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 007, Providence, United States. Springer Berlin / Heidelberg, 4741/007, pp.18-3, 007, Lecture Notes in Computer Science. <10.1007/978-3-540-74970-7_4>. <hal-00466675> HAL Id: hal-00466675 https://hal.archives-ouvertes.fr/hal-00466675 Submitted on 5 May 010 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
r t st Pr s str t t s t ë r 1 P tr é st 1 r t r rs 1 r 1 s rts ts s r ét q 1 rs t t s r t r r t q t s t t q P t s 1 str t t s r t t s r t sst r r t s st t s t r str t s t s t t q s t s q t 1 t s s t t s r s str ts rr s t 1 s s r st s 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 r t s ts s str t r r t s r s ss s t s r s rs s P t s r s rt t r t sst r t 1t s r ss s s q s s r r t t s r q r ts t r r s t s P t3 Pr r s s t s t r t s s t s r s t st s r st t r t tr str ts s s rs t r t s t t r t ts ts ts r ts s r s t r 1 st t s 1 t s r s t s t 1t str t s r str t 1 r r s t rt rs t ss t t s r r s r r t r s s rt rs s r t t r t r r t r r st rts r t s r t s t 1 r ss s t r t s s str t r r t s r r s r r t s t s s r r r str t r r str t s t q s s t r r t t r r s ts r t s tt s r r t r ts s
t s r r t sst r r r t s r s st t r s r s t ts t 1 s r t s tstr s t r r ss r t r s t 1 r tr t s r 33 s tstr rr s s t r rs r t tr t s s t r t t r sst r t s t r r ss r t r t r st t r r t s t t s t r r r r t r t sst r r t s r ss t r t r st t t t t r r ss r t r t r t st r t r t t ss rs t t r s t r t t r r t r r t t s r t r t r s t t r r t r r r s t s r s t r r t r r r r r r t t t ss r t 3 ts r r s t r r t ss s t t 3 s r t t s r t s s r s s r ss s r s s rs r t r st r s r t r s r s t r s s s t r s s r s rr s t t s st s t r s t r t t r
r t 1 r r s r s t 1 r ss t str ts r t t t s s r tr str ts r r s r t r r s t s r s r t r s s r t r t t t r t r r t t t t t t s s t s t t t s t t s t r t s r ss t r t 3 s s t ts t ts t r t st r 3 r t s s t t 1 r t tr t r s t r r s s t t r t r st s t 1 r t s t r ts r 1 r ss t ts r t r rs r s t t s s t s r s t t 1 r s r 1 s r s s t r r r s s r s r r s r s r t tr t s r t 1 r t r r s r s 1 r r s st t r s s r s 1 t r s t s r s r 1 t str t s t rr s t t r r t t s r t t t s t 1 r ss r t r st s r r t r r s r t 1 r ss t t r 1 r r s r r t t t 1 r s r t r st s r ss r s t r t r s t str ts s ss r st t r r s r str ts s r t 1 s r s s str ts s r t r s t ts s t t r str ts 1 r ss t r t r st s r tr t r t r r ss r ss s t st t t 1 t r s t s s t s s s t rr s s t r t r t t r s t s st ts r t r s s q s s t s r r s t s r s t 1 r r s s st t t t t s r s s t s s t r 1 r t t s r s t s r t 1 r r s 1 r t s t r t t r t r t s s r t P t s s rs t t r s ts s s t s t s rt s t s t 1 r t s t s s r s t st t s r s r r rt ts s s t t s t t 3 t t s s t
r q r s t t s t s s t t st t r s r st t s t 3 t r s t r t s t st t t r s t t s r é st t s s t s r t r t t r t s t r s s r t st r r t t t s t t s t t t 1t r r s s s s r t t t t t t t s r t s r r t t r r s t t t t r s t s t s rt r s r t rs t t r t r t t s r s t s r s t 1 r t s s s s t t t s t r s t s r s t s tr t t t t r r t s s P r s t r t t s s t t t r s t s t s t st s ss r r t r r t s t s r s r t t s t s t t s s r s r t s r t s r t s r s s 1 r t r t s s r t t r t s s t s t s t s t r s t s t s s s rs t t r r st s s s t st t r s t r s s t s r t r st s s r st ts s s r r t r t s r s r s r t t r s ts r r s t r t r s P r r t sst t s r P r r s r r r t t r t r t s r t ss tr t r r s t t P r s V,D,C r s r s s r t r t s s r t t s s r t s r rt t t r t s t r r s t s r t s t s str ts r s r t t 1 r ss s s t ss q t q t r t rs r s s s s r st s t r 1 r ts t r 1 r ss s s r t s s s r r st s s r st t s s r r s t t r s r st s ss t s Pr t rs t s str t t t t t s s s r t s q t s r t s r r s t s r r t s str t s t s t r s s
q r r r t rr s t s t t t ts t s r t s r st ss r r str t t r s s r 1 r t t s s s t s r t s r s r t s t s s t s 1 t s t s ss t t st s 1 r r s t s r st st s r s r ss s t t t s t s r s t str t r r t r st s s r t st s r t r r t r 1 r r s r tr t 1 r ss r r r t r s s r t s r ss t t s t s t 1 r r s r 1 t r t t r r s rr s t t r r t t st s t t r t t t s r ts t t s s ss 1 r t st s r t t s r s t r r s r t t t s t t t r r s s r s r s r t t s st r r ss s 1 s st t t s rt t t t t t 1 t r s s t r 1 t r s t s s
s t st t t s s r s r r s t s s r s r t s r s r t s t s 1 t r s s t t r t t t r s t s t t s r s rs r s t r r t s t t t rst s t t r s r rs s t r r s s r s s s r 3 r t r t t t t t r r t t r s s r r r s r s r st rt t 1t t r t s t r r r s r r s r t t r s t r r s r s ts r s t s s s t r ss t r r s r r r r s r s r t r str st rt r s t s t t s t t str t t r t s s t s r s r 1 r st 1 st t s ss t t st s rr t r s Pr s t t t r s s r s rs t t t s r r t s t s t r s rs s r s r s r r s t t t r t s s t s r t t s t s r s s r t t r s r r s t s s r s r r s r st 10 8 s t t r s s r s rs s s s s r t s t t r s r s r s t st r t r s t s r st t r r r t r s s r r s s t t t t t r t s t s r q r ts r s s 1 r r s r r t t s t r r 1 t t t s rs t s t r st t r t r r s s t t s t s s r t t s r s s r t t t t s s r s s r t s ss t s s rs t t t r s r t q t s r t s t q t s ss r r t r t r s t t t t t r s t s rs s r t ss t s r t r s t s r t r s str ts r st ts r s t r 1 r r s r t t s s s q t t s r t s s s r r t t r r s s s t r r t s t t s t t r s t s r t t t t s t t t s ss s r s 1 r t s r t s t s t t t s s t s
t t t st ts r s s str ts t r r t t t s r 1 s r t t s r s t t r t s t 1 r t t t r s r t s t s s t s s ss st ts r r rt s Cp = 1000 r = 87 γ = 1.4 t t s Z = 10500 M = 0.8 r r t r r t r st s TC TR = 8 η TRd = 0.9 η TRc = 0.8 ts η c = 0.75 η AT = 0.95 η t = 0.8 η NO = 0.9 η DI = 0.9 r s t t t T 5 = 78.15 p 5 = 85000 P q = 0.7 s P t s r t r st s kp = 0 tp = 0.001 s r s t t 1 r 1 [0.1, 1] 1 = 0.01 ss t r t τ [1, 8] τ = 0.5 t s 1 s r r r ExSurf h [1, 48] t s 1 s r r r ExSurf c [1, 48] t r t r s {0.01, 0.0,..., 0.} 1 r r s 1 r t r r t r st s roex [0, 10000] kw [0, 500] 1 r r ss r s P p [0, 1000000] p(p ) = 5% p 3 [0, 1000000] p(p 3) = 5% pe ic [0, 1000000] p(pe oc) = 5% pe oc [0, 1000000] p(pe oc) = 5% 1 r t r t r s T [0, 1000] p(t ) = 5% T 3 [0, 1000] p(t 3) = 5% Te ic [0, 1000] p(te ic) = 5% Te oc [0, 1000] p(te oc) = 5% 1 r r ss r ss s P Pe h [, + ] p( Pe h ) = 10% Pe c [, + ] p( Pe c) = 10% 1 r t ǫ [0, 1] p(ǫ) = 5% r s t 1 r s q ra [0, + ] p(q ra) = 0.001 q ma [0, + ] p(q ma) = 0.001 Pr ss r t r t t r P p 4 [0, 1000000] p(p 4) = 5% r t r t r t t r T 4 [0, 1000] p(t 4) = 5% 1 r r s r t t t t s s r t r st s r t r t ts b h rh h δ h β h b c rh c δ c β c JS h1 JS h JS h3 JS c1 JS c JS c3
t r t ts fs h1 fs h fs h3 fs c1 fs c fs c3 t r t ts KcS h1 KcS h KcS h3 KcS h4 KcS h5 KcS h6 KcS h7 KcS h8 KcS h9 KcS c1 KcS c KcS c3 KcS c4 KcS c5 KcS c6] KcS c7 KcS c8 KcS c9 t r t ts KeS h1 KeS h KeS h3 KeS h4 KeS h5 KeS h6 KeS h7 KeS h8 KeS h9 KeS c1 KeS c KeS c3 KeS c4 KeS c5 KeS c6 KeS c7 KeS c8 KeS c9 1 r r s s 1 t r s 1 r s s Ly = Lx Lz = 0.5 Lx s r t r st s α h = (b h β h ) (b h +b c+ δ h ) αc = (b c β c) (b h +b c+ δ c) σ h = α h rh h σ c = α c rh c s ηf h = tanh ml h tanh mlc ml h ηf c = ml c 1 s r s s A h = α h (Lx Ly Lz) A c = α c (Lx Ly Lz) Aw = Lx Ly n Ac h = σ h Af h Ac c = σ c Af c Af h = Lx Lz Af c = Ly Lz 1 s r η0 h = 1 Af h A h (1 ηf h ) η0 c = 1 Afc A c (1 ηf c) 1 r r t ss tw = (δ h+δ c) r t s n = r r t r st s t 1 r Lz b h +b c+ δ h G h = qma Ac h G c = qra Ac c µ h = 1.075e 5.5e 9 T 3 +1.75e 6 T 3 + 1.075e 5.5e 9 T +1.75e 6 T µ c = 1.075e 5.5e 9 Te oc+1.75e 6 Te oc + 1.075e 5.5e 9 Te ic +1.75e 6 Te ic ρ = p r T ρ 3 = p 3 r T 3 ρ ic = pe ic r Te ic ρ oc = peoc r Te oc Cp oh = 1003.7 + 6.8e (T 3 73.15)+.e 4 (T 3 73.15) Cp ih = 1003.7 + 6.8e (T 73.15)+.e 4 (T 73.15) Cp h = Cp oh+cp ih Cp oc = 1003.7 + 6.8e (Te oc 73.15)+.e 4 (Te oc 73.15) Cp ic = 1003.7 + 6.8e (Te ic 73.15)+.e 4 (Te ic 73.15) Cpc = Cpoc+Cp ic 1 r ss m ex = ρ ex Lx Ly (( σ h δ h rh h 1 r V = Lx Ly Lz r s t 1 r s C h = qma Ac h ρ Cc = t tr s r r t r st s λ = qra Cp ic q ma Cp ih Nut = q ma Cp ih + σc δc rh c qra Ac c ρ ic 1 + η0 h h h A tw h kw Aw + 1 η0c hc Ac ) Lz + n tw)
r ts r t t r h h = J h G h Cp h Pr /3 h hc = J c G c Cp c Prc /3 J h = e JS h1 log (Re h )+JS h log(re h )+JS h3 J c = e JS c1 log (Re c)+js h log(re c)+js h3 f h = e fs h1 log (Re h )+fs h log(re h )+fs h3 f c = e fs c1 log (Re c)+fs h log(re c)+fs h3 Pr t r Pr h = (0.85 0.00054 T 3+5.0e 7 T3 ) + (0.85 0.00054 T +5.0e 7 T ) Pr c = 0.85 0.00054 Teoc+5.0e 7 Te oc + 0.85 0.00054 Te ic +5.0e 7 Te ic s r Re h = 4 rh h G h µ h Re c = 4 rhc Gc µ c t r ss r ss s t Kc h = KcS h1 σh + KcS h σ h + KcS h3 log (Re h )+ KcS h4 σh + KcS h5 σ h + KcS h6 log(re h )+ KcS h7 σh + KcS h8 σ h + KcS h9 Kc c = KcS c1 σc + KcS c σ c + KcS c3 log (Re c)+ KcS c4 σc + KcS c5 σ c + KcS c6 log(re c)+ KcS c7 σc + KcS c8 σ c + KcS c9 t t r ss r ss s t Ke h = KeS h1 σh + KeS h σ h + KeS h3 log (Re h )+ KeS h4 σh + KeS h5 σ h + KeS h6 log(re h )+ KeS h7 σh + KeS h8 σ h + KeS h9 Ke c = KeS c1 σc + KeS c σ c + KeS c3 log (Re c)+ KeS c4 σc + KeS c5 σ c + KeS c6 log(re c)+ KeS c7 σc + KeS c8 σ c + KeS c9 t s r r t r st s T a = 88. 0.00649 Z p a = 10190 ( Ta 88.08 )5.56 r r t r t r t r s T 0 = T a (1 + M (γ 1) ) T 1 = T 0 (1 + 1 η T Rc (( p1 ) γ 1 γ 1)) p0 r r t r r ss r s P p 0 = p a (η TRd M (γ 1) + 1) γ γ 1 p 1 = TC TR p 0 s r r ss r s P po Dc = pi Dc (η DI M γ 1 + 1) γ γ 1 t r t r s To Dc = Ti Dc (1 + M γ 1 ) pi Dc = p a Ti Dc = T a 33 r ss r P pi Bc = pe oc po Bc = p a Ti Bc = Te oc t r t r s To Bc = Ti Bc (1 + η NO ( 1 + ( po Bc pi Bc ) γ 1 γ )) r t s r ν = r T 1 p 1 p 4 = p 5 q mav = q q ma ksi α = e (4.03108e 4 α +8.50089e α 1.5995 r s 1 t r s m h = h h kw δ h m c = h c kw δ c ml h = m h b h ml c = mc bc CPam h = Kc h + 1 (σh) CPd h = ( ρ ρ 3 1) CPr h = f h A h ρ Ac h ( ) ρ +ρ 3 CPav h = (Ke h + σh 1) rho rho3 CPam c = Kc c + 1 σc CPd c = ( ρ ic ρ ic ρ ic +ρ oc ) CPr c = f c Ac Ac c ( CPav c = (Ke c + σc 1) ρ ic ρ oc ρ oc 1)
str ts t exchsurf h = 1 JS h1 = 0.0314 KcS h9 = 1.71731 1 s r s exchsurf h = 48 JS h1 = 0.0369 KcS h9 = 1.551097 exchsurf c = 1 JS c1 = 0.0314 KcS c9 = 1.71731 exchsurf c = 48 JS c1 = 0.0369 KcS c9 = 1.551097 t r s r t T 473 roex = 8440 kw = 30 1 r T 473 roex = 8440 kw = 30 1 r s r t r r t τ = qra q ma t ǫ = 1 e λ Nut0. (e r t t s ǫ = T T 3 T T 0 t s r T 3 = T ǫ (T Te ic) t s r ss r ss s Pe h = p p 3 s r s r ss r ss s ts r s Nut 0.78 λ 1) Pe h = G h ρ (CPam h + CPd h + CPr h + CPav h ) Te oc = qma Cp ih q ra Cp ic (T T 3) + Te ic Pe c = pe ic pe oc Pe c = G c ρ ic (CPam c + CPd c + CPr c + CPav c) r ss r η c ( T T 1 1) = ( p p 1 ) γ γ 1 1 s t (T T 1) = η AT (T 3 T 4) r η t (1 ( p 4 p 3 ) γ 1 gamma ) r t q Cp T 5 = q ma Cp T 4 + q mav Cp T 1 p 1 p 4 = ksi α ν To Dc = Te ic po Dc = pe ic q mav (π Rv ) s t s s t s t t r t s r ss r t s t t t s t s s t r s rs rs t r t 3 s r s ss str t t r t r s s t t t t t t s r ss s s t s t s s r rs r str t s t str t t s t s t s r r r t r t t 1 r ts ss t r s s s t t s t s r r s t t 1 s r t s s r t t s t 1 r r s s t s t s s rt t 1 s r r r s r t t r t t s t 1 r t s rt t t t t t t r r s t s t t 1 s r s r t t t st s r r t r 1 s r
s t s s r t sst r r r t r ss t 1 r s t s s r t 1 r ss s rt t s 1 s r r r s
s r t s r s ts s rs tt r rst t s t s t t s r s ts s t t s t t t s r t sst s r r t 1 s r s s r t rt t r r t s t t str s s s P t st s t s s r st s s t 1 t t rst t t s t t 1 r t s s t t s t t r r s s t t r t r r r s r t s sst r s r s r t t t s s rs t t r t s t s t t r s r s t t t t t t r st s s r t s r r r r ts s s t t t r t s t r t s s 1 s r t t t t t s ss r t s P r s r s rt r t s r r t s s t r t t r ts t t r s t r r t ts s s 3 t r tt t r t r st s t r t r t r t s s s t r t r r s r t r r 1 r ss str s r r t s s r s r s t r s t s P r s t t t st t s s r ss t ss r s t r t r t r t t s t s t P r r t r r t t s t s t r s t s r t t t t s t s t s t t s t s str s r t t s r ts r s q t t s r t st s t t s t t r t r t t ts t r r r s t r s s s t 1 r ts 1 s r s r s ts r q t r t t t r t s t s t t t t str ts ss t t s r 1 r s str t s t s t t q s 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 s t s t s r t s t r r t s t s r t t t s t t t t st P t s r str ts s rs r t s r rs str ts rt r s rs t t str ts s r t t t rs r r t t t r s ts s t r s st s rs t t t t t t s s s r st t s 1 r r s 1 t r s s str ts tr 1 s s t r t s r t s s t r t t t t r s ts t t str t s r r t r s r t 1t s s 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 s st s r t 1 t 1 s tt r t s t t s r s r t s r s t t r r r t t s r t t t s r ss t s st s r st r s t t t t t t t s rs st t s 1 t s t 1 t t t r r t t r st s t s r s s t ss t rt s t s r st s r t r r ss s r t s t r r s str t s r t t t st t r s t s r t r t sst r r t s st t r t t t s t 1t s s t s r s r ts r s t rs r r t t r t 1 s s t s r s s ts r st s r r t r ss s r t r s s r r t s rt s t s s t s r t r t ss P s r t t r s t s s t s s t s t s r s t t s r ss t t t s r ts st t rt t s s t s t s s t str t r r s s r s t s t s 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 r r t ts s t s t r t t s t t s t t s r s r s r t t s t r t s rs t s rs t t r t s s r st t r t s s s str ts t str ts s rs s s t t r t s
s s t s r s s t r t r t r t 1 r ss str ts t t t t r t t r s t t r t s t t r t P r s s rs t tr s t s r ss s r t r r s t s r ss t t s t s t r r t t r s s s rs s s r r t t r s tt r r r t ss t s r s r r rs P t s 1 s st t r t r Pr r s Pr ss r tt s r s t r t s Ps P P s t s r st P P r str t s r t t q s t rt t s r t s 1 t str t t s t Pr s str ts s t t 1 rs r s st q s r r Ps ér r r t r s s Pr t rt r tt t r s s s t r tr P t s r str t t s Pr ss r P s P t3 r s st t r r r rt t str t t t r t s r t s s r t r r P t r t ts t P s r t 3 t P r tt P é st P P ès s r t s Pr t r t t é st P r P s r t s str t t s t Pr t P t r s s t r t s s s rt t s Pr s rt t 1 3 3 r r r s t t t t r s s Pr s t s r r s t t r t r s r t t r P st r r P st s s r Pr r r r s s
r s t q s r r str t t s t Pr s P t s s ss r st t t s P s rt r s t s 1 r r s t r s str t Pr r r t P r r t Pr s s str t Pr t t r s s r