Viscoplastic Fluids: From Theory to Application. Parameter identification: An application of inverse analysis to cement-based suspensions
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1 Viscoplastic Fluids: From Theory to Application Parameter identification: An application of inverse analysis to cement-based suspensions Célimène Anglade Aurélie Papon, Michel Mouret UPS-LMDC-INSA France 1
2 Why are we interested in identification? To link rheological parameters to cementitious material design To optimize the design regarding handling and placing context 2
![Bordeaux] Specific](/docs-images/91/106215073/images/3-5.jpg "impeller Helical ribbon or")
3 How to observe the behavior of cementitious materials? Rheometer has to avoid artefacts segregation, migration, sedimentation Complex velocity field Axial component Circular flow Fine particle concentration [CRPP, Bordeaux] Specific impeller Helical ribbon or Anchor [Franshahi and al. 05] LMDC equipped with RheoCAD 3
4 How to process the experimental data? Rheometer returns torques vs rotational speeds Only qualitative information, velocity and stress fields unknown For quantitative studies: Computation of the rheocad flow with COMSOL Coupled with an identification by means of inverse analysis 4 Strong hypotheses for simple computation
5 Cementitious materials: Viscoplastic fluids Bingham law Shear-thinning Shear-thickening τ 0 5 Herschel-Bulkley τ = τ 0 + Kγ n for τ τ 0 γ =0 for τ < τ 0 [Yahia and al., 01], [Papo, 88] Parameter meaning: τ 0 : residual structure n: shear-thinning/thickening feature K: slope Order of magnitude for cement pastes: Interval Unit n [ ] τ 0 [5 155] Pa K [5 105] Pa. s n [Cyr, Ph.D, 99]
6 1. Hypotheses Numerical modeling Continuous and homogeneous medium, no slipping Steady-state, incompressible, laminar and adiabiatic Two-dimensional flow Simplified model to validate the identification process 2. Model Geometry [mm]: 6
7 3. Sensitivity study: Numerical modeling A flow behavior index variation impact on the curvature 7
8 3. Sensitivity study: Numerical modeling A flow behavior index variation impact on the curvature 8
9 3. Sensitivity study: Numerical modeling A flow consistency index variation impact on the slope 9
10 3. Sensitivity study: Numerical modeling A yield stress variation translation 10
11 1. Principle 11 No experimental torque here, validation on computational data
12 1. Principle 11 Simulation with COMSOL, assumption of parameter set
13 1. Principle 11 Choice of an objective function for gap estimation
14 1. Principle 11 Choice and test of optimization algorithm
15 2. Objective function Enables gap estimation: common method Least square method F obj τ 0, K, n, p = 1 N ω w T exp (p) T sim (τ 0, K, n, p) 2 [N.m] 12
16 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
17 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
18 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
19 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
20 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
21 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
22 3. Deterministic optimization algorithm Simplex method: [Nelder and Mead, 65] Example for 2 parameter identification: Parameter 1 A (m+1) vertex polyhedron «strolling» on objective function surface with m the number of parameters. Vertices are directed towards objective function minimum. Only one solution: local or global minimum? 13 Parameter 2
23 3. Stochastic optimization algorithm Genetic algorithm: [Holland, 75; Poles, 03] First population (parameter set collection) created randomly, objective function evaluation for each individual (parameter set). Parameter 1 Formation of new population by crossover and mutation (perturbation) of individuals. Selection of individual created for building of new population Much longer as simplex but several solutions. Parameter 2 14
24 3. Stochastic optimization algorithm Genetic algorithm: [Holland, 75; Poles, 03] First population (parameter set collection) created randomly, objective function evaluation for each individual (parameter set). Parameter 1 Formation of new population by crossover and mutation (perturbation) of individuals. Selection of individual created for building of new population Much longer as simplex but several solutions. Parameter 2 14
25 3. Stochastic optimization algorithm Genetic algorithm: [Holland, 75; Poles, 03] First population (parameter set collection) created randomly, objective function evaluation for each individual (parameter set). Parameter 1 Formation of new population by crossover and mutation (perturbation) of individuals. Selection of individual created for building of new population Much longer as simplex but several solutions. Parameter 2 14
26 3. Stochastic optimization algorithm Genetic algorithm: [Holland, 75; Poles, 03] First population (parameter set collection) created randomly, objective function evaluation for each individual (parameter set). Parameter 1 Formation of new population by crossover and mutation (perturbation) of individuals. Selection of individual created for building of new population Much longer as simplex but several solutions. Parameter 2 14
27 4. Results Simplex algorithm Reference triplet (τ 0 -K-n)=( ) (τ 0 -K-n) F obj (N.m) (τ 0 -K-n) F obj (N.m) (τ 0 -K-n) F obj (N.m) Initial ( ) Initial ( ) Initial ( ) Initial ( ) Result ( ) Initial ( ) Initial ( ) Initial ( ) Initial ( ) Result ( ) Initial ( ) Initial ( ) Initial ( ) Initial ( ,45) Result ( ,75) Results very dependent on the initialization. ( ) compatible with the device error (0.005 N.m). Satisfactory triplet? (depending on experimental scatter) 15
28 4. Results Genetic algorithm Reference triplet (τ 0 -K-n)=( ) Population of 100 individuals 20 generations (τ 0 -K- n) F obj (N.m) 39/100 ( ) 9,83E-13 10/100 ( ) 0, /100 ( ) 0, /100 ( ) 0, /100 ( ) 0, n 71/ / / K 89/ / / τ 0 62/ / / Right triplet comes out from the 4 th generation. GA procedure is 8 times longer than the simplex one.
29 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
30 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
31 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
32 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
33 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
34 4. Results Objective function (N.m) Objective function is regular, simplex may be adequate. 17
35 Conclusions Validation of an identification procedure for numerical cases 2 kinds of optimization algorithms: Simplex Computational time + - Quality of the results (fiability, sensitivity, availability) GA - + Compromise? Shape of the objective function is decisive. 18
36 Prospects Test with model fluids To process real data, switchover to 2D from 3D Validation of the computational hypothesis for cement pastes To save time: Understand and demonstrate the behavior index conservation, to reduce the study to two parameter identification Cone-Plane and Helical rheometer, n very close (error: 5% by calibration method) [Pimenova and Hanley, 02] 19
37 Viscoplastic Fluids: From Theory to Application Parameter identification: An application of inverse analysis to cement-based suspensions Célimène Anglade Aurélie Papon, Michel Mouret UPS-LMDC-INSA France 20
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