engleski

Heat of Hydration by Inverse Method

Numerous laboratory techniques have been developed for determination of the heat of hydration of cement based materials, ranging from sophisticated (micro)calorimeters to (semi-)adiabatic temperature measurements at the centre of a large insulated block of representative sample. Calorimetric methods of investigations are important for better cement application, quality control of cement and optimization of process parameters, and contribute to better understanding of influence of the admixture, development of microstructure and mechanical stress in materials as well as predicting the strength of cement based material. This paper describes the development of a novel method for monitoring the heat of hydration of cement based materials for the sake of elaboration of the hydration model which observes hydration rate relative to hydration degree and temperature . In cement application, the model will enable a real simulation of temperature distribution in material and better planning of curing during early age of hydration to obtain better durability and functionality. The novel calorimetric method is based on the inverse method implementation for determination of heat generation from known (measured) material temperature distribution by solving transient heat conduction problem. The advantages of developed calorimetric method are: direct estimation of term = heat generation/thermal conductivity [(Wm-3)/(Wm-1K-1)], the knowledge of boundary condition and determination of heat loss from actual measurement. Moreover, the simple experimental technique which measures representative samples in isothermal and semi-adiabatic conditions enables the investigation of the temperature dependence of physico-chemical hydration processes. By solving a system of partial differential equations by a method of finite difference, beside material temperature distribution, a sensitivity of the developed method regarding the influential parameters was estimated and a measurement uncertainty analyses performed. For estimating the heat generation two approaches were adopted: Conjugate Gradient Method with Adjoint Problem for function estimation and Levenberg-Marquardt Method for parameter estimation of assumed function. A complete computer code for solving and optimizing the inverse problem is written in MATLAB® . The evolution of thermal conductivity and diffusivity is possible to determine by dynamic methods and can be used for the more accurate determination of heat generation and temperature distribution in cement based material. Results of the developed method are compared to and validated against the hydration heats determined by the differential micro-calorimetry and standard solution method as well as literature data. TOPLINA HIDRATACIJE INVERZNOM METODOM: Za određivanje topline hidratacije cementnih materijala postoje brojni laboratorijski postupci, od sofisticirani izotermnih (mikro)kalorimetara do (semi-)adijabatskog praćenja temperature u središtu izoliranog uzorka. Kalorimetrijske metode istraživanja doprinose boljoj primjeni cementa, kontroli kvalitete cementa i optimiranju procesnih uvjeta pri proizvodnji, razumijevanju utjecaja dodataka, razvoja mikrostrukture i mehaničkih naprezanja u materijalu kao i predviđanju čvrstoće cementnih materijala. U ovome je radu razvijena nova metoda praćenja topline hidratacije cementnog materijala radi razvoja modela hidratacije cementnog materijala koji će uzimati u obzir ovisnost brzine procesa hidratacije o dosegu hidratacije i temperaturi . Model procesa hidratacije cementnog materijala omogućit će, u primjeni, realnu simulaciju raspodjele temperatura u materijalu i lakše planiranje njegovanja u ranom razdoblju hidratacije sa svrhom postizanja bolje trajnosti i funkcionalnosti. Nova kalorimetrijska metoda kontinuiranog određivanja topline hidratacije temelji se na rješavanju i optimiranju inverznog zadatka za postavljeni model nestacionarnog prijenosa topline uz poznavanje (izmjerenog) polja temperature. Prednosti razvijene kalorimetrijske metode su: direktna procjena izraza = generacija topline/toplinska vodljivost [(Wm-3)/(Wm-1K-1)], poznavanje rubnog uvjeta i određivanje toplinskih gubitaka iz samog mjerenja. Nadalje, izvedba eksperimenta je jednostavna i mjerenje se izvodi na reprezentativnim uzorcima u izotermnim ili semi-adijabatskim uvjetima, što omogućava istraživanje temperaturne ovisnosti fizikalno-kemijskih procesa hidratacije cementa. Osim temperaturnog polja u materijalu, rješavanjem sustava parcijalnih diferencijalnih jednadžbi metodom konačnih razlika, određena je i osjetljivost razvijene metode s obzirom na utjecajne parametre radi analize mjerne nesigurnosti. Pri procjeni generacije topline primijenjena su dva pristupa: procjena funkcije konjugiranom gradijentnom metodom optimiranja (engl. Conjugate Gradient Method with Adjoint Problem for function estimation) i ugađanje parametara unaprijed zadane funkcije Levenberg-Marquardt-ovom metodom. Potpuni računalni kod za rješavanje i optimiranje ovog inverznog zadatka napisan je u MATLAB-u. Razvoj toplinske vodljivosti i toplinske difuzivnosti studiranog materijala moguće je odrediti dodatnim dinamičkim mjerenjima i uporabiti za točnije određivanje topline hidratacije i polja temperature u cementnom materijalu. Dobiveni rezultati uspoređeni su i vrednovani s toplinom hidratacije određenom izoperibolnim-kondukcijskim diferencijalnim mikro-kalorimetrom i standardnom kalorimetrijskom metodom otapanja te literaturnim podacima.

heat of hydration; calorimetry; inverse modeling; calcium aluminate cement

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