Frictional Pressure Drop Correlations Research Articles

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.

New experimental approach on the determination of condensation heat transfer coefficient using frictional pressure drop and void fraction models in a vertical tube

The comparison of 35 void fraction and 13 two-phase frictional pressure drop models and correlations with experimental results for the condensation of R134a in a 0.5 m vertical copper tube with an inner diameter of 8.1 mm and outer diameter of 9.52 mm are presented. The most predictive ones having a relation with the heat transfer coefficient at different vapor qualities (0.69–0.96), various mass fluxes (260 and 515 kg m −2 s −1), and different condensing temperatures (40 and 50 °C) are proposed. Three of 13 models belonging to the determination of two-phase frictional pressure drop and 8 of 35 models belonging to the determination of void fraction are found to be in good agreement, predicting the condensation heat transfer coefficient by means of von Karman’s universal velocity distribution and Kosky–Staub’s annular flow film thickness model with their deviations being within the range of ±30% for all tested conditions.

Flow condensation pressure drop characteristics of R410A–oil mixture inside small diameter horizontal microfin tubes

Flow condensation pressure drop characteristics of R410A–oil mixture inside small diameter (5.0 mm and 4.0 mm O.D.) horizontal microfin tubes were investigated experimentally covering nominal oil concentrations from 0% to 5%. The research results indicate that, comparing with the frictional pressure drop of pure R410A, the frictional pressure drop of R410A–oil mixture may decrease by maximum of 18% when the vapor quality is lower than 0.6, and increase by maximum of 13% when the vapor quality is higher than 0.6. A new frictional pressure drop correlation for R410A–oil mixture flow condensation inside microfin tubes is developed based on the refrigerant–oil mixture properties, and can agree with 94% of the experimental data within a deviation of −30% to +30%.

Answer to comments by M.M. Awad on “Measurement and correlation of frictional two-phase pressure drop of R410A/POE oil mixture flow boiling in a 7mm straight micro-fin tube”

Answer to comments by M.M. Awad on “Measurement and correlation of frictional two-phase pressure drop of R410A/POE oil mixture flow boiling in a 7mm straight micro-fin tube”

Correlations of two-phase frictional pressure drop and void fraction in mini-channel

Alternative correlations of two-phase friction pressure drop and void fraction are explored for mini-channels based on the separated flow model and drift-flux model. By applying the artificial neural network, dominant parameters to correlate the two-phase friction multiplier and void fraction are picked out. It is found that in mini-channels the non-dimensional Laplace constant is a main parameter to correlate the Chisholm parameter as well as the distribution parameter. Both previous correlations and the newly developed correlations are extensively evaluated with a variety of data sets collected from the literature.

Measurement and correlation of frictional pressure drop of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube

The objective of this paper is to investigate the effect of nanoparticle on the frictional pressure drop characteristics of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube, and to present a correlation for predicting the frictional pressure drop of refrigerant-based nanofluid. R113 refrigerant and CuO nanoparticle were used for preparing refrigerant-based nanofluid. Experimental conditions include mass fluxes from 100 to 200 kg m −2 s −1, heat fluxes from 3.08 to 6.16 kW m −2, inlet vapor qualities from 0.2 to 0.7, and mass fractions of nanoparticles from 0 to 0.5 wt%. The experimental results show that the frictional pressured drop of refrigerant-based nanofluid increases with the increase of the mass fraction of nanoparticles, and the maximum enhancement of frictional pressure drop is 20.8% under above conditions. A frictional pressure drop correlation for refrigerant-based nanofluid is proposed, and the predictions agree with 92% of the experimental data within the deviation of ±15%.

Frictional pressure drop during vapour–liquid flow in minichannels: Modelling and experimental evaluation

Condensation in minichannels is widely used in air-cooled condensers for the automotive and air-conditioning industry, in heat pipes and other applications for system thermal control. The knowledge of pressure drops in such small channels is important in order to optimize heat transfer surfaces. This paper presents a model for calculation of the frictional pressure gradient during condensation or adiabatic liquid–gas flow inside minichannels with different surface roughness. In order to account for the effects of surface roughness, new experimental frictional pressure gradient data associated to single-phase flow and adiabatic two-phase flow of R134a inside a single horizontal mini tube with rough wall has been used in the modelling. It is a Friedel (1979) [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: Proceedings of the European Two-Phase Flow Group Meeting, Ispra, Paper E2] based model and it takes into account mass velocity, vapor quality, fluid properties, reduced pressure, tube diameter, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, it has been built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and mist flow are here predicted. However, the suggested procedure is extended to the intermittent flow in minichannels and it is also applied with success to horizontal macro tubes.

Adiabatic Horizontal and Vertical Pressure Drop of Carbon Dioxide Inside Smooth and Microfin Tubes at Low Temperatures

This paper presents the pressure drop data and the analysis of adiabatic CO2 flow in horizontal and vertical smooth and microfin tubes at saturation temperatures around −20°C. The test tubes had 3.48mm inner diameter smooth tube and a 3.51mm melt-down diameter microfin tube. The test was performed over a mass flux range of 200–800kg∕m2s and at saturation temperatures of −25°C and −15°C. The effects of various parameters—mass flux, saturated temperature, and tube diameter—on pressure drop were qualitatively analyzed. The analyses showed that the frictional pressure drop characteristics of vertical two-phase flow were much different from that of the horizontal two-phase flow. The microfin tube can be considered as “very rough tube” having the roughness of “fin height.” The data were compared with several correlations. The existing frictional pressure drop correlation is sufficient to predict the horizontal pressure drop in smooth tube. For the vertical pressure drop, the simple combination of the frictional pressure drop and void fraction model was in comparatively good agreement. However, the qualitative results showed that there were some limits to cover the different mechanisms related to the interfacial shear stress. The average enhancement factors and penalty factors evidenced that it was not always true that the internally finned geometry guaranteed the superior in-tube condensation performance of microfin tube in refrigeration system and air-conditioning systems.

Measurement and Correlation of Frictional Pressure Drop of R-410A/Oil Mixture Flow Boiling in a 7 mm Straight Smooth Tube

Two-phase frictional pressure drop characteristics of an R-410A/oil mixture flow boiling inside a straight, smooth tube with an outside diameter of 7.0 mm were investigated experimentally. Experimental parameters include an evaporation temperature of 5°C, mass fluxes from 200 to 400 kg/(m2·s), heat fluxes from 7.56 to 15.12 kW/m2, inlet vapor qualities from 0.2 to 0.7, and nominal oil concentrations from 0% to 5%. The test results show that frictional pressure drop of an R-410A/oil mixture increases with the mass flux, the presence of oil enhances two-phase frictional pressure drop, and the effect of oil on frictional pressure drop is found to be more evident at higher vapor qualities where the local oil concentrations are higher. A new correlation to predict the local frictional pressure drop of an R-410A/oil mixture flow boiling inside a straight, smooth tube is developed based on the local properties of the refrigerant/oil mixture, and it agrees with 92% of the experimental data within a deviation of ±15%.

Experimental investigation and correlation of two-phase frictional pressure drop of R410A–oil mixture flow boiling in a 5 mm microfin tube

This study presents experimental two-phase frictional data for R410A-oil mixture flow boiling in an internal spiral grooved microfin tube with outside diameter of 5 mm. Experimental parameters include the evaporation temperature of 5 °C, the mass flux from 200 to 400 kg m −2 s −1, the heat flux from 7.46 to 14.92 kW m −2, the inlet vapor quality from 0.1 to 0.8, and nominal oil concentration from 0 to 5%. The test results show that the frictional pressure drop of R410A initially increases with vapor quality and then decreases, presenting a local maximum in the vapor quality range between 0.7 and 0.8; the frictional pressure drop of R410A–oil mixture increases with the mass flux, the presence of oil enhances two-phase frictional pressure drop, and the effect of oil on frictional pressure drop is more evident at higher vapor qualities where the local oil concentrations are higher. The enhanced factor is always larger than unity and increases with nominal oil concentration at a given vapor quality. The range of the enhanced factor is about 1.0–2.2 at present test conditions. A new correlation to predict the local frictional pressure drop of R410A-oil mixture flow boiling inside the internal spiral grooved microfin tube is developed based on local properties of refrigerant–oil mixture, and the measured local frictional pressure drop is well correlated with the empirical equation proposed by the authors.

Measurement and correlation of frictional two-phase pressure drop of R410A/POE oil mixture flow boiling in a 7 mm straight micro-fin tube

Two-phase frictional pressure drop characteristics of R410A/POE oil mixture flow boiling inside a straight micro-fin tube with the outside diameter of 7.0 mm were investigated experimentally. Experimental parameters include the evaporation temperature of 5 °C, the mass flux from 200 to 400 kg/(m 2 s), the heat flux from 7.56 to 15.12 kW/m 2, the inlet vapor quality from 0.2 to 0.7, and nominal oil concentration from 0% to 5%. The test results show that frictional pressure drop of R410A/POE oil mixture increases with the mass flux, the presence of oil enhances two-phase frictional pressure drop, and the effect of oil on frictional pressure drop is more evident at higher vapor qualities where the local oil concentrations are higher. New correlations to predict the local frictional pressure drop of R410A/POE oil mixture flow boiling inside the straight micro-fin tube are developed based on local properties of refrigerant–oil mixture, and the measured local frictional pressure drop is well correlated with the empirical correlations proposed by the authors.

Heat transfer and pressure drop during HFC refrigerant vaporisation inside a brazed plate heat exchanger

This paper presents the experimental heat transfer coefficients and pressure drop measured during HFC refrigerant 134a, 410A and 236fa vaporisation inside a small brazed plate heat exchanger: the effects of heat flux, refrigerant mass flux, saturation temperature, outlet conditions and fluid properties are investigated. The experimental results are reported in terms of refrigerant side heat transfer coefficients and frictional pressure drop. The heat transfer coefficients show great sensitivity to heat flux and outlet conditions and weak sensitivity to saturation temperature. The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow. HFC-410A shows heat transfer coefficients 40–50% higher than HFC-134a and 50–60% higher than HFC-236fa and frictional pressure drops 40–50% lower than HFC-134a and 50–60% lower than HFC-236fa. The experimental heat transfer coefficients are compared with two well-known equations for nucleate boiling [M.G. Cooper, Heat flows rates in saturated pool boiling – a wide ranging examination using reduced properties, Advanced Heat Transfer, Academic Press, Orlando, Florida, 1984, pp. 157–239; D. Gorenflo, Pool boiling, in: E.U. Schlünder (Ed.), VDI Heat Atlas, Dusseldorf, Germany, 1993, Ha1-25] and a correlation for frictional pressure drop is proposed.

An experimental study of flow pattern and pressure drop for flow boiling inside microfinned helically coiled tube

In this paper, flow patterns and their transitions for refrigerant R134a boiling in a microfinned helically coiled tube are experimentally observed and analyzed. All the flow patterns occurred in the test can be divided into three dominant regimes, i.e., stratified-wavy flow, intermittent flow and annular flow. Experimental data are plotted in two kinds of flow maps, i.e., Taitel and Dukler flow map and mass flux versus vapor quality flow map. The transitions between various flow regimes and the differences from that in smooth straight tube have also been discussed. Martinelli parameter can be used to indicate the transition from intermittent flow to annular flow. The transition from stratified-wavy flow to annular or intermittent flow is identified in the vapor quality versus mass flux flow map. The flow regime is always in stratified-wavy flow for a mass flux less than 100 kg/m 2 s. The two-phase frictional pressure drop characteristics in the test tube are also experimentally studied. The two-phase frictional multiplier data can be well correlated by Lockhart–Martinelli parameter. Considering the corresponding flow regimes, i.e., stratified and annular flow, two frictional pressure drop correlations are proposed, and show a good agreement with the respective experimental data.

HFC-410A vaporisation inside a commercial brazed plate heat exchanger

This paper experimentally investigates HFC-410A vaporisation inside a commercial brazed plate heat exchanger: the effects of heat flux, refrigerant mass flux, saturation temperature and outlet conditions are evaluated. The experimental results are reported in terms of refrigerant side heat transfer coefficients and frictional pressure drop. The heat transfer coefficients show great sensitivity to heat flux and outlet conditions and weak sensitivity to saturation temperature. The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow and therefore a quadratic dependence on the refrigerant mass flux. The experimental heat transfer coefficients are compared with two well-known equations [Cooper, M.G., Heat flows rates in saturated pool boiling – a wide ranging examination using reduced properties, in: J.P. Hartnett, T.F. Irvine Jr. (Eds.), Advanced in Heat Transfer, Academic Press, Orlando, FL, 1984, pp. 157–239; D. Gorenflo, D. Pool boiling, in: E.U. Schlünder (Ed.), VDI Heat Atlas, Dusseldorf, Germany, 1993 (Ha1-25).] for nucleate boiling and a correlation for frictional pressure drop is proposed.

Refrigerant R134a vaporisation heat transfer and pressure drop inside a small brazed plate heat exchanger

This paper presents the experimental heat transfer coefficients and pressure drop measured during refrigerant R134a vaporisation inside a small brazed plate heat exchanger (BPHE): the effects of heat flux, refrigerant mass flux, saturation temperature and outlet conditions are investigated. The BPHE tested consists of 10 plates, 72 mm in width and 310 mm in length, which present a macro-scale herringbone corrugation with an inclination angle of 65° and corrugation amplitude of 2 mm. The experimental results are reported in terms of refrigerant side heat transfer coefficients and frictional pressure drop. The heat transfer coefficients show great sensitivity both to heat flux and outlet conditions and weak sensitivity to saturation temperature. The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow. The experimental heat transfer coefficients are also compared with two well-known correlations for nucleate pool boiling and a correlation for frictional pressure drop is proposed.

1802 細管内気液二相流の伝熱・流動特性とその相関関係(G06-1 伝熱(1),G06 熱工学)

Heat transfer, pressure drop and void fraction were simultaneously measured for upward heated air-water two-phase flow in about 4 and 0.5mm I.D. tubes to investigate the analogy between heat transfer and fluid friction of two-phase flow in small diameter tubes. In the case of 4mm I.D., Void fraction agreed with the Armand's correlation, but it took the lower value in the case of 0.5mm I.D.. When the liquid superficial velocity j_l was very low, frictional pressure drop agreed with the empirical correlation of Mishima-Hibiki for small diameter tube, whereas agreed well with Chisholm-Laird correlation when j_l was relatively large. Heat transfer coefficients agreed with frictional pressure drop correlations of Chisholm-Laird except when j_l was very low for 4mm I.D. tube.

CO 2 and R410A flow boiling heat transfer, pressure drop, and flow pattern at low temperatures in a horizontal smooth tube

Flow boiling heat transfer coefficient, pressure drop, and flow pattern are investigated in the horizontal smooth tube of 6.1 mm inner diameter for CO 2, R410A, and R22. Flow boiling heat transfer coefficients are measured at the constant wall temperature conditions, while pressure drop measurement and flow visualization are carried out at adiabatic conditions. This research is performed at evaporation temperatures of −15 and −30 °C, mass flux from 100 to 400 kg m −2 s −1, and heat flux from 5 to 15 kW m −2 for vapor qualities ranging from 0.1 to 0.8. The measured R410A heat transfer coefficients are compared to other published data. The comparison of heat transfer coefficients for CO 2, R410A, and R22 is presented at various heat fluxes, mass fluxes, and evaporation temperatures. The difference of coefficients for each refrigerant is explained with the Gungor and Winterton [K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer 29 (1986) 351–358] correlation based on the thermophysical properties of refrigerants. The Wattelet et al. [J.P. Wattelet, J.C. Chato, B.R. Christoffersen, J.A. Gaibel, M. Ponchner, P.J. Kenny, R.L. Shimon, T.C. Villaneuva, N.L. Rhines, K.A. Sweeney, D.G. Allen, T.T. Heshberger, Heat Transfer Flow Regimes of Refrigerants in a Horizontal-tube Evaporator, ACRC TR-55, University of Illinois at Urbana-Champaign, 1994], and Gungor and Winterton [K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer 29 (1986) 351–358] correlations give the best agreement with the measured heat transfer coefficients for CO 2 and R410A. Pressure drop for CO 2, R410A, and R22 at various mass fluxes, evaporation temperatures and qualities is presented in this paper. The Müller-Steinhagen and Heck [H. Müller-Steinhagen, K. Heck, A simple friction pressure drop correlation for two-phase flow in pipes, Chem. Eng. Process. 20 (1986) 297–308], and Friedel [L. Friedel, Improved friction pressure correlations for horizontal and vertical two-phase pipe flow, in: The European Two-Phase Flow Group Meeting, Ispra, Italy, 1979 (paper E2)] correlation can predict most of the measured pressure drop within the range of ±30%. The relation between pressure drop and properties for each refrigerant is described by applying the Müller-Steinhagen and Heck correlation. The observed two-phase flow patterns for CO 2 and R410A are presented and compared with flow pattern maps. Most of the flow patterns can be determined by the Weisman et al. [J. Weisman, D. Duncan, J. Gibson, T. Crawford, Effect of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines, Int. J. Multiphase Flow 5 (1979) 437–462] flow pattern map.

Study of vapor liquid two-phase frictional pressure drop in a vertical heated spirally internally ribbed tube

Experiments of vapor liquid two-phase frictional pressure drop of upward flow boiling in a smooth tube and in a spirally internally ribbed tube were conducted, respectively. The spirally internally ribbed tube has an outside diameter of 22 mm and an inside diameter of 11 mm (an equivalent inside diameter of 11.6 mm) and the smooth tube has an outside diameter of 19 mm and an inside diameter of 15 mm. The test tubes were vertically installed and uniformly heated by electricity to achieve flow boiling test conditions. The available heated length of both test tubes is 2500 mm. The working fluids are water and kerosene, respectively. The experimental pressure is 6 bar for flow boiling of water and 3 bar for flow boiling of kerosene. The exit vapor quality of the test sections is about 0.3. The two-phase Reynolds number ranges from 8000 to 28,000. The experimental two-phase frictional pressure drops in the smooth tube are compared with the predicted results by the two-phase flow homogeneous model and the Friedel formula (Friedel, 1979. Improved friction pressure drop correlation for horizontal and vertical two-phase pipe flow. European Two-phase Flow Group Meeting, Ispra, Italy), respectively. It shows that the experimental results agree with the Friedel formula better than the two-phase flow homogenous model. By comparison, the two-phase frictional pressure drops in the spirally internally ribbed tube are 1.6–2.7 times greater than that in the smooth tube. A physical explanation of the increase of the two-phase frictional pressure drop in the spirally internally ribbed tube is given. According to the two-phase flow homogeneous model, a correlation of two-phase friction factor is proposed for the spirally internally ribbed tube and it is applicable to pressures up to 6 bar.

Experimental study on two-phase flow and pressure drop in millimeter-size channels

The present paper provides considerable insight into the structure of two-phase flow as well as its characteristics inside mini- and micro-channels. A new test facility was designed and constructed to investigate the two-phase flow regimes and pressure drop in mini- and micro-channels. The two-phase frictional pressure drop measurements and flow regimes experiments were performed with three different test sections, which are 3 mm, 1 mm, and 800 μm in diameter. The experimental pressure drop data was compared with the homogenous model, the Friedel [L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow, Paper E2, European Two-Phase Group Meeting, Ispra, Italy, 1979] model, and the Chisholm [D. Chisholm, A theoretical basis for the Lockhart Martinelli Correlation for two-phase flow, Int. J. Heat Mass Transfer, 10, 1967, pp. 1767–1778] model, in order to determine their validity range in mini- and micro-channel flows. The homogenous model and the Chisholm [D. Chisholm, A theoretical basis for the Lockhart Martinelli Correlation for two-phase flow, Int. J. Heat Mass Transfer, 10, 1967, pp. 1767–1778] model showed the most similarities with the data acquired for the 1 mm and 0.8 mm test sections, while the Friedel [L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow, Paper E2, European Two-Phase Group Meeting, Ispra, Italy, 1979] model over-predicted the pressure drop for every test section. The two-phase flow patterns were observed for high gas superficial velocities ( U GS ⩾ 10 m/s) using a 3CCD analog camera, and comparisons were made with the existing flow regime maps. The present data, as well as the available data in literature, were used to develop a simplified flow regime map for horizontal micro-channels. The flow regimes in this map were separated into surface-tension-dominated regimes and inertia-dominated regimes. The regimes were named bubbly, intermittent, churn and annular. The intermittent flow regime regroups all slug and plug flows, as well as all the transition flows occurring in the vicinity of the intermittent region. It was found that the simplified transition lines provide a good approximation of the regime transitions for all existing studies within the allowable range of the map.

Two-phase pressure drop in a horizontal thin annulus: Effects of channel vibration and wall gas injection

Two-phase pressure drop in a narrow horizontal annular test section was experimentally investigated, using air and water as the working fluids. The annular test section had inner and outer diameters of 7.93 mm and 9.53 mm, respectively. In one group of tests (constant quality tests) air and water were mixed before entering the test section. In another group (variable quality tests), gas was injected into the test section via the porous inner test section wall. The liquid Reynolds number varied in the Re L = 50–9000 range, and the test section exit qualities covered the 0–25% range. The measured total pressure drops were compared with the predictions of a one-dimensional model with several two-phase frictional pressure drop correlations. The pressure variations caused by flow acceleration were calculated based on the homogeneous flow assumption. The correlation of Beattie and Whalley [D.R.H. Beattie, P.B. Whalley, A simplified two-phase frictional pressure drop prediction method, Int. J. Multiphase Flow 18 (1982) 83–87] agreed reasonably well with results of both groups of tests. The effect of lateral mechanical vibrations, imposed at the center of the test section, on two-phase pressure drop was also studied, with vibration amplitudes in the 0.034–0.2 mm range, and frequencies in the range 5–400 Hz. These effects were generally small.