Implementation and Validation Open Source Code CFD Software for the Convection Heat Transfer Kittipos Loksupapaiboon Department of Mechanical Engineering, Faculty of
Chakrit Suvanjumrat
Engineering, Mahidol University Salaya, Nakorn Pathom, 73170, Thailand Tel: (66) 2-889-2138 Country Code: +66
Department of Mechanical Engineering, Faculty of Engineering, Mahidol University Salaya, Nakorn Pathom, 73170, Thailand Tel: (66) 2-889-2138 Country Code: +66
Email:
[email protected]
Email:
[email protected]
ABSTRACT The open source code software (OpenFOAM) was applied to simulate the convection heat transfer between the fresh air flow and a hot tube. The turbulence model was implemented to simulate the convection flow. The SIMPLE algorithm and Upwind method were used to solve the governing equations of the cross flow past a hot tube. Particularly, the computational fluid dynamics (CFD) results were compared with the experimental data of heat transfer by using the P3210 heat transfer bench of Cussons technology. The velocity of fresh air had been adjusted to vary between 5 and 20 m/s meanwhile the heat tube was improved to control temperature between 100 and 200 °C. The comparison between CFD model and physical experiments was in good agreement. The average error of CFD model obtained 4.12 % when compared with experimental data.
CCS Concepts • Computing analysis
methodologies → Model
development
and
simulations such as the water flow inside flumes [3], the water flow into the water heater [4] and jet flame simulation [5, 6] had been applied by using OpenFOAM. The flow past a hot tube is a simple case to study the convection heat transfer flow as a primary study of hot air distribution into the convection oven. Therefore, the validation of the open source software was less affected by experimental apparatus than otherwise. In this research, the OpenFOAM software was applied to study the convection heat transfer of the flow past a hot tube. The application of the study case will be used to design convection system of the rubber glove oven in a future work.
2. TURBULENCE MODEL The turbulent flow was considered in this research and was governed by conservative of mass, momentum and energy equation, respectively. ̅) = 0 𝑑𝑖𝑣(𝑼 𝜕𝑢̅𝑖 ̅) = + 𝑑𝑖𝑣(𝑢̅𝑖 𝑼 𝜕𝑡
Keywords “Simulation; cross flow; hot tube; open source cede; CFD”
1. INTRODUCTION A convection oven is a good economy to bake rubber gloves. The flow past a heater phenomenon always is investigated to control hot air flow into ovens. The simulation method is essential for studying this phenomenon before designing and constructing of the convection oven. The CFD is the flow simulation method which referred to estimate the hot air distribution and reduce an expensive cost and consuming time by trial and error. The commercial software such as ANSYS was used for simulation of the hot air distribution into the convection oven [1]. Unfortunately, this software usually has the expensive license cost and closed to applied codes for desirable cases. The open source code software (OSS) is flexible to develop and apply CFD codes for any flow simulations. OpenFOAM is one of OSS which used for CFD simulation under GNU license without cost [2]. The CFD Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from
[email protected]. ICIME 2016, November 02-05, 2016, Istanbul, Turkey © 2016 ACM. ISBN 978-1-4503-4761-7/16/11…$15.00
DOI: http://dx.doi.org/10.1145/3012258.3012271
(1)
1 𝜕𝑝 ̅) + 𝑑𝑖𝑣(𝑔𝑟𝑎𝑑𝑼 𝜌 𝜕𝑥𝑖 ′ 𝑢′ ) ̅̅̅̅̅̅̅ 𝜕(𝑢 𝑖 𝑗 ( ) 𝜕𝑥𝑖
𝜕𝑇̅ 1 𝜇 𝜇 ̅ ) = 𝑑𝑖𝑣 ( ( + 𝑡 ) 𝑔𝑟𝑎𝑑𝑇̅) + ̅̅̅ + 𝑑𝑖𝑣(𝑇̅𝑼 𝑆𝑇 𝜕𝑡 𝜌 𝜎 𝜎𝑇
(2)
(3)
̅ is time average velocity, 𝜎𝑇 is turbulent Prandtl where 𝑼 ̅̅̅𝑇 is source term and the Reynolds stress is number, 𝑆 written by: 2 ̅̅̅̅̅̅̅ 𝑢′ 𝑖 𝑢′𝑗 = 𝛿𝑖𝑗 3
𝜇𝑡 𝜕𝑈𝑖 𝜕𝑈𝑗 ( + ) 𝜌 𝜕𝑥𝑗 𝜕𝑥𝑖
(4)
The turbulence viscosity is given by: 2
(5)
𝜇𝑡 = 𝜌𝐶𝜇
where is turbulent kinetic energy, turbulent kinetic energy dissipation. The
is the rate of
model can be written as follow: 𝜕𝜌 𝜇 ̅ ) = 𝑑𝑖𝑣 ((𝜇 + 𝑡 ) 𝑔𝑟𝑎𝑑 ) 𝑡 + 𝑑𝑖𝑣(𝜌 𝑼 𝜕 𝜎𝑘 +2𝜇𝑡 𝑆𝑖𝑗 · 𝑆𝑖𝑗
𝜌
(6)
𝜕𝜌 𝜇 ̅ ) = 𝑑𝑖𝑣 ((𝜇 + 𝑡 ) 𝑔𝑟𝑎𝑑 ) + 𝑑𝑖𝑣(𝜌 𝑼 𝜕𝑡 𝜎𝜀 2
+𝐶1 2𝜇𝑡 𝑆𝑖𝑗 · 𝑆𝑖𝑗
(7)
𝐶2 𝜌
The constant into the
(9)
where 𝜙 is the general flow variable, 𝑆𝜙̅ is the source term and 𝛤𝜙̅ is the diffusion coefficient.
Where the velocity gradient yields 𝜕𝑈𝑖 𝜕𝑈𝑗 𝑆𝑖𝑗 = ( + ) 𝜕𝑥𝑗 𝜕𝑥𝑖
𝜕𝜙̅𝑖 𝜕(𝜙̅𝑖 ) ̅ ) = 𝛤𝜙̅ + 𝑑𝑖𝑣(𝜙̅𝑖 𝑼 + 𝑆𝜙̅ 𝜕𝑡 𝜕𝑥𝑖
(8)
model are accorded to [7].
3. EXPERIMENT SETUP The P3210 heat transfer bench of Cussons technology is employed to set up the physical experiment (Fig. 1). The heat transfer apparatus composes a rectangular cross section air inlet duct which is welded with a cylindrical air outlet duct. The internal dimensions of a square cross section duct are 145 mm height by 145 mm width, while an internal diameter of the cylindrical duct is 145 mm. The rectangular test section is improved by installation of a hot tube which is an external diameter of 13 mm. The hot tube can be adjusted the maximum temperature to vary from 100C to 450 C. The length of the rectangular duct is 790 mm, while the cylindrical duct is 1,000 mm. A tangential fan is mounted at the end of a cylindrical duct which is capable of adjusting the air velocity rise of 30 m/s. The fresh air will be sucked from an inlet and flow past a hot tube through end of an experimental duct. A measurement instrument is K-type thermocouples which used to record the steady temperatures by a data logger (Hioki: model LR8431-20) at ten points behind a hot tube. The velocity measurement uses a hot wire anemometer (Tenmars: model TM-4001) at two points in front of and nine points behind a hot tube, respectively. To measure the air flow, the hot wire anemometer was inserted into measurement holes at the centre axis of the experimental duct and received the velocity signals. The air temperatures were recorded using the data logger through the thermocouple wire at the same position of the flow measurement. Every the air velocity and temperature point were set air velocities which composed of 5.63, 10.47, 14.60 and 19.51 m/s.
4. CFD MODEL The governing equations in the previous section are written in the general form as:
The steady flow is considered to simulate the convection heat transfer, therefore, the transient term is zero. The governing equation is discretized by the finite volume method with C++ language which has been described in [8]. The 3-D unstructured grid is constructed under the grid independent test for convergent results of the finite volume domain as shown in Fig. 2. Total grids were 428,239. The duct domain with a length of 1.99 m is assigned the boundary conditions composing an inlet, an outlet, no-slip wall and adiabatic wall. The fresh air with the temperature of 28 C flows into the domain and past a hot tube through the outlet. The inlet is assigned a zero gradient pressure while the outlet air is set up by a uniform velocity according to the physical experiment including 5.63 m/s, 10.47 m/s, 14.60 m/s and 19.51 m/s, respectively. The hot tube temperature is also set up by a constant temperature of 100 C and 200 C. Consequently, the air velocity and temperature are investigated by eight simulated cases. The pressure-velocity couple problem in the governing equation is solved by using SIMPLE algorithm. The flow effect is used the Upwind method to reduce the wiggle solution [9]. The probe command will be written to describe velocity and temperature in CFD domain at positions along a duct axis according to the thermocouple and the hot wire anemometer recording, respectively.
5. RESULTS AND DISCUSSION The fresh air was sucked inside the CFD domain caused the air outlet flow. The air velocity increased from inlet to outlet is shown by graphs in Fig. 3. The CFD velocities were in good agreement with physical experiment. The hot tube obstructed flow, therefore, the flow velocity in front of a tube (upwind) was lower than behind a hot tube (downwind). The air flow had a constant velocity inside the cylindrical duct. The CFD velocities at probes had average errors of 4.57%, 5.84%, 5.96% and 6.05% comparing with experimental data under the outlet velocity of 5.63, 10.47, 14.6 and 19.51 m/s, respectively. The fresh air temperature rose up near a hot tube and was cool down when the flow was far from a hot tube. The air temperature
Figure 1. Experiment of the convection heat transfer.
Figure 2. (a) Domain and (b) grid structure for CFD simulation of the cross flow past a hot tube with middle X-Y plane. velocity of air near the duct wall was zero and highest on the axis of duct where a hot tube did not obstruct the air flow. The velocity which was recorded behind and near the hot tube was dropped by the hot tube. The maximum value of temperature is red and the minimum value of temperature is blue (Fig. 5b). The color of temperature changed from red to blue (Fig. 5b) along axis of the duct behind the hot tube caused of the air velocity increasing. The area behind the hot tube was happened the lowest velocity of air flow therefore the heat convection was more effective than the far area from the hot tube.
6. CONCLUSIONS
Figure 3. The air velocity along a duct axis under the outlet flow velocity of 5.63, 10.47, 14.60 and 19.51 m/s. distribution along duct is plotted by graphs as shown in Fig.4. The air temperature was high in the lower velocity zone (behind a hot tube of 0.285 m) and low in the higher velocity zone (downwind far from a hot tube of 1.075 m) caused by the flow speed effect. The CFD temperature result had an agreement with experimental data. The CFD temperature of fresh air flow past a 100 C hot tube had an average error of 1.66%, 2.08%, 2.16% and 1.09% when compared with experimental data under outlet flow velocity of 5.63 m/s, 10.47 m/s, 14.60 m/s and 19.51 m/s, respectively. Meanwhile, the CFD temperature of fresh air flow past a 200 C hot tube had an average error of 1.87%, 4.09%, 4.42% and 4.64% when compared with experimental data under flow velocity of 5.63 m/s, 10.47 m/s, 14.60 m/s and 19.51 m/s, respectively. The air velocity and temperature can illustrate by color contour on a middle X-Y plane as shown in Fig. 5. The maximum value of velocity is red while the minimum value is blue (Fig. 5a). The
The velocity and temperature of air flow past a hot tube were applied by using the open source software, OpenFOAM. The turbulence model was used to govern the convection heat transfer between the fresh air and a hot tube inside ducts. The SIMPLE algorithm and Upwind method were used to solve the governing equation. The accuracy of the CFD was valid by the experimental data. The average error of CFD velocity and temperature were 5.60% and 2.64%, respectively. The CFD code which applied by OpenFOAM will be used to simulate the temperature distribution inside the convection oven in the further work.
7. ACKNOWLEDGEMENTS This research was funded by the Thailand Research Fund (TRF) and W.A. Rubbermate co., ltd. under Research and Researchers for Industries (RRI) Master Scholarship (MSD58I0050). This work was also supported by the 60th year supreme reign of his Majesty King Bhumibol Adulyadej scholarship, granted by the faculty of graduate studies academic year 2014, Mahidol University.
Figure 4. The air temperature along a duct axis under the outlet flow velocity of: (a) 5.63, (b) 10.47, (c) 14.60 and (d) 19.51 m/s.
Figure 5. (a) Air velocity and (b) temperature distribution in X-Y plane of the CFD domain under an outlet flow velocity of 5.63 m/s.
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