Power company "E" in the Netherlands operates a fluidized bed combustion-based boiler with wood residues as fuel. The plant contains a simple steam turbine. The steam conditions at the inlet of the turbine are \(525^{\circ} \mathrm{C}\) and 100 bar. Assume that condensation of the steam takes place at a temperature of \(20^{\circ} \mathrm{C}\) and that isentropic expansion of steam occurs in the turbine. a. What is the specific power \(\left(\mathrm{kJ} \cdot \mathrm{kg}^{-1}\right)\) of the turbine expansion process? b. If the power plant generates \(25 \mathrm{MW}_{\mathrm{e}}\) and water pump work can be neglected, what is the mass flow rate of steam through the turbine? c. What assumptions have you made for these calculations?

Step by step solution

01

Finding specific enthalpy of steam at the inlet and outlet conditions

For the given steam inlet conditions of 525°C and 100 bar, we need to find the specific enthalpy (\(h_{in}\)) of the steam. As we are assuming isentropic expansion, we will have the same entropy in the outlet (condensation) as at the inlet. We can use the steam tables to find these values. For the given steam condensation conditions of 20°C, we need to find the specific enthalpy (\(h_{out}\)) in this state. Again, we can use the steam tables for this.

02

Calculating the specific power of the turbine expansion process

The specific power of the turbine expansion process can be calculated as the difference between the inlet and outlet specific enthalpy values. Specific Power = \(h_{in} - h_{out}\) Using the steam tables, we find \(h_{in} \approx 3495 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1}\) and \(h_{out} \approx 84 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1}\). Plugging these values, we have: Specific Power = \(3495 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1} - 84 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1} \approx 3411 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1}\)

03

Calculating the mass flow rate of steam through the turbine

The electrical output of the power plant is given as 25 MWe. Assuming the efficiency of converting mechanical power into electrical power is 100% (ideal case), we can find the mass flow rate by dividing the total output power by the specific power of the turbine. Mass Flow Rate = \( \frac{Total \, Power \, Output}{Specific \, Power}\) Plug in the values, 25 MWe = 25,000 kWe, we have: Mass Flow Rate = \(\frac{25,000 \, \mathrm{kW}}{3411 \, \mathrm{kJ} \cdot \mathrm{kg}^{-1}} \approx 7.33 \, \mathrm{kg} \cdot \mathrm{s}^{-1}\)

04

Listing the assumptions made for these calculations

1. We have assumed ideal behavior and neglected any losses. 2. We didn't take into account the water pump work. 3. We assumed isentropic (constant entropy) expansion of steam in the turbine. 4. We assumed that the efficiency of converting mechanical power into electrical power is 100%. So, in conclusion, the answers are: a. The specific power of the turbine expansion process is approximately 3411 kJ/kg. b. The mass flow rate of steam through the turbine is approximately 7.33 kg/s. c. The assumptions made are ideal behavior, constant entropy expansion, neglecting water pump work, and 100% conversion efficiency.

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