Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2014 Uncertainty Analysis on Prediction of Heat Transfer Coefficient and Pressure Drop in Heat Exchangers Due to Refrigerant Property Prediction Error Long Huang University of Maryland, College Park, United States of America, long730@umd.edu Vikrant Aute University of Maryland, College Park, United States of America, vikrant@umd.edu Reinhard Radermacher University of Maryland, College Park, United States of America, raderm@umd.edu Follow this and additional works at: http://docs.lib.purdue.edu/iracc Huang, Long; Aute, Vikrant; and Radermacher, Reinhard, "Uncertainty Analysis on Prediction of Heat Transfer Coefficient and Pressure Drop in Heat Exchangers Due to Refrigerant Property Prediction Error" (2014). International Refrigeration and Air Conditioning Conference. Paper 1399. http://docs.lib.purdue.edu/iracc/1399 This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html
2204, Page 1 Uncertainty Analysis on Prediction of Heat Transfer Coefficient and Pressure Drop in Heat Exchangers Due to Refrigerant Property Prediction Error Long HUANG 1, Vikrant AUTE 2 *, Reinhard RADERMACHER 3 Center for Environmental Energy Engineering Department of Mechanical Engineering, University of Maryland College Park, MD 20742 USA 1 Tel: 301-405-7314, 2 Tel: 301-405-8726, 3 Tel: 301-405-5286 Email: 1 long730@umd.edu, 2 vikrant@umd.edu, 3 raderm@umd.edu *Corresponding Author ABSTRACT Numerical simulation is extensively used in heat exchanger design and performance evaluation. While evaluating potential working fluids, pure fluids and fluid mixtures with different component combinations and fractions are compared based on simulation results. Two of the challenges while conducting such studies are the uncertainties of refrigerant properties and the applicability of empirical heat transfer and pressure drop correlations. Pure refrigerant property uncertainties are associated with experimental testing technique. The uncertainties of refrigerant mixtures are significantly higher when mixing rules are applied due the lack of measured data. Most of the empirical correlations are developed for certain refrigerants with a limited range of applicability of fluid states and tube geometry. Therefore, it is essential to understand the uncertainties in heat transfer coefficient and pressure drop calculations with different fluids. This paper presents a sensitivity analysis of heat transfer and pressure drop correlations for both in-tube condensation and evaporation cases. Multiple refrigerant such as R1234yf, R1234ze(E), R134a, R32, R410A, R445A, D2Y60 and L41a are analyzed based on commonly used heat transfer and pressure drop correlations from the literature. The parameters of the analysis are the thermodynamic and transport properties of the refrigerants. This study should be helpful to researchers and engineers in correlation selection during heat exchanger simulation and in understanding the potential prediction uncertainties while evaluating new fluids. 1. INTRODUCTION Air-to-refrigerant heat exchangers (HXs) are an essential component of almost all air-conditioning, refrigeration and heat pumping systems. Numerical simulations have been extensively applied in design and performance evaluation. Heat exchanger simulation tools are now used extensively in research and development of new generation of heat exchangers. With the aid of advanced HX simulation tools, the engineers are able to simulate the most complex HX designs, which would allow the engineers to further push the technology envelope. The development of HX simulation models started in the early 60s of the twentieth century. The heat exchanger model developed by Herman (1962) is one of the earliest effort that integrated mathematical heat exchanger models and computer technology. Most of the simulation models sprung up after year 2000 when the significant improvement of computing resource allows heat exchanger models to be used in optimization studies and system level simulations. Most of the heat exchanger models are highly dependent on not only the modeling technique, but also the refrigerant property prediction as well as heat transfer and pressure drop prediction. Previously, the prediction of pure refrigerant properties was mostly done using test data based library such as REFPROP (Lemmon et al., 2013). More recently, there was has been increasing interest in the performance evaluation of alternative lower global warming potential (GWP) refrigerant. As a part of such effort, several refrigerant blends are being analyzed, for which there is limited test data available. Especially when researchers are evaluating potential mixture combinations numerically, the accuracy of numerical mixture models remains questionable. The prediction of refrigerant properties is essential not only for the heat transfer model but also important for the empirical evaluation of heat transfer and pressure drop. Also, empirical correlations are tested for certain fluids for a limited range of operating conditions. The applicability
2204, Page 2 of existing correlations to newer fluids remains questionable. Thus it is important to understand how different correlations behave with a certain fluids and how the uncertainty in refrigerant property prediction affects the correlations. The other reason for evaluating the effect of refrigerant properties on the correlations is that most of the time for speed reasons, various simplified equations of state of other accelerated versions such an implicit and explicit methods are used for approximating properties. Such analyses will help in understanding how accurate the approximations should be and assist in making a judicious trade-off between computational complexity and accuracy. The objective of this paper is first to compare the behavior of different correlations on different fluids with changing geometry parameters and fluid conditions. Secondly, the impact of refrigerant property prediction uncertainty on heat transfer and pressure drop correlations is analyzed. The uncertainties of different refrigerant properties are analyzed individually to identify the properties that have the most impact on calculated heat transfer and pressure drop. Lastly, the overall impact of all the refrigerant property uncertainty is reported for different fluids. 2. CONDENSATION HEAT TRANSFER 2.1 Heat transfer correlations study In this section, five different correlations are studied, including Cavallini et al. (2003); Dobson and Chato (1998); Shah (1979); Shah (2013) and Traviss et al. (1973). The first goal is to compare the difference in heat transfer coefficient for different fluids. Then, different correlations will be compared with changing refrigerant quality, mass flux, saturation temperature and inner diameter in order to better understand different behaviors of the correlations. Finally, the uncertainty analysis of refrigerant property is conducted and reported. The behavior of different condensation heat transfer correlations under changing refrigerant quality is studied and shown in Figure 1. A 9 mm inner diameter tube is simulated under refrigerant condensing temperature of 45 C. The refrigerant mass flux in this comparison is 300 kg/m 2 s and the heat flux imposed on the tube is 30 kw/m 2 s. The trend of each correlation is consistent for both L41a and R134a. It can be clearly see that Shah (1979) and Traviss et al., (1973) show a smooth behavior. This is because Shah (1979) correlation uses one set of equations for all flow conditions. For Traviss et al., (1973), the transition of regions is not observed in this range of test conditions. Cavallini et al., model considers three flow regimes: annular flow, annular-stratified flow and stratified/slug flow. Dobson and Chato (1998) approach separates the correlation formulation based on mass flux and Froude number for stratified flow and annular flow. The can be clearly observed from Figure 1. Shah (2013) is currently the most comprehensive correlation in terms of verified data points, including 1735 data points from 51 studies with 24 different fluids. Three flow regimes are defined by Shah (2009) based on the extensive data set. Later, a complete correlations set was developed by Shah (2013). Figure 1: Condensation heat transfer correlations comparison under changing quality Figure 2 presents the heat transfer coefficient change with changing refrigerant mass flux for R410A and R1234yf. Again, although the correlations behave differently when compared with each other, the prediction trends are consistent between different fluids. Dobson and Chato (1998) suggests that the annular flow equation should be used when the mass flux is larger than 500 [kg/m 2 s], which causes the flow regime change, and hence a sudden jump, as observed from the figure.
2204, Page 3 Figure 2: Condensation heat transfer correlations comparison under changing mass flux Figure 3 shows the response of the correlations to changing saturation temperature. The saturation temperature change triggers a step change in flow regimes for R1234ze in this case but not for R32. Figure 3: Condensation heat transfer correlations comparison under changing saturation temperature Figure 4 presents the response of different heat transfer correlations on changing inner diameter. As shown in the figure, the heat transfer coefficient decrease monotonously with the increase of tube inner diameter. Figure 4: Condensation heat transfer correlations comparison under changing tube diameter
2204, Page 4 Knowing the differences and similarities of correlations, all 8 different refrigerants are then compared using Shah (2013) correlation as presented in Figure 5. R32 has the highest heat transfer coefficient mainly due to its high thermal conductivity. Figure 5: Condensation heat transfer coefficient comparison for different refrigerants based on Shah (2013) 2.2 Refrigerant property uncertainty on condensation heat transfer coefficient prediction In this section, the impact of thermophysical properties prediction error on condensation heat transfer coefficient is studied. The properties affecting the condensation heat transfer coefficient are: surface tension, liquid viscosity, liquid density, liquid specific heat, liquid conductivity, vapor density and vapor viscosity. Equation 1 shows the calculation of uncertainty where f is the correlation function and p 1,p 2,p 3 represent different properties. We imposed 1%, 5%, 10% and 15% refrigerant property prediction error and plotted the uncertainty on heat transfer coefficient for R134a using Cavallini et al. (2003) correlation in Figure 6. u f = ( f p 1 u p1 ) 2 + ( f p 2 u p2 ) 2 + ( f p 3 u p3 ) 2 +... (1) Figure 6: Condensation heat transfer coefficient uncertainty due to refrigerant property calculation error based on Cavallini et al. (2003)
2204, Page 5 As shown in Figure 6, liquid conductivity has the highest impact while surface tension has the lowest impact. Figure 7 plots the study where the prediction errors are imposed on all above properties for different refrigerants. In general, with 15% property calculation error, the condensation heat transfer coefficient prediction uncertainty is 13-14%. Figure 7: Condensation heat transfer coefficient uncertainty for different refrigerants based on Cavallini et al. (2003) 3. BOILING HEAT TRANSFER 3.1 Heat transfer correlations study Three boiling heat transfer correlations are studied in this section, viz., Gungor and Winterton (1987), Shah (1982) and Kandlikar (1990). The study is conducted based on a 9 [mm] inner diameter tube under refrigerant saturation temperature of 5 [ C]. The refrigerant mass flux in this comparison is 300 [kg/m 2 s] and the heat flux imposed on the tube is 30 [kw/m 2 s]. Figure 8 presents the effect of quality on boiling heat transfer coefficients. Kandlikar (1990) correlation including two separate equations for nucleate boiling and convective boiling which indicated by the results in Figure 8. Figure 8: Boiling heat transfer correlations comparison under changing quality Figure 9 shows the boiling heat transfer coefficient variation with changing mass flux. Shah (1989) correlation includes a set of comprehensive regime differentiation criteria. As a result, Shah (1989) s heat transfer prediction shifts a few times as the mass flux is increasing.
2204, Page 6 Figure 9: Effect of mass flux on boiling heat transfer coefficient The effect of saturation temperature inner diameter are s shown in Figure 10 and Figure 11. The increase in saturation temperature results in decreased heat transfer coefficient. As the mass flux decreases with the increase in diameter, the heat transfer coefficient decreases as well. Figure 10: Boiling heat transfer correlations comparison under changing saturation temperature Figure 11: Boiling heat transfer correlations comparison under changing tube diameter
2204, Page 7 The comparison of different refrigerants is shown in Figure 12. The ranking of refrigerant is very similar to the one in condensation heat transfer coefficient comparison. R32 has the highest boiling heat transfer coefficient under the test conditions. Figure 12: Boiling heat transfer coefficient comparison for different refrigerants 2.2 Refrigerant property uncertainty on boiling heat transfer coefficient prediction In this section, the impact of thermal properties and transport properties prediction error on boiling heat transfer coefficient calculation is studied. The properties affecting the boiling heat transfer coefficient calculation are: liquid viscosity, liquid density, liquid specific heat, liquid conductivity, vapor density and vapor viscosity. We imposed 1%, 5%, 10% and 15% refrigerant property prediction error and plotted the uncertainty on heat transfer coefficient for R134a using Gungor and Winterton (1987) correlation in Figure 13. Figure 13 Boiling heat transfer coefficient uncertainty due to refrigerant property calculation error based on Gungor and Winterton (1987) Base on Figure 13, liquid conductivity has the highest impact while vapor viscusity has the lowest impact. Figure 14 plots the study where the prediction errors are imposed on all above properties for different refrigerants. R445a has lower prediction uncertainty comparing to other fluids. In general, with 15% property calculation error, the boiling heat transfer coefficient prediction uncertainty is 8-10%.
2204, Page 8 Figure 14: Boiling heat transfer coefficient uncertainty for different refrigerants based on Gungor and Winterton (1987) 4. TWO-PHASE PRESSURE DROP 4.1 Pressure drop correlations study Four two-phase pressure drop correlations are studied in this section, Jung and Radermacher (1989), Lockhart and Martinelli (1949), Müller-Steinhagen and Heck (1986) and Friedel (1979). The study is conducted based on a 9 [mm] inner diameter tube is under refrigerant saturation temperature of 5 [ C]. The refrigerant mass flux in this comparison is 300 [kg/m 2 s] and the heat flux imposed on the tube is 30 [kw/m 2 s]. Figure 15 presents the effect of quality on pressure drop prediction. Under the test condition specified above, Jung and Radermacher (1989) as well as Lockhart and Martinelli (1949) correlation achieve the highest pressure drop per unit length near the transition from annular flow to annular flow with partial dryout. Figure 15: Boiling heat transfer correlations comparison under changing quality Figure 16 presents the comparison of pressure gradient for different fluids using Jung and Radermacher (1989) correlation.
2204, Page 9 Figure 16: Pressure drop correlation comparison for different refrigerants 4.2 Refrigerant property uncertainty on pressure drop prediction In this section, the impact of thermal properties and transport properties prediction error on boiling heat transfer coefficient calculation is studied. The properties affecting the condensation heat transfer coefficient calculation are: liquid viscosity, liquid density, vapor density and vapor viscosity. We imposed 1%, 5%, 10% and 15% refrigerant property prediction error and plotted the uncertainty on heat transfer coefficient for R134a using Lockhart and Martinelli (1949) correlation in Figure 17. As a result, the density calculation errors affect the pressure drop predictions significantly. Figure 17 Pressure drop calculation uncertainty due to refrigerant property calculation error based on Lockhart and Martinelli (1949) Figure 18 plots the study where the prediction errors are imposed on all above properties for different refrigerants. All the fluids tested yields to around 11% uncertainty with 15% property prediction error. Figure 18: Pressure drop calculation uncertainty for different refrigerants based on Lockhart and Martinelli (1949)
2204, Page 10 5. CONCLUSIONS This paper presented a comprehensive analyses of empirical correlations for two-phase heat transfer and pressure drop. The prediction abilities of these correlations were studied for different refrigerants including new lower GWP fluids. Furthermore, an uncertainty analyses was conducted on the various correlations to assess the impact of errors in refrigeration properties prediction. Thirteen different correlations including condensation heat transfer, boiling heat transfer and pressure drop correlations are studied with 8 different fluids. The behaviors of different correlations for different fluids under various geometries and flow conditions are compared. According to this study, up to 15% property prediction error can result in up to 14%, 13% and 10% prediction uncertainties for condensation heat transfer, boiling heat transfer and pressure drop calculation respectively. It was also observed that the liquid thermal conductivity has the highest impact on the calculated heat transfer coefficient. Such uncertainty can have significant impact on performance prediction of heat exchangers and corresponding systems. REFERENCES Shah, M.M. 1982. Chart correlation for saturated boiling heat transfer: equations and further study, ASHRAE Transactions 88 (1), 185-196. Cavallini, C., Del Col, D. L., Rossetto, Z. 2003. Condensation inside and outside smooth and enhanced tubes - a review of recent research. International Journal of Refrigeration 26, 373-392 Dobson, M. K., Chato, J.C. 1998. Condensation in Smooth Horizontal Tubes, Transactions of the ASME, Journal of Heat Transfer 120, 193-213. Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two phase pipe flow. Paper E2. European Two Phase Flow Group Meeting, Ispra, Italy Gungor, K.E., Winterton, R.H.S. 1987. Simplified general correlation for saturated flow boiling and comparisons of correlations with data, Transactions of the Institute of Chemical Engineers, Chemical Engineering Research and Design 65, 148-156. Herman, P.J. 1962. Simulation of steam generation in a heat exchanger. Institute of Ratio Engineers Transctions on Electronic Computers 53-57. Jung, D.S., Radermacher, R. 1989. Prediction of pressure drop during horizontal annular flow boiling of pure and mixed refrigerants, International Journal of Heat and Mass Transfer 32 (12), 2435-2446. Lemmon, E.W., Huber, M.L., McLinden, M.O. 2013, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg. Lockhart, R.W., Martinelli, R.C. 1949. Proposed correlation of data for isothermal two-phase, two-component flow in pipes, Chemical Engineering Progress 45 (1), 39-48. Müller-Steinhagen, H., and Heck, K. 1986. A simple friction pressure drop correlation for two-phase flow in pipes. Chemical Engineering Process 20, 297-308. Kandlikar, S.G. 1990. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes, Transactions of the ASME, Journal of Heat Transfer 112, 219-228. Shah, M. M. 1979. A General correlation for heat transfer during film condensation inside pipes, International Journal of Heat and Mass Transfer, 22, 547-556. Shah, M. M. 2009. An improved and extended general correlation for heat transfer during condensation in plain tubes. HVAC&R, 15(5), 889-914. Shah, M. M. 2013. General correlation for heat transfer during condensation in plain tubes: further development and verification. ASHRAE Winter Conference Traviss, D.P., Rohsenow, W.M., Baron, A.B., 1973. Forced convection condensation inside tubes: A heat transfer equation for condenser design. ASHRAE Transactions, 79, 157-165 ACKNOWLEDGEMENT The work was supported by the Integrated Optimization Consortium at the University of Maryland.