•Flow behavior of liquid film over horizontal tube was 3-dimensionally simulated.•The temporal variation of inline jet flow and staggered jet flow were analyzed.•The circumferential distribution of ...film thickness was given at different flow models.•The effects of Reynolds number on flow transformation was discussed.•The formation mechanism of inline flow and staggered flow was explored.
In this paper, the volume-of-fluid (VOF) model is adopted to simulate the distribution and flow of a liquid film on the outer surface of the horizontal tube of a falling-film evaporator. The plain tube diameter and the spray distance are 25.4 and 22 mm respectively. The temporal variation characteristics of inline jet flow, the adjacent liquid column, and the steady-state film thickness distribution over the horizontal tubes are analyzed. To better compare with the experimental results, two kinds of numerical simulation medium, water and ethylene glycol, are chosen. The results of the 3-D numerical simulations and experiment are in good agreement. The results show that the jet flow can be divided into inline jet flow and staggered jet flow. Furthermore, a trough forms between the adjacent liquid columns under inline jet flow, whereas a crest forms between the adjacent liquid columns under staggered jet flow. In addition, the liquid viscosity is a crucial factor affecting the spreading of the liquid film. The appearance of the crest between adjacent liquid columns results in staggered jet flow.
The numerical investigation was performed to analyze the film thickness characteristics over fully wetted horizontal round tube in a falling film evaporator using commercial CFD code Fluent 6.3.26. A ...two-dimension multi-phase flow model for numerical simulation was developed under adiabatic condition. The temporal variation characteristics of film flow process and the steady film thickness distribution over horizontal tubes were analyzed in detail. It was found that the whole process of liquid film flowing along the horizontal tube surface includes the transient sub-process and steady state sub-process, and the former can be divided into five stages to be analyzed. The obviously asymmetric distribution of film thickness is captured by the simulation results. The film thickness increases with the increase in film Reynolds number. An obvious zone without liquid is formed very closely to the lower stagnation point, and the size of the zone is bigger when the Reynolds number is higher.
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•A 3D numerical model with an implement of a random disturbance subjected to Gaussian distribution is built up.•The model is effective to predict droplets splashing process.•A ...geometric model is proposed to demarcate the impact region into semicircle regions and a series of rectangle regions.•Effects of Weber number, film thickness and droplets interval on central liquid sheet height, impact areas and residual film thickness are addressed.
Multiple droplets impinging on a thin liquid film simultaneously is numerically studied using a three-dimensional model with an implement of a random disturbance subjected to Gaussian distribution. This model is very effective to predict droplet splashing under relatively high impingement momentum. Interface evolutions and field distributions are addressed after droplets impact. Besides, a geometric model is built up to demarcate the impact region into two semicircular regions and a series of rectangular regions during simultaneous impact, further to discuss the variations of area and residual film thickness in each region as well as the total area and average film thickness.
This paper addresses interfacial phenomena associated with droplet array impact on solid surface experimentally, with aid of high-speed photography. Aside from the simultaneous case, droplet array ...impact is more represented by various non-simultaneous cases, which can be classified into three major subcases: edge/edge interaction with large droplet horizontal spacing, edge/droplet interaction with intermediate droplet spacing, and film/droplet interaction with small spacing. Outcomes include droplet coalescence induced at low velocities and central liquid sheet generated due to droplets interaction at relatively high impact velocities. In quantitative analysis, increasing droplet vertical spacing leads to decreases in both spreading factor and height of central liquid sheet due mainly to increased viscous dissipation. While both the two parameters decrease with increasing droplet horizontal spacing, its effect is weakened with increasing impact velocity, which acts as a positive role for evolution of the two parameters. Although the central sheet continues to descend under gravity at later stage, a sheet height shoulder raises attention because of cusp formation at top of the central sheet. This study provides a fundamental understanding for practical applications involving droplets impingement.
Several dimensionless parameters are studied to describe their effects on the deformation of a droplet after impact on a 2D round surface by using lattice Boltzmann implementation of pseudo-potential ...model. Four typical deformation process can be found: moving, spreading, nucleating and falling. In addition, in some special cases, part splashing is involved. It is observed that impact velocity of droplet has a significant influence on the droplet impacting dynamics. With the increasing of the impact velocity, different states have been found during the process. Moreover, when the surface is hydrophobic, splash occurs.
•Wheat straw rich in sulfur compared to coal was chosen as biomass material.•The behavior of alkali metal species during co-combustion was investigated.•The amount of KCl(g) and NaCl(g) was decreased ...by adding coal to wheat straw.•Most of fuel K was retained in the bottom ash as K2SO4, KAlSiO4 and KAlSiO6.•The amount of K2SO4 in the bottom ash decreased with temperature increase.
Co-combustion of coal and biomass is a low-cost, large-scale, and efficient way to utilize biomass energy, which has a wide range of potential applications. However, biomass, especially herbaceous fuels, contains high levels of volatile K, Na, and Cl, the use of which may result in ash-related operational problems, such as corrosion, fouling, and slagging during thermal utilization. The aim of this study is to investigate the effects of wheat straw and temperature on the release and transformation of alkali metal species during co-combustion of coal and S-rich wheat straw. Results indicate that the amounts of K and Na released during co-combustion could be reduced by the effects of Fe, Ti, S, Si, and Al from blended fuels. At lower wheat straw shares, the release of K decreased due to reactions of KCl with Fe species, and Ti species, forming K2Fe2O4 and K2TiO3. At high wheat straw shares, the release of K could be mainly captured in the form of K2SO4; small amounts of KAlSiO4 were also observed in the bottom ash. When the wheat straw share was 80wt.%, increasing temperatures enhanced the release of KCl(g) and NaCl(g) at 600–800°C. By contrast, in the range of 800–1000°C, the amounts of these gases released exhibited no apparent association with temperature. Compared with the release of K, fuel K was mainly retained in the bottom ash. The K2SO4 content in the bottom ash decreased with increasing temperature in the range of 600–1000°C, whereas the fraction of K in the form of KAlSiO4 and KAlSiO6 increased with increasing temperature, especially at temperatures between 800 and 1000°C.
•Although the second-order approximation closely matches the true distribution, it will not lead to a closed-form expression for the likelihood function, while the first-order approximation results ...in a simple closed-form expression at the expense of some accuracy loss.•Although the likelihood function deviates from its first-order approximation, the position of their maxima are close to each other, so the first-order approximation still results in an appropriate position estimate.•In the presence of orientation uncertainty, the proposed estimator outperforms the state-of-the-art estimators.
As the positioning accuracy of a visible light positioning (VLP) system is highly susceptible to changes in the orientation of the receiver, accurate knowledge of the receiver orientation is required. In practice, the orientation of the receiver is estimated with an external orientation estimation device. However, these devices generally suffer from drift and misalignment, causing an uncertainty in the measured orientation that will degrade the performance of standard positioning algorithms. In this paper, we derive a novel positioning algorithm that takes into account the effect of the orientation uncertainty. To this end, we need to cope with the non-linear relationship between the received signal strength (RSS) and the orientation uncertainty, which makes the likelihood function of the RSS, required to derive the maximum likelihood (ML) estimator, hard to obtain. To solve this issue, we consider the first and second-order Taylor series expansion of the RSS. Although the accuracy of the second-order approximation is better than the first-order approximation, the first-order approximation results in a closed-form expression for the likelihood function, while this is not possible with the second-order approximation. Because of this, we derive the ML estimator using the first-order approximation, and employ the multivariate gradient descent algorithm to obtain the position estimate. Computer simulations show that the proposed algorithm outperforms state-of-the-art VLP algorithms subject to orientation uncertainty.
Compared with film condensation, dropwise condensation based on droplet growth can significantly improve the condensing equipment’s water collection and thermal efficiency in the vapor condensate ...system. Therefore, as a critical behavior affecting the evolution of dropwise condensation, research on droplet growth is of great significance to further understanding the evolutionary characteristics and heat transfer mechanism of dropwise condensation. In this paper, a model for simulating the entire evolution process of dropwise condensation is improved and constructed, and the evolution process of dropwise condensation with different condensation nucleus densities on the vertical wall is simulated based on certain assumptions. Moreover, parameters such as evolution rate and size contribution are proposed to measure droplet growth’s influence on the evolution process of dropwise condensation. In the simulation, the Cassie model was used to describe the condensation growth of droplets. The neighbor finding algorithm and conservation law are coupled to simulate the coalescence growth process of droplets. Through the comparison of the theoretical model and experimental results, it is indicated that the simulation method in this paper is highly reliable. The simulation results demonstrate that more than 95% of the maximum droplet size of dropwise condensation is derived from coalescence growth, and its growth rate can characterize the evolution rate of dropwise condensation. The evolution rate reveals a linear growth trend with the increase of condensate nucleus density, and the average heat flux shows an increasing trend followed by a decreasing trend, reaching the peak, qaverage = 30.5 kW·m−2, at the NS = 5 × 109 m−2. The surfaces with a high coalescence frequency can increase the contribution of the coalescence growth to the maximum droplet size more effectively and, conversely, the contribution of condensation growth is weakened, which is less than 1% at the NS = 7.5 × 109 m−2.
The quadrature angular diversity aperture (QADA) receiver, consisting of a quadrant photodiode (QPD) and an aperture placed above the QPD, has been investigated for pose estimation for visible light ...systems. Current work on pose estimation for the QADA receiver uses classical camera sensor algorithms well known in computer vision. To this end, however, the light spot center first has to be obtained based on the RSS. However, this is less straightforward than for camera sensors, as in contrast to such sensors where the relationships are linear, the RSS output from the QADA is a non-linear function of the light spot position. When applying closed form solutions or iterative methods for cameras on a QADA, the non-linearity will degrade their performance. Furthermore, since in practice the aperture is not always perfectly aligned with the QPD, a procedure to calibrate the receiver is needed. Current work on calibration requires additional sophisticated equipment to measure the pose during calibration, which increases the difficulty of implementation. In this paper, we target the above problems for pose estimation and calibration of the QADA receiver. To this end, we first study the effect of the strategy of differencing and normalization on the probability density function (PDF), a commonly applied strategy for the QPD’s robustness against RSS variation, and it is shown that the applied strategy results in a complex PDF, which makes an effective and efficient estimation hard to achieve. Therefore, we derive an approximated PDF in a simple closed-form, based on which the calibration and the pose estimation algorithms using the least squares principle are proposed. The proposed calibration does not require any information about the pose of the receiver and is robust to variation of the received power and imperfect knowledge of the radiation pattern of the LED, making it easy to implement. We also derive the corresponding Cramér-Rao lower bound on the misalignment to benchmark the performance of the misalignment and to serve as an indicator to determine the required signal-to-noise ratio (SNR) or number of LEDs to obtain a desired accuracy. The calibration and pose estimation are evaluated by means of a Monte Carlo simulation. Computer simulations show that this theoretical bound is close to the RMSE of the proposed estimator and that the proposed pose estimator outperforms the PnP algorithm.
