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

#1 Pubblicato: 06/11/2023 00:13:14

67 apprezzamenti in 713 post.

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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) scaricato 1579 volta(e).

#2 Pubblicato: 06/11/2023 00:43:57

Valery Ochkov

67 apprezzamenti in 713 post.

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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 Pubblicato: 07/11/2023 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

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Valery Ochkov 07/11/2023 13:09:00

#4 Pubblicato: 07/11/2023 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 Pubblicato: 07/11/2023 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.

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

#6 Pubblicato: 08/11/2023 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) scaricato 1557 volta(e).
2RegP-Ideal-Cool_Prop-95.pdf (361,44 KiB) scaricato 950 volta(e).
Martin (and all), I am waiting for the solution - 3D-plot and optimal values of p1 and p2.

#7 Pubblicato: 08/11/2023 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) scaricato 1560 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Oscar Campo 08/11/2023 21:22:00, Valery Ochkov 08/11/2023 22:27:00

#8 Pubblicato: 09/11/2023 01:16:22

Valery Ochkov

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No optimization yet.
For checking

#9 Pubblicato: 09/11/2023 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 09/11/2023 18:37:00

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

Valery Ochkov

67 apprezzamenti in 713 post.

Gruppo: 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 Pubblicato: 11/11/2023 01:40:46

Jean Giraud

983 apprezzamenti in 6.866 post.

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... confirmed vs my formula IAPWS-97

#12 Pubblicato: 12/11/2023 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) scaricato 950 volta(e).
2RegP-Ideal-Cool_Prop-95_Kr_detail.sm (157,12 KiB) scaricato 1574 volta(e).

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) scaricato 904 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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

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

Valery Ochkov

67 apprezzamenti in 713 post.

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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 Pubblicato: 12/11/2023 09:07:21

Alvaro

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Wrote
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) scaricato 1497 volta(e).

Best regards.
Alvaro.

3 utenti hanno apprezzato questo post

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

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

Valery Ochkov

67 apprezzamenti in 713 post.

Gruppo: User

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