A gas-turbine power plant operating on the simple Brayton...

A gas-turbine power plant operating on the simple Brayton cycle has a pressure ratio of 7 . Air enters the compressor at $0^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. The maximum cycle temperature is $1500 \mathrm{~K}$. The compressor has an isentropic efficiency of 80 percent, and the turbine has an isentropic efficiency of 90 percent. Assume constant properties for air at $300 \mathrm{~K}$ with $c_{v}=0.718 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$ $c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, k=1.4$ (a) Sketch the $T-s$ diagram for the cycle. (b) If the net power output is $150 \mathrm{MW}$, determine the volume flow rate of the air into the compressor in $\mathrm{m}^{3} / \mathrm{s}$. (c) For a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being the same.

A gas-turbine power plant operating on the simple Brayton cycle has a pressure ratio of 7 . Air enters the compressor at $0^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. The maximum cycle temperature is $1500 \mathrm{~K}$. The compressor has an isentropic efficiency of 80 percent, and the turbine has an isentropic efficiency of 90 percent. Assume constant properties for air at $300 \mathrm{~K}$ with $c_{v}=0.718 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$ $c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, k=1.4$
(a) Sketch the $T-s$ diagram for the cycle.
(b) If the net power output is $150 \mathrm{MW}$, determine the volume flow rate of the air into the compressor in $\mathrm{m}^{3} / \mathrm{s}$.
(c) For a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being the same.

Key Concepts

Brayton Cycle

The Brayton cycle is the idealized thermodynamic cycle used to model gas-turbine engines, where working fluid (air) is compressed, heated at constant pressure, and then expanded in a turbine. Its analysis involves understanding the processes of compression, combustion/heat addition, expansion, and heat rejection, which are key to assessing the performance of power plants and propulsion systems.

T-s Diagram

A Temperature-Entropy (T-s) diagram is a graphical representation of the thermodynamic processes within a cycle. In the context of the Brayton cycle, the T-s diagram helps visualize the isentropic compression and expansion processes, as well as the constant pressure heat addition process, providing insight into the efficiency and work interactions of the cycle.

Pressure Ratio

The pressure ratio is the ratio of the compressor outlet pressure to the compressor inlet pressure. It is a critical design parameter in the Brayton cycle, influencing both the thermal efficiency and the work outputs during the compression and expansion processes. A higher pressure ratio typically improves cycle efficiency but may also introduce challenges related to material limits and compressor performance.

Isentropic Efficiency

Isentropic efficiency measures how closely a real compressor or turbine process approximates the ideal isentropic process. It is defined as the ratio of the ideal work (or enthalpy change) to the actual work (or enthalpy change) experienced by the device. In practical systems, deviations from isentropic behavior cause additional irreversibilities and losses, and thus this efficiency is crucial for accurate performance calculation of the cycle.

Volume Flow Rate and Inlet Conditions

The volume flow rate of air into the compressor is linked to the inlet temperature and pressure through the ideal gas law. With all other parameters fixed, an increase in the inlet temperature (such as during summertime operation) leads to a decrease in the density of the incoming air. This reduction in density results in a lower mass flow rate for the same volumetric flow rate, which in turn can lead to a reduction in net power output, assuming the compressor inlet velocity and flow area remain constant.

Transcript

00:01 In this problem 98 of the gas power cycles, a simple burden cycle with air as a working fluid updates at a specified pressure ratio and between the temperature limits, temperature limits and pressure limits.

00:14 The cycle is to be sketched on the t .s cycle and the volume flow rate of the air into the compressor is to determine.

00:21 Also, the effect of compressor inlet temperature on the mass flow rate and the net power are to be investigated.

00:27 Here the properties of air at room temperature are given as, that is, c .p.

00:32 Z equals to 1.

00:32 0 .005 kilojou per kg .k .k .k .k.

00:41 And r is equal to 0 .287 kilojou per kjol.

00:50 And the value of k is 1 .4 is given on the table.

00:58 Now first we will sketch the tns diagram.

01:03 That is like this.

01:13 This is 3, 4, 4s, 2 and 2s.

01:24 This is one point this is a temperature 273 kelvin and this is a temperature 1 ,500 now to start the problem for compression process it gives t2 s is equals to t1 into p2 divided by p1 power k minus 1 divided by k that is plus to 2 273 7 7 into 0 .1 given 4 divided 1 .4 that is a equal to 476 .0 kelvin.

02:19 And thermal efficiency of a compressor is given as power a compressor divided by 12 term of compressor.

02:34 That is equals to mass flow rate cp into t2s minus t1 divided by ncp t2 minus t o.

02:56 That is equals to t2s minus t1 divided by t2 minus t1.

03:04 This is given as 0 .80, that is equal to 476 .0 minus 273 divided by t2 minus 273...

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