Modeling of nucleate boiling in engine cylinder head cooling ducts

Transcription

1 HEAT 28, Fifth International Conference on Transport Phenomena In Multiphase Systems June 3 - July 3, 28, Bialystok, Poland Modeling of nucleate boiling in engine cylinder head cooling ducts J.P. Kroes 1, C. W. M. van der Geld 2, E. van Velthooven 3 1 Department of Mechanical Engineering, Technische Universiteit Eindhoven, Netherlands; J.P. Kroes@tue.nl. 2 Department of Mechanical Engineering, Technische Universiteit Eindhoven, Netherlands; c.w.m.v.d.geld@tue.nl. 3 DAF Trucks, CAE-Engines, Hugo van der Goeslaan 1, 5643 TW Eindhoven, Netherlands; Eric.van.Velthooven@DafTrucks.com ABSTRACT The merits of various existing 1D models for nucleate subcooled boiling heat transfer are assessed. The implementation of these models is occasionally not straightforward. Some physical inconsistencies have been identified in these models. Surprisingly, the Chen correlation predicts the measurements best, in particular for data sets with heat fluxes in the range of a diesel engine. INTRODUCTION The lifetime of the cylinder head of a diesel engine is very dependent on its thermal loading. Cooling of the head is achieved by pumping a water-glycol mixture through a system of connected cavities that we shall name channel here. Nucleate boiling occurs near the cylinder head flame deck since heat fluxes are locally high. The channel geometry is characterized by a widely varying cross-section area, a complex connectivity and varying temperatures and heat fluxes, see Fig. 1. Typical temperature difference between in- and outlet is 6 o C, typical cooling power about one third of the total engine power and typical total pressure drop is.3 MPa. State-of-the art of prediction of heat transfer in the cylinder head is done with 3D CFD/FE analysis in the block in combination with 1D-modeling of nucleate flow boiling in the cooling channel. 1D means using bulk properties averaged over a cross-section area normal to the mean flow. At some locations this definition is ambiguous, but other intrinsic difficulties exist that are more important. The 1D models used are essentially a set of correlations based on experimental data for well-established flow without swirl and measured over some length of tube with constant crosssection. They have to be applied locally to swirling, accelerated, undeveloped flows. On places with void fraction redistribution in a cross-section bubble-bubble interaction may differ significantly from that in straight channels. An essentially two-dimensional description of nucleate, subcooled boiling would possibly have the flexibility and generality required for accurate modeling of boiling phenomena in a diesel engine, but such two-dimensional modeling does not exist, as far as we know. The more recent boiling models that are applicable, to be listed below, are 1D although they attempt to incorporate some of the physical transport phenomena that occur in a cross-section area. The present study attempts to assess the merits of various existing 1D models for nucleate boiling. To this end, prediction results will be compared with published results by the authors of the models, with other predictions and with dedicated experiments of the literature. Inlet and heating parameters will be varied in a wide range. The complexity of implementation of the models will be analyzed. To this end, all models have been implemented in a new code and no use of existing or available codes has been made. No sensitivity analysis will be carried out and it will not be attempted to modify the models despite the fact that some physical modeling aspects could have been improved. This might be subject of future work. Intake Intake Exhaust Exhaust Figure 1: Coolant flow in the jacket right above the combustion chamber. The water side is shown in a top view. Coolant flows in the bridges between the intake- and exhaust manifolds. Reaching the injector it flows upwards in an annulus-type channel.

2 FLOW Condensation in bulk liquid Direct heating of bulk liquid Condensation at bubble top Boundary layer Evaporation Transient Enhanced conduction convection Sliding bubble Bubble lift-off Subcooled liquid Superheated liquid Wall Figure 2: Schematic of the Dhir model (Basu et al., 25). MAIN FEATURES OF THE 1D MODELS The models applied are the well-known correlation of Chen (1966) and the following bottom-up approaches based on mechanistic modeling: The Basu, Warrier and Dhir model (22, 23, 25), see also Wang and Dhir (1993), that assumes bubbles at the wall to create an additional surface roughness that enhances heat transfer, and forced convection to be enhanced by boiling bubbles disrupting the fluid layer adjacent to the wall. From the boundary layer heat is transferred either by evaporation and subsequent condensation (either at the bubble top or inside the bulk liquid) or by direct heating of the bulk liquid, see Fig. 2. The extension of Chen s correlation of (25) which is called by these authors the boiling departure lift-off model. It utilizes two suppression parameters, one the normal accounting for bubble growth suppression, see Fig. 3, the other for condensation at the bubble top in subcooled boiling. The model of Kolev (26) that assumes heat transfer to occur through flow and bubble induced turbulence and tries to account for bubble-bubble interaction. FLOW Bubble Distance Temperature Increasing flow Decreasing temperature at bubble center Figure 3: Principle of boiling suppression. At increased flow the steeper temperature gradients reduce the net superheat and henceforth bubble growth. MODELING CONSIDERATIONS The model of Dhir (Basu et al, 25) takes sliding of bubbles (Klausner et al., 1993) into account, and is therefore complex. The if-then criteria used inevitably result in discontinuities in the predicted boiling curve. The model of Kolev (26) tries to take turbulence into account and was developed essentially for pool boiling rather than for flow boiling. Direct private communication with Kolev revealed that for forced convective boiling a correlation for convective heat transfer has to be used in conjunction with the boiling model, without suppression factors as in the Chen correlation. The convective heat transfer part has quite an effect on the total heat transfer,see also Zuber (1963). In this paper, as in many boiling correlations, the Dittus-Boelter correlation for forced convection is used. Kolev evaluates physical properties as surface tension coefficient and evaporation enthalpy at the wall temperature, T wall, and at the corresponding saturation pressure, p sat (T wall ), rather than at system pressure and corresponding saturation temperature, see also Borishanskii et al., (1964) and Labuntsov (1974). Thie use of the temperature at the wall (next to the saturation temperature) rather than the bulk temperature can be considered as a first step towards correlations for use in 3D CFD codes. In computer codes, at the wall only local temperatures are available, and it would be nice to possess correlations that merely utilize these local temperatures. Kolev ( ) in total proposed three correlations for the active nucleation site density,, to be used. Direct private communication with Kolev taught us that different site densities are expected to correspond to different properties of the surface at which boiling takes place. All three site densities might therefore be appropriate. Computations of the heat flux in this paper are based on the Wang and Dhir correlation (25). The approach of Kolev basically consists of the computation of a detachment diameter from correlations for the nucleation site density, and subsequently the calculation of a heat flux. Figures 4 6 show that predictions of D dep and q wall published in Kolev (26) correspond to different correlations for the nucleation site density.

3 (#/m 2 ) Active nucleation site density Gaertner and Westwater (196) Wang and Dhir (25) new correlation by Kolev (26) Kolev (26) feature that the detailed description of bubble dynamics enables to compute the latent heat carried away by the fluid. It turns out (Fig. 9) that in some cases this heat flux exceeds the total heat flux that is predicted in an independent way. Obviously, this is physically impossible. Boiling suppression as defined by Chen is in the Steiner (25) model computed with the aid of a bubble growth model that yields a ratio of two radii that is used as suppression factor. However, in this model the temperature drop from wall to bulk, and hence the effect of boiling suppression itself, is not accounted for. Saturated pool boiling (Kolev) Figure 4. The three correlations of Kolev ( ) for the nucleation site density at.1 MPa and a static contact angle, β, of 35 o. Gaertner and Westwater (196) data correlated by Kolev (1994). The Wang and Dhir correlation is evaluated at wall temperature, see Kolev (1995). D b,dep (mm) Saturated pool boiling (Kolev) acc. to Gaertner and Westwater (196) acc. to Wang and Dhir (25) acc. to Kolev (26) Kolev (26) q wall ( W / m 2 ) acc. to Gaertner and Westwater (196) acc. to Wang and Dhir (25) acc. to Kolev (26) Kolev (26) 1 Figure 6: Predictions with the Kolev model for.1 MPa and a static contact angle of 35 o. The labeled curve is given by Kolev (26) Figure 5: Predictions with the Kolev model for.1 MPa and a static contact angle of 35 o. acc. means according. The labeled curve is given by Kolev (26). When his last expression (26) is used, previous results for the departure diameter, D dep, and the heat flux, q wall, are not recovered anymore, but this should be considered as a consequence of variation of surface properties. The procedure to compute the departure diameter as given by Kolev contains the following mistake, see Fig. s 7 8. Only after taking the absolute value of the predicted angle that the resulting force on an adhering bubble at a wall makes with the wall, θ, the results published by Kolev could be reproduced. Both the Dhir and Kolev models possess the remarkable 3 Figure 7: Predictions with the Kolev model (1994, Gaertner and Westwater data) for.1 MPa and a static contact angle, β, of 35 o. Note the θ in the equation. To be compared with Fig. 8. The thick solid line is the desired solution, where the sum of governing forces is zero.

4 6 5 Subcooled flow boiling () p = 1.5 bar, Re D = 5547 p = 1.5 bar, Re D = p = 1.5 bar, Re D = q wall Figure 8: Predictions with the Kolev model (1994, Gaertner and Westwater data) for.1 MPa and a static contact angle of 35 o. Note the θ in the equation. See caption Fig. 7. Part of the surface yields a curve in Fig. 5. ( q evap / q wall ) 1 (%) Dhir Kolev SUBCOOLED FLOW BOILING p = 2 bar (T sat =12.21 C) Subcooling T sat -T bulk = 5.21 K (T bulk =115 C) v bulk = 1.5 m/s D hydr = 15 mm θ = 49 ε = 26 µm g = 9.81 m/s 2 Wall temperature T wall ( C) Figure 9: The ratio of the evaporation enthalpy flux to the total enthalpy flux as computed with Kolev (26) and Dhir (Basu et al., 25) models. The new correlation of Kolev (26) for the nucleation site density is used. account for a second boiling suppression mechanism that was not considered by Chen since it only occurs in subcooled boiling: condensation at the bubble top. The predictions of could readily be reproduced (Fig. 1). Figure 1. Reproduction of boiling curves predicted by Steiner et al. (25). Subcooled flow boiling of water along a smooth surface (ε = ) at a pressure of 1.5 bar; subcooling of 16 K; bulk temperature, T bulk, is 95 ºC; D hydr = 34 cm. Predicted boiling curves are compared in Fig. 11. Significant prediction differences occur at superheats exceeding 2 o. Wall heat flux q wall SUBCOOLED FLOW BOILING p = 2 bar (T sat =12.21 C) Subcooling T bulk = 3.21 K (T bulk =9 C) v bulk = 1.5 m/s D hydr = 15 mm θ = 49 ε = 26 µm g = 9.81 m/s 2 Wall temperature T wall ( C) Chen Steiner Dhir Kolev Figure 11. Comparison of predicted boiling curves. The new correlation of Kolev (26) for the nucleation site density is used. 4

5 a) (25) b) (23) Prediction by Chen (1966) c) (1995) 1 mm Water d) (1954) Metal Figure 12: Schematics of geometries and locations where heat is added in the experiments used for validation. Table 1 Measuring conditions 1 1 Figure 13: Comparison of measurements and prediction with the correlation of Chen (1966). Dotted lines indicate the ± 5 % limits. Prediction by Steiner (25) Table 1a Author Shape/ Material Coo lant D hydr [mm] v bulk [m/s] q wall [kw/m 2 ] DAF engine misc/iron 5/ Steiner 25 rect/ alu 1 water Boyd 23 circ/copper water Gollin 1995 circ/alu water / circ/alu water Table 1b Author T sub T sup p bar] T sat T bulk T wall DAF engine Steiner 25 16/ /2 111/ Boyd Gollin Figure 14: Comparison of measurements and prediction with Steiner (25). Dotted lines indicate the ± 5 % limits. 1 In the setup of Steiner the heated surface is aluminium. The rest of the channel is made up from PTFE and glass windows. 5 COMPARISON WITH EXPERIMENTS Dedicated experiments were performed to mimic flow boiling situations that occur in practice, see for example (23), (1995), Abou-Ziyan (24),

6 (1954). Various cross-sections were used (Fig. 12), and various hydraulic diameters and heat flux ranges (Table 1). 1 Prediction by Dhir (25) 1 Figure 15: Comparison of measurements and prediction with the model of Kolev (26). Dotted lines indicate the ± 5 % limits. 1 Prediction by Kolev (26) 1 Figure 16: Comparison of measurements and prediction with the model of Dhir et al. (25). Dotted lines indicate the ± 5 % limits. In Fig s predictions of all four 1D models are compared with the experimental data. None of the models has an overall good performance. For forced convection results at heat fluxes below about 3 kw/m 2 deviations to ± 5 % occur. Errors are bigger at heat fluxes exceeding 3 kw/m 2. The data set of (25) is best predicted by their own correlation, as was to be expected The data set of (23) is most representative of the conditions that occur in a diesel engine, next to the set of, since it covers the complete heat flux range in the engine. This set is best predicted by the Chen (1966) correlation. Surprisingly, the best overall prediction is given by the Chen (1966) correlation. CONCLUSIONS Next to the correlation of Chen, three more recent 1D models for the prediction of heat transfer in subcooled boiling have been used to compare predictions with each other and with four experimental data sets. In these models, attempts were made to account for the dynamics of bubbles at or near a heated wall explicitly. Because of that, and occasionally because of ambiguous or even erroneous descriptions, the implementation of these models turned out to be complex. A library of both Matlab and Simulink procedures has been set up, and the results of the original authors have been reproduced. Some physical modeling inconsistencies have been identified. Surprisingly, the Chen correlation predicts the measurements best, in particular for the two data sets (Boyd and ) with heat fluxes in the range of those in a diesel engine. It is apparently difficult to reconcile detailed physical descriptions of bubble behavior with data in a 1 D model. The reasons for this difficulty are discussed by Dhir (26) in his Max Jakob Award paper. The authors believe that 2 D modeling, i.e. accounting for variations in radial direction in a cross-sectional plane, has better prospects. Acknowledgement The authors thank dr. Kolev for valuable information and a lively discussion of the version of this paper. NOMENCLATURE Roman D diameter (m) F Force (N) F σ Adhering force related to surface tension (N) g gravitational acceleration (9.81) (m/s 2 ) h heat transfer coefficient (W/m 2 K) N Nucleation site density (#/m 2 ) p Pressure (Pa) q Heat flux (W/m 2 ) T Temperature (K) v Velocity (m/s) 6 Greek β contact angle (rad)

7 ε surface roughness (m) σ Surface tension (N/m) Subscribts b bubble bulk bulk dep departure hydr hydraulic n normal to the wall sat saturation conditions sub subcooled sup superheated t tangential or parallel to the wall wall wall REFERENCES Abou-Ziyan H.Z., 24, Forced convection and subcooled flow boiling heat transfer in asymmetrically heated ducts of T-section, Energy Conversion and Management, Vol 45 pp Basu N, Warrier GR, Dhir V.K., 22, Onset of nucleate boiling and active nucleation site density during subcooled flow boiling, ASME J. Heat Transfer, Vol 124 no 4 pp Basu N, Warrier GR, Dhir V.K., 23, Wall heat flux partitioning during subcooled flow boiling at low pressures Proceedings of HT23 ASME Summer Heat Transfer Conference, July 21-23, 23, Las Vegas, USA. Basu, N. Warrier, G.R. and Dhir, V.K., 25, Wall heat flux partitioning during subcooled flow boiling: Part 1 model development, Journal of Heat Transfer, Vol.127, pp Borishanskii V, Kozyrev A, Svetlova L., 1964, Heat transfer in the boiling water in a wide range of saturation pressure, High Temperature, Vol 2 no 1 pp Boyd RD, Strahan M, Cofie P, Ekhlassi A, Martin R., 23, High heat flux removal using water subcooled flow boiling in a single-side heated circular channel, Int. Journal of Heat and Mass Transfer, Vol 46 pp Chen JC 1966, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. & Eng. Chem. Process Design and Development, Vol 5 no 3 pp Dhir V.K., 26, Mechanistic prediction of nucleate boiling heat transfer-achievable or a hopeless task?, J. of Heat Transfer, Vol. 128, pp Gaertner RF, Westwater JR 196, Population of active sites in nucleate boiling heat transfer, Chem. Eng. Prog. Symp. Ser., Vol 3 pp Gollin, M., McAssey, E.V., Stinson, C., 1995, Comparative performance of ethylene glycol/water and propylene glycol/water coolants in the convective and forced flow boiling regimes. SAE Technical Paper Series, Paper Klausner, J.F, Mei R, Bernard, D.M., Zeng, L.Z., 1993, Vapor bubble departure in forced convection boiling, Int. J. Heat Mass Transfer, Vol 36, no 3, pp Kolev, N.I., 1994, The influence of mutual bubble interaction on the bubble departure diameter, Experimental Thermal and Fluid Science, Vol 8, pp Kolev NI 1995, How accurately can we predict nucleate boiling? Experimental Thermal and Fluid Science, Vol 1 pp Kolev NI 26, Uniqueness of the elementary physics driving heterogeneous nucleate boiling and flashing Nuclear Engineering and Technology, Vol 38 no 2 (special issue on ICAPP 5 pp ). Kolev, N.I., 26, The internal characteristics of boiling at heated surfaces, Proc. of the ECI International conference on Boiling Heat Transfer, Spoleto. Labuntsov DA 1974, State of the art of the nucleate boiling mechanism of liquids, Heat Transfer and Physical Hydrodynamics, Moskva, Nauka, in Russian, pp , W.H., 1954, Heat transmission, McGraw Hill, New York. Steiner, H., Kobor, A. and Gebhard, L.A., 25, A wall heat transfer model for subcooled boiling flow, Int. J. of Heat and Mass Transfer, Vol. 48, pp Wang CH, Dhir VK 1993, Effect of surface wettability on active nucleation site density during pool boiling of water on a vertical surface, Trans. ASME J. Heat Transfer, vol 115 pp Zuber N 1963, Nucleate boiling, the region of isolated bubbles and the similarity with natural convection, Int. J. Heat Mass Transfer, Vol 6 pp