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Report

Radiation Models used

· Background Theory

· Numerical Solution Approach and Boundary condition used

· Participating media considerations

· Non-Participating media (air) vs participating media (Flue gases)

Simulation Parameters

· Radiation model specific parameters

· Mesh refinement

· Residual Refinement

· Has your solution converged Why?

Discussion on Results

· Include and discuss plots generated in slides 7 and 8

· Provide explanation for why could the temperature and total surface heat fluxes be the same or different What trends did you expect?

· Comments/suggestions for ANSYS Fluent software

Summary and Suggestions

· Which radiation model(s) can be used to most accurately simulate this problem? Why?

See attached problem statement

Background Theory:

Each Model has 5 steps to solve the problem

· Geometry

· Meshing

· Setup

· Solution

· Result

1st step Geometry

First creating Geometry using Ansys design modeler

Square Cube of 25 mm x 25 mm x 25 mm

2nd Step Meshing

created mesh using meshing software

· Mesh was generated with global mesh size of 0.001 m

· There are 15,625 elements generated in mesh

· Nodes: 17,576 nodes generated in mesh

Assign Problem Parameter and Material Properties

· Create zones

3rd Step Set up

· Launch Fluent

· Make sure you select double precision, display mesh after reading

· Set the solver process to 4

· Start

· Check and report quality

· Set the y-gravitational acceleration= -9.81m/s2

· Assign Problem parameter – Material Properties

· Set up the boundary Conditions

· Wall-Low-X Aluminum wall

· All other walls are insulated

· See attached picture of BC

· Select the which model you want to run

· Set the convergence criteria

· Here is the some of the Convergence Criteria

· Continuity and species=1 thousand

· X, Y, Z Velocity= .1 thousand

· Energy, do-intensity 1 x 10-6m

· As we all know that good convergence criteria means good results

· Initialize for the hybrid initialization

· Set the number of iterations to 500 to 1000 depend on which model you running

· Calculate

Residual Plots for Non-Participating media Air 1st Quadrant- S2S (enclosure Model) 2nd Quadrant –No Radiation (Flow and Convection Only) 3rd Quadrant P1 (Spherical Harmonics Model) 4th Quadrant – DO, DOM (Discrete Ordinate Model) No radiation Model only took 115 Iteration to converged S2S model took around 300 iteration to converged P1 model took around 460 iteration to converged and DOM model took around highest 560 iteration to converged

Similarly Residual Plots for Participating media Flue Gases 1st Quadrant- S2S (enclosure Model) 2nd Quadrant –No Radiation (Flow and Convection Only) 3rd Quadrant P1 (Spherical Harmonics Model) 4th Quadrant – DO, DOM (Discrete Ordinate Model) No radiation Model only took 92 Iteration to converged S2S model took around 335 iteration to converged P1 model took around 465 iteration to converged and DOM model took around highest 570 iteration to converged Do Intensity makes square wave and converged

Step 4 Solution

· Set up/generate plots

· Vertical centerline temperature(K) of the opposing cold wall T(y) at x=25 mm z=12.5mm

· Gas centerline temperature(k) T(x) y=12.5 mm z=12.5mm

· Vertical centerline total surface heat flux (W/m2) at the hot wall q(y) at x=0mm and z=12.5mm

· Vertical centerline total surface heat flux (W/m2) at the opposing cold wall q(y) at x=25mm z=25 mm

· Graph

· This is Vertical Centerline Temperature of Opposing Cold Wall Graph for air

· You can see an enormous difference in no radiation model compared to other radiation model.

· In all radiation model temperature profile behave very close to each other

· S2S and DOM model temperature profile is almost same

· Even air and Flue gases for no radiation model has different profile

· This is Vertical Centerline Temperature of Opposing Cold Wall Graph for Flue gases

·

This is Gas Centerline Temperature of Opposing Cold Wall Graph for air

We can see even difference between air and flue gases even though they are non-participating media

DO model is most accurate model Which is very close temperature profile with S2S model so DO model and S2S model is accurate

This is Gas Centerline Temperature of Opposing Cold Wall Graph for flue gases

This is Vertical Center Total Surface Heat Flux at the wall Graph for air

No radiation model lowest heat flux.

P1 is over predicting near the walls

This is Vertical Center Total Surface Heat Flux at the wall Graph for flue gases

No radiation model lowest heat flux.

P1 is over predicting near the walls

This is Vertical Center Total Surface Heat Flux at the opposing cold wall Graph for air

All the model has Total surface heat flux is negative- all the radiation is leaving from cold wall

It is getting infected and radiated off the medium that surrounding its box.

This is Vertical Center Total Surface Heat Flux at the opposing cold wall Graph for Flue gases

All the model has Total surface heat flux is negative- all the radiation is leaving from cold wall

It is getting infected and radiated off the medium that surrounding its box.

· Set up contour for visuals

· Heat flux contours

Summery:

Air and Flue gases

· Behaves differently when exposed to radiation due to the difference in their thermal properties

· Non-Participating media (Air) -absorption and re-emittance is negligible mostly N2 and O2

· Participating media (Flue gas) -Water vapor and Co2 absorb and re-emit radiation

DO model

· DO model is most accurate for radiation interaction with gases

· DO model is good for wide range of optical thickness

·

S2S model (enclosure model)

· S2S model is good for optically thin problems

· S2S model temp profile and heat flux profile very close to each other

· S2S and Do model is accurate for at least this problem

·

Spherical Harmonic (P1)

· Over predicts scattering of radiation

· Little to no geometry dependence on incident radiation

Vertical Centerline Temperature (K) of the Opposing Cold Wall-Air

Air NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX508.08 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX605.952 XXXXXXXXXX623.904 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX647.16 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX602.4Air S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.91 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.024Air P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.62 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX971.471

Temp (K)

Vertical Centerline Temperature (k)

Air NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX508.08 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX605.952 XXXXXXXXXX623.904 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX647.16 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX602.4Air S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.91 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.024Air P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.62 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX971.471FG NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX693.952 XXXXXXXXXX XXXXXXXXXX704.726706.1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.596 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.13 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.846974.476 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.255 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26986.26986.26986.26986.26986.26986.26 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.61 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX977.351 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Vertical Centerline Temperature (K) of the Opposing Cold Wall-Flue Gases

FG NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX693.952 XXXXXXXXXX XXXXXXXXXX704.726706.1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.596 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.13 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.846974.476 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.255 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26986.26986.26986.26986.26986.26986.26 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.61 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX977.351 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Gas Centerline Temperature(K) - Air

Air NR GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX691.69 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX672.08 XXXXXXXXXXAir S2S GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX988.87 XXXXXXXXXX985.428 XXXXXXXXXX982.678 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir P1 GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX994.726 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX990.88 XXXXXXXXXX989.57 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX987.86 XXXXXXXXXX987.322 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.37 XXXXXXXXXX986.16 XXXXXXXXXXAir DO GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000997.58 XXXXXXXXXX XXXXXXXXXX990.721 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX979.255 XXXXXXXXXX977.73 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.846 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.149 XXXXXXXXXX XXXXXXXXXX

Temp (K)

Gas Centerline Temperature(K) - Flue Gases

FG NR GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX736.31 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX746.274 XXXXXXXXXX XXXXXXXXXX748.54746.649 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000997.74 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX985.99 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.77 XXXXXXXXXX976.12 XXXXXXXXXX975.82 XXXXXXXXXX XXXXXXXXXX976.01 XXXXXXXXXXFG P1 GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX987.29 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26FG DO GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX978.803978.06 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.07 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Vertical Centerline Total Surface Heat Flux at the Hot Wall- Air

Air NR VCL TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX4940.38 XXXXXXXXXX4223.793936.233668.733422.963198.832995.832811.752641.412479.632322.382166.612009.451848.061682.351512.731339.431165.961001.78 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX1306.28 XXXXXXXXXXAir S2S TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21974.86 XXXXXXXXXX5098.845189.015258.325316.485364.025395.615421.085440.95452.075460.145465.455462.465451.695439.695421.455397.745369.945334.865289.195228.785155.07 XXXXXXXXXX5011.411966.41Air P1 TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22205.215379.295264.455223.345204.785194.67 XXXXXXXXXX5184.165181.12 XXXXXXXXXX5177.135175.82 XXXXXXXXXX5174.215173.9151745174.595175.835178.045181.675187.66 XXXXXXXXXX5217.085259.455376.272204.29Air DO TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22014.135061.34 XXXXXXXXXX XXXXXXXXXX5268.065358.875437.95503.885556.765597.035625.515643.065650.415647.995635.855613.635580.715536.335479.885411.095330.31 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX5046.052008.82

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Hot Wall- Flue Gases

FG NR TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX5410.865013.874782.75 XXXXXXXXXX XXXXXXXXXX4159.083949.233741.973536.513331.023123.552913.642701.27 XXXXXXXXXX2266.622045.51824.541609.031407.761235.55 XXXXXXXXXX1091.081225.971685.22 XXXXXXXXXXFG S2S TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22026.15 XXXXXXXXXX5103.88 XXXXXXXXXX5234.255285.775324.55357.135381.335396.335408.985417.285421.615418.855409.75396.225377.955359.655332.725295.35252.85 XXXXXXXXXX5143.215083.285074.262020.22FG P1 TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX5480.875276.88 XXXXXXXXXX5169.43 XXXXXXXXXX5139.7 XXXXXXXXXX5126.785122.925120.095118.075116.715115.96 XXXXXXXXXX5116.465117.96 XXXXXXXXXX XXXXXXXXXX5131.92 XXXXXXXXXX5161.465195.825271.085477.31 XXXXXXXXXXFG DO TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22082.855143.625088.29 XXXXXXXXXX5237.175321.725396.845460.155511.085549.875577.175593.85600.455597.575585.195563.015530.445486.845431.765365.215288.125203.325119.035061.455125.49 XXXXXXXXXX

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Opposing Cold Wall- Air

Air NR VCL TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-332.8 XXXXXXXXXX XXXXXXXXXX-402.82 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-506.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir S2S TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1037.5 XXXXXXXXXX XXXXXXXXXX-1037.2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir P1 TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1035.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Opposing Cold Wall- Flue Gases

FG NR TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-515 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-574.54 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-613 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1 TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1054-1054-1054-1054-1054-1054-1054-1054 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1054-1054-1054-1054-1054-1054-1054-1054 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1034 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1039.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1037.3 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Heat Flux

Radiation of Heat Transfer ProblemNon-Participating mediaAirSurface to Surface(S2S)Enclosure ModelSpherical Harmonics Model(P1)Discrete Ordinates Model(DO,DOM)No Radiation(Flow & Convection Only)Participating mediaFlue GasesSurface to Surface(S2S)Enclosure ModelSpherical Harmonics Model(P1)Discrete Ordinates Model(DO,DOM)No Radiation(Flow & Convection Only)

Radiation of Heat Transfer Problem

Non-Participating media

Air

Surface to Surface

(S2S)

Enclosure Model

Spherical Harmonics Model

(P1)

Discrete Ordinates Model

(DO,DOM)

No Radiation

(Flow & Convection Only)

Participating media

Flue Gases

Surface to Surface

(S2S)

Enclosure Model

Spherical Harmonics Model

(P1)

Discrete Ordinates Model

(DO,DOM)

No Radiation

(Flow & Convection Only)

Radiation Models used

· Background Theory

· Numerical Solution Approach and Boundary condition used

· Participating media considerations

· Non-Participating media (air) vs participating media (Flue gases)

Simulation Parameters

· Radiation model specific parameters

· Mesh refinement

· Residual Refinement

· Has your solution converged Why?

Discussion on Results

· Include and discuss plots generated in slides 7 and 8

· Provide explanation for why could the temperature and total surface heat fluxes be the same or different What trends did you expect?

· Comments/suggestions for ANSYS Fluent software

Summary and Suggestions

· Which radiation model(s) can be used to most accurately simulate this problem? Why?

See attached problem statement

Background Theory:

Each Model has 5 steps to solve the problem

· Geometry

· Meshing

· Setup

· Solution

· Result

1st step Geometry

First creating Geometry using Ansys design modeler

Square Cube of 25 mm x 25 mm x 25 mm

2nd Step Meshing

created mesh using meshing software

· Mesh was generated with global mesh size of 0.001 m

· There are 15,625 elements generated in mesh

· Nodes: 17,576 nodes generated in mesh

Assign Problem Parameter and Material Properties

· Create zones

3rd Step Set up

· Launch Fluent

· Make sure you select double precision, display mesh after reading

· Set the solver process to 4

· Start

· Check and report quality

· Set the y-gravitational acceleration= -9.81m/s2

· Assign Problem parameter – Material Properties

· Set up the boundary Conditions

· Wall-Low-X Aluminum wall

· All other walls are insulated

· See attached picture of BC

· Select the which model you want to run

· Set the convergence criteria

· Here is the some of the Convergence Criteria

· Continuity and species=1 thousand

· X, Y, Z Velocity= .1 thousand

· Energy, do-intensity 1 x 10-6m

· As we all know that good convergence criteria means good results

· Initialize for the hybrid initialization

· Set the number of iterations to 500 to 1000 depend on which model you running

· Calculate

Residual Plots for Non-Participating media Air 1st Quadrant- S2S (enclosure Model) 2nd Quadrant –No Radiation (Flow and Convection Only) 3rd Quadrant P1 (Spherical Harmonics Model) 4th Quadrant – DO, DOM (Discrete Ordinate Model) No radiation Model only took 115 Iteration to converged S2S model took around 300 iteration to converged P1 model took around 460 iteration to converged and DOM model took around highest 560 iteration to converged

Similarly Residual Plots for Participating media Flue Gases 1st Quadrant- S2S (enclosure Model) 2nd Quadrant –No Radiation (Flow and Convection Only) 3rd Quadrant P1 (Spherical Harmonics Model) 4th Quadrant – DO, DOM (Discrete Ordinate Model) No radiation Model only took 92 Iteration to converged S2S model took around 335 iteration to converged P1 model took around 465 iteration to converged and DOM model took around highest 570 iteration to converged Do Intensity makes square wave and converged

Step 4 Solution

· Set up/generate plots

· Vertical centerline temperature(K) of the opposing cold wall T(y) at x=25 mm z=12.5mm

· Gas centerline temperature(k) T(x) y=12.5 mm z=12.5mm

· Vertical centerline total surface heat flux (W/m2) at the hot wall q(y) at x=0mm and z=12.5mm

· Vertical centerline total surface heat flux (W/m2) at the opposing cold wall q(y) at x=25mm z=25 mm

· Graph

· This is Vertical Centerline Temperature of Opposing Cold Wall Graph for air

· You can see an enormous difference in no radiation model compared to other radiation model.

· In all radiation model temperature profile behave very close to each other

· S2S and DOM model temperature profile is almost same

· Even air and Flue gases for no radiation model has different profile

· This is Vertical Centerline Temperature of Opposing Cold Wall Graph for Flue gases

·

This is Gas Centerline Temperature of Opposing Cold Wall Graph for air

We can see even difference between air and flue gases even though they are non-participating media

DO model is most accurate model Which is very close temperature profile with S2S model so DO model and S2S model is accurate

This is Gas Centerline Temperature of Opposing Cold Wall Graph for flue gases

This is Vertical Center Total Surface Heat Flux at the wall Graph for air

No radiation model lowest heat flux.

P1 is over predicting near the walls

This is Vertical Center Total Surface Heat Flux at the wall Graph for flue gases

No radiation model lowest heat flux.

P1 is over predicting near the walls

This is Vertical Center Total Surface Heat Flux at the opposing cold wall Graph for air

All the model has Total surface heat flux is negative- all the radiation is leaving from cold wall

It is getting infected and radiated off the medium that surrounding its box.

This is Vertical Center Total Surface Heat Flux at the opposing cold wall Graph for Flue gases

All the model has Total surface heat flux is negative- all the radiation is leaving from cold wall

It is getting infected and radiated off the medium that surrounding its box.

· Set up contour for visuals

· Heat flux contours

Summery:

Air and Flue gases

· Behaves differently when exposed to radiation due to the difference in their thermal properties

· Non-Participating media (Air) -absorption and re-emittance is negligible mostly N2 and O2

· Participating media (Flue gas) -Water vapor and Co2 absorb and re-emit radiation

DO model

· DO model is most accurate for radiation interaction with gases

· DO model is good for wide range of optical thickness

·

S2S model (enclosure model)

· S2S model is good for optically thin problems

· S2S model temp profile and heat flux profile very close to each other

· S2S and Do model is accurate for at least this problem

·

Spherical Harmonic (P1)

· Over predicts scattering of radiation

· Little to no geometry dependence on incident radiation

Vertical Centerline Temperature (K) of the Opposing Cold Wall-Air

Air NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX508.08 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX605.952 XXXXXXXXXX623.904 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX647.16 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX602.4Air S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.91 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.024Air P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.62 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX971.471

Temp (K)

Vertical Centerline Temperature (k)

Air NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX508.08 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX605.952 XXXXXXXXXX623.904 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX647.16 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX602.4Air S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.91 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.024Air P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.62 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX971.471FG NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX693.952 XXXXXXXXXX XXXXXXXXXX704.726706.1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.596 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.13 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.846974.476 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.255 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26986.26986.26986.26986.26986.26986.26 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.61 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX977.351 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Vertical Centerline Temperature (K) of the Opposing Cold Wall-Flue Gases

FG NR VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX693.952 XXXXXXXXXX XXXXXXXXXX704.726706.1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.596 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.13 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.846974.476 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.255 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26986.26986.26986.26986.26986.26986.26 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO VCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX974.61 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX977.351 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Gas Centerline Temperature(K) - Air

Air NR GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX691.69 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX672.08 XXXXXXXXXXAir S2S GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX988.87 XXXXXXXXXX985.428 XXXXXXXXXX982.678 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir P1 GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX994.726 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX990.88 XXXXXXXXXX989.57 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX987.86 XXXXXXXXXX987.322 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.37 XXXXXXXXXX986.16 XXXXXXXXXXAir DO GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000997.58 XXXXXXXXXX XXXXXXXXXX990.721 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX979.255 XXXXXXXXXX977.73 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX975.846 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.149 XXXXXXXXXX XXXXXXXXXX

Temp (K)

Gas Centerline Temperature(K) - Flue Gases

FG NR GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX736.31 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX746.274 XXXXXXXXXX XXXXXXXXXX748.54746.649 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000997.74 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX985.99 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.77 XXXXXXXXXX976.12 XXXXXXXXXX975.82 XXXXXXXXXX XXXXXXXXXX976.01 XXXXXXXXXXFG P1 GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX987.29 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX986.26FG DO GCL Temp01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21000 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX978.803978.06 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX976.07 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Temp (K)

Vertical Centerline Total Surface Heat Flux at the Hot Wall- Air

Air NR VCL TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX4940.38 XXXXXXXXXX4223.793936.233668.733422.963198.832995.832811.752641.412479.632322.382166.612009.451848.061682.351512.731339.431165.961001.78 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX1306.28 XXXXXXXXXXAir S2S TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-21974.86 XXXXXXXXXX5098.845189.015258.325316.485364.025395.615421.085440.95452.075460.145465.455462.465451.695439.695421.455397.745369.945334.865289.195228.785155.07 XXXXXXXXXX5011.411966.41Air P1 TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22205.215379.295264.455223.345204.785194.67 XXXXXXXXXX5184.165181.12 XXXXXXXXXX5177.135175.82 XXXXXXXXXX5174.215173.9151745174.595175.835178.045181.675187.66 XXXXXXXXXX5217.085259.455376.272204.29Air DO TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22014.135061.34 XXXXXXXXXX XXXXXXXXXX5268.065358.875437.95503.885556.765597.035625.515643.065650.415647.995635.855613.635580.715536.335479.885411.095330.31 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX5046.052008.82

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Hot Wall- Flue Gases

FG NR TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX5410.865013.874782.75 XXXXXXXXXX XXXXXXXXXX4159.083949.233741.973536.513331.023123.552913.642701.27 XXXXXXXXXX2266.622045.51824.541609.031407.761235.55 XXXXXXXXXX1091.081225.971685.22 XXXXXXXXXXFG S2S TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22026.15 XXXXXXXXXX5103.88 XXXXXXXXXX5234.255285.775324.55357.135381.335396.335408.985417.285421.615418.855409.75396.225377.955359.655332.725295.35252.85 XXXXXXXXXX5143.215083.285074.262020.22FG P1 TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX5480.875276.88 XXXXXXXXXX5169.43 XXXXXXXXXX5139.7 XXXXXXXXXX5126.785122.925120.095118.075116.715115.96 XXXXXXXXXX5116.465117.96 XXXXXXXXXX XXXXXXXXXX5131.92 XXXXXXXXXX5161.465195.825271.085477.31 XXXXXXXXXXFG DO TSHF HW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-22082.855143.625088.29 XXXXXXXXXX5237.175321.725396.845460.155511.085549.875577.175593.85600.455597.575585.195563.015530.445486.845431.765365.215288.125203.325119.035061.455125.49 XXXXXXXXXX

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Opposing Cold Wall- Air

Air NR VCL TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-332.8 XXXXXXXXXX XXXXXXXXXX-402.82 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-506.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir S2S TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1037.5 XXXXXXXXXX XXXXXXXXXX-1037.2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir P1 TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXAir DO TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1035.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Heat Flux

Vertical Centerline Total Surface Heat Flux at the Opposing Cold Wall- Flue Gases

FG NR TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-515 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-574.54 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-613 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG S2S TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG P1 TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1054-1054-1054-1054-1054-1054-1054-1054 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1054-1054-1054-1054-1054-1054-1054-1054 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXFG DO TSHF CW01E-32E-33.0000000000000001E-34.0000000000000001E-35.0000000000000001E-36.0000000000000001E-37.0000000000000001E-38.0000000000000002E-38.9999999999999993E-30.011.0999999999999999E-21.2E-21.2999999999999999E-21.4E-21.4999999999999999E-21.6E-21.7000000000000001E-21.7999999999999999E-21.9E-20.022.1000000000000001E-22.1999999999999999E-22.3E-22.4E-22.5000000000000001E-2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1034 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1039.8 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX-1037.3 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX

Heat Flux

Radiation of Heat Transfer ProblemNon-Participating mediaAirSurface to Surface(S2S)Enclosure ModelSpherical Harmonics Model(P1)Discrete Ordinates Model(DO,DOM)No Radiation(Flow & Convection Only)Participating mediaFlue GasesSurface to Surface(S2S)Enclosure ModelSpherical Harmonics Model(P1)Discrete Ordinates Model(DO,DOM)No Radiation(Flow & Convection Only)

Radiation of Heat Transfer Problem

Non-Participating media

Air

Surface to Surface

(S2S)

Enclosure Model

Spherical Harmonics Model

(P1)

Discrete Ordinates Model

(DO,DOM)

No Radiation

(Flow & Convection Only)

Participating media

Flue Gases

Surface to Surface

(S2S)

Enclosure Model

Spherical Harmonics Model

(P1)

Discrete Ordinates Model

(DO,DOM)

No Radiation

(Flow & Convection Only)

May 05, 2021

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