A Novel Method in Investigation of Thermal Energy Storage in Packed Pebble Regenerator by using Design of Experiment

Abstract

A device which is used to transfer thermal energy between two fluids at different temperatures is a heat exchanger. Many engineering processes such as heating, refrigeration, airconditioning systems, power systems, food processing systems, chemical reactors, space and aeronautical applications have heat exchangers in them. Most industrial processes make use of heat exchangers for the purpose of transferring heat and require the process to be monitored. Different heat exchangers are used in many applications, but the most widely sought in energy storage application, is the packed SS pebble bed heat exchanger. In this study, experiments are conducted based on fully replicable five-factor, five-level central composite design. Regressions models are developed in order to analyze the effects of packed pebble bed heat exchange process parameters such as inlet temperatures of hot fluid, velocity of hot and cold fluid along with their effects. The output parameter of such a heat exchangers is used for analyzing the direct and interactive effects of heat transfer exchange parameters.

Full text

A Novel Method in Investigation of Thermal Energy
Storage in Packed Pebble Regenerator
by using Design of Experiment
Benjamin Franklin.S1,a*, Ramesh.K2,b
1Assistant Professor (Sr.Gr), Sri Ramakrishna Institute of Technology,
Coimbatore, India 1franklinshee@yahoo.co.in,
2Assistant Professor (Sr.Gr), Government College of Technology, Coimbatore, India.
Abstract — A device which is used to transfer thermal energy between two fluids at different temperatures is a heat exchanger. Many
engineering processes such as heating, refrigeration, air-conditioning systems, power systems, food processing systems, chemical reactors,
space and aeronautical applications have heat exchangers in them. Most industrial processes make use of heat exchangers for the purpose
of transferring heat and require the process to be monitored. Different heat exchangers are used in many applications, but the most widely
sought in energy storage application, is the packed SS pebble bed heat exchanger. In this study, experiments are conducted based on fully
replicable five-factor, five-level central composite design. Regressions models are developed in order to analyze the effects of packed pebble
bed heat exchange process parameters such as inlet temperatures of hot fluid, velocity of hot and cold fluid along with their effects. The
output parameter of such a heat exchangers is used for analyzing the direct and interactive effects of heat transfer exchange parameters.
Keywords — Packed pebble bed heat exchanger, Stainless Steel pebbles (SS), Energy storage, Design of Experiment
I. INTRODUCTION
This work presents an experimental and design of experiments study of transient heat transfer and flow of fluid through
porous media. The process of heat transfer and fluid flow through porous media is of interest to many applications such as
seperators, dryers, reactors, filters and heat exchangers. The Porous media used in this investigation is packed bed made up of
spheres.[1] Many researchers have taken place for increasing the performance characteristics of heat exchangers. The
Performance of this heat exchanger can be assessed by the overall heat transfer coefficient method but it requires detailed study
geometry of the exchangers.[2] Modeling is a an representation of physical or chemical process by a set of mathematical
relationship that adequately describes the significant process behaviors that can be used for understanding process operations. In
development of such process models, the main objective lies in understanding the process parameters involved and it becomes
the major objective. These models are often used for process design, safety system analysis and process controls.[3] In
experimental studies and engineering applications of thermal science, researchers and engineers intend to reduce experimental
data into one or more simple and more compact dimensionless heat transfer correlations.[4] Also when fluid properties which
depend on the fluid temperature are to be considered, there arises a disadvantage of the correlation methods such as the heat
transfer coefficients which strongly depends on their definitions and temperature differences and inevitably requires iterative
methods to obtain correlations.[5,6] The design experiments in Packed SS Pebble Bed Heat Exchanger are conducted using prior
knowledge to modify several variables and the study is conducted without varying the process parameters and expected to give
best results. A scientific approach involved in planning these experiments lies in analyzing the data by statistical methods and
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objective conclusions.[7] Also validated mathematical models can be developed by Using the result of the experiments to
correlate process parameters along with output response parameters.[8]
These Mathematical models can be used to simulate the heat transfer processes while allowing rapid system optimization
that can used to determine consistently predicting maximum values. [9] When the Reynolds number is increased for a sensible
heat storage system, the heat transfer coefficient increases to a maximum value until it eventually decreases; This can be obtained
with smaller sphere diameters which greatly improvises the heat transfer. In the present work, sensible heat storage system
consisting of a packed pebble bed heat exchanger and SS pebbles has been designed and fabricated for a thermal energy storage
system. These proposed heat exchanger has been fitted to a direct injection diesel engine exhaust with 10% of exhaust gas opened
and it stores thermal energy as sensible heat and is used as a waste heat recovery. The Inlet fluid used for the heat exchanger in
this experiment was compressed air along with diesel engine exhaust gas.
II. EXPERIMENTAL METHODOLOGY
A Packed SS bed heat exchanger was used for storage of thermal energy. A packed bed or porous media (PM) comprises
packing material activated alumina balls, which are randomly dumped and packed with an insulated tube that creates the outer
shell of the rod. The bed is charged by sending hot fluid air in the axial direction and hot fluid of air with engine exhaust gas with
axial direction. In the present study compressed air & diesel engine of 10% exhaust gas is supplied to the heat exchanger with
various velocities (2.5,3.5.4,4.5 and 5 m/s) and compressed air is given to the various velocities. A two stage air compressor with
a speed of 1430 rpm was used for experimental studies. The technical specifications of the multi stage compressor are given
below table 2.
FIGURE 1. Packed SS Pebble Bed Heat Exchanger
TABLE 1. Specification of geometry
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Total length of pipe (L)
550mm
Diameter (D)
45mm
Inlet length
25mm
Length of porous media
450mm
Outlet length
20mm
For porosity : 0.48 and diameter of spheres (d) = 6-10 mm
TABLE 2. Test Compressor Specification
Parameter
Specification
Producer
ELGI
Number of cylinders
3
Number of stages
2
Power
10 Hp
Speed
1430 rpm
Maximum Pressure
12.5 kg/cm2
Tank capacity
420 litres
Pressure switch
Diaphragm automatic
Orifice diameter
1.91 cm
TABLE 3. Process variable parameters
Factor levels
Parameters
Units
Notation
-1.682
-1
0
1
1.682
Velocity
m/s
V
2.5
3.5
4
4.5
5
Surface Temperature
º C
TW
110
108
106
104
100
Time in seconds
Sec
S
900
1800
2700
3600
4500
TABLE 4. Design of Matrix for Packed SS Pebble Bed Heat Exchanger
S. No
V
(m/s)
TW
(°C)
Time (Sec)
m
(kg/s)
Re
Nu
H
(W/m2 K)
∆P
(Pa)
Q
(Watts)
1
-1
-1
-1
0.0063
6809
23.07
16.78
10673.28
20.24
2
1
-1
-1
0.0071
8754
28.21
20.52
16543.584
22.15
3
-1
1
-1
0.0063
6809
23.07
16.45
10673.28
17.75
4
1
1
-1
0.0071
8754
28.21
20.13
16543.584
19.17
5
-1
-1
1
0.0063
6809
23.07
16.78
10673.28
17.04
6
1
-1
1
0.0071
8754
28.16
20.48
16543.584
23.40
7
-1
1
1
0.0063
6809
23.07
16.45
10673.28
16.72
8
1
1
1
0.0071
8754
28.19
20.10
16543.584
17.99
9
-1.682
0
0
0.0045
4420
16.30
11.85
5203.224
22.97
10
1.682
0
0
0.0090
9727
25.68
18.68
18144.576
18.97
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11
0
-1.682
0
0.0072
7782
25.63
19.01
12140.856
19.31
12
0
1.682
0
0.0072
7782
25.66
18.30
12140.856
18.59
13
0
0
-1.682
0.0072
7782
25.68
18.68
12140.856
22.53
14
0
0
1.682
0.0072
7782
25.68
18.68
12140.856
17.18
15
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
16
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
17
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
18
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
19
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
20
0
0
0
0.0072
7782
25.68
18.68
12140.856
18.97
Classical experimental design methods are too complex and are not easy to use A large number of experiments have to be
carried out when the number of process parameters are increased. To solve this problem a special method of central composite
design was developed. Also to ensure that the experimental data can be analyzed in a meaningful way, It becomes necessary to
consider the resources devoted to the experiment .Paying attention to the way in which results are reported is helpful in
identifying whether the objectives have been clearly formulated. The design of experiments deals with the procedure of selecting
number of trials and conditions. A set of representative experiments with regard to a set of input variables were used for running
the DOE. A Common approach used in DOE is to first define the interesting standard reference experiment and then new
representative experiments are performed on it. Here a central composite design quadratic model was employed. For each factors
in the design an imbedded factorial design with central points augmented with a group of star points that represent new existence
values (low and high) are considered. These new experiments are laid out in a symmetrical fashion around the standard reference
experiment. Hence the standard reference experiment is usually called the central point. In factorial design, the experiments are
conducted for all possible combinations.
The table shown below consists of combinations of the parameter levels and these combinations are written in the form of a
table, where the rows corresponds to different trial and the columns corresponds to the levels of the parameters and it forms a
design matrix. The selected design matrix is 4.There are five-level central composite rotatable design consisting of 20 sets of
coded conditions and are composed of a full factorial (23=8) design with a 6 center points and 6 star points. In the matrix , 20
simulation run provides ten estimates for the effect of three parameters.
III. RESULTS AND DISCUSSION\
TABLE 5. Packed SS Pebble Bed Heat Exchanger Experimental Results-1
S. No
Velocity (m/s)
Time sec
Temperature(ºC)
1
2.5
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
900
63
62
65
62
61
59
58
57
55
53
1800
84
83
86
81
81
78
74
74
71
69
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2700
99
98
102
91
96
91
88
86
85
81
3600
104
103
106
100
98
96
94
94
91
86
2
3.5
900
60
58
61
54
54
50
47
46
45
41
1800
81
80
81
79
80
78
74
72
71
64
2700
94
95
98
95
94
87
85
89
86
80
3600
101
101
104
99
99
96
93
97
91
85
3
4
900
58
56
59
52
51
50
46
45
41
39
1800
77
75
80
75
74
72
71
68
67
62
2700
91
89
95
88
86
85
82
81
79
75
3600
99
98
102
96
95
92
89
86
85
81
TABLE 6 Packed SS Pebble Bed Heat Exchanger Experimental Results-2
S. No
Velocity
(m/s)
Time
(Sec)
Temperature (ºC)
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
1
4.5
900
57
55
58
51
51
50
45
44
40
38
1800
76
74
79
74
73
71
70
67
66
61
2700
90
88
94
87
85
84
81
90
78
74
3600
98
97
101
85
94
91
88
85
84
80
2
5
900
55
54
57
50
50
50
44
43
41
37
1800
75
73
77
73
70
70
69
66
65
60
2700
89
87
93
86
84
83
80
89
77
73
3600
96
96
100
85
93
91
87
84
83
80
The thermal analysis of a packed pebble bed heat exchanger involves the determination of the heat transfer coefficient from
the individual velocity. The response function representing any of the dimensions such as the velocity, surface temperature and
time in seconds can be expressed as
Y = f (V, Tw, T ) (1)
Where Y is the response.
The second order polynomial regression used to represent the response surface for k factor is given
k k k
2
0 i i i i i i j
i 1 i 1 i,j 1
Y b b x b x b x x
  
   
  
(2)
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expressed as
Y = b0+b1V+ b2 TW+ b3 T + b11 (V) 2+ b22 (TW) 2 + b33 (T)2 + b12V TW + b13V T+ b23 TW T (3)
Where b0 is the free term of the regression equation. The coefficients b11, b22 - b33 are quadratic terms and the coefficients b12, b13 -
b23 are the interaction terms.
Conformity test
Also accuracy of the regression models were determined by conducting conformity test using the same system. In this procedure
the process variables were assigned with intermediate values to carry out the conformity test runs and the responses were
measured. The results shows that the regression models are accurate.
TABLE 7. Analysis of Variance for testing the Adequacy of Models
Parameters
Sum of Squares
Degree of freedom
Standard
F ratio
F ratio
Remarks
Regression
Residual
Regression
Residual
U
2.54
0.846
12
21
2.32
5.554
Adequate
TW
106.43
35.47
12
21
2.32
7.061
Adequate
S
1700
566.67
7
26
3.5
20.812
Adequate
TABLE 8. Comparisons of R2 values and standard Error of estimations for full and reduced models.
Parameter
Adjusted R2 Values
Standard error of estimate
Regression
Residual
Regression
Residual
U
0.426
0.617
0.298
0.241
TW
0.612
0.683
0.145
0.130
S
0.712
0.790
0.721
0.615
TABLE 9. Results of conformity Experiments
S.
No
Parameter
Measured values
Predicted value
V
TM
Time
m
Re
Nu
h
Q
∆P
m
Re
Nu
h
Q
∆P
1
3.5
108
1800
0.006
6711
23.0
16.6
19.95
10640
0.0063
6809
23.07
16.78
20.24
10673.28
2
4
106
2700
0.007
7710
25.2
18.9
19.0
12130
0.0072
7782
25.63
19.01
19.31
12140.85
3
5
100
4500
0.008
9701
25.0
18
18.1
18130
0.0090
9727
25.68
18.30
18.97
18144.57
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TABLE 10. % of error
S.No
Parameters
% Of error
U
TM
S
m
Re
Nu
h
Q
∆P
1
3.5
108
1800
4.76
1.43
0.30
1.07
1.43
0.31
2
4
106
2700
2.77
0.92
1.61
0.57
1.60
0.08
3
5
100
4500
10
0.26
2.64
1.6
4.58
0.08
95
100
105
110
0 2 4 6
Tw
V
V vs Tw
Tw
FIGURE 2. Velocity vs. Surface temperature
FIGURE 3. Velocity vs. Mass flow rate
FIGURE 4. Velocity vs. Reynolds Number
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FIGURE 5. Velocity vs. Nusselt Number
FIGURE 6. Velocity vs. Heat transfer coefficient
FIGURE 7. Velocity vs. Heat transfer coefficient
FIGURE 8. Velocity vs. Pressure Drop
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In Figure 2, It can be noted that the Velocity of the compressed air increases as the porous media temperature of the
packed bed decreases. In Figure 3, as the compressed air velocity increases, the predicted value of mass flow rate also increases
up to 10 %. In Figure 4, the compressed air velocity increases along with increase in the Reynolds number and flow becomes
turbulent. In Figure 5, As the compressed air velocity increases, the Nusselt number predicts a value of error up to a maximum of
2.64%. In Figure 6, As the compressed air velocity increases, the measured value of heat transfer coefficient decreases. In Figure
7, As the compressed air velocity increases, heat transfer rate also increases along with the predicted value. In Figure 8, As the
velocity of air increases, a maximum pressure drop of 0.31% of error is obtained.
Abbreviations
h - Heat transfer coefficient
Q - Heat transfer rate
m - Mass flow rate
Nu - Nusselt number
PM - Porous media
∆P - Pressure drop
Re - Reynolds number
S - Seconds
SS - Stainless steel
Tw - Surface temperature
V - Velocity
IV CONCLUSION
From the experiment, it was concluded that the inlet temperature of the hot fluid has a great impact on the heat transfer rate.
As the inlet temperature of the hot fluid increases, the heat transfer rate also increases drastically.The inlet temperature of the hot
fluid does not have any impact on pressure drop.Also as the Velocity of the compressed air increases the temperature of the
porous media decreases.
As the compressed air velocity increases, The predicted value of mass flow rate increases up to 10 % along with a increase
in the Reynolds number and the flow becomes turbulent. The Nusselt number is predicted with a value of error of maximum
2.64%. The measured value of heat transfer coefficient decreases. Heat transfer rate increase in the predicted value. A maximum
pressure drop of 0.31% of error is measured .The novelty of the research work is the recovery of waste heat using packed SS
pebble bed heat exchanger.
ACKNOWLEDGEMENT
The authors wish to thank the Laboratory in Department of Mechanical Engineering, Government College of Technology,
Coimbatore, India for providing facilities and support to execute the research work.
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REFERENCES
[1] Abid Hussanan,Mohd Z Salleh, Ilyas khan, Razman M Tahar & Zulkhibri Ismail 2015. Soret effects on unstea magneto hydrodynamic mixed convection
heat-and-mass transfer flow in a porous medium with Newtonian heating. Maejo Int. J. Sci. Technol. 9: 224,doi: 10.14456/ mijst.2015.17.
[2] Grujlcic, M., Zhao, C.I., Biggers, S.B., Kennedy, I.M. & Morgan, D.R. 2005, Heat transfer and effective thermal conductivity analyses in carbon-based
foams for use in thermal protection systems. Materials design and applications, 219, 1.
[3] Hafiz Muhammad Ali, Muhammad Danish Azhar, Musab Saleem, Qazi Samie Saeed & Ahmed Saieed 2005, Heat transfer enhancement of car radiator
using aqua based magnesium oxide. Thermal Science, 19: 2039.
[4] Krishnamurthy Sairam, Anantharaman Gopinath & Ramalingam Velraj 2015. Environmental emissions and efficiency of a direct injection diesel engine
fueled with various fatty acid methyl esters. Environment Protection Engineering, 41: 125, DOI:10.5277epe150110.
[15] Mohammad Mehdi Rashidi & Navid Freidooni Mehr 2014. Series solutions for the flow in the vicinity of the equations of an magneto hydrodynamic
boundary layer over a porous rotating sphere with heat transfer. Journal of Thermal Science, 18: 527, DOI 10.2298/TSCI120301155R.
[6] Navid Feroze, Tabassum Naz Sindhu, Muhammad Aslam & Wasif Yaseen 2015. Doubly censored mixture of two Rayleigh distributions. Maejo
International Journal of Science and Technology, 9: 312, doi: 10.14456/ mijst.2015.24.
[7] Singh, K.D. & Rana, S.K. 1992. Three dimensional flow and heat transfer through a porous medium, Indian Journal of pure Appl. Math, 23: 905.
[8] Singh, K.D. & Rana, S.K. 1999. Three dimensional flow and heat transfer through a porous medium. Indian Journal Pure Applied Mathematics, 23: 905.
[9] Takashi Mawatari & Hideo Mori 2016. An experimental study on characteristics of post-CHF heat transfer in the high sub critical pressure in the region
near to the critical pressure, Journal of Thermal science and Technology. 11(1).
[10] Xianke Meng, Zhongning Sun & Guangzhan Xu 2012. Single phase convection heat transfer characteristics of pebble – bed channels with internal heat
generation. Nuclear Engineering and Design, 252: 121.
[11] Pandiyarajan.V,Chinna Pandian.M,Malan.E,Velraj.E,Seeniraj.R.V 2011’Experimental investigation on heat recovery from diesel engine exhaust using
finned shell and tube heat exchanger and thermal storage system’, Applied Energy,Vol.88,pp. 77-87.
[12] Colas Hasse, Manuel Grenet,Andre Bontemps,Remi Dendievel,Habert Sallee 2011 ‘Realization,test and modeling of honeycomb wallboards containing a
Phase Chase Material’,Energy and Buidings,Vol.43,pp.232-238.
[13] Elisabeth Schroder,Andrews Class,Lambert Kerbs 2006’Measurements of heat transfer between particles and gas in packed beds at low to medium
Reynolds numbers’, Experimental Thermal and Fluid Science,Vol.30,pp545-558.
[14] Buonanno,Carotenuto.A,Giovinco.G,Massarotti N 2003 ‘Experimental and Theoretical Modeling of the Effective Thermal Conductivity of Rough Steel
Spheroid Packed Beds’, Journal of Heat Transfer,Vol.125,pp.693-702.
[15] Franck Pra,Patrice Tochon,Christian Mauget,Jan Fokkens,Sander Willemsen 2008 ‘Promising designs of compact heat exchangers for modular HTRs using
the Brayton cycle’,Nuclear Engineering and Design, Vol. 238,pp.3160-3173.
[16] Ali Abou-Sena,Alice Ying,Mohamed Abdou 2007 ‘Experimental Measurements of the Effective Thermal Conductivity of a Lithium Titanate (Li2TiO3)
pebbles – packed bed’,Journal of Mechanical Processing Technology,Vol..181.pp206 -212.
[17] Alshare.A.A,Strykowski.P.J,Simon.T.M 2010 ‘Modeling of unsteady and steady fluid flow, heat transfer and dispersion in porous media using unit cell
scale’ International Journal of Heat and Mass Transfer’,Vol.53.pp2294 -2310.
[18] Al-Juwayhel.F,El-Reface.M.M 1998 ‘Thermal performance of a combined packed bed-solar pond system – a numerical study’ Applied Thermal
Engineering,Vol.18.pp1207-1223.
[19] Rimkevicius.S,Uspuras.E 2008 ‘Experimental Investigation of Pebble Beds Hydraulic Characteristics’ Nuclear Engineering and Design,Vol.238.pp.940-
944.
[20] Srinivasan.R,Raghunandan.R.N, 2013 ‘Experiments on thermal response of low aspect ratio packed beds at high Reynolds numbers with varying inflow
temperature’ Experimental Thermal and Fluid Science,Vol.44.pp.323-333.
ISSN: 1748-0345 (Online)
© 2018 SWANSEA PRINTING TECHNOLOGY LTD
www.tagajournal.com
TAGA JOURNAL VOL. 14813

[21] Chris.H.Rycroft,Abdel Dehbi,Terttaliisa Lind,Salih Guntay 2013 ‘Granular flow in pebble-bed nuclear reactors: Scaling,Dust generation and stress’
Nuclear Engineering and Design,Vol.265.pp .69-84.
[22] Balamurugan.S,Salomon.D.P 2014 ‘Investigation of shell and tube heat exchangers by using a design of experiment’, Journal of Heat and Mass Transfer
Research,Vol.1.pp.59-66.
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