- #1
Funknatics
- 2
- 0
Homework Statement
I must find temperature at each state, for starters.
This is a Diesel cycle with a non-isentropic compression process, but standard the rest of the way. The specific heat is variable with temperature. Fluid is air
Givens:
compression efficiency [tex](\eta_{c})[/tex], initial temperature([tex]T_{1})[/tex], qH, compression ratio [tex]r_{c}[/tex] , curve fit for [tex]C_{v}(T)[/tex]
Homework Equations
Non-isentropic with constant specific heat, k = 1.4
(1) [tex]T_{2} = T_{1} + \frac{T_{2s} - T_{1}}{\eta_{c}}[/tex]
(2) [tex]\frac{T_{2s}}{T_{1}} = (\frac{V_{2}}{V_{1}})^{k-1}[/tex]
(3) [tex]\eta_{c}=\frac{C_{v_{2s}}(T_{2s}-T_{1})}{C_{v_{2}}(T_{2}-T_{1})}}[/tex]
(4) [tex]C_{v_{2s}}[/tex] - [tex]C_{v}[/tex] from average of T1 and T2s
The Attempt at a Solution
[tex]T_{2s}[/tex] is an ideal assumption of the process assuming that it is isentropic. Using this, and the compression efficiency, I can find a temperature for state 2 through equation (1), assuming that the specific heat is constant, which is not true in this case.
I believe that equation (3) is the key to this, with a good assumption on the values of [tex]C_{v_{2}} and C_{v_{2s}}[/tex]. One way I thought of doing this is to take the average of the temperatures and using the curve fit to find this specific heat. However, I can only do this for the ideal case as I don't have the final temperature.
This is where I am stuck.
Would it be valid to relate the compression efficiency to the change in temperature? If so, how? It would have to be a higher temperature because of the increase in entropy, and I would imagine it would look something along the lines of T1 + dT(1+ eta_c), or something (im not sure).
Any insight on this would be helpful. It frustrates me to have hit this road block right off the bat on this project.
Thanks in advance.
P.S. I got a bit lost in all the text and [tex] so if I left anything out, please let me know.