f(x, y) - 3D plot and optimal point

#1 Posted: 2023/11/6 00:13:14

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I have f(x, y) - thermal efficiency of a steam turbine with two steam extractions for heating feed water depending on the extraction pressures.
Question.
1. How to find the optimal pressure values at which the efficiency will be maximum?
2. Is it possible to build a surface? For now I have two separate 2D graphics.
More https://link.springer.com/book/10.1007/978-3-319-26674-9
2RegP-Ideal-new.sm (94.95 KiB) downloaded 931 time(s).

#2 Posted: 2023/11/6 00:43:57

Valery Ochkov

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No, you cannot replace WaterSteamPro with Cool Prop for water/steam.
WaterSteamPro is a certified program!
Compare please two plots

#3 Posted: 2023/11/7 03:44:54

Martin Kraska

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I am not familiar with CoolProps but I think I could make a nice 3D plot with Maxima if you provide the smath file

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 2023/11/7 13:09:00

#4 Posted: 2023/11/7 13:10:43

Valery Ochkov

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Wrote
I am not familiar with CoolProps but I think I could make a nice 3D plot with Maxima if you provide the smath file

Thanks, Martin!
Must be someone so

#5 Posted: 2023/11/7 14:53:03

Martin Kraska

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OK but I need a file where the wsp calls are replaced by coolprop ones. Even if plotting doesn't work as expected.

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

#6 Posted: 2023/11/8 13:05:10

Valery Ochkov

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Wrote
OK but I need a file where the wsp calls are replaced by coolprop ones. Even if plotting doesn't work as expected.

See please attach
2RegP-Ideal-Cool_Prop-95.sm (73.63 KiB) downloaded 919 time(s).
2RegP-Ideal-Cool_Prop-95.pdf (361.44 KiB) downloaded 475 time(s).
Martin (and all), I am waiting for the solution - 3D-plot and optimal values of p1 and p2.

#7 Posted: 2023/11/8 21:11:41

Martin Kraska

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Just the plot, no optimization yet.

2023-11-08 15_08_23-SMath Solver - [2RegP-Ideal-Cool_Prop-95_Kr.sm_].png

2RegP-Ideal-Cool_Prop-95_Kr.sm (300.35 KiB) downloaded 863 time(s).

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Oscar Campo 2023/11/8 21:22:00, Valery Ochkov 2023/11/8 22:27:00

#8 Posted: 2023/11/9 01:16:22

Valery Ochkov

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No optimization yet.
For checking

#9 Posted: 2023/11/9 18:31:08

Jean Giraud

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Wrote
No, you cannot replace WaterSteamPro with Cool Prop for water/steam.
WaterSteamPro is a certified program!

Agreed: CoolProp is CoolProp.
For quick visit, I use freeware Katmar IAPWS=97 in all sorts of units.
By same token, in Smath, we have lot of water/steam formulas.
What about you tabulate matrix style, then spline/interpolate.
I will be back on your document ... Jean

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Valery Ochkov 2023/11/9 18:37:00

#10 Posted: 2023/11/10 13:49:18

Valery Ochkov

64 likes in 670 posts.

Group: User

Wrote

Wrote
No, you cannot replace WaterSteamPro with Cool Prop for water/steam.
WaterSteamPro is a certified program!

Agreed: CoolProp is CoolProp.
For quick visit, I use freeware Katmar IAPWS=97 in all sorts of units.
By same token, in Smath, we have lot of water/steam formulas.
What about you tabulate matrix style, then spline/interpolate.
I will be back on your document ... Jean

#11 Posted: 2023/11/11 01:40:46

Jean Giraud

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... confirmed vs my formula IAPWS-97

#12 Posted: 2023/11/12 02:37:31

Martin Kraska

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Wrote
No optimization yet.
For checking

I get slightly different values. Still no automatic optimization because the objective function doesn't translate to Maxima. As a first step I made the function more robust by solving the two equations sequentially instead of simultaneously. In the original version sampling for the plot occasionally failed.

Plot MPa.pdf (219.47 KiB) downloaded 482 time(s).
2RegP-Ideal-Cool_Prop-95_Kr_detail.sm (157.12 KiB) downloaded 913 time(s).

2023-11-11 19_21_55-SMath Solver - [2RegP-Ideal-Cool_Prop-95_Kr_detail.sm_].png

2RegP-Ideal-Cool_Prop-95_Kr_detail.pdf (520.5 KiB) downloaded 470 time(s).

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 2023/11/12 02:41:00, Alvaro 2023/11/12 09:04:00

#13 Posted: 2023/11/12 02:51:46

Valery Ochkov

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Wonderful!
But I dare to note that a real steam turbine unit has up to eight steam extractions from the turbine to regenerative heaters. And not only mixing, but also surface type.

#14 Posted: 2023/11/12 09:07:21

Alvaro

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I get slightly different values. ...

Hi. Using the definition for partial derivatives and a pure numerical solver.

2RegP-Ideal-Cool_Prop-95_Kr_detail.sm (162.36 KiB) downloaded 877 time(s).

Best regards.
Alvaro.

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Martin Kraska 2023/11/12 09:10:00, Valery Ochkov 2023/11/12 14:12:00, Oscar Campo 2023/11/12 18:29:00

#15 Posted: 2023/11/14 02:13:59

Valery Ochkov

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f(x, y) - 3D plot and optimal point - Steam Turbine - Messages