do.

02:29 On the gas side of things, we can use the charts to get this reduced pressure.

02:35 I don't, this isn't really the classical reduced pressure because the reduced pressure, atmospheric temperatures should be very small because the critical pressure is for air is really high.

02:51 So i don't know what this is, but it's given in the table and we can use it.

02:55 Some relative pressure.

02:56 Maybe i should just call it a relative pressure because they're reduced pressure.

03:01 I'm not sure exactly what that number is, but it's in the charts and we can use it because all we need is to use it as an intermediate.

03:10 So if we know the temperature at the inlet of the compressor, we can get the enthalpy and this relative pressure.

03:19 And then we can get the relative pressure at the exit of the condenser, because we know the pressure ratio through the condenser.

03:31 This is 12.

03:32 So then that relative pressure winds up being 18 .6.

03:36 And from that, we can then look in the table to figure out what the, basically use interpolation to figure out what the enthalpy at 8 is.

03:47 We can also figure out the temperature at 8, which i didn't do.

03:51 But again, you could figure that out too from the chart.

03:55 Now, at 9, we have 1 ,400 kelvin, so we can get the enthalpy there.

04:00 And again, we can look, we can get off that same chart, the relative pressure.

04:08 And again, divide this by 12.

04:10 Because you can get this pressure ratio.

04:13 So we have this relative pressure at 10, so then we can get the enthalpy at 10...

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