Isentropic Expansion Within a Steam Turbine System

In summary: Regarding c),- The available power is equal to the steam flow rate multiplied by the turbine efficiencies:Available power = m(h1 - h2)- The energy available for low-grade heating is equal to the enthalpy of steam at saturation multiplied by the fraction of the steam that is at saturation:Energy available for low-grade heating = hs * (1 - hf)In summary,- Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure
  • #1
Matthew Hunter
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Homework Statement



Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure turbine to 1.0 bar and dryness fraction of 0.93. All ‘steam’ entering the feed pumps shall be a saturated fluid. Using steam tables only, calculate

a) the percentage of steam bled of to the feed heater

b) the power generated by the turbines per unit mass of steam leaving the boiler

c) the energy available for low grade heating from the condenser

2. The attempt at a solution

I have calculated the following enthalpy and entropy values for the inlet, high pressure turbine, and low pressure turbine:

Inlet - h = 3153.5 kJ/kg, s = 6.338 kJ/kgK
High Pressure - h2 = 2506.394 kJ/kg, h2s = 605 kJ/kg (25% isentropic efficiency)
Low Pressure - h2 = 2516.94 kJ/kg, h2s = 417 kJ/kg (23% isentropic efficiency)

Regarding a), I calculated the specific steam capacity of both the high pressure and low pressure turbine using SSC = 1 / h1 - h2. My assumption was that the SSC value in the low pressure turbine would be lower than the high pressure turbine, and then I would calculate the percentage difference and determine that this would be the amount to send to the feed heater to meet limitations. However, the SSC value in the low pressure turbine was larger. I want to know whether I'm barking up the completely wrong tree or not here.

For b), I realize that the power generated can be calculated from W = m(h1 - h2). I also know that the mass flow rate can be gotten from overall available power = m(h1 - h2). But without either a mass flow value or an overall power value I am struggling to progress here.
 
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  • #2
Hello Matthew, :welcome:

Let's start with the high-pressure turbine. From 9 MPa (your ##h_g## = 3153 kJ/kg, ##s_g## = 6.338 kJ/kg/K) to 0.4 MPa saturated.

in table A-5 here I find ##h_v## = 2738.1 kJ/kg, ##s_v## = 6.8955 kJ/kg/K, ##h_f## = 604.66 kJ/kg, ##s_f## = 1.7765 kJ/kg/K

Your 2506.394 kJ/kg looks more like the enthalphy at saturation when T = 4 ##^\circ##C ?!

Can you show how you calculate the isentropic efficiency ?
 
Last edited:

Related to Isentropic Expansion Within a Steam Turbine System

1. What is isentropic expansion within a steam turbine system?

Isentropic expansion is a process in which steam is allowed to expand through a turbine, converting its internal energy into mechanical work. This process is isentropic because it occurs without any change in entropy, meaning that there is no heat transfer or energy losses during the expansion.

2. How does isentropic expansion work?

In a steam turbine system, high pressure steam enters the turbine and is directed through a series of stationary and rotating blades. As the steam passes through these blades, its pressure and temperature decrease, causing it to expand and generate mechanical work. The isentropic nature of this process ensures that the steam expands without losing any of its energy.

3. What are the benefits of isentropic expansion within a steam turbine system?

Isentropic expansion allows for maximum utilization of the steam's energy, resulting in higher efficiency of the turbine. This process also helps to reduce wear and tear on the turbine blades, as there is no sudden change in pressure or temperature during the expansion.

4. How is isentropic efficiency calculated in a steam turbine system?

Isentropic efficiency is a measure of how well a turbine is able to convert the available energy in the steam into mechanical work. It is calculated by dividing the actual work output of the turbine by the work output that would be achieved if the process were isentropic. A higher isentropic efficiency indicates a more efficient turbine.

5. What are some real-world applications of isentropic expansion in steam turbine systems?

Isentropic expansion is commonly used in power generation, where steam turbines are used to convert the energy of high pressure steam into electricity. It is also used in industrial processes, such as in chemical plants, paper mills, and sugar refineries, where steam is used to power machinery and equipment.

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