Abstract

High-flux solar simulators consist of lamps that mimic concentrated sunlight from a field of heliostats or parabolic dish. These installations are used to test promising solar-thermal technologies for commercial potential. Solar simulators can be calibrated with cylindrical calorimeters, devices that approximate black body absorbers. Calorimeter accuracy is crucial to solar simulator characterization and maintenance. To discover the worst-case performance of a cylindrical calorimeter during flux measurement Monte Carlo ray tracing was coupled to finite volume simulations. Results indicated that the calorimeter can exhibit an observer effect that distorts the solar simulator flux profile. Furthermore, the proposed design was sensitive to changes in calorimeter optical properties, changes that can result from oxidation and/or photobleaching over time. Design fidelity and robustness were substantially improved through the use of a beveled (conical) calorimeter aperture.

© 2015 Optical Society of America

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References

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2014 (2)

R. Bader, S. Haussener, and W. Lipiński, “Optical design of multisource high-flux solar simulators,” J. Sol. Energy Eng. 137(2), 021012 (2014).
[Crossref]

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

2013 (1)

O. Behar, A. Khellaf, and K. Mohammedi, “A review of studies on central receiver solar thermal power plants,” Renew. Sustain. Energy Rev. 23, 12–39 (2013).
[Crossref]

2011 (1)

T. Cooper and A. Steinfeld, “Derivation of the angular dispersion error distribution of mirror surfaces for Monte Carlo ray-tracing applications,” J. Sol. Energy Eng. 133(4), 044501 (2011).
[Crossref]

2010 (1)

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

2009 (2)

M. Prakash, S. Kedare, and J. Nayak, “Investigations on heat losses from a solar cavity receiver,” Sol. Energy 83(2), 157–170 (2009).
[Crossref]

G. Sharma and J. Martin, “MATLAB®: a language for parallel computing,” Int. J. Parallel Program. 37(1), 3–36 (2009).
[Crossref]

2007 (2)

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

2006 (1)

C. Pérez-Rábago, M. Marcos, M. Romero, and C. Estrada, “Heat transfer in a conical cavity calorimeter for measuring thermal power of a point focus concentrator,” Sol. Energy 80(11), 1434–1442 (2006).
[Crossref]

2005 (1)

O. Kaya and I. Teke, “Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls,” Heat Mass Transf. 42(2), 129–137 (2005).
[Crossref]

2003 (1)

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

1998 (1)

J. Howell, “The Monte Carlo method in radiative heat transfer,” J. Heat Transfer 120(3), 547–560 (1998).
[Crossref]

1990 (1)

G. L. Fenves, “Object-oriented programming for engineering software development,” Eng. Comput. 6(1), 1–15 (1990).
[Crossref]

1983 (1)

R. Diver, D. Carlson, F. Macdonald, and E. Fletcher, “A new high-temperature solar research furnace,” J. Sol. Energy Eng. 105(3), 288–293 (1983).
[Crossref]

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

1967 (1)

Y. Mori and W. Nakayama, “Study on forced convective heat transfer in curved pipes (3rd report, theoretical analysis under the condition of uniform wall temperature and practical formulae),” Int. J. Heat Mass Transfer 10(5), 681–695 (1967).
[Crossref]

Alxneit, I.

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

Bader, R.

R. Bader, S. Haussener, and W. Lipiński, “Optical design of multisource high-flux solar simulators,” J. Sol. Energy Eng. 137(2), 021012 (2014).
[Crossref]

Ballestrin, J.

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

Behar, O.

O. Behar, A. Khellaf, and K. Mohammedi, “A review of studies on central receiver solar thermal power plants,” Renew. Sustain. Energy Rev. 23, 12–39 (2013).
[Crossref]

Bingham, C.

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

Brack, M.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Carlson, D.

R. Diver, D. Carlson, F. Macdonald, and E. Fletcher, “A new high-temperature solar research furnace,” J. Sol. Energy Eng. 105(3), 288–293 (1983).
[Crossref]

Cooper, T.

T. Cooper and A. Steinfeld, “Derivation of the angular dispersion error distribution of mirror surfaces for Monte Carlo ray-tracing applications,” J. Sol. Energy Eng. 133(4), 044501 (2011).
[Crossref]

Coray, P.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Diver, R.

R. Diver, D. Carlson, F. Macdonald, and E. Fletcher, “A new high-temperature solar research furnace,” J. Sol. Energy Eng. 105(3), 288–293 (1983).
[Crossref]

Epstein, M.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Estrada, C.

C. Pérez-Rábago, M. Marcos, M. Romero, and C. Estrada, “Heat transfer in a conical cavity calorimeter for measuring thermal power of a point focus concentrator,” Sol. Energy 80(11), 1434–1442 (2006).
[Crossref]

Fenves, G. L.

G. L. Fenves, “Object-oriented programming for engineering software development,” Eng. Comput. 6(1), 1–15 (1990).
[Crossref]

Fletcher, E.

R. Diver, D. Carlson, F. Macdonald, and E. Fletcher, “A new high-temperature solar research furnace,” J. Sol. Energy Eng. 105(3), 288–293 (1983).
[Crossref]

Frommherz, U.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Guillot, E.

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Haberling, P.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Haussener, S.

R. Bader, S. Haussener, and W. Lipiński, “Optical design of multisource high-flux solar simulators,” J. Sol. Energy Eng. 137(2), 021012 (2014).
[Crossref]

Hirsch, D.

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

Howell, J.

J. Howell, “The Monte Carlo method in radiative heat transfer,” J. Heat Transfer 120(3), 547–560 (1998).
[Crossref]

Kaya, O.

O. Kaya and I. Teke, “Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls,” Heat Mass Transf. 42(2), 129–137 (2005).
[Crossref]

Kedare, S.

M. Prakash, S. Kedare, and J. Nayak, “Investigations on heat losses from a solar cavity receiver,” Sol. Energy 83(2), 157–170 (2009).
[Crossref]

Khellaf, A.

O. Behar, A. Khellaf, and K. Mohammedi, “A review of studies on central receiver solar thermal power plants,” Renew. Sustain. Energy Rev. 23, 12–39 (2013).
[Crossref]

Kinamore, J.

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

Kräupl, S.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Lichty, P.

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

Lipinski, W.

R. Bader, S. Haussener, and W. Lipiński, “Optical design of multisource high-flux solar simulators,” J. Sol. Energy Eng. 137(2), 021012 (2014).
[Crossref]

Macdonald, F.

R. Diver, D. Carlson, F. Macdonald, and E. Fletcher, “A new high-temperature solar research furnace,” J. Sol. Energy Eng. 105(3), 288–293 (1983).
[Crossref]

Marcos, M.

C. Pérez-Rábago, M. Marcos, M. Romero, and C. Estrada, “Heat transfer in a conical cavity calorimeter for measuring thermal power of a point focus concentrator,” Sol. Energy 80(11), 1434–1442 (2006).
[Crossref]

Martin, J.

G. Sharma and J. Martin, “MATLAB®: a language for parallel computing,” Int. J. Parallel Program. 37(1), 3–36 (2009).
[Crossref]

Meier, A.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Mohammedi, K.

O. Behar, A. Khellaf, and K. Mohammedi, “A review of studies on central receiver solar thermal power plants,” Renew. Sustain. Energy Rev. 23, 12–39 (2013).
[Crossref]

Mori, Y.

Y. Mori and W. Nakayama, “Study on forced convective heat transfer in curved pipes (3rd report, theoretical analysis under the condition of uniform wall temperature and practical formulae),” Int. J. Heat Mass Transfer 10(5), 681–695 (1967).
[Crossref]

Nakayama, W.

Y. Mori and W. Nakayama, “Study on forced convective heat transfer in curved pipes (3rd report, theoretical analysis under the condition of uniform wall temperature and practical formulae),” Int. J. Heat Mass Transfer 10(5), 681–695 (1967).
[Crossref]

Nayak, J.

M. Prakash, S. Kedare, and J. Nayak, “Investigations on heat losses from a solar cavity receiver,” Sol. Energy 83(2), 157–170 (2009).
[Crossref]

Olalde, G.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Osinga, T.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

Pérez-Rábago, C.

C. Pérez-Rábago, M. Marcos, M. Romero, and C. Estrada, “Heat transfer in a conical cavity calorimeter for measuring thermal power of a point focus concentrator,” Sol. Energy 80(11), 1434–1442 (2006).
[Crossref]

Perkins, C.

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

Petrasch, J.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Petrasch, J. r.

J. r. Petrasch, “A free and open source Monte Carlo ray tracing program for concentrating solar energy research,” in ASME 2010 4th International Conference on Energy Sustainability (ASME, 2010), pp. 125–132.
[Crossref]

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Prakash, M.

M. Prakash, S. Kedare, and J. Nayak, “Investigations on heat losses from a solar cavity receiver,” Sol. Energy 83(2), 157–170 (2009).
[Crossref]

Romero, M.

C. Pérez-Rábago, M. Marcos, M. Romero, and C. Estrada, “Heat transfer in a conical cavity calorimeter for measuring thermal power of a point focus concentrator,” Sol. Energy 80(11), 1434–1442 (2006).
[Crossref]

Sans, J. L.

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

Santén, S.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Sharma, G.

G. Sharma and J. Martin, “MATLAB®: a language for parallel computing,” Int. J. Parallel Program. 37(1), 3–36 (2009).
[Crossref]

Steinfeld, A.

T. Cooper and A. Steinfeld, “Derivation of the angular dispersion error distribution of mirror surfaces for Monte Carlo ray-tracing applications,” J. Sol. Energy Eng. 133(4), 044501 (2011).
[Crossref]

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

Teke, I.

O. Kaya and I. Teke, “Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls,” Heat Mass Transf. 42(2), 129–137 (2005).
[Crossref]

Weimer, A.

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

Wendelin, T.

T. Wendelin, “SolTRACE: a new optical modeling tool for concentrating solar optics,” in ASME 2003 International Solar Energy Conference (ASME, 2003), pp. 253–260.
[Crossref]

Wieckert, C.

C. Wieckert, U. Frommherz, S. Kräupl, E. Guillot, G. Olalde, M. Epstein, S. Santén, T. Osinga, and A. Steinfeld, “A 300kW solar chemical pilot plant for the carbothermic production of Zinc,” J. Sol. Energy Eng. 129(2), 190–196 (2007).
[Crossref]

Willsh, C.

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

Woodruff, B.

P. Lichty, C. Perkins, B. Woodruff, C. Bingham, and A. Weimer, “Rapid high temperature solar thermal biomass gasification in a prototype cavity reactor,” J. Sol. Energy Eng. 132(1), 011012 (2010).
[Crossref]

Wuillemin, D.

J. Petrasch, P. Coray, A. Meier, M. Brack, P. Haberling, D. Wuillemin, and A. Steinfeld, “A novel 50kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps,” J. Sol. Energy Eng. 129(4), 405–411 (2007).
[Crossref]

Zedtwitz, P.

D. Hirsch, P. Zedtwitz, T. Osinga, J. Kinamore, and A. Steinfeld, “A new 45 kW high-flux solar simulator for high-temperature thermal and thermochemical research,” J. Sol. Energy Eng. 125(1), 117–120 (2003).
[Crossref]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Energy Procedia (1)

E. Guillot, I. Alxneit, J. Ballestrin, J. L. Sans, and C. Willsh, “Comparison of 3 heat flux gauges and a water calorimeter for concentrated solar irradiance measurement,” Energy Procedia 49, 2090–2099 (2014).
[Crossref]

Eng. Comput. (1)

G. L. Fenves, “Object-oriented programming for engineering software development,” Eng. Comput. 6(1), 1–15 (1990).
[Crossref]

Heat Mass Transf. (1)

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Figures (9)

Fig. 1
Fig. 1 A simulation framework for calorimeter evaluation. a) piping and instrumentation diagram of calorimeter cooling flows showing confounding radiation effects. In this work the operational temperature target was ΔT = 25°C and the faceplate coolant flowrate was fixed at 6 L/min. b) Radiative and thermal phenomena within and outside the calorimeter.
Fig. 2
Fig. 2 Validation of the new, parallel, grey body Monte Carlo ray tracer (CUtrace). a) predicted power intercepted by a disc at a solar simulator focus. Trace was the ANU and EPFL solar simulator with rigorous xenon filament modeling as described by Bader 2014 [4]. b) predicted power intercepted by a disc at a solar simulator focus. Trace was the ANU and EPFL solar simulator with simplified volumetric cylindrical sources in each lamp [4, 19 ]. Source cylinder length was 0.0045 meters and radius was 0.00075 meters. c) predicted power intercepted by a disc at a compound parabola outlet [21]. The compound parabola acceptance angle was 35° and the outlet radius was 1.3 meters. d) analytical view factors from Appendix C of Howell 2002 [22] are reproduced by CUtrace, wherein any surface can act as a diffuse source of radiation. The view factors represent radiative exchange within cones, cylinders and from spheres to cylinders and paraboloids,
Fig. 3
Fig. 3 CUtrace depiction of the calorimeter design at the focus of the ANU/EPFL solar simulator [4].
Fig. 4
Fig. 4 Peak Monte Carlo fluxes were mapped annularly around exposed calorimeter surfaces. a) actual fluxes and b) mapped fluxes.
Fig. 5
Fig. 5 details of the dimensions and discretization used in Monte Carlo ray tracing and finite volume simulation. Unless otherwise specified body cavity reflectivity was 0.05 diffuse, faceplate interior reflectivity was 0.95 diffuse, and face reflectivity was 0.05 diffuse. The faceplate coolant flow was a constant 6 L/min. Both the body and faceplate coolant flows [Fig. 1(a)] were drawn from a 20°C water supply.
Fig. 6
Fig. 6 The calorimeter induces an observer effect. a) percent distortion (◆) and power intercepted (■) by the large (10 cm) aperture faceplate as calorimeter face reflectivity increased. b) percent distortion (◆) and power intercepted (■) by the small (3 cm) aperture faceplate as calorimeter face reflectivity increased. c) flux distortion at the small (3 cm) calorimeter aperture induced by different face reflectivities.
Fig. 7
Fig. 7 Simulation results for variations in body reflectivity. a) results for the large (10 cm) aperture faceplate. b) results for the small (3 cm) aperture faceplate. In all cases face and faceplate interior reflectivities assumed their nominal values (0.05 and 0.95 diffuse, respectively). Faceplate coolant flow was a constant 6 L/min.
Fig. 8
Fig. 8 Simulation results for variations in faceplate interior reflectivity. a) results for the large (10 cm) aperture faceplate. b) results for the small (3 cm) aperture faceplate. In all cases face and body reflectivities assumed their nominal values (0.05 and 0.05 diffuse, respectively). Faceplate coolant flow was a constant 6 L/min.
Fig. 9
Fig. 9 Losses as a percentage of Q in for a calorimeter body coolant temperature rise of ΔT = 25°C and the nominal diffuse reflectivities (body = 0.05, face = 0.05, faceplate = 0.95). Symbols across all graphs: Q = Q reflective (◆), Q = Q convective (■), Q = Q emissive (▲) and Q = Q observer (X). a) Large (10 cm) square aperture faceplate. b) Small (3 cm) square aperture faceplate. c) Large (10 cm) square aperture faceplate. d) Small (3 cm) square aperture faceplate. e) Large (10 cm) beveled aperture faceplate. f) Small (3 cm) beveled aperture faceplate.

Tables (1)

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Table 1 Variable definitions in the finite volume simulation.

Equations (7)

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Q in m ˙ C p Δ T
Q in = m ˙ C p Δ T + Q reflective + Q emissive + Q convective Q observer
[ r N ( r , x ) ] r + r [ N ( r , x ) ] x = 0
N r = k T r
N x = k T x
N s = h ( T s T f )
N r a d = σ ε F T 4

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