Lecture Objectives:
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Transcript of Lecture Objectives:
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Lecture Objectives:
• Discuss HW3
• Introduce alternative conduction equation solution method
• Present a commercial software
eQUEST and define basic modeling
steps
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Homework 3 (Similar to HW2, but unsteady, and more realistic)
East
10 m 10 m
2.5 m
North
Tair_in
IDIR
Idif
Glass
Tinter_surf ≠ Tair
Teast_i
Teast_o
Tnorth_i Tnorth_oi
Tair_out
ConcreteIDIRIdif
Surface radiation
Surfaceradiation
Top view
Insulation
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Alternative: Response function methods for conduction calculation
NOTATION: θ(x,t)=T(x,)
Ts
0
T
-L / 2 L /2
h
h
h
To
T
h omogenous wa ll
L = 0.2 mk = 0 . 5 W/ m Kc = 9 20 J/kgK
= 120 0 k g/mp
2
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Laplace transformation
Laplace transform is given by
Where p is a complex number whose real part is positive and large enough to cause the integral to converge.
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Laplace transformation table
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Principles of Response function methods
The basic strategy is to predetermine the response of a system to some unit excitation relating to the boundary conditions anticipated in reality.
Reference:
JA Clarkehttp://www.esru.strath.ac.uk/Courseware/Class-16458/or http://www.hvac.okstate.edu/research/documents/iu_fisher_04.pdf
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Response functions
• Computationally inexpensive
• Accuracy ?
• Flexibility ????What if we want to calculate the moisture transport and we need to know temperature distribution in the wall elements?
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Modeling
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Modeling
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Modeling
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Modeling 1) External wall (north) node
2) Internal wall (north) node
Qsolar=solar·(Idif+IDIR) A
Qsolar+C1·A(Tsky4 - Tnorth_o
4)+ C2·A(Tground4 - Tnorth_o
4)+hextA(Tair_out-Tnorth_o)=Ak/(Tnorth_o-Tnorth_in)
C1=sky·surfacelong_wave··Fsurf_sky
Qsolar_to int surf =portion of transmitted solar radiation that is absorbed by internal surface
C3A(Tnorth_in4- Tinternal_surf
4)+C4A(Tnorth_in4- Twest_in
4)+ hintA(Tnorth_in-Tair_in)= =kA(Tnorth_out--Tnorth_in)+Qsolar_to_int_ considered _surf
C3=niort_in··north_in_to_ internal surface for homework assume ij Fiji
transmitedtotalsolarsurfconsideredenvelopetotalsurfconsideredernaLsurfconsideredtosolar QAAQ ___int_int____int_int___ )/(
A- wall area [m2]- wall thickness [m]k – conductivity [W/mK] - emissivity [0-1]- absorbance [0-1] = - for radiative-gray surface,sky=1, ground=0.95Fij – view (shape) factor [0-1]h – external convection [W/m2K]s – Stefan-Boltzmann constant [5.67 10-8 W/m2K4]
C2=ground·surfacelong_wave··Fsurf_ground
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Matrix equation
M × t = f
for each time step
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)
………………………………..
M × t = f
Modeling
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Modeling
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Modeling steps
• Define the domain
• Analyze the most important phenomena and define the most important elements
• Discretize the elements and define the connection
• Write the energy and mass balance equations
• Solve the equations (use numeric methods or solver)
• Present the result
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eQUEST
• Energy simulation software – Free: http://doe2.com/equest/– Graphical user interface (GUI) that uses DOE2– Easy to use it– Example of your HW1a
• ….