Modelling conical rock-bed solar thermal storage tank

An important application of solar thermal storage is for power generation or process heating. Low-temperature thermal storage in a packed rock bed is considered the best option for thermal storage for solar drying applications. In this chapter, mathematical formulations for conical have been developed. The model equations are solved numerically for charging/discharging cycles utilizing MATLAB. Results were compared with rock-bed storage with standard straight tank. From the simulated results, the temperature distribution was found to be more uniform in the truncated conical rock-bed storage. Also, the pressure drop over a long period of time in the conical thermal storage was as low as 25 Pa. Hence, the amount of power required from a centrifugal fan would be significantly lower. The flow of air inside the tank is simulated in SolidWorks software. From flow simulation, 3D modelling of flow is obtained to capture the actual scenario inside the tank.

Mathematical modelling of rock-bed solar thermal storage tank

An important application of thermal storage is solar energy for power generation or process heating. Low temperature thermal storage in a packed rock bed is considered best option for thermal storage for solar drying applications. In this paper, mathematical formulations for conical and cylindrical rock bed storage tanks have been developed. The model equations are solved numerically for charging/discharging cycles. From the simulated results, it was observed that for the same aspect ratio between the diameter and the length of the thermal storages, the conical thermal storage had better performance. The temperature distribution was found to be more uniform in the truncated conical shape rock bed storage. Also, the pressure drop over long period of time in the conical thermal storage was lower than that of the cylindrical thermal storage. Hence, the amount of power required from a centrifugal fan was lower.

Design of plane sand-bed channels affected by seepage

The importance of seepage in the design of channels is discussed. Experimental investigations reveal that seepage, either in the downward direction (suction) or in the upward direction (injection), can significantly change the resistance as well as the mobility of the sand-bed particles. A resistance equation relating 'particle Reynolds number' and 'shear Reynolds number' under seepage conditions is developed for plane sediment beds. Finally, a detailed design procedure of the plane sediment beds affected by seepage is presented.

Study of gas cavity size hysteresis in a packed bed using DEM

When a high velocity gas jet is introduced into a packed bed a cavity is formed. The size of the cavity shows hysteresis on increasing and decreasing gas flow rates. This hysteresis leads to different cavity sizes at same gas flow rate depending on the bed history. The size of cavity affects the gas flow profiles in the packed bed. In this study the cavity size hysteresis phenomenon has been modeled using discrete element method along with turbulent gas flow. A reasonable agreement has been found between computed and experimental results on cavity size ysteresis. The effect of various parameters, such as nozzle height from the bed bottom and packing height, on the cavity size hysteresis has been studied. It is found that inter-particle interaction forces along with gas drag and bed porosity play an important role in describing the cavity size hysteresis. The injection of gas flow allows the particles to go to an unconstrained state than they were previously in, and their ability to remain in that state, even under decreased gas drag force, leads to the phenomenon of cavity size hysteresis. (c) 2007 Elsevier Ltd. All rights reserved.

Analysis of gradually and spatially varied flow in sand-bed channels

Seepage through a sand bed affects the channel hydrodynamics, which in turn alters channel stability. Thus, the effect of seepage on its hydrodynamic parameters needs to be ascertained. The present work analyses spatially varied flow of a sand-bed channel subjected to seepage in the downward direction through a sand bed. Numerically calculated flow profiles affected by seepage have been verified using experimental observations. The present work also analyses the friction slope, velocity and bed shear stress variations along the channel for both seepage and no-seepage conditions. It was found that the downward seepage-induced channel flow has larger friction slope and bed shear stress than that of no-seepage.

Modelling of void initiation and breaking phenomena in a packed bed

Void breaking and formation in a packed bed are important phenomena in stabilising and optimising the performance of reactors such as the blast furnace, spouted bed and catalytic regenerator. These phenomena have been studied using a mathematical model. The model is based on a previously published force balance approach to predict the cavity size. Limited numbers of experiments, at room temperature, have been carried out in order to compare the experimental results with theory. A good agreement has been found between the experimental and theoretical results. In addition, the predictions have been compared with published data, which give reasonable agreement. The role of various forces (friction, pressure and bed weight) on void initiation and breaking has been investigated. The effect of bed height, particle diameter and density, void fraction, as well as gas flow rate on void formation and breaking has also been studied.

Analysis of a thick plate with a circular hole resting on a smooth rigid bed and subjected to axisymmetric normal load

A solution for the stresses and displacements in an radially infinite thick plate having a circular hole, one face of which resting on a smooth rigid bed and the other face subjected to axisymmetric normal loading is given. The solution is obtained in terms of Fourier-Bessel series and integral for the Love's stress function. Numerical results are presented for one particular ratio of thickness of plate to the hole radius and loading. It is also shown that the Poisson's ratio has a predominant effect on certain stresses and displacements. The solution would be useful in the stress analysis of bolted joints.Eine Lösung für die Spannungen und Verschiebungen in einer radial, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, wobei eine Seite auf einer ebenen, starren Unterlage aufliegt, die andere Seite durch eine achsensymmetrische Vertikallast belastet ist, wird angegeben. Die Lösung wird in Form von Fourier-Bessel-Reihen und Integralen der Loveschen Spannungsfunktion angegeben. Numerische Ergebnisse werden für ein bestimmtes Verhältnis der Plattendicke zum Lochradius sowie zur Belastung angegeben. Es wird auch gezeigt, daß das Poisssonsche Verhältnis einen besonderen Einfluß auf bestimmte Spannungen und Verschiebungen hat. Die Lösung ist anwendbar für die Spannungsermittlung von Bolzenverbindungen.

Incipient motion design of sand bed channels affected by bed suction

Seepage through sand bed channels in a downward direction (suction) reduces the stability of particles and initiates the sand movement. Incipient motion of sand bed channel with seepage cannot be designed by using the conventional approach. Metamodeling techniques, which employ a non-linear pattern analysis between input and output parameters and solely based on the experimental observations, can be used to model such phenomena. Traditional approach to find non-dimensional parameters has not been used in the present work. Parameters, which can influence the incipient motion with seepage, have been identified and non-dimensionalized in the present work. Non-dimensional stream power concept has been used to describe the process. By using these non-dimensional parameters; present work describes a radial basis function (RBF) metamodel for prediction of incipient motion condition affected by seepage. The coefficient of determination, R-2 of the model is 0.99. Thus, it can be said that model predicts the phenomena very well. With the help of the metamodel, design curves have been presented for designing the sand bed channel when it is affected by seepage. (C) 2010 Elsevier B.V. All rights reserved.

General model of a foam bed reactor

A general model of a foam bed reactor has been developed which rigorously accounts for the extent of gas absorption with chemical reaction occurring in both the storage and foam sections. Its applicability extends to a wide spectrum of reaction velocities. The possibilities of the predominance of the bulk-liquid reaction in the storage section or the absorption with reaction in the foam section can be handled as merely special cases of the general analysis. The importance of foam for carrying out a particular gas-liquid reaction is characterised by a criterion in terms of the fractional rate of reaction in the foam section. Trends of variations in the concentrations of dissolved free A, solute B, and gas-phase A with time of operation of the reactor are presented. The nature of the variation in the fractional rate of reaction in the foam section with time, at different reaction velocities, and the effect of the liquid flow rate (across the storage section) on the transience are also illustrated. Finally, the predictions of the general model have been validated using the available experimental data on the oxidation of sodium sulphide in a foam bed reactor. The agreement between the experimental and the present theoretical information is fairly good, apart from being more insightful than all the previous models of this reactor.

Variation of stream power with seepage in sand-bed channels

Downward seepage (suction) increases the mobility of the channel. In this study, experimental investigations were carried out to analyse the suction effect on stream power along the downstream side of the flume. It was observed that stream power has a major influence on the stability and mobility of the bed particles, due to suction. Stream power is found to be greater at the upstream side and lower at the downstream side. This reduces the increment in the mobility of the sand particles due to suction at the downstream side. Thus, there is more erosion at the upstream side than the downstream side. It was also found that the amount of deposition of sand particles at the downstream side, because of the high stream power at the upstream side, is greater than the amount of erosion of sand particles from the downstream side.

Seepage effects on sand-bed channels

ExperimentS were conducted to find the effects of seepage on flow over a sand bed in a straight rectangular flume under two conditions: (1) When the channel bed is plane, horizontal, and nontransporting; and (2) when the bed is transporting at a constant sediment concentration. Effects of both injection and suction, caused by seepage flow into and out of the channel bed, are studied for condition 1; and only suction effects are studied for condition 2, Three sands, sizes 0.34 mm, 0.53 mm, and 0.80 mm, are used in the study. It is found that seepage can cause an increase or decrease in the bed shear stress relative to no seepage for the two conditions. The change in bed shear stress depends on the relative magnitudes of the bed shear stress and the critical shear stress of particles under the no-seepage condition, sediment concentration, and the seepage rate. Quantitative relationships giving the ratio of bed shear stresses with and without seepage are presented for both conditions of the bed. A procedure to estimate the changes in bed shear stress, friction factor, Manning's n, and stream power due to seepage for known initial conditions of the channel and the amount of applied seepage is presented

Geometry of sand-bed channels with seepage

Literature suggests that apart from a significant percentage of water loss from seepage, downward seepage from the channel causes an increase in the mobility of channel bed materials and thus changes the channel stability. Consequently, regime conditions (which provide the relationship among hydraulic parameters) should also be revised by incorporating downward seepage as an additional parameter. In the present work, regime conditions for the prediction of channel geometry in alluvial channels affected by downward seepage have been formulated on the basis of experimental observations. (C) 2011 Elsevier B.V. All rights reserved.

Gas-phase controlled mass transfer in a foam-bed reactor

Gas-phase controlled absorption of ammonia in foams made of solutions of sulphuric acid has been studied experimentally. Effects of gas-phase concentration of ammonia and type of surfactant on the performance of the foam-bed reactor are investigated. Gas-phase controlled absorption from a spherical bubble is anaylzed using the asymptotic value of Sherwood number (Sh = 6.58), for both negligible as well as significant changes in the volume of the bubble. The experimental data are shown to be in good agreement with the single-stage model of the foam-bed reactor using these asymptotic sub-models, as well as the diffusion-in-sphere analysis available in literature. Influence of effective diffusivity on the time dependence of fractional gas absorption has been found to be unimportant for foam columns with large times of contact. The asymptotic sub-models have been compared and use of the rigid-sphere asymptotic sub-model is recommended for foam columns of practical relevence.

Stability and mobility of sand-bed channels affected by seepage

Seepage effects on the stability, mobility, and incipient motion of sand-bed particles are experimentally investigated. Seepage through a sand bed in a downward direction (suction) reduces the stability of particles, and it can even initiate their movement. The bed erosion is increased with the increased rates of suction. Whereas the seepage in an upward direction (injection) increases the stability of bed particles, it does not aid initiating their movement. The rate of bed erosion is reduced or even stopped by the increased infection rates. Hydrodynamic conditions leading to the so-called "pseudoincipient motion'' with suction (for the initiation of particles movement that are otherwise at rest under no-seepage conditions), and with injection (for only arresting the particles movement that are otherwise moving initially) are evaluated. The conventional Shields curve cannot be used to predict such pseudoincipient motion conditions with seepage. The concepts thus developed are useful for a better understanding of the sediment transport mechanics and in the design of stable alluvial channels affected by seepage.