Thermodynamic Questions and Solutions for Steam and Gas Turbine Plants

[cookie85]

Homework Statement

Can anyone help on the below? I have been working on this for days and still can't find the solutions?!?

Homework Equations

Steam ar 40 bar and 400C enters the high pressure turbine of a steam power plant at a rate of 20kg/s and explands to a pressure of 3 bar at which point it is just dry saturated. at this point part of the steam is re heated to 400C and then expands in the low pressure turbine to a condenser pressure of 0.05 bar with an isentropic efficiency of 88%. the remainder passes directly to asingle 'open' feed heater. the water leaving the condenser is raised to the feed heater pressure which it enters at a temp of 50C

1) Draw a schematic diagram of the plant and a corredponding cycle diagram on a temperature-entropy axes

2) neglecting feed pump work inputs, find:
a) the mass flow rates of steam and water entering the feed heater
b) the plnats power output and heat input
c) the plants thermal efficiency

A gas turbine plant is fuelled by Methane,. After compresssion the air and fuel enter the combustion chamber at a temp of 600K and excess air is supplied in order to limit the temp of the combustion products to 1200K after steady flow, adiabatic combustion.

1) Illustrate the combustion process on a temp-enthalpy axes (have got this question right i believe but wouldn't hurt to double check my graph)

2) Find the volumetric air-fuel-ratio used

3) What air-fuel-ratio would be required to achieve the maximum temp of the combustion products?

The Attempt at a Solution

 

[lalbatros]

cookie85,

I can have fun with this kind of problems, but how could I help you if your show nothing from your attempt at a solution?
In addition, there are two different problems (steam turbone, gas turbine). You should concentrate on each in differents threads.

You said you worked on that for days. What did you do during these days? Explaining that would help to start a discussion. Don't wait too much. You mentioned some graphics you did, why don't you show them here?

For the steam turbine, I think the statement of the problem is very clear.
You should at least try to make a drawing of that.
I have myself a bit difficulty to understand the last steps of the circuit (I don't always understand english proeperly).
What is a "single 'open' feed heater"?

If you read the statement of the problem, you will discover that the state of the stream is precisely defined at each step of the circuit. After the first turbine, you know the pressure and the saturation pressure. The state after the second turbine is determined by the expansion with a given efficiency. The last step is not totally clear for me, but it is not necessary to calculate the power of the plant. Still, it will be necessary to calculate the effciency, since some heat recuperation is involved.

For the gas turbine, the main point is about calculating how much air would lead to an adiabatic flame temperature of 1200K.
Have you written the enthalpy balance of the combustion process?
In this balance, the amount of air in an unknown, but the enthalpies of the input streams and output stream are known from thermodynamic tables. Therefore, you simply need to solve a linear equation to find the amount of air needed.

Finally, we can assume that the maximum temperature is achieved for a stoechiometric combustion. It is not difficult to calculate the corresponding volumes. Have you tried?

Note that near the stoechiometric combustion, the combustion products may be significantly different from CO2 and H2O. Carbon monoxide can be formed (CO) and below steochiometry a lot of chemical species can appear like CO, H2, unburnt CH4, or even soot (C). But nevertheles, it is an good approximation that the maximum temperature is reached at stoechiometric combustion and that CO2 and H2O are formed. (CO may be non neglible)

 

[cookie85]

lalbatros,

You have been most helpful in your response. I probably didnt make myself clear enough in my original query.

On the steam turbine question, i have no problem drawing the schematic diagram, what i am really struggling with is the second part of the question and calculating the outputs and efficiencys. I have no idea of how to do this. A single feed heater, would be a type of heat sink with one connection feed only. Do you understand?

Can you advise on any calculations

2) neglecting feed pump work inputs, find:
a) the mass flow rates of steam and water entering the feed heater
b) the plants power output and heat input
c) the plants thermal efficiency


As for the gas turbine question, again calculating the AFR and max temp from combustion is what i am having difficulty doing. I am not really sure how to balance the equations, but can take enthalpys of inputs and outputs from relevant steam tables.

lalbatros can you help me with this, it is critical for me to know this, and need written solutions to work through the answers. I don't think i am capable of doing this on my own.

Thanks, my email is cookiemyster1@hotmail.com

Would be most helpful.

 

[lalbatros]

cookie85,

I don't understand why you don't show us something.

To solve problems in technical termodynamics you must know when and how the state of a system is completely defined. When a system comprises one phase, it is completely defined by two (independent) variables like pressure and temperature. If there are two phases, you need three variable. You know the phase rule probably. When the state is defined, you can calculate all state functions like enthalpy, entropy, ... You do that with tables, or with thermodynamic charts or with computer programs. I don't konw the tools you have to solve that. I guess you are supposed to use chart: on charts you must learn to pinpoint a coordinate from the data specifying the state of the system and then read other data ploted of the chart.

steam turbine
To solve question a) you must find the state of the water+vapor system when it enters the "feed heater". To do that you must proceed step by step up to this point. Let's have a look at the successive states till there:

state1: 1 phase: steam, p=40 bar, T=400°C, H= ... kJ/kg, S= ... kJ/kg/°C
state2: 1 phase: steam, p=3 bar, steam is "saturated" psat(T)=3bar, T= ...°C, H= ..., S= ...
state3: 1 phase: steam, p=3 bar, steam is reheated, T=400°C, H= ..., S= ...
state4: 2 phases, p=0.05 bar, enthalpy determined by the is-efficient of the LP stage​

To determine state4, you must first determine the enthalpy H4' that would be obtained if the is-efficiency was 100%. The the actual enthalpy H4 would be obtained from the definition: H4-H3 = 0.88 (H4'-H3). All other data for this state are easily read on charts. Therefore:

state4: 2 phases, p=0.05 bar, H3=..., T=..., x(steam)=..., x(water)=..., S=...​

Once you have performed all these calculations, you can calculate easily the output power: P=(H2-H1)+(H4-H3) .
The heat consumption is (H1-H0) + (H3-H2), where state 0 is the pre-heated pressurised water. I guess this water is at 50°C and 40 bar.

Gas turbine
The stoechiometric AFR is calculated from the chemical balance equation:

CH4 + 2 O2 -> CO2 + 2 H2O​

Remember that air is used, not pure oxygen.
The approximate air composition is: 0.209 * moles_O2 + 0.791 * moles_N2
It is easy, I think, to calculate from this the volume of aire needed for a stoechiometric combustion of one volume of CH4. Calculating the flame temperature is an application of the heat balance equation:

a H_CH4(Tin) + b H_O2(Tin) + c H_N2(Tin) = e H_CO2(Tout) + f H_H2O(Tout) + g H_N2(Tout)

You must solve this balance equation for Tout.
The coefficient (a,b,c,d,e,f) are the quantities of each product, determined from the mass balance.
The various enthalpies H_xxx(T) are the total enthalpies including the heat of formation from the element.
It might be that you don't have exactly these data available, but other date. For example you might have specific heats and heat values. In that case you should first reconstruct the data you need, or write the balance equation in terms of the data you have available. In the end it amount to the same.

Solving the above equation can be done by different ways. If the enthalpies are approximated as linear functions of the temperature with constant specific heat, then you simply need to solve a linear equation for Tout. If the specific heat is not constant (much better assumption), then you will need to proceed iteratively. The exact way you do all these things will depend on the tools you are supposed to used, charts, tables, algebraic software, thermodynamic software, spreadsheet, ... paper and pencil. Keep the direction.

 

[cookie85]

Thank you.

You seem to have a very good understanding of what you are doing. Could you possible do the solutions for me?

I need the full solutions infront of me so i can work through them and learn it myself, with relevant equations used - or even have your best go?!?

I don't need this today, but with your help, i should know this very soon!

Could you get back to me soon?

 

[lalbatros]

Sorry, on this forum it is forbiden to give solutions.
You must work out the problem yourself, I am only allowed to help.
Be confident that if you make some effort you will get help and results.

First try to complete the dots in this line:

state1: 1 phase: steam, p=40 bar, T=400°C, H= ... kJ/kg, S= ... kJ/kg/°C

What is the enthalpy and entropy of pure steam at 40bar/400°C ?
What are your tools to solve this question?
Do you have a Mollier diagram, or do you have some steam table, or anything else?
There are many website where the water and steam thermodynamic data can be found.
One of the best is this one: http://webbook.nist.gov/chemistry/fluid/
Using a Mollier diagram is very instructive even it is "paper technology". I also suggest to give it a try.

 

[cookie85]

Yes that's no problem, i have steam tables that cover a whole range of enthalpys and entropys!...

So I find out wat the H's and S's are at 400 degrees C @ 40 bar, then i have for phase 1:

enthalpy, entropy, Temp and Pressure. Whats the next step. I always have an email address if its not aloud through this website.. This may take a while but you are being very helpful.

Whats the next stage, phase 2?...This is when expands to a pressure of 3 bar, the steam is then re-heated so what's my next step? Do i need to find the enthalpys and entropy again?!

 

[lalbatros]

cookie85,

I could give you an example.

Turbine input (state1): p = 50 bar, T = 480°C
Turbine output (state2): p = 5 bar, T = 250°C

reading the Mollier diagram or the tables you get:

H1 = 3387.7 kJ/kg, S1 = 6.917 kJ/kg/°C
H2 = 2961.1 kJ/kg, S2 = 7.273 kJ/kg/°C

You can conclude from this that the power output from this turbine is 426.6 kJ/kg, and for a flow of 10 kg/s, this would give 4266 kW. You can also observe that the entropy is higher at the output, therefore, the expansion was not isentropic. We can try to calculated the isentropic efficiency for this turbine.

Following the isentropic curve on the Mollier diagram (or by other means) you can reach the point (p = 5 bar, S = 6.917 kJ/kg/°C) where your can find H = 2789.7 kJ/kg. Therefore, if the expansion were isentropic the power would be 598.0 kJ/kg. Therefore also, the isentropic efficiency of the above turbine is 426.6/598.0 = 71.3%.

I hope this can inspire you to start your exercice.

 

[cookie85]

Thats great, but i have a few more questions if you have the time...Does that take into account the feed heater? and where does the water leaving the condenser come into it, as it enters the feed heater at 50 degrees C?

Its asking for the mass flow rate entering the feed heater? In your example you've said the flow is 10 kg/sec, and in mine its 20. So does that mean that is the flow going into the feed heater or do you calculate that another way.

Also on the gas turbine question (Part 1). do you think you could give me and example, as i found that most helpful in your last post. Finding the AFR and the max temp for combustion to take place?

Would be very useful??

 

[lalbatros]

cookie85,

Does that take into account the feed heater?

In the example I gave, the input and the output states to the turbine are fully specified.
There is no need to know how the high-pressure steam has been prepared.
Knowing the state of the high pressure and low pressure streams, you can calculate the work produced by the turbine. (note: it is possible to perform the same transformation from input to output without producing work but simply losing heat and pressure, by assumption this is not the case, the turbine works adiabtically).

... feed heater at 50 degrees C ...

As far as I understand the question, I think you can assume this plant has water at 50°C available for free. It is actually preheated in a heat exchanger with heat from the waste stream, but this does not really matter. You could check if that is really possible.

Its asking for the mass flow rate entering the feed heater? ...

It is asking for water and steam flow rates.
You need to determine how much water has condensated already at this point.
This is the less easy part of this exercice.
The easiest way to solve that is by using the Mollier diagram.
If you like analylical calculations or computers, you can also solve that of course. You simply need to consider a mixture of steam and water and write down the balance equation taking this mixture into account. Please note that the steam should be in equilibrium with the liquid water. This mean the pressure is the saturation pressure at assumed temperature.

Finding the AFR and the max temp for combustion to take place?

I explained you already in detail how to get the AFR and the temperature.
From my previous explanation, you can see that you need 2 volumes of oxygen for 1 volume of CH4.
Therefore you need 2/0.209 volume of air.
Roughly 10 volumes of air: 2 volumes of oxygen and 8 of nitrogen. (approximate numbers)
Therefore, you need to solve the following balance equation:

1 H_CH4(Tin) + 2 H_O2(Tin) + 2/0.209*0.791 H_N2(Tin) = 1 H_CO2(Tout) + 2 H_H2O(Tout) + 2/0.209*0.791 H_N2(Tout)

You have also: Tin=600K, you simply need to find Tout.
The simplest method is solving that by trial and error, it just needs a little bit of time.

 

[lalbatros]

I edited my post from 07:21 AM , because I had forgotten the re-heating phase.
I hope I did not introduce inconsistencies in the notations. Be carefull.

 

[cookie85]

Thanks for your help.

 

[lalbatros]

If you have some results, I can check them.

 

[cookie85]

Hello again, i was wondering if you can help?

I am using enthalpy equations to try and find h1 and h2 to work out 'work and heat transfers' for water, for a piston type question.

I have calculated work done using: [w = -PDV]

To find the heat transfer i need to use: [Q=m.(h2-h1)]

i have obtained h1 using: h1 = hf + x(hg-hf) (using steam tables)

This has been calculated at 1826 kg/m3, from a revision guide all it states to calculate h2 is:

''From the steam table using h1 find h2?''

This is the only piece of information i need to complete the heat transfer (to find h2) can you help at all? I don't now how to find h2.

I know m = 0.15, and h1 is 1826kg/m3 and Q is 223 kj

But h2?!

Guidance on how to look this up would be appreciated.