Single-phase forced and mixed convection in the laminar and transitional flow regimes of inclined smooth tubes with inlet disturbances

Abstract

Laminar and transitional flow regimes in tubes have been extensively investigated in the literature. However, there are several gaps in the forced and mixed convection literature, especially for inclined tubes with different inlet disturbances. The purpose of this study was to experimentally investigate the effect of tube inclination and inlet contraction ratio on the single-phase heat transfer and pressure drop characteristics in the laminar and transitional flow regimes for pure forced and mixed convection conditions. An experimental set-up was designed, constructed and validated against literature with the test section in a horizontal and different vertical orientation. The test section was 4.6 m long and was made from a smooth hard drawn copper tube with measured inner and outer diameters of 5.1 mm and 6.3 mm, respectively. Experiments were conducted at various inclination angles from vertical upward flow (+90º) to vertical downward flow (–90º), with horizontal flow (0º) and several other angles in between. A total of 2 679 mass flow rate measurements, 174 135 temperature measurements and 2 679 pressure drop measurements were conducted using water (Prandtl numbers between 3.5 and 8.1) as working fluid. The Reynolds number range covered were from 400 to 6 000 at constant heat fluxes varying from 1 to 8 kW/m2. Four different types of inlets namely; square-edged and re-entrant inlet with different inlet contraction ratios (5, 11, 14 and 33), as well as hydrodynamically fully developed and 90º bend inlets were used. It was found that an increase in the inclination angle from horizontal flow (0º) to vertical (±90º) flow, decreased the buoyancy effects which led to decreased laminar heat transfer coefficients and friction factors for both upward and downward flows. The onset of buoyancy effects was significant near the vertical inclination angles and caused a rapid increase in the laminar heat transfer coefficients and friction factors when the inclination angles moved from vertical to horizontal orientations. An inclined tube Grashof number which is a function of inclination angle was defined and used to express the laminar Nusselt numbers as a forced convection part plus an enhancement component owing to mixed convection. The laminar friction factors were expressed as a function of a forced convection/isothermal part multiplied by the mixed convection part. Furthermore, it was found that the critical Reynolds numbers at which transitional flow regime started increased as the inclination angles increased from horizontal to vertical, while the end of transitional flow regime were inclination angle independent. This caused the width of the transitional flow regime to decrease, as well as the transition gradients to increase, with increasing inclination angles at different heat fluxes. It was also found that the flow directions (upward and downward) had a negligible effect on the heat transfer coefficients and friction factors in the entire transition and quasi-turbulent regions. The fully developed laminar forced convection Nusselt numbers were not constant at 4.36, but were a function of Reynolds number for Reynolds numbers higher than 1 000. Therefore, a revised laminar Nusselt number correlation for smooth circular tubes was developed. The fully developed laminar forced convection friction factors were, as expected, equal to 64/Re. For both the forced convection heat transfer and pressure drop characteristics, transition occurred at the same mass flow rates for all the heat fluxes, including isothermal flow, but the critical Reynolds numbers increased with an increase in heat flux. For forced convection condition, the width of the transitional flow regime in the fully developed region remained constant for all heat fluxes. For a square-edged inlet geometry, the transition from the laminar to the turbulent flow regimes occurred earlier as the inlet contraction ratio increased, while for the re-entrant inlet, transition was delayed. The transitional flow regime was significantly affected by smaller contraction ratios and this effect increased with increasing heat flux. However, it was found that the critical Reynolds numbers were independent of inlet geometry for contraction ratios larger than 33. For the 90º bend inlet, transition occurred earlier than all the other inlet geometries and contraction ratios.