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

#1 Publicado: 6/11/2023 0:13:14

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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) descargado 1577 vez(es).

#2 Publicado: 6/11/2023 0:43:57

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 Publicado: 7/11/2023 3:44:54

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 7/11/2023 13:09:00

#4 Publicado: 7/11/2023 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 Publicado: 7/11/2023 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 Publicado: 8/11/2023 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) descargado 1551 vez(es).
2RegP-Ideal-Cool_Prop-95.pdf (361,44 KiB) descargado 945 vez(es).
Martin (and all), I am waiting for the solution - 3D-plot and optimal values of p1 and p2.

#7 Publicado: 8/11/2023 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) descargado 1557 vez(es).

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

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

#8 Publicado: 9/11/2023 1:16:22

Valery Ochkov

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No optimization yet.
For checking

#9 Publicado: 9/11/2023 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 9/11/2023 18:37:00

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

Valery Ochkov

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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 Publicado: 11/11/2023 1:40:46

Jean Giraud

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... confirmed vs my formula IAPWS-97

#12 Publicado: 12/11/2023 2:37:31

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) descargado 945 vez(es).
2RegP-Ideal-Cool_Prop-95_Kr_detail.sm (157,12 KiB) descargado 1572 vez(es).

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) descargado 903 vez(es).

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 2:41:00, Alvaro 12/11/2023 9:04:00

#13 Publicado: 12/11/2023 2:51:46

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 Publicado: 12/11/2023 9:07:21

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) descargado 1491 vez(es).

Best regards.
Alvaro.

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Martin Kraska 12/11/2023 9:10:00, Valery Ochkov 12/11/2023 14:12:00, Oscar Campo 12/11/2023 18:29:00

#15 Publicado: 14/11/2023 2:13:59

Valery Ochkov

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