Lecture Objectives:

15
Lecture Objectives: • Discuss HW3 • Introduce alternative conduction equation solution method • Present a commercial software eQUEST and define basic modeling steps

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Lecture Objectives:. Discuss HW3 Introduce alternative conduction equation solution method Present a commercial software eQUEST and define basic modeling steps. Top view. Homework 3 (Similar to HW2, but unsteady, and more realistic). Glass.  T north_oi. T north_i. - PowerPoint PPT Presentation

Transcript of Lecture Objectives:

Page 1: Lecture Objectives:

Lecture Objectives:

• Discuss HW3

• Introduce alternative conduction equation solution method

• Present a commercial software

eQUEST and define basic modeling

steps

Page 2: Lecture Objectives:

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

• ….