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Finding Specific Heat Ratios...
fkatzenb:
Hi all! This is my first post, and looking forward to interacting with everyone for my little side project. I am not a chemist or chem engineer. To my partial dismay, I am an electrical engineer that happens to be a car performance nut who loves to learn new topics. I did take 2 semesters of organic chemistry and a semester of thermo, however it didnt do much for me because I didnt care at the time. Now I do. :(.
Anyway, I am currently writing a spreadsheet tool for learning about how engines are effected by geometery, rpm, fuel mixtures, compression ratio, etc. One of the things that has gotten me started on this is the lack of learning guides that show how all of this interacts. There are desktop dynos which cost lots of money which show this in a way, but its only meant for end to end information. I wanted to create a free tool that anyone can use. This partly came about when I finally had to the chance to pickup John B Heywood's "Fundamentals of Internal Combustion Engines." Holy crap this book rocks. While I have alot of the information I need from this book, a few things are still lacking. These things that are lacking both in data and some understanding on my part.
This brings me to my question. 'Finding Specific Heat Ratios...' Becaue the compression cycle is a isentropic (or that is what i assumed... no heat loss), I used the equations that would net me this:
p2 / p1 = (v1 / v2) ^ (gamma)
T2 / T1 = (p2 / p1) ^ [(gamma - 1)/gamma]
with gamma being the specific heat ratio - cp/cv.
Since I know my start data of pressure and temperature, I was using them to calculate the next crank angle (or volume position)... and using this progression until I get to the end of the compression cycle.
Now it is my understanding that specific heat (or heat capacity) is temperature dependent. Isnt that a little recursive since my equations require me to calculate pressure first and then temperature? Or is it allowable to substitue and come up with:
T2/T1 = ([v1 / v2]^[gamma])^[(gamma - 1)/gamma)]
This would allow me to calculate temperature first to factor into the specific heat? I dunno. This is where I get horribly confused as this is new to me.
I appreciate your help and patience with me. Thanks!
Frank
eugenedakin:
Hello fkatzenb,
Personally having a mechanical background, I would be very interested in viewing your final product. I like your idea of your work on this topic.
To help with your question, the typical unit for specific heat is Btu/lb*F. In my interpretation of your question in this instance, the specific heat is related to the weight of fuel at the temperature of the air/mixed fuel inside the block during compression. Typical compression ratio's for internal spark ignition systems are between 7.5 and 10.0 for conventional street engines. During compression, there will be a very slight decrease in temperature due to boiling of rapidly condensed gases, and I think that this will be almost negligable when compared to the exothermic reaction of the controlled ignition of the fuel/air mixture. In my opinion, I believe that a signifacently larger factor would be the heat loss during the ignition of the air/fuel during the power stroke that is transferred to the cylinder sleeve (a.k.a. block).
Since I do not have John B Heywood's excellent book, I am only taking an educated guess. Feel free to post more information. This is also a very interesting topic for me.
Sincerely,
Eugene Dakin Ph.D., P.Chem.
Donaldson Tan:
--- Quote from: fkatzenb on June 14, 2005, 08:18:28 AM --- p2 / p1 = (v1 / v2) ^ (gamma)
T2 / T1 = (p2 / p1) ^ [(gamma - 1)/gamma]
--- End quote ---
i am not sure if the perfect gas assumption is valid for the conditions inside an internal combustion engine.
fkatzenb:
Thanks for the replies. This spreadsheet has been great for working thru the system of an automobile and all the different effects everything has. Below is a link for the spreadsheet I am building. I added alot of notes, etc to help you see the overall picture I am trying to achieve. There are still some more parameters and columns that will probably be needed... like entrapy, etc. You will also see that I assumed gamma so that I could fill the pressure temperature columns to get a small idea.
http://www.squirrelpf.com/site/files/tech/dd.xl
As for geodome's comment, I got the equations at the link below. What would you suggest I look at to determine what I need? Thanks!
http://www.grc.nasa.gov/WWW/K-12/airplane/compexp.html
If I can use the equations, can I use a subsitution of the equations to do the following to make the pressure and temperature more independent?
T2/T1 = ([v1 / v2]^[gamma])^[(gamma - 1)/gamma)]
If I do use specific heat for all of this to determine gamma, I was going to use 5 pressures against 5 temperatures to create two tables (for cp and cv) to do look ups on and do a rough interpolation to get me close.
Thanks again everyone!
Frank
Donaldson Tan:
the equations you got from http://www.grc.nasa.gov/WWW/K-12/airplane/compexp.html are all based on the perfect gas assumption, ie. PV = nRT. This assumption is only valid at conditions below 5bar. Any chance your internal combustion engine operates below 5bar?
I would recommend you to get hold on thermodynamic table of the fuel-air mixture. You may use perfect gas assumption to interpolate between the tabulated values, but not actually directly using perfect gas calculations.
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