纤维基材料受压下三维微结构模拟：气体扩散层在脊部和流道内部的变化
3D microstructure modeling of compressed fiber－based materials

Gerd Gaiselmann

Christian Tötzke

Ingo Manke

Werner Lehnert

Volker Schmidt

Abstract

A novel parametrized model that describes the 3D microstructure of compressed fiber－based materials is introduced． It allows to virtually generate the microstructure of realistically compressed gas－diffusion layers （GDL）． Given the input of a 3D microstructure of some fiber－based material， the model compresses the system of fibers in a uniaxial direction for arbitrary compression rates． The basic idea is to translate the fibers in the direction of compression according to a vector field which depends on the rate of compression and on the locations of fibers within the material． In order to apply the model to experimental 3D image data of fiber－based materials given for several compression states， an optimal vector field is estimated by simulated annealing． The model is applied to 3D image data of non－woven GDL in PEMFC gained by synchrotron tomography for different compression rates． The compression model is validated by comparing structural characteristics computed for experimentally compressed and virtually compressed microstructures， where two kinds of compression – using a flat stamp and a stamp with a flow－field profile – are applied． For both stamps types， a good agreement is found． Furthermore， the compression model is combined with a stochastic 3D microstructure model for uncompressed fiber－based materials． This allows to efficiently generate compressed fiber－based microstructures in arbitrary volumes．

Fig． 1． 3D image of non－woven GDL （yellow fibers） with flat stamp （left） and with stamp of flow－field structure （right）．

Fig． 2． Scheme of the principal experimental set up at the tomographic instrument．

scintillator闪烁晶体

Fig． 3． 3D image data gained by synchrotron tomography of non－woven GDL compressed by a flat stamp with compression rates c＝ 0％ （top left）， c＝10％ （top right）， c＝20％（bottom left） and c＝30％ （bottom right）．

Fig． 4． 3D image data gained by synchrotron tomography of non－woven GDL compressed by a flow－field stamp with compression rates c＝ 0％ （top left）， c＝10％ （top right）， c＝20％（bottom left） and c＝30％ （bottom right）． The red （yellow） marked fibers are located underneath the channel （the rips of the flow－field stamp）．

Fig． 5． 3D image of uncompressed GDL （left） and its extracted system of single fibers （right）．

Fig． 6． Cross－section view on non－woven GDL in uncompressed state （left） and in compressed state with c＝20％．

Fig． 7． Schematic 2D visualization of a fiber system （left） being represented by overlapping spheres （center） and subsequently translated to a system without overlaps between different fibers （right）．

Fig． 8． Fitting the vector field of the compression model for fixed c．

Fig． 9． Left column： realizations of two uncompressed microstructures drawn from the stochastic 3D simulation model； right column： compression model applied to the uncompressed
microstructures （left） for the vector fields Vc1 （top） and Vc2 （bottom）．

Fig． 10． The fitted vector fields bV1c （left） and bV2c （right） displayed by the surface， where the blue points are estimates of the vector field Vci at discrete points in the observation window W0 obtained by the simulated annealing algorithm．

Fig． 11． Blue points： estimated transition vectors by the fitting technique introduced in Section 3．2 and applied to the 10％ compressed GDL by a flow－field stamp． Surface： linear interpolation between these points．

Fig． 12． Fitted functions pi（c） for the compression by a flat stamp （left） and a flow－field stamp （right）， where p2， ．， p6 are appropriate scaled in order to check the goodness of fit．

Fig． 13． First row： experimental 3D image data of non－woven GDL compressed by flat stamp （left） and by a flow－field stamp （right） with compression rate c＝30％； second row：extracted fiber system virtually compressed by a flat stamp （left） and by a flow－field stamp （right） using the compression model with compression rate c＝30％．

Fig． 14． The blue boxes display the decomposition in two quite homogeneous subregions， i．e．， a channel and a land region

Fig． 15． Validation of compression model by comparing the porosities （top） and the mean spherical contact distances （bottom） computed for the experimentally compressed image data （black lines）， for data generated by virtually compressing the extracted fiber systems （red lines） and for data gained by compressing virtual non－woven GDL by the compression model （blue lines）， where we distinguish between compression by a flat stamp （left） and a flow－field stamp （right）．

图14和图15算是不懂模型能用的数据了。流道内部绝大部分空隙分布均匀，孔隙率和未压缩时差异不大。

也不知道各种材料获得图15差异有多大。

Fig． 16． First row： experimental （left） and synthetic （right） uncompressed non－woven GDL data； second row： non－woven GDL data compressed by a flat stamp （with compression rate c＝30％） experimentally （left） and using the compression model （right）； third row： non－woven GDL data compressed by a flow－field stamp （with compression rate c＝30％） experimentally （left） and applying the compression model on a virtual fiber system sampled from the stochastic non－woven GDL model （right）．

跨距790um

The compression device is able to compress GDL by different stamp types （see Figs． 3 and 4）， in particular， for a flat
stamp and a stamp consisting of a flow－field structure， where the width of the flow－field canal is 790 um．

GDL型号

The application of the compression model， introduced in the present paper， is based on tomographic data of the GDL type H2315， a non－woven， carbon fiber－based material produced by the company Freudenberg FFCCT． This material does not contain binder，wet proofing agents nor a micro porous layer （MPL）．

Conclusions

We have introduced a novel parametrized model that describes the 3D microstructure of compressed fiber－based materials． Given the input of a 3D microstructure of some fiber－system， the model compresses the system of fibers in a uniaxial direction for arbitrary compression rates． The compression model was applied to nonwoven GDL in PEMFC and subsequently validated by comparing structural characteristics computed for experimentally compressed and virtually compressed microstructures， where two kinds of compression —— using a flat stamp and a stamp with flow－field profile —— were considered． For both types of stamps， an excellent agreement between experimental compression and virtual compression was found． In addition， the compression model was combined with a stochastic model for uncompressed non－woven GDL． This allows to generate virtual GDL in arbitrarily large volumes with arbitrarily many replications and with low computational efforts． Thus， by systematically varying the parameters of these combined models， new virtual GDL can be generated and in combination with computational transport simulations， the microstructure－functionality relationship of the GDL can be investigated． Currently， the compression model is used for virtual scenario analyzes with the general aim to quantify the effect of compression using a stamp with a flow－field structure compared to compression by a flat stamp． The results of this ongoing research will be reported in a forthcoming paper． But note that the presented compression model is very flexible and can thus be applied to various problems not only in the field of GDL in PEMFC．