Anthony Servonet Stefano Nebuloni Bruno Agostini - supervisor

1. Micro-channel flow boiling correlations and 3-zone model plus comparison to recent published results Anthony Servonet Stefano Nebuloni Bruno Agostini - supervisor 08 February 2007 Heat and Mass Transfer Laboratory

2. Contents of the presentation • introduction to micro-channel features • heat transfer prediction models • Kandlikar and Balasubramanian (2004) • Zhang at al. (2004) • 3 zone model – Thome-Dupont-Jacobi (2004) • comparison with experimental data • conclusions Heat and Mass Transfer Laboratory

3. General considerations on micro-scale flow boiling trends (from experiments) • h is not dependent on mass velocity • h is not dependent on vapor quality (x>0.1) • h is dependent on heat flux • h is dependent on saturation temperature Heat and Mass Transfer Laboratory

4. Macro to micro-scale transition Kandlikar and Grande : 3 mm Mehandal et al. : micro-channels (1 – 100 μm) meso-channels (100 μm – 1mm) macro-channels (1 – 6 mm) conventional (Dh > 6 mm) Kew and Cornwell : Heat and Mass Transfer Laboratory

5. Kandlikar and Balasubramanian model (1/2) • this model is an extension of their macro-scale correlation to tube diameter <3mm, eliminating the dependency on Froude number • it is based on Reynolds number ReLO (all liquid), taking into account the laminar or turbulent flow condition Heat transfer coefficient can be calculated in the following way: if 100<ReLO <1600 : if ReLO <100 : FFL represents the nucleation characteristic of the liquid on a given surface Heat and Mass Transfer Laboratory

6. Kandlikar and Balasubramanian model (2/2) • The model predicts that nucleate boiling becomes dominant for low Reynolds numbers • convective boiling contribution becomes dominant to high vapor quality The model has been implemented in a MATLAB code (Excel compatible) Heat and Mass Transfer Laboratory

7. Zhang – modified Chen model (1/3) • this model (2004) is a modification of the macro-scale flow boiling correlation proposed by Chen (1966) where the correlation proposed by Foster and Zuber for nucleate boiling heat transfer is used • Chen model was developed to determine flow boiling heat transfer coefficients when both liquid and vapor phases were both in turbulent flows (Rek>2300) S: suppression factor F: Reynolds number factor C is a function of flow conditions (Re) Martinelli parameter Heat and Mass Transfer Laboratory

8. Zhang – modified Chen model (2/3) friction factors for circular channels for 1000<Rek<2000 an interpolation is used • single phase heat transfer correlations are modified to take into account laminar flow conditions and channels orientation w.r.t. gravity Solving for the wall temperature allows to obtain the heat transfer coefficient The model has been implemented in a MATLAB code with a bisection method solver Heat and Mass Transfer Laboratory

9. Zhang – modified Chen model (3/3) • A clear transition zone is identifiable in correspondence of sharp variation of heat transfer coefficient (subordinated to Reynolds number range) • At high vapor quality (x1-) the heat transfer coefficient diverges, due to the big contribution of convective boiling component Heat and Mass Transfer Laboratory

10. 3-Zone model - Thome-Jacobi-Dupont (2004) (1/6) • A three zone flow boiling model of the evaporation of elongated bubbles in micro-channels • the sequential passages of a liquid slug, an evaporating bubble and a vapor slug are assumed as a qualitative description of the flow pattern • local heat transfer coefficient is then obtained by a time average (over the period of the passage of the triple): Heat and Mass Transfer Laboratory

11. V L B 3-Zone model - Thome-Jacobi-Dupont (2004) (2/6) Major hypothesis: • liquid film remains attached to the wall (shear stresses are assumed negligible) and is assumed very small compared to channel radius • homogeneous flow (vapor and liquid velocities are the same) • heat flux is uniform and constant in time • neither liquid or the vapor phases are superheated Bubble departure frequency: • bubbles are assumed to grow until r= R where the fluid reaches saturation temperature (x=0) • from bubble departures frequency f =1/ it is possible to evaluate the length of the liquid slug and the residence time of vapor and liquid mass and volume conservation Heat and Mass Transfer Laboratory

12. 3-Zone model - Thome-Jacobi-Dupont (2004) (3/6) Residence time: (homogeneous flow) Local heat transfer coefficient: liquid slug and dry zone The flow is assumed to be hydrodynamically and thermally developing if Re 2300: London and Shah correlation if Re> 2300: Gnielinski correlation Asymptotic method (Churchill and Usagi) Heat and Mass Transfer Laboratory

13. 3-Zone model - Thome-Jacobi-Dupont (2004) (4/6) Thin film evaporation model Energy balance across the liquid layer gives the following evolution with time of the layer: mean heat transfer coefficient Since h tends to infinity if end tends to zero (and the choice of end is quite complicate) Liquid film thickness The prediction of initial liquid film thickness is based on the work done by done by Moriyama and Inoue (a correlation including a further constant C0) Heat and Mass Transfer Laboratory

14. 3-Zone model - Thome-Jacobi-Dupont (2004) (5/6) The constant C0. the bubble departure frequency and the end constitute the 3 parameter of the model that can be optimized on a specific database periodic heat transfer coefficient (vapor quality 8%) Heat and Mass Transfer Laboratory

15. 3-Zone model - Thome-Jacobi-Dupont (2004) (6/6) The two models (basic version – logarithm – and modified version) have been provided for the project development Heat and Mass Transfer Laboratory

16. Threshold diameter criteria Transitional diameter depends on the refrigerant properties Heat and Mass Transfer Laboratory

17. Sources Analysed 890 data in database of 2767 values (32%) Fluids : CO2, R11, R22, R134a, R141b, R410A, Water. • diameter between 0.263 et 2.87 [mm], • mass velocity between 23 and 6673 [kg/m2s], • saturation temperature between -18 and 105 [°C], • heat flux between 4.4 and 938 [kW/m2], • vapour qualities between 0 to 1, • heat transfer coefficient measured between 0.2 and 286 [kW/m2K] Heat and Mass Transfer Laboratory

18. Description of project Heat and Mass Transfer Laboratory

19. Previous database (collected by Ribatski G.) In interval ± 30% : • Kandlikar =6.2 % • Zhang = 11.4 % • TZM = 28.4 % MAPE(Mean Absolute Percentage Error) : • Kandlikar =74 % • Zhang = 116 % • TZM = 83 % Heat and Mass Transfer Laboratory

20. New database(Kew and Cornewell, Steinke, Lee and Mudawar, Qu and Mudawar) In interval ± 30% : • Kandlikar =12.6 % • Zhang = 43.7 % • TZM = 32.9 % MAPE : • Kandlikar =75 % • Zhang = 87% • TZM = 49 % Heat and Mass Transfer Laboratory

21. Conclusions A new set of experimental data of flow boiling heat transfer coefficient has been acquired and compared with three different models : • Kandlikar model is simple to be implemented, but the prediction error is quite significant • Zhang model predicts the heat transfer coefficient with a higher accuracy but with higher dispersion and it predicts trends which are not resulting from experiments • Three zones model is the most promising one, approaching the problem from the physics of the phenomena and therefore producing better results. Heat and Mass Transfer Laboratory