Moving Bed Heat Exchanger Research Articles

Analytical solution of a heat transfer model for a tubular co-current diluted moving bed heat exchanger with indirect heating and thermal losses to the environment

A mathematical model for a co-current moving bed heat exchanger (MBHE) is presented. The bed is diluted and composed of spheres of uniform radius which are transported by a dragging fluid in plug flow. The gas-solid mixture is heated indirectly by a flue gas, which flows in a jacket around the MBHE. Intraparticle temperature gradients and thermal losses to the external environment are considered. The model is solved analytically by the Self-Adjoint Operator method (SAO) and numerically by a combination of the Finite Analytical (FA) and the Finite Difference (FD) method. The results show excellent agreement and the comparison with experimental data validates the model, enabling its use in the design and analysis of MBHEs for which thermal losses are a relevant factor. MBHE effectiveness is defined, and it is shown - for a selected case - that the addition of 5.0 cm thick glass wool raises it by 25.5%.

Numerical study on gravity-driven granular flow around tube out-wall: Effect of tube inclination on the heat transfer

Heat recovery from granular flow in moving bed heat exchangers has wide industrial applications. However, more knowledge is still necessary for the heat transfer enhancement. For the slow descending of random particles, the flow structure has crucial roles on the heat transfer by conduction and radiation. In this paper, the effect of tube inclination was studied by discrete element method. Influences of particle update, contact and radial migration were carefully discussed. Moreover, heat resistance analysis was conducted to explore the clear law. It was found that, the heat is obviously improved by tube inclination due to the increasing area, but there are uncertainties for the local heat transfer coefficients. At the tube bottom, particles become denser with tube inclination, which is beneficial to increase the heat transfer coefficient. But for the top or middle area, there are two opposite effects. Tube inclination enhances radial migration around tube wall, while simultaneously weakens local particle update. Finally, contact resistance firstly increases and then decreases with inclination angle, but there is a reversal tendency for the sensitivity of penetration resistance to the flow rate. In actual applications, penetration resistance is the major resistance, and the inclination angle is therefore suggested between 15° and 37.5°.

Numerical investigation of heat resistances in uniform dense granular flows along a vertical plate

Moving bed heat exchangers have been the economic alternatives for the granular flow in industries. To predict the heat transfer coefficients, a better understanding is required of the contact resistance (1/hws) and the penetration resistance (1/hso). In this work, the heat transfer coefficients were simulated using the finite volume method to investigate these resistances in both ordered and random packing sphere particles. It was found that, the 1/hws is determined by the effective thermal conductivity in the wall region, of which the thickness is around 3/22 particle diameters. Moreover, the 1/hso is affected by the heat capacity, thermal conductivities and particulate structures. The effect is reflected by two modified equivalent heat absorption coefficients (1/p1 and 1/p3) in granular flows. Generally, p1 is smaller in the ordered structure because the peak local solid fraction is higher, while p3 is smaller in the random structure due to the lower average porosity.

Comparison of Heat Transfer in Gravity-Driven Granular Flow near Different Surfaces

Heat transfer in gravity-driven granular flow has been encountered in many industrial processes, such as waste heat recovery and concentrated solar power. To understand more about Moving Bed Heat Exchanger (MBHE) applied in this field, numerical simulation was carried out for the characteristics of granular flow near different surfaces through discrete element method (DEM). In this paper, both the performances of particles motion and heat transfer were investigated. It’s found that, even though the macroscopic granular flow is similar to fluid, there is still obvious discrete nature partly. The fluctuations of parameters in granular flow are inevitable which is more obvious in the circular tube cases. A special phenomenon, where competition motion is found, is resulted from discrete nature of particles. In terms of heat transfer, overall heat transfer coefficients for plate are higher than that of tube owing to better contact between particles and wall. However, due to competition motion, particles in high temperature tend to contact the tube, which is beneficial to heat transfer in some local zones. The heat transfer characteristics above will also affect the temperature distribution near the outlet of different geometries.

Numerical Study of Heat Transfer for Gravity-Driven Particle Flow along a Vertical Oscillating Pin-Fin Plate

Nowadays, moving bed heat exchanger (MBHE) is being gradually applied in the fields of industrial waste heat recovery and solar energy utilization, due to its easy production of clean energy and low cost. However, the heat transfer performance of the MBHE is relatively poor. In the present paper, the heat transfer performance of gravity-driven particle flow in a pin-fin plate heat exchanger unit (PFPHEU) is numerically studied using discrete element method. The effects of pin-fin and plate oscillation on the heat transfer of gravity-driven particle flow along a vertical plate are carefully analyzed. The results show that, the heat transfer coefficient of the static PFPHEU is about 12.5 % less than that of the PWPF due to the higher porosity around the pin-fin compared to the plate without pin-fin (PWPF). The plate oscillation can significantly improve the particle filling rate around pin-fins and enhance the thermal dispersion of particle flow. The heat transfer in a PFPHEU is enhanced, and the heat transfer coefficient of PFPHEU increased by 87.6 % and 113.5 % compared with that of PWPF as the amplitude was 1 mm and 2 mm.

Numerical investigation of tube oscillation in gravity-driven granular flow with heat transfer by discrete element method

In this paper, the gravity-driven granular flow was investigated by discrete element method (DEM) in the moving bed heat exchanger with tube oscillation. The particle update, the particle contact and the heat transfer were all discussed around tube out-wall. Moreover, the heat resistance analysis was developed to reveal the heat transfer mechanisms. It was found that, tube oscillation can significantly improve heat transfer coefficients (h). The relative growth of locally optimal h varies from 59.2% to 22.6%, when the outlet velocity (u) ranges from 0.65 mm/s to 6 mm/s. In details, the heat transfer can be enhanced by tube oscillation due to the smoother flow in the upstream, the denser contact in the downstream and the more particle mixing inside the flow. However, the particle separation aside the tube has a negative effect simultaneously. Therefore, there is a best frequency (f) to optimize h. The frequency is inversely proportional to the amplitude (DA) and decreases with u. Furthermore, the larger DA can increase the best h. In the present study, the optimal h was obtained as f locates between 3 and 5 Hz at DA > 1 mm.

An Analytical Solution for Moving Bed Heat Exchangers via Integral Transform Methods

A number of analytical solutions for moving bed heat exchangers (MBHEs) have been recently obtained by means of Laplace transforms. In this work, an alternative method for obtaining the analytical solution for a co-current parallel-plate MBHE is presented, by means of orthogonal expansions and integral transform techniques. This methodology provides a more robust approach for solving the problem, and opens the door to the identification of analytical solutions for more complex MBHE systems (e.g. moving beds with heat generation in the solids). To validate the solution, the expressions for the solid and fluid temperatures are explored graphically and compared with those in the literature and found to be identical.

Lumped analysis criteria for heat transfer in a diluted co – current moving bed heat exchanger with isothermal walls

In this study, a mathematical method was applied to establish modelling selection criteria for lumped parameter analysis (LPA), in the solid phase, of a diluted co-current moving bed heat exchanger (MBHE), with isothermal walls. Simplified expressions for particle temperature errors are obtained, showing, for certain parametric ranges, excellent agreement with the exact solution results. Another remarkable result is that for a MBHE with isothermal walls and very low particle Biot numbers, the possibility of steep intraparticle temperature gradients is demonstrated. Through a scale analysis, this behavior is explained, along with the physical foundations guiding the LPA selection criteria. The differences between two basic forms of approximation in MBHE modelling, that is, the uniform particle temperature assumption (UPTA) and LPA, are characterized. Also, new contributions are provided by the determination of parametric condition for the equality between the temperatures of the fluid and the particle surface and by limiting solutions.

Optimization of Gravity-Driven Granular Flow Around the Tube for Heat Transfer Enhancement

Nowadays, moving bed heat exchanger (MBHE) has been gradually adopted in the field of heat recovery from the granular flow. Compared with fluidized bed, the moving bed cost less. However, it usually brings with relatively poor heat transfer performance. The current study aims to optimize the heat transfer in gravity-driven granular flow through tube vibration, which is helpful to the efficient design of MBHE in the future. The vertical granular flow is numerically simulated with discrete element method, where careful discussion about vibration tube effect is developed. The model has been carefully validated. To focus on the mechanism of heat transfer enhancement, the geometry model is simplified as a single tube. The results show that, tube vibration in different directions could improve heat transfer performance, where the effect of horizontal vibrating direction is more remarkable. It’s also found that a slight sinusoidal vibration is able to accelerate particles update above the tube and drive some particles contact the bottom zone of tube. Therefore, it mitigates the negative effect of stagnation zone and void zone in cases of static tube. Then the heat transfer coefficients would increase. What’s more, tube vibration would rebound particles around the wall, where additional mass diffusion is beneficial to heat transfer at sides of tube at some extent. However, it should be noted that vibration would increase wear rate between tube and particles significantly at the same time. The industrial application relies on the development of wear-resistant technology.

Cooling of Particulate Solids and Fluid in a Moving Bed Heat Exchanger

Abstract The current technical brief is to analytically solve the coupled energy equations governing the thermal phenomenon of particulate solids and cooling fluid present inside moving bed heat exchangers constructed via a parallel plate system. The prime concern is to analytically evaluate the cooling effects of a heat sink (absorbent) placed within the media on the particulate and fluid and hence to obtain the relevant temperature fields for the latter. In the absence of such a source term, the solutions collapse onto the recent literature. Results clearly demonstrate how an effective cooling can be achieved with a heat sink mounted on industrial moving bed heat exchangers. Particularly, the existence of an energy sink results in cooler solid particles as compared to the flowing fluid.

Analytical solution of a heat transfer model for a tubular co-current diluted moving bed reactor with indirect heating and intraparticle gradients

The understanding of the multiphase flow and the thermal behavior in moving beds is important for design and process optimization. Thus, in the present work, the heat transfer in a tubular moving bed reactor indirect heated by a flue gas is modeled, considering the thermal interactions: “conveyor fluid-flue gas”, “conveyor fluid-particle”, as well as the intraparticle heat transfer. The model is solved analytically by the powerful Self-Adjoint Operators Method (SAO), which allows the maximum maintenance of the physical characteristics of the problem. The consistency of this novel solution is shown through limiting solutions and comparison with simpler models: a lumped capacity model (LP), whose solution is independently obtained through the Laplace Transform Method, and an existing isothermal wall moving bed heat exchanger (MBHE) solution. For low particle Biot numbers systems, the LP and SAO solutions showed a very good agreement. The results also showed good validation of the solutions by comparing with experimental data. A numerical hybrid solution, through a combination of the Finite Difference Method (FD) and the Finite Analytical Method (FA), is also given and the comparison with the analytical solution shows excellent agreement. Finally, a scale analysis is proposed and performed. The scale analysis made it possible to assign a physical meaning to the model's parameters, to infer about the thermal behavior of the system, to evaluate the use of simpler models and to present semi-theoretical expressions for the maximum temperature difference into the particle and between particle surface and conveyor fluid, for systems with low Bip.

Numerical investigation of dense granular flow around horizontal tubes: Qualification of CFD model with validated DEM model

Granular material offer many advantages which qualify them for use as heat transfer medium and heat storage material in solar thermal power plants and industrial processes. Moving bed heat exchangers (MBHE) with horizontal tubes are favorable to extract thermal energy from hot granular materials. However, due to the complex flow phenomena and heat transport mechanisms in granular materials precise design tools for MBHE are lacking.In previous studies we introduced a discrete particle model (DEM) to calculate the granular flow in MBHE and validated it by experiments. In this study we use this precise but computationally expensive DEM model to qualify a more efficient continuum model (CFD) which is being introduced in this work.We compare the two models with regard to the granular flow speed along the tube surface and find deviations of |Δu/uref| < 20% in the upper part of the tubes. Both models coherently predict the formation of a static area at the top of the tubes. The formation of the void area below the tubes is less accurately predicted, calling for further adaptations of the CFD model. The thus qualified CFD allows to study large heat exchanger geometries with substantially reduced computational effort.

Granular flow around the horizontal tubes of a particle heat exchanger: DEM-simulation and experimental validation

Moving bed heat exchangers are a central element in solar thermal power plants using granular heat transfer fluids. Their performance is determined by a complex granular flow field in the device. This calls for accurate simulation models forming the basis for novel design tools.In this study we propose a discrete element model (DEM) to calculate the dense granular flow field around the horizontal tubes of a moving bed heat exchanger.The simulation results are compared to measurement data using particle image velocimetry (PIV). In the upper part of the tube the model agrees well with the experiment, capturing the relevant flow phenomena like the stagnant zone on top of the tube.Below the tube, a void area is observed both in the experiment and the simulation. However, the PIV analysis of the experimental data doesn’t resolve the void area and the associated flow phenomena due to the highly dynamic flow state, the inherent nature of PIV technique and additional disturbing effects in the setup. Therefore, the model can’t be validated in the corresponding regions.Still, the deviations between simulation and experiment are confined to a very narrow region directly at the tube surface in the lower part of the tube. In the rest of the flow field, the model proves to be a reliable tool for further investigations and will be used in future studies.

Numerical investigation of heat transfer for elliptical tube in granular flow using DEM

Moving bed heat exchangers take important part in terms of extracting heat from granular materials. Circular tube is main part of heat exchanger in most studies and implements. Two heat transfer deterioration zone for circular tubes in granular flow is found and results in a low heat transfer coefficient. Elliptic tubes receive increase attention recent years for their better heat transfer performance for fluid. In this work numerical investigation based on DEM has been produced to obtain heat transfer performance of elliptic tubes in granular flow with different axis ratio. The result shows that elliptic tubes with axis ratio from 1.2 to 2.0 have a narrower area of heat transfer deterioration in granular flow and consequently a higher effective heat transfer coefficient from than circular tube (axis ratio =1.0) with the same long axis.

Assessing axial heat conduction in moving bed heat exchangers

An analytical solution is obtained for an energy model of a moving bed heat exchanger (MBHE) that includes axial heat conduction, subject to an external fluid at constant temperature. The problem formulation and nondimensionalization of the steady-state energy equations are presented for a parallel-plate system. The analytical solution is verified by examining it at the limit where axial heat conduction is neglected, and shown to simplify to expressions in the literature. The analytical solution is also compared to the results of a numerical solution under various conditions, and found to be in agreement. Finally, the solution is used to quantify the importance of axial heat conduction in a given MBHE, and the results are summarized in the form of error maps.

Innovative sensible heat transfer medium for a moving bed heat exchanger in solar central receiver power plants

Renewable energies are gaining importance due to the steadily increasing scarcity of fossil fuels, the ongoing climate change and last but not least the risks which accompany the use of nuclear power. In this growing market, solar thermal power plants offer a centralized, potentially load following electricity production. To serve this need, the integration of thermal energy storage systems is essential. The Moving Bed Heat Exchanger MBHX storage concept for CSP systems using sensible heat transfer medium aims at using a low cost solid storage media. This concept requires intermediate bulk cycles to transfer heat between the solar field and the storage material (the bulk). Heat Transfer Fluids (HTF) such as synthetic oils (mobiltherm 603) are typically used. In this work, granular materials such as sand and rocks are studied to present an additional HTF to represent an efficient and cost-effective alternative. Low cost solid particulates can store and transport heat at temperatures over 1000°C. For the purpose of heat recovery, a moving bed heat exchanger (MBHX) is applied and tested. In this study, the dense granular mass is gravity-driven through a heat exchanger. The performance of the MBHX with the utilization of Sand, Basalt, and a Mixture of Sand and Basalt as a granular material was experimentally investigated. It is found that the effectiveness of the MBHX using a mixture of 50% sand and 50% basalt improved by 30% compared to using sand alone.

Granular Flow Field in Moving Bed Heat Exchangers: A Continuous Model Approach

Moving Bed Heat Exchangers (MBHX) are a promising option to discharge thermal energy from hot bulk materials, which can be used in solar thermal power plants as heat transfer and storage medium. A precise determination of the flow field in a MBHX is required to predict its thermal performance. This paper presents a continuous model approach, based on the theory of soil mechanics to describe the granular flow inside the heat exchanger. The simulation results are compared to a preceding model and experimental data. For this purpose two different tube bundle geometries are analyzed. The results are evaluated by means of contour plots of the flow field and the velocity magnitude of the granular material at the tube surfaces. The new model captures the flow at the top of the tubes quite well but shows need for further improvement in the lower part of the tubes.

Co-current and counter-current vertical pipe moving bed heat exchangers: Analytical solutions

Recently, analytical solutions for parallel-plate moving bed heat exchangers have been obtained by means of integral transform methods. This study extends the analysis to vertical pipe geometries due to their important industrial applicability. Steady-state energy equations, for systems operating under co- and counter-current conditions, are formulated and nondimensionalized. Laplace transforms and various forms of the expansion theorem are then used to solve the problems, resulting in temperature functions for the solids and fluid domains. Limiting cases are then analyzed and the solutions are shown to simplify to various expressions in the literature. A graphical analysis is also presented, depicting representative behaviors of the solutions and addressing their physical consistency.

Development and Performance Assessment of a Moving Bed Heat Exchanger for Solar Central Receiver Power Plants

Abstract A concept for a moving bed heat exchanger (MBHX) for solar central receiver power plants with a particle-based storage is presented and substantiated with experimental results. The design of the tube bundle considers the rheological bulk properties and was supported by CFD simulations. The adapted MBHX and a conventional reference design were subject of a comparative performance assessment. Both the granular flow distribution as well as the thermal efficiency were examined for both designs. Due to the shorter contact time of the particles at the tube wall in the adapted tube bundle, the newly developed MBHX exhibits a better thermal performance with heat transfer coefficients up to 240 W/m2K for moderate superficial bulk velocities of 5 mm/s. Hence, this concept is considered a promising technology component option for future particle-based CSP plants.

Engineering design of direct contact counter current moving bed heat exchangers

A heat transfer model was applied to simulate heat exchange in a direct contact counter current moving bed (CCMB) heat exchanger associated with a dry slag granulation process developed by CSIRO. Cold air is used to recover heat from hot solid slag granules in the heat exchanger. Experimental data was used to calibrate the heat transfer model. The model was then used to predict the solid and gas temperature distributions along the height of the bed, the heat loss, and the operating and design conditions for scale-up of the CCMB to semi-industrial and industrial operations.Two scenarios were examined using the model to determine conditions for i) minimising the solid outlet temperature and ii) maximising the gas outlet temperature. The model can also be used to determine the nominal bed height to ensure that the designed gas outlet temperature is achieved. The modelling results suggest that a relatively small bed height (below 0.5m) will be sufficient for heat exchange. The model also suggests that a solid to gas mass flow rate ratio of 0.8 should be used to minimise the solid outlet temperature, while a ratio of 1.0 should be used to maximise the gas outlet temperature. Therefore an appropriate operating window for a CCMB heat exchanger for recovering heat from hot slag was found with a solid to gas mass flow rate ratio between 0.8 and 1.