()Submitted on 5 May 2010
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Solving an Air Conditioning System Problem in an Embodiment Design Context Using Constraint
Satisfaction Techniques Raphael Chenouard, Patrick Sébastian, Laurent Granvilliers
To cite this version: Raphael Chenouard, Patrick Sébastian, Laurent Granvilliers. Solving an Air Conditioning System Problem in an Embodiment Design Context Using Constraint Satisfaction Techniques. Principles and Practice of Constraint Programming, Sep 2007, Providence, United States. pp.18-32, 10.1007/978-3- 540-74970-7_4. hal-00466675
s♥ ♦♥str♥t tst♦♥
♣ë ♥♦r1 Ptr ést♥1 ♥ r♥t r♥rs2
1 ♦r ♥srts ♦♠♥ts s ♥rétq ♥
2 ♥rst ♦ ♥ts ♦rt♦r ♥♦r♠tq ♥ts t♥tq P ♥ts
strt ♥ ts ♣♣r t ♠♦♠♥t s♥ ♦ ♥ r ♦♥t♦♥ ♥ sst♠ ♥ ♥ rrt s ♥stt s♥ ♥tr ♦♥str♥t stst♦♥ t♥qs t ♠♦ s qt ♦♠♣ t♦ s♦ s♥ t ♦♥t♥s ♠♥ ♦♣ rs ♥ ♠♥ ♦♥str♥ts ♦rrs♣♦♥♥ t♦ ♦♠♣ ♣ss ♣♥♦♠♥ ♦♠ ♥ rsts ♥ ♥♦t♦♥s s ♦♥ ♠♦♠♥t s♥ ♥♦ r r ♥tr♦ t♦ ♥rt s♦♠ ♠♦♠♥t s♥ ♦♥♣ts ♥ t♦ ♦t♥ ♠♦r r♥t ♥ ♠♦r ♥t s♦♥ ♣r♦ss t♥ ss ♦rt♠s ♥ts ♦ s♥ ♦♥str♥t ♣r♦r♠♠♥ ♥ ♠♦♠♥t s♥ r sss ♥ s♦♠ ts ♦r s♥rs s♥ P t♦♦s r s♦rt t
♥ r ♦♥t♦♥♥ sst♠ ♣r♦♠
♦♥tt
s♥ ♣r♦ss s sq♥ ♦ ♣ss r♥♥ r♦♠ t ♥t♦♥ ♦ ♥s ♥ rqr♠♥ts t♦ ♣r♠♥r s♥ ♥ t s♥ P t Pr♠♥r s♥ ♥s ♦♥♣t s♥ ♥ t♦ ♣r♦t s♠s ♥ ♠♦♠♥t s♥ r st sts r ♥stt ♦r♥ t♦ ♦ ♠tr ♦♥str♥ts ♣ss ♦rs ♥ ♥trt♦♥s t♥ t ♣r♦t ts ♦♠♣♦♥♥ts ♥ ts ♥r♦♥♠♥ts
♦s ♥♦ r s♦tr st t♦ s♦ ♦♠♣ ♠♦♠♥t s♥ ♣r♦ ♠s ♥ ts ♦♥tt ♦♥str♥t s♦r ♥♠ ♦♥str♥t ♣♦rr s ♦♣ t♥ ♣rt♥rs♣ t♥ sst t♦♥ ♥ sr rsr ♦rt♦rs s ♣rt♥rs♣ s rt tr♦ t r♥ ♣r♦t r ♦r strts r♦♠ ts ♣r♦t ♥ ♠s t♦ ♣rss s♦♠ ♦tr ts s♥ ♦♥str♥t ♣r♦r♠♠♥ ♥ ♠♦♠♥t s♥ r ♣r♦♠s r ♦♣ ♦r♥ t♦ s♥ ♣♦♥t ♦ s s ♥ ♦♣♥ rr ♦r ♦♥str♥t ♣r♦r♠♠♥ ♥ ♦♥str♥t s♦♥ t♥qs s ♦♥ ♥tr rt♠t ♦♦r r ♦♣ s♦♠ ♥ ♦♥♣ts ♥ ♦rt♠s
tt♣s♦r♦r♥t♣r♦tss
♥ ts ♣♣r ♥ r ♦♥t♦♥♥ sst♠ ♦r ♥ rrt s r s ♥stt r srs t ♠♥ ♦♠♣♦♥♥ts ♦ ♥ ♥ ♥ t♦♥ s rt♦♥ ♠ s ♦♦tstr♣ ♦♠♣♦s ♦ tr♦♠♥ ♦♠♣rss♦r tr♥ ♥ ♦♣♥ st ♥ ♥r tr♠ t sr ♥ ♥♦ s ♦♦tstr♣ ♦rrs♣♦♥s t♦ rrs ♦rt♦♥ tr♠ t s s t♦ rt t r ♦♦♥ sst♠ ♥ r♥t st r ♣rssr ♥ t♠♣rtr ♥ ♠♦st ♦ t rrt stt♦♥s
♦ ♥t♦♥ r♠ ♦r ♥ rrt r ♦♥t♦♥♥ sst♠
♥ ♥ rrt sr ss♥t rtr ♠st t♥ ♥t♦ ♦♥t ♥ t r ♣rssr ♥ t♠♣rtr ♦ t ♥ ♠st r♥t ♦r t ♥ ♦ t ♣ss♥rs t t r ♦s t♥ r♦♠ t tr♦rt♦r ♥ r♦♠ t t♠♦s♣r t♦ r ♠♥ ♥ t ♥ rs t tr♦ rt♦r ♣r♦r♠♥s ♥ t ♥ s♦ ♥rs t rrt r ♦r ♦r♦r ♥ ♥ rrt t ♦♠ ♥ t ♠ss ♦ r ♠♥t ♣♥ ts ♣r♦r♠♥s tr♦r t ♠ss ♥ ♦♠s ♦ t t♦ ♠♥♠
♦ sr♣t♦♥
♥ ♠♦♠♥t s♥ ♣r♦t s sr s♥ sr sss ♦ rs ♥ s♥rs r ♠♥ ♥trst ♥ ♦♥ rs ♥ rtr s♥ rs ♥ tr s s♥ s♦t♦♥ ♣r♥♣s ♦ s♥ rs ♦rrs♣♦♥ t♦ t s♠st st ♦ rs ♥♥ t rttr
♦ ♣r♦t r rs r s t♦ ♣rss t ♦♥str♥ts rt t♦ t ♥♠ ♣ss ♦r ♦♠tr ♦♥str♥ts ♥ ♣r♦r♠♥s rtr r s t♦ ♥ s♥ rs ♥ rtr s♥ s♦♠ r♥t ♥♦ rt t♦ t rtr ♣r♠t t♦ t ♥ t♦ t t s♥ s♦t♦♥s t t ts ♣♦♥t t s t♦♦ r ♥ t s♥ ♣r♦ss t♦ r ♦♣t♠ s♥ s♦♠ ♦ t ♦♠♣♦♥♥ts ♠ ♥
t ♦♠♣♦♥♥ts ♦ t r ♥♦t st♥r ♦r t s ♦ s♠ ♣t ♦♥ t ♥r ♥ t tr♠ t r ♠♦ s♥ t ♣r ♦r♠♥s s♠ t♦ ♠♥ ♣♥♥ ♦♥ t rtrsts ♦ t ♥r ♥ ts ♦tr ♦♠♣♦♥♥ts r ♠♥ ♣rss t ♥ ♦♥ts ♣r♦ ♠♥trrs ♥ ♥r ♥s t♦ ts s♠♣ t♦♥s r s t ♠♦ ♦ t ♥r s r ♦♠♣ ♥ sr ♦♣ ♣ss ♣♥♦♠♥ ♥trr
r ♠♦ s ♦♠♣♦s ♦ rs r r s♥ rs ♦r t tr♠ t ♥ sr♥ t ♥r ♦tr rs r s♦♠ r rs ♦st ♦ t♠ rs ♠ ♦♥sr s ♣t rs ♥ ts rs r ♣t ♥ ♦♥str♥t s♥ t ♦rrs♣♦♥ t♦ ♥tr♠r ♦♠♣tt♦♥s r ♠♥t♥ t♥ t ♠♦ s t ♣rss ♥♦♥ rtrsts ♦r rtr ♣rsr t ♠♦ ♣rsst ♦tr r rs r ♠♥ rt t♦ t ♥r ♥s rtrsts ♣rssrs t♠♣rtrs ♥ t
♦♥str♥ts ♠ s♦ ss ♦r ♥st♥ tr r s ♥r ♦♥str♥ts sr♥ t♦ ♦ ♥ srs s ♦♥♦♥ ♦♥str♥ts sr t ♥r ♥s ♦ t ♦♠♣♦♥♥ts s ♥ t ♠♦ ♦tr ♦♥str♥ts ♣rss t rtrsts ♥ ♦r ♦♠tr t♠♣rtr ♣rssr ♦sss t ♠♦st ♦ t♠ ♥♥ t ♣t rs
♠♦♠♥t s♥ s♦t♦♥s
s♥ s♦t♦♥ ♦rrs♣♦♥s t♦ ♣r♦t rttr sts ♦♥ st♥ts ♥ rtr s ♦♥sq♥ s♥ s♦t♦♥ s r♣rs♥t s♥ r s ♠t♣ r rs s ♠st ♥♦t t♥ ♥t♦ ♦♥t ♥ ♦♥sr♥ s♥ s♦t♦♥s s♥ tr ♦♠♥ ♣♦rt♦♥ ♠ ♥ ♣t s♥ r s♦t♦♥s ♦r t r rs ♣♦rt♦♥ s ♠♥t♦r t♦ t ♣r♦t ♦r ♥ t ♣ss rt
P
♥ ♠♦♠♥t s♥ s♥rs t♦ tr♠♥ sts ♦ s♥ s♦t♦♥s t♦ s♣♣♦rt s♦♥ ♠♥ ♥ t♦♦s t♦ ♦ ♣♦r t s♦t♦♥s sr s♣
t♦st ♠t♦s r ♠♥ s r ♦♣ ♥ ♥♥r♥ ♣rt♠♥ts s♥ s♠t♦♥ t♦♦s ♦♣ t ♦♣t♠t♦♥ t♦♦s s ♠t♦
rqrs t ♦♣♠♥t ♦ s♠t♦♥ ♦s s♣ t♦ t ♥stt ♣r♦ ♠s ♦r ♥st♥ t♦♦ s♥ ♥ ♦♣t♠t♦♥ ♣♣r♦ s ♦♥ ♥ ♦ t♦♥r ♠t♦ s ♦♣ t♦ ♥stt t ♣rs♥t ♥ ts ♣♣r ést♥ t s s♠t♦♥ ♦s r ♦t♥ ♣♦r t t r ♥♦t s ♠♥t♥ ♥ rs s♦♥ ♦rt♠ ♠st r♥ ♦r ♣♣t♦♥ ♥ t♦ t s ♦t♥ t♠ ♦♥s♠♥ t♦ ♦♣ ♥ t ♦♥tt ♦ ♣r♠♥r s♥ ♣s ♠♥ s♦♥s r ♥♦t t♥ t tt ♣♦♥t ♥ t ♠♦ ♠ ♦ sr t♠s ♦r♦r t ♦t♦♥r ♣♣r♦s ♦ ♥♦t ♦♠♣t t ♥tr st ♦ s♦t♦♥s ♥ ♣rtr s♦♠ ♣r♠trs ♦ t ♥t ♦rt♠ r ♥♦t ♥ t♥ s♦♠ rs ♦ t sr s♣ ♠ ♥♦t ♣♦r ♠♦♠♥t s♥ ♣s s s t♦ tt st r s ♥ t sr s♣ ♥ ♥ ♦t s♦♠ ♠ tr♠♥t t♦ t t ♣♣r♦♣rt s♦♥s
P ♣♣r♦ ♦s t♦ rt t s♥ ♠♦s t♦t ♦♣♥ tr s♦♥ ♠t♦s ts t ♦st s ssr ♥ ♣r♠tr ♦r ♦♠ ♣♦♥♥t ♥s t s r s ♥ ♦♥rt♦♥ ♥ ♥ ♦♥♣t s♥ ♥ t♥s ♥♥♦ t ♥ t s♠s ♣r♦♠s ♥ ♦r ♠♦♠♥t s♥ ♠♠r t sr t sr s♣ s ♣♦r ♥tr ♥ t s sr t♦ tr♠♥ t s♣s ♦ t s♦t♦♥ st s ♥tr st ♦ s♦t♦♥s ♦s s♥rs t♦ t ♠♦r r♦st s♦♥s s♥ t ♥ ♥stt ♠♦r s t ♠♦ rs♣♦♥s t♦ s♦♠ rtrsts ♥s ♦r ♥st♥ ♦♠♣♦♥♥ts ♠♥s♦♥s ♦r rtr ♥ ts ♣rsr ♦♥ s♥ rttr ♥ s♦♠ ♦ ts ♣r♦r♠♥s t r♦♠ tr ♥s
♦ P
♥ ♦r r ♦♥t♦♥♥ sst♠ ♣♣t♦♥ s ♥r P r♠♦r s ♦♥ r♥♥♣r♥ ♦rt♠ ♥♥t♥r t
♦ ♦r♠t♦♥
♦♥sr t ss tr♣t r♣rs♥tt♦♥ ♦ P ♣r♦♠s V,D,C r s r ♥ s♥ srt ♦r ♦♥t♥♦s ♦♠♥s r♥ ♦♠♣tt♦♥s srt ♦♠♥s r ♦♥rt ♥t♦ ♥ ♥tr ♥ t s tr r♥ s♥ t srt s t ♦s ♦♥str♥ts r s ♦♥ rt♠t ♣rss♦♥s s♥ t ss qt ♥ ♥qt ♦♣rt♦rs
♦r s♦♠ ♣ss s r sts tr♦ ♣r♠♥ts ♥ t r ♣rss s ♣s ♥♦♥♥r ♥t♦♥s ♦s ♦♥ ♣s ♣♥♦♠ ♥ r ♥ ♦♥ r ♥ ♠♦st ♣ss ♣♥♦♠♥ r st♠t s♥ s♦♠ r♣rs♥tt ♥ ♥♦♥ rs ♦r ♥st♥ ♥ ♠♥s sst ♥♦s Pr♥t ♥♠rs t ♥ ♦ ♣s ♦♥str♥t t♦ ♥t ♦♠♣t tss ♣s ♥♦♥♥r ♥t♦♥s qt s♠r t♦ ♦s ♣♣r♦ ♦♥ ♥r ♣s ♥t♦♥s ♦ ♦r♦r ts ♦ ♦♥str♥t ♦s t♦ ♥ s t r♥ ♦ ♦s s♥
♥q rr♥ ♦r ♦♠♣♦♥♥t ♦rrs♣♦♥♥ t♦ s♥t♦♥ t♥ t ♦♠♣♦♥♥ts t♦ ♦♦s
♦♥ ♦rt♠s
r♦st ss r♦♥r♦♥ strt ♦♥ t rs ♦s ♦r ♣♦rt♦♥ ♦t♥ s s♦ s♦♥ t♠s ♦r ♠♦♠♥t s♥ ♣r♦♠s ♥ ♥rts ♠♥ ♣t s♥ s♦t♦♥s ♠♥ ♣♥t♦♥ s t sss ♦♠♣t t♦♥ st♣s ♠ ♦♥ r rs ts ♦♣ rst st♦♠ sr s ♦♥ r sss ♥ t♦ t ♠♦♠♥t s♥ ♣♦♥t ♦ ♥ s♥ rs ♥ t ♠♥ strtr♥ rtrsts ♥ ♠♦s r ♦t♥ sts r♦♥ t♠ ♥ r♦♥ rtr r r s r ♦♥ ♥tr♦ t♦ ♣rss ♣r♦r♠♥ rtr ♣ss ♦r t s r
♥♦ sst♦♥ ♥ ♥ ♠♦♠♥t s♥ ♠♦
♥ t♦♥ s♦♠ ♦ t r rs r ♣t ♥ ♦r ♥ t♦ ♦tr rs ♦rrs♣♦♥ t♦ ♥tr♠r ♦♠♣tt♦♥ st♣s t t r ♠♥t♥ ♥ t ♠♦ t♦ ♥sr ts ♥tt ♦ ♦ s♦♠ s ss ♣♦rt♦♥ st♣s ♦r♥ t♦ ts rs tr ♣rs♦♥ r ♥ t♦ t ♥♥t s♦ tt tr ♣rs♦♥s r s r s r ♦♠♣t t ♦♥sst♥ ♣r♥♥ ♣r♦ss s ♦♥ ♦♠♠ ♥ ♦ ♦♥sst♥ ♥♠♦ t t s ♠♣♦rt♥t t♦ t tt ♣t rs ♠ ♥ s♥ ♦tr ♣t rs ♥ ts s ♥♦
♣♥♥ s t♦ st♥ t♥ t♠ ♦♠ s♠ s♥ ♣r♦♠s r ♣rs♥t s♥ s rs ♦r ♥♦t ♥ s ♦r
s ♦rt♠s ♥ t s ♦ ♣t rs ♦ s t♦ ♦♠♣t ♠♦r ♥t t ♥tr s♦t♦♥ st ♦ ♠♦♠♥t s♥ ♣r♦♠s ♥ ♦rs rs ♦tr ♦rt♠s ♦ ♥♦t ♦♠♣t t rst s♦t♦♥ tr sr ♦rs
♥ s♦♠ ♦tr ♦rs ♠♦s r ♦♠♣♦s ♥ s♠ ♦s ♦r♥ ♥ rt r♣ t t t t ♠ ♥tr♣rt t♦ rs s♦♥ ♦rr r ♦s r s♦ ♦r strt♥ t ♥t ♦♥ ♥ t r♣ t s ♥ ♥t ♣♣r♦ ♦r ♣r♦♠s r ♦♣ rs r ♥♦t t♦♦ ♥♠r♦s ♥ ♥ tr r sr sts ♦ ♦♣ rs t ♠♦ s ♦♠♣♦s ♥ ♦s ♥ t r ♥ss ♦ t ♣r♦♠ r♠♥s ♦r♦r ♣r♠♥r s♥ ♣r♦♠s r ♦t♥ ♥r♦♥str♥ ♥ ♠♥ strt rs t♦ ♦s♥ t♦ ♦♠♣t ♦♠♣♦st♦♥ ♦ t ♦♥str♥t ♥t♦r ♥ ts s ts r ♦♠♥s r ♣♦r ♠♦st st ♥ t ♠ ♥ sss ♦♠♣tt♦♥ st♣s ♦♥ rr♥t rs
Prs♦♥ ♠♥♠♥t
♠♥♠♥t ♦ t ♣rs♦♥s rs ♣♣rs t♦ ♥♠♥t t♦ ♥sr r♥t s♦t♦♥ st ♦r s♥rs ♥ s♥ r s ♣rs♦♥ r♣rs♥t♥ t ♥tr t ♥s s♦t♦♥s ♦r♥ t♦ t s♥ ♣♦♥t ♦ s ♣rs♦♥s r ♥ t t♦r♥s ♥ r♦r s t
♥ ♠♥ ss ♦ ♣rs♦♥ ♦r rs ♦r ♥st♥ 10 −8 s t
t ♣rs♦♥ ♦♥ sr s♦rs s ♥♦ s♥s ♦♥sr♥ t s♥ ♣♦♥t ♦ t ♣rs♦♥ ♥ ♥ ♦r s♦♠ rs t ♠♦st r♥t rs ♦ ♥ ♠♦♠♥t s♥ ♣r♦♠ ♠st tr ♦♥ ♣♣r♦♣rt ♣rs♦♥ s♥ r ♣rs♦♥s t♦ ♥ t♥ ♥t♦ ♦♥t t ♣r♦t s♣t♦♥s ♥ rqr♠♥ts
♣rs♦♥s ♦♥ r rs r ♠♦r t t♦ st ♣r♦♣r ♦♠ ♦♠♣ ♣♥♦♠♥ ♠ t♥ ♥t♦ ♦♥t ♥ s♥rs ♠ ts t♦ ♦rst t r♥t r ♣rs♦♥s ♥ t ts ♣♥♦♠♥ ♥ t ♠ s s♦♠ ♦♥♥ ♣r♥t ♥ t♦ s♦♠ ♠♣rs♦♥s rt t♦ t ♦♠♣t s s ♠♣rs♦♥s r ♥ t♦ s♠♣♥ ss♠♣t♦♥s ♦ s♥rs t♦ ♥t tr♠s ♥ rt♥ ♥ q t♦♥s r♦♠ ts ♣♦♥t ♦ ♥ qt♦♥s ♦ ♠ss ♥r ♦r ♠♦♠♥t♠ r ♥ t♦ ♣rs♦♥ t♥ ♥t♦ ♦♥t t tr♠s ♥t s♥rs s ♦♥♥ ♣r♥t ♠ ss♦t s rt ♣rs♦♥ t♦ s♦♠ r ♥t rs ♦ ♦♥str♥ts ♦r ♥st♥ ♥ ♦♥ts ♦r s♦♠ ♦tr r rs ♠ rt t♦ s♦♠ ♣ss q♥tts ♦r t♦ s♦♠ ♣ss ♦rr ♦ ♠♥t ♥ tr ♣rs♦♥s s♦t ♦r rt s♦ ♥ t♥ ts ♥♦ ♥t♦ ♦♥t
♣rs♦♥ ♠♥♠♥t s r ♥♠♥t t♦ ♦t♥ ♥t s♦♥ t♠ ♥♦t ♦♠♣t sss sr s♣ ♣♦rt♦♥s ♥ r♥t s♦t♦♥s ♥♦t t♦♦ ♠♥ ♣t s♥ s♦t♦♥s
♦ ♠♣♠♥tt♦♥
t ♦♥st♥ts rs ♦♠♥s ♥ ♦♥str♥ts ♦ t ♣r♦♠ r t ♥ t ♦♦♥ ts ♦r ♥s rt t♦ s♦♠ rs ♥t t ♦ ♦r ♦t s ♦ t ♥r ♦ ♥♦t ♥ t ♦♠♥ ♦ t rs r♦♠ t s ♦♥♦♥ ts s♥ t s sss
♦♥st♥ts
r ♣r♦♣rts Cp = 1000 r = 287 γ = 1.4 t ♦♥t♦♥s Z = 10500 ♠ M = 0.8 r♦rt♦r rtrsts TCTR = 8 ηTRd = 0.9 ηTRc = 0.8 ♦♠♣♦♥♥ts ♥ ηc = 0.75 ηAT = 0.95 ηt = 0.8 ηNO = 0.9 ηDI = 0.9 r s♥t ♥t♦ t ♥ T5 = 278.15 p5 = 85000 P q = 0.7 s Pts rtrsts kp = 20 ♠ tp = 0.001 ♠
s♥ rs
t ♦ t ♥r ♠ ∈ [0.1, 1] ♣= 0.01 ss ♣t rt♦ τ ∈ [1, 8] ♣τ= 0.5 ♦ts ♥ sr rr♥ ExSurfh ∈ [1, 48] ♥t ♦s ♥ sr rr♥ ExSurfc ∈ [1, 48] ♥t r♠ t rs ♠ ∈ {0.01, 0.02, ..., 0.2}
r rs
♥r ♠tr rtrsts roex ∈ [0, 10000] kw ∈ [0, 500]
♥r ♣rssrs P p2 ∈ [0, 1000000] ∧ p(p2) = 5% p3 ∈ [0, 1000000] ∧ p(p3) = 5%
peic ∈ [0, 1000000] ∧ p(peoc) = 5% peoc ∈ [0, 1000000] ∧ p(peoc) = 5%
♥r t♠♣rtrs T2 ∈ [0, 1000] ∧ p(T2) = 5% T3 ∈ [0, 1000] ∧ p(T3) = 5%
Teic ∈ [0, 1000] ∧ p(Teic) = 5% Teoc ∈ [0, 1000] ∧ p(Teoc) = 5%
♥r ♣rssr ♦sss P Peh ∈ [−∞, +∞] ∧ p(Peh) = 10% Pec ∈ [−∞, +∞] ∧ p(Pec) = 10%
♥r ♥ ♦♥t ∈ [0, 1] ∧ p() = 5%
r ♦s ♥ t ♥r s qra ∈ [0, +∞] ∧ p(qra) = 0.001 qma ∈ [0, +∞] ∧ p(qma) = 0.001
Prssr tr t tr♥ P p4 ∈ [0, 1000000] ∧ p(p4) = 5%
♠♣rtr tr t tr♥ T4 ∈ [0, 1000] ∧ p(T4) = 5%
r rs
rt♥ t♦ t ts
♥s rtrsts bh rhh δh βh bc rhc δc βc
♦r♥ ♥tr♣♦t♦♥ ♦♥ts JSh1 JSh2 JSh3 JSc1 JSc2 JSc3
♥♥♥ ♥tr♣♦t♦♥ ♦♥ts fSh1 fSh2 fSh3 fSc1 fSc2 fSc3
♥tr♣♦t♦♥ ♦♥ts KcSh1 KcSh2 KcSh3 KcSh4 KcSh5 KcSh6
KcSh7 KcSh8 KcSh9
♥tr♣♦t♦♥ ♦♥ts KeSh1 KeSh2 KeSh3 KeSh4 KeSh5 KeSh6
KeSh7 KeSh8 KeSh9
KeSc7 KeSc8 KeSc9
♥r ♠♥s♦♥s ♠ Ly = Lx Lz = 0.25 ∗ Lx
♥s rtrsts αh = (bh∗βh) (bh+bc+2∗δh)
αc = (bc∗βc) (bh+bc+2∗δc)

ηfc = tanh mlc mlc
♥ sr ♠♥s♦♥s Ah = αh ∗ (Lx ∗ Ly ∗ Lz) Ac = αc ∗ (Lx ∗ Ly ∗ Lz) Aw = Lx ∗ Ly ∗ n Ach = σh ∗ Afh Acc = σc ∗ Afc
Afh = Lx ∗ Lz Afc = Ly ∗ Lz
♥ sr ♥ η0h = 1 − Afh
Ah ∗ (1 − ηfh) η0c = 1 − Afc
Ac ∗ (1 − ηfc)
♥r ♥♥r t♥ss ♠ tw = (δh+δc) 2
♠r ♦ ♣ts n = Lz bh+bc+2∗δh
r rtrsts ♥ t ♥r Gh = qma
Ach Gc = qra
√ T3
2 +
T2
2
Teoc
2 +
Teic
2
Cpoh = 1003.7 + 6.8e−2 ∗ (T3 − 273.15)+ 2.22e−4 ∗ (T3 − 273.15)2
Cpih = 1003.7 + 6.8e−2 ∗ (T2 − 273.15)+ 2.22e−4 ∗ (T2 − 273.15)2
Cph = Cpoh+Cpih
Cpoc = 1003.7 + 6.8e−2 ∗ (Teoc − 273.15)+ 2.22e−4 ∗ (Teoc − 273.15)2
Cpic = 1003.7 + 6.8e−2 ∗ (Teic − 273.15)+ 2.22e−4 ∗ (Teic − 273.15)2
Cpc = Cpoc+Cpic
rhh + σc∗δc
r s♣ ♥ t ♥r ♠s Ch = qma
Ach∗ρ2 Cc = qra
Acc∗ρic
t tr♥sr rtrsts λ = qra∗Cpic
qma∗Cpih
♦r♥ ♦♥ts Jh = eJSh1∗log2(Reh)+JSh2∗log(Reh)+JSh3
Jc = eJSc1∗log2(Rec)+JSh2∗log(Rec)+JSh3
♥♥♥ rt♦♥ t♦r fh = efSh1∗log2(Reh)+fSh2∗log(Reh)+fSh3
fc = efSc1∗log2(Rec)+fSh2∗log(Rec)+fSh3
Pr♥t ♥♠r Prh = (0.825−0.00054∗T3+5.0e−7∗T2
3 )
2 +
2 )
2
oc
2 +
ic
2
µh Rec = 4∗rhc∗Gc
µc
♥t ♣rssr ♦sss ♦♥t Kch = KcSh1 ∗ σ2 h + KcSh2 ∗ σh + KcSh3 ∗ log2(Reh)+
KcSh4 ∗ σ2 h + KcSh5 ∗ σh + KcSh6 ∗ log(Reh)+
KcSh7 ∗ σ2 h + KcSh8 ∗ σh + KcSh9
Kcc = KcSc1 ∗ σ2 c + KcSc2 ∗ σc + KcSc3 ∗ log2(Rec)+
KcSc4 ∗ σ2 c + KcSc5 ∗ σc + KcSc6 ∗ log(Rec)+
KcSc7 ∗ σ2 c + KcSc8 ∗ σc + KcSc9
tt ♣rssr ♦sss ♦♥t Keh = KeSh1 ∗ σ2 h + KeSh2 ∗ σh + KeSh3 ∗ log2(Reh)+
KeSh4 ∗ σ2 h + KeSh5 ∗ σh + KeSh6 ∗ log(Reh)+
KeSh7 ∗ σ2 h + KeSh8 ∗ σh + KeSh9
Kec = KeSc1 ∗ σ2 c + KeSc2 ∗ σc + KeSc3 ∗ log2(Rec)+
KeSc4 ∗ σ2 c + KeSc5 ∗ σc + KeSc6 ∗ log(Rec)+
KeSc7 ∗ σ2 c + KeSc8 ∗ σc + KeSc9
t♠♦s♣r rtrsts Ta = 288.2 − 0.00649 ∗ Z pa = 101290 ∗ ( Ta
288.08 )5.256
)
∗ (( p1 p0
) γ−1
γ − 1))
r♦rt♦r ♣rssrs P p0 = pa ∗ (ηTRd ∗ M2∗(γ−1) 2
+ 1) γ
γ−1 p1 = TCTR ∗ p0
sr ♣rssrs P poDc = piDc ∗ (ηDI ∗ M2 ∗ γ−1 2
+ 1) γ
γ−1
♥ t♠♣rtrs ToDc = TiDc ∗ (1 + M2 ∗ γ−1 2
) piDc = pa TiDc = Ta
♦ ♣rssr P piBc = peoc poBc = pa TiBc = Teoc
♥ t♠♣rtrs ToBc = TiBc ∗ (1 + ηNO ∗ (−1 + ( poBc
piBc )
p1 p4 = p5 qmav = q − qma
ksiα = e(4.03108e−4∗α2+8.50089e−2∗α−1.59295
r♦s ♣t rs mh = √
2∗hh
ρ3 − 1)
rho3
ρoc − 1)
ρoc
t♦ ♦ exchSurfh = 1 → JSh1 = 0.0314 ∧ · · · ∧ KcSh9 = 1.717231
♥ srs exchSurfh = 48 → JSh1 = 0.0369 ∧ · · · ∧ KcSh9 = 1.551097 exchSurfc = 1 → JSc1 = 0.0314 ∧ · · · ∧ KcSc9 = 1.717231 exchSurfc = 48 → JSc1 = 0.0369 ∧ · · · ∧ KcSc9 = 1.551097
trs ♦ ♦r t T2 ≤ 473 → roex = 8440 ∧ kw = 30 ♥r T2 ≥ 473 → roex = 8440 ∧ kw = 30
♥r sr♣t♦♥
r ♦ rt♦ τ = qra
qma
λ −1)
T2−T0
♦ts ♥r ♥ T3 = T2 − ∗ (T2 − Teic) ♦ts ♣rssr ♦sss Peh = p2 − p3
Peh = G2
qra∗Cpic ∗ (T2 − T3) + Teic
♦s ♣rssr ♦sss Pec = peic − peoc
Pec = G2
♦♠♣♦♥♥ts ♥r
T1 − 1) = ( p2
r♥ ηt ∗ (1 − ( p4
gamma )
r♠ t q ∗ Cp ∗ T5 = qma ∗ Cp ∗ T4 + qmav ∗ Cp ∗ T1
p1 − p4 = ksiα ∗ ν ∗ q2
mav
s♦t♦♥s
s♥ ts ♥♦ ♦t t ♠♦ r♥ t s♦♥ ♣r♦ss ♣r♠t s t♦ ♦♠♣t ♥t st ♦ s♥ s♦t♦♥ ♣r♥♣s ♥ ♦rs ♦♥ ♣rs♦♥ ♦♠♣tr t s r ♥ s♥ ss ♦♥♦♥ strt t r♥t ♣rs♦♥s t t♦t t♥ ♥t♦ ♦♥t s♥ r sss st ♦ s♦t♦♥s ♥ sr ♦rs
r strts t strt♦♥ ♦ t s♦t♦♥ st ♦♥sr♥ ♠♦r rtr t ♦♠ ♦ t ♥r ♥ ts ♠ss tr s♠♦s s t♦ ♣♦t s♦t♦♥s r♣rs♥t t ♥ sr t♣s s ♦r t ♦ts ♥ t ♥r r s♦s t s♦t♦♥s s♦rt t ♥ sr rr♥s r♦♠ t t♦ ♦r t ♦t s ♦ t ♥r t s ♠♣♦rt♥t t♦ t tt tr r ♥♦ s♦t♦♥s t t ♥ srs r♦♠ t t♦ ♥ t st ♦♥s r r♦♠ t ♦r ♥ sr ♠
s♦t♦♥s ♦♥sr♥ t ♠♥ sst♠ ♣r♦r♠♥ rtr ♦♠ ♥ ♠ss ♦ t ♥r
s♦t♦♥s ♦♥sr♥ t ♥r ♠ss s♦rt ♦ts ♥ sr rr♥s
♦♥sr♥ ts rsts s♥rs ♠ ttr ♥rst♥♥ ♦ t s♦t♦♥ st ♦ t s rsts ♦ s t♦ t s♦♠ t ♥♦ ♦t t s♥ ♦ r ♦♥t♦♥♥ sst♠s ♥ ♥ rrt ♦♠ ♥ srs ♠s ♣♣r t♦ ♣rt♣t ♥ ♠♦r ♣♦r ♥ t♦ s t♠ ♥ t ♣str♠ ♣ss ♦ s♥
♦ P
♦♣♠♥t ♦st
s ♣♣t♦♥ s ♦♣ ♥ sr st♣s s ♦ t ♦♠♣t ♦ t ♠♦ rst ♠♦ t♦t ♥s t♥ t ♥r ♣ts s ♦♣ t t♦♦ s t♦ t ♣r♠♥r ♠♦ s♥ s t t r♦♠ ♥ ♦t♦♥r ♣♣r♦ ♥ ♣r♦s ♦r ♦♥ ts sst♠ ♦r sr s r ♥ t♦ t ♠♦ t ♣ss ♦rs ♥ t ♥tr ♠♦ t ♥s t s t tr sr s ♦ ♥♦t ♦♥t t ♦♣♠♥t t♠ ♦ t rsts sr ♥ t s♦r
♦r ♦r ♥ ♣r♦ts s♣♣♦s tt t ♠♦ rt♥ ♣s t ♦♥r t s s ♦♠♣ s ♦r t t t♥ tt ♦♥ s ♦ ♥ssr t♦ s P ♠♦ ♦r s♥ ♣r♦♠s ♣rtr t s ♣r r♥t ♥ss ♦ t ♣r♦t t ♣r♠ts t♦ ♥t ♥ ♦r♥s ♥t♦ rr t ♦♠♣♦♥♥ts ♥ ♣ss ♣♥♦♠♥ ♠♥ t rtt ♥ t ♠♥ rtrsts ♦ t ♣r♦t r ♥ ♥ ♦♥ t r♥t ♣ss s ♥ t r♥t ♣r♦r♠♥s rtr r ♣rss
♥str s
r ♦r ♦♥ t s s ♦♥ ♣r♦s ♦r s♥ ♦tr s♦♥ ♠t♦s P ♣♣r♦ ♦s t♦ ♦ t tst ♥ ♠t♦ ♦♠♠♦♥ s ♥ s♥ ♣r♦ss ♥ t ss ♣♣r♦ ♠♦ s ♦♣ ♥ t♥ rtr t ♦r ♥♦t t s♦t♦♥s ♦♥♥ t P ♣♣r♦ rtr r t♥ t ♠♦ ♥ ♦♥ stst♦r s♦t♦♥s r ♦♠♣t ♥ t♦♥ ♠♦ ♦♣♠♥t ♠♦♠♥t s♥ ♥ t s♥ ts ♦t ♠♦♥ts ♥ t ♥s ♦ ♥str s♥ r ♥♦♠♣t t sr ♠♦ ♦♣♠♥ts
r ♠♦ s qt ♦♠♣t ♦♥sr♥ ♥ ♠♦♠♥t st s♥ t ts ♥t♦ ♦♥t ♠♦r t ♥♦ rt t♦ ♦♠♣♦♥♥ts ♥ tr ♣r♦r♠♥s t♥ ♣r♦s s ♠♦s ♥♠ t ♥r ♥ ts ♥ srs rsts r♦♠ ♥ q♥t ♠♦ r t♥ ♥t♦ ♦♥t ♦r t s♥ ♦ t ♥ st t♦ ♦♥♥tt ♦♥str♥ts ♦♣ sst t♦♥
♥ sr ♣r♥
s ♦ ♦♥str♥t stst♦♥ t♥qs ♥ ♠♦♠♥t s♥ ♣♣rs ♣r♦♠s♥ t♦ t s♦♥ ♣r♦ss s ♥♦t s ♥t ♥ s♦♥
s♦♠ ♠♦s ♠ t♠ ♦♥s♠♥ ♦♠♣r t♦ t ♦t♦♥r ♣♣r♦ ♥ t s♦t♦♥ st s ♥♦t s r♥t s♥ tr r ♠♥ ♣t s♦t♦♥s rt t♦ t s♥ ♣♦♥t ♦
t♥ tt ♠♦st P t♦♦s ♦r ♦♥str♥ts s♦rs r ♥♦t ♥♦ s♥ ♦r ♥♥rs ♥ ♦♥str♥ts ♥ ♣rtr s♥rs t♦ t ♦♥str♥ts ♥s r ♦t♥ ♥tt ♦rs r ♠♥ ♦♥r♥ t ♠t♠t rsts ♥ s ♦tr ♥s ♦st s♦rs ♦ ♥♦t t ♥t♦ ♦♥t ♥ ♠♥t ♥♦t♦♥s ♦ s♥ s ♦r ♥st♥ t s♥ ♥ r rs ♣t rs ♣s ♦♥str♥ts ♠tr s ♠♦s ♥ t r♦♠ t♦s ♦r tss t ♦r t♦ t ♣♦♥t t rsts ♦t♥ t ♦♥ str♥t s♦r r ♥♦t rs ♦r t ♥t ♣ss ♦ t s♥ ♣r♦ss r t♦♦s r ♠♥ s
♦r♦r t ♦♣♠♥t ♦ r ♣♣t♦♥s t ♠♥ ♦♥str♥ts ♥ r ♠♦♥ts ♦ t s t ♥ t ♥♦♥sst♥s r ♦t♥ ♦♠♣ t♦ ♣♥ s♥ ♦♥ tt ♥♦r♠t♦♥ s ♦t t s♦♥ rs ♥ ♦♥ ♦ ♠r t sr s t t ♣r♦♠ ♠ r ♣ ♥ ♦r ♣♣t♦♥ ts ♦ ♥♦r♠t♦♥ ♦t t s♦♥ ♣r♦ss ♥ t ♥♦♥sst♥s rst ♥rs t ♦♣♠♥t t♠ ♦ t ♠♦
♥ t♥ tt s♦rs ♠st ♥♦t s♦♠ ♦ t♦♦s t♦ ♥ t♥ t♦ t r ♣r♦♠ t♣ ♥t♦♥ ♦ rsts t sr s s♦ ♠ t ♣♦ss t♦ ♥rt ♠♦ s♣ts ♦r ♥st♥ ♦♥sr♥ t r♥ ♦ r sss ♦r♥ t♦ s♥ ♣♦♥t ♦ ♦r ♠♦r s♣ strts rt t♦ t ♥stt ♣r♦♠
♦♥s♦♥
♥ ts ♣♣r t ♠♦ ♦ ♥ r ♦♥t♦♥♥ sst♠ ♥ ♥ rrt s ♥st t ♦r♥ t♦ t ♠♦♠♥t s♥ ♦♥tt ♥ s♦♠ s♠♣t♦♥s r ♠ ♦♥ sr ♦♠♣♦♥♥ts rs ♦trs r ♠♦r t ♥ t rt ♦ ♦♠♣ ♣ss ♣♥♦♠♥ t sr ss ♦♠ ♥ ♦♥♣ts ♥ ♥ rsts r ♥ ♦r♥ t♦ r sss ♥ r♥t ♣rs♦♥s ♥ ♦rr t♦ s♣♣♦rt s♦♥ ♠♥ ♥ ♠♥ ♣t s♥ s♦t♦♥s r ♠♥t ♥ ♦♠♣r t♦ ss P s♦♥ ♣♣r♦ ♥ t ♥tr st ♦ s♥ s♦t♦♥s s ♦♠♣t s ♥ ♥♦t♦♥s ♥rs t ♥ ♦ t s♦♥ ♣r♦ss t tt s♦♠ ♠♣r♦♠♥ts ♥ st ♠ t♦ ♥rt t♦♥ s♥ ♠♦ s♣ts
♦♥ ♠♦♠♥t s♥ ♠♦s t ♦♥str♥t ♣r♦r♠♠♥ s♠s ♣r♦♠s ♥ t♦ s♦♠ ts ♠ ♣♣r ♦r ♥♥rs ♥ ♦♥str♥ts ♥ ♠♦st s♦rs r ♠t♠t t♦♦s r s♥ ♦♥♣ts r ♠ss♥ t ♦r P s t♦ ♣ t♥ ♥r ♣♣r♦ t♦ s♦ ♣r♦♠s ♥ ♦rr t♦ ♣ ts st♦s tr ♥ t t s♠ t♠ t♦ s♦ ♥t t♣s ♦ ♣r♦♠s
♦r sr ♥♠♥t ♥♦t♦♥s ♠ ♥trt ♥ s♦rs t♦ ♣ s♥rs t tr ts s ♦r ♥st♥ t r t♣s ♥ s♥ ♣s ♦♥str♥ts t ♦♥str♥ts s♦rs s♦ s♦ ♥ t ♦tr t♦♦s
♦♠♠♦♥ s ♥ s♥ t♦♦s ♥ ♣r♣s s ♥ ♦t ♦r ♦♠♣♦ ♥♥t ♦r♥t ♣♣r♦ t♦ ♣rss ♦♥str♥ts ♥ t♦ tt t rt♥ ♦ ♥♦ ♥ t♦ rs t ♥ ♦tr t♦♦s
♥ t ♦tr ♥ t P ♣♣r♦ ♦s s♥rs t♦ ♦ trs ♥ t s♥ ♣r♦ss s♥ rtr r s ♥ t s♦♥ ♣r♦ss t♦ ♦♠♣t ♦♥ stst♦r rttrs s s♥rs ♥ ♦♦s ♠♦♥ sr r ttrs ♥ ttr ♦r ♦ ♣r♦t ♣♦ssts
r♥s
♥♠♦ ♦r r♥rs Pt s♥ ♥ ♦ ♦♥sst♥ ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦ Pr♦r♠♠♥ ♣s Prss
r♦♠tt♦♥ s♥ r♣ ♦♠♣♦st♦♥ ♦r ♦♥ ♦♥t♥♦s Ps ♥ P Ps t
sr st♥ P P ♠♠r ♦♥str♥t s ♣ ♣r♦ ♦♠♥ t t♠♦♥ ♥qs t♦ ♣♣♦rt ♠♦♠♥t s♥ ♥ r♥♦
t♥s ♦♥ ♥ ♦♥t♦♥ ♦♥str♥t tst♦♥ Pr♦♠s ♦♥str♥ts
s ♦♥♦♥ ♦♠♣t t ♥rs r ♦♦ ♦♠♣♥
♦♠♠ ♦♥sst♥ ♥qs ♦r ♠r Ps ♥ ♠ ér r♥
♦♦r ♥tr ♥ss Pr♥t rt r♦♠tt♦♥ ♥ ♥tr ♥ss ♣s ♥
tr♦ tr♥ ♥ P ♥ts r♥ ♥ ♦♥str♥t ♦♥♣t s♥ Pr♦ss♦♥ ♥♥r♥
Ps♥ P t ♥♥r♥ s♥ st♠t ♣♣r♦ ♣r♥r rt ♠t ♦♥str♥t ♥♠♥t t♦♦♦ ♦r
♦♥♣t s♥ r♦ ts s♥ ♦r ♥ t♦♦♦ ♦♥r♥ r♥
♦ P t ♦♦♣rt♦♥ ♥ ts ♣♣t♦♥ ♥ Ps ♥r ♣t ♠t♦♥ P
rtt P ést♥ P Pès s♦♥♥ ♦r ♥ ♠♦♠♥t s♥ Pr♦♠ ♥tr♥t♦♥ t
ést♥ P ♥♦r P sr ♠♦♠♥t s♥ ♦♥str♥t tst♦♥ Pr♦♠ ♦ t P ♥ ♥tr ♥ss ♥ ♥t ♦rt♠ s s♦♥ s♣♣♦rt t♦♦s Pr♦♥s ♦ rt ♦♥ ♣t ♦
♠♥ rr♠ ♣rs♥tt♦♥ ♦ ♥t♦♥ ♥ ♦♠♣trs s♥ Pr♦♥s ♦ t s♥ ♥♥r♥ ♥ ♦♥r♥s t ♥tr♥t♦♥ ♦♥r♥ ♦♥ s♥ ♦r ♥ t♦ ♦♦
♥♥t♥r P str ♣r ♦♥ P♦♥♦♠ st♠s s♥ r♥ ♥ Pr♥ ♣♣r♦ ♦r♥ ♦♥ ♠r ♥ss ♦ ♣
♦r♦s ♦t♦♥ ♥qs ♦r ♠r ♦♥str♥t tst♦♥ Pr♦♠s P tss ss r ♥sttt ♦ ♥♦♦ ♥ s♥♥ P
♥♥♦ ♠♣s♦♥ rt♦♥ ♦rs ♦♥♣t s♥ ♣♦rr s♥ t♠♦♥ ♣♣r♦s ♥ ♦♥str♥t Pr♦r♠♠♥ ♥
♦ ♠♠r t P ♦ rrt Prs♥ s ♦♥ ♦♥str♥t Pr♦♣
t♦♥ ♥ ♥tr ♥ss ♥ ♦♥ r♠♥