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International Conference On Materials And Energy 2015, ICOME 15, 19-22 May 2015, Tetouan, Morocco, and the International Conference On Materials And Energy 2016, ICOME 16, 17-20 May 2016, La Rochelle, France The 15th International Symposium on District Heating and Cooling
Numerical Investigation Of transient Natural Convection In Assessing the feasibility of using heat demand-outdoor partitioned cavity filledthe with water temperature function for a long-term district heat demand forecast
Farah Zemani-Kaci*, Amina Sabeur-Bendehina* a b c c Andrić *, A. Maritime, Pinaa, Faculé P. Ferrão J. Fournier ., B. Lacarrière , O. Le d’Oran CorreMohamed LaboratoireI.des Sciences et Ingénierie de Génie,Mécanique, Université des Sciences et de la Technologie a,b,c
Boudiaf B.P. 1505 Oran El-M’naouar, 3-1000 Oran, Algérie IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract a
Transient natural convection in partitioned cavity filled with water is investigated numerically in this paper. The fluid flow and the heat transfer expressed in terms of continuity, linear momentum and energy equations were calculated by using the finite Abstract volume method. Prandtl number and Rayleigh number are fixed at 6.64 and 3,77x109, respectively, and the partition length of L/4. To approach heating arecalculations commonly were addressed in theinliterature as one the size mostand effective solutions for fluid decreasing theDistrict physical realitynetworks experience, performed a cavity with theofsame same priority of the with thethe greenhouseimposed gas emissions thewall building sector. These systems require high investments are returned through the heat temperature on the from cooled is equal to the average temperature Tm, also another which calculations with the temperature sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, imposed on the horizontal walls is equal to the average temperature Tm . prolonging investment return period. The achieved the results demonstrating the effects of the partition for the heat transfer and the thermal boundary layer are shown and The mainitscope of this is to assess the partition feasibility using the heat demandboth – outdoor temperature function discussed, illustrate thatpaper the existence of the onofthe hot wall influences heat transfer and fluid flow. for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 vary Published in both construction ©buildings 2017 The that Authors. by Elsevier period Ltd. and typology. Three weather scenarios (low, medium, high) and three district renovationunder scenarios were developed (shallow,committee intermediate, deep). 2015 To estimate the error, Peer-review responsibility of the scientific of ICOME and ICOME 2016.obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when onlyregime; weather change is considered, the margin of error could be acceptable Keywords: Natural Convection, unsteady partial partitions; Rayleigh Number; Nusselt Number; Partitions Length for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation considered). On the other function intercept increased forsince 7.8-12.7% per decade Naturalscenarios convection has fascinated a bighand, pact of interest from researchers its presence both(depending in nature on andthe coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and engineering applications. Natural convection flows in a differentially heated cavity are typically came upon in improve the accuracy of heat demand estimations. various industrial applications. A review of the literature demonstrates that there are a variety of studies on heat © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Keywords: Heat demand; Forecast; Climate change E-mail address:
[email protected] 1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016 10.1016/j.egypro.2017.11.218
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transfer in cavities without and with partition. Patterson et al [1] studied unsteady natural convection in a rectangular cavity with instantaneous cooling and heating of two opposite vertical sidewalls. They concluded that the flow had a strong dependence on the Prandtl number and cavity aspect ratio. Xu et al [2] observed using a shadowgraph technique the transition of the thermal boundary layer from start-up to a quasi-steady state in a side-heated cavity at the Raleigh number of 3.8 ×109. They concluded that the fin length significantly impacts on the transient thermal flow around the fin and heat transfer through the finned sidewall in the early stage of the transient flow development. Yucel et al [3] analysed numerically a laminar natural convection in enclosures with fins attached to an active wall indicating that with increasing number of fins the heat transfer first reaches a maximum and then approaches a constant, which is not affected by the number of fins. Nomenclature g h H l L Nu p Pr Ra T
gravitational acceleration (m/s2) convective heat transfer coefficient (W/m2 K) height of the enclosure (m) partition length (m) width of the enclosure (m) Nusselt number pressure (N/m2) Prandtl number Rayleigh number temperature (K) temperature of the hot surface (K) temperature of the cold surface (K) initial temperature (K) average temperature (k) Temperature variation, Th –Tc (k)
U V W x, y Greek symbols
Subscripts C H 0
velocity component in x direction (m/s) velocity component in y-direction (m/s) partition thickness Cartesian coordinates (m) dimensionless time thermal conductivity of fluid (W/m k) thermal diffusivity (m2/s) coefficient of volumetric expansion (1/K) dynamic viscosity (N s/m2) fluid density (kg/m3) Cold Hot Initial
Kolsi et al [4] in their study of the two-dimensional laminar natural convective transient flow characteristics in a differentially heated air-filled tall cavity revealed that as the Rayleigh number increases the flow becomes unstable. Effects on natural convective heat transfer through porous media in cavity due to top surface partial convection were showed by Pakdee et al [5], they found that the heat transfer coefficient, Rayleigh number affect considerably the characteristics of flow and heat transfer mechanisms and the flow pattern is found to have a local effect on the heat convection rate. Paul et al [6] treated the Effect of an adiabatic fin on natural convection heat transfer in a triangular enclosure by numerical simulations. Frederick et al [7] reported in their study that the heat transfer through the finned sidewall is reduced as the fin length increases due to the depression of the natural convection flows adjacent to the finned sidewall. the transition from a steady to an unsteady flow induced by an adiabatic fin on the side walls was also carried out by Therefore Xu et al [8] demonstrated that the fin may induce the transition to an unsteady flow and the critical Rayleigh number for the occurrence of the transition is between 3.72 x106 and 3.73x 106. The purpose of this study is to analysis the unsteady natural convection in a differentially heated cavity with a partition on the hot wall with different properties. The differentially heated cavity used is the same of Xu et al [9]. The thermal and flow behavior and heat transfer characteristics have been studied for a partition length of L/4. The working fluid media is water with Prandtl number of 6.64 and Rayleigh number of 3.77 x 109 . To approach the physical reality experience, calculations were performed in a cavity with the same size and same priority of the fluid with the temperature imposed on the cooled wall is equal to the average temperature Tm, also another calculations with the temperature imposed in the horizontal walls is equal to the average temperature Tm . Moreover results were obtained while copper walls were added on the sidewall
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2. Analysis and modeling 2.1 Problem position and mathematical formulation The aspect ratio of the domain of 0.24 is considered. One partition of L/4 is placed in the mid height of the hot wall with Th on the right wall and Tc in the left then the average temperature Tm = computational domain and boundary conditions are shown in Fig. 1.
Th + Tc and ∆T = 16K , the 2
(b)
(a)
(c) Fig.1 schematic diagrams of the physical domain
The governing equations (Navier Stokes and energy equations with the Boussinesq approximation) of the transient natural convection flows are written as (1) ∂u ∂v ∂x
+
∂y
=0
∂u ∂u ∂u ∂P Pr ∂ 2u ∂ 2u +u +v =− + + 1/2 ∂t ∂x ∂y ∂x Ra ∂x 2 ∂y 2
(2)
∂v ∂v ∂v ∂P Pr ∂ 2v ∂ 2v +u +v =− + + + PrT 1/2 ∂t ∂x ∂y ∂y Ra ∂x 2 ∂y 2
(3)
∂T ∂T ∂T 1 +u +v = 1/2 ∂t ∂x ∂y Ra
Where
∂ 2T ∂ 2T 2 + 2 ∂y ∂x
(4)
(5)
g β L3Ref ∆T
and Pr = µ µα ρ The average Nusselt number is defined as follows: L h .y h .L Nu = − dy = 0 k k
Ra =
∫
(6)
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The governing equations are implicitly solved using a finite volume PISO algorithm. All second derivatives and linear first derivatives are approximated by a second-order centred-differenced scheme. The time integration is by a second-order backward difference method. The discretized equations are iterated with under relaxation factors. A fine non-uniform grids concentrated near the partition is constructed and grid size of
563 × 199
3. Results and discussion 3.1. Horizontal walls of temperature Tm The temperature imposed in the horizontal walls is equal to the average temperature Tm .Fig.1.a 302 301 300
T(k)
299
Temperature of horizontal walls Tm Adiabatic horizontal walls
298 297 296 295 0
2000
4000
6000
8000
10000
t(s)
Fig. 2. Temperature time series calculated by using different temperatures of horizontal walls for the case of Ra= 3.77*109, and partition length of L/4, at the point (0.498,0.09) plotted.
The figure 2 shows the temperature time series during the transient regime. First a creation of a perturbation resulting from the instability of the thermal layer was noticed. This perturbation is then convected away from the wall; the boundary layer becomes stationary until the arrival of a flow coming from the cold wall. The instability of the boundary layer for the average temperature imposed on the horizontal walls gives oscillations more than the adiabatic walls. For t> 10000S the thermal boundary layer reached the quasi stationary stage with a low increase in temperature.
100s
500s
1000s
2500s
4500s
6500s
7500s
10000s
12000s
Fig. 3. Isotherms contours at different time for Ra=3.77*109
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The isotherms contours of Fig. 3 show a stratification of the fluid throughout the cavity; it can be seen that at t = 100s the phenomenon of separation had been started, the flow may very flat near the partition The shedding flow separating from the partition induces two peaks wave, and the two peaks eventually merge into a single one while they propagate downstream .The phenomenon of average temperature imposed in the horizontal walls induces more instability in the flow. 3.2. Symmetry of the flow ∆T = 8K Calculations were performed on the same size cavity with the same properties of the fluid. The temperature imposed on the cooled wall is equal to the mean temperature Tm and Fig.1.b. (a) t=500s
(b) t=1000s
(a)
(b)
Fig. 4 comparison of isotherms, for partition length L/4 and Ra=3.77*109 (a)
∆T = 16K
and (b)
∆T = 8K
It is noted that the two flows (Fig.4) in the vicinity of the partitioned hot wall are similar as the cold side has no influence on the hot side (t≤1000s) 3.3. Adding copper walls Copper walls of 0,00113m of thickness and 400W/mK of conductivity were added, Fig.1.c
Fig. 5. isotherms comparison at t=150s, (--- reference case)
Calculations showed that the addition of the vertical walls of copper has no influence on the development of flow and this is due to the thinness of the walls and the high conductivity of copper (Fig.5) Conclusion Transient natural convection in partitioned cavity filled with water is investigated numerically in this paper. Results reveal three stages: an initial stage, a transitional stage and a quasi steady stage. The effect of partitions on the sidewall has been observed by monitoring the transient natural convection and heat transfer through a differentially heated cavity at Rayleigh number of 3.77*109. It was also seen that the two flows in the vicinity of the partitioned hot wall are similar in setting the temperature at the cold wall equal to the average temperature, as the cold side has no influence on the hot side, also it was found that the addition of the vertical walls of copper had no influence on the development of the flow due to low wall thickness and high conductivity copper. As well when imposing the temperature at the horizontal walls equal to the average temperature induces perturbation in the flow.
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Acknowledgements The authors wish to thank the scientific committee of ICOME 16 for the time that will be provided to give us the opportunity to publish our work. References [1] Patterson, J.C., Armfield, S.W. Transient features of natural convection in a cavity. J. Fluid Mech; 1990. 219, 469-497. [2] Xu.F, Patterson.J.C, Lei.C. Shadowgraph observations of the transition of the thermal boundary layer in a side-heated cavity. Experiments in Fluids, 38;2005. 770–779 DOI 10.1007/s00348-005-0960-1 [3] Yucel. N, Turkoglu.H. Numerical analysis of laminar natural convection in enclosures with fins attached to an active wall. Heat and Mass Transfer 33;1998.307-314 [4] Kolsi.L, Ben Hamida.M.B, Hassen.W, Kadhim Hussein.A, Borjini.M.N, S. Sivasankaran, Saha.S.C, Awad.M.M, Fathinia.F, Ben Aissia.H. Experimental and Numerical Investigations of Transient Natural Convection in Differentially Heated Air-Filled Tall Cavity.30-43;2015doi: 10.11648j.ajme. 0102.12 [5] Pakdee. W, Rattanadecho.P. Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection. Applied Thermal Engineering 26;2006. 2316–2326 . [6] Paul.S.C, Saha.S.C, Gu .Y. T, Effect of an adiabatic fin on natural convection heat transfer in a triangular enclosure, 1(4): 78-83, doi: 0.11648;2013.0104.16 [7] Frederick. R.L. Natural convection in an inclined square enclosure with a partition attached to its cold wall. Int. J. Heat Mass Transfer 32;1989. 87e94. [8] Xu .F, Patterson. J.C ,. Lei. C. natural convection adjacent to a sidewall with three fins in a differentially heated cavity. ANZIAM J.48,CTAC; 2007. PP C806-C819 [9] Xu. F,.Saha S. V. Transition to an unsteady flow induced by a fin on the sidewall of a diiferentially heated air filled square cavity and heat transfer. International Journal of Heat and mass Transfer 71; 2014. 236-244
