35. MEĐUNARODNI KONGRES O KLIMATIZACIJI, GREJANJU I HLAĐENJU Beograd, 1-3. decembra 2004. 35th CONGRESS ON AIR CONDITIONING, HEATING AND REFRIGIRATING Belgrade, December 1-3, 2004 PRIMENA TRODIMENZIONE METODE KONAČNIH ELEMENATA U PROCENI ENERGETSKE EFIKASNOSTI OMOTAČA ZGRADE ON THE THREEDIMENSIONAL FINITE ELEMENT METHOD IN THE ENERGY EFFICIENCY OF BUILDING’S ENVELOPE Dr Dubravka Mijuca*, Dr Dušan Gajić**, Marko Vukobrat** *Matematički fakultet, Univerzitet u Beogradu, P. FAH 550 **Institut "Kirilo Savić", Beograd dmijuca@matf.bg.ac.yu

ENERGIJA KOJA SE TROSI U ZGRADAMA BUILDING ENERGY USE Na energiju koja se koristi u zgradama (za zagrevanje, hladjenje, osvetljavanje, i zadovoljavanje drugih važnih energetskih usluga) otpada oko ¼ celokupne energije upotrebljene u centralnoj i istočnoj Evropi Energy used in buildings (to heat, cool, light, and provide other important energy services) accounts for about one-fourth to one-third of all energy used in Central and Eastern Europe.

MOTIV - MOTIVE Projektovanje građevinskih objekata primenom savremenih metoda računske mehanike je danas brže, efikasnije i jeftinije, a strukturalni kvalitet i energetska efikasnost projektovanog, rekonstruisanog ili revitalizovanog objekta se njenom primenom povećava. Contemporary design in the civil engineering becomes shorter in time, more efficient and less expensive by the use of numerical methods of computational mechanics, while structural quality and energetic efficiency are increased

CILJ - GOAL Pokazati da je analiza energetske efikasnosti građevinskih objekata i brža i jeftinija korišćenjem trodimenzionalne metode konačnih elemenata To show that analysis of the energy efficiency of the civil facilities is faster and cheaper by the use of threedimensional finite element method

ORIGINALNOST ISTRAŽIVANJA ORIGINALITY OF THE RESEARCH Upotreba originalnog in-house softvera “FEMIX” baziranog na mešovitoj metodi konačnih elemenata, a koji je potupno integrisan u pre i post processing komercialnog koda “Straus7” The use of the original in-house software “FEMIX” based on the mixed finite element method, which is fully integrated in the pre and post-processing of the commercial code “Straus7”

KLJUČNE REČI - KEYWORDS building envelope non-homogenous wall heat transfer mathematical model numerical simulation energy efficiency finite element method CAD, CAE HVAC U-value omotač zgrade nehomogeni zid prenos toplote matematički model numerička simulacija energetska efikasnost metoda-konačnih elemenata KGH sistem CAD, CAE U-vrednost

LITERATURA - REFERENCES Hellen T. How to Use Elements Effectively. NAFEMS Ltd – he International Association for Engineering Analysis Community, http://www.nafems.org, 2002 G+DComputing, “Straus7”, Finite element analysis system software package, Australia http://www.strand.aust.com Mijuca D. On hexahedral finite element HC8/27 in elasticity, Computational Mechanics, 33 (2004), 6, pp 466-480 Mijuca D, Žiberna A, Medjo B. A New multifield finite element method in steady state heat analysis. Thermal Science, 2004; accepted for publishing Todorović B, Projektovanje postrojenja za centralno grejanje, Mašinski fakultet Univerziteta u Beogradu,1966 Todorović M, Živković B. Prednosti numeričke simulacije termičkog ponašanja zgrade pri projektovanju sistema za klimatizaciju, Zbornik radova Trideset drugog kongresa o grejanju, hlađenju i klimatizaciji, Beograd, 2001 Balocco C, A simple model to study a ventilated facade energy performance. Energy and Buildings, 34 (2002) pp. 469-475 Mijuca D, Gajic D, Vukobrat M. Three-dimensional finite element method in energetic efficiency of buildings” Termotehnika, accepted for publication (in Serbian) CEN. 1996. Building components and building elements - Thermal resistance and thermal transmittance - Calculation method. European Committee for Standardization, rue de Stassart 36, B‑1050 Brussels, Belgium. Ref. No. EN ISO 6946:1996. Bazjanac V. Building energy performance simulation as part of interoperable software environments, Building and Environment, 39 (2004), 8, pp. 879-883 CEN. 1995. Thermal bridges in building construction - Heat fows and surface temperatures - Part1: General calculation methods. European Committee for Standardization, rue de Stassart 36, B-1050 Brussels, Belgium. Ref. No. EN ISO 10211-1

METODA KONAČNIH ELEMENATA FINITE ELEMENT METHOD 3-D metoda konačnih elemenata koristi se za analizu stacionarnog problema prostiranja toplote kroz nehomogeni omotač zgrade 3-D finite element method is used for the analysis of the steady-state building inhomogeneous envelope heat transfer Please note that present research is now standard in the developed countries !!! Therefore in this presentation - nothing is new or before time, except the use of original mixed FE approach!

METODA KONAČNIH ELEMENATA FINITE ELEMENT METHOD HEXA8 Primal approach Software package Straus7 2 FEA methods HC20/27 Mixed approach Original in-house software FEMIX

SAVREMENO PROJEKTOVANJE ZGRADA STATE OF THE ART IN THE BUILDING DESIGN Proračun temperature i toplotnog fluksa kroz zidove, prozore i krovove zgrada je prvi korak proceni u energetske efikasnosti zgrade, kao i u preventivi problema koji nastaju usled termalnih napona i kondenzacije. The calculation of temperature and heat flow through the walls, windows and roof of a building is the first step in estimates of energy efficiency of buildings, as well as in preventing problems arising from thermal stresses and condensation. [1] Canadian Building Digest – 52: Heat Transfer at Building Surfaces

Numerical examples Heat flow through inhomogeneous wall Investigation of dependence of heat transfer coefficient (U–value) on the material properties of wall components. [2] CEN. 1996. Building components and building elements - Thermal resistance and thermal transmittance - Calculation method. European Committee for Standardization, Ref. No. EN ISO 6946:1996. Heat flow through a corner To determine heat losses throughout the structures. [3] CEN. 1995. Thermal bridges in building construction - Heat fows and surface temperatures - Part1: General calculation methods. European Committee for Standardization, Ref. No. EN ISO 10211-1 Four storey building To investigate change of heat losses if the thermally efficient materials are used – the thermalvision camera effects

Heat flow through inhomogeneous wall geometry The inhomogeneous wall build of light expanded clay aggregate block filled with polystyrene, mortar, with or without mineral wool is considered.

Heat flow through inhomogeneous wall numerical results and convergence

Heat flow through inhomogeneous wall

Heat flow through inhomogeneous wall Without mineral wool strip With mineral wool strip

Heat flow through inhomogeneous wall

Heat flow through a corner This example deals with heat flow through a corner and a single floor.

Heat flow through a corner

Heat flow through a corner Temperature “Straus7” Temperature “FEMIX”

Heat flow through a corner Heat Flux “Straus7” Heat Flux “FEMIX” From the results obtained, we may see that with a computationally inexpensive mesh (7 sec) we successfully meet the target results.

Heat flow through a corner animation Heat Flux “Straus7”

Four-storey building thermalvision camera like effects By the use of different material on the the last two floors of building’s envelope energetic efficiency is increased

Conclusion Described FEA methods are cheaper, more efficient and precise, in regard to standard “hand-out” calculating methods. It gives wide opportunities in the design process of the buildings and prediction of its thermal behavior. The three-dimensional visualization of the calculated temperature and heat flux fields is provided. Optimization of the cost/energy efficiency rate is enabled in the design process of the building’s envelope and HVAC system.

Phone 064-15-12-780 www.matf.bg.ac.yu/~dmijuca CONTACT Dr. Dubravka Mijuca Faculty of Mathematics Department of Mechanics University of Belgrade Studentski trg 16 11000 Belgrade P.O.Box 550 Serbia and Montenegro Phone 064-15-12-780 www.matf.bg.ac.yu/~dmijuca QUESTIONS