How Does an Ideal Rankine Cycle with Open Feedwater Heater Operate?

[pearltt]

Homework Statement

consider an ideal rankine cycle with 1 open feedwater heater, the operates at a condenser pressure of 1inch of mercury absolute pressure and a turbine inlet pressure of 950psig and 850 deg F. The cycle produces turbine output power of 30MW.
a)draw system diagram---done
b)first determine the amount of turbine extraction steam flow rate for a turbine inlet flow of 100 lb/h to heat the feedwater water to 325 deg F and state the gauge pressure of the extraction steam. ---- no idea how to set this up,
c)determine the actual amount of extraction stream(lb/h) to produce 30MW fo turbine power. ----im guessing this would be easily done once i figure out part b
d)cycle efficiency --- i see no problem in doing this part
e) t-s diagram-----done.

Homework Equations

The Attempt at a Solution

nothing noteworthy...i need most of the help on getting started and setting up, i am pretty sure everything else will follow pretty easily from there

 

[KataKoniK]

.

Thank you for your post. I would like to help you with your question.

To start, let's review the basic principles of an ideal Rankine cycle. The cycle consists of four main components: a boiler, a turbine, a condenser, and a pump. The working fluid, usually water, is first pumped to high pressure and then heated in the boiler to produce high-pressure, high-temperature steam. This steam then expands through the turbine, producing work that is used to drive a generator and produce electricity. The steam is then condensed back into liquid form in the condenser, and the cycle starts again.

Now, let's address the specific details of your problem. You have mentioned that the cycle operates at a condenser pressure of 1 inch of mercury absolute pressure and a turbine inlet pressure of 950 psig and 850 degrees Fahrenheit. From this information, we can calculate the specific volume of the steam at the turbine inlet using the ideal gas law. This will be necessary for determining the flow rate of steam through the turbine.

Next, we need to determine the amount of turbine extraction steam flow rate for a turbine inlet flow of 100 lb/h to heat the feedwater to 325 degrees Fahrenheit. This can be done by setting up an energy balance equation for the open feedwater heater. We know the inlet and outlet conditions of the steam and water, so we can solve for the extraction steam flow rate. We also need to find the gauge pressure of the extraction steam, which can be calculated using the steam tables.

Once we have the extraction steam flow rate, we can use it to determine the actual amount of extraction steam needed to produce 30 MW of turbine power. This can be done by setting up an energy balance equation for the turbine.

Finally, we can calculate the cycle efficiency using the Carnot efficiency formula. This will give us an idea of how well the cycle is operating and if there are any areas for improvement.

I hope this helps you get started on your problem. Please let me know if you need any further assistance. Good luck!

 

[piercas]

a) A system diagram for an ideal Rankine cycle with an open feedwater heater may look like this:

[IMAGE HERE]

b) To determine the amount of turbine extraction steam flow rate, we can use the following equation:

m(fw) * (h(fw) - h(cw)) = m(es) * (h(es) - h(cw))

Where m(fw) is the mass flow rate of feedwater, h(fw) is the specific enthalpy of feedwater at 325 deg F, h(cw) is the specific enthalpy of condensate water, m(es) is the mass flow rate of extraction steam, and h(es) is the specific enthalpy of extraction steam.

We can rearrange the equation to solve for m(es):

m(es) = (m(fw) * (h(fw) - h(cw))) / (h(es) - h(cw))

To find the specific enthalpy values, we can use a steam table or a thermodynamic properties calculator. Let's assume that the specific enthalpy of feedwater at 325 deg F is 1300 Btu/lb and the specific enthalpy of condensate water is 50 Btu/lb. We also know that the turbine inlet pressure is 950 psig, which is equivalent to 972.5 psia.

Using a steam table, we can find that the specific enthalpy of extraction steam at a pressure of 972.5 psia and a temperature of 850 deg F is approximately 1477 Btu/lb.

Plugging in these values, we get:

m(es) = (100 lb/h * (1300 Btu/lb - 50 Btu/lb)) / (1477 Btu/lb - 50 Btu/lb)

m(es) = 6.7 lb/h

Therefore, the amount of extraction steam flow rate needed to heat 100 lb/h of feedwater to 325 deg F is 6.7 lb/h.

To determine the gauge pressure of the extraction steam, we can use the ideal gas law:

P = ρRT

Where P is the pressure, ρ is the density, R is the gas constant, and T is the temperature.

Assuming that the extraction steam is an ideal gas, we can use the following equation to find the density:

ρ = P / (RT)

Plugging