 Open Access
 Total Downloads : 278
 Authors : K Siva Satya Mohan, Dr. S. K. Bhatti, K P V K Varma
 Paper ID : IJERTV2IS120058
 Volume & Issue : Volume 02, Issue 12 (December 2013)
 Published (First Online): 06122013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Periodic Simulation for Heat Transfer Applications Using CFD
K Siva Satya Mohan1, Dr. S. K. Bhatti2, K P V K Varma3

Asst Professor, Department of Mechanical Engineering, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad.

Professor, De Department of Mechanical Engineering, Andhra University, Visakhapatnam

Asst Professor, Department of Mechanical Engineering, CMR college of Engineering and Technology, Hyderabad.
Abstract
Many heat transfer applications, such as steam generators in a boiler or air cooling in the coil of an air conditioner, can be modeled in a bank of tubes containing a flowing fluid at one temperature that is immersed in a second fluid in a cross flow at different temperature. Fluids considered in the present study are water and air. Flow is classified as laminar and steady, with Reynolds number between 100600. In the present paper tubes of different diameters and different mass flow rates are considered to examine the optimal flow distribution. The various static pressures, velocities, and temperatures obtained are reported. Further the problem has been subjected to effect of materials used for tubes manufacturing on heat transfer rate. Materials considered are aluminum, copper and alloys. Results show significant variations between aluminum, copper and alloy as tube materials. Results emphasize the utilization of alloys in place of aluminum and copper as tube material serves better heat transfer with most economic way.
Introduction
The geometry and flow features in industrial applications can be repetitive in nature. In such cases, it is possible to analyze the flow system using only the section of geometry or single building. Doing so helps to reduce the computational effort, without compromising the accuracy. The repetition may be either translational as shown in fig.
Figure: Schematic representation of periodic planes
It is easy to see from the above fig. if the entire region consists the large numbers of modulus were used as a calculation domain the required computer storage and time would be truly excessive. A practical alternative is provided by recognizing that, beyond a certain development length, the velocity fields and temperature fields will repeat itself module after module. Therefore, it is possible to calculate the flow and heat transfer directly for typical model.
Model description
Many industrial applications, such as steam generation in a boiler, air cooling in the coil of air conditioner and different type of heat exchangers uses tube banks to accomplish a desired total heat transfer.
The system considered for the present problem, consisted bank of tubes containing a flowing fluid at one temperature that is immersed in a second fluid in cross flow at a different temperature. Both fluids are water, and the flow is classified as laminar and steady, with a Reynolds number of approximately 100.The mass flow rate of cross flow is known, and the model is used to predict the flow and temperature fields
that result from convective heat transfer due to the fluid flowing over tubes.
Figure: Configuration of the physical and computational domain
The figure depicts the frequently used tube banks in staggered arrangements. The situation is characterized by repetition of an identical module shown as transverse tubes. Due to symmetry of the tube bank, and the periodicity of the flow inherent in the tube geometry, only a portion of the geometry will be modeled as two dimensional periods heat flows with symmetry applied to the outer boundaries.
CFD modeling of a periodic model

Creating physical domain and meshing

Creating periodic zones

Set the material properties and imposing boundary conditions

Calculating the solutions using segregated solver.
Modeling details and meshing
Figure: Schematic of the problem
The modeling and meshing package used is GAMBIT. The geometry consists of uniformly spaced tubes with a diameter D which are staggered in the direction of cross flow. Their centers are separated by a distance of 2cm in xdirection and 1 cm in ydirection.
Material properties and boundary conditions
The material properties of working fluid (water) flowing over tube bank at bulk temperature of 300K, are:
= 998.2kg/m3
Âµ = 0.001003kg/ms
Cp = 4182 J/kgk K= 0.6 W/mk
The boundary conditions applied on physical domain are as followed
Boundary 
Assigned as 
Inlet 
Periodic 
Outlet 
Periodic 
Tube walls 
Wall 
Outer walls 
Symmetry 
Table: Boundary conditions assigned in FLUENT
Fluid flow is one of the important characteristic of a tube bank. It is strongly effects the heat transfer process of a periodic domain and its overall performance. In this paper, different mass flow rates at free stream temperature, 300Kwere used and the wall temperature of the tube which was treated as heated section was set at 400K as periodic boundary conditions for each model which are tabulated as follows:
Tube diameter(D) 
Periodic condition 
0.8cm 
m=0.05kg/s,0.10kg/s 
1.0cm 
m=0.05kg/s,0.10kg/s 
1.2cm 
m=0.05kg/s,0.15kg/s 
1.4cm 
m=0.05kg/s,0.15kg/s 
Table: Mass flow rates for different tube diameter
In this present paper three different materials such as aluminum, copper and a alloy are considered for analysis and compared with each other.
Results and Discussions:
The static pressure for different tube diameters and mass flow rate are considered
Fig: static pressure for D=1.0cm and m=0.30 for aluminum as tube material.
Fig: static pressure for D=0.8cm and m=0.05 for copper as tube material.
Fig: static pressure for D=0.8cm and m=0.05 for nickel chromium base super alloy as tube material.
The pressure contours for different tube materials are shown figures. The figures reveal that the static pressure exerted at stagnation point for different tube materials and mass flow rates have significant variations. From the figures it can be conclude that alloy as tube material is best selection as we can see that very low pressure drop in case of alloys.
The static temperatures for different tube diameters and mass flow rate are considered
Fig: static temperature for D=1.0cm and m=0.30 for aluminum as tube material
Fig: static temperature for D=0.8cm and m=0.05 for copper as tube material.
Fig: static temperature for D=0.8cm and m=0.05 for nickel chromium base super alloy as tube material.
The temperature contours for different tube materials are shown figures. It can be seen that higher heat flow rate was obtained from alloy as tube material.
The velocity for different tube diameters and mass flow rate are considered.
Fig: velocity for D=1.0cm and m=0.30 for aluminum as tube material
Fig: velocity for D=0.8cm and m=0.05 for copper as tube material.
Fig: velocity for D=0.8cm and m=0.05 for nickel chromium base super alloy as tube material
The velocity contours for different tube materials are shown figures. If the mass flow rate increases the veocity also increases and narrow stream of maximum velocity fluid is flow through tube bank.
Verification of Results
The maximum velocity magnitude obtained from the simulation is used to calculate the Reynolds number from the following expression,
ReD,max= umaxD/Âµ
With the above ReD,max the nusselt number was calculated using correlation
Nu=C1(C Ren Pr0.33)
The total surface heat flux values obtained from simulation was used to calculate the Nu values at x=0.01 at middle of the first tube which was used to compare with correlation valves. The table presents results generated using different mass flow rates for different tube materials. The results obtained from the simulation were compared to correlation results.
Fig: Nusselt number for D=1.0cm and m=0.30 for aluminum as tube material.
Fig: Nusselt number for D=0.8cm and m=0.05 for copper as tube material
Fig: Nusselt number for D=0.8cm and m=0.05 for nickel chromium base super alloy as tube material
Results comparison
Table. Comparison values of Fluent Vs Correlation of Aluminum tubes 

Diameter(cm) 
Mass Flow Rate(kg/s) 
Max Velocity(m/s) 
ReD 
Pr 
NuD(corr) 
NuDx=0.01 
% Error 
D=0.8 
M=0.05 
0.0115 
91.559 
6.99091 
9.296 
8.278 
0.1095 
M=0.10 
0.0238 
189.488 
6.99091 
13.97 
8.975 
0.3575 

M=0.15 
0.0382 
304.137 
6.99091 
18.20 
8.125 
0.55405 

M=0.20 
0.0512 
407.639 
6.99091 
21.45 
5.675 
0.7356 

M=0.25 
0.0654 
520.690 
6.99091 
24.606 
2.650 
0.8923 

M=0.30 
0.0795 
632.95 
6.99091 
27.449 
4.740 
0.827 

D=1.0 
M=0.05 
0.0095 
94.545 
6.99091 
34.30 
13.336 
0.6114 
M=0.10 
0.0201 
200.03 
6.99091 
14.40 
18.465 
0.2198 

M=0.15 
0.0324 
322.44 
6.99091 
18.81 
23.785 
0.2208 

M=0.20 
0.0425 
422.96 
6.99091 
21.90 
27.082 
0.191 

M=0.25 
0.0593 
590.16 
6.99091 
24.89 
27.750 
0.1027 

M=0.30 
0.0689 
685.70 
6.99091 
28.707 
28.590 
0.00409 

D=1.2 
M=0.05 
0.00752 
89.808 
6.99091 
9.19 
16.150 
0.4305 
M=0.10 
0.01625 
194.066 
6.99091 
14.158 
22.230 
0.36309 

M=0.15 
0.02534 
302.62 
6.99091 
18.15 
24.820 
0.2684 

M=0.20 
0.03675 
438.889 
6.99091 
22.36 
27.120 
0.1755 

M=0.25 
0.04635 
553.53 
6.99091 
25.463 
27.345 
0.0688 

M=0.30 
0.05780 
690.28 
6.99091 
28.814 
27.565 
0.0433 

D=1.4 
M=0.05 
0.006103 
85.033 
6.99091 
8.919 
6.830 
0.234 
M=0.10 
0.0131 
182.522 
6.99091 
13.680 
7.450 
0.455 

M=0.15 
0.0210 
292.593 
6.99091 
17.818 
7.825 
0.560 

M=0.20 
0.0295 
411.023 
6.99091 
21.55 
7.935 
0.631 

M=0.25 
0.0382 
532.240 
6.99091 
24.91 
7.995 
0.679 

M=0.30 
0.0475 
661.817 
6.99091 
28.143 
8.001 
0.750 
Table. Comparison values of Fluent Vs Correlation of Copper tubes 

Diameter(cm) 
Mass Flow Rate(kg/s) 
Max Velocity(m/s) 
ReD 
Pr 
NuD(corr) 
NuDx=0.01 
% Error 
D=0.8 
M=0.05 
0.0103 
82.005 
6.99091 
8.740 
8.12 
0.0709 
M=0.10 
0.0227 
180.730 
6.99091 
13.60 
8.48 
0.3760 

M=0.15 
0.0363 
289.010 
6.99091 
17.69 
7.61 
0.5701 

M=0.20 
0.0512 
417.990 
6.99091 
21.75 
5.02 
0.769 

M=0.25 
0.0682 
542.988 
6.99091 
25.19 
2.532 
0.8995 

M=0.30 
0.0826 
657.637 
6.99091 
28.04 
4.940 
0.823 

D=1.0 
M=0.05 
0.00913 
90.863 
6.99091 
9.256 
13.000 
0.6114 
M=0.10 
0.0199 
198.04 
6.99091 
14.32 
18.245 
0.2151 

M=0.15 
0.0327 
325.43 
6.99091 
17.45 
23.567 
0.2592 

M=0.20 
0.0432 
429.93 
6.99091 
22.10 
27.254 
0.1889 

M=0.25 
0.0515 
512.53 
6.99091 
24.36 
27.895 
0.1256 

M=0.30 
0.0599 
596.133 
6.99091 
26.543 
28.674 
0.0743 

D=1.2 
M=0.05 
0.00783 
93.510 
6.99091 
9.406 
14.150 
0.335 
M=0.10 
0.01656 
197.768 
6.99091 
14.309 
19.532 
0.267 

M=0.15 
0.02534 
302.62 
6.99091 
18.15 
24.820 
0.2684 

M=0.20 
0.0383 
457.4005 
6.99091 
22.883 
27.120 
0.156 

M=0.25 
0.0498 
594.74 
6.99091 
26.508 
28.645 
0.0746 

M=0.30 
0.05245 
626.38 
6.99091 
27.289 
29.565 
0.0769 

D=1.4 
M=0.05 
0.006546 
91.205 
6.99091 
9.276 
6.430 
0.306 
M=0.10 
0.0165 
229.894 
6.99091 
15.567 
7.875 
0.494 

M=0.15 
0.0210 
292.593 
6.99091 
17.818 
7.925 
0.555 

M=0.20 
0.0299 
416.596 
6.99091 
21.717 
7.978 
0.6326 

M=0.25 
0.0395 
550.3535 
6.99091 
25.38 
8.05 
0.682 

M=0.30 
0.0475 
661.817 
6.99091 
28.143 
8.12 
0.711 
Table. Comparison values of Fluent Vs Correlation of NickelChromium base super alloy based tube 

Diameter(cm) 
Mass Flow Rate(kg/s) 
Max Velocity(m/s) 
ReD 
Pr 
NuD(corr) 
NuDx=0.01 
% Error 
D=0.8 
M=0.05 
0.0103 
82.005 
6.99091 
8.740 
8.12 
0.0709 
M=0.10 
0.0227 
180.730 
6.99091 
13.60 
8.48 
0.3760 

M=0.15 
0.0363 
289.010 
6.99091 
17.69 
7.61 
0.5701 

M=0.20 
0.0512 
417.990 
6.99091 
21.75 
5.02 
0.769 

M=0.25 
0.0682 
542.988 
6.99091 
25.19 
2.532 
0.8995 

M=0.30 
0.0826 
657.637 
6.99091 
28.04 
4.940 
0.823 

D=1.0 
M=0.05 
0.00913 
90.863 
6.99091 
9.256 
13.000 
0.6114 
M=0.10 
0.0199 
198.04 
6.99091 
14.32 
18.245 
0.2151 

M=0.15 
0.0327 
325.43 
6.99091 
17.45 
23.567 
0.2592 

M=0.20 
0.0432 
429.93 
6.99091 
22.10 
27.254 
0.1889 

M=0.25 
0.0515 
512.53 
6.99091 
24.36 
27.895 
0.1256 

M=0.30 
0.0599 
596.133 
6.99091 
26.543 
28.674 
0.0743 

D=1.2 
M=0.05 
0.00783 
93.510 
6.99091 
9.406 
14.150 
0.335 
M=0.10 
0.01656 
197.768 
6.99091 
14.309 
19.532 
0.267 

M=0.15 
0.02534 
302.62 
6.99091 
18.15 
24.820 
0.2684 

M=0.20 
0.0383 
457.4005 
6.99091 
22.883 
27.120 
0.156 

M=0.25 
0.0498 
594.74 
6.99091 
26.508 
28.645 
0.0746 

M=0.30 
0.05245 
626.38 
6.99091 
27.289 
29.565 
0.0769 

D=1.4 
M=0.05 
0.006546 
91.205 
6.99091 
9.276 
6.430 
0.306 
M=0.10 
0.0165 
229.894 
6.99091 
15.567 
7.875 
0.494 

M=0.15 
0.0210 
292.593 
6.99091 
17.818 
7.925 
0.555 

M=0.20 
0.0299 
416.596 
6.99091 
21.717 
7.978 
0.6326 

M=0.25 
0.0395 
550.3535 
6.99091 
25.38 
8.05 
0.682 

M=0.30 
0.0475 
661.817 
6.99091 
28.143 
8.12 
0.711 
Conclusion
A TwoDimensional numerical solution of flow and heat transfer in a bank of tubes which is used in industrial applications was carried out. Laminar flow past a bank is numerically simulated in the low Reynolds number regime. Nusselt number variations are obtained and they are correlated with the theoretical values. The effect of mass flow rates on both flow and heat transfer is significant. This is due to the variation of space of the surrounding tubes. It was concluded that 1.0 cm diameter of tubes and
0.30 kg/sec mass flow rate yields optimum results for aluminum as tube material, where as it was 0.8 cm and 0.05 kg/sec mass flow rate in case of copper as tube material. From the above result we can conclude that alloys serves as a better material for tube when compared with copper and aluminum. Flow process has an important effect on heat transfer. An optimal flow distribution can result in high temperature and low pressure drop. From the simulation the optimal flow distribution was found for 0.8 cm diameter and 0.05 kg/sec mass flow rate in case of alloy as tube material. Alloy (Nickel Chromium based) serves as a better material for heat transfer applications with low cost. Further improvements of heat transfer and fluid flow modeling can be possible by modeling three dimensional model and changing the working fluid.
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