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• The process of melting-reconsolidation of the frost layer is considered. • Improvement of the existing Eulerian multiphase flow model of frost formation. • The whole process of frost layer growth under prolonged periods of time was studied. • Changes of ice-phase volume fraction and melt-reconsolidation region with time are discussed. Frost growth is a complex heat and mass transfer process, which involves the vapor-liquid-solid three-phase interconversion problem, and the investigation of the frost growth process helps to understand the mechanism of frost growth. In this paper, frost model is considered, taking into account the role of the frost layer melting-reconsolidation. The aim is to improve the existing Eulerian multiphase flow model. Using the improved frost model, the whole process of the frost layer growth is simulated. In addition, an investigation is presented dealing with, the frost layer growth in various stages of the ice phase volume fraction and melting-reconsolidation area, considering the change and the proportion of the situation. The results showed that the volume fraction of the ice phase increased with time. Additionally, the melting-reconsolidation process starts from the front area of the frost layer surface and then gradually spreads to the whole surface. Moreover, it is shown that the proportion of the melting area increases and then decreases with time before attaining a constant value. On the other hand, the proportion of the solidifying area increases with time and finally tends to 0. [ABSTRACT FROM AUTHOR]

Particles in the environment not only threaten people's health, but the adhesion of particles on the equipment also threatens the safe operation of the equipment and the adhesion of particles in the heat exchange field also causes a large amount of energy waste. In this paper, the transportation and deposition processes of particles with different particle sizes were studied by numerical simulation. A random function method is introduced to improve the particle deposition model in order to consider the different characteristics between clean and fouled surfaces. As an example, the particle deposition characteristics of a two-dimensional channel were simulated using the clean surface model, fouling layer model, and random function method. The results show that as the particle size and inlet velocity increase, the gap between the three models increase. In particular, in the simulation of mixed particle size, the random function method better simulates the change in deposition rate during formation of fouling layer and the composition of fouling layer. Furthermore, the growth of the fouling was accelerated by the first layer of sediments, and the first layer of the sediments usually consisted of small particles. • The deposition of particle can cause changes in the physical properties of the sedimentary surface. • The particle deposition slowly in the initial stage and gradually accelerates with fouling layer formation. • The inner layer of the fouling is small particles, and the outer layer is mainly composed of large particles. • Preventing the deposition of small particles is the key to prevent deposition. [ABSTRACT FROM AUTHOR]

Highlights • A numerical simulation method is used to study the deposition of gas-side fly ash particles on heating surface. • The critical deposition velocity is calculated by user-defined function. • Effects of velocities and particle diameters on the deposition efficiency of each wall are analyzed. • The simulation results are compared with experimental data to verify the rationality. • For large particle, the floor exhibits the largest particles deposition efficiency. Abstract The flue gas of the coal-fired boiler is composed of a great number of fly ash particles. Such particles may easily form ash deposition on the heating surface of the heat exchanger when recovering the wasted heat energy from the flue gas. Here, we study the deposition of gas-side fly ash particles on the heating surface in a three-dimensional rectangular heat transfer channel by a numerical simulation method. First, the critical deposition velocity is calculated using the user-defined function (UDF) and the deposition process of the ash particles are simulated using the discrete phase model (DPM). Then, the rationality of the proposed method is verified by comparing the simulation results with the experimental data. In addition, we investigate the effects of the inlet velocities and particle diameters on the deposition efficiency of each wall of the rectangular channel. The results show that the particle deposition efficiency of different locations of the channel, i.e., the floor, the two sidewalls, and the ceiling, may be varied by the changing the particle diameter and the flow velocity. Moreover, we show that for a large particle, the ceiling and sidewalls, respectively, the first and second lowest particles deposition efficiency, while the floor exhibits the largest particles deposition efficiency. [ABSTRACT FROM AUTHOR]

Abstract Use of passive vortex generators (VGs) is an efficient heat-transfer enhancement technique, which utilizes a special type of extended surface that mainly generates vortices parallel to the flow direction to not only improve the heat transfer performance of the heat exchangers, but also prevent the formation of fouling. In order to study the growth characteristics of fouling on the rectangular channel with different VGs, three types of VGs with the same frontal area were used in the present study and the deposition process of calcium sulfate (CaSO 4) fouling was studied by numerical simulation method. First, the effects of the changes in inlet velocity from 0.5 to 0.8 m/s, concentration of CaSO 4 from 2.0 to 3.5 kg/m3, and surface temperature from 320 to 350 K on fouling characteristics were investigated. Then, the Performance Evaluation Criterion (PEC) was used to evaluate the heat transfer characteristics and fouling characteristics on a channel with different types of VGs. The results showed that the fouling resistance of the three types of VGs followed the same trend. The value of asymptotic fouling resistance decreased with the increase of the velocity, and increased with the increase of the concentration and surface temperature, respectively. For the rectangular channels with three different types of VGs, when the flow resistance was taken into account, the Performance Evaluation Criterion with fouling (PEC f) of the half-cylinder VG was found to be the best among the three different types of VGs. [ABSTRACT FROM AUTHOR]

Highlights • Heat transfer enhancement in a channel with VGs with and without a hole. • The rectangular VGs with a hole can effectively decrease the flow resistance. • Effect of the hole diameter and position of the rectangular VGs with a hole. • Simulated results were validated based on the experimental date and formula data. Abstract Vortex generators (VGs) can enhance the heat transfer of the channel, but it can also cause a certain pressure loss. In order to decrease the flow resistance of VGs, the VGs with a punched hole was proposed. In this research, three-dimensional numerical simulations of VGs are performed to analyze the heat transfer enhancement and the flow resistance in a rectangular channel with two-row rectangular vortex generators with and without a hole at the Re from 214 to 10,703. The heat transfer enhancement and the pressure drop are described by using the dimensionless factors Colburn factor j , friction factor f , and thermohydraulic performance factor PEC = j /(f)1/3. Then, the effects of the hole diameter and the hole position were investigated. The results show that the values of PEC in the rectangular vortex generators with a hole are larger than those in the rectangular vortex generators without a hole. Through the analysis of the values of PEC , j and f , the optimal diameter of the hole is determined as d = 5 mm. In the vertical direction, the PEC increases with the increase of c and has the maximum value at c = 4.5 mm. In the lateral direction, the PEC first increases and then decreases slightly and has the maximum value at e = 18 mm. [ABSTRACT FROM AUTHOR]

The vortex generators (VGs) are among the most popular actuators for the heat transfer enhancement of heat exchangers. Using pure water as the working fluid, the characteristics of heat transfer and flow resistance in a rectangular channel with novel types of VGs were studied numerically at the Reynolds number range of Re = 8900–29,900. Five types of VGs with the same frontal area were used in the present study and the corresponding mechanism of heat transfer was analyzed. The heat transfer enhancement and flow resistance were examined by using the dimensionless parameters j / j 0 , f / f 0 , R = ( j / j 0 )/( f / f 0 ), and R ∗ = Nu c / Nu 0 . The results revealed that, when the thermohydraulic performance factor R and Performance Evaluation Criterion R ∗ were considered as the comprehensive evaluation criteria, the half-cylinder VG was the best. Then the effects of arrangement, length, radius, and spacing of the half-cylinder VGs on the heat transfer and flow resistance were investigated. When the half-cylinder VGs were arranged along the side-lined row, the thermohydraulic performance factor R was the largest. With the increase in the generator length, the thermohydraulic performance factor R increased at first and then decreased, and exhibited the maximum value at A / B = 0.50. With the increase in the radius and decrease of the spacing, the thermohydraulic performance factor R decreased. [ABSTRACT FROM AUTHOR]

The ash deposition problem majorly affects the stability, safety, and economy of industrial production processes. To investigate the transient ash deposition characteristics of the flue gas flowing across a tube, the Eulerian multiphase model combined with a dynamic mesh technique is first used in this work. The deposition and the removal processes are both taken into account. Four deposition mechanisms are considered in the deposition process, including Brownian and eddy diffusion, gravity, thermophoretic, and turbophoretic forces. Based on the experimental verification results, it is found that the Eulerian multiphase model combined with a dynamic mesh technique can more accurately predict the ash deposition behavior. The overall fouling characteristics are analyzed by the changes in net deposition mass and deposition morphology under seven different working conditions. The results showed that the ash deposits are mainly formed in two regions: β = 165° ∼ 195° and β = 305° ∼ 55°. In addition, one peak is observed in the deposition region on the windward side, and three peaks exist in the deposition region on the leeward side. The periodic shedding regularity of vortices, the separation process of the boundary layer, and the flow patterns of each feature point on the tube surface are studied to investigate the influence of the flow field characteristics on the deposition characteristics. In addition, the causes of the ash deposition in various locations are discussed in detail from the perspective of the deposition mechanism. The findings of this study are beneficial for understanding the ash deposition process and provide an improved approach for ash deposition simulation. [Display omitted] • The Eulerian deposition model combined with dynamic mesh technique is proposed. • Deposition behavior is predicted considering deposition and removal processes. • Effect of flow field characteristics on deposition characteristics is analyzed. • Distribution of major deposition parameters along tube wall is investigated. • Contribution of four deposition mechanisms to net deposition mass is explored. [ABSTRACT FROM AUTHOR]

• A new frosting model based on the supporting function of frost layer is proposed. • Using the ice phase volume fraction threshold to represent the supporting capacity of the frost layer. • The threshold is proportional to the change of frost thickness, density, temperature and wet air velocity. • Compared with the related experimental data, the average error of frost thickness and density were 4.9% and 5.5%, respectively. The existence of frost has adverse effects the normal operation of air source heat pumps. Therefore, establishing an accurate frost model is of great significance to suppressing the formation of frost layers on cold surfaces. Since the frost layer grows gradually and cumulatively layer by layer in the actual physical frosting process, it is important to consider the supporting function of the lower frost layer in the process. This study proposes the use of the ice volume fraction threshold of the frost layer to determine whether the supporting condition is satisfied, in addition to using the threshold to determine the occurrence of frosting. A new frost model is developed with the given volume fraction threshold fitting formula. In order to verify the accuracy of the proposed model, the simulation results were compared with 17 groups of experimental results from four representative experiments. It was found that the simulation results of this model were in good agreement with the experimental data, and the average error of thickness did not exceed 4.9%, while the average error of density was less than 5.5%. [ABSTRACT FROM AUTHOR]

• A local calculation method based on the Eulerian approach is proposed to simulate the deposition characteristics of fly ash particles. • A fouling model on the outer side of tubes considering deposition and removal mechanism is established. • The particle deposition process considers the effects of Brownian and eddy diffusion, gravity, thermophoretic, turbophoretic, and electrostatic forces. • The approach was verified by comparison with two representative experimental results. For the first time, this article proposes a practical Eulerian approach for simulating the deposition characteristics of fly ash particles in flue gas on the outer surface of tubes. In the present work, the deposition of fly ash particles includes both deposition and removal processes. The particle deposition process considers the effects of Brownian and eddy diffusion, gravity, thermophoretic, turbophoretic, and electrostatic forces. For validation purposes, the simulation results by the Eulerian approach are compared to two sets of representative experimental data from the literature. The average deviation in deposition height/mass between the first set of experiments in two different working conditions and simulations in this study is respectively 11.24 percent and 6.37 percent. In contrast, the second set of experiments and simulations has a deviation of 7.05 percent. [ABSTRACT FROM AUTHOR]

A local calculation method, based on the crystallization fouling model, is proposed to simulate the fouling process. Calcium carbonate crystallization fouling process occurring in a rectangular channel, with and without a vortex generator, is simulated by the integral and local calculation methods. The local calculation method is verified against the experimental data from the relevant literature. Fouling resistance obtained via local calculation method has shown stronger correlation with the experimental data as opposed to the integral calculation method. With an increase in the complexity of the channel structure, a greater distinction between the results obtained by the two methods is observed. The local calculation method has shown an advantage by providing the local fouling information, whereas the integral calculation method was unable to do so. • A local calculation method is proposed to simulate the crystallization fouling process. • The fouling resistance is calculated by utilizing the integral and local numerical methods. • The model was verified by comparison with experimental results. • The local method demonstrates certain advantages when compared to the integral method. [ABSTRACT FROM AUTHOR]

• An integrated Eulerian model for fouling in turbulent flow was developed to simulate the particulate fouling characteristics. • The model comprises a deposition process and removal process and considers various factors affecting the particle deposition. • The important parameters are calculated and extracted by the User-defined function (UDF) code. • The model was applied to predict particulate fouling on the heat transfer surface in two real cases. • The simulation results obtained from the model in the two cases agrees well with published experimental data. In this work, an integrated Eulerian model for fouling in turbulent flow was developed to simulate the particulate fouling characteristics. The model comprises a deposition process and removal process and considers various factors affecting the particle deposition, such as Brownian and eddy diffusion, gravity deposition, thermophoresis, and turbophoretic deposition. Several important parameters are calculated and extracted directly from the computational fluid dynamics model by the code, instead of relying on empirical formulas. The model was applied to predict particulate fouling in two experimental cases: particulate fouling on the surface of ventilation ducts and asphaltene fouling on the heat transfer surface in oil transport pipelines. The results show that the deposition rate obtained from the model in the two cases agree well with published experimental data. Furthermore, for the case of asphaltene fouling, at the early stage of fouling generation, the mass of asphaltene deposit on the surface also agrees well with the experimental results. [ABSTRACT FROM AUTHOR]

When water is used as the working medium in heat exchange equipment, precipitates and particulate suspensions can accumulate within parts of the heat exchanger, leading to particulate fouling. To address the issue of local fouling in channels, numerical simulations were conducted to study particulate deposition in a pulsating flow channel equipped with curved rectangular vortex generators. Specifically, the study analyzed the effects of varying the number, angle of attack, relative length, and relative height of the vortex generators on particulate deposition. The results indicate that the local fouling resistance fluctuates along the length of the channel, with peaks occurring at the leading and trailing edges of the vortex generators. The fouling resistance curve and the area covered on the bottom surface exhibit significant fluctuations at the vortex generator positions. There is a negative correlation between the local fouling resistance and both the number of vortex generators and their angle of attack, with the optimal values being 18 and 90°, respectively. Furthermore, as the relative length and relative height of the vortex generators increase, the local fouling resistance first decreases and then increases, with the optimal relative length and relative height found to be 0.125 and 0.3, respectively. • A particulate fouling model that can obtain local fouling is constructed. • The peak value of local fouling resistance with channel distribution is obtained. • The local fouling resistance decreases with the increase of the numbers and angles of VGs, and the best anti-fouling effect is 40.6% and 33.5%, respectively. • The local fouling resistance decreases first and then increases with the increase of the relative length and relative height of VGs, and the best anti-fouling effect is 41.6% and 44.5%, respectively. [ABSTRACT FROM AUTHOR]

Based on the layer-by-layer growth phenomenon existing in the actual formation of frost layer, we constructed a frost model with supporting criterion and studied the growth process of the frost layer on the horizontal cold surface at the bottom of the channel. Comparison with relevant experimental data revealed a maximum error of 25.3% in the calculated thickness and 13.1% in the density. The change in density and thickness over time under different working conditions, especially the variation in the thermal resistance under refrigeration conditions, were analyzed from local and overall perspectives. From a local perspective, thickness and density were highest at the frost front and slowly decrease along the flow direction before increase again at the end of the frost layer by 7.3% and 32.9% respectively. The local thermal resistance of the frost layer first increased sharply along the flow direction, reached a local peak and then decreased slowly. From an overall perspective, both the average thickness and average density increased with time, while the average thermal resistance first increased sharply with time, reached a peak, and then decreased slowly. [ABSTRACT FROM AUTHOR]

A local calculation method based on the crystallization fouling model, is proposed to simulate the fouling process. The CaCO 3 fouling deposition process was studied using the numerical simulation method, aiming to observe fouling characteristics of the rectangular channel of the finned vortex generators. The CaCO 3 fouling was studied by local fouling resistance on the rectangular channel under different fins parameters. The main influencing parameters were the number of rows, spacing, and height of the finned vortex generators. The results have shown that the finned vortex generator anti-fouling ability mainly depends on the number and strength of induced vortices produced by the fins. On the other hand, the increase in vortex strength will generally increase the wall shear force, thereby decreasing the fouling resistance. With the increase in the number of finned vortex generators, the number of produced vortices increased, while the rectangular channel fouling resistance decreased. Moreover, with the increase in the spacing ratio between the finned vortex generators, the vortex intensity influence range diminished, while the fouling resistance slightly increased. Additionally, as the finned vortex generator height ratio increased, the vortex-generated intensity range gradually increased and the fouling resistance decreased. • A local calculation method is proposed to simulate the complex heat transfer surface is established. • The method is verified by comparison with experimental results. • CaCO 3 fouling characteristic in a heat transfer channel with finned vortex generators is studied. • Effects of the number of rows, spacing, and height of the finned on fouling characteristics are discussed. [ABSTRACT FROM AUTHOR]