CFD modelling of momentum and heat transfer using the Large Eddy Simulation (LES) approach has been presented for a Kenics static mixer. The simulations were performed with the commercial code ANSYS Fluent 15 for turbulent flow of three values of Reynolds number, Re = 5 000, 10 000 and 18 000. The numerical modelling began in the RANS model, where standard k−ε turbulence model and wall functions were used. Then the LES iterations started from the initial velocity and temperature fields obtained in RANS. In LES, the Smagorinsky–Lilly model was used for the sub-grid scale fluctuations along with wall functions for prediction of flow and heat transfer in the near-wall region. The performed numerical study in a Kenics static mixer resulted in highly fluctuating fields of both velocity and temperature. Simulation results were presented and analysed in the form of velocity and temperature contours. In addition, the surface-averaged heat transfer coefficient values for the whole insert length were computed and compared with the literature experimental data. Good compliance of the LES simulation results with the experimental correlation was obtained.
Geometry of plate heat exchangers (PHE) is characterized by a complex net of narrow channels. It enhances turbulence and results in better heat transfer performance. Theoretically, larger number of channels (plates) should proportionally increase the PHE heat power capacity. In practice a nonuniform massflow distribution in consecutive flow channels can significantly deteriorate the overall heat exchange performance. The flow maldistribution is one of the most commonly reported exploitation problems and is present in PHE with and without phase-change flows. The presented paper investigates numerically a flow pattern in PHE with evaporation of R410A refrigerant. Various sizes of PHE are considered. The paper introduces a robust methodology to transform the complicated geometry of a real 3D PHE to its 2D representation. It results in orders of magnitude faster calculations and allows for fast evaluation of different geometrical changes of PHE and their effect on flow maldistribution.
Helical coil heat exchangers are widely used in a variety of industry applications such as refrigeration systems, process plants and heat recovery. In this study, the effect of Reynolds number and the operating temperature on heat transfer coefficients and pressure drop for laminar flow conditions was investigated. Experiments were carried out in a shell and tube heat exchanger with a copper coiled pipe (4 mm ID, length of 1.7 m and coil pitch of 7.5 mm) in the temperature range from 243 to 273 K. Air – propan-2-ol vapor mixture and coolant (methylsilicone oil) flowed inside and around the coil, respectively. The fluid flow in the shell-side was kept constant, while in the coil it was varied from 6.6 to 26.6 m/s (the Reynolds number below the critical value of 7600). Results showed that the helical pipe provided higher heat transfer performance than a straight pipe with the same dimensions. The convective coefficients were determined using theWilson method. The values for the coiled pipe were in the range of 3–40 W/m2 ·K. They increased with increasing the gas flow rate and decreasing the coolant temperature.
Flow boiling and flow condensation are often regarded as two opposite or symmetrical phenomena. Their description however with a single correlation has yet to be suggested. In the case of flow boiling in minichannels there is mostly encountered the annular flow structure, where the bubble generation is not present. Similar picture holds for the case of inside tube condensation, where annular flow structure predominates. In such case the heat transfer coefficient is primarily dependent on the convective mechanism. In the paper a method developed earlier by the first author is applied to calculations of heat transfer coefficient for inside tube condensation. The method has been verified using experimental data from literature on several fluids in different microchannels and compared to three well established correlations for calculations of heat transfer coefficient in flow condensation. It clearly stems from the results presented here that the flow condensation can be modeled in terms of appropriately devised pressure drop.
The paper describes issues related to pressure drop that accompanies the phenomenon of maldistribution of working fluid between the channels of a model minichannel plate heat exchanger. The research concerns a single exchanger’s plate containing 51 (in every geometry) parallel rectangular minichannels of hydraulic diameters 461 μm, 571 μm, 750 μm, and 823 μm. In addition, more complex geometry has been investigated, equipped with additional diagonal channels (so called extended geometry). The moment of the liquid phase transition through the heat exchanger was recorded at the flow rates ranging from 0.83 g/s to 13.33 g/s in the inlet manifold. The paper discusses the total pressure drop as a function of the flow rate and the characteristic dimension of minichannels, as well as the pressure drop as a function of the time of the fluid passage through the main part of the measuring section in which measurements were done. The resulting profiles correlate with the images of the flow distribution between channels recorded using the fast shutter speed camera, that allows to draw a further conclusions about the specifics of the maldistribution process. The impact of the total pressure drop on the actual range of optimum operating conditions of the heat exchanger was analyzed.
General principles of mathematical modelling of transient heat transfer in cross-flow tube heat exchangers with complex flow arrangements which allow a simulation of multipass heat exchangers with many tube rows are presented. First, a system of differential equations for the transient temperature of both fluids and the tube wall with appropriate boundary and initial conditions is formulated. Two methods for modelling heat exchangers are developed using the finite difference method and finite volume method. A numerical model of multipass steam superheater with twelve passes is presented. The calculation results are compared with the experimental data.
In the paper presented are the issues related to the design and operation of micro heat exchangers, where phase changes can occur, applicable to the domestic micro combined heat and power (CHP) unit. Analysed is the stability of the two-phase flow in such unit. A simple hydraulic model presented in the paper enables for the stability analysis of the system and analysis of disturbance propagation caused by a jump change of the flow rate. Equations of the system dynamics as well as properties of the working fluid are strongly non-linear. A proposed model can be applicable in designing the system of flow control in micro heat exchangers operating in the considered CHP unit.
The combined effect of conjugation, external magnetic field and oscillation on the enhancement of heat transfer in the laminar flow of liquid metals between parallel plate channels is analyzed. In order to make our results useful to the design engineers, we have considered here only the wall materials that are widely employed in liquid metal heat exchangers. Indeed, all the results obtained through this mathematical investigation are in excellent agreement with the available experimental results. The effective thermal diffusivity κ_e is increased by 3×10^6 times due to oscillation and that the heat flux as high as 1.5×10^10 (W/m^2) can be achieved. Based on our investigation, we have recommended the best choice of liquid metal heat carrier, wall material and its optimum thickness along with the optimum value of the frequency to maximize the heat transfer rate. At the optimum frequency, by choosing a wall of high thermal conductivity and optimum thickness, an increase of 19.98% in κ_e can be achieved. Our results are directly relevant to the design of a heat transfer device known as electromagnetic dream pipe which is a very recent development.
The production of thermal energy from solar energy by flat collectors finds nowadays many applications due to their innumerable economic and environmental interests. Currently, conservation of energy resources has become a global priority. On the other hand, given the dizzying demand for energy, has led specialists to find new techniques, such as renewable energies (solar, wind and geothermal). The present work is a contribution, by numerical simulation, to the study of heat transfer in flat solar collectors. On the basis of some experimental data, several simulation calculations have been carried out in order to determine the influencing parameters allowing better performance of the sensors and ensuring a good homogeneity of the temperature distributions. Based on the observation that, due to the low thermophysical properties of the air used as heat transfer fluid, solar air collectors rather give poor yields. It has been found very useful to have ‘baffling’ obstacles of various shapes and forms in the solar collector duct. This increases the thermal transfer of a coolant, which clearly improves the thermal efficiency of the solar air collector. This article consists mainly of studying the effects on heat transfer of turbulent forced convection by baffles of zigzag shapes, placed in a rectangular channel, using the finite volume method. The pressure-velocity coupling has been processed by the SIMPLEC algorithm. The results are presented in terms of the average Nusselt number and temperature field for different positions.
Analysis of the state of-the-art in research of minichannel heat exchangers, especially on the topic of flow maldistribution in multiple channels, has been accomplished. Studies on minichannel plate heat exchanger with 51 parallel minichannels with four hydraulic diameters, i.e., 461 μm, 574 μm, 667 μm, and 750 μm have been presented. Flow at the instance of filling the microchannel with water at low flow rates has been visualized. The pressure drop characteristics for single minichannel plate have been presented along with the channels blockage, which occurred in several cases. The impact of the mass flow rate and channels’ cross-section dimensions on the flow maldistribution were illustrated.
In this work, numerical modeling of steady state heat and mass transfer is presented. Both laminar and hydrodynamically fully developed turbulent flow in a pipe are shown. Numerical results are compared with values obtained from analytical solution of such problems. The problems under consideration are often denoted as extended Graetz problems. They occur in heat exchangers using liquid metals as working fluid, in cooling systems for electric components or in chemical process lines. Calculations were carried out gradually decreasing the mesh size in order to examine the convergence of numerical method to analytical solution.
In the paper presented are the results of calculations using authors own model to predict heat transfer coefficient during flow boiling of carbon dioxide. The experimental data from various researches were collected. Calculations were conducted for a full range of quality variation and a wide range of mass velocity. The aim of the study was to test the sensitivity of the in-house model. The results show the importance of taking into account the surface tension as the parameter exhibiting its importance in case of the flow in minichannels as well as the influence of reduced pressure. The calculations were accomplished to test the sensitivity of the heat transfer model with respect to selection of the appropriate two-phase flow multiplier, which is one of the elements of the heat transfer model. For that purpose correlations due to Müller-Steinhagen and Heck as well as the one due to Friedel were considered. Obtained results show a good consistency with experimental results, however the selection of two-phase flow multiplier does not significantly influence the consistency of calculations.
The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.
The paper presents experimental studies on boiling heat transfer in rectangular minichannels. The investigations focus on the transition from single phase forced convection to nucleate boiling, i.e., in the zone of boiling incipience. The experiment has been carried out with FC-72, R-123 and R-11 at the Reynolds number below 4700, corresponding to mass flow rate range 95-710 kg/(m s). The main part of the test section is a minichannel of pre-set depth from 0.7 to 2 mm and width (20, 40 and 60 mm), with different spatial orientations from vertical to horizontal and 30% inclination angle adjustment. The objective of the paper includes the impact of selected parameters (liquid flow velocity, pressure and inlet liquid subcooling, channel dimensions and spatial orientation) on the boiling incipience in minichannels. The investigations are intended to develop a correlation for the calculations of the Nusselt number under the conditions of boiling incipience in the minichannel as a function of changeable parameters.
Miniature heat exchangers are used to provide higher cooling capacity for new technologies. This means a reduction in their size and cost but the identical power. The paper presents the method for determination of boiling heat transfer coefficient for a rectangular minichannel of 0.1 mm depth, 40 mm width and 360 mm length with asymmetric heating. Experimental research has focused on the transition from single phase forced convection to nucleate boiling, i.e., the zone of boiling incipience. The ‘boiling front’ location has been determined from the temperature distribution of the heated wall obtained from liquid crystal thermography. The experiment has been carried out with R-123, mass flux 220 kg/(m2s), pressure at the channel inlet 340 kPa. Local values of heat transfer coefficient were calculated on the basis of empirical data from the experiment following the solution of the two-dimensional inverse heat transfer problem. This problem has been solved with the use of the finite element method in combination with Trefftz functions. Temperature approximates (linear combinations of Trefftz functions) strictly fulfill the governing equations. In presented method the inverse problem is solved in the same way as the direct problem. The results confirmed that considerable heat transfer enhancement takes place at boiling incipience in the minichannel flow boiling. Moreover, under subcooling boiling, local heat coefficients exhibit relatively low values.
The production of thin-walled castings with wall thickness in the range of 1.5 to 3 mm and below requires the development of insulation moulding sands and/or core materials. The test has been taken to develop these kind of materials. The study included a description of their thermophysical properties. Authors described problems related to the heat flow in the casting-mould system, i.e. mathematically described the main dependence of heat give-up during crystallization of the casting. The influence of the content of polyglicol on the thermophysical properties of the mould with gypsum and cement binder was examined. Using the ATD method determined were the increments ΔT1 and ΔT2 describing the temperature changes in the mould during crystallization of hypoeutectic alloy of AlSi6 and the temperature difference between casting material and mould during the crystallization. In the considered range of technological parameters a description of the heat flow kinetics was given.
The work deals with experimental and numerical thermodynamic analyses of cross-flow finned tube heat exchangers of the gas-liquid type. The aim of the work is to determine an impact of the gas non-uniform inlet on the heat exchangers performance. The measurements have been carried out on a special testing rig and own numerical code has been used for numerical simulations. Analysis of the experimental and numerical results has shown that the range of the non-uniform air inlet to the considered heat exchangers may be significant and it can significantly affect the heat exchanger efficiency.
Cu–4.7 wt. % Sn alloy wire with Ø10 mm was prepared by two-phase zone continuous casting technology, and the temperature field, heat and fluid flow were investigated by the numerical simulated method. As the melting temperature, mold temperature, continuous casting speed and cooling water temperature is 1200 °C, 1040 °C, 20 mm/min and 18 °C, respectively, the alloy temperature in the mold is in the range of 720 °C–1081 °C, and the solid/liquid interface is in the mold. In the center of the mold, the heat flow direction is vertically downward. At the upper wall of the mold, the heat flow direction is obliquely downward and deflects toward the mold, and at the lower wall of the mold, the heat flow deflects toward the alloy. There is a complex circular flow in the mold. Liquid alloy flows downward along the wall of the mold and flows upward in the center.
The main task of mathematical modelling of thermal and flow processes in vertical ground heat exchanger (BHE-Borehole Heat Exchanger) is to determine the unit of borehole depth heat flux obtainable or transferred during the operation of the installation. This assignment is indirectly associated with finding the circulating fluid temperature flowing out from the U-tube at a given inlet temperature of fluid in respect to other operational parameters of the installation. The paper presents a model of thermal and flow processes in BHE consisting of two analytical models separately-handling processes occurring inside and outside of borehole. A quasi-three-dimensional model formulated by Zeng was used for modelling processes taking place inside the borehole and allowing to determine the temperature of the fluid in the U-tube along the axis of BHE. For modelling processes occurring outside the borehole a model that uses the theory of linear heat source was selected. The coupling parameters for the models are the temperature of the sealing material on the outer wall of the borehole and the average heat flow rate in BHE. Experimental verification of the proposed model was shown in relation to BHE cooperating with a heat pump in real conditions.
This paper presents the results of studies in two phase gasliquid flow around tube bundle in the model of shell tube heat exchanger. Experimental investigations of heat transfer coefficient on the tubes surface were performed with the aid of electrochemical technique. Chilton-Colburn analogy between heat and mass transfer was used. Twelve nickel cathodes were mounted on the outside surface of one of the tubes. Measurement of limiting currents in the cathodic reduction of ferricyanide ions on nickel electrodes in aqueous solution of equimolar quantities of K3Fe(CN)6and K4Fe(CN)6in the presence of NaOH basic solution were applied to determine the mass transfer coefficient. Controlled diffusion from ions at the electrode was observed and limiting current plateau was measured. Measurements were performed with data acquisition equipment controlled by software created for this experiment. Mass transfer coefficient was calculated on the basis of the limiting current measurements. Results of mass transfer experiments (mass transfer coefficient) were recalculated to heat transfer coefficient. During the experiments, simultaneously conducted was the the investigation of two-phase flow structures around tubes with the use of digital particle image velocimetry. Average velocity fields around tubes were created with the use of a number of flow images and compared with the results of heat transfer coefficient calculations.
Nowadays, the energy cost is very high and this problem is carried out to seek techniques for improvement of the aerothermal and thermal (heat flow) systems performances in different technical applications. The transient and steady-state techniques with liquid crystals for the surface temperature and heat transfer coefficient or Nusselt number distribution measurements have been developed. The flow pattern produced by transverse vortex generators (ribs) and other fluid obstacles (e.g. turbine blades) was visualized using liquid crystals (Liquid Crystal Thermography) in combination with the true-colour image processing as well as planar beam of double-impulse laser tailored by a cylindrical lens and oil particles (particle image velocimetry or laser anemometry). Experiments using both research tools were performed at Gdańsk University of Technology, Faculty of Mechanical Engineering. Present work provides selected results obtained during this research.
In this work we investigate the present capabilities of computational fluid dynamics for wall boiling. The computational model used combines the Euler/Euler two-phase flow description with heat flux partitioning. This kind of modeling was previously applied to boiling water under high pressure conditions relevant to nuclear power systems. Similar conditions in terms of the relevant non-dimensional numbers have been realized in the DEBORA tests using dichlorodifluoromethane (R12) as the working fluid. This facilitated measurements of radial profiles for gas volume fraction, gas velocity, bubble size and liquid temperature as well as axial profiles of wall temperature. After reviewing the theoretical and experimental basis of correlations used in the ANSYS CFX model used for the calculations, we give a careful assessment of the necessary recalibrations to describe the DEBORA tests. The basic CFX model is validated by a detailed comparison to the experimental data for two selected test cases. Simulations with a single set of calibrated parameters are found to give reasonable quantitative agreement with the data for several tests within a certain range of conditions and reproduce the observed tendencies correctly. Several model refinements are then presented each of which is designed to improve one of the remaining deviations between simulation and measurements. Specifically we consider a homogeneous MUSIG model for the bubble size, modified bubble forces, a wall function for turbulent boiling flow and a partial slip boundary condition for the liquid phase. Finally, needs for further model developments are identified and promising directions discussed.
The paper presents the results of experimental research of pressure drop and heat transfer coefficients of ice slurry during its flow through tubes of rectangular and slit cross-sections. Moreover, the work discusses the influence of solid particles, type of motion and cross-section on the changes in the pressure drop and heat transfer coefficient. The analysis presented in the paper allows for identification of the criterial relations used to calculate the Fanning factor and the Nusselt number for laminar and turbulent flow, taking into account elements such as phase change, which accompanies the heat transfer process. Ice slurry flow is treated as a generalized flow of a non-Newtonian fluid.