- Email: [email protected]
Modeling of transient natural convection heat transfer in electric ovens
Applied Thermal Engineering 26 (2006) 2448–2456 www.elsevier.com/locate/apthermeng
Modeling of transient natural convection heat transfer in electric ovens Hitesh Mistry a
a,*
, Ganapathi-subbu a, Subhrajit Dey a, Peeush Bishnoi a, Jose Luis Castillo
b
General Electric ACFD Lab, GE Global Research Centre, 122, EPIP, Whitefield Road, Bangalore 560 066, Karnataka, India b Mabe Mexico S de RL de CV, Acceso B #406, Parque Industrial Jurica, Queretaro 76120, Qro., Mexico Received 22 December 2005; accepted 10 February 2006
Abstract Prediction of transient natural convection heat transfer in vented enclosures has multiple applications such as understanding of cooking environment in ovens and heat sink performance in electronic packaging industry. The thermal field within an oven has significant impact on quality of cooked food and reliable predictions are important for robust design and performance evaluation of an oven. The CFD modeling of electric oven involves three-dimensional, unsteady, natural convective flow-thermal field coupled with radiative heat transfer. However, numerical solution of natural convection in enclosures with openings at top and bottom (ovens) can often lead to non-physical solutions such as reverse flow at the top vent, partly a function of initialization and sometimes dependent on boundary conditions. In this paper, development of a physics based robust CFD methodology is discussed. This model has been developed with rigorous experimental support and transient validation of this model with experiments show less than 3% discrepancy for a bake cycle. There is greater challenge in simulating a broil cycle, where the fluid inside the cavity is stably stratified and is also highlighted. A comparative analyses of bake and broil cycle thermal fields inside the oven are also presented. 2006 Elsevier Ltd. All rights reserved. Keywords: CFD; Natural convection; Radiation; Electric oven; Cooking; Thermal load
1. Introduction Domestic ovens, both gas and electric ranges are common appliances used for cooking. The thermal field within an oven has significant impact on quality of cooked food and reliable predictions are important for robust design and performance evaluation of an oven. The present study covers detailed approach of constructing numerical model of electric oven. While extensive experimental work goes into helping build a robust CFD model, the final outcome is a flexible, predictive tool based on CFD methodologies. Food is cooked in oven by radiative heating, convective heating or a combination of both. Cooking cycle with heat generated only from top heater is known as broil cycle and cooking mainly through the bottom heater is known as bake cycle. The typical bake cycles involve top heater cycling at less than half load to enhance heat transfer. *
Corresponding author. Tel.: +91 80 250 32658. E-mail address: [email protected] (H. Mistry).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.02.007
Broiling utilizes advantage of the radiation from the heater to rapidly heat the top of the food, which promotes browning and suppresses the natural convection current since the hot air is blocked by the ceiling of the oven. In bake cycle, heating primarily takes place because of buoyancy driven hot air flow. Nature of heat transfer mechanism plays a critical role in quality of food. For example, natural convection fluid flow is important in maintaining the quality of delicate food products that require a dry atmosphere (e.g. cream puffs, pastry shells). The CFD modeling of electric oven involves threedimensional, unsteady, natural convective flow field coupled with radiative heat transfer. A series of papers published by Abraham and Sparrow [1–6] consider heat transfer in vented enclosures involving radiation when bottom heater is operating. These set of papers involving experimental and numerical studies discuss the importance of modeling buoyancy forces directly rather than using pseudo-density difference in the model, sensitivity studies of thermal load and measurement probe with respect to
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
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Nomenclature 3 Rayleigh number bgDTL am temperature (K) wattage (W) heat transfer coefficient (W m2 K1) thermal conductivity (W m1 K1) specific heat (J kg1 K1) thermocouple tip diameter (m) density (kg m3) Stefan Boltzmann constant (W m2 K4) emissivity velocity of air (m s1) pressure (Pa) length of thermocouple (m) centre oven temperature
their radiative properties. Though heat transfer in enclosures with bottom heating has been studied [1–7], researchers have not attempted thermal field prediction for broil cycle. In this paper, CFD modeling of an electric oven cavity to simulate bake and broil cycles has been discussed; stably stratified flow being a characteristic of the latter. 2. Experimental details A typical freestanding electric range was used for experiments as shown in Fig. 1 with the Cartesian co-ordinate system. This range consists of an inner cavity with insulated walls and hinged front door, and two heating elements—a top-heating element (broil) and a bottomheating element (bake). The cross section of the heater consists of Ni–Cr wire placed within MgO filled Incoloy sheath. The cavity has a vent located on the rear side of the top wall of the cavity for continuous removal of hot and humid air. There is a deliberate leakage path known as gasket opening at the front door, which entrains fresh air. Heating of the cavity (oven set point) is controlled by a thermostat, which keeps the heating elements ON/OFF according to the pre-determined set point. Fig. 2 shows operating condition during broil cycle, where the oven set
Fig. 1. Electric oven.
TC a m g b L
thermocouple thermal diffusivity (m2/s) kinematic viscosity (m2/s) gravitational acceleration (m/s2) coefficient of thermal expansion (1/K) height of cavity (m)
Subscripts H heater c thermocouple w oven wall g gas or air inside the oven s suction
Broil Cycle : COT 540
Temperature (K)
Ra T W h k Cp d q r e v P x COT
Oven Set Point Temperature
490 440 390 340 290 0:00:00
0:07:12
0:14:24
0:21:36
0:28:48
0:36:00
0:43:12
Time (hr:min:s) Fig. 2. A typical broil cycle.
point is reached in 15 min after which the heater element starts cycling. The initial transient before heater starts cycling is known as preheating. The front doors have a double glazed window, which helps the operator to monitor the cooking without opening the door. Tin oxide coating is provided on inner glass walls to ensure low transmissivity for reduced radiation losses. Convection fans are normally provided at the rear wall of the cavity to enable faster cooking. A series of steady state experiments were carried out to understand the contribution of various heat loss mechanisms in the oven such as loss through the walls, heat loss through vent opening and glass viewing window of front door. To facilitate steady state operation, the control circuit for heating elements was bypassed and the heater was maintained at the required wattage. Heater power rating was set according to center oven temperature (COT). Thermal field inside the cavity was tracked through thermocouples distributed inside the cavity. For oven surface temperature measurements and cavity air temperature measurements, J (Iron-Constantan) type thermocouples (0.0100 ) with SS sheathing were used. These thermocouples were calibrated within 1% of a reference thermometer traceable to ITS-90 in liquid bath. For heater temperature
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measurements, K (chromul–alumel) type thermocouples were used. To facilitate easy location of thermocouples and ensure repeatability, thermocouples were mounted at eight corners of an open cuboid and at the center. It is well known that thermocouple measurements are prone to offset due to heat transfer in the exposed ambient. This is due to the fact that temperature of the junction, which is the equilibrium temperature, is not the temperature of the medium. Energy balance performed on a thermocouple junction at temperature Tc exposed to a gas at temperature Tg yields the following relationship: Tg Tc ¼
qc Cpc d oT c k c d o2 T c þ þ reðT 4H; w T 4c Þ. 4h 4h ox2c ot
ð1Þ
It can be seen that the difference between the gas temperature and the thermocouple reading is due to transient response of the thermocouple (first term on the right side of equation), conduction heat transfer along the thermocouple (second term), radiation heat transfer with surroundings (third term). A thermocouple located at center of the oven to measure air temperature participates in radiation with heater elements and the wall. These errors were minimized by providing radiation shields and avoiding direct viewing of thermocouple tip with heater surfaces. Highly polished aluminum foils were used as radiation shields. Thermocouple wires of 10–15 D length were kept inside the oven to minimize conduction error. Maximum uncertainty in temperature measurements was arrived as 9%, inclusive of all error/uncertainty components. This includes less than 2% variation observed during repeatability trials; for thermocouples distributed inside the oven cavity, a variation of 2% of temperature data was observed when thermocouple location was varied within 5 cm in space. The remaining 5% attributed to thermocouple participating in heat transfer. As indicated by the transient term of Eq. (1), it will require small diameter bare wire thermocouples to exactly track the transient slope. In order to overcome the sluggish response of thermocouples and to minimize radiation losses, thermocouples were buried inside an aluminum rod and heating of the aluminum rod was tracked. This also simulates a thermal load used in oven experiments. A rod of 1 in. · 1 in. · 20 in. size was used for these trials. 3. Numerical modeling Due to complex geometry, the internal volume of the oven cavity was meshed with tetrahedral element. The grid size of the oven cavity was largely decided by the mesh resolution near the heaters, gasket opening and the vent outlet. The surface mesh was generated using GAMBIT and volume mesh in TGrid. The difference in steady state thermal field predicted by grid size with 0.97 million cells and 1.5 million cells was of the order of 0.5%, much within the required accuracy of prediction for oven thermal performance. So, the grid with 0.97 million cells was chosen for all future numerical studies, steady state and transient,
presented in this paper. The commercially available solver FLUENT 6.1 was used for current studies. 3.1. Material properties The thermal properties of air were evaluated considering water vapor content in it. An ideal incompressible formulation for density has been used to capture natural convection heat transfer. The multi layered oven sidewalls, heater and door were modeled using effective conductive resistance through a lumped thickness. Literature review [2,3] revealed that radiation heat transfer inside the oven cavity is the most dominant mode of heat transfer. Higher dependence on radiative mode of heat transfer made it essential to pay due attention to radiative model and the radiative properties. Sensitivity studies of heater and oven sidewall emissivity ascertained unknown emissivity values for these surfaces and to understand their importance in heat transfer participation. With 30% reduction in heater emissivity, temperature at oven wall reduced by 10% but for reduction of 20% in wall emissivity, temperature at oven wall reduced by 0.2%. This observation indicates that thermal field inside the oven is more dependent on heater emissivity compared to sidewall emissivity. Finally, the emissivity values for heater and sidewall were chosen as 0.85 and 0.9, respectively, which were subsequently substantiated by IR camera measurements. 3.2. Boundary conditions The heaters have been modeled as volumetric heat source to capture the effect of heat capacity of the heater materials during the transient simulations. The outside surfaces of the oven wall and the glass door were modeled as a combination of convective and radiative heat transfer with the ambient. The gasket opening and vent outlet were specified as pressure boundary conditions. The inlet air temperature at gasket opening was considered to be at ambient temperature 296 K. 3.3. Radiation model For radiation models, discrete ordinate (DO) and surface-to-surface (S2S) were short-listed based on the applicability and accuracy required for the current study. The DO model takes into account media participation in addition to the surface-to-surface radiation effects. However, the S2S radiation model considers the latter only. The difference of temperature prediction at the center of the oven and oven walls by the DO and S2S models for a simplified but similar geometry were of the order of 0.2%. While, the comparison of the thermal field was similar, the computational time for S2S model was almost half of the DO model for an identical grid. Moreover, air in the current operating temperature range can be considered as non-participating media in radiation [8]. Considering all of the above, S2S seemed a suitable choice for the electric oven modeling.
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3.4. Laminar vs turbulent In a natural convective field, the order of Rayleigh number gives an indication of whether the flow field is laminar or turbulent. Calculations of Rayleigh number based on vertical height of cavity and temperature difference across the cavity show Ra O (108). Transient nature of thermal field indicates a variable Rayleigh number. Under such conditions, it is difficult to numerically predict the flow field, particularly during transition regime, due to nonavailability of a suitable modeling approach. Hence, it was decided to compare thermal fields in both laminar and turbulent regimes. A comparison of thermal field for assumption of completely laminar flow and completely turbulent flow at thermocouple locations inside the cavity showed a maximum of 3% difference in the temperature data. It has been observed that the thermal field is similar for both cases and henceforth a laminar approach should be able to predict the thermal performance with reasonable accuracy. It is important to note that the computational time involved in solving a laminar flow field is less compared to the turbulent approach. Abraham and Sparrow [6] have also made similar observations while studying steady state thermal-flow field of an electric oven when bottom heater is ON and thus carried out their numerical solution with laminar assumption. 4. Results and discussion Steady state solution takes less computational time than the full transient oven cycle. It is practical to do validation and accounts of heat losses initially on steady state cases. Moreover, steady state solution would give an opportunity to check on ‘‘effective’’ thermal conductivities of the composite wall material before going on to transient calculations, which involve effect of specific heat as well. 4.1. Steady state validation—vent suction pressure Fig. 3 shows velocity vectors on the oven mid-plane (Y–Z) with atmospheric pressure boundary condition set at the vent outlet. It indicates reversed flow at vent outlet and front door gasket opening leading to numerical oscillations. This reversed flow is contradictory to experimental observations. The reason for having reversed flow at vent outlet is due to the ‘‘ambient’’ boundary condition that was employed at the vent outlet and front door gasket opening in the numerical model. In reality, there is a local low pressure region that will be created at the vent outlet that causes the flow to move out of the vent from the top of the oven. This low pressure region is a combined effect of hydrostatic pressure difference due to density difference along the cavity height and the pressure drop when air enters the oven vent (from the cavity) due to the sudden change
Fig. 3. Velocity vectors at oven mid-plane (Y–Z) with atmospheric pressure BC at vent outlet.
in area. This pressure drop will be the proportional to 1 qv2 , the density being mean density of air at temperature 2 corresponding to air temperature at vent entry. Temperature of air at vent entry is guided by heater temperature and position of the heater. However, it is difficult to calculate pressure drop in oven vent without knowing air temperature at the oven vent entry apriori. Moreover, the natural convection velocity magnitude also depends upon the heater rating and the heating cycle being used. The boundary condition set at vent outlet should take into account this pressure drop. This was simulated by applying a ‘‘numerical’’ suction pressure at the vent outlet. A detailed exercise was carried out to arrive at the right magnitude of this suction pressure through a series of steady state experiments combined with numerical analysis to establish the suction pressure dependence on cavity temperature and the cycle.
Fig. 4. Velocity vectors at oven mid-plane (Y–Z) with suction pressure (2 Pa) at vent outlet.
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Table 1 Vent sensitivity studies for broil cycle Suction pressure: 0.5 Pa
Suction pressure: 1 Pa
Suction pressure: 2 Pa
Heater Inside left wall Outside left wall Inside glass wall Outside glass wall
% Discrepancy
% Discrepancy
% Discrepancy
+14.7 +21.6 +4.9 +26.4 +6.8
+11.4 +10.5 +3.3 +13.9 +3.9
+8.4 +0.5 +1.9 +1.2 +0.3
Fig. 4 shows velocity vectors on the oven mid-plane (Y–Z) with suction pressure of 2 Pa set at vent outlet. It shows air movement in the expected direction. This flow field matches qualitatively with experimental observation. The procedure used to identify the correct suction pressure value for given operating conditions would now be described. Thermal field data inside the cavity and cavity walls (total 12 points) obtained through experiments at different heater wattages for both bake and broil cycles were compared with the numerical model results at the same conditions. Since suction pressure has to be applied in the numerical model to simulate physical flow conditions, this suction pressure value was varied to keep the discrepancy between measured temperature and the numerical prediction within 10%. The suction pressure that provides thermal field closely matching with experimental data has been chosen as the suction pressure for that operating condition. Though it is possible to obtain an accurate value of suction pressure by keeping the discrepancy within 5%, from modeling point of view, 10% accuracy was deemed reasonable. Table 1 shows an example of this comparison matrix for broil cycle operating at 1200 W steady state that fixes the suction pressure as 2 Pa. The synergy between experimental and numerical studies at different wattages helped to build a transfer function between the heater temperature and vent suction pressure. These functions (Fig. 5) are as follows:
Transfer function for broil cycle P s ¼ ð4:1e06 T 2H Þ þ ð0:0011T H Þ þ 0:26. 1 Numerical: COT/Tmax Experimental: COT/Tmax
0.975
Numerical: Tload/Tmax 0.95
Experimental: Tload/ Tmax
0.925
T/ T maximum
Location of temperature measurement
0.9 0.875 0.85 0.825 0.8 0.775 0.75 0
200
400
600
800
1000
Time (s)
a 1
Numerical: Tload/Tmax Experimental: Tload/Tmax Numerical: COT/ Tmax Experimental: COT/Tmax
0.95
0.9
0.00 Broil Bake
T/Tmax
Suction Pressure
-1.00
-2.00
-3.00
0.85
0.8
0.75
-4.00 0.7 -5.00 0.65 -6.00 300
0 600
900
1200
b
200
400
600
800
1000
Time (s)
TH (K) Fig. 5. Transfer function between vent suction pressure and heater temperature.
Fig. 6. Comparison of experimental COT and load temperature with numerical prediction for preheating: (a) broil cycle (1200 W) and (b) bake cycle (1200 W).
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
4.2. Transient validation: preheating cycle
Transfer function for bake cycle P s ¼ ð3e
06
T 2H Þ
ð0:0011T H Þ þ 0:11.
Suction pressure dependence on the type of oven cycle and the heater rating is clear in Fig. 5. Since bake cycle velocities are higher than broil cycle increased suction pressure is attributed to increased pressure drop for flow through the vent. It may be noted that these transfer functions are applicable only for the range of wattages for which trials have been carried out, that indeed covers the operating range of oven.
1.00 10
Experimental: TLoad/ TMax Numerical: TLoad/ TMax Current
0.95
8 0.90
Current (ampere)
TLoad / TMax
2453
6
0.85
0.80 4
It is common practice to use a load in the oven to simulate the food being cooked for transient validation studies [1–6]. Moreover, TC inserted inside the thermal load avoids radiation and convection errors. A platform of low conductivity material was used to restrict heat being pumped out from thermal load through base of the oven. Aluminum has been selected as a thermal load because of its high thermal conductivity and also reasonably high diffusivity. Fig. 6a and b show comparison of experimentally measured COT and load temperature with numerical prediction for preheating broil (1200 W) and bake (1200 W) cycles, respectively. The suction pressure BC at vent outlet has been set as a function of heater temperature. The maximum discrepancy between experimental measurement and numerical prediction with air temperature (COT) was 6% with the broil cycle and 8.5% with the bake cycle. However, with load temperature, discrepancies dropped to 2% and 2.5%, respectively. This confirms the surmise that transient phenomenon is better captured with thermal load.
0.75 2 0.70
0.65
0 0
200
400
600
800 1000 1200 1400 1600
Time (s)
a 1.00
12
Experimental: TLoad/ TMax Numerical: TLoad/TMax Current
0.95
10
0.85 8 0.80 6
0.75 0.70
4
Current (ampere)
TLoad / TMax
0.90
0.65 2 0.60 0.55
0 0
b
250
500
750
1000
1250
Time (s)
Fig. 7. Comparison of experimental COT and load temperature with numerical prediction for full cycle: (a) bake cycle (2300 W) and (b) broil cycle (2900 W).
Fig. 8. Thermal field at oven mid-plane (Y–Z) for transient bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
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4.3. Transient validation: full cycle The cooking cycles of oven involve intermittent ON/ OFF operation of the heaters as has already been mentioned in an earlier section. It is important to validate the CFD model with transient thermal response of load in cooking cycles too. Fig. 7a and b shows comparison of experimentally measured load temperature with numerical prediction for bake (2300 W) and broil (2900 W), respectively through the ON–OFF cooking cycle. Heater ON– OFF conditions are also plotted as heater current in these figures. The maximum percentage discrepancy with bake cycle was 2.7% and 10% with broil cycle. The relatively higher percentage discrepancy with broil cycle is a common observation and is a matter of further investigation. 4.4. Comparison of bake and broil cycle heating Figs. 8–11 show temperature profile (in K) at the midplanes (Y–Z and X–Y) for bake and broil cycles at two
Fig. 9. Thermal field at oven mid-plane (Y–Z) for transient broil cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
times (360 s and 900 s). Broil cycle shows higher temperatures close to the heater that indicates stably stratified fluid inside the oven cavity. As a result of stable stratification there is hardly any fluid movement inside the cavity leading to non-uniform temperature distribution inside the cavity. Thus the dominant mode of heat transfer in a broil cycle would be through surface-to-surface radiation between heater and oven walls and radiation between walls themselves. It is observed that bake cycle has more uniform temperature throughout the domain. This is mainly due to convection currents formed at the bottom heater heating the cavity volume before moving out through the top vent. Thus dominant mode of heat transfer in bake cycle is radiation heat transfer between the heater and oven walls combined with convective heat transfer contributing to temperature uniformity. There is more efficient heat transfer between oven walls and the adjacent fluid layers due to higher flow velocities and more active boundary layer close to oven wall for a bake cycle. Fig. 12 shows temperature profile on the oven central– vertical axis through its height for a broil and bake cycle. It indicates a temperature gradient as a result of stable stratification for a broil cycle and highly uniform temperature for a bake cycle because of efficient convective heat transfer. The plot indicates there will be same broil
Fig. 10. Thermal field at oven mid-plane (X–Y) for transient bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
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800 Broil Bake
750
Temperature (K)
700 650 600 550 500 450 400 350 300 0.1
0.2
a
0.3 Y (m)
0.4
0.5
800 Broil Bake
750
Temperature (K)
700 650 600 550 500 450 400 350 300 0.1
b Fig. 11. Thermal field at oven mid-plane (X–Y) for transient broil cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
performance if the cooking load is kept within 5 cm from the heater (essentially the top grid locater at ovens is at this height). Beyond this there is a temperature gradient, which will not contribute to efficient cooking for a broil cycle. 5. Conclusions Development of a three-dimensional transient CFD model has been described to simulate natural convection heat transfer in ovens for two different cooking cycles. In order to establish a physically reasonable flow pattern through vent openings, a suction pressure was applied at top vent. This suction pressure was found to depend on the cavity heating pattern (bake, broil) and the heater temperature. In order to establish this relationship, steady state experimental trials were carried out at different heater ratings. A transient validation of bake cycle showed the model’s capability to simulate the thermal field and the effect of cyclic heater ON–OFF conditions on a thermal load inside the oven within 4% accuracy. Broil cycle heating, where the heater is close to top vent matched with experimental data within 10%. A comparison of bake and broil cycle heating pattern shows that the oven cavity is more uniformly heated with a bake cycle due to convective heating.
0.2
0.3 Y (m)
0.4
0.5
Fig. 12. Temperature profile at oven central–vertical axis for broil and bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
Acknowledgements We would like to thank Todd Graves, Business Program Manager, GE Consumer and Industrial and Francisco Anton, R&D manager, MABE for their support during the course of this work. We would also like to thank Amol Mulay, Sudeep Pradhan, Balaji Parthasarthy, Christopher Omalley of GE Consumer and Industrial and Nath Gopalaswamy for their participation and contributions in various discussions on modeling approaches. References [1] J.P. Abraham, E.M. Sparrow, Experiments on discretely heated, vented/unvented enclosures for various radiation surface characteristics of the thermal load, enclosure temperature sensor, and enclosure walls, International Journal of Heat and Mass Transfer 45 (2002) 2255–2263. [2] E.M. Sparrow, J.P. Abraham, Heat transfer coefficients and other performance parameters for variously positioned and supported thermal loads in ovens with/without water-filled or empty blockages, International Journal of Heat and Mass Transfer 45 (2002) 3597– 3607. [3] E.M. Sparrow, J.P. Abraham, A computational analysis of the radiative and convective processes that take place in preheated and non-preheated ovens, Heat Transfer Engineering 24 (5) (2003) 25–37. [4] E.M. Sparrow, J.P. Abraham, A new buoyancy model replacing the standard pseudo-density difference for internal natural convection
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gases, International Journal of Heat and Mass Transfer 46 (2003) 3583–3591. [5] J.P. Abraham, E.M. Sparrow, A simple model and validating experiments for predicting the heat transfer to a load situated in an electrically heated oven, Journal of Food Engineering 62 (2004) 409– 415. [6] J.P. Abraham, E.M. Sparrow, Three-dimensional laminar and turbulent natural convection in a continuously/discretely wall-heated
enclosure containing a thermal load, Numerical Heat Transfer, Part A (44) (2003) 105–125. [7] P. Verboven, N. Scheerlinck, J.D. Baerdemaeker, B.M. Nicolai, Computational fluid dynamics modeling and validation of the isothermal airflow in a forced convection oven, Journal of Food Engineering 43 (2000) 41–53. [8] M.F. Modest, Radiative Heat Transfer, McGraw-Hill, New York, 1993.
Modeling of transient natural convection heat transfer in electric ovens Hitesh Mistry a
a,*
, Ganapathi-subbu a, Subhrajit Dey a, Peeush Bishnoi a, Jose Luis Castillo
b
General Electric ACFD Lab, GE Global Research Centre, 122, EPIP, Whitefield Road, Bangalore 560 066, Karnataka, India b Mabe Mexico S de RL de CV, Acceso B #406, Parque Industrial Jurica, Queretaro 76120, Qro., Mexico Received 22 December 2005; accepted 10 February 2006
Abstract Prediction of transient natural convection heat transfer in vented enclosures has multiple applications such as understanding of cooking environment in ovens and heat sink performance in electronic packaging industry. The thermal field within an oven has significant impact on quality of cooked food and reliable predictions are important for robust design and performance evaluation of an oven. The CFD modeling of electric oven involves three-dimensional, unsteady, natural convective flow-thermal field coupled with radiative heat transfer. However, numerical solution of natural convection in enclosures with openings at top and bottom (ovens) can often lead to non-physical solutions such as reverse flow at the top vent, partly a function of initialization and sometimes dependent on boundary conditions. In this paper, development of a physics based robust CFD methodology is discussed. This model has been developed with rigorous experimental support and transient validation of this model with experiments show less than 3% discrepancy for a bake cycle. There is greater challenge in simulating a broil cycle, where the fluid inside the cavity is stably stratified and is also highlighted. A comparative analyses of bake and broil cycle thermal fields inside the oven are also presented. 2006 Elsevier Ltd. All rights reserved. Keywords: CFD; Natural convection; Radiation; Electric oven; Cooking; Thermal load
1. Introduction Domestic ovens, both gas and electric ranges are common appliances used for cooking. The thermal field within an oven has significant impact on quality of cooked food and reliable predictions are important for robust design and performance evaluation of an oven. The present study covers detailed approach of constructing numerical model of electric oven. While extensive experimental work goes into helping build a robust CFD model, the final outcome is a flexible, predictive tool based on CFD methodologies. Food is cooked in oven by radiative heating, convective heating or a combination of both. Cooking cycle with heat generated only from top heater is known as broil cycle and cooking mainly through the bottom heater is known as bake cycle. The typical bake cycles involve top heater cycling at less than half load to enhance heat transfer. *
Corresponding author. Tel.: +91 80 250 32658. E-mail address: [email protected] (H. Mistry).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.02.007
Broiling utilizes advantage of the radiation from the heater to rapidly heat the top of the food, which promotes browning and suppresses the natural convection current since the hot air is blocked by the ceiling of the oven. In bake cycle, heating primarily takes place because of buoyancy driven hot air flow. Nature of heat transfer mechanism plays a critical role in quality of food. For example, natural convection fluid flow is important in maintaining the quality of delicate food products that require a dry atmosphere (e.g. cream puffs, pastry shells). The CFD modeling of electric oven involves threedimensional, unsteady, natural convective flow field coupled with radiative heat transfer. A series of papers published by Abraham and Sparrow [1–6] consider heat transfer in vented enclosures involving radiation when bottom heater is operating. These set of papers involving experimental and numerical studies discuss the importance of modeling buoyancy forces directly rather than using pseudo-density difference in the model, sensitivity studies of thermal load and measurement probe with respect to
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
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Nomenclature 3 Rayleigh number bgDTL am temperature (K) wattage (W) heat transfer coefficient (W m2 K1) thermal conductivity (W m1 K1) specific heat (J kg1 K1) thermocouple tip diameter (m) density (kg m3) Stefan Boltzmann constant (W m2 K4) emissivity velocity of air (m s1) pressure (Pa) length of thermocouple (m) centre oven temperature
their radiative properties. Though heat transfer in enclosures with bottom heating has been studied [1–7], researchers have not attempted thermal field prediction for broil cycle. In this paper, CFD modeling of an electric oven cavity to simulate bake and broil cycles has been discussed; stably stratified flow being a characteristic of the latter. 2. Experimental details A typical freestanding electric range was used for experiments as shown in Fig. 1 with the Cartesian co-ordinate system. This range consists of an inner cavity with insulated walls and hinged front door, and two heating elements—a top-heating element (broil) and a bottomheating element (bake). The cross section of the heater consists of Ni–Cr wire placed within MgO filled Incoloy sheath. The cavity has a vent located on the rear side of the top wall of the cavity for continuous removal of hot and humid air. There is a deliberate leakage path known as gasket opening at the front door, which entrains fresh air. Heating of the cavity (oven set point) is controlled by a thermostat, which keeps the heating elements ON/OFF according to the pre-determined set point. Fig. 2 shows operating condition during broil cycle, where the oven set
Fig. 1. Electric oven.
TC a m g b L
thermocouple thermal diffusivity (m2/s) kinematic viscosity (m2/s) gravitational acceleration (m/s2) coefficient of thermal expansion (1/K) height of cavity (m)
Subscripts H heater c thermocouple w oven wall g gas or air inside the oven s suction
Broil Cycle : COT 540
Temperature (K)
Ra T W h k Cp d q r e v P x COT
Oven Set Point Temperature
490 440 390 340 290 0:00:00
0:07:12
0:14:24
0:21:36
0:28:48
0:36:00
0:43:12
Time (hr:min:s) Fig. 2. A typical broil cycle.
point is reached in 15 min after which the heater element starts cycling. The initial transient before heater starts cycling is known as preheating. The front doors have a double glazed window, which helps the operator to monitor the cooking without opening the door. Tin oxide coating is provided on inner glass walls to ensure low transmissivity for reduced radiation losses. Convection fans are normally provided at the rear wall of the cavity to enable faster cooking. A series of steady state experiments were carried out to understand the contribution of various heat loss mechanisms in the oven such as loss through the walls, heat loss through vent opening and glass viewing window of front door. To facilitate steady state operation, the control circuit for heating elements was bypassed and the heater was maintained at the required wattage. Heater power rating was set according to center oven temperature (COT). Thermal field inside the cavity was tracked through thermocouples distributed inside the cavity. For oven surface temperature measurements and cavity air temperature measurements, J (Iron-Constantan) type thermocouples (0.0100 ) with SS sheathing were used. These thermocouples were calibrated within 1% of a reference thermometer traceable to ITS-90 in liquid bath. For heater temperature
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measurements, K (chromul–alumel) type thermocouples were used. To facilitate easy location of thermocouples and ensure repeatability, thermocouples were mounted at eight corners of an open cuboid and at the center. It is well known that thermocouple measurements are prone to offset due to heat transfer in the exposed ambient. This is due to the fact that temperature of the junction, which is the equilibrium temperature, is not the temperature of the medium. Energy balance performed on a thermocouple junction at temperature Tc exposed to a gas at temperature Tg yields the following relationship: Tg Tc ¼
qc Cpc d oT c k c d o2 T c þ þ reðT 4H; w T 4c Þ. 4h 4h ox2c ot
ð1Þ
It can be seen that the difference between the gas temperature and the thermocouple reading is due to transient response of the thermocouple (first term on the right side of equation), conduction heat transfer along the thermocouple (second term), radiation heat transfer with surroundings (third term). A thermocouple located at center of the oven to measure air temperature participates in radiation with heater elements and the wall. These errors were minimized by providing radiation shields and avoiding direct viewing of thermocouple tip with heater surfaces. Highly polished aluminum foils were used as radiation shields. Thermocouple wires of 10–15 D length were kept inside the oven to minimize conduction error. Maximum uncertainty in temperature measurements was arrived as 9%, inclusive of all error/uncertainty components. This includes less than 2% variation observed during repeatability trials; for thermocouples distributed inside the oven cavity, a variation of 2% of temperature data was observed when thermocouple location was varied within 5 cm in space. The remaining 5% attributed to thermocouple participating in heat transfer. As indicated by the transient term of Eq. (1), it will require small diameter bare wire thermocouples to exactly track the transient slope. In order to overcome the sluggish response of thermocouples and to minimize radiation losses, thermocouples were buried inside an aluminum rod and heating of the aluminum rod was tracked. This also simulates a thermal load used in oven experiments. A rod of 1 in. · 1 in. · 20 in. size was used for these trials. 3. Numerical modeling Due to complex geometry, the internal volume of the oven cavity was meshed with tetrahedral element. The grid size of the oven cavity was largely decided by the mesh resolution near the heaters, gasket opening and the vent outlet. The surface mesh was generated using GAMBIT and volume mesh in TGrid. The difference in steady state thermal field predicted by grid size with 0.97 million cells and 1.5 million cells was of the order of 0.5%, much within the required accuracy of prediction for oven thermal performance. So, the grid with 0.97 million cells was chosen for all future numerical studies, steady state and transient,
presented in this paper. The commercially available solver FLUENT 6.1 was used for current studies. 3.1. Material properties The thermal properties of air were evaluated considering water vapor content in it. An ideal incompressible formulation for density has been used to capture natural convection heat transfer. The multi layered oven sidewalls, heater and door were modeled using effective conductive resistance through a lumped thickness. Literature review [2,3] revealed that radiation heat transfer inside the oven cavity is the most dominant mode of heat transfer. Higher dependence on radiative mode of heat transfer made it essential to pay due attention to radiative model and the radiative properties. Sensitivity studies of heater and oven sidewall emissivity ascertained unknown emissivity values for these surfaces and to understand their importance in heat transfer participation. With 30% reduction in heater emissivity, temperature at oven wall reduced by 10% but for reduction of 20% in wall emissivity, temperature at oven wall reduced by 0.2%. This observation indicates that thermal field inside the oven is more dependent on heater emissivity compared to sidewall emissivity. Finally, the emissivity values for heater and sidewall were chosen as 0.85 and 0.9, respectively, which were subsequently substantiated by IR camera measurements. 3.2. Boundary conditions The heaters have been modeled as volumetric heat source to capture the effect of heat capacity of the heater materials during the transient simulations. The outside surfaces of the oven wall and the glass door were modeled as a combination of convective and radiative heat transfer with the ambient. The gasket opening and vent outlet were specified as pressure boundary conditions. The inlet air temperature at gasket opening was considered to be at ambient temperature 296 K. 3.3. Radiation model For radiation models, discrete ordinate (DO) and surface-to-surface (S2S) were short-listed based on the applicability and accuracy required for the current study. The DO model takes into account media participation in addition to the surface-to-surface radiation effects. However, the S2S radiation model considers the latter only. The difference of temperature prediction at the center of the oven and oven walls by the DO and S2S models for a simplified but similar geometry were of the order of 0.2%. While, the comparison of the thermal field was similar, the computational time for S2S model was almost half of the DO model for an identical grid. Moreover, air in the current operating temperature range can be considered as non-participating media in radiation [8]. Considering all of the above, S2S seemed a suitable choice for the electric oven modeling.
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3.4. Laminar vs turbulent In a natural convective field, the order of Rayleigh number gives an indication of whether the flow field is laminar or turbulent. Calculations of Rayleigh number based on vertical height of cavity and temperature difference across the cavity show Ra O (108). Transient nature of thermal field indicates a variable Rayleigh number. Under such conditions, it is difficult to numerically predict the flow field, particularly during transition regime, due to nonavailability of a suitable modeling approach. Hence, it was decided to compare thermal fields in both laminar and turbulent regimes. A comparison of thermal field for assumption of completely laminar flow and completely turbulent flow at thermocouple locations inside the cavity showed a maximum of 3% difference in the temperature data. It has been observed that the thermal field is similar for both cases and henceforth a laminar approach should be able to predict the thermal performance with reasonable accuracy. It is important to note that the computational time involved in solving a laminar flow field is less compared to the turbulent approach. Abraham and Sparrow [6] have also made similar observations while studying steady state thermal-flow field of an electric oven when bottom heater is ON and thus carried out their numerical solution with laminar assumption. 4. Results and discussion Steady state solution takes less computational time than the full transient oven cycle. It is practical to do validation and accounts of heat losses initially on steady state cases. Moreover, steady state solution would give an opportunity to check on ‘‘effective’’ thermal conductivities of the composite wall material before going on to transient calculations, which involve effect of specific heat as well. 4.1. Steady state validation—vent suction pressure Fig. 3 shows velocity vectors on the oven mid-plane (Y–Z) with atmospheric pressure boundary condition set at the vent outlet. It indicates reversed flow at vent outlet and front door gasket opening leading to numerical oscillations. This reversed flow is contradictory to experimental observations. The reason for having reversed flow at vent outlet is due to the ‘‘ambient’’ boundary condition that was employed at the vent outlet and front door gasket opening in the numerical model. In reality, there is a local low pressure region that will be created at the vent outlet that causes the flow to move out of the vent from the top of the oven. This low pressure region is a combined effect of hydrostatic pressure difference due to density difference along the cavity height and the pressure drop when air enters the oven vent (from the cavity) due to the sudden change
Fig. 3. Velocity vectors at oven mid-plane (Y–Z) with atmospheric pressure BC at vent outlet.
in area. This pressure drop will be the proportional to 1 qv2 , the density being mean density of air at temperature 2 corresponding to air temperature at vent entry. Temperature of air at vent entry is guided by heater temperature and position of the heater. However, it is difficult to calculate pressure drop in oven vent without knowing air temperature at the oven vent entry apriori. Moreover, the natural convection velocity magnitude also depends upon the heater rating and the heating cycle being used. The boundary condition set at vent outlet should take into account this pressure drop. This was simulated by applying a ‘‘numerical’’ suction pressure at the vent outlet. A detailed exercise was carried out to arrive at the right magnitude of this suction pressure through a series of steady state experiments combined with numerical analysis to establish the suction pressure dependence on cavity temperature and the cycle.
Fig. 4. Velocity vectors at oven mid-plane (Y–Z) with suction pressure (2 Pa) at vent outlet.
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Table 1 Vent sensitivity studies for broil cycle Suction pressure: 0.5 Pa
Suction pressure: 1 Pa
Suction pressure: 2 Pa
Heater Inside left wall Outside left wall Inside glass wall Outside glass wall
% Discrepancy
% Discrepancy
% Discrepancy
+14.7 +21.6 +4.9 +26.4 +6.8
+11.4 +10.5 +3.3 +13.9 +3.9
+8.4 +0.5 +1.9 +1.2 +0.3
Fig. 4 shows velocity vectors on the oven mid-plane (Y–Z) with suction pressure of 2 Pa set at vent outlet. It shows air movement in the expected direction. This flow field matches qualitatively with experimental observation. The procedure used to identify the correct suction pressure value for given operating conditions would now be described. Thermal field data inside the cavity and cavity walls (total 12 points) obtained through experiments at different heater wattages for both bake and broil cycles were compared with the numerical model results at the same conditions. Since suction pressure has to be applied in the numerical model to simulate physical flow conditions, this suction pressure value was varied to keep the discrepancy between measured temperature and the numerical prediction within 10%. The suction pressure that provides thermal field closely matching with experimental data has been chosen as the suction pressure for that operating condition. Though it is possible to obtain an accurate value of suction pressure by keeping the discrepancy within 5%, from modeling point of view, 10% accuracy was deemed reasonable. Table 1 shows an example of this comparison matrix for broil cycle operating at 1200 W steady state that fixes the suction pressure as 2 Pa. The synergy between experimental and numerical studies at different wattages helped to build a transfer function between the heater temperature and vent suction pressure. These functions (Fig. 5) are as follows:
Transfer function for broil cycle P s ¼ ð4:1e06 T 2H Þ þ ð0:0011T H Þ þ 0:26. 1 Numerical: COT/Tmax Experimental: COT/Tmax
0.975
Numerical: Tload/Tmax 0.95
Experimental: Tload/ Tmax
0.925
T/ T maximum
Location of temperature measurement
0.9 0.875 0.85 0.825 0.8 0.775 0.75 0
200
400
600
800
1000
Time (s)
a 1
Numerical: Tload/Tmax Experimental: Tload/Tmax Numerical: COT/ Tmax Experimental: COT/Tmax
0.95
0.9
0.00 Broil Bake
T/Tmax
Suction Pressure
-1.00
-2.00
-3.00
0.85
0.8
0.75
-4.00 0.7 -5.00 0.65 -6.00 300
0 600
900
1200
b
200
400
600
800
1000
Time (s)
TH (K) Fig. 5. Transfer function between vent suction pressure and heater temperature.
Fig. 6. Comparison of experimental COT and load temperature with numerical prediction for preheating: (a) broil cycle (1200 W) and (b) bake cycle (1200 W).
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4.2. Transient validation: preheating cycle
Transfer function for bake cycle P s ¼ ð3e
06
T 2H Þ
ð0:0011T H Þ þ 0:11.
Suction pressure dependence on the type of oven cycle and the heater rating is clear in Fig. 5. Since bake cycle velocities are higher than broil cycle increased suction pressure is attributed to increased pressure drop for flow through the vent. It may be noted that these transfer functions are applicable only for the range of wattages for which trials have been carried out, that indeed covers the operating range of oven.
1.00 10
Experimental: TLoad/ TMax Numerical: TLoad/ TMax Current
0.95
8 0.90
Current (ampere)
TLoad / TMax
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6
0.85
0.80 4
It is common practice to use a load in the oven to simulate the food being cooked for transient validation studies [1–6]. Moreover, TC inserted inside the thermal load avoids radiation and convection errors. A platform of low conductivity material was used to restrict heat being pumped out from thermal load through base of the oven. Aluminum has been selected as a thermal load because of its high thermal conductivity and also reasonably high diffusivity. Fig. 6a and b show comparison of experimentally measured COT and load temperature with numerical prediction for preheating broil (1200 W) and bake (1200 W) cycles, respectively. The suction pressure BC at vent outlet has been set as a function of heater temperature. The maximum discrepancy between experimental measurement and numerical prediction with air temperature (COT) was 6% with the broil cycle and 8.5% with the bake cycle. However, with load temperature, discrepancies dropped to 2% and 2.5%, respectively. This confirms the surmise that transient phenomenon is better captured with thermal load.
0.75 2 0.70
0.65
0 0
200
400
600
800 1000 1200 1400 1600
Time (s)
a 1.00
12
Experimental: TLoad/ TMax Numerical: TLoad/TMax Current
0.95
10
0.85 8 0.80 6
0.75 0.70
4
Current (ampere)
TLoad / TMax
0.90
0.65 2 0.60 0.55
0 0
b
250
500
750
1000
1250
Time (s)
Fig. 7. Comparison of experimental COT and load temperature with numerical prediction for full cycle: (a) bake cycle (2300 W) and (b) broil cycle (2900 W).
Fig. 8. Thermal field at oven mid-plane (Y–Z) for transient bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
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4.3. Transient validation: full cycle The cooking cycles of oven involve intermittent ON/ OFF operation of the heaters as has already been mentioned in an earlier section. It is important to validate the CFD model with transient thermal response of load in cooking cycles too. Fig. 7a and b shows comparison of experimentally measured load temperature with numerical prediction for bake (2300 W) and broil (2900 W), respectively through the ON–OFF cooking cycle. Heater ON– OFF conditions are also plotted as heater current in these figures. The maximum percentage discrepancy with bake cycle was 2.7% and 10% with broil cycle. The relatively higher percentage discrepancy with broil cycle is a common observation and is a matter of further investigation. 4.4. Comparison of bake and broil cycle heating Figs. 8–11 show temperature profile (in K) at the midplanes (Y–Z and X–Y) for bake and broil cycles at two
Fig. 9. Thermal field at oven mid-plane (Y–Z) for transient broil cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
times (360 s and 900 s). Broil cycle shows higher temperatures close to the heater that indicates stably stratified fluid inside the oven cavity. As a result of stable stratification there is hardly any fluid movement inside the cavity leading to non-uniform temperature distribution inside the cavity. Thus the dominant mode of heat transfer in a broil cycle would be through surface-to-surface radiation between heater and oven walls and radiation between walls themselves. It is observed that bake cycle has more uniform temperature throughout the domain. This is mainly due to convection currents formed at the bottom heater heating the cavity volume before moving out through the top vent. Thus dominant mode of heat transfer in bake cycle is radiation heat transfer between the heater and oven walls combined with convective heat transfer contributing to temperature uniformity. There is more efficient heat transfer between oven walls and the adjacent fluid layers due to higher flow velocities and more active boundary layer close to oven wall for a bake cycle. Fig. 12 shows temperature profile on the oven central– vertical axis through its height for a broil and bake cycle. It indicates a temperature gradient as a result of stable stratification for a broil cycle and highly uniform temperature for a bake cycle because of efficient convective heat transfer. The plot indicates there will be same broil
Fig. 10. Thermal field at oven mid-plane (X–Y) for transient bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
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800 Broil Bake
750
Temperature (K)
700 650 600 550 500 450 400 350 300 0.1
0.2
a
0.3 Y (m)
0.4
0.5
800 Broil Bake
750
Temperature (K)
700 650 600 550 500 450 400 350 300 0.1
b Fig. 11. Thermal field at oven mid-plane (X–Y) for transient broil cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
performance if the cooking load is kept within 5 cm from the heater (essentially the top grid locater at ovens is at this height). Beyond this there is a temperature gradient, which will not contribute to efficient cooking for a broil cycle. 5. Conclusions Development of a three-dimensional transient CFD model has been described to simulate natural convection heat transfer in ovens for two different cooking cycles. In order to establish a physically reasonable flow pattern through vent openings, a suction pressure was applied at top vent. This suction pressure was found to depend on the cavity heating pattern (bake, broil) and the heater temperature. In order to establish this relationship, steady state experimental trials were carried out at different heater ratings. A transient validation of bake cycle showed the model’s capability to simulate the thermal field and the effect of cyclic heater ON–OFF conditions on a thermal load inside the oven within 4% accuracy. Broil cycle heating, where the heater is close to top vent matched with experimental data within 10%. A comparison of bake and broil cycle heating pattern shows that the oven cavity is more uniformly heated with a bake cycle due to convective heating.
0.2
0.3 Y (m)
0.4
0.5
Fig. 12. Temperature profile at oven central–vertical axis for broil and bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
Acknowledgements We would like to thank Todd Graves, Business Program Manager, GE Consumer and Industrial and Francisco Anton, R&D manager, MABE for their support during the course of this work. We would also like to thank Amol Mulay, Sudeep Pradhan, Balaji Parthasarthy, Christopher Omalley of GE Consumer and Industrial and Nath Gopalaswamy for their participation and contributions in various discussions on modeling approaches. References [1] J.P. Abraham, E.M. Sparrow, Experiments on discretely heated, vented/unvented enclosures for various radiation surface characteristics of the thermal load, enclosure temperature sensor, and enclosure walls, International Journal of Heat and Mass Transfer 45 (2002) 2255–2263. [2] E.M. Sparrow, J.P. Abraham, Heat transfer coefficients and other performance parameters for variously positioned and supported thermal loads in ovens with/without water-filled or empty blockages, International Journal of Heat and Mass Transfer 45 (2002) 3597– 3607. [3] E.M. Sparrow, J.P. Abraham, A computational analysis of the radiative and convective processes that take place in preheated and non-preheated ovens, Heat Transfer Engineering 24 (5) (2003) 25–37. [4] E.M. Sparrow, J.P. Abraham, A new buoyancy model replacing the standard pseudo-density difference for internal natural convection
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gases, International Journal of Heat and Mass Transfer 46 (2003) 3583–3591. [5] J.P. Abraham, E.M. Sparrow, A simple model and validating experiments for predicting the heat transfer to a load situated in an electrically heated oven, Journal of Food Engineering 62 (2004) 409– 415. [6] J.P. Abraham, E.M. Sparrow, Three-dimensional laminar and turbulent natural convection in a continuously/discretely wall-heated
enclosure containing a thermal load, Numerical Heat Transfer, Part A (44) (2003) 105–125. [7] P. Verboven, N. Scheerlinck, J.D. Baerdemaeker, B.M. Nicolai, Computational fluid dynamics modeling and validation of the isothermal airflow in a forced convection oven, Journal of Food Engineering 43 (2000) 41–53. [8] M.F. Modest, Radiative Heat Transfer, McGraw-Hill, New York, 1993.