SINGLE-PHASE CONVECTIVE HEAT TRANSFER AND PRESSURE DROP COEFFICIENTS IN CONCENTRIC ANNULI

UNIVERSITY OF PRETORIA SOUTH AFRICA SINGLE-PHASE CONVECTIVE HEAT TRANSFER AND PRESSURE DROP COEFFICIENTS IN CONCENTRIC ANNULI By: Warren Van Zyl Supervisors: Dr J Dirker Prof J.P Meyer 1

Topic Overview Experimental investigation of counter flow tube-in-tube heat exchanger. Focused on the annulus. Fully turbulent annulus flow 10 000 < Re Dh < 45 000. Four annular diameter ratios tested. Both heated and cooled annuli were tested. Measured outer tube and inner tube wall temperatures. Mean and local Nusselt numbers in the annulus. Energy balance errors below 1.5% and 3.5% for a heated and cooled annulus respectively. Annulus friction factors. 2

Background and Motivation for Study Varying annular diameter ratios affect: Heat transfer. Friction factors. Inconsistencies between existing correlations. More accurate means of measuring local wall temperatures. Local heat transfer. Minimal obstruction within annulus. Influence of the direction of the heat flux. Comparison of various experimental data reduction methods. 3

Literature Review Heat Transfer Existing Correlations. 4

Literature Review Friction Factor Existing Correlations. 5

Experimental Setup-Test Facility Topic Introduction and Background. Literature Study. Experimental Facility. Test Section. Data Reduction. 6

Experimental Setup-Test Section Annular Diameter Ratio 7

Experimental Setup-Test Section Inner Tube Bush 0.55m 3mm 0.55m T i 1,1 T i 2,1 T i 3,1 T i 4,1 T i 5,1 T i 6,1 T i 7,1 T i 8,1 T i 9,1 2.475m 3.025m T i 1,2 T i 2,2 T i 3,2 T i 4,2 T i 5,2 T i 6,2 T i 7,2 T i 8,2 T i 9,2 Tube sectioned here Thermocouple leads fed through inner tube. Tube sectioned and re-attached at centre. 9 temperature measurement stations. Thermocouple exiting to inlet/ outlet section 8

Experimental Setup-Test Section Inner Tube Thermocouple Junction Insulated Thermocouple D1 Di 3mm Solder 1.2mm Inner tube Wall Thermocouples embedded within inner tube wall. 9

Experimental Setup-Test Section Outer Tube Outer tube divided into 8 modular sections of equal length. 8 temperature measurement stations. Outer tube sections were located concentrically around inner tube using concentricity spacers. 10

Experimental Setup-Test Section Complete Test Section 11

Data Reduction Heat Transfer Both mean and local Nusselt numbers calculated. Mean heat transfer utilizes only inlet and outlet temperatures. Local heat transfer utilizes local fluid properties and temperatures measured along the tubes length. Three methods used for mean transfer: 1. Linear regression - Modified Wilson plot method (Briggs and Young (1969)). 2. Nonlinear regression (Khartabil and Christensen (1992)). 3. Mean logarithmic temperature difference method (LMTD). Local LMTD method used for calculating local Nusselt numbers. 12

Data Reduction Heat Transfer Linear and Nonlinear Regressions Using large data sets these methods employ iterative schemes to calculate the constants C i, C o and P of the Sieder and Tate equations. 13

Data Reduction Heat Transfer Local LMTD Test section divided equally into 9 control volumes. Outer tube wall temperatures measure fluid temperatures. Inner tube wall temperatures measured. 14

Data Reduction Heat Transfer Local LMTD Using local inlet and outlet temperatures the TLMTD is calculated. Local bulk temperature calculated for each control volume. Local Nusselt numbers calculated at each control volume. Control Volume 15

Data Reduction Friction Factor Friction factors calculated across the heat exchanger length. Calculated directly from measured pressure drops. Pressure transducers calibrated in the ranges 0-22kPa, 0-35kPa and 0-140kPa. 16

Data Representation Mean Heat Transfer (Cooling) Correlations under predict regression models by up to 10%. Regression models agree with each other. Scatter in LMTD results. Cooled Annulus 17

Data Representation Mean Heat Transfer (Heating) Correlations under predict regression models by up to15%. Regression models agree with LMTD. Heated Annulus 18

Data Representation Mean Heat Transfer (Heating and Cooling) On average 35% larger for heated annulus. 19

Data Representation J - Factors Removes the effects of the Prandtl number (Pr). On average 2.6% larger for heated annulus. 20

Data Representation Temperature Profiles Heat transfer errors with of 130% with temperature errors of 1 C. Second Order polynomial curve fitted to minimize errors. 21

Data Representation Local Heat Transfer (Cooling) Higher Reynolds numbers have larger drop from inlet to outlet. Developing thermal boundary layer. Cooled Annulus 22

Data Representation Local Heat Transfer (Heating) Higher Reynolds numbers have larger drop from inlet to outlet. Developing thermal boundary layer. Heated Annulus 23

Data Representation Annular Ratio Comparison Heat Transfer Regression models elevated. 24

Data Representation Annular Ratio Comparison Heat Transfer Regression models elevated. 25

Data Representation Friction Factors Correlations under predict experimental results. Larger friction factors for a cooled annulus. 26

Data Representation Annular Ratio Comparison Friction Factor Decreasing friction factor with increasing annular diameter ratio. (10%) Agrees with data point of Ntuli et al (2010). 27

Conclusions Nusselt numbers for a heated annulus on average 35% larger than a cooled annulus. The experimental Nusselt numbers (from regression models) were larger than those of existing correlations. 10% and 15% for a heated and cooled annulus respectively. The mean LMTD method agreed with the regression methods for 10 000 < Re < 25 000. For 25 000 < Re < 45000 the mean LMTD was lower than the regression analysis. (Only tested for a cooled annulus). Local Nusselt numbers (local LMTD method) were larger at the annulus inlet and decreased towards the outlet. Up to 240% and 200% for a heated and cooled annulus respectively. 28

Conclusions - Continued Differences in Colburn j-factors between a heated and cooled annulus lower than Nusselt number differences. Changes in Pr as a result of the different fluid temperature. The annular diameter ratio affected Nusselt numbers: For a heated annulus there was a decrease in Nusselt number with an increase in annular diameter ratio. For a cooled annulus a maximum Nusselt number was obtained in the mid-range of annular diameter ratio. Increasing the annular diameter ratio from 0.483 to 0.712 resulted in a friction factor drop of 10%. This is more than the existing correlations predict. 29