analysis of particle based thermal storage solutions for

Master Thesis

Analysis of Particle Based Thermal Storage Solutions for Gas Turbine Applications

For the purpose of obtaining the academic degree of a Master of Science under the supervision of

Univ.Prof. Dipl.-Ing. Dr.tech. Markus HAIDER

Institute for Energy Systems and Thermodynamics

Submitted at Vienna University of Technology

Faculty of Mechanical Engineering and Business Sciences

from

Kühne David Emanuel Matrikelnr. 01326668

Vienna, July 2021 ________________________

David, Kühne

Abstract

The growth of installed renewable energy sources as a reaction to the rising interest in a low-carbon energy production has an impact on the load activity of conventional power plants. The generated power from wind parks and photovoltaic power stations is fluctuating based on the local weather conditions, which are often unpredictable and change in a short amount of time. This behavior results in many load changes of conventional power plants to provide a stable frequency in the electricity grid. The lifespan of these power plants, which are often thermal power plants, will be reduced due to the load changes and that the operating point is not the design case. This leads to higher maintenance costs, reduced efficiency and often to a higher carbon output. To maintain a constant load on conventional power plants, the fluctuating share of the electricity fed into the grid needs to be stored when the supply exceeds the demand, or the produced energy from a conventional power plant needs to be stored to enable a flexible supply. The aim of this thesis is to develop a sensible particle-based heat storage system that allows the load flexibility of combined cycle power plants (CCPP) to be increased by diverting the exhaust gas from a gas turbine, which is normally used in a steam generator to drive a steam turbine. Two systems are envisioned for this task, a fluidized bed heat exchanger (HEX) and a plate type moving bed HEX. For the first system the exhaust gas from a gas turbine will be used to fluidize a sand bed and heat the particles. With the exhaust gas fluidizing the solid bulk, additional components are reduced to bulk conveying systems which transport the heat storage material from the HEX to storage tanks and back. The second system consists of several channels arranged in parallel, which are traversed by air. The heat storage material falls between these channels, reducing the auxiliary energy to bulk conveying systems. Both systems will be analyzed numerical to gain information about viable operating conditions and the physical values of both streams. In a second step computational fluid dynamic (CFD) systems are used to optimize the proposed systems.

Kurzfassung

Aufgrund des stetig wachsenden Interesses an einer CO2 neutralen Energieproduktion, wächst dementsprechend auch der Anteil an erneuerbaren Energiequellen. Dies führt zu zusätzlichen Belastungen bei konventionellen Kraftwerken, da die produzierte Energie von Wind- und Solarparks aufgrund der jeweiligen Wettersituation,- welche sich oft innerhalb kurzer Zeit ändert-, unstetig ist. Dies führt dazu, dass konventionelle Kraftwerke mehrere Lastwechsel haben, um eine stabile Frequenz im Stromnetz zu garantieren. Die Lebenserwartung dieser Kraftwerke, welche oft thermische Kraftwerke sind, verringert sich dadurch erheblich da die Lastwechsel den Verschleiß deutlich erhöhen und zusätzlich die Kraftwerke oftmals nicht in ihrem Auslegungspunkt betrieben werden. Dies führt zu erhöhten Wartungskosten, einer reduzierten Effizienz und oftmals zu einem erhöhten Kohlenstoffausstoß. Um konventionelle Kraftwerke unter konstanter Belastung zu betreiben, muss der schwankende Anteil, der in das Stromnetz eingespeisten Energie, gespeichert werden, wenn das Angebot die Nachfrage übersteigt. Alternativ dazu kann auch die überschüssig produzierte Energie von konventionellen Kraftwerken zwischengespeichert werden, um einen flexiblen Nachschub zu ermöglichen. Das Ziel dieser Arbeit ist es, einen Sandbasierten, sensiblen Wärmespeicher zu entwickeln, welcher eine erhöhte Lastflexibilisierung von Kombikraftwerken ermöglicht. Dazu wird das Abgas einer Gasturbine einem Wärmetauscher mit Sand zugeführt, anstelle des Dampferzeugers einer Dampfturbine. Für diese Anwendung werden zwei Systeme genauer betrachtet. Ein Wärmetauscher auf der Basis einer Wirbelschicht und ein Plattenwärmetauscher. Bei dem ersten System ist der Kontakt zwischen den zwei Wärmeträgermedien direkt, indem das Abgas zur Fluidisierung einer Sandschüttung genutzt wird. Dadurch reduzieren sich die zusätzlich benötigten Anlagenteile auf Fördereinrichtungen für den Sand zu den jeweiligen Speichertanks. Der Plattenwärmetauscher besteht aus mehreren parallel angeordneten Kanälen, welche von dem Abgas durchströmt werden. Das Wärmespeichermaterial rinnt dabei zwischen den Kanälen nach unten wodurch sich auch bei diesem System die zusätzlich benötigten Anlagenteile auf Fördersysteme und Speichertanks reduzieren. Beide Systeme werden basierend auf dem bisherigen Wissensstand mathematisch analysiert, um die physikalischen Zusammenhänge abzubilden und um Informationen über rentable Betriebsbedingungen zu gewinnen. Anschließend werden mit numerischen Strömungssimulationen die Systeme optimiert.

Content 1 Introduction ................................................................................................................. 1

1.1 Motivation .............................................................................................................. 1 1.2 Overview ............................................................................................................... 2

2 Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX ............. 4 2.1 Operating Principle and Design ............................................................................. 4 2.2 Parameter Analysis ............................................................................................... 4

2.2.1 Cross Section .................................................................................................................... 5 2.2.2 Particle Diameter ............................................................................................................... 6 2.2.3 Terminal Velocity ............................................................................................................... 6 2.2.4 Fluidization Velocity ........................................................................................................... 7 2.2.5 Pressure Drop ................................................................................................................... 8

2.2.5.1 Pressure Drop Distribution Floor ............................................................................................ 9 2.2.6 Voidage ........................................................................................................................... 10 2.2.7 Heat Exchange ................................................................................................................ 11

2.2.7.1 Local Heat Transfer ............................................................................................................. 11 2.2.7.2 Heat Transfer per Stage ...................................................................................................... 18 2.2.7.3 Heat Transfer in the Multistage Fluidized Bed HEX ............................................................. 19

2.3 CPFD Simulation ................................................................................................. 23 2.3.1 Introduction ...................................................................................................................... 23 2.3.2 Parameter Data ............................................................................................................... 23 2.3.3 Simulation Plate Inclination ............................................................................................. 24 2.3.4 Simulation Downcomer ................................................................................................... 25 2.3.5 Simulation Heat Transfer ................................................................................................. 30

2.4 Conclusion ........................................................................................................... 31 2.5 Nomenclature ...................................................................................................... 32

3 Indirect Contact Plate Type Moving Bed HEX ......................................................... 34 3.1 Operating Principle and Design ........................................................................... 34 3.2 Local Heat Distribution ......................................................................................... 34

3.2.1 Nomenclature .................................................................................................................. 38

3.3 Analytical Calculation Of A Multistage Moving Bed HEX ...................................... 39 3.3.1 Heat Exchange Single Stage .......................................................................................... 39 3.3.2 Pressure Drop ................................................................................................................. 44

3.3.2.1 Pressure Drop in Flow Through Pipes ................................................................................. 45 3.3.2.2 Pressure Drop from a Helical Coil ........................................................................................ 47 3.3.2.3 Pressure Drop from Bends .................................................................................................. 48 3.3.2.4 Pressure Drop from changes of the Cross Section .............................................................. 49

3.3.2.5 Pressure Drop from Collector and Distributor ...................................................................... 51 3.3.2.6 Conclusion Pressure Drop ................................................................................................... 52

3.3.3 Multistage Algorithm ........................................................................................................ 53 3.3.4 Heat Exchange Multistage .............................................................................................. 53 3.3.5 Dimension Multistage System ......................................................................................... 56 3.3.6 Conclusion ....................................................................................................................... 58 3.3.7 Nomenclature .................................................................................................................. 58

4 Alternative TES Approaches .................................................................................... 60 4.1 sandTES .............................................................................................................. 60 4.2 Packed Bed Heat Exchanger ............................................................................... 60 4.3 Cyclone Heat Exchanger ..................................................................................... 61 4.4 Falling Particle Heat Exchanger ........................................................................... 62

5 TES Integration Into CCPP ....................................................................................... 63

6 Summary and Conclusion ........................................................................................ 66

7 Attachment ................................................................................................................ 67 7.1 List of Tables ....................................................................................................... 67 7.2 List of Figures ...................................................................................................... 67 7.3 References .......................................................................................................... 69

Introduction 1

1 Introduction

1.1 Motivation

During the last years the global population was growing steadily which leads to a higher energy demand. In addition to that trend the individual energy demand is rising, and many countries move towards more advanced technologies. Combined with shorter product cycles, globalization, and more competing markets these developments lead to a higher overall carbon emissivity and waste production. These negative effects are not unnoticed and a lot of environmental concerns are rising. To tackle these problems international environment associations have been founded, treaties signed between nations and measures to reduce the emissions specified.

Especially industries with high energy consumption have a big potential to limit their emissions and the overall energy production. In the last decades, the sector of renewable energy production is steadily increasing. This positive trend has negative consequences on fossil power plants. Through a larger share of wind and solar energy, the existing power plants need to perform a lot more load changes to enable a stable frequency in the electricity grid. Most of these power plants are built for a constant load and long running times. These are huge facilities which need longer times to start and stop as wind and solar energy, which are heavily affected by weather changes, which cannot be predicted accurately enough. With more flexible loads the power plants need shorter maintenance intervals, and their overall lifespan decreases which leads to higher operating costs. To counteract this problem, it is necessary to develop large scale electricity storage or find a way to operate fossil power plants more flexible without causing additional stress on the system.

This study is focused on heat storage systems to increase the load flexibility of combined cycle power plants. The exhaust heat from the gas turbine is stored while the produced energy from the following steam turbine is not necessarily needed, due to sufficient carbon neutral produced electricity. Because of this arrangement the gas turbine can remain in base load which benefits its lifespan. In addition to the mechanical advantages the electricity grid retains a higher operating reserve. When a disruption occurs in the energy grid, spinning reserves have the advantage to be instantaneous available and do not need to start from standstill, so the preferred grid frequency will be stable.

Introduction 2

1.2 Overview

The main thermal energy storage (TES) systems are sensible and latent storage systems. In addition to these two well studied systems there are thermochemical storage systems. For sensible storage systems the heat is transferred with the aid of a heat exchanger into a storage material. When the temperature of a material rises, its energy content also increases. This way heat can be stored within insulated tanks and released at a later point in time. The energy that is absorbed or released by a material when a temperature change occurs is called sensible heat. When a material undergoes a phase change there is energy absorbed or released for the material to change its state. This energy is called latent energy and in most applications the phase change between solid and liquid is applied, because there is a much smaller change in the density as when a liquid is evaporated. For a thermochemical energy storage system, the heat is stored during an endothermic process which separates two elements or chemical compounds. The reaction enthalpy is released in an exothermic process when the separated reactants are brought back together. The reactions must be reversible to make the material viable for multiple load cycles. For further insights on thermal energy storage the work of Gil et al [1] has a good overview on available systems. The focus in this work is on sensible heat storage for the exhaust gas of gas turbines.

The material for large scale heat storage systems affects the project cost, possible temperature range and the HEX design. There are many solid powers suitable for sensible TES systems. The used material in this study is quartz sand with the main component SiO2. Sand has a good thermal capacitance (m*cp), low cost, non-toxicity, is readily available and has a high temperature range of operation which makes it a good candidate as storage material.

The technical university of Vienna has done a lot of research on sand systems as heat storage [2] and is steadily expanding the research on possible heat exchange systems. The focus in this work is on two systems, a fluidized bed HEX with direct contact between the two material flows and a moving bed HEX with indirect contact, both shown in Fig. 1. For the fluidized bed HEX, sand will pass a cascade of stages to store the heat of the exhaust gas stream which is used to fluidize the sand bulk. In a recovery step cold air can flow through the HEX with the hot sand as feed mass flow to regain the stored heat. The moving bed HEX uses several channels to separate the exhaust gas stream from the sand stream, which will fall between the channels. This system also allows a recuperation step with cold air and the stored hot sand to produce an additional hot air stream for the steam generator of a CCPP. Both systems need additional sand storage tanks and bulk conveying systems.

Introduction 3

Fig. 1. Fluidized Bed HEX Design and Moving Bed HEX Design The main limitation of the storage systems is the allowed pressure drop in the exhaust stream of a gas turbine which is set to 4000 Pa. For higher pressure drops the performance of the gas turbine deteriorates too much. The main pressure drop in the direct contact HEX is the distribution floor of each stage and the fluidization of the respective sand bulk. For the indirect contact HEX the piping of the gas flow needs to be optimized to limit the pressure drop to an appropriate level.

Both systems are assessed according to the following steps. Relevant literature is screened, and the necessary calculation steps evaluated. With this knowledge a simulation tool in MatLab will be written to analyze possible operating conditions and gain information about the overall pressure drop, viable temperature ranges and the geometry. The results from the numerical simulation will be checked with the CFD program Barracuda from CPFD. In the following step the proposed systems will be optimized.

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 4

2 Analytical Calculation Of A Direct Contact

Multistage Fluidized Bed HEX

2.1 Operating Principle and Design

The concept of this system is based on the local heat transfer between a fluidization gas and the particles of its passing bed. When the gas stream surpasses the minimal fluidization velocity the particles of the bed material are rapidly mixed which enhances the heat transfer between the gas stream and solid stream. To improve the efficiency of the system multiple HEX stages are connected in a crossflow configuration, which leads to an overall counterflow behavior.

Fig. 2. Design of a multistage fluidized bed HEX 2.2 Parameter Analysis

To determine the possible operating range for the sand heat exchanger the influence of the respective parameters must be analyzed. The main goal is to keep the upper and lower temperature difference of both streams as small as possible within a compact building volume. The pressure drop in the hot exhaust stream is limited to 4000 Pa to avoid performance losses in the gas turbine. The following calculations are according to the VDI heat atlas [3] and marked if the presented equations have another origin.

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 5 2.2.1 Cross Section

The main factor for the building volume is the gas-stream velocity which is determined by the exhaust mass flow and the HEX cross section. For the determination of a minimal gas velocity the cross section is calculated as shown in equation (1) and the volumetric gas flow by equation (2)

When the exhaust gas progresses through the HEX the gas temperature decreases and the gas density increases. Therefore, the maximum needed area is in the HEX stage with the highest gas temperature. Typical exhaust gas parameters are presented in Tab. 1 To keep the building volume low, the gas velocity should be at least 3 m/s at the gas inlet for an exhaust mass flow of 200 kg/s. Tab. 1. Exhaust Gas Parameter from the Siemens Product Range

Product Power Output Exhaust Mass Flow Exhaust TemperatureSiemens MW kg/s °C

SGT6-9000H 310 650 645SGT6-5000F 215 478 612

SGT-800 54 135 563

𝐴 = �̇�𝑢 (1) �̇� = �̇�𝜌𝐺 (2)

Fig. 3. HEX cross section for a gas density of 0.6 kg/m³

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 6 2.2.2 Particle Diameter

The effective diameter deff of a particle is calculated by its spherical diameter dsph and the sphericity ΦS as shown in equation (3). dsph represents the diameter of a sphere with the same volume as the used particle. The sphericity compares the surface of a sphere to the surface of a particle with the same volume as the sphere. For sand the sphericity is in a range from 0.53 to 0.86 and will be assumed as 0.8 throughout this study [4].

The particle diameter affects the heat transfer between the fluidization gas and the bed material and has an impact on the possible gas velocity. If both the charge and discharge step of the bed material are realized with a direct contact HEX bigger grain sizes up to 1000 µm should be preferred to enable higher gas velocities. When the storage material is connected to an indirect HEX the grain size should not exceed 500 µm or the chances for abrasion increase. Particle transportation with the gas stream should be avoided to lower the risk of clogging the distribution floor from the following HEX-stage. Bigger particles have a negative impact on indirect contact HEX from the TU-Project SandTES, where pipes are immersed in the fluidized bed. With increasing particle size, the auxiliary power to maintain a stabilized bed and the abrasion on the immersed pipes increases. Therefore the particle diameter has to be optimized for both the discharging and charging process or the discharging process has to be realized as a direct contact HEX to avoid unreasonable power and material losses.

2.2.3 Terminal Velocity

The gas velocity also affects the minimal grain size to avoid particle transportation with the gas stream. The following calculations are in the transition area between a laminar and turbulent flow specified by 0.2 < Re < 1000. It would not be convenient to use the system outside these parameters. A laminar flow leads to a high HEX-cross section and a turbulent flow to particle transportation. For the determination of the flow area the Reynolds number is calculated as shown in equation (4)

The upper velocity limit of the possible gas velocity is determined by the terminal velocity ut of the used particles in the HEX. A local equilibrium of weight force and buoyancy force plus resilience force is considered for each grain to calculate the terminal velocity with equation (4) and (5).

𝑑𝑒𝑓𝑓 = 𝜙𝑆 ∗ 𝑑𝑠𝑝ℎ (3)

𝑅𝑒 = 𝜌𝐺 ∗ 𝑢 ∗ 𝑑𝑒𝑓𝑓𝜇𝐺 (4)


In the calculation of ut the Archimedes number Ar (6) is included which can be interpreted as correlation of buoyancy force to friction force.

Fig. 4. Terminal velocity for a gas density of 0.6 kg/m³, ρP=2650 kg/m³, µG=2.9*10^(-5) kg/(m*s) 2.2.4 Fluidization Velocity

The lower velocity limit is determined by the minimum fluidization velocity umf (7). umf represents the velocity which marks the transition from a fixed bed to a fluidized bed. The most used correlation to calculate the Reynolds number at the minimum fluidization is equation (8) from Wen and Yu. In this equation the voidage at minimum fluidization is neglected which leads to an inaccuracy. There are a lot of different correlations given to calculate the minimum fluidization velocity. These deviations come from a flow behavior which is hard to depict in fluidized beds. To determine the exact value of umf the pressure drop in the fluidized bed must be measured over an increasing velocity.

𝑅𝑒𝑡 = √43 ∗ 𝐴𝑟 (5)

𝐴𝑟 = 𝜌𝐺 ∗ 𝑑𝑒𝑓𝑓3 ∗ (𝜌𝑃 − 𝜌𝐺) ∗ 𝑔𝜇𝐺2 (6)

𝑢𝑚𝑓 = 𝑅𝑒𝑚𝑓 ∗ 𝜇𝐺𝜌𝐺 ∗ 𝑑𝑒𝑓𝑓 (7) 𝑅𝑒𝑚𝑓 = 33.7 ∗ (√1 + 3.6 ∗ 10−5 ∗ 𝐴𝑟 − 1) (8)


Fig. 5. Minimum fluidization velocity for a gas density of 0.6 kg/m³, ρP=2650 kg/m³, µG=2.9*10^(-5) kg/(m*s) 2.2.5 Pressure Drop

The allowed overall pressure drop limits the use of multiple stages and can be calculated for each stage as shown in equation (9) to (11).

The development of the pressure drop Δpfb induced by the bulk material in relation to an increasing bed height is shown in figure 4 for a particle density of 2650 kg/m³. These values can also be used for higher fluidization grades since the voidage of the expanded bed and the expanded bed height cancel each other in equation (9).

Δ𝑝𝑓𝑏 = (1 − 𝜀) ∗ (𝜌𝑃 − 𝜌𝐺) ∗ 𝑔 ∗ ℎ𝑓𝑏 (9) Δ𝑝𝑓 = 𝑢 ∗ 𝑠 ∗ (𝜇𝐺𝛼𝐵 + 𝑢 ∗ 𝜌𝐺𝛽𝐵 ) (10)

Δ𝑝𝑆 = Δ𝑝𝑓𝑏 + Δ𝑝𝑓 (11)


Fig. 6. Pressure Drop in the fluidized bed 2.2.5.1 Pressure Drop Distribution Floor

To provide a uniform gas distribution, which enables small bed heights, sinter plates are used as nozzle distribution floor. The pressure drop from the distribution floor Δpf is calculated according to the manufacturer GKN Sinter Metals (10). The quadratic dependency of the gas velocity restricts the available materials which can be used for the distribution of the exhaust gas and the possible gas velocity. Different permeability coefficients are represented in Tab. 2. The progress of the pressure drop shown in Fig. 7 is for SIKA-B 200 with a thickness of 5mm which is currently the thinnest available version of these sinter plates.

Fig. 7. Pressure Drop in the Distribution Floor SIKA-B 200, ρG=0.4 kg/m³, s=5 mm

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 10 Tab. 2. Permeability coefficients from the GKN-Sika product catalogue

2.2.6 Voidage

The voidage ε indicates the correlation between the empty space in the fluidized bed and the overall bed volume. The progress of the voidage with an increasing gas velocity can be approximated with equation (12) by Richardson and Zaki.

Higher velocities lead to a higher voidage because of an increasing bubble size in the sand bed. These bubbles will form a bypass canal which hinders the heat transfer between the exhaust gas and the bed material. Further explanations are discussed in 2.2.7. The expanded bed height can be calculated as shown in (14). These equations can’t be applied above the terminal velocity due to particle transportation.

𝜀𝑛 = 𝑅𝑒𝑅𝑒𝑡 (12) 𝑛 = ln (𝑅𝑒𝑚𝑓/𝑅𝑒𝑡)ln (𝜀𝑚𝑓) (13)

ℎ𝑒𝑥𝑝 = ℎ𝑚𝑓 ∗ 1 − 𝜀𝑚𝑓1 − 𝜀 (14)


Fig. 8. Voidage in the fluidized bed for a particle diameter of 500 µm, additional material parameters in Tab. 3. 2.2.7 Heat Exchange

To determine the temperature distribution through the whole system, it must be split in smaller sections. In 2.2.7.1 the heat transfer between the involved material flows will be analyzed. With this knowledge the calculations can be expanded on a single bed to determine the outlet temperatures of each material flow after one HEX-stage as seen in 2.2.7.2. A final calculation of the temperature progress of each material flow through the whole system is presented in Tab. 4 and Tab. 5. These calculations must be validated experimentally.

2.2.7.1 Local Heat Transfer

The heat transfer between fluid and particle will be calculated like the suggested model in the VDI heat atlas. This model takes the uneven distribution of bubbles into account and the mixing of suspension and fluid.

𝜂𝑡𝑜𝑡 = 𝜗𝐺,𝑜𝑢𝑡 − 𝜗𝐺,𝑖𝑛𝜗𝑃 − 𝜗𝐺,𝑖𝑛 (15)


Fig. 9. Model for the calculation of the heat transfer between fluid and particle, Source: [3] The temperature change of the fluidization gas through the bed (15) assumes a constant particle temperature. This local consideration is based on the intensive mixing of the particles in the fluidized bed. The total heat transfer efficiency (16) is a combination of the heat transfer efficiency from the bubble fluid (17) and the heat transfer efficiency of the suspension fluid (18) and presented in Fig. 10. for different particle diameters.

𝜂𝑡𝑜𝑡 = 𝜈 ∗ 𝜂𝑏𝑢𝑏 + (1 − 𝜈) ∗ 𝜂𝑠𝑢𝑠 (16) 𝜂𝑏𝑢𝑏 = 1 − 𝜔2 ∗ 𝑒𝜔1 − 𝜔1 ∗ 𝑒𝜔2𝜔2 − 𝜔1 (17)

𝜂𝑠𝑢𝑠 = 1 − (𝜔2 + 𝑁𝑇𝑈𝑎𝑝𝑝1 − 𝜈 ) ∗ 𝑒𝜔1 − (𝜔1 + 𝑁𝑇𝑈𝑎𝑝𝑝1 − 𝜈 ) ∗ 𝑒𝜔2𝜔2 − 𝜔1 (18) 𝜔1,2 = 𝑁𝑇𝑈𝑖2 ∗ 𝜈 ∗ {− [1 + 𝜈1 − 𝜈 ∗ (1 + 𝑁𝑇𝑈𝑎𝑝𝑝𝑁𝑇𝑈𝑖 )]

± √[1 + 𝜈1 − 𝜈 ∗ (1 + 𝑁𝑇𝑈𝑎𝑝𝑝𝑁𝑇𝑈𝑖 )]2 − 4 ∗ 𝜈1 − 𝜈 ∗ 𝑁𝑇𝑈𝑎𝑝𝑝𝑁𝑇𝑈𝑖 }

(19)

𝜈 = 𝜈𝑟 ∗ 𝑢 − 𝑢𝑚𝑓𝑢 (20)


Fig. 10. Total heat transfer efficiency for ρG=0.6 kg/m³, additional material parameters in Tab. 3. The volume share of the bubbles is calculated in equation (20). The correlation factor νr depends on the Geldart classification of the used bed material. For group B and a bed “height to length” ratio < 1.7 the factor is 0.67 and for group D with a ratio < 0.55 it is 0.26. This leads to the conclusion that the empty volume share in materials of Geldart group D is less affected by increasing gas velocities.

The apparent number of transfer units (22) contains Nuapp (25) which considers the mixing of the gas which has already passed the suspension on its way. The, in the heat exchange involved, volumetric particle surface is calculated in equation (23).

𝑃𝑟 = 𝜇𝐺 ∗ 𝑐𝑝,𝐺𝜆𝐺 (24)

𝑁𝑇𝑈𝑖 = ℎ𝑒𝑥𝑝(𝑚𝑚)50 (21) 𝑁𝑇𝑈𝑎𝑝𝑝 = 𝑁𝑢𝑎𝑝𝑝𝑅𝑒 ∗ 𝑃𝑟 ∗ 𝐴𝑣 ∗ ℎ𝑒𝑥𝑝 (22)

𝐴𝑣 = 6 ∗ (1 − 𝜀)𝑑𝑒𝑓𝑓 (23)

𝑁𝑢𝑎𝑝𝑝 = 𝑅𝑒𝐴𝑣 ∗ ℎ𝑒𝑥𝑝 ∗ ln (1 + 𝑁𝑢𝐺 ∗ 𝐴𝑣 ∗ ℎ𝑒𝑥𝑝𝑅𝑒 ∗ 𝑃𝑟 ) (25) 𝑁𝑢𝐺 = 𝛼𝐺𝑃 ∗ 𝑑𝑒𝑓𝑓𝜆𝐺 (26)

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 14 The heat transfer coefficient αGP (27) of a fluidized bed is bigger as for a singular particle. It can be calculated by the Nusselt number of a singular particle (28) and the form factor fa (32).

𝑁𝑢𝛼 = 𝑓𝑎 ∗ 𝑁𝑢𝑠𝑖𝑛𝑔𝑙𝑒 (28)

In Fig. 11. a comparison of the temperature behavior for different fluidization grades (33) and a particle diameter of 500 µm and 1000 µm is shown. A better heat transfer can be achieved with lower fluidization grades. This is contrary to the desired high gas velocities for a compact building volume. The main heat transfer happens in the first third of the bubbling bed for a particle diameter of 1000 µm. For a particle diameter of 500 µm the main heat transfer happens in an even smaller area. The gas inlet temperature in the comparisons of Fig. 11. is 570°C for all variations. Due to the fast assimilation of the gas temperature to the sand temperature the temperature gradient is so big that the resolution of Fig. 11. is too small to depict it correctly. At this point it is necessary to mention that there are different calculation methods in the VDI heat atlas for the heat transfer between the fluidization gas and the particle bed. To study the feasibility of a direct contact HEX the recommended heat transfer model was used. If the results from a laboratory setup differ too much from the calculated results, the other calculation models should be investigated.

𝛼𝐺𝑃 = 𝑁𝑢𝛼 ∗ 𝜆𝐺𝑑𝑒𝑓𝑓 (27)

𝑁𝑢𝑠𝑖𝑛𝑔𝑙𝑒 = 2 + √𝑁𝑢𝑙𝑎𝑚2 + 𝑁𝑢𝑡𝑢𝑟𝑏2 (29) 𝑁𝑢𝑙𝑎𝑚 = 0.664 ∗ √𝑅𝑒 ∗ √𝑃𝑟3 (30)

𝑁𝑢𝑡𝑢𝑟𝑏 = 0.037 ∗ 𝑅𝑒0.8 ∗ 𝑃𝑟1 + 2.443 ∗ 𝑅𝑒−0.1 ∗ (𝑃𝑟(23) − 1) (31) 𝑓𝑎 = 1 + 1.5 ∗ (1 − 𝜀) (32)

𝑓𝑙𝑔𝑟𝑎𝑑𝑒 = 𝑢𝑢𝑚𝑓 (33)


Fig. 11. Progress of the fluid temperature through a sand bed with an initial height of 0.04 m, Gas inlet temperature of 570°C, additional material parameters in Tab. 3. For further calculations, where the particle flow experiences a temperature change, the circulation time and the particle flow velocity need to be compared. The circulation is driven by the particle drift and wake formed subsequent to the rising bubble in the fluidized bed [5].


Fig. 12. Wake and Drift of a bubble in a fluidized bed, Source: [5] The time to circulate the entire bed material is calculated as shown in equation (35). The factor Y in Fig. 13. considers the deviation of modeled bubbles in a fluidized bed compared to their real behavior. The fractions of wake and drift are shown in Fig. 14. The system values displayed in Tab. 3. lead to a circulation time of 0.44 s. The mean travel distance from a particle, in flow direction, for a balanced bed can be approximated with (34). In our case a discretization grid of 0.5 m is applied in particle flow direction. This should provide enough time for the heat exchange between gas and particles.

Fig. 13. Correction factor for two-stage theory, Source: [5]

𝐿 = 𝑡 ∗ �̇�ℎ𝑓𝑏 ∗ 𝜌𝐵 ∗ 𝐵 (34) 𝑡𝐶 = ℎ𝑒𝑥𝑝(𝛽𝑤 + 0.38 ∗ 𝛽𝑑) ∗ 𝑌 ∗ (𝑢 − 𝑢𝑚𝑓) (35)


Fig. 14. Proportion of Wake and Drift, Source: [5] With these findings, the recommended parameters for the analysis of the heat exchange can be narrowed down to the values presented in Tab. 3. These parameters lead to the temperatures in Tab. 4. and Tab. 5. The dwell time of the sand mass in a stage and the associated velocity in flow direction need to be analyzed with computational fluid dynamics. For now, the bulk velocity is assumed as constant and only depending on the incoming mass flow. This assumption can be tested experimentally, and the analytical results altered by a correction factor, depending on the bed geometry. Tab. 3. Material parameters for the HEX analysis

500 µm0.8

0.672650 kg/m³1620 kg/m³0.04 m150 m²

4570 °C

20 °C200 kg/s

1044 J/(kg*K)200 kg/s

1010.4 J/(kg*K)1126.5 J/(kg*K)

1.84*10^-5 kg/(m*s)4.45*10^-5 kg/(m*s)

0.02 W/(m*K)463*10^-121046*10^-7

0.006 m


2.2.7.2 Heat Transfer per Stage

The findings in 2.2.7.1. lead to a discretization as depicted in Fig. 15. The sand inlet temperature is given for the first cell and the gas inlet temperature for each cell. A constant sand temperature is adopted for each cell and the gas outlet temperature can be calculated as shown in (15).

Fig. 15. Discretization Grid of a single HEX-Stage The heat flow rate of the passing gas is calculated in (36). With this value the sand outlet temperature of a cell is determined and can be used as the inlet temperature for the next cell.

This leads to the temperature profile shown in Fig. 16. where an apparatus of 18 m is divided into 25 cells. The sand inlet temperature is given with 300°C and the gas inlet temperature with 570°C. For the mass flow of the fluidization gas 200 kg/s are used and 200 kg/s for the sand flow. The calculations above lead to a sand outlet temperature of 395°C and a mean gas outlet temperature of 475°C.

�̇� = �̇� ∗ 𝑐𝑝 ∗ (𝜗𝐻𝑜𝑡 − 𝜗𝐶𝑜𝑙𝑑) (36)


Fig. 16. Temperature Profile inside a HEX-Stage, ϑG,in=570°C, ϑS,in=300°C, additional material parameters in Tab. 3 2.2.7.3 Heat Transfer in the Multistage Fluidized Bed HEX

With the previous knowledge an algorithm can be created to calculate the temperatures in each stage. Due to the pressure drop in each stage the following calculations were carried out for a four-stage apparatus. To start the iteration the sand inlet temperature for each stage is assumed with an even distribution of the temperature difference between the inlet temperatures of both streams. After the first values for the gas outlet temperatures are calculated, the sand temperature in each stage can be determined. A temperature difference of 0.1°C between the results of the iteration loops serves as termination condition. The gas inlet temperature for each cell within a stage is assumed as the same temperature. In respect to the transformation from α-quartz to β-quartz at 575°C [6] the gas inlet temperature was restricted to 570°C to avoid fracturing of the bed material. The temperatures shown in Tab. 4. are calculated with a sand inlet temperature of 20°C, a gas inlet temperature of 570°C, a fluidization gas mass flow of 200 kg/s, a sand mass flow of 200 kg/s, a particle diameter of 500 µm and a cross section of 150 m². Additional material parameters can be found in Tab. 3.


Fig. 17. Multistage Algorithm for a Fluidized Bed HEX Tab. 4. HEX-Temperatures charge

The efficiency of the heat exchanger is calculated via equation (37) where the hot stream is indicated as stream 1 and the cold stream as stream 2. With the temperatures in Tab. 4. the efficiency for the heating of the sand is 0.64.

With the assumption of a sand storage unit without losses the sand outlet temperature from Tab. 4. can be used in a recuperation step to heat ambient air. The resulting temperatures for a sand mass flow of 200 kg/s, an air mass flow of 200 kg/s, a particle diameter of 500 µm and a cross section of 150 m² are presented in Tab. 5. This leads to an overall heat loss of

Stage ϑS,in / °C ϑS,out / °C ϑG,in / °C ϑG,out / °C1 20 112 308 2172 112 205 398 3083 205 296 485 3984 296 386 570 485

𝜂𝐻𝐸𝑋,𝐻𝑜𝑡𝑆𝑖𝑑𝑒 = 𝜗1,𝐻𝑜𝑡 − 𝜗1,𝐶𝑜𝑙𝑑𝜗1,𝐻𝑜𝑡 − 𝜗2,𝐶𝑜𝑙𝑑 (37) 𝜂𝑡𝑜𝑡 = 𝜂𝑐ℎ𝑎𝑟𝑔𝑒 ∗ 𝜂𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (38)

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 21 approximately 300°C on the gas side. These values lead to a HEX efficiency of 0.65 and an overall efficiency (38) of 0.42. Tab. 5. HEX Temperatures discharge

The cold and hot mass flow rate have the biggest influence on the outlet temperatures and the efficiency of the HEX. For the hot stream the efficiency is calculated via equation (37) and for the cold stream as shown in (39).

For a better understanding of possible part load scenarios, the efficiencies of both streams are displayed in Fig. 18. with variable mass flows on the hot and cold side. For the following figures both mass flows are varied in the range of 60 to 350 kg/s and the cross section of the HEX is fixed at 150 m². To enable higher exhaust gas mass flows the cross section of the HEX must be increased to avoid exceeding the terminal velocity of the particles. As seen in Fig. 18. the summation of ηGas and ηSand has the highest values when the capacitance (61) of both streams is the same. Due to similar heat capacitances of both streams the ideal working point of the system is when both streams have about the same mass flow.


𝜂𝐻𝐸𝑋,𝐶𝑜𝑙𝑑𝑆𝑖𝑑𝑒 = 𝜗2,𝐻𝑜𝑡 − 𝜗2,𝐶𝑜𝑙𝑑𝜗1,𝐻𝑜𝑡 − 𝜗2,𝐶𝑜𝑙𝑑 (39)


Fig. 18. Efficiency progress for variable mass flows, additional material parameters in Tab. 3 With high gas mass flows and low sand mass flows the sand outlet temperature can be increased but the gas outlet temperature is increased at the same time. The opposite behavior can be obtained for high sand mass flows and low gas mass flows. This enables a wide range of applications with dynamic controls of the outlet temperatures which are displayed in Fig. 19.

Fig. 19. Temperature progress for variable mass flows, material parameters in Tab. 3


2.3 CPFD Simulation

2.3.1 Introduction

The stream behavior of both streams is tested with the computational fluid dynamic software Barracuda®. The mixing and transportation of the sand mass feed is studied for various inclined bed configurations to get a better understanding of the particle residence time in a single stage. The next step is to analyze the downcomer geometry to provide enough room for the sand mass flow and limit the gas flow from passing the distribution floor through the downcomer. These findings can be utilized for a laboratory test setup to verify the heat transfer which is tested in 2.3.5, despite the experience that the heat transfer is sometimes not simulated sufficiently.

2.3.2 Parameter Data

Barracuda uses the Eulerian-Lagrange approach. In this approach the fluid is modeled as a continuum and the particle as a set of discrete individual particles. The conservation equations are solved for the particles to calculate their trajectories. This way a reasonable compromise between computation time and accuracy can be achieved.

The geometry of the studied case is imported as an STL-file. The best way to achieve a precise model is to use the STL-file for the outline and to model all surfaces which are inside the geometry as baffles. Baffles are 2-dimensional shapes (beams, arcs, plates) which act like solid walls for particles and can induce a pressure drop to fluids. The pressure drop is defined with the factor K from (40). Their behavior is like a porous media, and they can also be impenetrable for fluids with a high enough K-factor.

SiO2 is used to model the sand bed. For the grain diameter a range of 450 µm to 550 µm is used with a sphericity of 0.8. The drag model is calculated according to Wen and Yu to match the calculations from 2.2.4. The general approach with boundary conditions (BC) is to set flow BCs for fluid and solid inlets and pressure BCs for the associated outlets.

∆𝑝 = 12 ∗ 𝜌 ∗ 𝐾 ∗ 𝑣2 (40)

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 24 2.3.3 Simulation Plate Inclination

The delay in the balancing process of the bed height in flow direction is big enough to take a closer look at the slope of the sinter floor. For this simulation a rectangular box with sufficient storage room for the outlet mass flow is chosen as geometry. The sand inlet is a flow BC on the left-hand side with a mass flow of 200 kg/s and an inlet temperature of 300 °C. Sand with the same temperature and a height of 4 cm is present in the stage as initial condition. In order to better distinguish the two species, they were colored differently. The gas inlet is also modeled with a flow BC and has a pressure of 101325 Pa, a Temperature of 570 °C and a velocity of 3 m/s. For the sinter floor, which is modeled with a baffle, four different inclinations and their influence on the particle transport have been studied. A horizontal bed with no slope and beds with slopes of 0.5°, 1°, 1.5° and 2° inclination were simulated for 60 seconds. In Fig. 20 is a comparison of the sand progress for the mentioned slopes at the end of the simulation time.

0° Inclination

0.5° Inclination

1° Inclination

1.5° Inclination

2° Inclination Fig. 20. Mixing Progress for Various Slope Angles after 60 Seconds

A slope of 1.5° matches the calculations, of the distance the feed mass flow covers (34), the most and is recommended to provide a sufficient advance of the sand mass in horizontal direction. Due to the long distance in flow direction and the low height of the sand bed, the slope has a strong influence on the bed height. If the inclination exceeds 0.5°, the sand will bulk up on the outlet border or too much sand is conveyed in the simulation and the HEX stage starts to empty itself. With less inclination the sand starts to bulk up at the inlet of the respective HEX-Stage. It is likely that the typical overflow principle with no inclination cannot be applied. In Fig. 21. shows a comparison of the bed height for different slopes. The height of the overflow border was defined with 7.5 cm after a test was carried out in Barracuda to measure the expanded bed height for the given resting bed height and fluid velocity. There are a lot of

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 25 approaches to calculate the expanded bed height of a fluidized bed. Since the real behavior of fluidized beds depend on the sphericity of the grain, the grain diameter and the gas flow behavior between the particles, an accurate prediction is hard to make. The mass flow of 1.5° matches the calculations the best and the inclination of 0.5° is the best depiction for the distribution of the sand, therefore a slope of 1° is chosen for further simulations.

0° Inclination

0.5° Inclination

1° Inclination

1.5° Inclination

2° Inclination

Fig. 21. Bed Height for Various Slope Angles after 60 Seconds 2.3.4 Simulation Downcomer

The downcomers are studied in detail to determine the flow behavior of the sand which falls through the downcomer from an upper stage to a lower stage. In addition to transfer the solid particles, the downcomer needs to provide a gas seal to hinder the gas stream from bypassing the distribution floor. The channel needs to be as small as possible to suppress any bypass movement but large enough to avoid constipation of the down coming sand mass flow. A large number of design variants are contained in the book by Kunii and Levenspiel [4]. Three geometries fit for the application of this multistage fluidized bed HEX and are presented in Fig. 22. To determine the sand flow behavior the development of the sand bulk is studied with the focus on the bulk volume fraction (41) to determine possible bottlenecks and problematic areas. The duration of these simulations is set to eleven seconds since possible bypass flows and constipation can be seen in this timeframe.

For the top of the downcomer an overflow border is used to restrict the sand movement and set the bed height. The crucial part is the lower restriction of the downcomer where the gas flow should be at a standstill to have no interference on the solid flow. The simplest version is a straight channel (1) in Fig. 22. from top to bottom. Since this is an ideal bypass channel the width must be reduced to the absolute minimum to hinder a possible gas flow with the down coming sand mass. This approach provides a stable behavior at the design point, but it tends

Θ = 𝜌𝐵𝜌𝑃 (41)

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 26 to clog for bigger mass flows. When the mass flow falls below the design point, the gas stream can flow through the channel and elevate the down coming particles.

(1) Channel

(2) Channel with Inlet

(3) Channel with Gas Inlet

(4) L-Valve

(5) L-Valve with low Inflow

(6) L-Valve with Gas Inlet Fig. 22. Design Approaches for Downcomers

The channel design can be improved with an inlet (2) at the bottom of the channel. Two design variations were considered for the inlet, a horizontal inlet and one with a slope of 45°. Both options had the same problems as the channel without an inlet. Although the horizontal inlet had a much higher chance of clogging and the inlet with a 45° inlet looks stable at first glance. At closer investigations, the channel still had a big gas flow and as soon as the down coming mass was big enough to stop the gas flow, the channel starts to clog. Due to this behavior, the channels are no longer considered as a viable solution for a downcomer. This solution may work for high sand mass flows and applications with a low fluidization grade. In the case of a multistage fluidized bed with minimal bed height and high fluidization grades, the solution for the downcomer must hinder the gas flow a lot more to provide a stable flow behavior. This leads to the L-valve (4), because the gas flow needs to change his direction for 90° to flow through the downcomer. The induced pressure drop from the sinter distribution floor is so high, that the gas stream detours through the downcomer, elevating the sand mass which needs to fall through the channel. The design is improved to an inlet which is on the same level as the distribution floor (5). This hinders the gas flow a bit more than the previous design, but the gas velocity is still high enough to hinder the sand movement. Since these systems could not

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 27 provide a sufficient gas seal, additional gas inlets, with the same gas velocity as the fluidization gas, are used to hinder a bypass flow of the gas stream through the downcomer (3) & (6). The additional gas flow does not hinder the formation of a bypass flow in the channel configuration. When the velocity of the additional gas flow exceeds the velocity of the fluidization gas, the fluidized bed above gets a negative effect, which means that a channel configuration is not suitable for a fluidized bed with high fluidization grades. The L-valve with an additional gas flow (6) can form a sufficient gas seal and reduce the vertical gas velocity in the downcomer to a standstill. These results are displayed in Fig. 23. and Fig. 24.


Fig. 23. CFD-Analysis of Channel Downcomers, Cells W = Vertical Gas Velocity m/s, Pressure in Pa


Fig. 24. CFD-Analysis of L-Valve Downcomers, Cells W = Vertical Gas Velocity m/s, Pressure in Pa

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 30 2.3.5 Simulation Heat Transfer

To test whether it makes sense to model a multi-stage device, the heat transfer in Barracuda was simulated. The temperatures of a four-stage system calculated in the algorithm were used for this purpose. This leads to the initial particle temperatures of 20, 112, 205 and 296°C from left to right in Fig. 26. The respective gas inlet temperatures are 310, 400, 480 and 570°C. The heat transfer between particles and gas is shown in Fig. 25. and can be adjusted. Since there are no measurement results available, the standard settings of the program are used.

Fig. 25. Fluid-to-particle heat transfer coefficient Barracuda With the described initial temperatures, an initial bed height of 4 cm, a particle diameter of 500 µm and a gas velocity of 3 m/s the temperature changes of the particles are displayed in Fig. 26. for a time step of ten seconds. The temperature changes over an interval of 60 seconds are higher than the calculated values. The sand reaches almost the same temperature as the fluidization gas. If these simulations can be verified through trials, this would increase the efficiency of a direct contact fluidized bed heat exchanger and thus make the technology more interesting. However, as previously described, the development of a suitable distributor floor is essential so that the pressure drop remains low enough for an application to recover the exhaust heat of a gas turbine.


10 s

20 s

30 s

40 s

50 s

60 s Fig. 26. CPFD Heat Transfer

2.4 Conclusion

To maintain a compact building volume, the gas velocity should be at least 3 m/s at the gas inlet for an exhaust gas mass flow of 200 kg/s. To avoid particle transportation with a gas velocity of 3 m/s, the particles used for the HEX bed must be bigger than 300µm as seen in Fig. 4. The lower velocity limit is marked by the minimum fluidization velocity which is so low (Fig. 5.) that there will not be any disturbances in the fluidization of the bed material. To maintain a stabilized bed a bed height of 0.04 m is recommended. This leads to a pressure drop of about 635 Pa (Fig. 6.) in the fluidized bed. The additional pressure drop from the distribution floor is presented in (Fig. 7.) and is the current limiting factor of the system. To reduce the thickness of the sinter floor even more, additional support structures should be considered to avoid high pressure drops. The minimum bed height for a stable operation must be tested in a laboratory model and alternatively a nozzle floor to reduce the pressure drop from the fluid distribution floor. Despite the excessive pressure drop an algorithm was created to calculate the heat transfer. The overall heat loss at four stages (Tab. 4. and Tab. 5.) is too big to make an application of a direct contact HEX viable. To enable a multistage application with six to eight stages, which reduces the heat loss to an acceptable level, the pressure drop from the distribution floor must be decreased. For this task it is necessary to develop a distribution floor which reduces the pressure drop to a minimum and provides an even gas distribution to operate a low height fluidized bed. The deviation between the calculated results and the simulation come from the dwell time, which is difficult to determine. To make more accurate depictions about the total heat transfer, laboratory experiments are needed to determine correction factors for the geometry and the according dwell time. If the experiments deviate too much from the experiments, the alternative calculation approaches from the VDI

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 32 heat atlas can be applied to the multistage algorithm. However the used method is the most recommended one.

2.5 Nomenclature Symbol Unit Description 𝐴 m² HEX Cross Section 𝐴𝑟 - Archimedes Number 𝐴𝑣 1/m Volumetric Particle Surface 𝐵 m Bed Width 𝑐𝑝,𝐺 J/(kg*K) Gas Heat Capacity 𝑐𝑝,𝑆 J/(kg*K) Sand Heat Capacity 𝑑𝑒𝑓𝑓 m Effective Sand Particle Diameter 𝑑𝑠𝑝ℎ m Spherical Sand Particle Diameter 𝑓𝑎 - Form Factor 𝑓𝑙𝑔𝑟𝑎𝑑𝑒 - Fluidization Grade 𝑔 m/s² Gravitational Acceleration ℎ𝑒𝑥𝑝 m Expanded Bed Height ℎ𝑓𝑏 m Height of the Fluidized Bed ℎ𝑚𝑓 m Bed Height at Fluidization Point 𝐿 m Distance in Flow Direction �̇�𝐺 kg/s Gas Mass Flow �̇�𝑆 kg/s Sand Mass Flow 𝑁𝑢𝑎𝑝𝑝 - Apparent Nusselt Number 𝑁𝑢𝛼 - Nusselt Number Fluidized Bed 𝑁𝑢𝐺 - Nusselt Number Gas 𝑁𝑢𝑙𝑎𝑚 - Laminar Nusselt Number 𝑁𝑢𝑠𝑖𝑛𝑔𝑙𝑒 - Nusselt Number Singular Particle 𝑁𝑢𝑡𝑢𝑟𝑏 - Turbulent Nusselt Number 𝑁𝑇𝑈𝑎𝑝𝑝 - Apparent Number of Transfer Units 𝑁𝑇𝑈𝑖 - Empiric Number of Transfer Units 𝑃𝑟 - Prandtl Number �̇� W Total Heat Flux 𝑅𝑒 - Reynolds Number 𝑅𝑒𝑚𝑓 - Reynolds Number Fluidization Velocity 𝑅𝑒𝑡 - Reynolds Number Terminal Velocity 𝑠 m Thickness Sinter Floor 𝑡𝐶 s Circulation Time 𝑢 m/s Velocity

Analytical Calculation Of A Direct Contact Multistage Fluidized Bed HEX 33 𝑢𝑚𝑓 m/s Fluidization Velocity �̇� m³/s Volumetric Gas Flow 𝑌 - Correction Factor for Two-Stage Theory 𝛼𝐵 m² Permeability Coefficient Sinter Floor 𝛼𝐺𝑃 W/(m²*K) Heat Transfer Coefficient (Gas-Particle) in a Fluidized Bed 𝛽𝐵 m Permeability Coefficient Sinter Floor 𝛽𝐷 - Drift Fraction 𝛽𝑤 - Wake Fraction Δ𝑝𝑓𝑏 Pa Pressure Drop Fluidized Bed Δ𝑝𝑓 Pa Pressure Drop Distribution Floor Δ𝑝𝑆 Pa Pressure Drop of a Stage 𝜀 - Voidage 𝜀𝑚𝑓 - Voidage at Fluidization Point 𝜂𝑏𝑢𝑏 - Heat Transfer Efficiency Bubble Fluid 𝜂𝑐ℎ𝑎𝑟𝑔𝑒 - Efficiency of the Charging Step 𝜂𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 - Efficiency of the Discharging Step 𝜂𝐻𝐸𝑋 - Efficiency of the Heat Exchanger 𝜂𝑠𝑢𝑠 - Heat Transfer Efficiency Suspension Fluid 𝜂𝑡𝑜𝑡 - Total Heat Transfer Efficiency 𝜗𝐺,𝑖𝑛 °C Gas Inlet Temperature 𝜗𝐺,𝑜𝑢𝑡 °C Gas Outlet Temperature 𝜗𝑃 °C Particle Temperature 𝜗𝑆,𝑖𝑛 °C Sand Inlet Temperature 𝜗𝑆,𝑜𝑢𝑡 °C Sand Outlet Temperature 𝛩 - Volume Fraction 𝜆𝐺 W/(m*K) Thermal Conductivity Gas 𝜇𝐺 kg/(m*s) Dynamic Viscosity 𝜈 - Volume Share of Bubbles in a Fluidized Bed 𝜈𝑟 - Correlation Factor Bubble Share 𝜌𝐺 kg/m³ Gas Density 𝜌𝐵 kg/m³ Bulk Density 𝜌𝑃 kg/m³ Particle Density 𝜙𝑆 - Sand Sphericity 𝜔1,2 - Efficiency Calculation Factor

Indirect Contact Plate Type Moving Bed HEX 34

3 Indirect Contact Plate Type Moving Bed HEX

3.1 Operating Principle and Design The geometry of the investigated arrangement is shown in Fig. 2. The particles used to store the heat move downwards between the plate tubes in which the gas stream flows in horizontal direction. This leads to a local crossflow HEX and an apparatus with a counterflow behavior. To store and recuperate as much energy as possible the plates of each stage are arranged with an offset to mix the individual solid streams and gain a more uniform temperature profile.

Fig. 27. Design of a multistage moving bed HEX 3.2 Local Heat Distribution

A numerical method to calculate the heat distribution in the solid phase was developed by Mehos [7]. In these calculations the gas stream is supposed to flow in an upward motion and the solid stream moves downward driven by gravitational acceleration as shown in Fig. 28. The local consideration of the heat distribution is therefore for a counterflow HEX. Although this system differs from the overall setup, it provides valuable results for the dimensioning of the sand channel.


Fig. 28. Temperature Profile of a Single Stage in a Moving Bed HEX The work of Mehos will be summarized in this chapter. The general approach is a step-by-step solution from the top end under the condition of a known gas outlet temperature. This problem can be solved with the implementation of an iteration loop where the gas outlet temperature is adapted till the calculated gas inlet temperature matches the actual gas inlet temperature. The temperature profile of the solid phase is calculated as shown in (42) where the subscript n is the vertical discretization distance and i={1, 2, …, m} the horizontal discretization grid.

The boundary conditions are defined in (43) as local temperature equilibrium between the gas- and sand-stream at the partition wall. The local gas temperature is calculated in (44).

The values in the Matrix A are presented below and depict the heat transfer in the solid stream.

�̅�𝑆𝑛+1 = �̿� \ �̅�𝑆𝑛 (42)

[ 𝑇1𝑇2𝑇3⋮𝑇𝑚]

𝑆

𝑛+1= [

𝑏1 𝑐1 0 0 0𝑎2 𝑏2 𝑐2 0 00 𝑎3 𝑏3 ⋱ ⋮⋮ ⋱ ⋱ ⋱ 𝑐𝑚−10 0 0 𝑎𝑚 𝑏𝑚 ] \ [

𝑇1𝑇2𝑇3⋮𝑇𝑚] 𝑆

𝑛

𝑇𝑆,1𝑛 = 𝑇𝑆,𝑚𝑛 = 𝑇𝐺𝑛 (43) 𝑇𝐺𝑛 = 𝑇𝐺,𝑜𝑢𝑡 + �̇�𝑆 ∗ 𝑐𝑝,𝑆�̇�𝐺 ∗ 𝑐𝑝,𝐺 ∗ (𝑇𝑆,𝑚𝑒𝑎𝑛𝑛 − 𝑇𝑆,𝑖𝑛) (44)

𝑎𝑖 = −𝜆 (45) 𝑎1 = 0 (46)


These calculations lead to the temperature profiles in Fig. 29. with the input values displayed in Tab. 6. and the plate height H. To enhance the heat distribution in the solid phase multiple HEX stages with offset plates are necessary. With an offset arrangement the coldest particles from the previous stage are the closet particles to the HEX-wall in the next stage. To limit the building volume of a multi-stage arrangement there were no heights higher than 1.5 m investigated. Varying the geometry also changes the overall heat transfer and therefore the heat transfer coefficient (55). With the knowledge of the HEX surface area, the total heat flux (57) and the logarithmic temperature difference (56), the heat transfer coefficient can be evaluated. For Fig. 29. the heat transfer coefficient ranges from 160 W/(m²*K) for a plate height of 1.4 m to 180 W/(m²*K) for a plate height of 0.6 m. These results include a backwards calculation since the overall heat transfer coefficient (gas-wall-solid) has to be specified for (45) to (54).

𝑎𝑚 = − 𝜆𝑆,𝑒𝑓𝑓𝛼 ∗ Δ𝑥 (47) 𝑏𝑖 = 1 + 2 ∗ 𝜆 (48)

𝑏1 = 1 + 𝜆𝑆,𝑒𝑓𝑓𝛼 ∗ Δ𝑥 (49) 𝑏𝑚 = 1 + 𝜆𝑆,𝑒𝑓𝑓𝛼 ∗ Δ𝑥 (50)

𝑐𝑖 = −𝜆 (51) 𝑐1 = − 𝜆𝑆,𝑒𝑓𝑓𝛼 ∗ Δ𝑥 (52)

𝑐𝑚 = 0 (53) 𝜆 = 𝜆𝑆,𝑒𝑓𝑓 ∗ Δ𝑧𝜌𝑆 ∗ 𝑐𝑝,𝑆 ∗ 𝑢𝑆 ∗ (Δ𝑥)2 (54)

𝑘𝑡𝑜𝑡 = �̇�∆𝑇𝑙𝑜𝑔 ∗ 𝐴 (55) ∆𝑇𝑙𝑜𝑔 = ∆𝑇𝑚𝑎𝑥 − ∆𝑇𝑚𝑖𝑛ln (∆𝑇𝑚𝑎𝑥∆𝑇𝑚𝑖𝑛) (56)


Fig. 29. Temperature Profile between two HEX-Plates in a Moving Bed HEX, TG,in=570°C, TS,in=300°C, mG=0.5 kg/s, mS=0.6 kg/s The mean sand outlet temperature for a plate height of 1.5 m and a varying plate distance is shown in Fig. 30. This analysis is for one channel with a sand mass flow of 0.5 kg/(s*cm). Smaller gaps lead to a higher average sand temperature, but the building volume increases because there are more channels needed to cope with the same sand mass flow.

Fig. 30. Mean Sand Temperature of a single Channel in a Moving Bed HEX, TG,in=570°C, TS,in=300°C, mG =0.5 kg/s, mS/(Plate_Distance) =0.5 kg/(s*cm)

Indirect Contact Plate Type Moving Bed HEX 38 Tab. 6. Material parameters for the local heat distribution

3.2.1 Nomenclature

Symbol Unit Description �̿� - Transformation Matrix 𝐴 m² Plate Surface Area 𝑐𝑝,𝐺 J/(kg*K) Gas Heat Capacity 𝑐𝑝,𝑆 J/(kg*K) Sand Heat Capacity 𝑘𝑡𝑜𝑡 W/(m²*K) Overall Heat Transfer Coefficient �̇�𝐺 kg/s Gas Mass Flow �̇�𝑆 kg/s Sand Mass Flow �̇� W Total Heat Flux 𝑢𝑆 m/s Sand Velocity 𝑇𝐺 K Gas Temperature 𝑇𝑆 K Sand Temperature 𝛼 W/(m²*K) Heat Transfer Coefficient (Gas-Wall-Solid) Δ𝑥 - Grid Spacing x-Direction (Horizontal) Δz - Grid Spacing z-Direction (Vertical) 𝜆𝑆,𝑒𝑓𝑓 W/(m*K) Effective Thermal Conductivity Sand 𝜌𝑆 kg/m³ Sand Bulk Density

15 mm6 m

2000.05 mm

2.5 mm

300 °C120 kg/s

1044 J/(kg*K)1510 kg/m³

570 °C100 kg/s

1010.4 J/(kg*K)1126.5 J/(kg*K)

0.4 W/(m*K)150 W/(m²*K)

Geometry

Material


3.3 Analytical Calculation Of A Multistage Moving Bed

HEX To calculate a multistage plate type moving bed HEX the method in 3.2 is not suitable due to its high runtime which comes from the iteration loop that determines the gas outlet temperature. A steady state reduced-order model of a plate type moving bed HEX is presented by Albrecht [8] for a multistage arrangement. This allows to investigate different design options for a multistage moving bed HEX. The heat exchange in a single stage is a crossflow configuration and leads to a global counterflow configuration for the combined stages as seen in Fig. 27.

3.3.1 Heat Exchange Single Stage

The conservation equations (57) for the hot and cold stream are linked by the effectiveness (60) of the HEX and need to be calculated for each stage, marked with the index i. The single stages can be linked by the temperatures of the material flows, which act as boundary conditions to solve the multistage algorithm shown in 3.3.3.

To determine the effectiveness of the HEX, it is necessary to determine the number of transfer units (63) and the capacitance ratio (62). The thermal capacitance (61) of both streams should be similar, to avoid high temperature losses. Therefore, the main variable to regulate the effectiveness is the number of transfer units whose effect can be seen in Fig. 31.

�̇�𝑖 = �̇� ∗ 𝑐𝑝 ∗ Δ𝑇 (57) �̇�𝑖 = 𝜀𝑖 ∗ �̇�𝑖,𝑚𝑎𝑥 (58) �̇�𝑖,𝑚𝑎𝑥 = �̇�𝑚𝑎𝑥,𝑖 ∗ Δ𝑇𝑚𝑎𝑥,𝑖 (59) 𝜀𝑖 = 1 − exp(𝑁𝑇𝑈𝑖0.22𝐶𝑅,𝑖 ∗ (exp(−𝐶𝑅,𝑖 ∗ 𝑁𝑇𝑈𝑖0.78) − 1)) (60)


Fig. 31. Dependency of HEX-effectiveness from NTUi for a capacitance ratio of 1 and inlet temperatures of 200°C for the sand stream and 350°C for the gas stream, additional material parameters in Tab. 8.

The number of transfer units can be regulated by changing the geometry of the HEX unit. The surface area of the HEX-walls has a direct impact in (63) and is shown in Fig. 32. Variations of the channel width affect the solid-wall convection coefficient (65) and the stream velocities, which effect the overall heat transfer coefficient (64). To aim for a viable effectiveness the number of transfer units should be two or higher.

�̇� = �̇� ∗ 𝑐𝑝 (61) 𝐶𝑅,𝑖 = �̇�𝑚𝑖𝑛,𝑖�̇�𝑚𝑎𝑥,𝑖 (62)

𝑁𝑇𝑈𝑖 = 𝑘𝑡𝑜𝑡,𝑖 ∗ 𝐴𝑖�̇�𝑚𝑖𝑛,𝑖 (63)


Fig. 32. Dependency of NTUi from the HEX Surface Area for a thermal capacitance of 500 W/K, an overall heat transfer coefficient of 75 W/(m²*K), an inlet temperature of 200°C for the sand stream and 350°C for the gas stream, additional material parameters in Tab. 8.

𝑘𝑡𝑜𝑡,𝑖 = 11𝛼𝐺𝑊 + 𝑠𝑊𝜆𝑊 + 1𝑅𝑐 + 1𝛼𝑆𝑊 (64) 𝛼𝑆𝑊 = 𝑁𝑢𝐷ℎ,𝐻 ∗ 𝜆𝑆,𝑒𝑓𝑓2 ∗ 𝑏𝑆 (65)

𝑁𝑢𝐷ℎ,𝐻 = [(2 ∗ 0.886√𝐺𝑧−1)12 5⁄ + 1212 5⁄ ]5 12⁄ (66)

𝐺𝑧 = ( 𝐿𝑃𝑒 ∗ 𝐷𝐻,𝑆)−1 (67)

𝑃𝑒 = 𝑢𝑆 ∗ 𝐷𝐻,𝑆 ∗ 𝜌𝑆 ∗ 𝑐𝑝,𝑆𝜆𝑆,𝑒𝑓𝑓 (68) 𝛼𝐺𝑊 = 𝑁𝑢𝐺 ∗ 𝜆𝐺𝐷𝐻,𝐺 (69)

𝑁𝑢𝐺 = √𝑁𝑢𝐺,𝑙𝑎𝑚2 + 𝑁𝑢𝐺,𝑡𝑢𝑟𝑏2 (70) 𝑁𝑢𝐺,𝑙𝑎𝑚 = 0.664 ∗ √𝑅𝑒 ∗ √𝑃𝑟3 (71)


The mean temperature of the respective channel is used to determine the physical properties of the gas flow for the calculation of the heat transfer coefficient. To improve the heat transfer on the gas side, wire coils can be attached to the channel [9]. The bottleneck of the proposed moving bed HEX is the overall pressure drop, which would be significantly increased by adding helical coils. This can be seen in 3.3.2.2. The overall heat transfer coefficient (64) is mostly affected by the heat transfer on the gas side. The heat transfer on the sand side can only be varied by a small margin, because the sand velocity does not change a lot when the channel geometry is varied or the rate of the sand mass flow. This is based on the high density of the particle flow, compared to the gas mass flow. The near wall thermal resistance Rc and the effective thermal conductivity of the sand λS,eff must be evaluated from experiments for a range of particle diameter and mass flows. The heat transfer coefficient for the gas side and the overall heat transfer coefficient are presented in Fig. 33. for a channel width of 20 mm on both sides. The heat transfer coefficients for one plate and varying gas velocities are shown in Fig. 34.

Fig. 33. Gas heat transfer coefficient and total heat transfer coefficient for a single moving bed HEX-Stage, pin=101325 Pa, mG=0.25 kg/s, mS=0.25 kg/s, HP=1.5 m, LP=6 m

𝑁𝑢𝐺,𝑡𝑢𝑟𝑏 = 0.037 ∗ 𝑅𝑒0.8 ∗ 𝑃𝑟1 + 2.443 ∗ 𝑅𝑒−0.1 ∗ (𝑃𝑟23 + 1) (72) 𝐷𝐻 = 4 ∗ 𝐴𝑈 (73)


Fig. 34. Heat Transfer through one plate, TG=400°C, TS=300°C The gas and sand outlet temperature for a plate height of 1.5 m and a varying plate distance on the gas side is shown in Fig. 35. This analysis is for one channel with a gas mass flow of 0.125 kg/s and a sand mass flow of 0.125 kg/s in a 20 mm wide sand channel. The sand inlet temperature has an average temperature of 300°C and the gas inlet temperature is 570°C. Bigger gaps lead to lower sand outlet temperatures, but the building volume decreases because there are fewer channels needed to cope with the same gas mass flow. With a higher plate distance on the gas side the pressure drop in the gas stream also decreases.

Fig. 35. Outlet Temperatures of a single Channel in a Moving Bed HEX with a varying plate distance on the gas side, TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s With the same input parameters as in Fig. 35. and a gas channel width of 15 mm an analysis of the outlet temperatures for a varying width of the sand channel is presented in Fig. 36. Varying both channel widths with a constant gas mass flow of 0.125 kg/s and a sand mass

Indirect Contact Plate Type Moving Bed HEX 44 flow of 0.125 kg/s, leads to the outlet temperatures of Fig. 37. This shows that smaller gaps on both sides enhance the heat transfer with the drawback of an increasing build volume.

Fig. 36. Outlet Temperatures of a single Channel in a Moving Bed HEX with a varying plate distance on the sand side, TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s

Fig. 37. Outlet Temperatures of a single Channel in a Moving Bed HEX with varying plate distances, TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s 3.3.2 Pressure Drop

It is necessary to investigate the pressure drop of the exhaust stream, since it is limited to 4000 Pa. If the pressure drop is too high, the performance losses in the gas turbine would make the system uneconomical. The following calculations are according to the VDI heat atlas [3] and marked if the presented equations have another origin.

Indirect Contact Plate Type Moving Bed HEX 45 A distinction in the calculation is made between laminar and turbulent flows. The separation of these fields is marked by the critical Reynolds number (4) Recrit = 2320. Although the transition from a laminar flow to a turbulent one can stretch up to Reynolds numbers of 8000 for hydrodynamic stable streams with smooth entrances. Since we do not have these conditions and rather big mass flows, all calculations will be in the turbulent area. The physics in turbulent flows are hard to depict for rough surfaces. This means that the calculation of the pressure drop will be an estimation and may vary for different cross sections of the gas channels and pipe arrangements.

3.3.2.1 Pressure Drop in Flow Through Pipes

The pressure drop in a pipe is determined by (74). This equation can be used for pipes with a circular cross section and for pipes with a noncircular cross section. For the second case the hydraulic diameter needs to be adapted as shown in (73) where A is the cross section and U the according perimeter. The Pressure drop in long pipes with temperature changes and the related variations of the stream velocity and density, is calculated with the average temperature in the pipe. According to Malinovec [9] equation (74) can be adapted as show in (75) for big temperature changes in the stream.

The drag coefficient ζ depends on the Reynolds number in the tube. The three areas for the calculation of the drag coefficient can be separated in laminar flow, turbulent flow in smooth pipes and turbulent flow in rough pipes. In the laminar region ζ is calculated with eq. (76).

The turbulent region for smooth pipes is separated by the Reynolds number from ~3000 to 105 and ζ is calculated as shown in (77), according to Blasius. For Reynolds numbers between ~2*104 to 2*106 the Hermann equation (78) can be applied. And for Reynolds numbers bigger than 106 the Prandtl/Kármán equation (79) is suitable to determine the drag coefficient.

𝜁 = 0.3164√𝑅𝑒4 (77)

∆𝑝 = 𝜁 ∗ 𝐿𝐷𝐻 ∗ 𝜌𝐺 ∗ 𝑢𝐺22 (74) ∆𝑝 = 𝜁 ∗ 𝐿𝐷𝐻 ∗ 𝜌𝐺 ∗ 𝑢𝐺22 + (𝑢𝐺,𝑖𝑛2 − 𝑢𝐺,𝑜𝑢𝑡2 ) ∗ 𝜌𝐺2 (75)

𝜁 = 64𝑅𝑒 (76)

𝜁 = 0.0054 + 0.3964𝑅𝑒0.3 (78)


For rough pipes in the turbulent region the distinction in the calculation method is made between flows which are governed by roughness or the transition area between smooth and rough surfaces. For streams which are completely governed by roughness, the Prandtl/Kármán equation is adapted to (80). Whereas the Colebrook/White equation (81) can be applied for the transition area. K is the average height of all elevations of the pipe surface.

All these equations are summarized in the Moody-Diagram Fig. 38.

Fig. 38. ζ for flow through pipes, Source: VDI Heat Atlas 2010 The main influence on the pressure drop in a channel is by the hydraulic diameter. This dependency is shown in Fig. 39. For the channel length the pressure drop shows a linear behavior and increases with increasing channel length. Considering Fig. 35. and Fig. 39. the channel width should be around 20mm.

1√𝜁 = −0.8 + 2 ∗ log (𝑅𝑒 ∗ √𝜁) (79)

1√𝜁 = 1.14 + 2 ∗ log (𝐷𝐻𝐾 ) (80) 1√𝜁 = −2 ∗ log ( 2.51𝑅𝑒 ∗ √𝜁 + 𝐾𝐷𝐻 ∗ 3.71) (81)


Fig. 39. Pressure Drop in a Channel with a Plate Height of 1.5 m, Length of 6 m and a constant gas velocity of 23 m/s 3.3.2.2 Pressure Drop from a Helical Coil

An enhancement in the heat transfer on the gas side can be achieved by adding helical coils into the channel. These inserts cause an additional pressure drop and are case of the study from Malinovec [9]. To consider an implementation of these inserts the allowed pressure drop in the gas stream must have enough clearance. The pressure drop can be calculated with (82) and for information on the drag coefficient it is recommended to investigate the work of Malinovec. There are many factors which influence the drag coefficient and since the aim of this work is to reduce the pressure drop to the lowest level possible the insert of helical coils is lined up at the back.

∆𝑝 = 𝜁 ∗ 𝜌𝐺 ∗ 𝑢𝐺22 (82)


Fig. 40. Pressure Drop in a Channel with a Helical Coil, HP=1.5 m, L=6 m, bG=20 mm, ρG=0.4 kg/m³, ζ=0.3 3.3.2.3 Pressure Drop from Bends

The induced pressure drop from bends is calculated with (82). For high Reynolds numbers Fig. 41. can be used to obtain the drag coefficient. With decreasing Reynolds numbers the drag coefficient will increase Fig. 42.

Fig. 41. Drag Coefficient for Bends and Reynolds Numbers > 105, Source: VDI Heat Atlas 2010


Fig. 42. Drag Coefficient for Bends in Smooth Pipes, Source: VDI Heat Atlas 2010 3.3.2.4 Pressure Drop from changes of the Cross Section

An abrupt widening of the cross section is calculated with (83). For a continuous widening (Fig. 44.) (83) must be modified like shown in (84) and the angle dependent drag coefficient can be taken from Fig. 45.

Fig. 43. Abrupt Widening of the Cross Section, Source: VDI Heat Atlas 2010 ∆𝑝 = (1 − 𝐴1 𝐴2⁄ )2 ∗ 𝜌𝐺 ∗ 𝑢𝐺22 (83)

∆𝑝 = 𝜁′ ∗ (1 − 𝐴1 𝐴2⁄ )2 ∗ 𝜌𝐺 ∗ 𝑢𝐺22 (84)


Fig. 44. Continuous Widening of the Cross Section, Source: VDI Heat Atlas 2010

Fig. 45. Drag Coefficient for Continuous Widening of the Cross Section, Source: VDI Heat Atlas 2010 For an abrupt reduction of the cross section, (82) can be used with the drag coefficient from Fig. 46. When the cross section is continuously reduced the drag coefficient can be reduced up to 0.04 [VDI]. This reduction is only possible for α < 40°.


Fig. 46. Drag Coefficient for an Abrupt Reduction of the Cross Section, Source: VDI Heat Atlas 2010 3.3.2.5 Pressure Drop from Collector and Distributor

For tee junctions and oblique junctions, (82) can be applied with the velocity from the z-Arm shown in Fig. 47. and Fig. 48. The drag coefficients for the chosen stream are presented in Fig. 47. and Fig. 48 for turbulent flows, as these drag coefficients can be applied for all Reynolds number > 103.

Fig. 47. Drag Coefficient Tee Junctions and Oblique Junctions, Source: VDI Heat Atlas 2010


Fig. 48. Drag Coefficient Tee Junctions and Oblique Junctions, Source: VDI Heat Atlas 2010

3.3.2.6 Conclusion Pressure Drop

With all these information the pressure drop was calculated for different design approaches. The highest losses for a system as shown in Fig. 27. occur at the channel inlet and outlet, and in the collector channel, due to the high gas velocity. This leads to a pressure drop of 65 kPa for a four-stage moving bed HEX. This pressure drop is too high and must be decreased. To reduce the pressure drop for the proposed geometry, additional analysis of the gas flow need to be done and the geometry optimized. Especially the expansions should be improved. The geometry was changed as shown in Fig. 49 to a configuration where each gas channel continuous through the whole apparatus to reduce the overall pressure drop. This way the pressure drop can be reduced to 1300 Pa for a four stage HEX at the expense of the building volume. Enabling the possibility of up to eighteen HEX stages without exceeding the allowed pressure drop of 4000 Pa.

Fig. 49. Optimized Channel Geometry for a Multistage Moving Bed HEX

Indirect Contact Plate Type Moving Bed HEX 53 3.3.3 Multistage Algorithm

Since the inlet temperatures of both material streams in each stage are unknown, an algorithm is needed to determine the missing information. The sand inlet temperatures of each stage are assumed by an equal division of the temperature difference between the cold and hot stream inlet. With this assumption all the gas temperatures can be determined and the sand outlet temperature of each stage. These calculated sand temperatures are used for the next iteration loop. This cycle continues until the differences of the calculated sand temperatures from two iteration loops meet the set termination condition, which is 0.1°K in our case. The algorithm shows a stable behavior for varying geometry and mass flows, when the thermal capacitance of both streams is similar.

Fig. 50. Multistage Algorithm for a Moving Bed HEX 3.3.4 Heat Exchange Multistage

In respect to the transformation from α-quartz to β-quartz at 575°C [6] the gas inlet temperature was restricted to 570°C to avoid fracturing of the bed material. The temperatures in each stage of the HEX (Tab. 7.) are calculated with the algorithm presented in 3.3.3. and the input data from Tab. 8. for a four stage apparatus. With the improved geometry from 3.3.2.6. and the resulting decreased pressure drop, there are more than four stages possible. For a comparison with the four-stage fluidized bed HEX, the analysis of the moving bed HEX is primary for a four stage system. This is followed by a multistage analysis concerning the

Indirect Contact Plate Type Moving Bed HEX 54 overall heat transfer coefficient, the pressure drop and the outlet temperatures for different numbers of stages. Tab. 7. HEX-Temperatures charge

Tab. 8. Material parameters for the HEX analysis

The efficiency of the heat exchanger is calculated via equation (37) where the hot stream is indicated as stream 1 and the cold stream as stream 2. With the temperatures in Tab. 7. the efficiency for the heating of the sand is 0.76.

With the assumption of a lossless sand storage unit, the sand outlet Temperature from Tab. 7. can be used as sand inlet temperature in a recuperation step to heat ambient air and leads to the temperatures shown in Tab. 9. Without any additional temperature losses during storage and transportation there will be an approximated heat loss of 200°C on the gas side. These values lead to a HEX efficiency of 0.78 when the sand is cooled and an overall efficiency (38)


6 m1.5 m

5 mm200

20 °C50 kg/s

1044 J/(kg*K)1510 kg/m³

570 °C50 kg/s

1010.4 J/(kg*K)1126.5 J/(kg*K)

50 W/(m*K)0.02 W/(m*K)150 W/(m²*K)0.3 W/(m*K)

Geometry

Material

20 mm

mm20

Indirect Contact Plate Type Moving Bed HEX 55 of 0.59. The highest gas velocity is in the channels of the HEX-stage with the highest temperature and has a value of 19.5 m/s. Tab. 9. HEX Temperatures discharge

With the same approach as for the four stage system, a variety of multistage configurations are evaluated. In Fig. 51. are the stream outlet temperatures, for the input parameters of Tab. 8. displayed. The outlet temperatures do not change significantly above a ten stage system. The respective gas outlet temperature for a ten stage system is 79°C and 520°C for the sand outlet temperature. This leads to an HEX-efficiency of 0.89 when the particles are heated, 0.89 when ambient air is heated to 477°C with a sand inlet temperature of 525°C, and therefore an overall efficiency of 0.79. The gas outlet temperature for the discharge process is 468°C which reduces the overall heat loss to 100°C. The sand outlet temperature can be decreased by reducing the sand mass flow, which will also increase the gas outlet temperature.

Fig. 51. Multistage Moving Bed HEX Outlet Temperatures, Sand and Gas Mass Flow of 50 kg/s Material Parameter Tab. 8, Geometry Fig. 49 With the input parameters of Tab. 8. the overall heat transfer coefficient ktot is, according to (55), evaluated for multiple stages. With increasing stage numbers, the surface area of the whole system increases and leads to a smaller temperature loss. For a system design as shown in Fig. 49. the induced pressure drop would allow up to eighteen stages without exceeding 4000 Pa.



Fig. 52. Heat Transfer Coefficient for Multistage Moving Bed Configurations, Material Parameter Tab. 8., Geometry Fig. 49. 3.3.5 Dimension Multistage System

With exceeding HEX-stages the overall dimension of the apparatus rises. The gas velocity in the channels of Fig. 49. should be limited to 20 m/s. Equation (1) and (2), and a gas inlet stream with a temperature of 570°C and a density of 0.42 kg/m³ lead to a cross section of 6 m² per 50 kg/s exhaust mass flow. The hottest stage is the critical one since the gas density decreases when the gas temperature decreases. The overall width of the system is defined by the number of channels, the respective distance between the channel plates on the gas side and on the sand side, as well by the plate thickness. The evaluated values in Tab. 8. lead to a combined width of 5 cm for one gas and sand channel. To determine the number of channels it is necessary to specify the plate height and the number of HEX-stages. These two parameters define the total height of the device, which should not exceed 20 meters, as there should be enough space for the sand distribution and conveyance. A plate height of 1.5 m leads to 200 channels per 50 kg/s exhaust mass flow. This results in an overall width of 10 meters, a height of 2 meters per stage and a length of 10 meters including the bends in the channels which link the HEX-stages. For a better understanding, the resulting dimensions of a HEX setup for common gas turbines from GE and Siemens are shown in Tab. 10. The number of channels results from the gas temperature and the limitation of the gas velocity to 20 m/s.

Indirect Contact Plate Type Moving Bed HEX 57 Tab. 10. Dimension of a Multistage Moving Bed HEX

A setup for a moving bed HEX with the associated storage tanks is shown in Fig. 53. The cold sand will be transported to the HEX sand inlet with the help of screw conveyors and a bucket conveyor. A bucket conveyor is not suitable for the handling of the hot sand, as the operating temperature limit for most systems is approx. 200°C. A pan conveyor is better suited for this task. These systems require an inclination in the range of 30 to 60 degrees and can handle the high temperatures of the heated storage material.

Fig. 53. Plate Type Moving Bed HEX Setup The shown setup is for an eight-stage HEX device for a GE 7E.03 with an exhaust mass flow of 299 kg/s. These input parameters lead to a width of approx. 20 meters and a length of 23

Power Output / MWExhaust Mass Flow / kg/sExhaust Temperature / °CChannel Width / mChannel Height / mChannelsTotal Width / mTotal Length / mHEX-StagesTotal Height / mSand Mass Flow / kg/sSand Inlet Temperature / °CSand Outlet Temperature / °CGas Outlet Temperature / °C 192 135

410

820

2

446127

503122

410

820

10.544

27020

8702

138069

10.5

493

40020

555502194

565137

410

820

2

43020

435 492174 122

20

10.54 810 20

500

GE MS7001FA1724456010.02

GE 7E.0389

2995480.02

150075

10.5

SGT5-2000E SGT6-5000F2154786120.02

21600

80

1875585360.02

Indirect Contact Plate Type Moving Bed HEX 58 meters for the HEX, which is divided into two modules. The overall height is approximately 35 meters, the overall width 60 meters and the total length is about 30 meters, excluding the connection lines for the gas stream and the overall structural components.

3.3.6 Conclusion

The previous calculations are based on [8], the values for the near wall thermal resistance Rc and the effective bulk thermal conductivity λS,eff are also taken from this study. For an application with exhaust gas and varying sand diameter it is necessary to determine the mentioned parameters in a laboratory setting. With these findings the calculations can be updated and compared to the laboratory setting to gain a reliable calculation method for a scalable apparatus. If these findings match with the calculation method above, the technology has a promising overall efficiency with little mechanical effort. The geometry of the channels, their inlets, outlets as well as the bends, collector and distributor in the gas tube need to be optimized to reduce the pressure drop in the system. The geometry of Fig. 49. reduces the pressure drop significantly, which would allow multiple stages and increase the overall efficiency even more.

3.3.7 Nomenclature

Symbol Unit Description 𝐴𝑖 m² Plate Surface Area 𝐴 m² Channel Cross Section 𝑏𝐺 m Plate Distance Gas Side 𝑏𝑆 m Plate Distance Sand Side 𝑐𝑝,𝐺 J/(kg*K) Gas Heat Capacity 𝑐𝑝,𝑆 J/(kg*K) Sand Heat Capacity �̇� W/K Thermal Capacitance �̇�𝑚𝑎𝑥,𝑖 W/K Maximum Thermal Capacitance �̇�𝑚𝑖𝑛,𝑖 W/K Minimum Thermal Capacitance 𝐶𝑅,𝑖 - Capacitance Ratio 𝐺𝑧 - Graetz Number 𝐻 m Plate Heigth (Gas Flow Direction) 𝑘𝑡𝑜𝑡,𝑖 W/(m²*K) Overall Heat Transfer Coefficient 𝐿 m Plate Length (Gas Flow Direction) 𝐷𝐻 m Hydraulic Diameter 𝐾 m Average Height of Surface Elevations �̇�𝐺 kg/s Gas Mass Flow �̇�𝑆 kg/s Sand Mass Flow 𝑁𝑢𝐷ℎ,𝐻 - Average Nusselt Number

Indirect Contact Plate Type Moving Bed HEX 59 𝑁𝑢𝐺 - Nusselt Number Gas Side 𝑁𝑢𝐺,𝑙𝑎𝑚 - Laminar Nusselt Number Gas Side 𝑁𝑢𝐺,𝑡𝑢𝑟𝑏 - Turbulent Nusselt Number Gas Side 𝑁𝑇𝑈𝑖 - Number of Transfer Units 𝑃𝑒 - Peclet Number 𝑃𝑟 - Prandtl Number �̇�𝑖 W Total Heat Flux �̇�𝑖,𝑚𝑎𝑥 W Maximum Total Heat Flux 𝑅𝑒 - Reynolds Number 𝑅𝑐 W/(m²*K) Near-Wall Thermal Resistance 𝑠𝑊 m Plate Thickness 𝑇𝐺 K Gas Temperature 𝑇𝑆 K Sand Temperature 𝑢𝑆 m/s Sand Velocity 𝑢𝐺 m/s Gas Velocity 𝛼𝐺𝑊 W/(m²*K) Heat Transfer Coefficient Gas-Wall 𝛼𝑆𝑊 W/(m²*K) Heat Transfer Coefficient Sand-Wall 𝛥𝑝 Pa Pressure Drop 𝜀𝑖 - HEX Effectiveness 𝜁 - Drag Coefficient Δ𝑇 K Temperature Difference 𝜆𝐺 W/(m*K) Thermal Conductivity Gas 𝜆𝑆,𝑒𝑓𝑓 W/(m*K) Effective Thermal Conductivity Sand 𝜆𝑊 W/(m*K) Thermal Conductivity Wall 𝜌𝑆 kg/m³ Sand Bulk Density 𝜌𝐺 kg/m³ Gas Density

Alternative TES Approaches 60

4 Alternative TES Approaches

As a final outlook, possible usages of sand as a heat storage medium in different heat exchange systems is discussed. Therefore, the operating principle of each system will be explained, the respective advantages and their disadvantages discussed.

4.1 sandTES

This heat exchanger system is a project at the Technical University of Vienna [2] and based on a fluidized bed HEX. The sand based thermal energy storage (sandTES) consists of fluidized bed with an immersed tube bundle. The sand is conveyed through the system with the fluidization principle, where an auxiliary power input is needed to fluidize the bed material with air. This system is an active HEX, since the storage material will be cycled through the device from a cold storage tank to a hot one and back. The immersed tube bundle contains a heat transfer fluid which has no contact to the storage material, opening the possibility to use a broad variety of heat transfer fluids as thermal oil from concentrated solar power plants, steam from a combined cycle power plant or the exhaust stream from a gas turbine. The induced pressure drop in the gas stream can be regulated by the geometry of the tube bundle and is not related to the fluidization of the sand bed.

Fig. 54. sandTES setup, Source: [2] 4.2 Packed Bed Heat Exchanger

These passive storage systems consist of a packed bed of storage material in a tank. The heat transfer fluid can either pass directly through the storage material, when the heat transfer


fluid is gaseous and the grain size of the storage material is big enough to enable a gas flow through the bed, or the heat transfer fluid can be guided in pipes for an indirect heat exchange. The heat transfer between the pipes and the bed material can be optimized with finned tubes and allows a much smaller grain size. The storage silos are limited by thermal expansion of the material over multiple load cycles. Thermal ratcheting can be avoided through suitable dimensioning of the storage tank. It is also possible to use multiple storage tanks for one system which provides a great flexibility of these systems. The ongoing project in Gmunden [10] shows that a storage container with a height of 18 meters and a diameter of 15 meters can handle a gas mass flow of 50 kg/s without exceeding a pressure drop of 4000 Pa.

Fig. 55. Packed Bed HEX setup, Source: [11] 4.3 Cyclone Heat Exchanger

Cyclones are used in the cement industry to preheat solid particles and are also suitable for a heat exchange system with sand as storage material [12, 13]. These systems allow high gas velocities [14] and provide a high heat transfer due to the fast mixing of the particles and the gas. The downside of cyclone towers as a heat exchange system is their big building volume. For a typical cement production, the towers of multiple cyclones reach heights up to 120 meters [15] and the typical mass flow rates are at about 50 kg/s for the solid material [16] for a temperature range of 700 to 800°C. In addition to the heat exchanger comes the setup to transport and store the particles. This overall big build volume makes the technology not suitable for an exhaust gas heat storage.


Fig. 56. Multistage Cyclone Setup in the cement industry, Source: [17] 4.4 Falling Particle Heat Exchanger

A concept for concentrated solar power plants are falling particle receivers [18]. In these systems particles fall through a chamber and are heated by the bundled sun rays. This concept is taken further and also used as a heat exchange setup between two gas streams [19], as seen in Fig. 57. Currently this concept has the problem with the formation of currents in the particle stream when the gas stream elevates particles. Currently no applications as a direct contact heat exchange system between a gas stream and a particle stream are being investigated. This opens the possibility of testing the technology for an application as a direct contact heat exchanger.

Fig. 57. Falling Particle HEX Setup for two gas streams, Source: [19]

TES Integration Into CCPP 63

5 TES Integration Into CCPP

The integration of a thermal energy storage into a power plant is possible during construction or as retrofit. A CCPP usually consists of a gas turbine, a heat recovery steam generator (HRSG), steam turbines and generators to produce electrical energy. In the combustion chamber of the gas turbine, the gas is mixed with compressed air and ignited, this hot mixture expands in the gas turbine and powers a shaft which is connected to a generator. The hot exhaust gas from the gas turbine is utilized to generate steam for a steam turbine and led into the surrounding environment through a stack. In Fig. 58. a steam turbine with three pressure levels (high pressure, intermediate pressure, and low pressure) is shown. The steam turbine also drives a shaft which can be the same as the shaft driven by the gas turbine.

Fig. 58. Process flow diagram of a standard 3-pressure CCPP, Source: course “applied thermodynamics - 302.696 “ To integrate a gas/sand based thermal energy storage into existing power plants, it is necessary to divert the exhaust gas stream from the gas turbine before the HRSG, as shown in Fig. 59. This is possible for power plants with an electrical output up to 100 MW. The exhaust gas mass flow in bigger power plants is too high and leads to leaks in the diverter valves.

Fig. 59. CCPP with exhaust gas diverting dampers Storage systems can now be integrated with a controllable exhaust gas flow. Fig. 60. shows a system with a packed bed heat storage. The exhaust gas is led through the packed bed, to


store the excess heat, and fed into the surrounding environment through stack 2. To release the stored heat, compressed air flows through the storage system and can be utilized in the HRSG afterwards. The size of the storage system can be adjusted by adding multiple packed bed reactors. This system has the disadvantage that it is difficult to regulate the output.

Fig. 60. CCPP with exhaust gas diverting dampers and integration of packed bed TES A wider and more flexible range of energy is possible with a plate type moving bed HEX. When the storage is heated, the hot exhaust gas flows through the HEX from the bottom to the top and cold sand falls through the HEX as seen in Fig. 61. During the discharge process, hot sand falls through the HEX and the air inlet stream is cold (Fig. 62). This mutual thermal load must be carefully considered from a design point of view.

Fig. 61. CCPP with exhaust gas diverting dampers and integration of moving bed sand heat exchanger, charging process


Fig. 62. CCPP with exhaust gas diverting dampers and integration of moving bed sand heat exchanger, discharge process The gas side integrated TES-systems with either packed bed or moving bed are difficult to implement in existing power plants and are more suited for new power plants. The integration of a gas diverter between the gas turbine and the HRSG is problematic since the exhaust gas flow has a swirl that requires some piping to allow a proper flow situation for the following built-in components. This means that there is hardly any space to implement a diverter. Therefore, a steam to sand TES-system (sandTES, Fig. 63) is easier to implement into existing power plants since it uses steam as HTF.

Fig. 63. 3-pressure multi-shaft CCPP retrofit with steam to sand TES, Source: course “applied thermodynamics - 302.696 “

Summary and Conclusion 66

6 Summary and Conclusion

The aim of this study was to check the usability of a fluidized bed direct contact HEX mathematically and a plate type moving bed HEX for scalable waste heat recovery to increase the load flexibility of combined cycle power plants. An important design condition was that the HEX must not exceed a pressure drop of 4000 Pa, otherwise the performance of the gas turbine suffers. This requirement could not be met with the sinter distribution floor of the fluidized bed HEX. The pressure drop can be reduced with a nozzle floor, which requires a bigger bed height to create a stable fluidized bed. Therefore, it is necessary to develop a distribution floor which reduces the pressure drop to a minimum and provides an even gas distribution to operate a low height fluidized bed. Once this problem has been solved, a laboratory system can be set up to verify the calculation method and to determine possible correction factors for the heat transfer, depending on the bed inclination and the grain diameter. With a reduced pressure loss, multi-stage devices should also be possible, which significantly increases the performance of the direct contact fluidized bed heat exchanger. In the case of plate type moving bed heat exchanger, the pressure loss can be greatly reduced by optimizing the gas flow, making multi-stage devices feasible. When the results of the two created algorithms are compared, the plate type moving bed HEX has a much better performance in terms of the stored amount of heat and the induced pressure drop. The drawback of the plate type moving bed is the complex structure, which consists of several hundred gas channels to be able to process the exhaust gas mass flow of a gas turbine. The amount of transferred heat in a fluidized bed HEX is lower than in the other system, but the cfd simulation has shown a much higher heat transfer than the mathematical approach. A direct heat exchanger, with the advantage of its simple construction, is a technology that should be tested in laboratory setup, provided the problem with the pressure drop of the distribution floor can be solved. One possibility would be to reduce the thickness of the distribution floor as far as possible, in terms of production technology, and to attach it to a supporting structure. The disadvantage of this design could be an uneven distribution of the fluidization gas through the support structure, which can impair the stability of the fluidized bed. This shows that additional tests are necessary as the currently available distribution floors offer no possibility to operate a direct contact fluidized bed heat exchanger without exceeding the set limit for the allowed pressure drop in the gas stream.

Attachment 67

7 Attachment

7.1 List of Tables Tab. 1. Exhaust Gas Parameter from the Siemens Product Range ....................................................... 5

Tab. 2. Permeability coefficients from the GKN-Sika product catalogue .............................................. 10

Tab. 3. Material parameters for the HEX analysis ................................................................................ 17

Tab. 4. HEX-Temperatures charge ....................................................................................................... 20

Tab. 5. HEX Temperatures discharge .................................................................................................. 21

Tab. 6. Material parameters for the local heat distribution ................................................................... 38

Tab. 7. HEX-Temperatures charge ....................................................................................................... 54

Tab. 8. Material parameters for the HEX analysis ................................................................................ 54

Tab. 9. HEX Temperatures discharge .................................................................................................. 55

Tab. 10. Dimension of a Multistage Moving Bed HEX .......................................................................... 57

7.2 List of Figures Fig. 1. Fluidized Bed HEX Design and Moving Bed HEX Design ........................................................... 3

Fig. 2. Design of a multistage fluidized bed HEX .................................................................................... 4

Fig. 3. HEX cross section for a gas density of 0.6 kg/m³ ........................................................................ 5

Fig. 4. Terminal velocity for a gas density of 0.6 kg/m³, ρP=2650 kg/m³, µG=2.9*10^(-5) kg/(m*s) ...... 7

Fig. 5. Minimum fluidization velocity for a gas density of 0.6 kg/m³, ρP=2650 kg/m³, µG=2.9*10^(-5)

kg/(m*s) ................................................................................................................................................... 8

Fig. 6. Pressure Drop in the fluidized bed ............................................................................................... 9

Fig. 7. Pressure Drop in the Distribution Floor SIKA-B 200, ρG=0.4 kg/m³, s=5 mm ............................. 9

Fig. 8. Voidage in the fluidized bed for a particle diameter of 500 µm, additional material parameters in

Tab. 3. ................................................................................................................................................... 11

Fig. 9. Model for the calculation of the heat transfer between fluid and particle, Source: [3] ............... 12

Fig. 10. Total heat transfer efficiency for ρG=0.6 kg/m³, additional material parameters in Tab. 3. ..... 13

Fig. 11. Progress of the fluid temperature through a sand bed with an initial height of 0.04 m, Gas inlet

temperature of 570°C, additional material parameters in Tab. 3. ......................................................... 15

Fig. 12. Wake and Drift of a bubble in a fluidized bed, Source: [5] ....................................................... 16

Fig. 13. Correction factor for two-stage theory, Source: [5] .................................................................. 16

Fig. 14. Proportion of Wake and Drift, Source: [5] ................................................................................ 17

Fig. 15. Discretization Grid of a single HEX-Stage ............................................................................... 18

Fig. 16. Temperature Profile inside a HEX-Stage, ϑG,in=570°C, ϑS,in=300°C, additional material

parameters in Tab. 3 ............................................................................................................................. 19

Fig. 17. Multistage Algorithm for a Fluidized Bed HEX ......................................................................... 20

Attachment 68

Fig. 18. Efficiency progress for variable mass flows, additional material parameters in Tab. 3 ........... 22

Fig. 19. Temperature progress for variable mass flows, material parameters in Tab. 3 ...................... 22

Fig. 20. Mixing Progress for Various Slope Angles after 60 Seconds .................................................. 24

Fig. 21. Bed Height for Various Slope Angles after 60 Seconds .......................................................... 25

Fig. 22. Design Approaches for Downcomers ...................................................................................... 26

Fig. 23. CFD-Analysis of Channel Downcomers, Cells W = Vertical Gas Velocity m/s, Pressure in Pa

.............................................................................................................................................................. 28

Fig. 24. CFD-Analysis of L-Valve Downcomers, Cells W = Vertical Gas Velocity m/s, Pressure in Pa29

Fig. 25. Fluid-to-particle heat transfer coefficient Barracuda ................................................................ 30

Fig. 26. CPFD Heat Transfer ................................................................................................................ 31

Fig. 27. Design of a multistage moving bed HEX ................................................................................ 34

Fig. 28. Temperature Profile of a Single Stage in a Moving Bed HEX ................................................. 35

Fig. 29. Temperature Profile between two HEX-Plates in a Moving Bed HEX, TG,in=570°C,

TS,in=300°C, mG=0.5 kg/s, mS=0.6 kg/s ............................................................................................. 37

Fig. 30. Mean Sand Temperature of a single Channel in a Moving Bed HEX, TG,in=570°C,

TS,in=300°C, mG =0.5 kg/s, mS/(Plate_Distance) =0.5 kg/(s*cm) ...................................................... 37

Fig. 31. Dependency of HEX-effectiveness from NTUi for a capacitance ratio of 1 and inlet temperatures

of 200°C for the sand stream and 350°C for the gas stream, additional material parameters in Tab. 8.

.............................................................................................................................................................. 40

Fig. 32. Dependency of NTUi from the HEX Surface Area for a thermal capacitance of 500 W/K, an

overall heat transfer coefficient of 75 W/(m²*K), an inlet temperature of 200°C for the sand stream and

350°C for the gas stream, additional material parameters in Tab. 8. ................................................... 41

Fig. 33. Gas heat transfer coefficient and total heat transfer coefficient for a single moving bed HEX-

Stage, pin=101325 Pa, mG=0.25 kg/s, mS=0.25 kg/s, HP=1.5 m, LP=6 m ......................................... 42

Fig. 34. Heat Transfer through one plate, TG=400°C, TS=300°C ........................................................ 43

Fig. 35. Outlet Temperatures of a single Channel in a Moving Bed HEX with a varying plate distance

on the gas side, TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s ................................... 43

Fig. 36. Outlet Temperatures of a single Channel in a Moving Bed HEX with a varying plate distance

on the sand side, TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s ................................. 44

Fig. 37. Outlet Temperatures of a single Channel in a Moving Bed HEX with varying plate distances,

TG,in=570°C, TS,in=300°C, mG=0.125 kg/s, mS=0.125 kg/s .............................................................. 44

Fig. 38. ζ for flow through pipes, Source: VDI Heat Atlas 2010 ............................................................ 46

Fig. 39. Pressure Drop in a Channel with a Plate Height of 1.5 m, Length of 6 m and a constant gas

velocity of 23 m/s .................................................................................................................................. 47

Fig. 40. Pressure Drop in a Channel with a Helical Coil, HP=1.5 m, L=6 m, bG=20 mm, ρG=0.4 kg/m³,

ζ=0.3 ...................................................................................................................................................... 48

Fig. 41. Drag Coefficient for Bends and Reynolds Numbers > 105, Source: VDI Heat Atlas 2010...... 48

Fig. 42. Drag Coefficient for Bends in Smooth Pipes, Source: VDI Heat Atlas 2010 ........................... 49

Fig. 43. Abrupt Widening of the Cross Section, Source: VDI Heat Atlas 2010 ..................................... 49

Attachment 69

Fig. 44. Continuous Widening of the Cross Section, Source: VDI Heat Atlas 2010 ............................. 50

Fig. 45. Drag Coefficient for Continuous Widening of the Cross Section, Source: VDI Heat Atlas 2010

.............................................................................................................................................................. 50

Fig. 46. Drag Coefficient for an Abrupt Reduction of the Cross Section, Source: VDI Heat Atlas 2010

.............................................................................................................................................................. 51

Fig. 47. Drag Coefficient Tee Junctions and Oblique Junctions, Source: VDI Heat Atlas 2010 ........... 51

Fig. 48. Drag Coefficient Tee Junctions and Oblique Junctions, Source: VDI Heat Atlas 2010 ........... 52

Fig. 49. Optimized Channel Geometry for a Multistage Moving Bed HEX ........................................... 52

Fig. 50. Multistage Algorithm for a Moving Bed HEX ............................................................................ 53

Fig. 51. Multistage Moving Bed HEX Outlet Temperatures, Sand and Gas Mass Flow of 50 kg/s Material

Parameter Tab. 8, Geometry Fig. 49 .................................................................................................... 55

Fig. 52. Heat Transfer Coefficient for Multistage Moving Bed Configurations, Material Parameter Tab.

8., Geometry Fig. 49. ............................................................................................................................ 56

Fig. 53. Plate Type Moving Bed HEX Setup ......................................................................................... 57

Fig. 54. sandTES setup, Source: [2] ..................................................................................................... 60

Fig. 55. Packed Bed HEX setup, Source: [11] ...................................................................................... 61

Fig. 56. Multistage Cyclone Setup in the cement industry, Source: [17] .............................................. 62

Fig. 57. Falling Particle HEX Setup for two gas streams, Source: [19] ................................................ 62

Fig. 58. Process flow diagram of a standard 3-pressure CCPP, Source: course “applied

thermodynamics - 302.696 “ ................................................................................................................. 63

Fig. 59. CCPP with exhaust gas diverting dampers ............................................................................. 63

Fig. 60. CCPP with exhaust gas diverting dampers and integration of packed bed TES ..................... 64

Fig. 61. CCPP with exhaust gas diverting dampers and integration of moving bed sand heat exchanger,

charging process ................................................................................................................................... 64

Fig. 62. CCPP with exhaust gas diverting dampers and integration of moving bed sand heat exchanger,

discharge process ................................................................................................................................. 65

Fig. 63. 3-pressure multi-shaft CCPP retrofit with steam to sand TES, Source: course “applied

thermodynamics - 302.696 “ ................................................................................................................. 65

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