STUDY ON SOLIDIFICATION PROPERTIES OF ICE STORAGE IN A FLAT AND RECTANGULAR CAPSULE

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1 Internationa Journa on Arcitectura cience, Voue 3, Nuer 4, p.35-39, TUDY ON OLIDIFICATION PROPERTIE OF ICE TORAGE IN A FLAT AND RECTANGULAR CAPULE G.Y. Fang Departent of Pyic, Nanjing Univerity, Nanjing 93, Cina H. Li Departent of Materia cience and Engineering, Nanjing Univerity, Nanjing 93, Cina (Received 3 June ; Accepted 8 epteer ) ABTRACT Ti paper preent a oidification proce ode of pae cange coo torage ateria in a fat and rectanguar capue, and iprove te tera reitance etod for oving pae cange oving interface. Te etod ake ue of firt order accuracy oution to otain econd or iger order accuracy oution. Ti paper ao anaye te infuence of te on pae cange oidification tickne and rate on te ai of te cacuation reut.. INTRODUCTION Air conditioning coo torage yte conit of cier and coo torage yte. Coo torage yte i divided into ice on coi, ice a, ice rectanguar capue, ice arveter and ice urry. Ice torage in rectanguar capue i one of yte tat are widey ued in air conditioning coo torage. Te fat and rectanguar capue for ice torage i typicay ade fro a poyer ateria and fied wit water to approxiatey 9% to 95% of te free voue. During te freezing proce, a water in te rectanguar capue cange pae to oid pae, expanion occur and te capue ecoe preurized. Conequenty, oe diation of te capue occur, to a greater or eer degree, depending on te fexiiity of te capue kin. Merit of ice torage in rectanguar capue are arger eat tranfer area, aer tera reitance and arger coo torage denity unit voue. During te carging proce, te poition of oid-iquid interface in te rectanguar capue continuouy ove inward, and te penetration rate of pae cange interface of ice torage continuouy cange. Cen et a. [] invetigated te tera perforance of ice-water coo torage yte teoreticay and experientay. A ateatica ode for a tera energy torage yte utiizing rectanguar container wa deveoped y Prua et a. []. Te perforance of pae-cange tera energy torage yte uing perica capue wa deveoped y Bedecarrat et a. [3]. Ti paper preent a ateatica ode decriing oidification propertie of ice torage in a fat and rectanguar container unit. inet. MATHEMATICAL MODEL AND METHOD OF OLUTION A one dieniona ode of ice torage in a fat and rectanguar capue i own in Fig.. In Fig., te fat rectanguar capue are tacked on top of eac oter wit pacing in etween ucceive container in order to provide fow canne for te eat tranfer fuid (5% gyco oution) [4]. y iquid oid Fig. : ceatic diagra of one dieniona ode grid ice torage tank Fig. : ceatic diagra of ice torage tank For a ateatica decription, te foowing auption are ade: A teropyica propertie are contant. oid-iquid interface teperature i uncangeae. x ice torage pate outet 35

2 Internationa Journa on Arcitectura cience Initia teperature in te capue i equa to ice freezing teperature. ince te capue tickne i uc aer tan te engt and widt, it i conidered to e one dieniona eat conduction aong tickne direction. During te freezing proce, ince interface oveent veocity i uc ower tan teperature oveent veocity, te teperature in oid region i aued to e quai-tae ditriution [5]. Referring to te ode given in Fig., te governing equation for oid region and iquid region are: T T k ; for x < y () t T T k ; for y < x () t Te oundary condition are given y: T T ; at x (3) T ; at x (4) Te initia condition i: T (x,) T ; at t (5) Te oid-iquid interface condition are: T T T ; at x y (6) y T T ρ H k y k y ; at x y (7) t We ave introduced te foowing nondieniona quantitie: T T θ, T T x X, y, c te (T H T ) utituting tee quantitie into equation () to (7), te fina equation for te preent proe ecoe: θ (X, τ) θ α (X, τ) α Te oundary condition: ; for X < (8) ; for < X (9) θ ; at X () ; at X () Te initia condition: θ ; at τ () Te oid-iquid interface condition: θ θ ; at X (3) k te k ; at X (4) Integrating equation (8) and (9) one otain: θ dx dx (5) α θ dx dx α (6) Fro equation (5) and (6) one a: (7) α α dx α α dx (8) utituting equation (7) and (8) into equation (4), one get: α t k t τ, te ρc dx (9) 36

3 Internationa Journa on Arcitectura cience Epoying te reation of Equation (9) ay e written a: te ρc dx (9a) dx (7) utituting equation (), (6) and (7) into equation (9), one otain: te ( te) Integrating equation (8), one a: (8) te ρc dx dx (9) In ter of auption (5), oid region teperature ditriution in te fat rectanguar capue i conidered to e inear, one get: θ a X () One ay otain te foowing expreion for te teperature ditriution at X, θ, and X, θ fro equation (). θ X () Fro equation () one a, X () te te τ τ (9) te te Fro preceding cacuation, one know tat te etod of oution i ipe ut ony firt order accuracy. Now te oid region teperature ditriution i aued to e a poynoia, one get: θ c ex (3) In te igt of te oundary condition X, θ and X, θ, fro equation (3) one a: c (3) d e (3) Fro equation (4), one otain: te d e (33) X (3) utituting equation (8) into equation (33), one get: In ter of preceding auption, te iquid teperature profie i given y te foowing expreion: T T (4) Nondienionaizing equation (4), one otain: θ Fro equation (4a) one a: (4a) d e te (34) Fro equation (3) and (34), one a: ( te) d ( te) (35) te e ( te) (36) (5) utituting equation (3), (35) and (36) into equation (3), one otain: Fro equation (3) and (5), one get: dx (6) ( te) X te X θ (37) ( te) ( te) Fro equation (37) one a: 37

4 Internationa Journa on Arcitectura cience X ( te) ( te) ( te) X ( te) te X ( te) 3 (38) (39) reitance during initia period. It i own in Fig. 5 tat oidification rate varie wit tie. We know fro Fig. 5 tat oidification rate decreae a ice torage tie increae. Te greater te tefen nuer, te greater te oidification rate. utituting equation (38), (39) and (7) into equation (9), one get: ( 6te 6te ) (6 6te te ) (4) θ Integrating equation (4), one otain: te te τ 6 6te te (4) Fro equation (4) one a: te te 6 6te te τ (4) x/ Fig. 3: Teperature ditriution in oid region Wen te oidification proce i fina,,one get: 6 6te te te τ f (43) te te te ( te) 3. REULT AND DICUION Ice torage proce in fat and rectanguar capue i anayed y ti ode. Teperature ditriution in oid region for different tefen nuer i own in Fig. 3. We know fro Fig. 3 tat tefen nuer a itte infuence on teperature ditriution in oid region. A teperature ditriution concentrate on a traigt ine, and accord wit quai-tae teperature ditriution auption. It i own in Fig. 4 tat tefen nuer a infuence on oidification tickne. Wie tefen nuer increae, te oidification tickne ao increae. Te ower te wa teperature of ice torage capue, te greater te tefen nuer. Te wa teperature i retricted y econdary refrigerant teperature. Te econdary refrigerant teperature i generay -4 o C to -6 o C in te ice torage yte. If te econdary refrigerant teperature i uc ower, te cier efficiency wi e ower. It i own in Fig. 4 tat oidification tickne increae fat during initia ice torage period. Ti i due to tinner oidification ayer and aer tera τ Fig. 4: oidification tickne varie wit tie τ Fig. 5: oidification rate varie wit tie 38

5 Internationa Journa on Arcitectura cience 4. CONCLUION Te teperature in oid region i approxiatey inear ditriution. Te tefen nuer a itte infuence on it. Te oidification tickne increae a tefen nuer increae, and increae fat during initia ice torage period. Te oidification rate decreae a ice torage tie increae. Greater tefen nuer enefit oidification proce, ut it i retricted y econdary refrigerant teperature. tefen nuer i generay. in te ice torage yte. Ti ode can predict oidification proce in a fat and rectanguar capue ice torage yte, and provide uefu reut for deign and ue of fat and rectanguar capue. Journa of Energy Reearc, Vo. 6, pp (99).. J. Prua, G.M. Maxwe and K.J. Tier, A ateatica ode for a pae cange tera energy torage yte utiizing rectanguar container, AHRAE Tranaction, Vo. 97, No., pp (99). 3. J.P. Bedecarrat, F. tru, B. Facon and J.P. Dua, Pae cange tera energy torage uing perica capue: perforance of a tet pant, Internationa Journa of Refrigeration, Vo. 9, No. 3, pp (996). 4. G.Y. Fang and H. Li, tudy on dynaic carging perforance of ice torage of tacked rectanguar capue, Internationa Journa on Arcitectura cience, Vo., No. 4, pp (). 5. Z.. Cen, A ipe eat reitance etod for te oution to eat conduction undergoing oidification, Journa of Univerity of cience and Tecnoogy of Cina, Vo., No. 3, pp (99). NOMENCLATURE c pecific eat, Jkg - K - H oidification atent eat of ice, Jkg - af tickne of te capue, k tera conductivity, W - K - dienione oidification tickne of ice te tefan nuer T teperature, K t tie, X dienione ongitudina coordinate x ongitudina coordinate y oidification tickne of ice, Greek yo α tera diffuivity, - θ dienione teperature ρ denity, kg -3 τ dienione tie ucript wa of te capue iquid pae-cange ateria (water tate) freezing point of water oid pae-cange ateria (ice tate) ACKNOWLEGEMENT Ti tudy wa upported y Nanjing Univerity Taent Deveopent Foundation. REFERENCE..L. Cen, M.T. Ke and P.. ung, Anayi of coo torage for air conditioning, Internationa 39