Question

The gas-turbine portion of a combined gas-steam power plant has a pressure ratio of 16. Air enters the compressor at 300 K at a rate of 14 kg/s and is heated to 1500 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400C400^{\circ} \mathrm{C} at 10 MPa in a heat exchanger. The combustion gases leave the heat exchanger at at 420 K. The steam leaving the turbine is condensed at 15 kPa. Assuming all the compression and expansion processes to be isentropic, determine (a) the mass flow rate of the steam. (b) the net power output, and (c) the thermal efficiency of the combined cycle. For air, assume constant specific heats at room temperature.

Solution

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To solve this problem we will need the enthalpies at all points of the steam cycle.

For the enthalpy\textbf{enthalpy} h1h_1 we will use the saturated liquid water tables and the given pressure p1=15 kPap_1=15\text{ kPa}.

h1=226kJkg\begin{equation*} h_1=226\,\frac{\text{kJ}}{\text{kg}} \end{equation*}

For the enthalpy\textbf{enthalpy} h2h_2 we will add the work done by the pump wp1w_{p1} to the enthalpy h1h_1. For the work wp1w_{p1} we will need the specific volume of the water v1=0.00101 m3/kgv_1=0.00101\text{ m}^3\text{/kg} and the pressure p1p_1 and p2=10000 kPap_2=10000\text{ kPa} .

h2=h1+v1(p2p1)h2=226kJkg+0.00101m3kg(10000 kPa15 kPa)h2=236.08kJkg\begin{align*} h_2&=h_1+ v_1\cdot (p_2 - p_1) \\ h_2&=226\,\frac{\text{kJ}}{\text{kg}}+ 0.00101\,\frac{\text{m}^3}{\text{kg}}\cdot (10000\text{ kPa}- 15\text{ kPa}) \\ h_2&=236.08\,\frac{\text{kJ}}{\text{kg}} \end{align*}

To determine the enthalpy h3\textbf{enthalpy }h_3 we will use the given pressure p3=10000 kPap_3=10000\text{ kPa} and the temperature T3=400°CT_3=400\text{\textdegree}\text{C} in the appropriate software.

h3=3100kJkg\begin{equation*} h_3=3100\,\frac{\text{kJ}}{\text{kg}} \end{equation*}

The entropy s3=6.210 kJ/kg Ks_3=6.210\text{ kJ}\text{/kg K} is equal to entropy s4s_4 and we can use that and the pressure p4=15 kPap_4=15\text{ kPa} in the appropriate software to determine the enthalpy\textbf{enthalpy} h4h_4.

h4=2010kJkg\begin{equation*} h_4=2010\,\frac{\text{kJ}}{\text{kg}} \end{equation*}

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