Experimental study of in-tube cooling heat transfer and pressure drop characteristics of R134a at supercritical pressures

The in-tube cooling flow and heat transfer characteristics of R134a at supercritical pressures are measured experimentally for various pressures and mass fluxes in a horizontal tube. The tube is made of stainless steel with an inner diameter of 4.01 mm. Experiments are conducted for mass fluxes from 70 kg/m² s to 405 kg/m² s and pressures from 4.5 MPa to 5.5 MPa. The inlet refrigerant temperature is from 80 °C to 140 °C. The results show that the refrigerant temperature, the mass flux and the pressure all significantly affect the flow and heat transfer characteristics of R134a at supercritical pressures. The experimentally measured frictional pressure drop and heat transfer coefficient are compared with predicted results from several existing correlations. The comparisons show that the predicted frictional pressure drop using Petrov and Popov’s correlation accounting for the density and viscosity variations agree well with the measured data. Gnielinski’s correlation for the heat transfer coefficient agrees best with the measured data with deviations not exceeding 25%, while correlations based on supercritical CO₂ heat transfer data overcorrect for the influence of the thermophysical property variations resulting in larger deviations. A new empirical correlation is developed based on the measured results by modifying Gnielinski’s equation with thermophysical property terms including both the property variations from the inlet to the outlet of the entire test section and from the bulk to the wall. Most of the experimental data is predicted by the new correlation within a range of 15%.     

Experimental study on condensation heat transfer in vertical minichannels for new refrigerant R1234ze(E) versus R134a and R236fa

Experimental condensation heat transfer data for the new refrigerant R1234ze(E), trans-1,3,3,3-tetrafluoropropene, are presented and compared with refrigerants R134a and R236fa for a vertically aligned, aluminum multi-port tube. Local condensation heat transfer measurements with such a multi-microchannel test section are very challenging due to the large uncertainties related to the heat flux estimation. Presently, a new experimental test facility was designed with a test section to directly measure the wall temperature along a vertically aligned aluminum multi-port tube with rectangular channels of 1.45 mm hydraulic diameter. Then, a new data reduction process was developed to compute the local condensation heat transfer coefficients accounting for the non-uniform distribution of the local heat flux along the channels. The condensation heat transfer coefficients showed the expected decrease as the vapor quality decreased (1.0-0.0) during the condensation process, as the mass velocity decreased (260-50 kg m⁻² s⁻¹) and as the saturation temperature increased (25-70 °C). However, the heat transfer coefficients were not affected by the condensing heat flux (1-62 kW m⁻²) or by the entrance conditions within the tested range. It was found that the heat transfer performance of R1234ze(E) was about 15-25% lower than for R134a but relatively similar to R236fa. The experimental data were then compared with leading prediction methods from the literature for horizontal channels. In general, the agreement was poor, over-predicting the high Nusselt number data and under-predicting the low Nusselt number data, but capturing the mid-range quite well. A modified correlation was developed and yielded a good agreement with the current database for all three fluids over a wide range of operating conditions.     

Flow boiling heat transfer of R134a in the multiport minichannel heat exchangers

The flow boiling heat transfer characteristics of R134a in the multiport minichannel heat exchangers are presented. The heat exchanger was designed as the counter flow tube-in-tube heat exchanger with refrigerant flowing in the inner tube and hot water in the gap between the outer and inner tubes. Two inner tubes were made from extruded multiport aluminium with the internal hydraulic diameter of 1.1 mm for 14 numbers of channels and 1.2 mm for eight numbers of channels. The outer surface areas of two inner test sections are 5979 mm² and 6171 m², while the inner surface areas are 13,545 mm² and 8856 mm² for 14 and eight numbers of channels, respectively. The outer tube of heat exchanger was made from circular acrylic tube with an internal hydraulic diameter of 25.4 mm. The experiments were performed at the heat fluxes between 15 and 65 kW/m², mass flux of refrigerant between 300 and 800 kg/m² s and saturation pressure ranging from 4 to 6 bar. For instance the boiling curve, average heat transfer coefficients are discussed. The comparison results of two test sections with different the number of channels are investigated. The results are also compared with nine existing correlations. The new correlation for predicting the heat transfer coefficient was also proposed.     

Evaporation heat transfer of R-134a inside a microfin tube with different tube inclinations

An experimental investigation has been carried out to study the heat transfer characteristics during evaporation of R-134a inside a single helical microfin tube. The microfin tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The experiments were performed for seven different tube inclinations, α, in a range of −90° to +90° and four mass velocities of 53, 80, 107 and 136 kg/m² s for each tube inclination angle during evaporation of R-134a. The results demonstrate that the tube inclination angle, α, affects the boiling heat-transfer coefficient in a significant manner. For all refrigerant mass velocities, the best performing tube is that having inclination angle of α = +90°. The effect of tube inclination angle, α, on heat-transfer coefficient, h, is more prominent at low vapor quality and mass velocity. An empirical correlation has also been developed to predict the heat-transfer coefficient during flow boiling inside a microfin tube with different tube inclinations.     

Subcooled flow boiling of R-134a in vertical channels of small diameter

Subcooled flow boiling heat transfer for refrigerant R-134a in vertical cylindrical tubes with 0.83, 1.22 and 1.70 mm internal diameter was experimentally investigated. The effects of the heat flux, q″ = 1–26 kW/m², mass flux, G = 300–700 kg/m² s, inlet subcooling, ΔT_sub,i = 5–15 °C, system pressure, P = 7.70–10.17 bar, and channel diameter, D, on the subcooled boiling heat transfer were explored in detail. The results are presented in the form of boiling curves and heat transfer coefficients. The boiling curves evidenced the existence of hysteresis when increasing the heat flux until the onset of nucleate boiling, ONB. The wall superheat at ONB was found to be essentially higher than that predicted with correlations for larger tubes. An increase of the mass flux leads, for early subcooled boiling, to an increase in the heat transfer coefficient. However, for fully developed subcooled boiling, increases of the mass flux only result in a slight improvement of the heat transfer. Higher inlet subcooling, higher system pressure and smaller channel diameter lead to better boiling heat transfer. Experimental heat transfer coefficients are compared to predictions from classical correlations available in the literature. None of them predicts the experimental data for all tested conditions.     

Low-GWP refrigerants flow boiling heat transfer in a 5 PPI copper foam

This paper reports an experimental investigation of the heat transfer performance of the new low-GWP refrigerants, R1234yf and R1234ze(E), during flow boiling heat transfer inside a horizontal high porosity copper foam with 5 Pores Per Inch (PPI). Metal foams are a class of cellular structured materials consisting of a stochastic distribution of interconnected pores; these materials have been proposed as effective solutions for heat transfer enhancement during both single and two-phase heat transfer. R1234yf and R1234ze(E) refrigerants are appealing alternatives of the more traditional R134a by virtue of their negligible values of GWP and normal boiling temperatures close to that of R134a, which make them suitable solution in several different applications, such as: refrigeration and air conditioning and electronic thermal management. This work compares the two-phase heat transfer behaviour of these new HFO refrigerants, studying the boiling process inside a porous medium and permitting to understand their effective heat transfer capabilities. The experimental measurements were carried out by imposing three different heat fluxes: 50, 75, and 100 kW m⁻², at a constant saturation temperature of 30 °C; the refrigerant mass velocity was varied between 50 and 200 kg m⁻² s⁻¹, whilst the mean vapour quality varied from 0.2 to 0.95. The two-phase heat transfer and pressure drop performance of the two new HFO refrigerants is compared against that of the more traditional R134a.     

Flow boiling heat transfer and pressure drop of R-134a in a mini tube: an experimental investigation

This paper presents the results of an experimental study carried out with R-134a during flow boiling in a horizontal tube of 2.6 mm ID. The experimental tests included (i) heat fluxes in the range from 10 to 100 kW/m², (ii) the refrigerant mass velocities set to the discrete values in the range of 240-930 kg/(m² s) and (iii) saturation temperature of 12 and 22 °C. The study analyzed the heat transfer, through the local heat transfer coefficient along of flow, and pressure drop, under the variation of these different parameters. It was possible to observe the significant influence of heat flux in the heat transfer coefficient and mass velocity in the pressure drop, besides the effects of saturation temperature. In the low quality region, it was possible to observe a significant influence of heat flux on the heat transfer coefficient. In the high vapor quality region, for high mass velocities, this influence tended to vanish, and the coefficient decreased. The influence of mass velocity in the heat transfer coefficient was detected in most tests for a threshold value of vapor quality, which was higher as the heat flux increased. For higher heat flux the heat transfer coefficient was nearly independent of mass velocity. The frictional pressure drop increased with the increase in vapor quality and mass velocity. Predictive models for heat transfer coefficient in mini channels were evaluated and the calculated coefficient agreed well with measured data within a range 35% for saturation temperature of 22 °C. These results extend the ranges of heat fluxes and mass velocities beyond values available in literature, and add a substantial contribution to the comprehension of boiling heat transfer phenomena inside mini channels.     

Numerical simulation of dynamic contact angle using a force based formulation

A method for the numerical simulation of the dynamic response of the contact angle is presented and its development discussed. The proposed method was developed within a level-set framework by modelling forced capillary flows and it is based on the introduction of a force function to capture the balance of forces in the contact region between solid boundaries and a diffuse free-surface fluid interface. The proposed approach allows the system to define its own dynamic contact angle and its own contact line dynamics, without introducing numerical discontinuities such as locally prescribed angles or slip-length. The method was developed through numerical testing and comparisons with experimental and empirical models reported in the literature. These showed the validity of the proposed approach, which was able to reproduce the experimental correlation between the capillary number and the dynamic contact angle reported by [R.L. Hoffman, Study of advancing interface. 1. Interface shape in liquid-gas systems, J. Colloid Interf. Sci. 50 (1975) 228-241]. By using a single constitutive model for the force function, the simulation results of the dynamic contact angle showed an excellent agreement with the values predicted by Jiang’s empirical equation [T.S. Jiang, O.H. Soo-Gun, J.C. Slattery, Correlation for dynamic contact angle, J. Colloid Interf. Sci. 69 (1979) 74-77] through different material properties and flow speeds. The proposed approach also demonstrated the ability to work with meshes of low resolution.     

Effects of contact angle on condensate topology, drainage and efficiency of a condenser with minichannels

Epoxy coatings with good adhesion characteristics have been developed that are suitable for large-scale manufacturing and application in compact heat exchangers. Two of them, with a static contact angle for water of 105° and 79° have been tested in a finned-tube condenser comparing flat plate minichannels on the gas-side. Contrary to the expectation, the thermal efficiency of the 105° condenser is slightly less than that of the 79° one. This is due to a reduction of condensate drop size at detachment, resulting in relatively small dry paths after drainage. In the present study, geometry and coating thickness of the two coated exchangers used have not been optimized, since emphasis has been on the effect of contact angle. The finned-tube geometry is shown to be less favourable, for a condenser, than the compact cross-flow plate geometry with minichannels on both the gas- and coolant side that was tested previously.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

In part 1 (Gouin, [13]), we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.Received: 5 June 2001, Accepted: 24 May 2003, Published online: 29 July 2003PACS: 02.90, 47.50, 66.20, 68.03, 68.08     

Condensation pressure drop of HFC-134a and R-404A in a smooth and micro-fin U-tube

The frictional pressure drop during condensation of HFC-134a and R-404A in a smooth (8.56 mm ID) and micro-fin U-tubes (8.96 mm ID) are experimentally investigated. Different from previous studies, the present experiments are performed for various condensing temperatures. The test runs are done at average saturated condensing temperatures ranging from 35 °C to 60 °C. The mass fluxes are between 90 and 800 kg/m²s. The experimental results indicate that the average frictional pressure drop increases with mass flux but decreases with increasing condensing temperature for both smooth and micro-fin-tubes. The average frictional pressure drops of HFC-134a and R-404A for the micro-fin-tubes were 1-1.7 and 1-2.1 times larger than that in smooth tube respectively. New correlations based on the data gathered during the experimentation for predicting frictional pressure drop are proposed for wide range of operating conditions.     

Visual observation of two-phase flow pattern of R-22, R-134a, and R-407C in a 6.5-mm smooth tube

Two-phase flow pattern and friction characteristics for R-22, R-134a, and R-407C inside a 6.5 mm smooth tube are reported in this study. The range of mass flux is between 50 and 700 kg/(m² s). The experimental data show that the two-phase friction multipliers are strongly related to the flow pattern. For a stratified, wavy flow pattern a mass-flux dependence of the multipliers is seen. The flow pattern transition for the mixture refrigerant shows a considerable delay, compared with that of pure refrigerant.     

On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces

In this work, it is suggested that a unique set of the interfacial stiffness constants, K_N and K_T, is sufficient to characterize the macroscopic elastic response of an interface between two rough contacting surfaces regardless of the direction of incidence of the ultrasonic wave. It is also shown that by combining ultrasonic spectroscopy with the theoretical procedures developed for a single imperfect interface, the stiffness constants of a double interface can be successfully recovered. The values of the stiffness constants determined from ultrasonic measurements are related to the micromechanical interaction and topography of the contacting surfaces using a micromechanical model of two rough surfaces in contact.     

Experimental two-phase pressure gradients during evaporation of pure and mixed refrigerants in a smooth horizontal tube. Comparison with correlations

The paper reports the results of an experimental study on pressure drop during horizontal flow boiling of refrigerants R22, R507, R404A, R134a, R407C and R410A. The test section is a smooth, horizontal, stainless steel tube (6 mm I.D., 6 m length) uniformly heated by Joule effect. The experimental tests are carried out at an almost constant evaporating pressure of 7.0 bar varying the mass flow rate in the range 280–1,080 kg/m² s. The experimental comparison clearly shown that the pressure drop of R22 is significantly higher as compared to all the other fluids. The results are compared against well-known pressure drop prediction methods. The available correlations can be used for both pure fluids and mixtures with no corrective factors, provided the mixture properties are evaluated at local compositions. The Chawla friction correlation is the best-fitting of our experimental data in combination with the heterogeneous momentum pressure drop model on the basis of the Rouhani-Axelsson void fraction correlation.     

On the relationship between the work of adhesion and the critical shear stress for the onset of flow instabilities

The relationship between the critical shear stress for the onset of flow instabilities and the work of adhesion at the interface has been evaluated experimentally for a series of polyolefins on several steels, brasses, and coated steels. The critical shear stress was considerably affected by the chemical nature of the die. Low-surface-energy materials were found to produce smooth extrudates presumably by inducing slippage at the wall. Steel, tungsten carbide, and brass surfaces promoted sharkskin defect at shear stresses above the first critical shear stress. A linear relationship between the critical shear stress and the work of adhesion was found to be valid for values of work of adhesion smaller than approximately 30 mN/m. This indicates that slippage occurs due to a breakdown of the adhesion at the interface. For values of work of adhesion greater than approximately 30 mN/m a stronger interaction at the interface may induce a cohesive failure at the interface and subsequently, extrudate distortions.     

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

It is known that contact lines keep relatively still on solids until static contact angles exceed an interval of hysteresis of static contact angle(HSCA), and contact angles keep changing as contact lines relatively slide on the solid.Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force(MCF) on the seta.Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, exerting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake–Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed 23 cm · s-1. As insects brush the water by laterally swinging legs backwards,setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward.If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as F~C_1 U + C_2U~(2+ε), where C_1 and C_2 are determined by the dimple depth. Discrete points on this curve could give fitted relations as F~U~b(Suter et al., J. Exp. Biol. 200, 2523–2538, 1997). Finally,the axial torque on the inclined and partially submerged seta was found determined by the surface tension, contact angle,HSCA, seta width, and tilt angle. The torque direction coincides with the orientation of the spiral grooves of the seta,which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.     

The effect of the VOF–CSF static contact angle boundary condition on the dynamics of sliding and bouncing ellipsoidal bubbles

The static contact angle is the only empiricism introduced in a Volume of Fluid–Continuum Surface Force (VOF–CSF) model of bubbly flow. Although it has previously been shown to have a relatively limited effect on the accuracy of velocity and shape predictions in the case of large gas bubbles sliding under inclined walls (e.g. Cook and Behnia, 2001), it may have a more determining influence on the numerical prediction of the dynamics of smaller ellipsoidal bubbles which were shown by Tsao and Koch (1997) to bounce repeatedly when sliding under inclined walls at certain wall inclinations. The present paper reports on the influence of surface tension and the static contact angle on the dynamics of an ellipsoidal air bubble of equivalent diameter D_e = 3.4 mm. The bubble Eötvös and Morton numbers are Eo = 1.56 and Mo = 2 × 10⁻¹¹ respectively. The computational results are achieved with a Piecewise Linear Construction (PLIC) of the interface and are reviewed with reference to experimental measurements of bubble velocity and interface shape oscillations recorded using a high speed digital camera. Tests are performed at plate inclination angles θ ∈ {10°, 20°, 30°, 45°} to the horizontal and computational models consider three static contact angles θ_c ∈ {10°, 20°, 30°}. The static contact angle has been found to have a significant effect on the bubble dynamics but to varying degree depending on the plate inclination. It is shown to promote lift off and bouncing when the plate inclination angle reaches 30° in a way that does not necessarily reflect experimental observations.     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.