Modelling heat transfer and fluid flow inside a pressure cooker

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1 17 th Euroean Symosium on Comuter Aided Process Engineering ESCAPE17 V. Plesu and P.S. Agachi (Editors) 2007 Elsevier B.V. All rights reserved. 1 Modelling heat transfer and fluid flow inside a ressure cooker Denis Flick, Richard Rocca, Christohe Doursat, Jean Vasseur UMR Génie Industriel Alimentaire Cemagref, ENSIA, INRA, INAPG INAPG 16 rue Claude Bernard Paris Cedex 05, flick@inag.fr ENSIA 1 av. des Olymiades Massy Cedex, vasseur@ensia.fr Abstract Heat transfer and fluid flow were simulated with a 3-dimensionnal CFD aroach inside a ressure cooker in order to redict gas and roduct temerature evolution and its heterogeneity. Different difficulties aear because of geometric comlexity and of many couled henomena: evaoration and condensation of vaour in resence of non-condensable gas, natural convection in an unstable configuration, ressure increase with time, density variation with comosition, temerature and ressure. The general trends exerimentally observed could be reroduced by simulation and some henomena which are very difficult to characterise exerimentally (fluid flow) could be better understood. The further aim of the work is to use numerical simulation for the choice of oerating conditions and equiment design. Keywords : ressure cooker, CFD, heat transfer, fluid flow, condensation 1. Introduction Pressure cooker allows raid and energy saving cooking of various food roducts. Short time - high temerature heat treatment combined with absence of oxygen (exceted at the beginning of treatment) can also lead to a better reservation of some nutriments. But both thermal henomena and bio-chemical transformation of food during ressure cooking are very oorly understood.

2 2 D. Flick et al This leads to an emirical choice of oerating conditions (required heating ower at different stages of cooking, etc) and equiment design (vessel, basket, lid geometry, etc). Indeed, literature which refers to ressure cookers concerns mainly its utilisation to reach temeratures higher than 100 C in resence of water in order to analyse the effect of temerature on various food roerties (texture, nutriments, colour, etc) [1]. Some studies are related to energy consumtion [2] and a lumed thermal model was roosed for a solar ressure cooker [3]. Some CFD studies were erformed on cooking rocesses [4] including natural convection but few studies deal with evaoration/condensation in resence of non condensable gas in closed cavities [5]. The aim of this study was to simulate with a CFD aroach the thermal henomena inside a ressure cooker in order to redict the temerature evolution in the food roduct. 2. Modelling aroach Couled unsteady equations for fluid flow, heat transfer and mass transfer (air and water vaour) were solved using the finite volume method (Fluent software 6.2). The 3-dimensional geometry comrised an almost cylindrical vessel equied with a ressure valve and a basket containing 7 sherical food roducts. This geometry was meshed using tetrahedral and hexahedral cells (figure 1) uer ring of the basket (not erforated) Lateral wall of the basket (erforated) Figure 1 : geometry and mesh According the Rayleigh number value (based on cooker height and tyical temerature difference of 60K) Ra , gas flow is assumed as laminar in the vessel. The erforated basket is reresented by a ressure dro roortional to the squared suerficial velocity according to the relation roosed by Van Winkle et al [6], the holes area being 50% of the total area. It has to be mentioned that only the bottom and the lateral cylindrical walls of the basket are erforated, the uer ring is a non erforated wall.

3 Modelling heat transfer and fluid flow inside a ressure cooker 3 Water evaorates from the bottom and condensates on lateral wall, cover and food roduct surface (liquid water flow is not reresented). There is no tool in the software to reresent directly condensation or evaoration. But it includes a surface reaction tool which can be used to take into account the couled mass and energy balances of condensation and evaoration. This aroach also takes into account the resence of air which limits condensation. Two reactions were defined with secific reaction rates : R 1 and R 2 (mol.m -2.s -1 ) H 2 0 va H 2 0 liq R 1 = k T c va (eq.1) where T is the temerature and c va is the local molar concentration of water vaour (near the condensation surface) sat (T) sat (T0 ) ΔH 1 1 H 2 0 liq H 2 0 va R 2 = k k ex (eq.2) R R R T T0 where T is the surface temerature, ΔH is the molar latent heat of vaorisation and T 0 is a reference temerature. Thus, at equilibrium (R 1 = R 2 ), the dew oint equation would be satisfied: sat (Tdew ) cva = RT (eq.3) The net molar condensation flux can be exressed using the dew oint temerature (T dew ) and the surface temerature T: sat (T) k kt c va = ( sat (Tdew ) sat (T)) (eq.4) RT R This condensation flux corresonds to a heat flux of : k k dsat ( sat (Tdew ) sat (T)) ΔH ΔH(Tdew T) = h(tdew T) (eq.5) R R dt with h = k R d dt sat T0 k ΔH ΔH = 2 R T sat T0 (T 0 ) In the resent study T 0 =373K and h=500 W.m -2.K -1. This corresonds to the thermal resistance of a condensate film of about 1mm. The air and water vaour mixture was considered as a erfect gas, mixing and diffusion was taken into account. Heat transfer included convection and conduction in the gas, conduction inside the food roducts and latent heat of evaoration or condensation. The thermal roerties of otatoes [7] were chosen for the food roduct. A conducting shell model was used for the cooker walls made in stainless steal. An external heat transfer coefficient of 10 W.m -2.K -1 was assumed (value obtained from exerimental heat loss estimation). At the beginning of cooking the valve is closed and the ressure increases u to 1.5 bar because of gas temerature rise and imbalance between evaoration and

4 4 D. Flick et al condensation. The Mach number is very low and the Navier-Stokes equations can still be used with a slowly variable and heterogeneous density. At this stage, fluid flow is due to natural convection (density deending on local temerature and comosition) and to evaoration/condensation (vaour flowing from or toward the fluid hase boundaries). Further, the ressure is ket constant at 1.5 bar at the valve outlet. At this stage, fluid flow in the vessel is also due to the gas outflow through the valve. 3. Results and discussion The numerical results were comared with temerature measurements obtained during cooking of almost sherical otatoes. No velocity measurements were erformed. The heat flux imosed at the bottom face was 1000 W during all the cooking time. Figure 2 comares exerimental and numerical results for the ressure, the gas temerature at the center of the cooker and the core temerature of the central otato. The general trends are similar. But there is a time lag between exerimental and numerical results because of the thermal inertia of the hotlate which is not taken into account in the simulation. Other differences aear also which can be due to the aroximation of the geometry and of some arameters. For examle, the external heat transfer coefficient and the thermal resistance of condensate film should be more recisely estimated and should be different for the cover and the lateral wall. At this stage, the CFD model is not aroriate for quantitative rediction. But it can give qualitative information about fluid flow, air stagnation and heterogeneity of heat transfer. ressure (bar) ressure (bar) 1,5 1,4 1,3 1,2 1,1 numerical T gas time (s) 393 1, ,4 1,3 1,2 1,1 exerimental T gas time (s) Figure 2 : ressure, gas temerature, core food roduct temerature temerature (K) temerature (K)

5 Modelling heat transfer and fluid flow inside a ressure cooker 5 Just before valve oening (t=145s), it can be observed from the simulation (figure 3) that there is a hot and wet zone near the bottom where water is heated u and evaorates. The sherical roducts and the uer ring of the basket act as a searation between the bottom and to regions. The to zone is quite homogeneous; temerature and humidity remaining close to the initial values at this moment. In the bottom region, convection is due notably to evaoration at the water surface and condensation on the lateral wall (figure 4). In the to region, there is also an intensive gas circulation due to natural convection. But mixing is low between the two regions because of the searation effect of the food roducts and uer ring of the basket. This tye of basket was relaced by some manufactures by totally erforated baskets and the resent study confirms the interest of such new tyes of basket. temerature min 293 K, max 288 K vaour mass fraction min 1.4%, max 53.1% Figure 3 : Temerature and vaour mass fraction in the symmetry lane (vertical lane including the valve) just before valve oening (t=145s). Figure 4 : Velocity in the symmetry lane (t=145 s) (v max =0.38 m/s) Condensation is much more imortant at the bottom face of the food roducts than at the uer face (figure 5). This can lead to heterogeneity of cooking because starch gelatinization, texture modification, etc are highly thermal deendent.

6 6 D. Flick et al to view bottom view Figure 5 : Condensation mass flow rate (maximal value : 2.5 g.s -1.m -2 ) 4. Conclusions/future work In site of the modelling difficulties (condensation of vaour in resence of air, ressure increases, etc) the general trends exerimentally observed could be reroduced with 3D CFD. Some henomena which are difficult to characterise exerimentally were observed in the simulation, as for examle a searation effect related to an old basket design. The further aim is to use numerical simulation for the choice of oerating conditions and equiment design (vessel, basket, lid geometry). The aroach used for condensation in resence of non condensable gas could also be alied to analyse satial heterogeneity for other rocesses like autoclave sterilisation or industrial cooking in vaour oven. Acknowledgements This study was carried out in collaboration with grou SEB (Selongey France) References 1. P. Leelayuthsoontorn and A Thiayarat, Textural and morhological changes of jasmine rice under various elevated cooking conditions, Food chemistry. 96 (2006) T. Das, R Subramanian, A. Chakkaravarthi, V.Singh, S.Z.Ali and P.K.Bordoloi, Energy conservation in domestic rice cooking, J of Food Engineering, 75 (2006) I.A.Olwi and A.M. Khalifa, Comuter simulation of the solar ressure cooker, Solar energy, 40 (1988) L.Rabiey, D.Flick, A.Duquenoy. 3D simulations of heat transfer and liquid flow during sterilisation of large articles in a cylindrical vertical can. J. of Food Eng. (in ress) 5. V.Daru, M.C.Duluc, O le Maître, D.Juric and P Le Quéré, Modeling a numerical simulation of liquid-vaor hase change in an enclosed cavity. C.R.Mecanique 334 (2006) R.H.Perry, D.Green, Perry s chemical engineering handbook. McGraw Hill (1984) 7. S.Rahman, Food roerties handbook, CRC Press (1995)