Equivalent Hydraulic Diameter Research Articles

Opposing Mixed Convection Heat Transfer for Turbulent Single-Phase Flows

Convection, wherein forced and natural convections are prominent, is known as mixed convection. Specifically, when a forced convection flow is downward, this flow is called opposing flow. The objectives of this study are to gain a comprehensive understanding of opposing flow mixed convection heat transfer and to establish the prediction methodology by evaluating existing correlations and models. Several heat transfer correlations have been reported related to single-phase opposing flow; however, these correlations are based on experiments conducted in various channel geometries, working fluids, and thermal flow parameter ranges. Because the definition of nondimensional parameters and their validated range confirmed by experiments differ for each correlation reported in previous studies, establishing a guideline for deciding which correlation should be selected based on its range of applicability and extrapolation performance is important. This study reviewed the existing heat transfer correlations for turbulent opposing flow mixed convection and the single-phase heat transfer correlations implemented in the thermal–hydraulic system codes. Furthermore, the authors evaluated the predictive performance of each correlation by comparing them with the experimental data obtained under various experimental conditions. The Jackson and Fewster, Churchill, and Swanson and Catton correlations can accurately predict all the experimental data. The effect of the difference in the thermal boundary conditions, i.e., uniform heat flux and uniform wall temperature, on the turbulent mixed convection heat transfer coefficient is not substantial. The authors confirmed that heat transfer correlations using the hydraulic-equivalent diameter as a characteristic length can be used for predictions regardless of channel-geometry differences. Furthermore, correlations described based on nondimensional dominant parameters can be used for predictions regardless of the differences in working fluids. The authors investigated the extrapolation performance of the mixed convection heat transfer correlations for a wide range of nondimensional parameters and observed that the Jackson and Fewster, Churchill, and Aicher and Martin correlations exhibit excellent extrapolation performance with respect to natural and forced convection flows, indicating that they can be applied beyond the parameter range validated experimentally.

Study of the structure of yttrium-based nanoporous ceramic materials

Porous ceramic materials with high filtration performance are widely used in conditions of high chemical, thermal and radiation loads. The results of studying the structure and morphology of the pore space of ceramic membranes are presented. Ultradispersed refractory powder Y2O3 was used as a main component-filler. The synthesis was carried out using compaction, technological combustion and self-propagating high-temperature synthesis. The use of ultradisperse sintering additives with highly developed surface (MgO — 5 μm, SiC — 3, SiO2 — 5 μm) allowed us to ensure the energy efficiency of synthesis of high- porous ceramic materials at low temperatures. Analysis of the structure and pore space using mercury porometry and alternative methods showed that the average pore size in the synthesized 3D matrix composite material based on yttrium orthosilicate matrix with yttrium oxide filler is 1.1 μm, the equivalent hydraulic pore diameter being about 100 nm. The difference is attributed to the variability of cross sections and high tortuosity of pore channels. Since the density of the material is 2.3 g/cm3 and the compressive strength is about 2 MPa, it can be easily machined with carbide tools being a promising material for manufacturing products with complex shapes. The obtained results can be used in developing energy-efficient technologies of one-stage production of yttrium oxide-based filters with high porosity to be used under conditions of exposure to radiation, aggressive media and high temperatures.

Study of the effect of the morphology of initial powders on the structural and dimensional characteristics of SiC-based porous ceramic materials

The realization of the necessary energy-efficient technological solutions for the production of highly porous SiC-ceramic materials requires appropriate research. The results of developing energy-efficient one-step methods for the synthesis of porous SiC-based ceramics and studying the characteristics of the obtained ceramics are presented. The effect of the morphology of initial powders on the synthesized product is considered. Ultrafine silicon carbide powders of two types, identical in characteristic particle size, but quite different in the surface morphology, were used as fillers in the synthesis of experimental samples of porous ceramics. The first one was obtained by the traditional furnace method (SiCf), the second one was synthesized by the technology of self-propagating high-temperature synthesis (SiCshs). It is shown that the particle morphology of initial powder components determines the structural parameters and characteristics of synthesized porous ceramics. The pore space parameters (average pore size, specific surface area, equivalent hydraulic diameter, permeability, etc.) can vary significantly. Porous ceramic materials synthesized on the basis of SiCf have an open porosity of 47%, high liquid permeability (up to 2 mDarcy), overwhelming dominance of α-SiC phase, and a narrow pore distribution with an average pore size of about 1 μm. High open porosity (more than 58 %), highly developed nanostructured pore space surface with an area of more than 12 m2/g, and wider pore size distribution (average pore size — 140 nm) are observed in porous ceramic materials based on SiCshs. The obtained results can be used to improve energy-efficient synthesis technologies and methods for predicting the properties of highly porous SiC-based ceramic materials. This will make it possible to create highly porous SiC ceramics within a priory predicted limits of effective applicability for the processes of ultrafiltration or catalysis.

Drift-flux model for upward dispersed two-phase flows in a vertical rod bundle

The present study investigates the drift-flux model for upward dispersed two-phase flows in a vertical rod bundle. The drift-flux model is critical to formulating the interfacial drag force in one-dimensional simulation codes. A rod bundle includes three length scales: a large outer casing width, a medium hydraulic equivalent diameter of a subchannel, and a small gap between rods. Existing research does not provide comprehensive information on an appropriate geometrical length scale for a rod bundle. The present study calculates the evolution process of the drift velocity using the two-bubble-group approach. The two-bubble-group-based formulation is simplified to calculate the drift velocity behavior at the transition between bubbly and beyond-bubbly flows. A scheme is proposed to explicitly calculate the distribution parameter and drift velocity with operating parameters. The new drift-flux correlation is validated by 317 data collected for the pressure from 0.1 to 12 MPa. The extensive evaluation identifies that an appropriate length scale characterizing a two-phase flow in a rod bundle is an outer casing width of a rod bundle. The prediction bias of the new drift-flux correlation was negligibly small, and the random error was 0.0571 in an absolute value measure and 16.1 % in a relative value measure.

Two-phase interfacial structure development in vertical narrow rectangular channels

This study has experimentally investigated flow characteristics of two group bubbles in upward two-phase flows in a vertical narrow rectangular channel with 0.993 mm in gap, 40 mm in width, 2000 mm in height, and 1.94 mm in equivalent hydraulic diameter, Dh. The local measurements are performed at seven axial positions (z/Dh =52, 104, 155, 207, 415, 622, 829 (z: the axial distance from the inlet) using a high-speed camera. The database of the locally evolving parameters has been established by processing the images from the high-speed camera measurements. The measured parameters include the void fraction, interfacial area concentration (IAC), Sauter mean diameter and number density of group-1 and -2 bubbles, and gas-phase velocity of all bubbles. A total of 14 flow conditions are set at four different superficial liquid velocities ranging from 0.214 m/s to 2.08 m/s and different superficial gas velocities ranging from 0.0755 m/s to 1.70 m/s at the inlet. The observed flow regimes cover the bubbly, cap-bubbly, and slug flows. The measured void fraction ranges from 3.92 % to 42.6 %. The axially developing features of the two-phase flows are analyzed for the three flow regimes. Abrupt and gradual axial two-group bubble evolutions with intensive bubble coalescence at the flow regime transition are, respectively, observed at low and high superficial liquid velocity conditions. The newly-obtained experimental database has been used to evaluate the existing two-group interfacial area transport equation (IATE) and its corresponding source and sink models for the two-phase flow in the vertical narrow rectangular channel. Group-1 bubble IAC mean relative error of 21.1% and group-2 bubble IAC mean relative error of 33.4% have been obtained in the evaluations. The existing two-group IATE cannot satisfactorily predict the intensive bubble coalescence and the intragroup transport of the two-group bubbles at the transition from bubbly to slug flow in the vertical narrow rectangular channel. Therefore, it is necessary to improve the existing models of the intergroup and intragroup bubble interactions in the existing two-group IATE in the future.

A First Assessment of an Aerodynamic Barrier Layer for Filtering Airborne Hygroscopic Particles.

In this work, consideration is given to an aerodynamic concept to boost the filtration in face masks of airborne hygroscopic particles such as those caused by an infected person when coughs or sneezes. Nowadays, increasing the filtration efficiency of face masks implies either increasing the number of crisscrossing fiber layers or decreasing the equivalent hydraulic diameter of the pore, however, both measures are in clear detriment of its breathability. Here, a novel strategy is proposed in which the filtration of an airborne particle is boosted by increasing its diameter. We called properly this concept as the aerodynamic barrier layer. In this concept, a traditional crisscrossing fiber layer is replaced by a parallel rearranged of the fibers in the direction of the flow. This rearrangement will promote central lift forces which will push the particles toward the center of the channel where after clustering they will coalesce resulting in a bigger particle that can be now easily captured by a conventional fiber crisscrossing layer. Utilizing a simplified geometrical model, an expression for the required length of the aerodynamic barrier layer was derived. It is shown that an aerodynamic barrier layer with a length of only a few millimeters can aerodynamically focus water droplets around 1 μm-diameter and the penetration of airborne particles can be reduced up to 55%.

Experimental and numerical investigation on heat transfer of supercritical water flowing upward in 2 × 2 rod bundles

This paper presents the investigation of heat transfer of supercritical water flowing upward in 2 × 2 rod bundles, both experimentally and numerically. The experiment conditions are as follows: pressures from 22.9 MPa to 26.1 MPa, mass fluxes ranging from 450 kg/m2/s to 1500 kg/m2/s and heat fluxes ranging from 0.4 MW/m2 to 1.5 MW/m2. Four heated-rods of 8 mm outer diameter formed 2 set of experiment sections with pitch to diameter ratio (P/D ratio) 1.18 and 1.3. Heat transfer coefficients between the heated rod and fluid were conducted by 3 different methods and the effect of spacer grids was clearly observed. The experiment results show that heat transfer to supercritical water in rod bundles is strongly affected by flow channels and spacer grids. Moreover, a large database of heat transfer in rod bundles was carried out and HTC were compared with tube and annuli with the equivalent hydraulic diameter. The phenomenon of heat transfer difference in rod bundle circumferential direction and enhancement heat transfer in downstream of spacer grids were observed and investigated. In addition, Computational Fluid Dynamics (CFD) method was applied to give a deep insight of velocity profile, spacer effect and heat transfer enhancement in this research.

Permeating behaviour of porous SiC ceramics fabricated with different SiC particle sizes

Permeating behaviour is one of the most important factors of porous ceramics used for gas/liquid filters or membrane/catalysis supporters. Insufficient research has reported on the effect of raw particle size on permeating behaviour and the relationship between particle size and pore size of fabricated porous ceramics. In this work, porous SiC ceramics were fabricated with raw SiC particles of different grit designations and the effect of particle size on the permeating behaviour and equivalent pore size of the resulting porous ceramics were investigated. Due to oxidation of the SiC particles during the firing process, resulting materials with finer raw particles exhibited higher mass gain and lower bulk and true density. When the grit designation changed from 2000# to 120#, the strength of the resulting materials declined, and the Darcy permeability k1 increased from 6.65 × 10−15 to 4.85 × 10−13 m2. The ratio of the hydraulic equivalent diameter of pores to raw particle size in the resulting materials decreased from 0.25 to 0.11, indicating that the hydraulic equivalent pore size did not increase proportionally with the particle size increase. Further measures should be employed to enlarge pore size in porous ceramics to enhance its permeability.

Nuclear policy-nuclear fuels for peaceful, safer co-generation and environmentally benign applications

Here, safer nuclear fuels which can sustain in the high temperature and fluence environment of the reactor core are investigated to utilize nuclear energy peacefully. At Nuclear Fuel Complex in Hyderabad, nuclear fuels are being manufactured which are best suited for high temperature and fluence environment of the reactor core even in accidental scenarios. In this paper, nuclear fuels manufactured at NFC, Hyderabad are presented. The developed nuclear fuels have higher equivalent hydraulic diameter and breeding capability to produce U^233. Nuclear fuels having higher equivalent hydraulic diameter reduce the reactor core temperature substantially. These fuels have negative temperature coefficient of reactivity. Thus, in case of an accident, the fuel temperature never exceeds the safety limit. Therefore, the thermal heat available across the secondary of a heat exchanger can be utilized for different industrial processes. This allows the development of key technologies, such as safer co-generation of electricity and Hydrogen. The Three-Stage Indian Nuclear Power Program has been explained for nuclear disarmament. The product Hydrogen gas has been utilized in many ways for different applications. Moreover, the processing of iron ore with the energy obtained from the IHX secondary side, eliminates the burning of coals and CO2 emissions into the environment. Several radioisotopes have been developed for medical applications from spent fuel.

Heat Transfer From Elliptic Cylinder Immersed In A Fluidized Bed

In the present work, heat transfer characteristics and flow field from a heated elliptic cylinder immersed in fluidized bed is studied numerically using CFD package. The flow pattern and heat transfer fields around the heated cylinder is predicted using a two fluid Eulerian-Eulerian model coupled with kinetic theory of granular flow (KTGF) with heat transfer. Runs were carried out under uniform heat flux condition, with air as a fluidizing gas and pulverized coal as a bed material. The Reynolds number based on the equivalent cylinder hydraulic diameter, Dh, was ranged from 941to 1263. The simulation results of the present study showed that, for the range of gas velocity considered, at minimum fluidization velocity, Re = 914, the Nuθ is maximum at the sides of the cylinder and minimum at the stagnation, θ=0o, and top, θ=180o, of the cylinder. The average Nusselt number for the elliptic cylinder increases with the increase of the fluidization velocity. The present data is compared with a previous well-known correlation from the literature for a circular cylinder and a reasonable deviation is found.

Experimental study of the effect of ullage height on flame characteristics of pool fires

A series of experiments were carried out to investigate the effect of ullage height, i.e. the distance between fuel surface and the pool upper rim, on flame characteristics of heptane and ethanol pool fires. The pool diameters included 10 cm, 15 cm, and 20 cm. For each pool, ullage height was increased from zero to the value that the flame self-extinguished. During each test, the ullage height was kept constant by a fuel level maintaining device. Results show that ullage height has a significant effect on flame characteristics. When the ullage height equals zero, there is a stable conical structure near the pool upper rim, above which the unstable plume develops. Under lower ullage height conditions, plume puffing happens. The unstable plume begins to initiate around the pool upper rim, then rolling and expanding upward. At the same time, its beneath flame is stretched thinner and thinner and eventually breaks from the bulk. When the ullage height further increases, plume puffing becomes less evident. While for the mass loss rate, it generally decreases with the increase of h/D. It was proved in literature that the previous flame height model is inapplicable to pool fires with large ullage height. In this paper, to consider the effect of ullage height on plume flow structures, an equivalent hydraulic diameter, Deq., is proposed to establish one new flame height correlation. By comparing previous model predictions with the current experimental data, it is found that conventional flame oscillation models are unsuitable to pool fires with large ullage height. Based on Deq., two new dimensional and dimensionless flame oscillation models were proposed according to the current experimental data. The correlated flame height model and proposed flame oscillation models were validated and agreed well with reference data.

Non-Newtonian Effects on Gas-Liquid Slug Flow in Micro-channel with T-junction Mixer

The length of liquid slug and gas bubble, gas bubble velocity and pressure drop of gas-liquid two-phase flow in a rectangular channel were measured using a high speed camera and a different pressure transducer. Water and Glycerol-solution as Newtonian liquids and Sodium carboxymethyl cellulose, Xanthan gum and Polyacrylamide-water solution as non-Newtonian liquids were used as the liquid phase, and N2 gas was used as the gas phase. The equivalent hydraulic diameter of the rectangular channel was 0.51 mm. The measured pressure drop data were compared with unit cell model, which applied to gas bubble pressure drop prediction proposed by Kurimoto et al. (2017). The following conclusions were obtained: (1) Different flow pattern was observed only in Polyacrylamide-water solution. (2) Frictional pressure drop on two-phase flow can associate with an effective viscosity of liquid. (3) Effects of elasticity of liquid on non-Newtonian two-phase two-phase flow should be accounted to predict accurately pressure drop.

Fractal-Like Flow-Fields with Minimum Entropy Production for Polymer Electrolyte Membrane Fuel Cells

The fractal-type flow-fields for fuel cell (FC) applications are promising, due to their ability to deliver uniformly, with a Peclet number Pe~1, the reactant gases to the catalytic layer. We review fractal designs that have been developed and studied in experimental prototypes and with CFD computations on 1D and 3D flow models for planar, circular, cylindrical and conical FCs. It is shown, that the FC efficiency could be increased by design optimization of the fractal system. The total entropy production (TEP) due to viscous flow was the objective function, and a constant total volume (TV) of the channels was used as constraint in the design optimization. Analytical solutions were used for the TEP, for rectangular channels and a simplified 1D circular tube. Case studies were done varying the equivalent hydraulic diameter (Dh), cross-sectional area (DΣ) and hydraulic resistance (DZ). The analytical expressions allowed us to obtain exact solutions to the optimization problem (TEP→min, TV=const). It was shown that the optimal design corresponds to a non-uniform width and length scaling of consecutive channels that classifies the flow field as a quasi-fractal. The depths of the channels were set equal for manufacturing reasons. Recursive formulae for optimal non-uniform width scaling were obtained for 1D circular Dh -, DΣ -, and DZ -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for Dh -, DΣ -, and DZ -based 1D models (Cases 4-6). As a reference case, Murray’s law was used for circular (Case 7) and rectangular (Case 8) channels. It was shown, that Dh-based models always resulted in smaller cross-sectional areas and, thus, overestimated the hydraulic resistance and TEP. The DΣ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The DZ -based models fitted best to the 3D CFD data. All optimal geometries exhibited larger TEP, but smaller TV than those from Murray’s scaling (reference Cases 7,8). Higher TV with Murray’s scaling leads to lower contact area between the flow-field plate with other FC layers and, therefore, to larger electric resistivity or ohmic losses. We conclude that the most appropriate design can be found from multi-criteria optimization, resulting in a Pareto-frontier on the dependencies of TEP vs TV computed for all studied geometries. The proposed approach helps us to determine a restricted number of geometries for more detailed 3D computations and further experimental validations on prototypes.

Investigation of the relationship between fractal and hydraulic properties of porous structures of the upper respiratory tract of some Arctic animals

The respiratory ducts of animals and humans are presented by curved tubes with complex geometries. The open areas in such structures are filled with moving air governed by a pressure drop between the inlet and outlet of the duct. The complex structures formed by thin walls and warmed by constant blood flow at the body temperatures T=36-39 C serve for fast and efficient warming of the inhaled air to the body temperature and its moistening up to 100% humidity. The Arctic animals possess the most efficient nasal ducts allowing the heating of the inhaled air from T=-30-60C to T=38-39 C during the duct with the length L=8-15 only. The detailed geometry of the nasal ducts of some Arctic animal has been studied on the computed tomograms (CT) scans of the heads of the animals found in the open databases and published in literature. The highly porous structures on some slices are formed by fractal-like divisions of the walls protruded into the nasal lumen. Since the fractal structures are characterized by their fractal dimensions D, the relationships between the hydrodynamic properties and fractal dimensions of the porous structures of the upper respiratory tract of some Arctic animals has been studied. The dimensions D of the cross sections of the tract have been calculated by the counting box method. The porosities of the samples, the tortuosity of the pores, and the equivalent hydraulic diameter Dh of the channel have been calculated. Sierpinski fractals of various types have been used as models of porous structures, for which the above listed parameters, as well as hydraulic resistance to a stationary flow, have also been computed. A number of statistical dependencies between the calculated parameters were revealed, but the absence of their correlations with D was shown. It was obtained, the structures with different porosities and hydraulic resistance Dh can have the same values ​​of D. Therefore, the choice of an adequate model based on only D value introduces significant errors in the calculations of air heating along the upper respiratory tract. The statistical dependences inherent in the natural samples studied can be obtained only on the basis of multifractal models in which the number and shape of the channels, as well as the scale of their decrease, change in a certain way at each generation.

Experimental investigation of flow and heat transfer characteristics on matrix ribbed channel

The effect of the rib width to height ratio t/e and width to pitch ratio t/p on the local heat transfer distribution in a rectangular matrix ribbed channel with two opposite in line 45? ribs are experimentally investigated for Reynolds numbers from 54000 to 150000. The rib height to channel height ratio e/H is 0.5, t/p and t/e both varies in range of 0.3-0.5. To simulate the actually situation in turbine blades, and provide useful direct results for turbine blade designers, the parameters are same with the blade. The experiments results show that, in comparison to fully developed flow in a smooth pipe of equivalent hydraulic diameter, the Nusselt number inside the matrix-ribbed rectangular channel is increased up to 5 to 9 times higher, while total pressure drop is enlarged by up to significant magnitude. The Nusselt number ratio increases with t/p and t/e increased. Semi-empirical heat transfer is developed for designing of cooling channel.

Numerical Study of Heat Transfer from Elliptic Tube in a Fluidized Bed

In the present work, heat transfer characteristics and flow field from a heated elliptic cylinder immersed in fluidized bed is studied numerically using CFD package. The flow pattern and heat transfer fields around the heated cylinder is predicted using a two fluid Eulerian-Eulerian model coupled with kinetic theory of granular flow (KTGF) with heat transfer. Experiments were carried out under uniform heat flux condition, with air as a fluidizing gas and pulverized coal as a bed material. The Reynolds number based on the equivalent hydraulic diameter, Dh, was ranged from 941to 1263. The simulation results of the present study showed that, for the range of gas velocity considered, at minimum fluidization velocity, Re = 914, the Nuθ is maximum at the sides of the cylinder and minimum at the stagnation, θ=0o, and top, θ=180o, of the cylinder. The average Nusselt number for the elliptic cylinder increases with the increase of the fluidization velocity. The present data is compared with a previous well-known correlation from the literature for a circular cylinder and a reasonable deviation about 11-30% is found.

Numerical Analysis of the Effect of Fire Source Configuration on Fire-Wind Enhancement

Detailed investigation of fire-wind interaction is highly instrumental in understanding the cause of the devastating consequences of major fire events in windy weather conditions. Enhancement of wind downstream of the fire source is a phenomenon caused by fire-wind interaction. The main objective of this study is to compare the behavior of wind enhancement for fire of either line or point sources under similar wind and heat release rate conditions. This paper uses the OpenFOAM platform as a numerical simulation tool to fundamentally investigate fire-wind enhancement phenomenon in both point and line source of the fire. A module has been developed and implemented in the FireFOAM solver to extract different components of fire-induced longitudinal and vertical forces. A new parameter expressed as an equivalent hydraulic diameter of line fire sources was introduced to represent the non-dimensional bushfire intensity. The results indicate that under the same intensity of heat release rate per unit area, enhancement of longitudinal wind in line fire is significantly higher than that of the point fire source. On the other hand, the fire-induced vertical velocity of point source fire is higher than that of the line source case.

Experimental study on the flow boiling oscillation characteristics in a rectangular multiple micro-channel

Multiple micro-channels can be used as heat sink components of many electronic devices due to high heat transfer capacity. In this paper, the flow boiling oscillation characteristics of a multiple micro-channel test section made of six rectangular micro-channels with an equivalent hydraulic diameter of 526.2 μm were experimentally studied. The experiments were operated with heat flux qeff 11.58–99.56 kW/m2, mass flux G 20.40–107.04 kg/m2·s and inlet temperature Tin = 55 °C. The flow pattern evolution process in the multiple micro-channel was visually studied and analyzed. Also, the pressure drop characteristics of the multiple micro-channel test section and two individual channels of the multiple micro-channel were measured and studied with time domain and frequency domain analyses, and the relationship between amplitude-frequency characteristics of test section pressure drop and qeff/G under typical working conditions was gained. The results showed that under oscillation conditions different flow pattern evolution modes may occur for different micro-channels due to the coupling effects of inertial force, the evaporation momentum, heating wall etc. During boiling, reverse flow of bubbles could be observed, and liquid may also be pushed upstream by the bubbles. The differences of oscillation waveform, frequency, phase position as well as the interaction effects of individual channels were found to get smaller with an increase of outlet equilibrium quality. Based on the amplitude-frequency characteristics, five flow boiling patterns were identified as boiling developed, i.e. the single phase pattern, the boiling onset pattern, the reverse flow onset pattern, the reverse flow infecting pattern, and the complete reverse flow pattern. The boundaries of the flow boiling patterns were very clear from a view of oscillation amplitude-frequency characteristics, and it was found that the boundaries can be roughly determined with parameter qeff/G.

Transient behavior of a plate-fin-and-tube heat exchanger taking into account different heat transfer coefficients on the individual tube rows

Plate-fin and tube heat exchangers (PFTHE) are made of round, elliptical, oval or flat tubes to which continuous fins ( lamellas) are attached. Liquid flows inside the tubes and gas flows outside the tubes perpendicularly to their axes and parallel to the surface of continuous fins. Experimental studies of multi-row plate-fin and tube heat exchangers show that the highest average heat transfer coefficient on the air side occurs in the first row of tubes when the air velocity in front of the exchanger is less than approximately 3.5 m/s when a Reynolds number based on an equivalent hydraulic diameter equal to the distance between tube rows in the direction of air flow is less than 10,000. In the subsequent rows of tubes up to about the fourth row the heat transfer coefficient decreases. In the fifth and further rows, it can, that the heat transfer coefficient is equal in each tube row. It is necessary to find the relationships for the air-side Nusselt number on each tube row to design a PFTHE with the appropriate number of tube rows. The air-side Nusselt number correlations can be determined experimentally or by CFD modeling (Computational and Fluid Dynamics). The paper presents a new mathematical model of the transient operation of PFTHE, considering that the Nusselt numbers on the air side of individual tube rows are different. The heat transfer coefficient on an analyzed tube row was determined from the equality condition of mass- average air temperature differences on a given tube row determined using the analytical formula and CFD modeling. The results of numerical modeling were compared with the results of the experiments.

One-dimensional drift-flux correlation for vertical upward two-phase flow in a large size rectangular channel

The study of two-phase flow in rectangular channels is of great importance due to their use in marine reactors, chemical reactors, test reactors, and neutron spallation sources. Due to the practical importance of the drift-flux correlation for two-phase flow analysis in industrial systems, distribution parameter and drift velocity have been studied for vertical upward two-phase flow in a large size rectangular channel. Due to the presence of liquid recirculation in the bubbly flow regime in large size rectangular channels, the distribution parameter, drift velocity, and flow regime transition criteria are different from those found in small or medium size rectangular channels. The use of hydraulic equivalent diameter as the characteristic length scale in channels with significant asymmetry and its effect on interfacial area concentration prediction are also discussed. Under these considerations a new drift-flux correlation has been developed for upward two-phase flow in large size rectangular channels. Comparison of the newly developed correlation with several datasets shows reasonable agreement.