Multiphysical modelling of building structures and its difficulties

1. PANM 15 in Dolní Maxov Jiří Vala (Vala.J@fce.vutbr.cz) Brno University of Technology, Faculty of Civil Engineering Inverse problems of heat transfer Inverzní problémy přenosu tepla • Multiphysical modelling of building structures and its difficulties • Identification of material characteristics in heat transfer • Numerical analysis – from direct to sensitivity and adjoint problems • Example of MATLAB-supported real measurement device • Still other approaches

2. Multiphysical modelling ofbuilding structures • principal processes: • heat transfer (conduction, convection, radiation) • air flow • moisture propagation (partially irreversible occupation of pore structure) • additional processes: • propagation of salt, contaminant(s), … • chemical reactions (maturing silicate mixtures, carbonation, …) • phase changes (vapour / liquid water / ice, solid structure from silicate mixture, …) • mechanical deformation (strain-stress relations: elasticity, creep, fracture, …) • … • thermodynamic principles: generalized • mass balance → continuity equation(s) • (linear and angular) momentum balance → Navier-Stokes equations • energy (enthalpy) balance → Fourier equation(s)

3. Some unpleasant difficulties • different scales from micro- (or nano-) • to macro-scales, non-periodic structures • – RVE-based homogenization techniques, • statistical approaches • non-transparent existence of solutions of corresponding BVPs and IVPs for PDEs of evolution (at least in standard Lebesgue & Sobolev spaces) • non-deterministic BCs in open systems – climatic information, day and year quasi-cycles • strongly non-linear formulations – non-trivial analysis of convergence of iterative computational algorithms (based on FEM, FVM, sequences of Rothe, …) • difficult choice of effective material characteristics – non-expensive identification of characteristics from laboratory measurements and their validation by observations in situ required • cracks in tension (quasi-brittle behaviourof concrete, micro- and macro-fractured zones), effect of additional (classical or pre-stressed) reinforcement

4. Identification problems • restrictions of this contribution: • identification of basic thermal technical characteristics: • λ thermal conductivity→ insulationability • c thermal capacity → accumulationability • ρ material density • macroscopic effective constant values (for expected interval of temperatures T), dryhomogeneous and isotropic material, no air flow • one (in general) 3D-nonstationary Fourier equation • a closed system (artificially arranged laboratory conditions) • standard measurement techniques: • λ from 1D-stationary Fourier equation (algebraic relation available) • c various types of calorimeters, contact with water usually required, • bad results e.g. for maturing concrete mixtures • ρ easy • new measurement technique: • λ, κ=cρfrom a nonstationaryFourier equation, evolution of T(x,t) • forced by controlled generation of heat in the system

5. 1D experiment configuration

6. Numerical analysis

12. evaluation of uncertainties in measurements: • uncorrelated adjusted heat fluxes and measured temperatures • normal (Gaussian) probability distribution(justified by the central limittheorem) • uncertainties of a,bevaluated fromsimilarformulaeagain…

13. Illustrative practical example ecological thermal insulation for building structures prepared from the wood waste

14. results from preparatory direct computations

15. original nonstationary measurement device at FCE BUT in Brno (S. Šťastník, H. Kmínová)

16. errors in 1D identificationof a,b

17. convergence of Newton iterations

18. Still other approaches… Simplified problems (1D configurations): semi-analytical solutions, Fourier series, integral transformations. Least squares techniques: classical approaches, whole-domain first-order regularization (discrepancy principle), sequential function specification, iterative regularization. Deterministic optimization: steepest descent method, conjugate gradient method, Newton-Raphson method with restarting strategy, quasi-Newton method with approximated Hess matrix, Levenberg-Marquardt method. Evolutionary and stochastic optimization: standard genetic algorithms, simulated differential evolution method, particle swarm method a simulated annealing method, hybrid approaches. Other stochastic approaches: spectral stochastic versions of numerical method (as FEM, FVM, FDM), representation of stochastic processes by Fourier series (polynomial chaos expansion, Karhunen-Loève expansion), application of Markov chains, Mote Carlo simulations, Bayesian statistics.

19. References ATCHONOULGO, A., BANNA, M., VALÉE, C., DUPRÉ, J.C. Inverse transient heat conduction problems and identification of thermal parameters. Heat Mass Transfer 45(2008), 23-29. COLAÇO, M., ORLANDE, H.R.B., DULIKRAVICH, G.S. Inverse and optimization Problems in Heat Transfer. J. Brazil Soc. Mech. Sci. & Eng. 28 (2006), 1-24. DAVIES, M.G. Building Heat Transfer. John Wiley & Sons, 2004. GOBBE, C., ISERNA, S., LADEVIE, B. Hot strip method: application to thermal characterization of orthotropic media. Int. J. Therm. Sci. 43 (2004), 951-958. GUIMARÃES G., PHILIPPI, P.C., THERY, P. Use of parameters estimation method in the frequency domain for the simultaneous estimation of the thermal diffusivity. Rev. Sci. Inst. 66 (1996), 2582-2588. ISAKOV, V. Inverse Problems for Partial Differential Equations. Springer, 2006. KOZHANOV, A.I. Solvability of the inverse problem of finding thermal conductivity. Siberian Math. J. 46 (2005), 841-856. PARKER, W.J., JENKINS, R.J., BUTTER, C.P., ABBOT, G.P. Flash method of determining thermal diffusivity, heat capacity and thermal conductivity. J. Appl. Phys. 32 (1961), 1679-1684. ŠŤASTNÍK, S., VALA, J., KMÍNOVÁ, H. Identification of basic thermal technical characteristics of building materials. Kybernetika 43 (2007), 561-576. ZABARAS. N. Inverse problems in heat transfer. In: MINKOWYCZ, W.J., SPARROW, E.M., MURTHY, J.Y. (eds.),Handbook of Numerical Heat Transfer, Chap. 17. UIC College of Engineering, 2006.

20. THANK YOUFOR YOUR ATTENTION. QUESTIONS AND REMARKSARE WELCOME.