Analysis of thermal stratified storage tank

Transcription

1 ARCHIVES OF ELECRICAL ENGINEERING VOL. 66(3), pp (07) DOI 0.55/aee Analysis of themal statified stoage tank ROBER SMUSZ, PAWEŁ KIELAN, DAMIAN MAZUR 3 Depatment of hemodynamics and Fluid Mechanics, Reso Univesity of echnology Resó, Poland obsmus@p.eso.pl he Faculty of Electical Engineeing, Mechatonic Depatment, Silesian Univesity of echnology 4400 Gliice, Poland pael.kielan@polsl.pl 3 he Faculty of Electical and Compute Engineeing, Reso Univesity of echnology Resó, Poland mau@p.edu.pl (Received: , evised: ) Abstact: he basic aim of the task is to compile a tempeatue statification system in an accumulation tank. he ange of the thesis concens the shape and dimensions of a statification system fo an accumulation tank. hemal statification is a pocess that compises the maintaining of tempeatue statification at diffeent levels of an accumulation tank hich educe to a minimum the pocess of tempeatue equaliation. It esults fom the fact that the themal statification in a tank significantly inceases the installation efficiency and impoves the pocess of enegy stoing. It is connected ith a themodynamic element quality, that is the highe the tempeatue, the highe the enegy, and, thus, the themosdynamic element quality. In this phenomenon, thanks to the same amount of accumulated themal enegy and aveage tempeatue, as in a fully mixed tank, the use has a highe tempeatue in the uppe pat of the tank at his disposal. It has significant impotance in the case hen thee is a lo-tempeatue heating medium that tansfes heat to the accumulation tank. Such a situation occus hen heat is absobed fom synthetic feons used in cooling and ai-conditioning systems. Key ods: tempeatue statification, themal enegy, heat ecovey, convection. Intoduction Poviding vetical statification of tempeatue in a tank is extemely impotant fom the pespective of enegy effectiveness of the pocess of utilising aste enegy. It is connected ith pope location of inlet and outlet pots, sies, shape, the method of distibuting hot ate ithin a tank, as ell as the placement of elements that potentially intefee ith tempeatue Donload Date 0/9/8 0:8 PM

2 63 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. statification, such as heat exchanges, booste heates etc. It equies pope configuation of the statification system elements so as to educe mixing of cold and hot ate in a tank. he application of the statification system enables diect tansfe of heated ate to uppe pats of a tank, ithout mixing ith cold ate, hich inceases the effectiveness of the heat ecovey system. Fig. pesents thee cases of the accumulation of the same value of themal enegy, but ith diffeent levels of statification. he fist case coesponds to the highest level of the tempeatue statification and is the most beneficial one. It is detemined by the fact that the shae of the one of the highest tempeatues in an accumulation tank is the geatest. With the incease of the mixing level, the one of themoclines expands until full mixing. Hot one hemocline Hot one hemocline Homogenous tempeatue in a tank. Full mixing Cold one Cold one Fig.. Diffeent levels/layes of tempeatue statification by the same amount of the accumulated themal enegy Poviding vetical statification of tempeatue in a tank is impotant and its quality is connected ith sies, the shape of a tank, the method of distibuting hot ate in a tank, as ell as the aangement of elements that may potentially intefee ith tempeatue statification. It equies pope configuation of the statification system elements so as to educe mixing of cold and hot ate in a tank. Heat, mass and momentum exchange ae the basic instumental pocesses that influence the pocesses taking place inside an accumulative tank. he main factos destabiliing themal statification ae: Foced convection inside a tank, caused by supplying cold ate and eception of am ate by the extenal hydaulic system. he steams of supplying and eceiving ate hile filling the tank induce mixing of ate in a tank. Fee convection that is a esult of the density diffeence beteen cold and am ones in an accumulative tank. Heat conductance beteen levels of ate ith diffeent tempeatues.. Vitual/eal model he subject of the analysis is an accumulation tank ithout a statification system (Fig. ) and ith the statification system (Fig. 3). Donload Date 0/9/8 0:8 PM

3 Vol. 66 (07) Analysis of themal statified stoage tank 633 Fig.. 3D visualiation of an accumulation tank hee ae thee heating coils inside the tank: the uppe one, the bottom one and the coil of aste heat ecovey system. he high-tempeatue heating element flos though the uppe coil, the bottom one is used by the themal sola collectos system []. he coil of the aste heat ecovey system is used fo eceiving heat fom a cooling/ai-conditioning element. Accoding to the assumption, ate (high-tempeatue heating element) fom the cental heating system is the heating element floing though the uppe coil. he heating element floing though the bottom coil is the liquid solution of popylene glycol. he oking element floing though the coil of the heat ecovey system is R43a Feon. he geometic sies of the coils ae pesented in Fig., and the tank in Fig.. Fig. 3. 3D visualiation of an accumulation tank ith a statification system Donload Date 0/9/8 0:8 PM

4 634 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. able. Geometic sies of coils Desciption Uppe/bottom coil Waste heat ecovey system coil Unit coil aveage diamete mm coil pitch p 4 3 mm coils numbe 0 0 intenal diamete 6.5 mm all thickness mm mateial coppe coppe able. Geometic shapes of a tank Desciption Value Unit extenal diamete of the tank jacket 480 mm all thickness.5 mm height of jacket/boile casing 000 mm height of boile end plate 03 mm type of boile end plate cage boile end plate DIN 803 mateial stainless steel 3. Physical model Fom the mathematical pespective, the phenomena occuing in fluid filling of an accumulation tank may be modelled by means of the equations of enegy, momentum and mass exchange [] as mass consevation equation continuity equation: () t ( ) = 0, movement equation: d = g p τ ij, () dt enegy equation: d c = ( k ) Φ, (3) dt hee: is the density, c is the specific heat, is the velocity, p is the pessue, is the tempeatue, g is the acceleation of gavity, τ ij is the stess tenso, k is the coefficient of conductivity, Φ is the dissipation function. Donload Date 0/9/8 0:8 PM

5 Vol. 66 (07) Analysis of themal statified stoage tank 635 In the analysed case the folloing assumptions ee assumed: the fluid that flos in a tank is incompessible, tubulent and unsteady, the fluid is Netonian, the popeties of the fluid ae constant and do not depend on tempeatue, except fo the density, the influence of a dissipation function on the enegy equation is significantly small, thee is no adiative heat exchange ithin the fluid (the fluid is tanspaent in infaed adiation), the configuation is D-axisymetical, inside the coils, convective bounday conditions take place (Neton's La of Cooling), thee is no heat exchange beteen the extenal boile casing/jacket and exteio, the initial tempeatue of the cold ate in the tank: 0 C, the ate tempeatue in the uppe coil: 75 C, the tempeatue of the ate solution of glycol in the bottom coil: 60 C, the feon tempeatue in the coil of heat ecovey system: 50 C, the coefficients of heat tansfe fo ate glycol solution and feon ee detemined fom coelation equations (pesented in a sepaate pat of this epot). Fo the peviously pesented assumptions the equations of mass, momentum and enegy exchange take the folloing fom: ( ) ( ), = 0 t (4) ( ) ( ) ( ) ( ), 3 F p t μ μ = (5) ( ) ( ) ( ) ( ) ( ), 3 3 F F p t μ μ μ μ = (6), t c k = (7) hee: is the adial coodinate, is the axial coodinate, =, is the siling velocity, F is the mass foces, c is the specific heat. On the basis of the assumed assumptions and the Reynolds hypothesis (hich enables one to ite don speed vecto constituencies and the pessue field as a sum of aveaged values Donload Date 0/9/8 0:8 PM

6 636 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. and fluctuations) and time aveage to model the tubulent flo, the RANS model (Reynoldsaveaged Navie-Stokes equations) as applied: t x i ( ) = 0, i (8) t x j p xi x j x j ij ' 3 i j xi x j ( ) ( ) j ' = μ i δ i, i i j xi (9) hee: i, j ae the indices defining diections (, ), δ ij is the Koneke delta, ' ' i j is the tenso of Reynolds tubulent stesses. In ode to solve Reynolds equations fo the pocess of fluid flo in a tank, a tubulence model k-ε as applied, due to the fact that it povides moe ealistic esults by the highe Reynolds numbes in the aeas significantly fa fom channel alls [4]. Moeove, the k-ε model descibes bette the flo though a cylindical hole ith eciculation, hich takes place in the case of using a statification system. Additionally, it is the tubulence model that is the most veified, and gives the most ealistic desciption of tubulences [3]. Fig. 4. Calculation model: ithout statification system (a); ith statification system (b) In the analysed case, a pocess of unsteady heating of ate that fills the tank by means of coils as discussed. No-stationay fee convection of extenal sufaces of coils takes place in the tank. 4. Results and conclusions In the analysed model, e concentated on defining the level-distibution of heat in a tank duing heat ecovey system coil opeation and its inteaction ith othe elements, as ell as Donload Date 0/9/8 0:8 PM

7 Vol. 66 (07) Analysis of themal statified stoage tank 637 defining pope geometical dimensions/sies of a statification system in ode to minimie the pocess of cold and hot ate mixing. In the fist vaiant, the calculations ee made fo the opeating coil of a aste heat ecovey system ithout a statification unit, Fig. 4a, in the second vaiant, the influence of diffeent geometic vaiants as analysed and descibed in Fig. 5. his geomety includes a statification unit fo tempeatue statification in an accumulation tank. he paametes that changed duing the simulation ee: diametes D, D, D 3, heights H 0, H, H, H 3, H 4, an angle of the conical shape of pat of statification device α. Diffeent geometical configuations ee analysed, and the final vesion of the statificato is pesented in Figs. 4b and 3. he values of geometic paametes ae pesented in able 3. he height of the H 4 gap in the calculation model as assumed to be equal to 0 mm. In the eal constuction pesented in Fig. 3, hoeve, the H 4 height as inceased to mm, so as to maintain an unchanged coss section aea fo the fluid floing out. In a simila ay, the height H 0 as inceased. able 3. Geometic shapes of a tank Symbol Value Unit D 80 mm D 60 mm D 3 40 mm H 0 70 mm H 4 mm H 084 mm H 3 50/00 mm H 4 0 mm α o Fig. 5. Statification system diagam Numeical simulations ee made by using the COMSOL Multiphysics commecial softae. In the model pesented in Fig. 4a, finite elements ee applied ( theenode tiangula elements, 350 fou-node squae elements as ell as and 60 bounday and apex elements. Fo the model pesented in Fig. 4b, finite elements ee applied (5 95 thee-node tiangula elements, fou-node squae elements as ell as and 888 bounday and apex elements) [5]. Fo the needs of the folloing epot, ate tempeatue distibution in the tank, as ell as speed distibutions fo selected time points, i.e. 5, 0, 0 minutes fom the moment of the initiating coil opeation of the heat ecovey system ee pesented. Fo the aim of quantitative evaluation of the statification pocess, non-dimensional tempeatue as defined: Donload Date 0/9/8 0:8 PM

8 638 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. Θ = min, (0) max hee : min is the minimal tempeatue of ate in the tank, max is the maximal tempeatue, hich is equal to the feon tempeatue, is the aveage integal tempeatue on a paticula height of the tank, R is the extenal adius of a tank. R min = R = () (, t) (, = idem, t idem) d. 0 Moeove, in ode to define the level of accumulated enegy at paticula time, the aveage tempeatue in the tank as defined in the fom: av () t (,, t) da, = () hee: A is the aea of the computational domain. Fig. 6 shos non-dimensional tempeatue in a elative height function fo time points: 5, 0, 0 minutes. he chaacteistic featue is that the tempeatue incease occus stating fom the tank's bottom, and ate tempeatue stabilies at the level of 60%, 50% and 40% of the tank's height. he maximal tempeatue values fo /H = amount to 0.05, 0.04, 0.068, espectively. he aveage values of the tempeatues calculated fom elation () amount to 0.49 C, 0.98 C,.85 C, espectively. hee occus the pocess of natual statification in the tank, hee intensive mixing of hot and cold ate takes place, highe tempeatue ate flos toad the uppe steam and cold ate stays in inetia, hich is visible in Figs One may notice stong ciculation of ate paticles in the uppe pat of the tank, hich contibutes to intensification of cold and hot ate mixing. Fig. 6. Non-dimensional tempeatue in elative height function ithout statification system Fig. 7 shos distibution of non-dimensional tempeatue as the function of elative height, fo a tank ith a statification system installed. Fo the fist 5 minutes of the heat exchange, thee as no incease in the ate tempeatue up to the level of 60% of the elative height of the tank, hich is a adical change in compaison to the case of a tank ithout statification. Donload Date 0/9/8 0:8 PM

9 Vol. 66 (07) Analysis of themal statified stoage tank 639 he highest tempeatue fo /H = amounted to 0.07 and it as only 6.8% highe than in the case of a system ithout statification. he aveage tempeatue in the tank afte 5 minutes as 0.75 C and it is only % highe, hich coesponds to the incease of the amount of accumulated themal enegy of 53%. Fo the time point of 0 minutes afte stating the heat ecovey system, the tempeatue at the highest point of the tank eached a value of 0.08 and it as 5.5% highe than in analogical time, but ithout statification. Moeove, the aveage tempeatue in the tank eached a value of.3 C, hich coesponds to the incease of the amount of the accumulated enegy by about 35%. Fig. 7. Non-dimensional tempeatue in a elative height function ith a statification system Afte 0 minutes the tempeatue at the highest point of the tank, the aveage tempeatue and the incease of the amount of the accumulated themal enegy in compaison to analogical time, but ithout statification equal to 0.88,.50 C and 35%, espectively. Fig. 8. empeatue distibution and speed afte 5 minutes Donload Date 0/9/8 0:8 PM

10 640 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. Fig. 9. empeatue distibution and speed afte 0 minutes Fig. 0. empeatue distibution and speed afte 0 minutes In the light of the esults pesented above, it should be stated that the application of the statification system has positive influence not only on tempeatue leveling in a tank, hich can be clealy seen in Figs. -3, but also on the amount of accumulated enegy. It is the Donload Date 0/9/8 0:8 PM

11 Vol. 66 (07) Analysis of themal statified stoage tank 64 esult of sepaating heated and cold ate steams by means of a all, and adial gaps, though hich the heated ate flos, educing the ate of mixing. Fig.. empeatue distibution and speed afte 5 minutes Fig.. empeatue distibution and speed afte 0 minutes Donload Date 0/9/8 0:8 PM

12 64 R. Smus, P. Kielan, D. Mau Ach. Elect. Eng. Fig. 3. empeatue distibution and speed afte 0 minutes Refeences [] Abadie M.O., de Camago M.M., Mendonca K.C., Blondeau P., Impoving the pediction of onal modeling fo foced convection aiflos in ooms, Building and Envionment, pp (0). [] Choi S.-K., Lee.-H., Kim Y-I., Hahn D., Numeical analysis of themal statification in the uppe plenum of the monju fast eacto, Nuclea Engineeing and echnology, vol. 45, iss., pp. 9-0 (03). [3] Zhang H., Niu F., Yu Y., Zhang S., Wang H., Gang Z., Modeling and expeimental studies on mixing and statification duing natual convection in containments, Annals of Nuclea Enegy, vol. 85, pp (05). [4] Gilani S., Montaei H., Blocken B., CFD simulation of tempeatue statification fo a building space: validation and sensitivity analysis, 3th Confeence of Intenational Building Pefomance Simulation Association, Chambéy, Fance, August 6-8 (03). [5] Li H., Villanueva W., Kudinov P., Appoach and Development of Effective Models fo Simulation of hemal Statification and Mixing Induced by Steam Injection into a Lage Pool of Wate, Science and echnology of Nuclea Installations (04). Donload Date 0/9/8 0:8 PM