new solar setup with acoustic diagnostic techniques for ... · in a concentrated solar power plant,...

New solar setup with acoustic diagnostic techniques for CSP materials

Test materials and geometries selection Proposed thermo-mechanical behaviour

SFERA II Project Solar Facilities for the European Research Area -Second Phase

Grant agreement number: 312643

Start date of project: 01/01/2014

Duration of project: 48 months

WP13 – Task 1.A Deliverable 13.1

Due date: 06/2015

Submitted 12/2015

File name: WP13 – Task 1.A Deliverable 13.1

Version 1

Partner responsible CNRS

Person responsible Emmanuel Guillot

Author(s): Yasmine Lalau, Emmanuel Guillot

Dissemination Level PU

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WP13-T1.A — Deliverable D13.1

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List of content

1. Context and objectives ........................................................................................................................ 4

1.1. Context ..................................................................................................................................... 4

1.2. Objectives and method ............................................................................................................ 4

2. Description of the new setup ............................................................................................................... 5

2.1. Principle .................................................................................................................................... 5

2.2. Solar facility .............................................................................................................................. 6

2.3. Measurements and diagnostics ............................................................................................... 7

2.3.1. Acoustic emission techniques ............................................................................................... 7

2.3.2. Photo-‐mechanic techniques .................................................................................................. 8

3. Selected samples: materials properties .............................................................................................. 9

3.1. Material selection .................................................................................................................... 9

3.2. Properties at ambient temperature ....................................................................................... 10

3.3. Temperature dependant properties ...................................................................................... 11

4. Samples: sizing and geometric considerations ................................................................................. 13

4.1. Optimization for acoustic measurement ............................................................................... 13

4.1.1. Ex situ localization tests ...................................................................................................... 13

4.2. Optimization for photomechanical measurement ................................................................. 18

4.2.1. Model: physical conditions .................................................................................................. 19

4.2.2. Model validation ................................................................................................................. 20

5. Conclusions ....................................................................................................................................... 23

References ............................................................................................................................................ 24

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Executive Summary The EU-funded research project SFERA2 – grant agreement 312643 – aims to boost

scientific collaboration among the leading European research institutions in solar

concentrating systems, offering European research and industry access to the best research

and test infrastructures and creating a virtual European laboratory.

This deliverable is part of the results of the task 1 of the workpackage 13 Determination of

physical properties of CSP materials under concentrated solar irradiation within the Joint

Research Activities.

This workpackage 13 aims to provide a better evaluation of the material behaviour for CSP

applications and other fields with similar thermal stress, such as high temperature steels or

SiC ceramics, thanks to better or new experimental tests bed and associated theoretical

models. These results will lead to help users developing higher performance materials for

higher process efficiency.

The task 1 of workpackage 13 is focused on two principal targets:

- Define and validate new methodologies for comparative evaluation of the ability of

key CSP components to sustain cyclic thermal gradient.

- Improve CSP test facilities by developing news instruments and methods for in-situ

thermo-mechanical investigation using acoustic methods.

The work presented here focus on the selection of the samples to validate these new

instruments and methods based on acoustic measurements. This selection is made by

studying the acoustic and thermo-mechanical properties of the test materials.

After a brief introduction, the materials properties experimentally measured are summarized.

Then, the solar setup and the new measurement methods to be developed are presented.

This presentation of the development direction is required to allow the reader understands

which variables are needed to be studied to determine the optimal sample size: this

optimisation process is the fourth and main part of this report, followed by this work

conclusion.

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1. Context and objectives

1.1. Context In a concentrated solar power plant, the receiver transfers the solar energy collected and

concentrated by the mirrors field to the heat transfer fluid used in vapour electricity

generation or any other heat processes (Figure 1). Therefore, the materials used for such

receivers are subjected to very high thermal loads. As illustrated by Figure 2, their

temperature varies:

Temporally due to the DNI (Direct Normal Irradiation, W.m-2) evolution, which is cyclical in alternating day/night and brutal in the clouds passing or any other atmospheric event;

Spatially due to the non-homogenous distribution of the concentrated solar energy on the front irradiated face and to the coolest heat transfer fluid imposed by the rear face.

Figure 1: Flat solar receiver drawing

Figure 2: Thermal load: cyclic and abrupt DNI, solar flux distribution and heat transfer fluid circulation

Refractory ceramic (SiC) are promising candidates for these applications as they allow

higher operating temperature than the usual metals, but their brittleness requires a thorough

thermo-mechanical behaviour study to estimate their durability. However, thus far there is

no in-situ monitoring means specifically developed for these applications to assess the

potential of existing or new materials.

1.2. Objectives and method To address these issues, the SFERA II European project aims to develop new devices under

Fluide caloporteur

Champ solaire

Récepteur

Flux solaire concentré 4 days insolation, Odeillo

Cycling

Cloudy day insolation, Odeillo

Shock

Solar flux : Gaussiandistribution

Heat transfer fluid

Temporal variation of T (°C) Spatial variation of T (°C)

zt

Φi

Φrear

Φloss

Φfront

Tamb

Tfluidhrear

hfront

Heat transfer fluid

Concentratedsolar irradiation

DNI (W.m

-‐2)

DNI (W.m

-‐2)

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concentrated solar radiation and define in-situ thermo-mechanical study methods of these

receivers materials, either already used or with promising potential (WP 13 - Task 1).

A new innovative setup in real solar test conditions will be developed in WP13-T1 in order

to determine the following receivers material behavior:

Damage localization and monitoring thanks to acoustic techniques; Strain field estimation thanks to photo-mechanical methods (potential development

in a second step).

In order to design this new experimental setup, initial exploratory studies need to be conducted: assessment of these characterisation technologies, definition of the application boundaries, choice of samples to experimentally validate the concepts and the potential.

Figure 3 shows the main functions to be fulfilled by this new setup to help determining the

receivers material’s thermo-mechanical behaviour.

Figure 3: Diagnostic setup diagram block

This setup is developed following the steps below:

1. Describe the test conditions; 2. Determine the nuisance parameters; 3. Design the samples as a function of material properties, including through a single

numerical model (Code_Aster); 4. Carry out ex situ feasibility tests; 5. Realize the first tests in situ; 6. Experimentally validate the numerical model; 7. Define testing methodologies taking account materials thermo-mechanical behaviour

indicators (using the numerical model).

2. Description of the new setup

2.1. Principle The new setup can be defined as follow:

• Use of controlled concentrated solar from a solar furnace as thermal source.

THERMAL

STRESS

Solar flux

THERMO-‐MECHANICAL BEHAVIOUR

Temperatures

Crack monitoring & localisation

Strain field

Functions of test bedCYLINDRICAL

SAMPLE

Symmetrical mechanical stress field

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• Possibility to change the samples, including metallic and ceramics materials.

• Geometry of the sample is defined by the setup: we will not test functional

components from a receiver.

• Different measurement techniques to assess thermo-mechanical behaviour,

specifically acoustic based methods never used before in such conditions:

o Damage localization and monitoring thanks to acoustic techniques;

o Strain field estimation thanks to photo-mechanical methods (potential

development in a second step).

Several constraints have been especially identified:

• To achieve proper results, the characterization setup must be used in thermal and

mechanical controlled and known conditions, and the noising parameters affecting

acoustic and photomechanical measures must be minimized.

• As the setup objective is to localize thermal gradients and fatigue defects, the sample

must not be mechanically constrained. Therefore, it has been decided that the

waveguides used to transmit the acoustic waves will also hold the sample on a three

points plane support. The pressure will be guaranteed by springs, allowing thermal

expansion.

2.2. Solar facility The solar receiver irradiation conditions are reproduced on a few centimeters-sized samples

by a 2 m solar parabolic furnace. This parabolic furnace is part of the Grand Four Solaire

d’Odeillo, France (see Figure 4Erreur ! Source du renvoi introuvable.).

The solar irradiation is collected by a heliostat at the bottom of the building (Figure 4Erreur !

Source du renvoi introuvable.), then reflected to the upper floors through a trap door in the

ground, to finally be focused by a parabolic dish.

The concentrated solar irradiation can be regulated by shutters (Figure 5Erreur ! Source du

renvoi introuvable.).

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Figure 4: Odeillo’s solar furnace. This setup will use the facility showed on the left of the schema.

Figure 5: Heliostat vertical furnace: door view through

the shutters.

2.3. Measurements and diagnostics

2.3.1. Acoustic emission techniques

2.3.1.1. Principle

Acoustic emission is the generation of transient elastic waves due to the release of energy

from local micro-displacement internal to a material [1]. The wave frequency ranges from a

few tens of kHz to several MHz, typically 1 MHz. The emergence of micro-displacements is

induced by:

• Mechanical events: plastic strains, fractures, impact, delamination, interface sliding, friction, leaks, etc.

• Physical-Chemical events: corrosion, gassing and grain growth, etc.

Acoustic emission is also, by extension, the test method based on this phenomenon. It is a

passive and non-destructive method that tracks the real-time damage progression in a

component. This technique finds applications in laboratory to study the fracture behaviour or

material fatigue, and in industry to qualify and monitor structures.

A: volumic wave

B: surfacic wave

C: sensor

Figure 6: Creation, propagation and detection of acoustic emission wave [2]

The waves generated by events propagate in the structure and are detected by sensors: the

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material movements are converted into electrical signalsErreur ! Source du renvoi

introuvable.. These signals are processed by specific instrumentation and methods.

On one hand, the acoustic emission signals study provides information on the

stressed material mechanical and physico-chemical behaviour.

On the other hand, it is possible, from the information received by a sensor mesh, to

locate the acoustic emission signal source.

2.3.1.2. Accuracy

The event location accuracy is affected by calculation uncertainties (mathematical

uncertainty, multiple solutions) and by measurement errors.

In an industrial environment (large structures, generally steel), the typical error is estimated

at 5% of the distance between the sensors, or about 4.3 mm for a sample of 100 mm in

diameter.

In order to verify this approximation for the samples studied (dimensions and materials), ex-

situ localization tests have been conducted by using experimental setups existing at CNRS-

SPCTS/UNILIM laboratory in Limoges, France (see section on samples below).

2.3.2. Photo-mechanic techniques

2.3.2.1. Principle

Optical methods estimates in situ and without contact surface strain field in plane (1 camera)

or in relief (multiple cameras). To consider out of plane displacements related to the sample

deformation, it is best to choose a stereo measurement with 2 cameras.

Figure 7: Principle of the displacement field measurement

by optical method [3]

Figure 8: Schematic diagram of a surface displacement measurement

by stereo tracking markers [5]

Comparison between 2 pictures: reference / deformed

Strain field assessment

In situ & without contact

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2.3.2.2. Accuracy

In previous tests (AZTECH project, ANR MATETPRO 2012), it was observed that a strain

accuracy of ± 2.10-5 could be obtained. This was achieved by drastically minimizing the

influence parameters.

In addition, a calibration for several positions (Z change) has been performed to better

estimate the x and y deformations; and a "non deformable" reference has been used to

correct any deformations due to nuisance parameters (e.g. cameras support dilatation due to

room temperature variation).

3. Selected samples: materials properties

3.1. Material selection In order to validate this new setup, different materials typically used in existing or in next

generation solar plants have been considered. Inconel 625 and SiC ceramics have been

selected as representative of current and of next generation materials.

A recent study [4] summarize the reasons of this choice. The authors compared the

behaviour of several materials potentially suitable for concentrated solar power systems.

They described the behaviour by thermo-mechanical (resistance to fracture and creep

resistance) and oxidation indicators (spalling resistance), which they summarized in the

properties map below.

Figure 9: Resistance to spalling of oxide Figure 10: Resistance to fracture by

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by thermal shock vs Creep Resistance thermal shock vs Creep Resistance

In the Figure 9, ceramics and Ni-alloys (including Inconel) appear to be suitable candidates,

and that’s confirmed in Figure 10, even if some ceramics have a very low fracture resistance.

SiC is on the top of ceramic category, but still weak on this point: that confirms the interest on

scrutinize its thermo-mechanical behaviour.

It must be noted that Mo Silicides seems to have an interesting potential, and they could be

investigated with the new setup, once validated with the two “classical” materials SiC and

Inconel.

3.2. Properties at ambient temperature The majority of properties were determined at SPCTS laboratory in Limoges, France. Some

of the characteristics are from the literature (data sheets); these are indicated in bold.

The laboratory methods used were the following:

• The density was measured with a pycnometer,

• The elastic properties were measured by ultrasonic methods,

• The rupture properties were measured by 4-point bendings,

• The conductivity was measured by LFA.

Table 1: Properties at ambient temperature

Properties Unit SiC α Inconel 625

Bulk density kg.m-3 3.135 8.44

Propagation velocity

Longitudinal (vL) Transversal (vT)

m.s-1 12 050 7 620

5 940 3 015

Poisson Coefficient - 0.17 (0.16) 0.33 (0.312)

Shear modulus (G) GPa 182 (180) 77

Young modulus (E) GPa 425 (420) 204 (204.8)

Breaking stress (σR)

(Flexion 4 points) MPa 160 827-1034

Yield strenght MPa 414-655

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Conductivity (λ) W.m-1.K-1 180 9,8

Specific heat (Cp) J.kg-1.K-1 680 410

Emissivity (ε) - 0,85 0,75

Absorptivity (α) - 0,85 0,75

It should be noted that the emissivity of Inconel is given in an oxidized state, and its absorptivity is assumed equivalent.

Figure 11: Spectral hemispherical emissivity for some materials [5]

The Figure 11 shows that the emissivity varies with the surface condition of Inconel, and it is

not constant over the range of measurements considered.

3.3. Temperature dependant properties These properties were measured by ultrasonic methods, by a dilatometer and by LFA at

Limoges, France.

Table 2: Properties of materials studied in function of temperature

Ppts SiC α Inconel 625

vL

m.s-2

Under air: -2% à -4% Under argon: -1% à -2%

Under air: -27% Under argon: -25%

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E

GPa

αTH

10-6

λ

W.m-1.K-1

Cp

J.kg-1.K-1

For this project the tests will be performed at different temperatures, or Table 2 reveals that

the propagation velocity is dependent on the temperature: If this dependence is not taken

into account, this will induce an additional localization error.

10000

10500

11000

11500

12000

0 500 1000 1500v

(m.s

-1)

T (°C)

v

3000

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v (m

.s-1)

T (°C)

Mesure du module d'Young en fonction de la température

v

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E (G

Pa)

T (°C)


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Figure 12: Localization error induced by propagation velocity variation at 1000°C

Figure 12 shows that in the case of SiC, the error induced by the velocity variation is less

than 5%: this can be neglected. In contrast, in the case of Inconel, the induced error

becomes too large (up to 15 mm for a sample of 100 mm in diameter): the thermal

dependence of the velocity should be taken into account.

Two strategies can be adopted:

The velocity is adjusted with the temperature, based on the ex situ material characterization. Advantage: separated experiment keeps the new setup simpler. Disadvantage: the in situ experimental value can be a little different than the characterized value due to differences in samples and in their evolution.

The velocity can be measured during the test, using an additional module: sensors separated by a known distance emit signals, and the propagation velocity is deduced from the travel time. Disadvantage: as it emits sound in the samples, it cannot be done simultaneously with the emission method, thus the velocity evolution may not be well described when the temperature changes suddenly.

In both cases, due to software and calculation limitations, this speed adjustment cannot be

made during the test: a post processing routine will certainly be necessary to correct the

defect location estimations. The definite choice between both options will be made during the

commissioning of the solar setup.

4. Samples: sizing and geometric consideration

4.1. Optimization for acoustic measurement

4.1.1. Ex situ localization tests

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 0.05 0.1 0.15 0.2 0.25

Erre

ur (

m)

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SiC Inc 625 Erreur 5%

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The acoustic emission methods, the selected materials and the acquisition system for the

new setup have first been assessed in laboratory with different tests. The final assessment

aim is to conduct a 2D localization on cylindrical samples, thin enough to assimilate them to

a 2D structure for easier comparison with modelled theoretical behaviour.

4.1.1.1. Hsu-Nielsen test

This test is defined by the EN 1330-9 standard. It is used to simulate an acoustic event by

means of a broke pencil pit. The mine should have a hardness of 2H, a diameter of 0.5 mm

and a length of 3 mm. The amplitude of the detected signal must be greater than 80 dB.

Figure 13: Hsu-Nielsen test principle

The test is made on one hand to check the proper coupling of the sensors, and on other

hand to verify the proper localization of the acoustic source.

4.1.1.2. Sliding time slots definition

The acoustic bursts discretization is achieved by means of 3 time indicators specific to

studied material, shown in Figure 14:

Peak Definition Time (PDT): Set the highest amplitude peak arrival time, from the first threshold is exceeded;

Hit Definition Time (HDT): defines the total duration of the burst; Hit Lockout Time (HLT): sets the system blind time during which threshold violations

will not be considered (eliminates echoes).

Table 3. Temporal parameters

SiC Inc 625

PDT 30 300

HDT 150 600

HLT 300 1000

Figure 14: Sliding time slots (PDT, HDT, HLT) The experiment has been conducted several times for the different materials. The reported in

PDT HDT HLT

seuil

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Table 3.

Results: Specific time indicators have been determined for Inconel and SiC

4.1.1.3. 1D localization

Linear localization tests have been performed to verify that the material does not exhibit

characteristics affecting the localization: too high attenuation, large heterogeneities, etc.

Figure 15: Sensors arrangement for linear location

As shown schematically in Figure 15, the tests are carried over distances of 90 mm between

sensors, which was the maximum possible with the available samples. This distance is

similar to expected distances on future samples: for a proposed 100 mm diameter sample,

the distance between 3 sensors at 120° is 87 mm.

Figure 16: Burst amplitude varying with position on SiC sample (Hsu-Nielsen Test)

Figure 17: Burst amplitude varying with position on Inc. sample (Hsu-Nielsen Test)

Figure 16 and Figure 17 shows that the SiC and Inconel do not induce significant attenuation

for studied dimensions.

The accuracy and repeatability of measurements are shown in Figure 18 and Figure 19. The

repeatability is quite good, with an average deviation about 1 mm. Accuracy is about 1.5 mm.

C1 C2

90 mm

00.511.522.533.54

405060708090

100110120

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Ecart type (dB)

Amplitu

de (d

B)

Position (mm)

00.511.522.533.54

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r (m

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Moyenne Précision MOY Précision Ecart type MOY Ecart type

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Figure 18: 1D localization of Hsu-Nielsen sources on SiC sample

Accuracy and standard deviation

Figure 19: 1D localization of Hsu-Nielsen sources on Inconel 625 sample

Accuracy and standard deviation

Results: Inconel 625 and SiC are homogeneous and do not attenuate the acoustic signal.

4.1.1.4. 2D localization

The planar locating tests were conducted using a 76 mm diameter and 5 mm thick cylindrical

steel sample, with propagation velocity similar to Inconel 625. The sensors are spread over

the cylinder side, and maintained by clamps.

For a 2D location, it takes at least three sensors. The corresponding optimal mesh is an

equilateral triangle. It is possible to obtain better accuracy by increasing the number of

sensors used. It is also expected to gain in accuracy with the use of new SFERA2

experimental setup, whose design will enhance the localisation accuracy by improving the

quality of the contacts.

3 sensors 4 sensors 6 sensors

Figure 20: 2D localization of Hsu-Nielsen sources on cylindrical steel sample (ø76 mm)

Figure 20 represents experimental events localization with respect to the theoretical points.

For measurement with 3 sensors, the localization is satisfying within the sensors mesh while

it strongly degrades outside. This has prompted us to increase the number of sensors, to

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expand the mesh surface. The accuracy seems to be improved, but is still lower outside the

mesh symmetry axes.

This analysis is confirmed by the values of the accuracy given in Table 10: for locating with 3

sensors, it is around 3.2 mm on the axes of symmetry (In) and 8.9 mm outside (Out); while

these values are respectively 2.4 mm and 4.6 mm for the 6 sensors configuration. However,

the standard deviation varies less, and is about 1 mm, the measurement repeatability is good

enough.

Table 4: Standard deviation and accuracy (In and Out symmetry axes))


In Out In Out In Out

Standard deviation (mm) 1.1 1.1 1.1 0.7 0.83 0.83

Steel spatial accuracy (mm) 3.2 8.9 2.3 6.3 2.4 4.6

From this spatial accuracy, it is possible to find the temporal accuracy (Equation 1), time

being the measured quantity. The temporal accuracy is largely influenced by the device (and

specific settings) and the sensor mesh type (number and arrangement of sensors), it is

considered to be equivalent for other homogeneous materials. It is then possible to estimate

the SiC and Inconel 625 spatial accuracy (Equation 2).

Relation between spatial and time

accuracies: 𝑃!"#$%&"''" =

𝑃!"#$%#&'𝑣!"#$%

Equation 1

Relation between sample and reference

steel accuracies: 𝑃é!! =

𝑃!"#$%𝑣!"#$%

×𝑣é!! Equation 2

The resulting values are presented in the Table 5.

Table 5: Measurement spatial and temporal accuracy (In and Out symmetry axes)


In Out In Out In Out

Temporal accuracy (µs) 0.5 1.5 0.4 1 0.4 0.8

Inconel spatial accuracy (mm) 3.2 8.2 2.3 6.3 2.3 4.6

SiC spatial accuracy (mm) 6.5 18 4.7 12.7 4.8 9.3

Defining this spatial precision will allow us to define the desired diameter for the samples in

order to limit the location error.

Results: Localization accuracy is clearly better when using more sensors. A compromise

between accuracy and solar facility clutter should be found with scrutinizing the acceptable

error induced by each sensor meshing.

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4.1.2. Experimental error estimation

The localisation error as a function of SiC and Inconel 625 sample diameter is illustrated by

the Figure 21, Figure 22, and Figure 23, respectively for a localisation by 2, 4 and 6 sensors.

As pointed in the planar localisation accuracy evaluation, the use of 6 sensors significantly

improves the localization. In this most favourable case, the minimum diameters SiC samples

and Inconel 625 are respectively 90 mm and 50 mm for a localisation within the symmetry

axes, and respectively 160 mm and 80 mm outside.

Figure 21: 3 sensors localization – Localization error vs sample diameter



Results: The 6 sensors mesh should lead to 160 mm SiC samples and 80 mm Inconel

samples. In order to scrutinize the relevance of such dimensions, these values have to be

compared to the predicted sample behaviour.

4.2. Optimization for photomechanical measurement To limit the strain field estimation error at 10%, the measured deformation must be at least

2.10-4 (in optimal conditions). To determine which sample sizes are needed to obtain

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SiC IN INC 625 IN SiC OUT INC 625 OUT

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sufficient deformation values, simulations are carried out for each material using Code_Aster.

4.2.1. Model: physical conditions

4.2.1.1. Mechanical conditions

One of the new setup functions is to maintain the sample without mechanical stress, thus the

modelling should also let the sample free to expand.

This means for the model to set three degrees of

freedom, which is done by defining isostatic points on

the sample rear face (Figure 24): a point at the centre

is fixed in x and y, while three points at 120° on the

circumference (corresponding to the sample support

points) are fixed in z. One of them is also fixed in x.

Figure 24: Mechanical boundary conditions

With these conditions, only the thermal gradients due to radiation cause stresses in the

sample.

4.2.1.2. Thermal conditions

Boundary conditions

The thermal boundary conditions are illustrated in Figure 25, and described by Equation 3 to

Equation 6: the sample (thickness e and diameter D), irradiated locally homogeneously

through a kaleidoscope, is subjected to convection and radiation on all its outer sides, and to

an inner conduction.

Figure 25: Samples boundary conditions

𝑆 = 𝜋×𝐷!

4 Equation 3

Conduction

𝜑!"#$ = ℎ!"#$×𝑆× 𝑇é!! − 𝑇!"# Equation 4

Convection

𝜑!"#$ =𝜆𝑆𝑒× 𝑇é!! − 𝑇!"# Equation 5

Rayonnement

𝜑!"# = 𝜀×𝑆×𝜎×𝑇é!!! Equation 6

z, x

y, x

zz

D

Φemis

Tamb = 20°C

Φ conv

Concentrated solar flux

E = 500 kW.m-‐2

Kaleidoscope

e

SAMPLE

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Convection is approximated to an average convective coefficient ℎ!"#$ = 10 𝑊.𝑚!.𝐾!!, and

ambient temperature is fixed at 𝑇!"# = 20°𝐶.

Radiation

The measure feasibility must be studied for tests resulting in most difficult measurement

conditions, inflicting minimum constraints in the samples. The chart below shows a summary

of incident concentrated solar flux in the kaleidoscope in the solar furnace for different

positions of the shutters, for a standardized DNI = 1000 W/m2.

Figure 26: Normalized irradiation on solar furnace focus varying with shutter opening

In nominal conditions, the tower plant receivers collect between 300 and 600 kW.m-2 [1] [2].

The objective is to study the material aging mechanisms by amplifying the applied stress,

hence the incident solar radiation shall be at least equal to the nominal flux conditions.

Results: The thermal conditions should be applied to modelled samples in order to observe

the resulting strain field. A "low" value of the incident flux is chosen to optimize the sample

size in unfavourable and realistic strain measurement condition: 500 kW.m-2, about half of

the applicable radiation with the solar installation to be used with the new setup.

4.2.2. Model validation On Figure 27, the results obtained with the SiC behaviour modelling were compared to the

sample temperature measured by a pyrometer at the focus of the solar furnace under simple

conditions.

0

200

400

600

800

1000

1200

0% 20% 40% 60% 80% 100%

Ecla

irem

ent

norm

alis

é (k

W.m

-2)

Ouverture des obturateurs

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Figure 27: SiC sample temperature varying with irradiation – Experimental and theoretical value

There is a similar trend, but rather different values as the model overestimates the

temperature: it reveals that the model follows the correct physical behaviour, but should be

refined to better match the reality. Furthermore, the test parameters and measuring means

should also be controlled in the best possible way: the values difference may be partly due to

an erroneous estimate of the solar radiation or to a perfectible pyrometer measurement.

4.2.3. Parametric study results

Using the software Code_Aster, SiC and Inconel 625 strain were calculated for a 500 kW.m-2

solar irradiation for different sample dimensions (thickness and diameter). The nominal

dimensions were arbitrary set to a diameter D = 100 mm and a thickness e = 5 mm.

The Figure 28 to Figure 31 represent the maximum temperature (at the irradiated surface

centre), the minimum temperature (in the periphery), and the corresponding minimum and

maximum strain.

The observed strain is only due to the static temperature gradient in the sample: it is

therefore lower than during cycling conditions.

Inconel 625

200

400

600

800

1000

1200

0 250 500 750 1000

Tem

pera

ture

(°C

)

Eclairement (kW.m-2)

T Exp T ASTER

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Figure 28: Inconel Temperature and Strain varying with thickness (D = 100 mm)

Figure 29: Inconel Temperature and Strain varying with diameter (e = 5 mm)

SiC

Figure 30: SiC Temperature and Strain varying with thickness (D = 100 mm)

Figure 31: SiC Temperature and Strain varying with diameter (e = 5 mm)

For sample diameters less than 150 mm, SiC and Inconel strain is greater than the

measurement limit (shown by a red dotted line). The measure is feasible, but the margin is

not comfortable enough (a factor of 10 or less): special attention should be paid to the

limitation of nuisance parameters. The temperature level reached corresponds to the desired

temperature range.

Results: Inconel 625 strain measurement is feasible between 50 and 150 mm diameter, and

the side temperature decrease quickly with diameter: small diameters should be preferred.

SiC strain measurement will be more difficult to realize under 150 mm (side strain only

reaches minimum value), but high temperatures (>500°C) are difficult to reach: a

compromise between 100 mm and 150 mm should be chosen.

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

0

100

200

300

400

500

600

700

800

900

1000

0 0.002 0.004 0.006 0.008 0.01 0.012

Def

orm

atio

n ε X

X

Tem

pera

ture

(°C

)

Thickness (m)

EP T max EP T min EP Def max EP Def min

DEF MIN FOR ERROR < 10%0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

0

100

200

300

400

500

600

700

800

900

1000

0 0.05 0.1 0.15 0.2 0.25

Def

orm

atio

n ε X

X

Tem

pera

ture

(°C

)

Diameter (m)

DIAM T max DIAM T min DIAM Def max DIAM Def min

DEF MIN FOR ERROR < 10%

0

0,0002

0,0004

0,0006

0,0008

0,001

0,0012

0,0014

0,0016

0,0018

0,002

0

100

200

300

400

500

600

700

800

900

1000

0 0,002 0,004 0,006 0,008 0,01 0,012

Stra

in ε

XX

Tem

pera

ture

(°C

)

Thickness (m)


0

0,0002

0,0004

0,0006

0,0008

0,001

0,0012

0,0014

0,0016

0,0018

0,002

0

100

200

300

400

500

600

700

800

900

1000

0 0,05 0,1 0,15 0,2 0,25

Stra

in ε

XX

Tem

pera

ture

(°C

)

Diameter (m)


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5. Conclusions

This preliminary work has studied the measurement feasibility and the suitable sample size.

Sizing Inconel 625 material was not problematic; the measures should be done on samples

between 50 and 100 mm diameter and 5 mm thick for the best measurement performance.

Measurements on SiC will be more problematic: its high acoustic propagation velocity leads

to high error in localization and its feeble strain field leads to difficulties in photo-mechanic

method. Diameter samples should range between 100 mm and 150 mm.

In both case, a 5 mm thickness is suitable.

This work enabled to design the solar device, which will be used to confirm these first

estimations before command the sample with definitive size.

Figure 32: Acoustic emission measurement solar setup

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References

[1] ISO 12716, “Essais non destructifs -‐ Contrôle par émission acoustique -‐ Vocabulaire.” 2001.

[2] J. Roget, “Émission acoustique,” Techniques de l’Ingénieur, vol. r3200, 1990.

[3] Laboratoire mécanique multi-‐échelles -‐ Polytechnique Montréal, “Modélisation micrométrique,” 2015. .

[4] D. G. Morris, a. López-‐Delgado, I. Padilla, and M. a. Muñoz-‐Morris, “Selection of high temperature materials for concentrated solar power systems: Property maps and experiments,” Sol. Energy, vol. 112, pp. 246–258, Feb. 2015.

[5] J. Dory, F. Evin, and M. Piro, “Chauffage par rayonnement infrarouge.” Techniques de l’Ingénieur, 1999.

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