Moving Bed Heat Exchanger Research Articles

Experimental study on heat storage characteristics of an air-sand moving bed heat exchanger

The air-sand moving bed heat exchanger, designed for storing fluctuating medium-temperature gas waste heat, offers significant potential for energy conservation and carbon reduction in industrial settings. However, its operational characteristics are insufficiently explored. This study investigates the heat storage process involving direct contact and cross-flow of air and quartz sand within a rectangular heat exchanger chamber. Comprehensive analyses were conducted to explore flow resistance characteristics, temperature response, and heat storage performance. Results indicate that pressure drop increases with higher air velocity and temperature, and lower air pressure, particle diameter. The relative discrepancy between fitted pressure drops and experimental data is below 10%. The primary heat transfer zone exists during particle descent. As the air-particle mass flow ratio increases, the descent rate of this zone along the airflow direction slows. Additionally, higher air temperatures elevate the optimal air-particle mass flow ratio. With inlet temperatures for air and particles set at 350 °C and 30 °C respectively, and a mass flow ratio of 0.81, an exergy efficiency of 58.93% and a power density of 600.64 kW·m−3 are achieved. These findings offer crucial insights for air-sand moving bed heat exchangers for medium-temperature gas waste heat recovery.

Simulation study on heat and mass transfer characteristics within tubular moving bed heat exchangers

In the field of waste heat recovery, tubular moving bed heat exchangers (MBHEs) hold great promise as equipment capable of effectively handling large-sized granular materials with high temperature. To further clarify the heat and mass transfer characteristics within tubular MBHEs, this study firstly conducted detailed investigations on the contributions of different heat transfer mechanisms. The result shows that heat radiation (∼45 %) and gas film heat conduction (∼42 %) control the heat transfer processes involving tube walls, with an inlet particle temperature of 600 °C, tube wall temperature of 50 °C, and particle descent velocity of 2 mm/s. These contributions can be influenced by the inlet particle temperature and the tube wall temperature, rather than the particle descent velocity. Additionally, for a specific particle, its heat transfer state is highly depended on where it is located. Subsequently, the time-varying and space-varying characteristics of the heat transfer processes involving tube walls are studied. The results suggest that the time-varying and space-varying characteristics are inherent in tubular MBHEs due to the difficulty to achieve complete stability. Meanwhile, temporal fluctuations intensify with an increase in the inlet particle temperature, a decrease in wall temperature, or an increase in particle descent velocity. The result of power spectral density (PSD) indicates that the heat transfer processes exhibit a degree of chaotic behavior due to the nonlinear property of sub-models, as well as the randomness in particle feeding and contacts. The space-varying characteristic is mainly determined by the inlet particle temperature and the tube wall temperature, rather than the particle descent velocity. This characteristic can be observed in both the axial and circumferential directions, with the circumferential variation being more pronounced than the axial variation. Furthermore, a double-tube MBHE, a topic that has received scant attention in previous research, is investigated in comparison to a single-tube MBHE to explore the differences in heat and mass transfer between the two configurations. It indicates that under the same boundary conditions, there are differences in heat transfer results, which are attributed to the interactions between two vertically arranged tubes. These interactions are reflected in the reconstruction of particle flow patterns and the effect altering the temperature distribution for the particles or fluid surrounding the tubes. The obtained results provide valuable insights into the mass and heat transfer behaviors of particles and fluids within tubular MBHEs, laying a foundation for advancing the development of efficient tubular MBHEs.

Optimization of exergy destruction minimization in moving bed heat exchanger with airflow-assisted cooling

Introducing cooling airflow is an effective method for achieving the localized cooling rate required during waste heat recovery of blast furnace slag. However, the associated parasitic loads must be considered. This study investigates moving bed heat exchanger with airflow-assisted cooling from an exergy perspective. The effects of the granular side Peclet number, airflow side Reynolds number, and the height ratio of the airflow section on heat loss, exergy destruction, and its distributions were examined experimentally. The results show that the trends of temperature and pressure exergy destruction with each parameter tend to be opposite. Therefore, optimizing the parameters requires a trade-off between different types of destruction. Additionally, reducing exergy destruction while meeting the cooling rate requirement was considered. The optimal parameter set was determined by taking the cooling rate requirement as a constraint and minimizing the dimensionless temperature and pressure exergy destruction to obtain the Pareto front.

Waste heat recovery of blast furnace slag considering resource utilization: Localized cooling enhancement in moving bed heat exchanger

When utilizing moving bed heat exchanger for waste heat recovery from blast furnace slag, it's essential to enhance the cooling rate in the high-temperature section to meet the requirements for resource utilization. In this study, we introduced moving bed heat exchanger with airflow-assisted cooling, building upon the shell-and-tube design. This innovation enhanced the cooling rate of the section above the glass transition temperature in the heat exchanger, surpassing the critical cooling rate, through the introduction of cooling airflow in the high-temperature section. Experimental studies were conducted to investigate the impact of airflow Reynolds number, granular Peclet number, and the dimensionless height of the section with cooling airflow on Nusselt number, recovery efficiency, local cooling rate, and pressure drop. Multi-objective optimization of these parameters were performed using hierarchical analysis, leading to the determination of the optimal operational parameters for airflow-assisted cooling moving bed heat exchanger, resulting in Pes=10.18, Reg=2969, and Hap/H=1/9. The Nusselt number, recovery efficiency and pressure drop corresponding to the optimal parameters were 3.593, 79 % and 407.57 pa, respectively.

A comprehensive heat transfer prediction model for tubular moving bed heat exchangers using CFD-DEM: Validation and sensitivity analysis

This study established a complete heat transfer prediction model that integrates four heat transfer sub-models, including contact heat conduction, gas film heat conduction, heat radiation, and heat convection, along with an artificial softening correction based on combined approach of computational fluid dynamics and discrete element method (CFD-DEM). The model’s precision was confirmed by experimental results with relative errors below 5 %. The discussion on the heat flux contributions of the above four heat transfer mechanisms shows that with an initial particle temperature of 200℃, tube wall temperature of 30℃, and particle descent velocity of 1.3 mm/s, gas film conduction heat flux is the primary contributor to the total tube wall heat flux at 60.5 %, followed by radiation heat flux (19.5 %), contact conduction heat flux (12.1 %), and convection heat flux (7.9 %). Besides, the presentation of physical fields related to particles and the fluid showcases the model’s capability in elucidating the heat and mass transfer characteristics of the particle–fluid-wall system within tubular MBHEs. Furthermore, a local nominal range sensitivity analysis, along with a study of factors’ influence rules, was performed to quantify the effects of the 8 key model parameters on heat transfer results. The analysis indicates that fluid thermal conductivity is the predominant factor with its nondimensionalized first-order sensitivity coefficient of 54.9 %, succeeded by particle-to-wall angle factor (15.4 %), wall emissivity (14.4 %), gas film thickness (9.6 %), wall thermal conductivity (2.3 %), wall roughness (-1.6 %), particle Young’s modulus (-1.4 %), and particle specific heat capacity (0.4 %). Finally, their impacts on the heat prediction results were presented in detail.

DEM Investigation on the Flow and Heat Transmission Characteristics of Multi-Size Particles Mixed Flow in Moving Bed

The moving bed heat exchanger (MBHE) has been widely applied in the recovery of waste heat of industrial particles. Currently, investigations focus on uniform-size particles in the MBHE, but few studies are conducted on multi-size particles produced by industrial granulation. Therefore, based on the discrete element method (DEM), the heat transmission model of multi-size particles is established, and flow and heat transmission processes of typically normal distribution particles in the MBHE are studied. In conclusion, there are significant differences in particles tangential velocity and contact number in local regions of a heat exchanger pipe, resulting in different local heat transmission coefficients. In addition, the increases in outlet particle velocity and inlet particle temperature significantly enhance the heat transmission. When the outlet particle velocity grows from 1 mm/s to 5 mm/s, the overall heat transmission coefficient increases by 36.4%, and as the inlet particle temperature rises from 473 K to 873 K, the overall heat transmission coefficient increases by 16.1%.

Effective waste heat recovery from industrial cohesive granular materials: A moving bed indirect heat exchanger with special flow control

Particle-based moving bed heat exchangers are increasingly playing a significant role in industrial energy conservation and solar energy utilization. However, the moving bed heat exchanger used for cohesive granular materials still needs to be developed. This paper investigates the feasibility of indirect heat transfer of cohesive granular materials through a moving bed heat exchanger. A vibrating moving bed heat exchanger is developed for the metallurgical slag of vanadium-titanium (MSVT) from industry. The experiment demonstrates that the vibrating moving bed heat exchanger can establish an approximate mass flow regime of MSVT in the experimental section. The vibration device designed for the experimental and discharge section effectively resolves bridging and the intermittent collapse of arching in cohesive granular materials. The outer side of the tube is tightly wrapped by MSVT with vibration. Significant differences are observed in the flow and heat transfer behavior of MSVT between the aligned and staggered tubes. The local heat transfer coefficient at the top and bottom of the aligned tubes exhibits much lower sensitivity to flow velocity compared to the staggered tubes. The relationship between Nu−1 and Pe−0.5 or MSVT around the aligned and staggered tubes follows a linear correlation. Compared to aligned tubes, Nu−1 for MSVT in staggered tubes shows an average reduction of 28%.

Exergy transfer characteristics and structural parameters optimization in blast furnace slag heat recovery device

Thermodynamic analysis was employed to evaluate an MBHE (moving bed heat exchanger) for heat recovery from BFS (blast furnace slag). The study conducted experimental investigations to assess the influence of several factors on heat transfer, exergy transfer, and exergy destruction, including the granular side Peclet number, waterside Reynolds number, arrangement, tube spacing, and tube shape. Structural parameters of the MBHE were optimized based on the heat transfer enhancement number, resulting in the determination of the optimal parameters: staggered arrangement, Dh/D=2, Dv/D=3, and elliptical tubes.

Experiment study and heat resistance analysis on heat transfer characteristics in staggered tube moving bed heat exchangers

Heat transfer of high temperature granules in the moving bed heat exchanger is an important thermal process in a blast furnace slag waste heat recovery system. Gaining a comprehensive understanding of granular side heat transfer characteristics is crucial. Here, we experimentally investigated the effects of velocity, diameter, diameter distribution, inlet temperature and granule type on granular side heat transfer and the development of heat transfer in the flow direction in a staggered tube array. Furthermore, the experimental results were analysed via the thermal resistance theory. The obtained results indicate that the heat transfer coefficient increases with increasing velocity and inlet temperature and decreases with increasing diameter. Multi-sized granules and blast furnace slag have better heat transfer than mono-sized granules and phosphorus slag, respectively. The heat transfer coefficient tends to increase and then decrease in the flow direction, with the location of the peak, depending on the ratio of the contact and penetration thermal resistance. The semi-empirical formula based on experimental results can provide a theoretical basis required to design.

Solution by the self-adjoint operator method for a model of a co/counter-current moving bed heat exchanger with heat losses

A solution by the self-adjoint operator method (SAO) (still not widely used in engineering) is presented for a lumped parameter model (LM) of a co/counter-current, indirect heated, diluted, tubular, vertical moving bed heat exchanger (MBHE), with heat loss to surroundings. The self-adjoint formulation of the problem and several mathematical techniques enabled the development of an ingenious methodology capable of solving the difficult problem of establishing the character of the eigenvalues of the MBHE operator - only partially known to date - for co/counter flow.For co-current flow, it is demonstrated that the self-adjoint solution corresponds to a solution from the literature - obtained by the Laplace transform - but with the character of the roots not yet established. Therefore, the work aims to, through analysis, study the character of the eigenvalues of the MBHE operator to generalize results from the literature, allowing the use of the solution in a comprehensive parametric range, as well as for different flow arrangements, discussed within the scope of case studies. From the analysis of the eigenvalue equation, five thermal behaviors of the MBHE could be identified. The model was also solved numerically, and the results show excellent agreement in both calculation methods. The obtained analytical solution reveals a possible inconsistency in a literature solution of the analogous heat transfer problem in a triple tube heat exchanger (the) with thermal losses at the outer surface. The study generalizes previous results and allows its extension, by analogy, to the solution for the TTHE with thermal losses at the outer surface.

Limit Solutions for a Lumped Parameter Model of Heat Transfer in a Diluted and Indirectly Heated Co-Current/Counter-Current Moving Bed Heat Exchanger with Heat Loss to Surroundings

Limit solutions and solutions by analogy play an important role in the interrelation of engineering problems. However, research with this approach is extremely rare in heat transfer in particulate systems. Given this scarcity, a series of limit solutions are developed for a lumped capacity (LP) model of a co/counter-current tubular moving bed heat exchanger (MBHE), vertically arranged, indirectly heated, diluted and with heat losses to the surroundings. In the solution methodology, the problem is formulated by analyzing the model parameters and the eigenvalues of the system operator, and by identifying indeterminate forms (INDs). Then, INDs are usually calculated by algebraic rearrangement and/or L'Hôpital's rule. Among the results, there are almost a dozen new solutions, the systematization of INDs in the counter-current flow and the verification of agreement between experimental data and the LP model for infinitely diluted bed - provided that the simplifying hypotheses are observed. Finally, the interconnection of LP models of MBHE in a decreasing order of complexity and in a historical perspective provides a broad understanding of the evolution of the LP modeling of this important industrial equipment.

Evaluation of Mathematical Models for CO2 Frost Formation in a Cryogenic Moving Bed

Moving bed heat exchangers (MBHE)s are used in industrial applications including waste heat recovery and the drying of solids. As a result, energy balance models have been developed to simulate the heat transfer between a moving bed and the gas phase. Within these energy balance models, phase change of components within the gas phase has not been considered as the liquefaction or desublimation of the gas phase does not occur in typical industrial applications. However, available energy balance models for cryogenic CO2 capture (CCC) have only focused on fixed packed beds. The development of a suitable energy balance model to predict the energy duties for MBHEs that include phase change would be beneficial for CCC applications. This work investigated the development of moving bed energy balance models for the design of moving bed columns that involve phase change of CO2 into frost, using existing models for MBHEs and fixed-bed CCC capture. The models were evaluated by comparison with available moving bed experimental work and simulated data, predicted energy duty requirements and bed flow rates from the suggested moving bed CCC models to maintain thermal equilibrium. The comparisons showed a consistent prediction between the various methods and closely align with the available experimental and simulated data. Comparisons of energy duty and bed flow rate predictions from the developed energy balance models with simulated cases for an oil-fired boiler, combined cycle gas turbine (CCGT) and biogas upgrading showed energy duty requirements for the gas phase with a proximity of 0.1%, 20.8%, and 3.4%, respectively, and comparisons of gas energy duties from developed energy balance models with energy duties derived from experimental results were compared with a proximity of 1.1%, 1.1% and 0.6% to experimental results for CO2 % v/v concentrations of 18%, 8% and 4%.

Numerical study of heat transfer for gravity-driven binary size particle flow around circular tube

As the primary working medium in moving bed heat exchangers, solid bulk materials are composed of multiple size particles. To clarify the effect of particle size distribution (PSD) on heat transfer, the discrete element method (DEM) is used to study the flow and heat transfer of binary size particle flow around a circular tube. The heat transfer model for multiple size particles is developed and coupled with DEM method. The particle flow characteristics with PSD width are analyzed in detail. The results show that particle size segregation, competitive flow and flow instability are the unique characteristics of binary size particle flow around a tube. Wider PSD will enhance these characteristics and have a positive effect on particle renewal in the stagnation zone, which could decrease the local heat resistance. The total heat transfer coefficient between particle flow and tube wall increases at most by 9.73% as PSD is wider. • Binary size particle flow around a circular tube is studied with DEM method. • Binary size particle flow can form local particle size segregation around tube. • Binary size particles can decrease the stagnation zone above the tube. • A wider binary particle size distribution can increase the flow instability. • A wider binary particle size distribution can enhance heat transfer performance.

Dynamic characteristics and real-time control of a particle-to-sCO2 moving bed heat exchanger assisted by BP neural network

The transient response of a particle-to-sCO2 moving bed heat exchanger (MBHE) is investigated by a continuum model when perturbations are applied to the particle inlet temperature, sCO2 inlet temperature, and the sCO2 mass flow rate. Upon disturbance, the outlet temperatures of the sCO2 and particle flows deviate from the designed values and gradually approach a new steady state. The transient process can be described by exponential functions when the disturbance is applied to one of the input parameters while the transition becomes unpredictable when multiple input parameters are simultaneously varied. Two real-time control strategies are then adopted to maintain the sCO2 outlet temperature at its designed value. In strategy 1, the particle flow rate is adjusted; In strategy 2, the sCO2 flow is divided into two branches: one branch flows through the heat exchanger for heating, and the other enters a bypass. The values of the adjusting parameters are instantly determined based on the BP neural network. By setting 50 random disturbance cases, we demonstrate that the control strategy based on sCO2 bypass and BP neural network can effectively make the outlet temperatures of particle and sCO2 flows reach their designed values with minimal deviations.

Experimental validation of a continuum model for local heat transfer in shell-and-tube moving-bed heat exchangers

• Local heat transfer coefficients in shell-and-tube moving bed heat exchangers were simulated. • Local heat transfer coefficients were measured using a small heat exchanger mockup. • Experimental results were used to validate a comprehensive thermal model. • Simulation results were in good agreement with the experiments. Moving-bed heat exchangers with a horizontal tube arrangement offer a promising solution to exchange high-temperature heat with a particle stream. However, in order to guide the design of such heat exchangers, accurate and time-efficient simulation tools capable of capturing the complex heat transfer characteristics still need to be improved. In this article we present experimental results of the local heat transfer coefficients around the tube circumference of a heat exchanger mockup. To this end, specially prepared measuring probes were developed and a test campaign was conducted. A comprehensive thermal model was applied to the setup under consideration. This model takes into account the temperature-dependent thermophysical properties of the bulk, variable temperature boundary conditions, and the increased thermal resistance caused by the stagnation and void zones. To validate the model, calculated and experimental results were compared. It turns out that the predicted heat transfer coefficients well match the experimental data, albeit with slight deviations at the stagnation and void zones of the tubes. The prediction of a tube’s area-weighted heat transfer coefficient, which constitutes the most important factor for design purposes, yields results with errors of less than 3%. Therefore, it is concluded that the proposed thermal model is able to well predicts the heat transfer in shell-and-tube moving-bed heat exchangers.

Heat transfer of granular flow around aligned tube bank in moving bed: Experimental study and theoretical prediction by thermal resistance model

Gravity-driven granular flow has been the heat transfer mediums in moving bed heat exchangers, which play vital roles in industrial heat saving and solar energy utilization. However, the heat transfer mechanism of granular flow is still worth of investigating around the tube bank. In this work, the aligned tubes were arranged in the moving bed, and the heat transfer of metallurgical slag was experimentally tested. It was found that, the heat transfer coefficients are significantly sensitive to the flow rate in the slow granular flow. The smooth flow with particle mixing can improve the heat transfer, while the local particle lagging will worsen the heat transfer around aligned tubes. To predict heat transfer coefficients of granular flow, the contact thermal resistance and the penetration thermal resistance are built with empirical factors (χ, a and η). In the near-wall region, x represents the sensitivity of the contact thermal resistance to particle sizes. Meanwhile, the contact time can be modified by a and η for the penetration thermal resistance in the funnel flow structure. The values of a and η are affected by the granular flow pattern, which tend to decrease in the smooth flow with strong particle mixing. Verified with the present experimental results and the previous literature data, the thermal resistance model has great potentials to explain the heat transfer around the aligned tube bank.

A Simple Solution for Heat Transfer in a Triple Tube Heat Exchanger

Triple tube heat exchangers in general perform better when compared to double tube heat exchangers, mainly because they improve the heat transfer due to the passage of additional fluid and also of its larger heat transfer area per length unit. Nevertheless, for triple tube heat exchangers, the analytical solutions available in the literature are limited to specific boundary conditions or are cumbersome. Therefore, this work aims to obtain a compact form of the analytical solution, suitable for co-current and counter-current flow arrangements. The solution form is developed based on a solution from literature for a co-current moving bed heat exchanger model, through analogies with triple tube heat exchangers. From the solution form, explicit expressions for the crossover points are also obtained. For a better understanding of the underlying physics, a scale analysis is performed. When compared to experimental data and more complicated solutions from literature, the obtained results presented good agreement.

Pseudo counter-current turbulent fluidized bed process with sensible heat recovery for energy-efficient CO2 capture using an amine-functionalized solid sorbent

A fluidized bed adsorption (FLBA) process with internal heat integration is considered an energy-efficient method for large-scale CO2 capture. Herein, we propose a pseudo counter-current FLBA process for post-combustion CO2 capture as a proof-of-concept based on a rationally designed moving bed heat exchanger by incorporating the internal heat integration concept of the conventional amine scrubbing CO2 capture process. The proposed FLBA process consists of an adsorption bed, desorption bed, and moving bed heat exchangers for cooling and heating the solid sorbent. The design of the proposed FLBA process enables internal heat integration by recovering sensible heat from the cooling process. Furthermore, by installing multiple adsorption processes, the pseudo counter-current operation in the adsorption bed enhances the CO2 cyclic capacity of the amine-functionalized solid sorbent with high CO2 recovery. The proposed process complements the two weaknesses of FLBA, namely, large sensible heat and low cyclic capacity of the sorbent. The energy analysis, based on rigorous mathematical modeling, estimates that the energy demand of the optimized FLBA using SiO2/0.37 EB-PEI is approximately 258.6 kWh/t-CO2 with 45% sensible heat recovery. This low energy demand is comparable to that of the most mature amine-based absorption process (271 kWh/t-CO2) owing to the effect of internal heat integration, supporting the feasibility of the FLBA process for post-combustion CO2 capture.

Heat transfer prediction of granular flow in moving bed heat exchanger: Characteristics of heat transfer enhancement and dynamic control

To realize the heat transfer between granular flow and sCO2 cycle, moving bed heat exchangers have been widely applied in Concentrating Solar Power systems. This work developed a prediction model for heat transfer enhancements and dynamic control strategies in a shell-and-plate moving bed heat exchanger. For fast evaluation of heat transfer performances in granular flow, the continuum model was adopted with different thermal resistances. The wall effect of near-wall region was modified by contact thermal resistance, and the equivalent heat diffusion in bulk region was reflected by penetration thermal resistance. The results showed that, the decrement of penetration thermal resistance can improve heat transfer effectively. To weaken the penetration thermal resistance, the thinner thermal boundary layer and the higher effective thermal conductivity are urgently required. The staggered arrangement is a valid way to limit the development of thermal boundary layer. The bank of heat exchanger plates offset horizontally from the previous bank, and the re-evolution of temperature distributions is equal to the equivalent thermal mixing between different banks. Meanwhile, the effective thermal conductivity can be improved by particle self-diffusions perpendicular to the major flow direction. For the particle migrations, the local disturbances can be applied. The relatively decrement of penetration thermal resistance can achieve 45.7% at a disturbance intensity of 5 × 10−7 m2/s. The outlet temperature of sCO2 can be well controlled by the transient temperature–velocity feedback method with relaxation coefficients. The relatively decrement of temperature fluctuation is larger than 80% with a relaxation coefficient of 40.

Numerical investigation of flow and energy dissipation for granular materials in moving bed heat exchangers based on μ(I) theory

A comprehensive Eulerian model based on μ(I) rheology theory is established to describe the granular flow inside moving bed heat exchangers (MBHEs). The established model is validated, and the rheological parameters involved in μ(I) model are determined using the experimental results of velocity distributions for three kinds of typical granular materials in a thin silo. Detailed results regarding the particle velocity, solid volume fraction, particle intergranular shear stress, resistance, and energy dissipation of three different granular flows in a staggered-arranged MBHE and an aligned-arranged MBHE are revealed and discussed. The relationship among dimensionless dissipation, velocity, and pressure in the transition zone is analyzed to demonstrate the influences of granular properties and pipe arrangement on granular flow.