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Lecture Objectives:

Lecture Objectives:. Address Project 1 issues Modeling steps Compare HW2 and software modeling Define building system of equations suitable for linear equation solvers. Modeling. Modeling. Modeling. Modeling. 1) External wall (north) node.

herrod-warren
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Lecture Objectives:

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  1. Lecture Objectives: • Address Project 1 issues • Modeling steps • Compare HW2 and software modeling • Define building system of equations suitable for linear equation solvers

  2. Modeling

  3. Modeling

  4. Modeling

  5. Modeling 1) External wall (north) node Qsolar+C1·A(Tsky4 - Tnorth_o4)+ C2·A(Tground4 - Tnorth_o4)+hextA(Tair_out-Tnorth_o)=Ak/(Tnorth_o-Tnorth_in) A- wall area [m2] • - wall thickness [m] k – conductivity [W/mK]  - emissivity [0-1] • - absorbance [0-1] • =  - for radiative-gray surface, esky=1, eground=0.95 Fij –view (shape) factor [0-1] h – external convection [W/m2K] s – Stefan-Boltzmann constant [5.67 10-8 W/m2K4] Qsolar=asolar·(Idif+IDIR)A C1=esky·esurface_long_wave·s·Fsurf_sky C2=eground·esurface_long_wave·s·Fsurf_ground 2) Internal wall (north) node C3A(Tnorth_in4- Tinternal_surf4)+C4A(Tnorth_in4- Twest_in4)+hintA(Tnorth_in-Tair_in)= =kA(Tnorth_out--Tnorth_in)+Qsolar_to_int_ considered _surf Qsolar_to int surf =portion of transmitted solar radiation that is absorbed by internal surface C3=eniort_in·s·ynorth_in_to_ internal surface for homeworkassume yij = Fijei

  6. Modeling b1T1 + +c1T2+=f(Tair,T1,T2) a2T1+b2T2 + +c2T3+=f(T1 ,T2, T3) a3T2+b3T3+ +c3T4+=f(T2 ,T3 , T4) ……………………………….. a6T5+b6T6+ =f(T5 ,T6 , Tair) Matrix equation M × t = f for each time step M × t = f

  7. Modeling

  8. Preprocessor Solver Postprocessor ES program Modeling steps • Define the domain • Analyze the most important phenomena and define the most important elements • Discretize the elements and define the connection • Write energy and mass balance equations • Solve the equations • Present the result

  9. Characteristic parameters • Conduction (and accumulation) solution method • finite dif (explicit, implicit), response functions • Time steps • Meteorological data • Radiation and convection models (extern. & intern.) • Windows and shading • Infiltration models • Conduction to the ground • HVAC and control models

  10. Discretization of a non-homogeneous wall structure Section considered in the following discussion

  11. Linearized radiation means linear system of equations Calculated based on temperature values from previous time step T0 F0 B0 C0 A1 B1 C1 T1 F1 T2 F2 A2 B2 C2 x These coefficient will have Some radiation convection coefficients = T3 F3 A3 B3 C3 A4 B4 C4 T4 F4 T5 F5 C5 A5 B5 A6 B6 T6 F6

  12. Energy balance for air unsteady-state heat transfer QHVAC

  13. Example Tair is unknown and it is solved by system of equation :

  14. System of equations (matrix) for single zone (room) 8 elements Three diagonal matrix for each element x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Air equation x

  15. System of equations for a building Matrix for the whole building 4 rooms Rom matrixes Connected by common wall elements and airflow in-between room – Airflow simulation program (for example CONTAM) Energy Simulation program “meet” Airflow simulation program

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