Effect of surface roughness on the mass flow rate predictions for adiabatic capillary tubesEffet de la rugosité de surface sur les prévisions de débit massique pour les tubes capillaires adiabatiques

https://doi.org/10.1016/j.ijrefrig.2020.05.020Get rights and content

Highlights

  • Experimental measurements of surface roughness for two capillary tubes are presented.

  • The impact of surface roughness on mass flow rate predictions is quantified.

  • CO2 and R600a are investigated with straight and coiled capillary tubes.

  • Correlations to estimate the sand-grain roughness for capillary tubes are assessed.

Abstract

In this paper, the effect of surface roughness on the mass flow rate through adiabatic capillary tubes was analyzed. Initially, relevant information about the surface roughness of capillary tubes and available correlations to estimate the sand-grain roughness were summarized. Subsequently, experimental measurements by stylus profilometry were performed for two different capillary tubes, presenting the Ra, Rq, Rp, and Rz as the roughness parameters. Algebraic solutions for straight and coiled adiabatic capillary tubes were considered for the refrigerants CO2 and R600a. A simulation-based factorial design was performed and the results showed that the effect of altering the surface roughness was about 2.5 times more prominent for CO2 than for R600a. The roughness change was found to be more significative than the shape alteration, for CO2, while for R600a the effect was the inverse. Besides, the mass flow rate was slightly more affected for the straight capillary tube than for the coiled one, for both refrigerants. Concerning the correlations to estimate the sand-grain roughness, it was shown that differences greater than 3 µm could be found by altering the estimator used. For the conditions investigated, two correlations demonstrated to be suitable for characterizing the surface roughness of capillary tubes, presenting 95% and 91.7% of the predicted mass flow rates within a ± 10% error band.

Introduction

Capillary tubes are commonly used as the expansion device in small scale refrigeration or heat pump systems and consist of a segment of a tube with constant cross-section area. Some advantages of using them include the low cost and lower compressor starting torque, due to the pressure equalization between the condenser and the evaporator during the off-cycle (Peixoto and Bullard, 1994). On the other hand, a major drawback is the low capacity to adapt to different load conditions. Despite being a simple component, the flow inside the capillary tube is quite complex, due to the simultaneous pressure drop and refrigerant phase-change. Once it is installed, it is not possible to modify or to regulate it, and, therefore, the proper sizing before installation is essential to the system performance (Chang et al., 1996). In this sense, many researches, comprising experimental and theoretical studies, have been studying the refrigerant flow characteristics inside the capillary tubes.

As early as in 1948, the inner diameter, the length, and the surface roughness were identified as some of the most important factors influencing the flow through these components (Lathrop, 1948). Zhang and Ding (2004) said that the friction factor was weakly dependent on the surface roughness of capillary tubes. On the other hand, the numerical model of Lee and Jeong (2019) indicated significant absolute average deviations (AAD) when reference data of surface roughness were not provided, concluding that the roughness is an influential factor for mass flow rate predictions.

The effect of surface roughness on pressure drop was identified as an important aspect in the nineteenth century by Henry Darcy, who introduced the concept of relative roughness (Taylor et al., 2006). However, the first work to quantify the effect of surface roughness on the pressure drop and friction factor was presented by Nikuradse (1950). In his work, tubes with different diameters were roughened by coating the internal surface with a layer of sand grains of uniform and known size. The absolute surface roughness was considered equal to the sand grains diameter, and most of the subsequent friction factor studies incorporated this concept. Since actual channels and pipes do not have such a regular surface as the sand grains, it is essential to understand how to estimate the surface roughness and which roughness parameter to choose among those given by the roughness measurement techniques. Fig. 1 illustrates some parameters commonly used and defined in ISO 4287 (ISO 4287, 1997). Ra is the distance from the arithmetic average line to the mean line. Rq is the distance from the root mean square profile line to the mean line; Rp is the distance from the mean line to the highest peak. Finally, Rz is the average distance from the five highest peaks (P) to the five lowest valleys (V).

Kandlikar et al. (2005) experimentally investigated the effect of relative roughness on single-phase flow of water and air through rectangular mini-channels, in laminar and turbulent regimes. They proposed a new set of equations to estimate the roughness and the constricted hydraulic diameter. For the laminar region, they verified a maximum mean deviation of 5% between the data, with the new set of equations, and the laminar theory. For the turbulent region, the results disagreed with the turbulent theory, being recommended further investigations.

Hrnjak and Tu (2007) studied the frictional pressure drop of R134a in rectangular microchannels, with different hydraulic diameters and aspect ratios, in the laminar and turbulent regimes. They reported that the Ra parameter might not be the best choice to characterize the surface roughness of microchannels.

Young et al. (2009) examined a variety of surface roughness samples suitable for fluid flow applications. They reviewed the equation of Kandlikar et al. (2005) and proposed a new correlation to estimate the roughness. The authors concluded that the Ra parameter is not adequate to characterize surfaces for fluid flow applications.

Zhou and Yao (2011) studied the effect of surface roughness on pressure drop for liquid flow in the laminar flow. They compared existing models with experimental data for microchannels, collected from the literature. The results showed that when the Rp parameter is used instead of Ra, the models achieved a better agreement, with maximum error of ±15%.

Farshad et al. (2001) analyzed the surface roughness of internally coated pipes and the pressure drop due to the fluid flow. According to them, at relatively high velocities, the surface roughness becomes an important factor that affects the turbulence. Besides, they concluded that the parameter Rz is a good choice for analyzing turbulent flow.

Adams et al. (2012) experimentally studied the effect of surface roughness on the flow of water. They proposed three different correlations regarding to Ra, Rq, and Rz roughness parameters, to estimate the sand-grain roughness. The authors argue that the direct measurement of surface roughness may not be suitable for fluid flow calculations. The results showed that for relatively small roughness (Rz between 1.5 and 2.5 µm), the corrected Rz value is the best choice among the three proposed correlations. For Rz between 4 and 5 µm, the experimental roughness fell between the corrected Ra and Rz, while for Rz bigger than 15 µm, the corrected Ra performed better.

Del Col et al. (2013) experimentally studied two-phase pressure drop inside minichannels with hydraulic diameters from 0.96 mm to 2 mm, different fluids and relative roughness. They proposed a new liquid-only friction factor and considered the roughness equal to two times the value of the Ra parameter (ε=2Ra). According to them, in the laminar region, the model was not influenced by the relative roughness of the tube; it was only for the transition and turbulent regions.

Rocha (2020) theoretically and experimentally analyzed the flow of CO2 through adiabatic coiled capillary tubes. They developed an algebraic solution and proposed a new equation to estimate the sand-grain roughness. The proposed solution, together with the roughness correlation, predicted the 60 experimental points of mass flow rate with an average deviation (AD) and AAD of 0.1% and 4.4%, respectively.

Several works investigated the effect of surface roughness on fluid flow characteristics through mini/microchannels and ducts, in general. Some of these studies do not recommended the Ra parameter, although it was commonly used (Attalla et al., 2016; Yuan et al., 2016; Mohiuddin Mala and Li, 1999). As a result, correlations to estimate the sand-grain roughness have been proposed. Concerning capillary tubes specifically, it seems that surface roughness is an influential factor in the flow characteristics. However, there is a lack of studies emphasizing and quantifying the impact of changing the surface roughness and choosing different correlations to estimate a proper sand-grain roughness. Therefore, this paper aims to investigate and quantify the surface roughness impact on mass flow rate predictions for adiabatic capillary tube solutions, for straight and coiled shapes, with CO2 and R600a refrigerants. Initially, a survey on some available roughness estimators was summarized, as well as studies with relevant information about the surface roughness of capillary tubes. Then, four roughness parameters measured by stylus profilometry were presented for two different capillary tubes. The roughness estimators, the capillary tube information and the experimental measurements were assessed with algebraic solutions.

Section snippets

The surface roughness of capillary tubes

The conventional approaches used to study capillary tubes are mainly based on numerical models, algebraic solution and dimensionless correlations. In this last technique, the correlations are formed by grouping dimensionless parameters and fitting their coefficients to experimental data. Generally, the surface roughness is not considered in such groups since its effect is considered to be already incorporated on the empirical coefficients. However, they can be employed only within the

Experimental measurements

Sweedyk (1981) reported that depending on the manufacturing process and wall thickness, the surface roughness of capillary tubes can significantly change, which, in turn, affects the refrigerant flow. Hence, it is essential to have actual data to develop reliable theoretical studies. In this sense, the internal surface roughness of two capillary tubes made of copper was measured by stylus profilometry. In this technique, a stylus in contact with the surface to be measured moves at a constant

Algebraic solutions and validation

To identify the impact of altering the capillary tube surface roughness on the mass flow rate predictions, algebraic solutions were used for straight and coiled shapes, with carbon dioxide and R600a. According to de Paula et al. (2020), these two fluids are among the most studied low GWP refrigerants in recent years. For the first refrigerant, the study of Rocha (2020) for transcritical CO2 cycle was adopted. Their solution was developed for coiled capillary tubes and has already been checked

Effect of surface roughness on mass flow rate predictions

Jadhav and Agrawal (2018) presented a brief investigation about the impact of changing the surface roughness in coiled capillary tubes for transcritical CO2 cycle. According to their model, a reduction of 20.5% in ε (from 0.576 to 0.456 µm) caused an increase of only 1.4% on the mass flow rate. An augment of 1.5% was found with the algebraic solution of Rocha (2020), for the same conditions, as seen in Table 5. However, the same percentage change on surface roughness, but with an absolute

Conclusions

In this work, the effect of changing the surface roughness on mass flow rate predictions of CO2 and R600a was evaluated using algebraic solutions for straight and coiled capillary tubes. Correlations to estimate the sand-grain roughness, as well as information on surface roughness of capillary tubes, in theoretical and experimental studies, were summarized. Experimental measurements by stylus profilometry were performed and four roughness parameters for two capillary tubes were presented.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors appreciate the support of FAPEMIG, CNPq, and CAPES for guidance. Specially thank to the PhD student, Diogo Azevedo de Oliveira, who assisted us with the experimental measurements.

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