This document summarizes research optimizing the conductance of energy piles using finite element modeling and fractional factorial design of experiments. It describes developing a finite element model to simulate an energy pile and identifying 9 controlling factors that influence conductance. Experiments were designed using uniform design and regression was used to develop a statistical model relating factors to conductance. The results identified the combination of factors producing maximum conductance, including having more U-tubes, larger tube diameter, greater distance between tubes, and higher thermal conductivity and heat transfer coefficient.

1. Optimization of Energy Pile Conductance
using Finite Element and Fractional Factorial
Design of Experiment
Dr. Khaled Ahmed
Mechanical & Industrial Engineering Department,
Qatar University,
Doha, Qatar.
Dr. Mohammed Al-Khawaja
Mechanical & Industrial Engineering Department,
Qatar University,
Doha, Qatar.
Dr. Muhannad Suleiman
Civil and Environmental Engineering,
Lehigh University,
Bethlehem, PA, USA.
2017 International Joint Conference on Civil and Mechanical Engineering
JCCME 2017

2. Outline
2
Dr. Khaled Ahmed
 Introduction
 Review
 Problem Statement
 Objectives
 Finite Element Model
 Controlling Factors
 Design of Experiment
 Results & Discussion
 Conclusions

3. Introduction
3
Dr. Khaled Ahmed
 Review
 Cooling Buildings with AC is increasing

4. Introduction
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Dr. Khaled Ahmed
 Review
 GSHP, Ground Source Heat Pump

5. Introduction
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Dr. Khaled Ahmed
 Review
 Wellbores

6. Introduction
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Dr. Khaled Ahmed
 Review
 Energy Piles work as heat
exchangers

7. Introduction
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Dr. Khaled Ahmed
 Review
 Energy Piles has three materials and 5 geometrical factors.
1 U-tube 2 U-tubes 3 U-tubes

8. Introduction
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Dr. Khaled Ahmed
 Problem Statement
 Energy Piles has many controlling factors ( >> 5).
 Interaction between these factors is missed.
 Optimization based on all possible factors is missed.
 Proper design of experiment is required.

9. Introduction
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Dr. Khaled Ahmed
 Objectives
 Use well verified finite element model.
 Define wide range of possible controlling factors.
 Define design of experiment considering all factors.
 Predict a statistical correlation between factors.
 Predict statistically the optimum controlling factors.

10. Finite Element Model
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Dr. Khaled Ahmed
 Geometrical Model
 Symmetrical Pattern

11. Finite Element Model
11
Dr. Khaled Ahmed
 Energy Balance using Galerkin Method
 Boundary Conditions
 Post Analysis
𝐵 𝑇
𝐾 𝐵 𝑑𝐴
𝐴
+ ℎ 𝑁𝑠 𝑇
𝑁𝑠
𝑑𝑆
𝑆
𝑇 = 𝑞𝑠
𝑁𝑠 𝑇
𝑑𝑆
𝑆
+ ℎ𝑇𝑓 𝑁𝑠 𝑇
𝑑𝑆
𝑆
𝛛𝐓
𝛛𝐒
= 𝟎
𝑻𝐀−𝐁 = 𝟐𝟓 𝐨
𝐂
−𝐊𝐬
𝛛𝐓
𝛛𝐒
= 𝐇 𝐓𝐬 − 𝐓𝐟
𝑪𝐩,𝐅𝐄 =
𝐐𝐀−𝐁
𝐓𝐭 − 𝐓𝐂−𝐃

12. FE Model Verification
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Dr. Khaled Ahmed
 Mesh Density Sensitivity.
𝑅𝑝 =
1
4𝜋𝐾𝑝
ln
𝑑𝑝
4
4𝑑𝑜𝑆3
𝑑𝑝
8
𝑑𝑝
8
− 𝑆8
𝐾𝑝−𝐾𝑠
𝐾𝑝+𝐾𝑠
+
1
2𝑛𝜋
1
2𝐾𝑡
ln
𝑑𝑜
𝑑𝑖
+
1
𝑑𝑖𝐻 𝑡

13. Controlling Factors
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Dr. Khaled Ahmed
 Geometrical Factors
 n: Number of U-tubes
 dp [m]: Pile diameter.
 di [m]: Tube inner diameter
 t [m]: Tube thickness
 S [m]: Tubes spacing.
 Physical Factors
 Kp [W/m.K]: Pile thermal conductivity.
 Ks [W/m.K]: Soil thermal conductivity.
 Kt [W/m.K]: Tube thermal conductivity.
 Operational Factors
 H [W/m2.K]: Convection heat transfer coefficient.
9
Factors

14. Controlling Factors
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Dr. Khaled Ahmed
 Factors Range
n
dp
[m]
di
[m]
t
[m]
S
[m]
Kp
[W/m.K]
Ks
[W/m.K]
Kt
[W/m.K]
H
[W/m2.K]
-1 1 0.4 0.02 0.002 0.4 dp 1.0 0.5 0.5 10
0 2 0.7 0.03 0.003 0.6 dp 1.75 1 16 55
+1 3 1.0 0.04 0.004 0.8 dp 2.25 1.5 32 100

15. Design of Experiment
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Dr. Khaled Ahmed
 Taguchi Design
 Minimum number of experiments.
 Works fine with small number of factors.
 Linear correlation.
 Box-Behnken Design
 Large number of experiments.
 Works fine with up to 7 factors.
 Quadratic correlation.
 Uniform Design
 Offer wide range of number of experiments
 Works fine with large number of factors.
 Quadratic correlation using step regression.
Taguchi
Box-Behnken
Uniform

16. Design of Experiment
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Dr. Khaled Ahmed
 Uniform Design
 Choosing number of experiments
U
27
(3
9
)
U
36
(3
9
)
U
51
(3
9
)
Fang et a., Number-theoretic methods in statistics, CRC Press, 1993.

17. Design of Experiment
17
Dr. Khaled Ahmed
 Uniform Design Tables
Fang et a., Number-theoretic methods in statistics, CRC Press, 1993.
n dp di t S Kp Ks Kt H
Conductance
1/Rp
1 1 1 1 1 1 0 -1 -1 1 7.84
2 0 1 -1 0 1 -1 0 1 1 2.27
3 1 -1 1 1 -1 0 1 0 0 4.64
4 0 -1 1 -1 0 1 -1 -1 -1 3.05
5 -1 0 0 1 1 -1 1 0 1 1.86
6 -1 1 0 1 0 -1 1 1 0 1.38
7 1 0 0 -1 -1 1 1 -1 1 5.17
8 0 0 0 0 0 0 0 0 0 3.22
9 0 0 0 1 1 -1 -1 -1 0 2.93
10 0 1 -1 -1 0 1 1 0 1 2.70
11 0 1 0 1 -1 1 -1 0 -1 1.90
12 0 1 1 0 -1 -1 1 -1 1 2.86
13 1 1 0 1 1 1 0 1 0 5.37
14 0 0 0 0 0 0 0 0 0 3.22
15 -1 0 0 1 -1 0 0 -1 -1 0.96
16 -1 -1 1 0 1 1 1 0 1 3.67
17 1 1 1 0 0 1 0 0 0 6.42
18 0 0 1 1 1 1 1 0 -1 3.10
19 0 -1 0 0 0 0 0 -1 1 4.23
20 1 -1 0 0 -1 -1 -1 0 1 3.12
21 1 0 1 -1 0 -1 0 0 1 5.26
22 -1 0 -1 0 -1 1 1 1 0 1.00
23 1 0 -1 -1 1 1 -1 0 0 3.05
24 -1 0 -1 -1 0 -1 -1 -1 1 1.10
25 -1 1 1 0 1 -1 -1 0 -1 1.25
26 -1 0 1 1 0 1 -1 1 1 3.31
27 -1 1 -1 0 1 1 0 -1 -1 0.55

18. Results & Discussion
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Dr. Khaled Ahmed
 Signal to Noise Ratio
𝑆 𝑁 = −10 log10
1
𝑚
𝑖=1
𝑚
𝑅𝑝,𝑖
2

19. Results & Discussion
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Dr. Khaled Ahmed
 Cubic Regression
𝑌
= 𝑎0 +
𝑘=1
9
𝑎𝑘𝑥𝑘
+
𝑖=1
9
𝑗=𝑖
9
𝑏𝑖𝑗𝑥𝑖𝑥𝑗
+
𝑖=1
9
𝑗=𝑖
9
𝑘=𝑗
9
𝑐𝑖𝑗𝑘𝑥𝑖𝑥𝑗𝑥𝑘

20. Results & Discussion
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Dr. Khaled Ahmed
 Maximum Conductance
U27(39) U36(39) U51(39) Optimum
Number of Tubes ( n ) +1 +1 0 +1
Pile Diameter ( dp ) -1 +1 -1 -1
Tube Inner Diameter ( di ) +1 0 0 +1
Tube Thickness ( t ) -1 -1 -1 0
Distance between Tubes ( S ) +1 +1 +1 +1
Pile Thermal Conductivity ( Kp ) +1 +1 +1 +1
Ground Thermal Conductivity ( Ks ) -1 0 -1 0
Tube thermal Conductivity ( Kt ) 0 0 +1 +1
Heat Transfer Coefficient ( H ) 0 +1 +1 +1
Energy Pile Thermal Conductance ( Cp ) 24.4 21.33 17.75 34.52

21. Results & Discussion
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Dr. Khaled Ahmed
 Verification & Comparison
Maximum expected
34.52

22. Conclusions
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Dr. Khaled Ahmed
 Defined the optimum condition with the least
number of experiments using uniform design
 Three uniform designs have been tested;
U27(39), U36(39), and U51(39).
 U36(39) has shown acceptable level of error with
significantly low number of experiments….

23. Conclusions
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Dr. Khaled Ahmed
 The maximum energy pile steady state thermal
conductance is achieved with;
 the highest number of U-tubes, (n++).
 largest tube diameter, (di++).
 largest distance between tubes, (S++).
 highest pile thermal conductivity and (Kp++).
 highest heat transfer coefficient (H++).

24. THANKS
ACKNOWLEDGEMENTS
This publication was made possible by grant No. NPRP
7-725-2-270 from the Qatar National Research Fund (a
member of Qatar Foundation). The statements made
herein are solely the responsibility of the authors.