THERMAL SIMULATION OF FULLY AND PARTIALLY BURIED STRUCTURES

GROUP- B6

Under the guidance of Mr. Dhananjay R. Mishra

Made by:Gautam Kumar Mishra (111635)Kartik Jain (111642)Raghav Mehta (111660)Rohit Kr. Gupta (111666)Yuvraj Sharma (111695)

INTRODUCTION• Underground buildings or earth sheltered structures are very

important from energy conservation point of view. Contact of various buildings with earth is a part of thermal envelope and are protected from extremes of seasonal and diurnal variations of environment.

• So we are basically calculating the heat loses and analyzing different geometries of underground structures, these geometries include cylindrical, cuboidal, cubical, pyramid in shape.

• The steady state thermal simulation is based on fact that the rate of heat transfer Q between the ground, whose surface is a temperature Tg and a fully and partially underground structure, whose surface is a temperature Ts is given by:

(Source:Sodha, MS. ‘Simulation of periodic heat transfer between ground and underground structures’. Int J Energy Res 2001;25:689–93.)

• where K is the thermal conductivity of the soil, L is the typical length of the system and F is a dimension parameter ,called shape factor.

Basis of Simulation• The flow of heat in earth is given by:

(Source:Sodha MS, Goyal IC, Kaushik SC, Tiwari GN, Sethi AK, Malik MAS. 1980. ‘Periodic heat transfer to a cylindrical cavity in ground, having air at constant temperature’. Proceedings of the Indian National Science Academy A46:167)

where T is the temperature at any point at time t, is the density of the soil, c is the specific heat of the soil and K is the thermal conductivity of the soil.

TEMPERATURE DISTRIBUTION IN UNDISTURBED EARTH

• At any given location, the earth's surface temperature and subsurface temperature are determined by the balance between the solar energy absorbed at the surface, convective heat exchange of the surface with the ambient air, heat loss by outgoing long wave radiation to the sky and rate of water evaporation from the surface.

CHARACTERISTIC LENGTH• For depths greater than a certain value the earth’s temperature

is almost constant. This value is known as the ‘Characteristic Length’.

• The depth of the characteristic length depends upon the nature of the ground for e.g. dry ground has low thermal conductivity, smaller rate of heat transfer and hence lower characteristic length.

• Due to this reason when structures are constructed below this characteristic length, their temperature is maintained at a comfort zone throughout the year.

Characteristic length

THERMAL SIMULATION METHOD (EXPERIMENT)

• This method is very useful to determine the steady heat losses from partially sunken structures and buried structures.

• For the normal buildings the characteristic length 'a' is of the order of 3-4 m . If a small model of the structure with characteristic length of 5-10 cm is made, F(shape factor) can be determined in the laboratory by heating the model from inside with a given heat source of known power .

Sphere Cube

Triangular Pyramid Square Pyramid

EXPERIMENTAL SETUP• In this experiment, a reduced scale model of the structure

made from copper (copper is chosen on account of its large thermal conductivity) is placed in sand contained in a box of 1mx1mx1m size.

• The size of the reduced scale model should be such that sand in the box can be treated as semi-infinite medium.

• The hollow model is heated with an incandescent lamp(12V,30W) placed inside the model in the case of buried buildings .

• (Source:Mahendra Singh Sodha, Dhananjay R. Mishra, ‘Shape factor for bermed wall’, Heat Mass Transfer (2011) 47:1143–1146 DOI 10.1007/s00231-011-0782-z)

Schematic diagram for determining thermal conductivity of sand.

Photograph of actual experimental setup.

• The lamp/heater is energized by a 12V DC power supply. • The current (Im) in the circuit and voltage (Vm) across the

heating source (bulb/element) are measured with the help of a digital voltmeter.

Power=Vm Im

The temperature of the surface of the model (Tg) and ambient temperature (Ts) should be measured with the help of two calibrated copper thermocouples.

• After starting the experiment, the two temperatures to be measured after every ten minutes, till the steady state is reached which takes about 6-7 hours.

Photograph of square pyramid being welded

CHARACTERIZATION OF MEDIA Thermal Conductivity• Loosely filled sand is the medium chosen to validate the thermal

simulation model.• The thermal conductivity is determined by measuring the steady

state heat flux from the hollow copper sphere buried in sand.

Photograph of copper sphere ( 3 cm )

The heat flux Q from a sphere is given by:Q=V × I = K. F(a,d).a.(Ts-Tg)

The nomenclature of the used symbols have already been discussed.

DensityA vessel of known volume is loosely filled with sand /coal dust and its mass is measured. Density is just mass divided by volume.

OBSERVATION AND RESULTS• Determination of thermal conductivity of simulating media

(sand) Thermal conductivity of sand was determined with the help of

hollow copper sphere of 3 cm diameter based on four observations at different depths by using the shape factor of hollow sphere as a standard geometry and using the formula discussed earlier.

By taking average of all the corresponding values, we calculate the shape factor for different geometries.

S. No D/r F

1 1 16.86

2 2 14.31

3 3 14.46

4 4 13.94

5 5 13.69

6 6 13.6

Shape factor of copper hollow Sphere at different D/r ratio

Source: Mahendra Singh Sodha, Dhananjay R. Mishra, ‘Shape factor for bermed wall’, Heat Mass Transfer (2011) 47:1143–1146 DOI 10.1007/s00231-011-0782-z

0 1 2 3 4 5 6 7 810

11

12

13

14

15

16

17

18

D/r

F

Determination of thermal conductivity of simulating media (sand)

• The average thermal conductivity for the sand comes out to be K=0.507683 (W/mK).

S. No D/r Ts(oC) Tg(oC) V(Volt) I(Amp) Q(Watt) F K(W/mK)

1 1.6 65 47 11.62 0.2 2.324 14.930.540327

2 3.2 63 43 11.5 0.195 2.2425 14.350.520688

3 4.8 61 38 11.66 0.2 2.332 13.740.491952

4 6.4 65 40 11.78 0.2 2.356 13.150.477765

Determination of shape factor for a cubical structure

• Cube Length: 10 cm

S. No D/L Ts(oC) Tg(oC) Ts-Tg(oC) V(Volt) I(Amp) Q(Watt) F

1 0.2 53 42 11 8.90 0.99 8.811014.77756

2 0.4 57 43 14 9.01 1.01 9.100112.80341

3 0.6 59 44 15 9.07 1.00 9.070011.91032

4 0.8 56 39 17 9.08 1.01 9.170810.62590

Variation of shape factor F with D/L for a cube body; bullet represents experimental points while the fitted continuous curve is

represented by a line.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.96

8

10

12

14

16

18

f(x) = 10.560848748825 x² − 18.7348865401459 x + 18.9784851407445R² = 0.978749119769689

D/L

F

Determination of shape factor for a triangular pyramid structure

• Height of Pyramid=h=13.5 cm• Base Width=L=10 cm

S. No D/(h/L) Ts(oC) Tg(oC) Ts-Tg(oC) V(Volt) I(Amp) Q(Watt) F

10.740741

66 51 15 9 1.1 9.99.629806

21.481481

62 46 16 9.05 0.99 8.95958.170289

32.222222

60 42 18 8.97 1.03 9.23917.48912

42.962963

59 38 21 9.02 1 9.026.267017

Variation of shape factor F with D/(h/L) for a triangular pyramid; bullet represents experimental points while

the fitted continuous curve is represented by a line.

0.5 1 1.5 2 2.5 3 3.55

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

f(x) = 0.108171981123761 x² − 1.85452450737208 x + 10.8782102797479R² = 0.985250603366172

FPolynomial (F)

D/(h/L)

F

Determination of shape factor for a square pyramid structure

• Height of Pyramid=h=13.5 cm• Base Width=L=10 cm

S. No D/(h/L) Ts(ͦoC) Tg(oͦC) Ts -Tg(oͦC) V(Volt) I(Amp) Q(Watt) F

10.740741

70 60 10 9.01 0.99 8.919913.01468

21.481481

68 56 12 9.08 1.01 9.170811.15063

32.222222

57 42 15 9.07 1 9.078.822459

42.962963

65 47 18 9.04 1.01 9.13047.401009

• Variation of shape factor F with D/(h/L) for a square pyramid; bullet represents experimental points while the fitted continuous curve is represented by a line

0.5 1 1.5 2 2.5 3 3.55

6

7

8

9

10

11

12

13

14

f(x) = 0.201658810714547 x² − 3.33472637234037 x + 15.4427438352644R² = 0.994925323699858

D/(h/L)

F

Designing of standard geometries using CATIA V5

• Sphere (Diameter=d=3 cm)

• Cube (Side=L=10 cm)

Conclusion• At the end of the experiment we have come to the conclusion

that the method used by us to determine shape factor of various geometries can be used to find the shape factor of any arbitrary geometry .This is explained as follows:

• First Q=KFa(Ts-Tg) was used to determine the conductivity of the simulating media (sand) by burying a hollow sphere at various depths. Using this conductivity we found out the shape factors of various other standard geometries. By, this we conclude that if we can find the shape factors of the standard geometries we can also find out the shape factor of any other arbitrary body. And by doing so, we can also find the heat flux, the thermal conductivity of any other simulating media.

THANK YOU