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Jan
23
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
Glad we are on the same page. I have to check but I think $Pv^{\gamma}=C$ applies only to reversible-adiabatic or to irreversible but isentropic (rejection of entropy with heat), but not to adiabatic irreversible process which is usually what a turbine expansion well modeled as. So that equation won't fit for the desired expansion. That "polytropic process" and the polytropic efficiency are just different concepts. Also, once one starts using lookups one stops bothering about these simplified models
Jan
23
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
Your approach may work as well in theory, but fundamental property look ups tend to be easier and more accurate.
Jan
23
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
OK. If you have fits (look ups) for Cp Cv you also have look up for $h$, and $s$ directly. So you dont have to use $Pv^{cp/cv}$ etc. Simply write a loop which sets new state (reduced pressure), look up the h the gas will be if isentropic (implicitly solve for new h at new P that has same s at old P), new h minus old h gives isentropic work, multiply this with the polytropic efficiency of the device gives you real work, repeat for N steps... if you don't know the polytropic efficiency of the machine you will need to know some intermediate states or the total actual work and isentropic eff
Jan
23
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
However, I don't know what level of problem you are working with, i.e., is this some back of the envelope calculation, homework problem, or real-life problem ! Also, we need to take this conversation off-line via email(?) . Meanwhile please do look up Cantera. it helps you query steam properties for any T,P allowing you to numerically integrate to get the correct non-reversible work.
Jan
23
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
OK. Sorry that the PDF was not as useful as I thought it would. It is not possible not analytically integrate a polytropic expansion for a general non-ideal gas much less steam close to its saturation where it might even be two phase. I could help you write a computational code for polytropic expansion of steam using Matlab and a thermodynamic software like Cantera where Cantera is used to evaluate the state properties along the path. It cannot be written out in analytical expression (technically it can but one needs to find polynomial fits for properties and it is messy).
Jan
22
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
Polytropic efficiency and the polytropic gas coefficient $\gamma$ are two different things all together. Polytropic efficiency is a machine (turbine) efficiency metric no what kind of gas/liquid it is. How you calculate different intermediate enthalpies from temperature pressure will depend on the equation of state of the gas, i.e., $h(T), s(T,P)$. And yes, you will have to integrate along the path of expansion in the steam turbine so no calculus free approach here. You can use computational tools that use lookup steam-table data (check out Chemkin, Cantera, also NASA gas properties)
Jan
21
comment Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
Isentropic efficiency turbine = $\frac{\delta W_{actual}}{\delta W_{isentropic}}= \frac{h_2-h_1}{h_{2s}-h_1}$ and Polytropic efficiency is $\frac{dW_{actual}}{d W_{isentropic}}= \frac{dh}{dh_{s}}$. Since the isobars diverge from each other on a T-s plot along higher s, for each incremental pressure drop the denominator is changing as well. I found this online: take a look phad.cc.umanitoba.ca/~wang44/Teaching/MECH%204310/Ch_3/…
Jan
21
comment Meaning of chemical equilibrium between two phases
Regardless my point holds. You put a certain amount of water in a box at a T,P if it can go to equilibrium it will by equating chem potentials. IF it can't that is because there are some kinetic restraints in play, just means its waiting for a random pertubation of right energy to push it over the hill.
Jan
21
comment Meaning of chemical equilibrium between two phases
So you can be at equilibrium in only one phase: Water above melting point (the value of $\mu_{ice}\neq 0$ at that temp). However, you can also remain in non-equilibrium if you carefully prevent nucleation. You can subcool water below its freezing point, if you do that carefully without allowing ice to nucleate. See online videos of people subcooling water in glass bottles (smooth surfaces) and degassing (removing internal nucleation sites) and when they tap the water it instantly freezes.
Jan
21
comment Meaning of chemical equilibrium between two phases
Lets see if this explains. Chemical potential doesn't go to zero when the amount stuff in a phase is zero. Chemical potential is technically $\frac{\partial G}{\partial N}$, i.e., the differential change in free energy when a new phase nucleates which is non-zero even if the other phase is zero. In other words it is a slope. The definition $g/n=\mu$ holds only for ideal gases which neither ice or water is. So no matter where you start with $\mu_{water} >\mu_{ice}$ or the opposite the system will (don't hinder it in other ways) go to equilibrium.
Jan
16
answered Meaning of chemical equilibrium between two phases
Jan
16
answered Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?
Sep
30
awarded  Explainer
Aug
17
awarded  Yearling
Jul
2
awarded  Curious
Aug
17
awarded  Yearling
May
23
asked Phase Space dimension of Lorenz Strange Attractor
Apr
30
accepted Ising Ferromagnet: Spontaneous symmetry breaking or not?
Apr
30
comment Ising Ferromagnet: Spontaneous symmetry breaking or not?
I thought so but wanted to confirm the terminology. Thanks for a simple and elegant confirmation.
Apr
9
comment Phase volume contraction in dissipative systems
I still think that the phase volume must be increase. Of course I am going to assume ergodicity and coarse-graining to stay away from the irreversibility paradox