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H2020-LCE-2014-1

D3.2 - System 1-D dynamic model report and open-source model library

Nature of the deliverable1

☐R ☐P ☐D ☒O

Dissemination level2 ☒PU ☐PP ☐RE ☐CO

Due date 30/11/2015

Status Final Version

Date of Submission 14/07/2016

1 Please indicate the nature of the deliverable using one of the following codes (according to the DoW): Report (R), Prototype (P), Demonstrator (D), Other (O)

2 Please indicate the dissemination level using one of the following codes (according to the DoW): PU = Public PP = Restricted to other programme participants (including the Commission Services) RE = Restricted to a group specified by the consortium (including the Commission Services) CO = Confidential, only for members of the consortium (including the Commission Services)

Ref. Ares(2016)3411654 - 14/07/2016

Work Package 3 – D3.2

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Authors and Entities

Responsible Authors and Entities

Author(s) Organization(s)

Susana López IK4-TEKNIKER

Jesús Febres IK4-TEKNIKER

Iván Mesonero IK4-TEKNIKER

Collaborating Authors and Entities

Author(s) Organization(s)

Frank Meyer H&B

Alexander Mantler H&B

Antonio Luis Ávila PSA

Steffen Kunze IKTS

CAPTure Partners

Document History

Version Date Organisation Change History

0.1 01/11/2015 TEK Initial version

1.0 19/05/2016 TEK Initial mayor version

1.1 26/05/2016 TEK Final draft for review

1.2 14/07/2016 TEK Final version


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2.0

Executive Summary

This document describe the modelling task of a regenerative bed for the design of a regenerative heat exchange system. The selected modelling assumptions and the corresponding methodology are presented for a metallic and a ceramic regenerative bed with some preliminary simulation results and initial validation exercises.


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Table of Contents

EXECUTIVE SUMMARY ..................................................................................................................................... 2

TABLE OF CONTENTS ........................................................................................................................................ 3

LIST OF FIGURES ............................................................................................................................................... 3

LIST OF TABLES ................................................................................................................................................. 5

INTRODUCTION ................................................................................................................................................ 6

1. METALLIC REGENERATIVE BED MODEL ................................................................................................................ 6 1.1. Assumptions .................................................................................................................................... 6 1.2. Model structure ............................................................................................................................... 7

1.2.1. Solid phase .................................................................................................................................................. 8 1.2.1.1. Matrix materials .................................................................................................................................. 10 1.2.2. Fluid phase ................................................................................................................................................ 11

1.3. Preliminary results ......................................................................................................................... 14 1.4. Initial validation ............................................................................................................................. 15

1.4.1. Comparison with experimental data from Ciemat-PSA ............................................................................ 15 1.4.2. Comparison with experimental data from Haver and Boecker ................................................................ 19

2. CERAMIC REGENERATIVE BED MODEL ............................................................................................................... 24 2.1. Assumptions and methodology ..................................................................................................... 24 2.2. Model structure ............................................................................................................................. 25

2.2.1. Solid phase ................................................................................................................................................ 27 2.2.2. Fluid phase ................................................................................................................................................ 28

2.3. Preliminary results ......................................................................................................................... 29

CONCLUSIONS ................................................................................................................................................ 31

REFERENCES ................................................................................................................................................... 32

List of Figures

FIGURE 1: THREE RANDOMLY STACKED SCREENS (PLAIN SQUARE WEAVE): 3D VIEW (LEFT), FLOW DIRECTION VIEW (RIGHT) .............. 6 FIGURE 2: DIAGRAM OF METALICREGENERATIVEBED1D MODEL ..................................................................................... 7 FIGURE 3: DROP DOWN MENU FOR MATERIAL SELECTION IN THE PARAMETER DIALOG OF METALICREGENERATIVEBED1D .......... 9 FIGURE 4: DIAGRAM OF NODECYLINDRICAL .................................................................................................................. 9 FIGURE 5: MATERIALS LIBRARY ................................................................................................................................... 10 FIGURE 6: SPECIFIC HEAT CAPACITY AND CONDUCTIVITY OF DIN EN 10095 – MANUFACTURER DATA AND SELECTED CURVE FITTINGS

(LOGARITHMIC AND LINEAR) ............................................................................................................................... 11 FIGURE 7: DROP DOWN MENU OF HEAT TRANSFER OPTIONS OF THE CLASS DYNAMICREGENERATIVEBEDFLUIDPHASE ............ 13 FIGURE 8: EXPERIMENTS WITH TWO BED ARRANGEMENT FOR THE REGENERATIVE SYSTEM (LEFT: VARIABLE DIFFERENTIAL PRESSURE,

RIGHT: VARIABLE MASS FLOW RATE) ..................................................................................................................... 14 FIGURE 9: PRELIMINARY RESULTS OF A TWO BED ARRANGEMENT REGENERATIVE SYSTEM MODEL ............................................... 15 FIGURE 10: SCHEMATIC OF THE EXPERIMENTAL SETUP FOR WIRE MESH VOLUMETRIC RECEIVERS ................................................ 16 FIGURE 11: PICTURE OF THE EXPERIMENTAL SETUP FOR WIRE MESH VOLUMETRIC RECEIVERS AT CIEMAT-PSA ............................. 16 FIGURE 12: SIMULATION MODEL FOR CIEMAT-PSA EXPERIMENTAL SETUP ............................................................................ 17 FIGURE 13: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR 10 MESHES OF A TYPE.......................................................... 17 FIGURE 14: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR 9 MESHES OF A TYPE............................................................ 18 FIGURE 15: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR 6 MESHES OF F TYPE ............................................................ 18


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FIGURE 16: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR 5 MESHES OF F TYPE ............................................................ 19 FIGURE 17: SCHEMATICS OF THE EXPERIMENTAL SETUP FOR PRESSURE DROP MEASUREMENTS IN STACKED MESHES ....................... 19 FIGURE 18: PICTURE OF THE EXPERIMENTAL SETUP FOR PRESSURE DROP MEASUREMENTS IN STACKED MESHES AT H&B ................ 20 FIGURE 19: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 1 OF HAVER & BOECKER ............................................... 21 FIGURE 20: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 2 OF HAVER & BOECKER ............................................... 22 FIGURE 21: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 3 OF HAVER & BOECKER ............................................... 22 FIGURE 22: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 4 OF HAVER & BOECKER ............................................... 22 FIGURE 23: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 5 OF HAVER & BOECKER ............................................... 23 FIGURE 24: EXPERIMENTAL DATA AND SIMULATION RESULTS FOR TEST 6 OF HAVER & BOECKER ............................................... 23 FIGURE 25: CORDIERITE HONEYCOMB BRICK WITH HIGH DENSITY OF STRAIGHT CHANNELS ........................................................ 24 FIGURE 26: MODELICA CERAMIC REGENERATIVE BED MODEL ICON ...................................................................................... 25 FIGURE 27: INITIALIZATION TAB OF THE CERAMICREGENERATIVEBED1D MODEL .............................................................. 26 FIGURE 28: GENERAL TAB CERAMICREGENERATIVEBED1D MODEL ............................................................................... 26 FIGURE 29: DIAGRAM OF THE CERAMIC REGENERATIVE BED MODEL ..................................................................................... 27 FIGURE 30: MODELICA MODEL OF THE NODE ELEMENT ( DISTRIBUTEDTHERMALCONDUCTOR) ............................................. 27 FIGURE 31: SOLID PHASE PARAMETERS TAB ..................................................................................................................... 28 FIGURE 32: FLUID PHASE PARAMETERS TAB ..................................................................................................................... 28 FIGURE 33: LEFT HAND SITE, SINGLE SHOT EXPERIMENT. RIGHT HAND SITE, CYCLING REGIME EXPERIMENT ................................... 29 FIGURE 34: PRELIMINARY RESULTS (SINGLE SHOT EXPERIMENT) .......................................................................................... 30 FIGURE 35: PRELIMINARY RESULTS (CYCLING REGIME EXPERIMENT) ..................................................................................... 31


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List of Tables

TABLE 1: VOLUMETRIC POROSITY EQUATIONS IMPLEMENTED IN THE METALLIC MODEL............................................................... 7 TABLE 2: GEOMETRIC CHARACTERISTICS OF THE MESHES TESTED BY CIEMAT-PSA ................................................................... 15 TABLE 3: REGENERATIVE BED CHARACTERISTICS OF THE DIFFERENT TESTS PERFORMED BY HAVER AND BOECKER ........................... 20


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Introduction

In the framework of WP3 the design of the regenerative heat exchange system, and its corresponding control system, it is based on the usage of a dynamic Modelica model as the main tool. This model has to be parametric and flexible enough allowing the analysis of the effect of the different design variables (material characteristics, bed geometry, etc) in the behaviour of the regenerative heat exchange. In the present document the model developed for the explained purpose is described.

1. Metallic regenerative bed model

1.1. Assumptions

A cylindrical regenerative bed has been modelled (MetalicRegenerativeBed1D) with the following main assumptions:

Regenerative beds that are made by a randomly stacked woven-screen matrix with plain square weave (metallic materials).

Figure 1: Three randomly stacked screens (plain square weave): 3D view (left), flow direction view (right)

The matrix is made of metallic materials and the model does take into account the dependency of their conductivity and specific heat capacity with the temperature.

One-dimensional fluid flow is assumed, including only as heat transfer phenomenon the heat convection between the fluid and the matrix (radiative heat transfer is disregarded).

One-dimensional heat conduction along the matrix (parallel to the fluid flow) is assumed. Perfect insulation is considered at the lateral area so heat losses can only be taken into account through upper and lower end of the matrix


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1.2. Model structure

The model is mainly composed of two components that represent the solid and the fluid phases of the regenerative bed as can be appreciated in the following figure.

Figure 2: Diagram of MetalicRegenerativeBed1D model

It also includes a replaceable porosity function for the calculation of the volumetric porosity of the matrix. The following options are available to be chosen from a drop down menu: EDSUPorosity, NASAPorosity, ArmourCannonPorosity and XuWirtzPorosity. All four options where described by Li & Peterson [3] but some discrepancies have been found for the porosity calculation defined by Xu & Wirtz [4] so the original reference has been selected in this case in order to define the necessary equations in the code.

The following table describe how to calculate the porosity in each option

Table 1: Volumetric porosity equations implemented in the metallic model

Porosity function name Equation

EDSU(Engineering Sciences Data Unit

in London)

𝒗𝒐𝒍𝒖𝒎𝒆𝒕𝒓𝒊𝒄𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚 = 𝟏 − 𝟎. 𝟐𝟓 ∗ 𝝅 ∗𝒅𝒘𝒑𝒊𝒕𝒄𝒉

NASA 𝒗𝒐𝒍𝒖𝒎𝒆𝒕𝒓𝒊𝒄𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚

= 𝟏 − 𝟎. 𝟐𝟓 ∗ 𝝅 ∗ 𝒄𝒓𝒊𝒎𝒑𝒊𝒏𝒈𝑭𝒂𝒄𝒕𝒐𝒓 ∗𝒅𝒘𝒑𝒊𝒕𝒄𝒉

Armour & Cannon 𝒗𝒐𝒍𝒖𝒎𝒆𝒕𝒓𝒊𝒄𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚

= 𝟏 − 𝝅 ∗ (𝑨 ∗ 𝑩

𝟐 ∗ (𝑨 + 𝑩)) ∗ √𝟏 + (

𝑨

𝟏 + 𝑨)𝟐


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Where:

dw is the wire diameter

pitch is the distance between two wires or the aperture

crimpingFactor is a factor that describes how compressed are the meshes in the matrix

t is the thickness of the mesh

L is the regenerative bed length

nlayer is the number of layers in the matrix

It must be noted that for the two last options the user must provide the value of some more parameters (the thickness of the wire mesh or the number of layers in the matrix).

1.2.1. Solid phase

Solid phase component is an instance of the class SolidPhase that is a lumped parameter thermal system in the radial direction (there is no radial variation of the solid temperature). It is composed of an array of instances of the class NodeCyclindrical that represents one section of the solid material along its axis. Each node is composed by two instances of a class that describes de axial conduction along the material and one instance of a class that behaves as the equivalent thermal inertia of the material section (see Figure 4). The node class includes a replaceable instance of a class that describes the material that is selected, this selection can be done easily at the upper class that represents the regenerative bed MetalicRegenerativeBed1D.

𝑨 =𝒅𝒘

𝒑𝒊𝒕𝒄𝒉 − 𝒅𝒘; 𝑩 =

𝒅𝒘𝒕

Xu & Wirtz 𝑪𝒇 =

𝑳

𝒏𝒍𝒂𝒚𝒆𝒓 ∗ 𝟐 ∗ 𝒅_𝒘

𝑪 = 𝟏𝟐𝟑 ∗ (𝒅𝒘𝒑𝒊𝒕𝒄𝒉

)𝟒

− 𝟑𝟖𝟒 ∗ (𝒅𝒘𝒑𝒊𝒕𝒄𝒉

)𝟐

− 𝟔𝟒𝟎

𝒗𝒐𝒍𝒖𝒎𝒆𝒕𝒓𝒊𝒄𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚 = 𝟏 +𝟎. 𝟎𝟎𝟎𝟑𝟗𝟎𝟔 ∗ 𝝅 ∗ 𝑪 ∗ (

𝒅𝒘𝒑𝒊𝒕𝒄𝒉

)

𝑪𝒇


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Figure 3: Drop down menu for material selection in the parameter dialog of MetalicRegenerativeBed1D

Once a predefined material is selected from a drop down menu (see Figure 3) the instances of the classes that describe the thermal inertia and the heat conduction through the solid are changed in order to take into account the specific properties of the substance that has been chosen.

Figure 4: Diagram of NodeCylindrical

The list of available materials depends on the material classes stored in a library of solid materials (Materials) that is described in [1] that has been expanded within CAPTure project in order to include specific classes that describe the behaviour of porous materials and more in concrete woven-screen matrixes. The basic classes that have been created are the PartialHeatCapacitorPorousMaterial and the

PartialThermalConductorBoxWovenScreenMatrix. The first one is a partial model for the heat capacity of a porous material. No specific geometry is assumed beyond a total volume with uniform temperature for the entire volume. Furthermore, it is assumed that the specific heat capacity is function of temperature. The second one is also a partial model for transport of heat through a randomly stacked woven-screen matrix without storing it. According to Martini [2] this class takes into account the porosity of the matrix and


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Figure 5: Materials

library

the conductivities of the solid and the fluid in order to calculate the real thermal conductivity of the matrix with the following equation.

𝑘𝑚𝑎𝑡𝑟𝑖𝑥 = 𝑘𝑔𝑎𝑠 ∗

(

(1 + (

𝑘𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑘𝑔𝑎𝑠

)

1 − (𝑘𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑘𝑔𝑎𝑠

)) − (1 − 𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦)

(1 + (

𝑘𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑘𝑔𝑎𝑠

)

1 − (𝑘𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑘𝑔𝑎𝑠

)) + (1 − 𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦)

)

Where:

kmatrix is the thermal conductivity of the matrix

kgas is the thermal conductivity of the gas in the matrix

kmaterial is the thermal conductivity of the matrix material (solid)

It can be seen in Figure 2 and Figure 4 that the class for the solid phase has an array of inputs named k_gas in order to have access to the instantaneous value of the thermal conductivity of the gas in the matrix. The array of elements called RealExpression in Figure 2 is “connected” with the internal variable of the fluid phase fluidPhase.heatTransfer.lambdas that is exactly the instantaneous value of the thermal conductivity of the gas in the different nodes along the matrix.

1.2.1.1. Matrix materials

Apart from the basic partial models described in the previous sections, four specific materials have been added to the Materials library: DIN EN 10095, DIN 17742, DIN 17470 and DIN EN 10302. These materials have been proposed by Haver & Boecker taking into account the expected operating temperatures, their availability as meshed material, thermal and mechanical properties as well as sintering possibility. In all cases it has been assumed a constant value for the density but temperature dependent values for the specific heat capacity and thermal conductivity.

Regarding this two last properties, the available information from datasheets has been fitted to polynomial expressions (linear or quadratic) in most cases and logarithmic expressions in others (as can be seen in Figure 6 for the material DIN EN 10095)


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Figure 6: Specific heat capacity and conductivity of DIN EN 10095 – Manufacturer data and selected curve

fittings (logarithmic and linear)

1.2.2. Fluid phase

Fluid phase component is an instance of the class DynamicRegenerativeBedFluidPhase that is based in the DynamicPipe class from the Modelica Standard Library [5][6] that is the model of a straight pipe with distributed mass, energy and momentum balances providing the complete balance equations for one-dimensional fluid flow. It treats the partial differential equations with the finite volume method and a staggered grid scheme for momentum balances.

The main differences between the original DynamicPipe and the DynamicRegenerativeBedFluidPhase are the following:

Specific equations have been implemented under the Detailed option of

FlowModel. When the Detailed option is selected, the relationship between the mass flow rate and the pressure loss is determined with experimental correlation for a flow through an infinite randomly stacked woven-screen matrix.

Flow friction characteristics were originally defined by Kays & London [8] that determined experimentally the relationship between the friction factor and the Reynolds number for different porosity values of the matrix. But the equations


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implemented within this model correspond to the following approximation determined by Martini [2]:

𝑑𝑝 =𝑚𝑓𝑙𝑜𝑤2 ∗ 𝐿 ∗ 𝐶𝑤

2 ∗ 𝐴2 ∗ 𝜌 ∗ (𝐷ℎ4 )

𝑖𝑓 𝑅𝑒 < 60 → log 𝐶𝑤 = 1.73 − 0.93 ∗ log𝑅𝑒

𝑖𝑓 60 < 𝑅𝑒 < 1000 → log 𝐶𝑤 = 0.714 − 0.365 ∗ log𝑅𝑒

𝑖𝑓 𝑅𝑒 > 1000 → log 𝐶𝑤 = 0.015 − 0.125 ∗ log 𝑅𝑒

Where:

o dp is the pressure drop along the matrix

o mflow is the fluid mass flow rate

o L is the length of the matrix

o Cw is the factor of friction for matrix

o A is the area of flow

o ρ is the density of the fluid at regenerator

o Dh is the hydraulic diameter of the matrix

o Re is the Reynolds number

A new option has been added to the list of classes that describe the convective heat transfer within this model (see Figure 7). It is especially suited for gas flow through an infinite randomly stacked woven-screen matrix being a correlation from Organ [9] of experimental data from wire screens and crossed rods simulating wire screens from Kays & London [8].

Main assumptions of the correlation are: perfect stacking, i.e., screens touching is assumed, and volumetric porosity between 0.602 and 0.832.

𝑆𝑡 ∗ 𝑃𝑟23 =

1.25

𝑅𝑒12

Where:

o St is the Stanton number

o Pr is the Prandtl number

o Re is the Reynolds number


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Figure 7: Drop down menu of heat transfer options of the class DynamicRegenerativeBedFluidPhase

Regarding the parameterization of the fluid phase model it must be taken into account that according to Organ [7] and Kays & London [8] the hydraulic radius of an individual wire screen and matrixes can be determined by the following equations:

𝑟ℎ =𝑝𝑖𝑡𝑐ℎ

𝜋−𝑑𝑤

4 or 𝑟ℎ =

𝑑𝑤∗𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦

4∗(1−𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦) when porosity is defined by the expression

defined by EDSU.

It is worth to mention also that for both correlations (flow friction and convective heat transfer) the Reynolds number is calculated with a velocity (vs) that is not the real velocity of the fluid along the matrix.

𝑅𝑒 =𝜌 ∗ 𝑣𝑠 ∗ 𝐷ℎ

𝜇=

𝑚𝑓𝑙𝑜𝑤𝐴𝑐

∗ 𝐷ℎ

𝜇=

𝑚𝑓𝑙𝑜𝑤𝐴𝑓𝑟 ∗ 𝑝

∗ 𝐷ℎ

𝜇

Where:

ρ is the density of the fluid at the matrix

Dh is the hydraulic diameter of the matrix

µ is the cinematic viscosity of the fluid

mflow is the fluid mass flow rate

Ac is the free flow area of the matrix

Afr is the frontal area of the matrix

p is the volumetric porosity of the matrix

The reason for that is that the free flow area is calculated as the product of the frontal area of the matrix and its volumetric porosity. Usually the volumetric porosity and the screen porosity have different values, being the second one bigger that the first one. Accordingly it must be taken into account that the computed values for the fluid velocity within the fluid phase model will be bigger than the real ones.


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1.3. Preliminary results

In order to test the robustness of the model exposed to the discontinuous operating conditions of the regenerative beds, several experiments have been created with one or two beds and variable inputs to the beds. The experiments aim to reproduce cyclic operation of the beds alternating charge and discharge phases paying special attention to the bed switching (fast and abrupt discontinuities in pressure, mass flow rate, velocities,…). The inputs to the beds are variable differential pressure between the inlet and the outlet of the bed or variable mass flow rate. It has also been tested the expected arrangement for the necessary valves that will be installed in order to operate the regenerative system.

Figure 8: Experiments with two bed arrangement for the regenerative system (Left: variable differential pressure, Right: variable mass flow rate)

Regarding the heat transfer fluid that flows through the matrix, it has been assumed by the consortium that there is no reason for considering moisture in the air. According to that, classes for dry air have been selected from the Modelica Standard Library in order to test the models for the regenerative system.

DryAirNasa ("Air: Detailed dry air model as ideal gas"): Ideal gas medium model for dry air with reliable data up to 1000 ºC (for higher temperatures some physical properties are linearly extrapolated) inside a 200K to 6000K temperature range.

ReferenceAir: Detailed dry air model with a large operating range (130 ... 2000 K, 0 ... 2000 MPa) based on Helmholtz equations of state.

In a first approach the first model (DryAirNasa) has been chosen for model testing due to its simpler formulation.

Preliminary results have been obtain that confirm the robustness of the class formulation under oscillating mass flow rate operation. Figure 9 shows the results for a two bed arrangement. It can be seen the evolution of the matrix temperature at 3 different positions along the matrix in relation with the position of the valves that manage the operation of the system. When the valve called valveBed1Change1 is open (opening=1) the bed1 is charged and the bed2 is discharged and when it is closed the operating modes are switched.


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Figure 9: Preliminary results of a two bed arrangement regenerative system model

1.4. Initial validation

Two different validation exercises have been done with experimental data from Haver and Boecker and Ciemat – PSA. In both cases the available information has been generated through pressure loss tests at ambient temperature.

It is expected to develop a cross comparison with a CFD model made in Fluent in order to perform a partial validation of the thermal behaviour of the regenerative bed model.

1.4.1. Comparison with experimental data from Ciemat-PSA

In Figure 10 and Figure 11 it can be seen the experimental setup developed by Ciemat – PSA to measure the pressure drop across stacked meshes. The experimental data from two different types of meshes (A and F types) has been compared with model results. The geometric characteristics of the tested meshes are summarized in the following table:

Table 2: Geometric characteristics of the meshes tested by Ciemat-PSA

0 500 1000 1500 2000 2500 3000 0

200

400

600

800

1000 bed1.upperLayer bed1.lowerLayer bed1.middleLayer

0 500 1000 1500 2000 2500 3000 0

200

400

600

800

1000 bed2.upperLayer bed2.lowerLayer bed2.middleLayer

0 500 1000 1500 2000 2500 3000 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

valveBed1Charge1.opening

Mesh type Wire diameter (mm) Pitch (mm)

A 1 5

F 0.13 0.33


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Figure 10: Schematic of the experimental setup for wire mesh volumetric receivers

Figure 11: Picture of the experimental setup for wire mesh volumetric receivers at Ciemat-PSA

In order to reproduce the experimental conditions, the experiment of Figure 12 has been created. The pressure drop measured by Ciemat-PSA has been established as external condition for the regenerative bed model and the volumetric flow rate has been calculated by the model.


Page 17 of 32

Figure 12: Simulation model for Ciemat-PSA experimental setup

The following figures summarize the results obtained for the four different configurations that were tested (two different number of meshes for each mesh type). As can be seen the error for A type meshes is below 15% for volumetric flow rates higher than 0.005m3/s. Results with acceptable error values correspond to operating points that lead to the usage of a the third branch (with Reynolds number bigger than 1000) of the experimental correlation for the calculation of pressure losses (see section 1.2.2). The comparison with experimental data for F type meshes show unacceptable error values, especially for low volumetric flow rates. In these cases, errors lower than 20% correspond to operating points within the second branch of the experimental correlation.

It must also be taken into account that first points of the experimental data, with the lowest volumetric flow rates, correspond with very low pressure losses (<20Pa) that have almost the same order of magnitude of the expected measurement error.

Figure 13: Experimental data and simulation results for 10 meshes of A type

0

2

4

6

8

10

12

14

16

18

20

0

50

100

150

200

250

300

0 0.005 0.01 0.015 0.02 0.025 0.03

del

taP

(Pa

)

Vflow (m3/s)

10 meshes A type

Vflow measured V1Vflow measured V2Vflow measured V3Vflow simulated V1Vflow simulated V2Vflow simulated V3Model error [%] V1Model error [%] V2


Page 18 of 32

Figure 14: Experimental data and simulation results for 9 meshes of A type

Figure 15: Experimental data and simulation results for 6 meshes of F type

0

10

20

30

40

50

60

70

0

20

40

60

80

100

120

140

160

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

del

taP

(Pa

)

Vflow (m3/s)

9 meshes A type

Vflow measured V1

Vflow measured V2

Vflow simulated V1

Vflow simulated V2

Model error [%] V1

Model error [%] V2

0

10

20

30

40

50

60

70

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

del

taP

(Pa

)

Vflow (m3/s)

6 meshes F type

Vflow measured V1 Vflow measured V2

Vflow simulated V1 Vflow simulated V2

Model error [%] V1 Model error [%] V2


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Figure 16: Experimental data and simulation results for 5 meshes of F type

1.4.2. Comparison with experimental data from Haver and Boecker

In Figure 17 and Figure 18 it can be seen the experimental setup employed by Haver and Boecker to measure the pressure drop across stacked meshes.

Figure 17: Schematics of the experimental setup for pressure drop measurements in stacked meshes

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Figure 18: Picture of the experimental setup for pressure drop measurements in stacked meshes at H&B

The experimental data from 6 configurations with the same types of mesh (wire diameter=0.05mm, pitch=0.13mm) has been compared with model results. The following table summarizes the characteristics of the regenerative bed used on each test:

Table 3: Regenerative bed characteristics of the different tests performed by Haver and Boecker

Test number

Sintered (YES/NO) Nº of meshes

Sample diameter (mm)

1 NO 710 40

2 NO 5 50

3 NO 4 50

4 NO 3 50

5 NO 2 50

6 YES 15 100


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The pressure drop measured by Haver & Boecker has been established as external condition for the regenerative bed model and the volumetric flow rate has been calculated by the model.

The following figures summarize the results obtained for the 6 different test conditions. From the results it can be concluded that for the selected mesh the model provide a good prediction of the expected pressure losses when the operating volumetric flow rate corresponds with Reynolds numbers bigger than 60.

In the case of test number 6, as expected, the error is very high because the selected experimental correlation is not suited for sintered regenerative beds.

Figure 19: Experimental data and simulation results for test 1 of Haver & Boecker

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2. Ceramic regenerative bed model

2.1. Assumptions and methodology

The type of regenerator to be modelled is a honeycomb with straight channels coming from the pre-selection of ceramic type regenerator done by IKTS and TEK. The material selected is a Cordierite (C520).

Figure 25: Cordierite honeycomb brick with high density of straight channels

This model (CeramicRegenerativeBed1D) is based on the modelling approach presented by Muske et al. in [10]. Even though it was originally meant for representing ceramic regenerators, the model may be used for other regenerators with the same type of geometry, i.e. parallel straight channel geometry (two dimensions honeycomb). Each regenerator´s channel is modelled as a hollow cylinder tube, whose external wall is assumed to be perfectly isolated. The radius of the fluid channel, the internal radius 𝑟𝑖, is one half of the average hydraulic diameter of the real fluid channels and the outside radius is given by:

𝑟𝑜 = √𝑚

𝜋 ∗ 𝜌 ∗ 𝑁𝑐 ∗ 𝐿+𝐷ℎ2

4

Where:

𝑁𝑐 is the total number of gas channels;

𝐷ℎ is the hydraulic diameter of the gas channel;

𝑚 is the total mass of the bed;

𝜌 is the density of the bed material;

𝐿 is the length of the bed.

The following considerations were taken into account when modelling the ceramic regenerative bed:

The fluid velocity in the tubes is determined assuming a uniform distributed fluid flow through all channels;


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In order to model the fluid, an instance of the DynamicPipe model found in Modelica standard library was used;

As in the metallic bed, the ceramic regenerative bed model is constituted by two parts (called phases in this report), namely solid and fluid phases;

Regarding the solid phase, there is no radial variation of the temperature (lumped parameter model in the radial direction is assumed).

Note that for simulations where cycling regimes are required, the last assumption is expected to be valid only when the cycle time of the system is, at least, an order of magnitude bigger than the characteristic time for radial heat conduction in the material [10] which is defined by:

𝜏 =(𝑟𝑜 − 𝑟𝑖)

2

𝛼

Where:

𝜏 is the characteristic time for radial heat conduction

𝛼 is the thermal diffusivity of the bed material

𝑟𝑖 is the radius of the gas channel in the tube

𝑟𝑜 is the outside radius of the tube

For the case of highly channelled honeycombs the reduced thickness of walls assures a good agreement with the last assumption.

2.2. Model structure

Figure 26 shows the Modelica model of the ceramic generator. Both heat and fluid ports are taken directly from the Modelica standard library (MSL), which means the model is compatible with any element found in Modelica.Fluid and Modelica.Thermal.

Figure 26: Modelica ceramic regenerative bed model icon

Outlet/inletfluid port

Inlet/outletfluid port

Heat ports


Page 26 of 32

The model allows users to initialise the temperature of the fluid and the solid elements. Initial values can be inputted in the “Initialization” tab, as Figure 27 shows. If no value is passed to the model, 24 ºC is used as default value for both temperatures. Any other initial value must be entered making use of the “Add modifier” tab in the instance of the model.

In order to define the geometry of the regenerative bed, six parameters can be inputted in the “General” tab. The GUI of this tab is presented in Figure 28. In addition, the figure provides a brief description of each geometry parameter.

Note that the model is discretised in finite volumes (solid and fluid volumes) and the degree of discretisation is defined by the “nNodes” parameter.

As mentioned previously, the model is composed, as can be appreciated in Figure 29, by two components that represent the solid and the fluid phases of the regenerative bed.

Figure 28: General tab CeramicRegenerativeBed1D model

Figure 27: Initialization tab of the CeramicRegenerativeBed1D model


Page 27 of 32

2.2.1. Solid phase

Solid phase component is an instance of the class DistributedThermalconductor that is a lumped parameter thermal system in the radial direction (there is no radial variation of the solid temperature). It is composed of an array of instances of the class HollowCylinder that represents one section of the solid material along its axis. Each node is composed by two instances of a class that describes the conduction along the material and one instance of a class that represents the thermal inertia of the material section (see Figure 30).

Figure 30: Modelica model of the node element ( DistributedThermalconductor)

Radial direction

Hea

t tr

ansf

er d

irec

tio

n

Figure 29: Diagram of the ceramic regenerative bed model


Page 28 of 32

In order to calculate the thermal characteristics of the solid phase model, the material properties have to be entered in the model. DistributedThermalconductor class includes a replaceable instance of a class that describes the material of the regenerative bed. This material can be selected in the “Solid” tab of the main model shown in Figure 31. In addition, the regenerative bed total mass can be entered as a parameter (“m” in the figure). If no value of the total mass is used, it is calculated multiplying the material density by the total volume of the solid.

The material class have to be declared as a Modelica package. This package must contain the thermal and physical properties of the chosen material. The minimal set of properties required consists of: the density, the thermal conductivity and the specific heat capacity. All of them may be defined either as a constant or as function of the temperature.

2.2.2. Fluid phase

The fluid phase component is an instance of the class the DynamicPipe class from the Modelica Standard Library hat is the model of a straight pipe with distributed mass, energy and momentum balances providing the complete balance equations for one-dimensional fluid flow. It treats the partial differential equations with the finite volume method and a staggered grid scheme for momentum balances.

Most of the parameters that define the DynamicPipe have been fixed and only three of them (the fluid medium, the heat transfer model and the flow model) are accessible from the GUI. Figure 32 shows the “Fluid” tab of the main model.

Figure 32: Fluid phase parameters tab

Figure 31: Solid phase parameters tab


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2.3. Preliminary results

In order to test the model performance, two experiments have been set up (see Figure 33). In the first experiment (called single shot experiment), the regenerator model is tested only as an energy storage. A flow of the selected fluid passes through the channels of the bed. In this way, the generator can be charged or discharged (depending on the inlet fluid temperature and initial temperature of the bed). In this experiment, the user may set up, among other parameters, the direction of the fluid flow (upward or downward), the phase of the cycle (charging or discharging), the mass flow rate and the charging/discharging temperature.

The second experiment (called cycling regime experiment) tests the robustness of the model exposed to the non continuous operating conditions of the regenerative beds. The experiments aim to reproduce cyclic operation of the beds alternating charge and discharge phases paying special attention to the bed switching (fast and abrupt discontinuities in the fluid flow direction). The cycling time is controlled by the outlet fluid temperature, i.e. the direction of the fluid flow is changed when the outlet temperature reach user-defined threshold. In this experiment, the user may set up, among other parameters, the mass flow rate and the charging/discharging temperature.

Figure 34 shows the thermocline (at the top, in the middle and at the bottom of the regenerator length) generated when a charging phase is simulated with the single shot experiment model. The figure was generated using the following experiment conditions:

Bed Length: 1 m; bed cross-section area: 0.25 m2; channel cross-section area: 4 mm2; channel cross-section perimeter: 8 mm;

Number of nodes (discretisation): 60;

Figure 33: Left hand site, single shot experiment. Right hand site, cycling regime experiment


Page 30 of 32

Fluid model: DryAirNasa ("Air: Detailed dry air model as ideal gas"): Ideal gas medium model for dry air with reliable data up to 1000 ºC (for higher temperatures some physical properties are linearly extrapolated);

Bed material: Cordierite honeycomb (free cross-section: 65%, bulk density: 2 g/cm3, thermal conductivity (constant): 1.9 W/mK (@100 ºC), specific heat capacity (constant): 810 J/kgK (@100 ºC);

Flow direction: downward; charging temperature: 700 ºC; regenerator initial temperature: 100 ºC; air mass flow rate: 0.15 kg/s; ambient pressure.

In addition, preliminary results have been obtain that confirm the robustness of the class formulation under oscillating mass flow rate operation. Figure 35 shows the temperature (at the top, in the middle and at the bottom of the regenerator) of the regenerative bed under a cycling regime. The figure was generated using the following experiment conditions:

Bed Length: 1 m; bed cross-section area: 0.25 m2; channel cross-section area: 4 mm2; channel cross-section perimeter: 8 mm;

Number of nodes (discretisation): 60;

Fluid model: DryAirNasa ("Air: Detailed dry air model as ideal gas"): Ideal gas medium model for dry air with reliable data up to 1000 ºC (for higher temperatures some physical properties are linearly extrapolated);

Bed material: Cordierite honeycomb (free cross-section: 65%, bulk density: 2 g/cm3, thermal conductivity: 1.9 W/mK, specific heat capacity: 810 J/kgK);

Initial charging direction: downward; charging temperature: 700 ºC; discharging temperature: 100 ºC; regenerator initial temperature: 100 ºC; air mass flow rate: 0.15 kg/s;

Outlet temperature thresholds: for charging 160 ºC; for discharging: 640 ºC

Figure 34: Preliminary results (single shot experiment)

Air flow at 700 ºC


Page 31 of 32

Figure 35: Preliminary results (cycling regime experiment)

As it can be seen the switching time (determined by the output temperature threshold defined) is varying over the simulation time until the system reach a cyclic stationary state where the half cycle time is around 3 minutes.

Conclusions

Two different Modelica models have been described for the dynamic simulation of two different types of regenerative beds, a metallic one (based on stacked wire meshes) and a ceramic one (based on straight channelled honeycomb).

Preliminary results have been presented for both models where thermocline behaviour can be observed along the bed length and simulation time. For the metallic model a comparison with experimental data from pressure loss tests has been presented too.


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References

[1] S. López and I. del Hoyo, "Proposal for standardization of Heat Transfer Modelling in NewThermal Library," Proceedings of 10th International Modelica Conference, 2014, Lund, Sweden.

[2] W.R. Martini, "Stirling Engine Desing Manual", University Press of the Pacific, Honolulu, Hawaii, 2004

[3] C. Li and G.P. Peterson, "The effective thermal conductivity of wire screen", International Journal of Heat and Mass Transfer 49 (2006) 4095 -4105

[4] J. Xu and R.A. Wirtz, "In-plane effective thermal conductivity of plain-weave screen laminates", IEEE TCPT 25 (4) (2002) 615-620

[5] Modelica Association, "A Unified Object-Oriented Language for Physical System Modeling", 2012

[6] F. R. Casella et all. "Standardization of Thermo-Fluid Modeling in Modelica.Fluid", Proceedings of 7th International Modelica Conference, 2009, Como, Italy,

[7] A. J. Organ, "The Regenerator and the Stirling Engine", Mechanical Engineering Publications Limited, London and Bury St Edmunds, UK, 1997

[8] W.M. Kays and A.L. London, "Compact Heat Exchangers", Krieger Publishing Company, Malabar, Florida, 1998

[9] A. J. Organ, "Thermodynamics and Gas Dynamics of the Stirling Cycle Machine", Cambridge University Press, Cambridge, 2010

[10] K.R. Muske et all, "Model-based control of a thermal regenerator. Part 1: dynamic model", Computers and Chemical Engineering 24 (2000) 2519-2531

[11] R.B. Bird et all, "Transport phenomena", Wiley, New York, 1960

[12] S. Kakac et all, "Handbook of single-phase convective heat transfer", Wiley, New York, 1987

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