laminar and turbulent flow in pipes pdf creator

Laminar and turbulent flow in pipes pdf creator

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Numeric and experimental analysis of the turbulent flow through a channel with baffle plates. Demartini; H.

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In this study, single-phase heat transfer enhancement in internally finned tubes is investigated numerically. The influence of fin number, helix angle, fin height, fin width, and shape on the flow and heat transfer characteristics is studied. The research results indicate that the resistance coefficient and Nusselt number both increase with the increment of these parameters, among which the helix angle has the largest impact on the heat transfer enhancement. In addition, the shape of fins also has a small effect on the flow and heat transfer, and the heat transfer effect of triangular fins is the best.

Single-phase convection heat transfer enhancement techniques are widely applied in industries such as petroleum, chemical engineering, etc. In recent years, its applications in the field of nuclear technology has been an engaging research area of heat transfer augmentation. In order to strengthen the single-phase convection heat transfer technology, many heat exchanger elements have been developed, the internally finned tube is one of them.

Ji et al. Much work has been done to investigate the heat transfer characteristics of internally finned tubes in condensation Seo and Kim, ; Kim et al. The internally finned tube has high requirements for water quality, and the working fluid is required to be clean enough with almost no impurities, otherwise they may affect the heat transfer performance. Compared with other heat exchanger elements, the tremendous advantage of internally finned tubes is that its heat transfer effect is greater than the increase of pressure drop.

Generally, this effect can be seen in turbulent state, but neither the enhancement of heat transfer nor that of pressure drop is obvious in laminar state, thus they are recommended to be used in turbulent flow Al-Fahed et al. Previous experimental studies have been carried out on single-phase flow of different working media to investigate the influence of different geometrical sizes fin height, fin width, helix angle, diameter, fin number on the heat transfer characteristics.

Wang et al. Han and Lee studied the single-phase heat transfer and flow characteristics of water in four internally finned tubes with different diameters, fin heights, helix angles and fin pitchs experimentally, and developed correlations for friction factor and heat transfer coefficients.

Jensen and Vlakancic carried out experimental studies on turbulent flow in eight internally finned tubes with different geometrical parameters of helix angles, fin heights, fin numbers and fin widths, they obtained the correlations between friction coefficient and Nusselt number.

Later Zdaniuk et al. Empirical correlations for one particular internally finned tubes was developed by Siddique and Alhazmy through experimental research. And a critical Reynolds number R e cr was discovered by Li et al. Friction formula was also developed by Celen et al. Due to the limitations of manufacturing and experimental conditions, only a few tubes with specific geometrical parameters have been studied in previous experiment research, so it is difficult to obtain the detailed and comprehensive heat transfer characteristics in different tubes.

There are only a few numerical studies on the heat transfer characteristics of internally finned tubes. Agra et al. Their results also indicated that the internally finned tube has a higher heat transfer coefficient than the corrugated tube. Celen et al. Dastmalchi et al. They concluded that there is an optimal height and an optimal helix angle which leads to the maximum performance of heat transfer. The foregoing literatures indicate that a comprehensive study on the flow and heat transfer characteristics considering a wide range of parameters including fin number, helix angle, fin height, fin width and shape of fins remains to be conducted.

Influence of geometric parameters on characteristics of heat transfer could be implemented with modern visualization techniques and computational fluid dynamics CFD tools. Therefore, the purpose of the study is to conduct a comprehensive numerical study on the factors affecting the heat transfer efficiency of the internally finned tubes. The fins are uniformly distributed in circumferential direction and along the axis with the same helix angle, so they are periodic in geometric structure.

The cross section is shown in Figure 1. Using the periodicity of the internally finned tube and taking one pitch of the fully developed segment as the computational domain, the difficulty of grid generation is greatly reduced. The established model is shown in Figure 1.

In order to determine a proper grid for the numerical simulations, a grid independence study is carried out for the smooth and internally finned tubes. A section of circular tube with a diameter of 20 mm and a length of 20 mm is taken as the computing domain, and meshing is used to generate grids. The mesh number chosen in this paper is the minimum of the mesh number that does not affect the simulation results.

When the number of grids is lower than a certain value, the change of the number of grids will have an impact on the simulation results. The larger the number of grids, the closer to the stable result. When the number of grids is higher than a certain value, the encrypted grid will have no impact on the simulation results. As shown in Figures 2A,B , the grid of smooth tube is made by independence verification.

Figure 2. Grid distribution and volume grid quality of heat transfer tube. A Smooth tube. B Internally finned tube. Realizable k-epsilon model satisfies the constraint conditions of Reynolds stress, so it can be consistent with the real turbulence at Reynolds stress.

This is something neither the standard k-epsilon model nor the RNG k-epsilon model can do. The advantage of this feature in the calculation is that it can more accurately simulate the diffusion velocity of plane and circular jets.

Meanwhile, in the calculation of rotating flow, boundary layer with directional pressure gradient and separation flow, the calculation results are more in line with the real situation. The Realizable k-epsilon model is a newly emerging k-epsilon model, and although its performance has not been proven to be superior to the RNG k-epsilon model, studies on separated flow calculations and complex flow calculations with secondary flows show that the Realizable k-epsilon model is the most excellent turbulence model among all the models.

Given the advantages of the Realizable k-epsilon model, this paper chooses this model for calculation. The enhanced wall treatment is selected to obtain the detailed flow condition near the tube wall.

In the two-layer zone model, the near-wall flow can only be divided into two regions, namely the region affected by viscosity and complete turbulence.

The two regions are distinguished by Re y based on the distance y to the wall. Based on the pressure drop value per unit length obtained, the average f can be calculated using Darcy formula:. Based on the difference between the average wall temperature and the average fluid temperature, the average Nusselt number can be calculated:.

For forced convection heat transfer in smooth circular tubes, the resistance coefficient can be calculated using the Filonenko formula Filonenko, :. The nussel number can be calculated according to the Gnielinski Gnielinski, formula:. The selected grid scheme is used for verification. The comparison results with the classical experimental formula are shown in Figures 3A,B. The calculated values of f and Nu are compared with the values of Filonenko formula Filonenko, and Gnielinski formula Gnielinski, , respectively.

It can be seen that the calculated value of the resistance coefficient and the Nusselt number are in good agreement with the theoretical value. The maximum error between the calculated value and the theoretical value of the resistance coefficient is 6. The maximum error between the calculated value and the theoretical value of nusserl number is The maximum error occurs in the lower Reynolds number region.

The results show that the application of periodic boundary conditions and the established calculation model are correct and can accurately simulate the turbulent flow and heat transfer in the tube. Figure 3. Comparison between the calculated value and the theoretical value in smooth tubes. In this section, the effect of fin number, fin height, fin width, helix angle and the shape of fins on the heat transfer characteristics of internally finned tube are studied.

Figure 4 shows the effect of the fin number on the Nu and f at different helix angles. The fin height and fin width are fixed at 0. It can be seen that the Nu and f both increase with the augment of the fin number and helix angle.

Figure 4. The effect of the fin number on the Nu and f at different helix angles. Table 1 shows the variation of the increment of heat exchange area with fin number and the helix angle. Here the increment of heat exchange area is defined as:. It can be seen that the rate at which Nu increases is bigger than the increase speed of heat exchange area and f, which indicates that the enhancement effect of heat transfer is greater than the increase of resistance and heat transfer area. Table 1. Increment of heat exchange area under different fin number and helix angle.

Figure 5 shows the velocity cloud diagram and temperature cloud diagram of internally finned tubes with fin number of 15, 30, and It can be seen that at the sharp corners of the windward side, the wall is the most strongly impacted by the fluid, the boundary layer is the thinnest, and the velocity gradient is the largest, so a great shear stress is generated which means that there is a great loss of energy.

Meanwhile, the corresponding fluid temperature is the lowest, and the heat transfer convection is the strongest. As the fin number increases, the number of sharp corners increase, resulting in an increase in both f and Nu. Along with the increase of fin number, the intercostal region decreases accordingly, the fluid viscosity of the intercostal channel increases, which reduces the fluid velocity of fin root and surface, thickens boundary layer, and inhibits the heat transfer.

Figure 5. The velocity cloud diagram and temperature cloud diagram with different fin numbers. Figure 6 shows the changes of Nu and f with the fin height under different helix angles. The fin number is 30, the fixed fin width is 0.

It can be seen that the Nu and f both increase with the augment of the fin height, as it not only increases the heat transfer area on both fin sides, but also promotes the interactions between the fin top. Figure 6. The effect of the fin height on the Nu and f at different helix angles. Table 2 shows the changes of heat exchange area with the fin height and helix angle.

Nu and f both increase with fin height, because the higher the fin height, the greater the disturbance to the fluid near the wall surface.

Therefore, the heat transfer coefficient is enhanced and the resistance coefficient is increased. Increasing the spiral angle will further enhance the heat transfer and the resistance. Table 2. Increment of heat exchange area under different fin height and helix angle. The increment of the fin height increases the interaction between fins and fluid, resulting in rapid increase in f and Nu. Generally, the fin width has a complex effect on the flow and heat transfer in internally finned tubes.

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In dispersed two-phase flows, the particle size is probably the most important parameter in determining the particle dynamics. Interphase forces, heat and mass transfers are all functions of the particle diameter. Diameters of the particles are unlikely to be uniform and for droplets and bubbles they can change continuously due to breakup and coalescence. Methods of moments have been used very successfully in modeling particle size distributions in dispersed two-phase flows. The model described in this paper is based on the method of moment. It contains models for droplet breakup and coalescence. For coalescence, the model considers the probability of collisions of the droplets, the contact time of two colliding drops and the drainage time of the liquid film between the drops.

In physics and engineering , fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids — liquids and gases. It has several subdisciplines, including aerodynamics the study of air and other gases in motion and hydrodynamics the study of liquids in motion. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft , determining the mass flow rate of petroleum through pipelines , predicting weather patterns , understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines —that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity , pressure , density , and temperature , as functions of space and time.


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1 comments

  • Policarpo A. 08.05.2021 at 16:15

    For a pipe or duct the characteristic length is the hydraulic diameter.

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