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Computer-Aided Design & Applications, PACE (1), 2011, 77-86© 2011 CAD Solutions, LLC, http://www.cadanda.com

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Incorporation of Variations in Simulation Softwares to Better Predict RealLife Scenarios - Natural Convection: a Case Study

Shrutakeerti M V1, Varun B Rao2, Vishwas B Pai3 and Royston Fernandes4

1 PES Institute of Technology, Bangalore, India, [email protected] PES Institute of Technology, Bangalore, India, [email protected] PES Institute of Technology, Bangalore, India, [email protected]

4 PES Institute of Technology, Bangalore, India, [email protected]

ABSTRACT

This paper first compares results obtained by simulation of natural convection from aflat plate for different orientations with theoretical results, to understand simulationprocedures. It further compares experiments and simulations of natural convectiveheat transfer from a cylinder for different orientations of the cylinder, to verify theaccuracy of the simulation. Plausible reasons for the variances between the resultsobtained have been analyzed and presented and improvements in simulationprocedures are explored.

Keywords: simulation, experimentation, ANSYS Fluent, natural convection.DOI: 10.3722/cadaps.2011.PACE.77-86

1 INTRODUCTION

Natural convection occurs when fluid motion set up is due to buoyancy effects resulting from densitydifference caused due to a temperature difference in the fluid. Experimentation usually consumes a lotof resources and time. As an alternative to this, simulation is used as a method of analyzing problems.But there is always a disconnect between experimental results and results obtained by simulation. Inorder to further explore this disconnect, a case study of natural convection is selected to be analyzedusing both methodologies.

1.1 Simulation Setup Details – Flat Plate

The flat plate which is 300mm x 300mm x 20mm is modeled. Simulation is carried out at threeorientations: Vertical, horizontal and at a 45o inclination. Natural convection from the plate is observedat four operating temperatures: 400K, 500K, 550K and 600K. Surrounding ambient temperature in allcases is set to be 300K.

1.2 Experimental Setup – Cylinder

The rig consists of a hollow cylinder (commercial oxidized copper) which is heated from the inside byan electric heater so that the outer surface gives out a uniform heat flux. The experiment was


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conducted for five orientations of the cylinder – horizontal, vertical and inclined at 30o, 45o and 60o tothe vertical. The heat input to the cylinder is varied by varying the voltage and current passing througha resistive element in the cylinder. The temperatures at specific points on the cylinder are measuredthrough nine thermocouples embedded at equidistant points in the cylinder. This gives us nine datapoints for analysis per heat flux. Thus providing us with forty five data points per orientation upontaking five different heat flux inputs. This should give us sufficient data to obtain a correlation.However, in the case when the cylinder is horizontal, owing to the orientation, we can obtain only fivedata points i.e. one data point per heat input, since all the thermocouples read approximately the sametemperature.

Some assumptions made during calculations were:• Air is a perfect gas (β = 1/T)• There is no heat loss from the side faces of the cylinder.• Emissivity of the cylinder is constant and is equal to 0.65 (commercial oxidized copper).• External influences (like drafts of air in the room) are negligible.

Fig. 1: Schematic of the Experimental Setup a) Vertical Orientation b) Horizontal Orientation c) InclinedOrientation (θ degrees to the vertical).

θ


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1.3 Simulation Setup – Cylinder

The simulation consists of two enclosures one inside the other as shown. The inner enclosure acts asthe cylinder geometry. The outer enclosure serves as the atmosphere. The space in between that ismeshed is the air. The size of the outer enclosure is taken to be sufficiently large in order to minimizeinternal flow effects. However, the iteration time due to a large mesh is a deterrent. We have thus takenan optimum size such that accuracy is not compromised and the iteration time is reasonable.The geometries for the cylinder and flat plate are similar and the difference lies in the setting of thethickness parameter on FLUENT. The flat plate has its third dimension as the thickness parameterwhereas the cylinder has its thickness parameter set to an insignificant value – corresponding to across-section of the physical model.

Some considerations made during simulation:• A density based solver was used.• Heat Flux boundary conditions at the ends of the cylinder was set to zero. (In order to account

for the insulation present at the ends of the cylinder, in the experimental setup)• The cylinder material was selected as Copper.• Radiative Heat Flux was set to zero.• Variation of thermodynamic properties were treated as a piecewise linear approximation with

eighteen control points between the working temperatures of 20oC and 400oC

Fig. 2: Schematic of the Simulation Setup a) Vertical Orientation b) Horizontal Orientation c) InclinedOrientation (θ degrees to the vertical).


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1.4 Methodology Employed

1.4.1 Experimental Procedure

The cylinder was aligned to the required orientation and the heat input was set. The setup was leftundisturbed for two hours to let steady state natural convection to be established. Temperatures at thenine thermocouple locations were noted down. Nusselt and Rayleigh numbers were calculated for eachjunction. The experiment was repeated for different values of heat input. All the values of Nusselt andRayleigh numbers are tabulated and their correlation is calculated by the method of least squares.

1.4.2 Simulation Procedure

The setup was modeled as shown in Figure 2, with the outer rectangle representing the enclosure andthe inner rectangle representing the cylinder. The region between the cylinder and the enclosure(representing the air) was discretized into a fine mesh. Thermodynamic property values were enteredas a piecewise linear approximation into the simulator. All boundary conditions were set as describedin the Figure 2. Solution was initialized and 3000 iterations were run. The different property contours,graphs and charts were recorded. The Nusselt and Rayleigh numbers were calculated from thesimulation results and compared with experimental correlations, in order to verify accuracy ofsimulation.

2 RESULTS

2.1 Flat Plate – Results and comparisons

2.1.1 Plate Inclined Vertically

The correlation calculated after simulation was: Nux= 0.3012(Ra

x) 0.233

The standard correlation (Vliet and Liu) is: Nux= 0.6(Ra

x) 0.2

2.1.2 Plate Inclined Horizontally


x) 0.2622

The standard correlation (McAdams) is: Nux= 0.27(Ra

x) 0.25

2.1.3 Plate Inclined at 45o to the vertical


x)0.21

The standard correlation (McAdams) is: Nux= 0.27(Ra

x

*)0.25

Plate Temperature(K) and Average Heat Transfer Coefficient(h)

Orientations 400K 500K 550K 600K%

Deviation

havg

(obs)

havg

(theo)

havg

(obs)

havg

(theo)

havg

(obs)

havg

(theo)

havg

(obs)

havg

(theo)

VERTICAL 7.808 6.28 8.76 7.049 9.24 7.44 10.04 8.08 19.6

HORIZONTAL 7.115 7.12 8.027 7.99 8.47 8.44 9.2 9.16 0.44

INCLINED (45deg) 4.34 3.67 4.87 4.12 5.14 4.35 5.58 4.73 15.3

Tab. 1: Comparison of simulation and theoretical results for the flat plate.


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2.2 Cylinder – Results

2.2.1 Cylinder Inclined Vertically

The correlation calculated after experimentation was: Num

= 0.6775 [RaL

*] 0.207

The correlation calculated after simulation was: Num

= 0.4155 [RaL

*] 0.207

2.2.2 Cylinder Inclined at 45⁰ to the Vertical


= 0.9745 [RaL

*] 0.186


= 0.707 [RaL

*] 0.186



= 1.135 [RaL

*] 0.175


= 0.975 [RaL

*] 0.175



= 0.7589 [RaL

*] 0.197


= 0.4797 [RaL

*] 0.197

2.2.5 Cylinder Inclined Horizontally

Since there were insufficient number of data points to form a correlation, Rayleigh numbers obtainedby experimentation and simulation are directly compared with each other.

2.3 Cylinder – Comparisons

2.3.1 Horizontal Comparisons

Rad

(Fluent) Rad

(Expt) % Deviation

523142.02 431480.40 21.24

532988.48 433243.21 23.02

566959.12 476617.62 18.95

437515.03 363173.96 20.47

481606.29 399356.24 20.60

Tab. 2: Percentage Deviations for Horizontal Orientation.

2.3.2 Vertical and inclined comparisons

Orientation Num

Expt RaLExpt Nu

mFluent Ra

LFluent % Deviation

Vertical 95.20 2.37E+10 73.13 7E+10 -23.15

45O 90.49 3.8E+10 71.70 6.1E+10 -20.76

60O* 89.55 3.3E+10 64.00 6.1E+10 -28.52

30O* 77.34 3E+10 72.62 5.5E+10 -6.09

Tab. 3: Percentage Deviations for Vertical and Inclined Orientations.


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Graph 1: Ln(Nu) vs Ln(Ra) Plots for all the orientations along with their correlationsTotal number of data points = 45*8 = 360.

Note: The individual points represent an actual data point obtained by simulation or experimentation.The lines of best fit represent their respective local correlations

2.4 Contour Plots of the Simulations

2.4.1 Flat Plate

Fig. 3: Contour Plots of Temperature for different orientations. (a) Vertical, (b) Horizontal, (c) 45o tovertical.


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2.4.2 Cylinder

Fig. 4: Contour Plots of velocity for different orientations. (a) Vertical, (b) Horizontal, (c) 30o degrees tovertical, (d) 45o to vertical, (e) 60o to vertical.


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3 ANALYSIS OF RESULTS

As can be seen from the comparisons, the Nusselt numbers predicted by the correlation obtained bysimulation is lower than their experimental counterpart, for all inclinations. This incongruity may beexplained by the following reasons: As can be seen from the contour plots, internal flow effects can never be fully eliminated.

Slight drafts of air in the experimental environment can cause variations.

In the experimental setup, emissivity of the cylinder may not be constant all along the cylinder due

to continuous usage.

In the experimental setup, the end insulations might not be completely effective.

In the experimental setup, heat is transferred from the heater at the center of the cylinder to the

surface of the cylinder through conduction. The temperature drop because of this has not been

accounted for in the simulations.

Radiative effects which have been considered in the experimental calculations have been

eliminated in the simulation by assuming all the heat lost to be convective in nature.

3.1 Possible Solutions

In order to minimize the effect of the previously discussed disparities, the following solutions havebeen proposed.

Internal Flow Effects.

In order to simulate natural convection perfectly, the air surrounding the cylinder must extend

infinitely in all sides. This, however, is impossible. Increasing the size of the outer enclosure

greatly increases computational time and requires a greater computational capability, in terms

of hardware. Changing the outer enclosure type from a static wall (to moving wall, outflow,

outlet-vent and pressure-outlet) yielded no positive results.

Drafts of air.

ANSYS Fluent has no option to include random, inevitable factors occurring in the

experimental scenario such as drafts of air. These inevitable environmental factors cannot be

ignored when dealing with simulations involving real-life projects. For example, in the

structural analysis of a building, the building should be analyzed for gales and pulsating

shockwaves due to an earthquake. By including an option to incorporate random

environmental effects based on the type of simulation (Structural, Thermal, Electrical) ANSYS

simulations will attain a new degree of realism.

Varying Emissivity.

An option to include the varying emissivity of the cylinder might increase the accuracy of the

results obtained.

Ineffective End Insulations.

Instead of setting the heat flux boundary condition to zero in the simulation set up, one can

measure the surface temperature of the insulating material in the experimental set up and

incorporate it accordingly in the simulation.

Temperature Drop due to Conduction.

Conducting materials such as packed steel wool or copper powder is hard to model on Fluent.

An option to account for this, by researching the temperature drop due to conduction across

these materials, can be provided.


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Radiative Effects.

From among all the obtained correlations, the correlation with the highest deviation was found

to be the one at 60o to the vertical. After choosing this scenario for further analysis, two

alternate simulation methodologies were experimented with.

Scenario 1: Existing scenario, with radiative effects set to zero.

Scenario 2: In the experimental setup, we find that temperature varies along the length of the

cylinder. The implication being that, radiative losses also increase gradually from the lowest

point to the highest point on the cylinder. In order to account for this, the walls of the cylinder

were split into nine parts. And each part was assigned with its individual convective heat flux

value, after deducting the estimated radiative losses.

Scenario 3: The Discrete Radiation Transfer Model (DTRM) option on Fluent was used.

The comparison of results obtained has been shown below.

Char. Length(m)

Experimental ValuesT (oC) h (W/m2K)

Scenario 1 ValuesT (oC) h (W/m2K)



0.05 85.80 8.47 98.75 3.80 82.18 3.43 78.76 6.25

0.10 91.20 7.07 104.56 3.58 85.08 3.13 77.93 6.39

0.15 94.90 6.24 109.29 3.37 85.68 2.85 79.80 6.15

0.20 99.50 5.31 114.16 3.25 86.20 2.60 81.42 6.00

0.25 102.30 4.80 113.62 3.26 86.54 2.49 81.17 6.01

0.30 103.80 4.54 112.00 3.25 86.75 2.37 81.35 6.02

0.35 105.70 4.22 116.46 3.17 86.42 2.40 82.68 5.87

0.40 104.80 4.37 117.20 3.14 85.94 2.46 82.00 5.84

0.45 103.30 4.62 102.54 3.69 75.70 2.85 77.90 6.35

Tab. 4: Results yielded from three different radiation simulation scenarios.

As can be seen from the results shown above, the DTRM method is the most accurate forpredicting heat transfer coefficient values. Hence a Nusselt number comparison will yield lowdeviations. However, Rayleigh number comparisons will not be contiguous, because temperaturevalues are not comparable. Hence there is a need for a more effective method to incorporateradiative effects into simulations.

4 CONCLUSION

Accurate prediction of the behavior of real-life scenarios, using simulations is crucial sinceexperimentation is not always feasible. By using natural convection as a case study, we have obtainedinsights into the crucial aspects about the methodology involved in simulation, thereby providing aground for improvement in simulation techniques.

5 REFERENCES

[1] Özişik, N. M.: Heat Transfer: A Basic Approach (Mc.Graw Hill) 1985


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[2] Lienhard J. V.: A Heat Transfer Textbook (Phlogiston Press) 2006[3] Incropera F.P.; Dewitt D. P.: Fundamentals of Heat and Mass Transfer, (John Wiley and Sons) 2006[4] Cornell Fluent Learning Modules

https://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Modules

6 APPENDIX

Nomenclature

Nux

: Local Nusselt Number

Rax

: Local Rayleigh Number

havg

(obs) : Average Heat Transfer Coefficient (Observed)

havg

(theo) : Average Heat Transfer Coefficient (Theoretical)

Num

: Mean Nusselt Number

RaL

* : Modified Rayleigh Number at the largest value of Characteristic Length

Rad

: Rayleigh Number with the diameter of the cylinder as the Characteristic Length

RaL

: Rayleigh Number at the largest value of Characteristic Length

T : Local temperature at the corresponding Characteristic Lengthh : Local Heat Transfer Coefficient at the corresponding Characteristic Length

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