Abstract

This paper proposes a combined method for two-dimensional temperature and velocity measurements in liquid and gas flow using a schlieren system. Temperature measurements are made by relating the intensity level of each pixel in a schlieren image to the corresponding knife-edge position measured at the exit focal plane of the schlieren system. The same schlieren images were also used to measure the velocity of the fluid flow. The measurement is made by using particle image velocimetry (PIV). The PIV software used in this work analyzes motion between consecutive schlieren frames to obtain velocity fields. The proposed technique was applied to measure the temperature and velocity fields in the natural convection of water provoked by a heated rectangular plate.

© 2012 Optical Society of America

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  1. A. K. Agrawal, N. K. Butuk, S. R. Gollahalli, and D. Griffin, “Three-dimensional rainbow schlieren tomography of a temperature field in gas flows,” Appl. Opt. 37, 479–485 (1998).
    [CrossRef]
  2. V. P. Tregub, “A color schlieren method,” J. Opt. Technol. 71, 785–790 (2004).
    [CrossRef]
  3. T. Wong and A. K. Agrawal, “Quantitative measurements in an unsteady flame using high-speed rainbow schlieren deflectometry,” Meas. Sci. Technol. 17, 1503–1510 (2006).
    [CrossRef]
  4. E. M. Popova, “Processing schlieren-background patterns by constructing the direction field,” J. Opt. Technol. 71, 572–574 (2004).
    [CrossRef]
  5. M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
    [CrossRef]
  6. R. B. Teese and M. M. Waters, “Inexpensive schlieren video technique using sensor dead space as a grid,” Opt. Eng. 43, 2501–2502 (2004).
    [CrossRef]
  7. S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
    [CrossRef]
  8. C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
    [CrossRef]
  9. R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304(1991).
    [CrossRef]
  10. R. J. Adrian, “Bibliography of Particle Image Velocimetry using imaging methods: 1917–1995,” TAM Report 817 (University of Illinois at Urbana-Champaign, 1996).
  11. I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. Part C 211, 55–76 (1997).
    [CrossRef]
  12. M. Raffel, C. E. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide2nd ed. (Springer, 2007).
  13. H. C. H. A. Townsend, “A method of airflow cinematography capable of quantitative analysis,” J. Aeronaut. Sci. 3, 343–352 (1936).
  14. D. I. Papamoschou, “A two-spark schlieren system for very-high velocity measurement,” Exp. Fluids 7, 354–356 (1989).
    [CrossRef]
  15. S. Fu and Y. Wu, “Detection of velocity distribution of a flow field using sequences of schlieren images,” Opt. Eng. 40, 1661–1666 (2001).
    [CrossRef]
  16. M. A. Kegerise and G. S. Settles, “Schlieren image-correlation velocimetry and its application to free-convection flows,” in Proceedings of the Ninth International Symposium on Flow Visualization, G. M. Carlomagno and I. Grant, eds. (2000), paper 380.
  17. D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
    [CrossRef]
  18. J. K. Sveen and S. B. Dalziel, “A dynamic masking technique for combined measurement of PIV and synthetic schlieren applied to internal gravity waves,” Meas. Sci. Technol. 16, 1954–1960 (2005).
    [CrossRef]
  19. S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
    [CrossRef]
  20. C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
    [CrossRef]
  21. D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).
  22. W. Merzkirch, Flow Visualization2nd ed. (Academic, 1987).
  23. G. S. Settles, Schlieren and Shadowgraph Techniques, 1st ed. (Springer, 2001).
  24. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972).
  25. R. J. Goldstein and T. H. Kuehn, “Optical system for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics MeasurementR. J. Goldstein, ed. (Taylor and Francis, 1996), pp. 451–508.

2011 (1)

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

2009 (2)

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
[CrossRef]

2007 (1)

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

2006 (2)

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
[CrossRef]

T. Wong and A. K. Agrawal, “Quantitative measurements in an unsteady flame using high-speed rainbow schlieren deflectometry,” Meas. Sci. Technol. 17, 1503–1510 (2006).
[CrossRef]

2005 (1)

J. K. Sveen and S. B. Dalziel, “A dynamic masking technique for combined measurement of PIV and synthetic schlieren applied to internal gravity waves,” Meas. Sci. Technol. 16, 1954–1960 (2005).
[CrossRef]

2004 (3)

2001 (2)

S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
[CrossRef]

S. Fu and Y. Wu, “Detection of velocity distribution of a flow field using sequences of schlieren images,” Opt. Eng. 40, 1661–1666 (2001).
[CrossRef]

2000 (1)

M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
[CrossRef]

1998 (1)

1997 (1)

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. Part C 211, 55–76 (1997).
[CrossRef]

1991 (1)

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304(1991).
[CrossRef]

1989 (1)

D. I. Papamoschou, “A two-spark schlieren system for very-high velocity measurement,” Exp. Fluids 7, 354–356 (1989).
[CrossRef]

1936 (1)

H. C. H. A. Townsend, “A method of airflow cinematography capable of quantitative analysis,” J. Aeronaut. Sci. 3, 343–352 (1936).

Adrian, R. J.

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304(1991).
[CrossRef]

R. J. Adrian, “Bibliography of Particle Image Velocimetry using imaging methods: 1917–1995,” TAM Report 817 (University of Illinois at Urbana-Champaign, 1996).

Agrawal, A. K.

T. Wong and A. K. Agrawal, “Quantitative measurements in an unsteady flame using high-speed rainbow schlieren deflectometry,” Meas. Sci. Technol. 17, 1503–1510 (2006).
[CrossRef]

A. K. Agrawal, N. K. Butuk, S. R. Gollahalli, and D. Griffin, “Three-dimensional rainbow schlieren tomography of a temperature field in gas flows,” Appl. Opt. 37, 479–485 (1998).
[CrossRef]

Alexandre, P.

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

Alvarez-Herrera, C.

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

Barrientos-García, B.

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

Butuk, N. K.

Carr, M.

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

Cattafesta, L. N.

S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
[CrossRef]

Dalziel, S. B.

C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
[CrossRef]

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

J. K. Sveen and S. B. Dalziel, “A dynamic masking technique for combined measurement of PIV and synthetic schlieren applied to internal gravity waves,” Meas. Sci. Technol. 16, 1954–1960 (2005).
[CrossRef]

Davies, P. A.

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

Francis, A.

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

Fu, S.

S. Fu and Y. Wu, “Detection of velocity distribution of a flow field using sequences of schlieren images,” Opt. Eng. 40, 1661–1666 (2001).
[CrossRef]

Garg, S.

S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
[CrossRef]

Goldstein, R. J.

R. J. Goldstein and T. H. Kuehn, “Optical system for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics MeasurementR. J. Goldstein, ed. (Taylor and Francis, 1996), pp. 451–508.

Gollahalli, S. R.

Grant, I.

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. Part C 211, 55–76 (1997).
[CrossRef]

Griffin, D.

Guerrero-Viramontes, J. A.

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

Ihle, C. F.

C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
[CrossRef]

Jochem, W. F.

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

Jonassen, D. R.

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
[CrossRef]

Kegerise, M. A.

M. A. Kegerise and G. S. Settles, “Schlieren image-correlation velocimetry and its application to free-convection flows,” in Proceedings of the Ninth International Symposium on Flow Visualization, G. M. Carlomagno and I. Grant, eds. (2000), paper 380.

Kompenhans, J.

M. Raffel, C. E. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide2nd ed. (Springer, 2007).

Kuehn, T. H.

R. J. Goldstein and T. H. Kuehn, “Optical system for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics MeasurementR. J. Goldstein, ed. (Taylor and Francis, 1996), pp. 451–508.

Meier, A. G. E. A.

M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
[CrossRef]

Merzkirch, W.

W. Merzkirch, Flow Visualization2nd ed. (Academic, 1987).

Moreno-Hernández, D.

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

Niño, Y.

C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
[CrossRef]

Papamoschou, D. I.

D. I. Papamoschou, “A two-spark schlieren system for very-high velocity measurement,” Exp. Fluids 7, 354–356 (1989).
[CrossRef]

Popova, E. M.

Raffe, M.

M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
[CrossRef]

Raffel, M.

M. Raffel, C. E. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide2nd ed. (Springer, 2007).

Richard, H.

M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
[CrossRef]

Settles, G. S.

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
[CrossRef]

M. A. Kegerise and G. S. Settles, “Schlieren image-correlation velocimetry and its application to free-convection flows,” in Proceedings of the Ninth International Symposium on Flow Visualization, G. M. Carlomagno and I. Grant, eds. (2000), paper 380.

G. S. Settles, Schlieren and Shadowgraph Techniques, 1st ed. (Springer, 2001).

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972).

Sveen, J. K.

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

J. K. Sveen and S. B. Dalziel, “A dynamic masking technique for combined measurement of PIV and synthetic schlieren applied to internal gravity waves,” Meas. Sci. Technol. 16, 1954–1960 (2005).
[CrossRef]

Teese, R. B.

R. B. Teese and M. M. Waters, “Inexpensive schlieren video technique using sensor dead space as a grid,” Opt. Eng. 43, 2501–2502 (2004).
[CrossRef]

Townsend, H. C. H. A.

H. C. H. A. Townsend, “A method of airflow cinematography capable of quantitative analysis,” J. Aeronaut. Sci. 3, 343–352 (1936).

Tregub, V. P.

Tronosky, M. D.

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
[CrossRef]

Waters, M. M.

R. B. Teese and M. M. Waters, “Inexpensive schlieren video technique using sensor dead space as a grid,” Opt. Eng. 43, 2501–2502 (2004).
[CrossRef]

Willert, C. E.

M. Raffel, C. E. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide2nd ed. (Springer, 2007).

Wong, T.

T. Wong and A. K. Agrawal, “Quantitative measurements in an unsteady flame using high-speed rainbow schlieren deflectometry,” Meas. Sci. Technol. 17, 1503–1510 (2006).
[CrossRef]

Wu, Y.

S. Fu and Y. Wu, “Detection of velocity distribution of a flow field using sequences of schlieren images,” Opt. Eng. 40, 1661–1666 (2001).
[CrossRef]

Yuan, D.

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

Annu. Rev. Fluid Mech. (1)

R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304(1991).
[CrossRef]

Appl. Opt. (1)

Exp Fluids (1)

M. Raffe, H. Richard, and A. G. E. A. Meier, “On the applicability of background oriented optical tomography for large scale aerodynamic investigations,” Exp Fluids 28, 477–481 (2000).
[CrossRef]

Exp. Fluids (3)

S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
[CrossRef]

D. I. Papamoschou, “A two-spark schlieren system for very-high velocity measurement,” Exp. Fluids 7, 354–356 (1989).
[CrossRef]

D. Yuan, P. Alexandre, A. Francis, and W. F. Jochem, “Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge,” Exp. Fluids 10, 1007 (2011).

J. Aeronaut. Sci. (1)

H. C. H. A. Townsend, “A method of airflow cinematography capable of quantitative analysis,” J. Aeronaut. Sci. 3, 343–352 (1936).

J. Opt. Technol. (2)

Meas. Sci. Technol. (4)

J. K. Sveen and S. B. Dalziel, “A dynamic masking technique for combined measurement of PIV and synthetic schlieren applied to internal gravity waves,” Meas. Sci. Technol. 16, 1954–1960 (2005).
[CrossRef]

S. B. Dalziel, M. Carr, J. K. Sveen, and P. A. Davies, “Simultaneous synthetic schlieren and PIV measurements for internal solitary waves,” Meas. Sci. Technol. 18, 533–547 (2007).
[CrossRef]

C. F. Ihle, S. B. Dalziel, and Y. Niño, “Simultaneous particle image Velocimetry and synthetic schlieren measurement of an erupting thermal plume,” Meas. Sci. Technol. 20, 125402 (2009).
[CrossRef]

T. Wong and A. K. Agrawal, “Quantitative measurements in an unsteady flame using high-speed rainbow schlieren deflectometry,” Meas. Sci. Technol. 17, 1503–1510 (2006).
[CrossRef]

Opt. Eng. (2)

S. Fu and Y. Wu, “Detection of velocity distribution of a flow field using sequences of schlieren images,” Opt. Eng. 40, 1661–1666 (2001).
[CrossRef]

R. B. Teese and M. M. Waters, “Inexpensive schlieren video technique using sensor dead space as a grid,” Opt. Eng. 43, 2501–2502 (2004).
[CrossRef]

Opt. Laser Technol. (1)

C. Alvarez-Herrera, D. Moreno-Hernández, B. Barrientos-García, and J. A. Guerrero-Viramontes, “Temperature measurement of air convection using a schlieren system,” Opt. Laser Technol. 41, 233–240 (2009).
[CrossRef]

Opt. Lasers Eng. (1)

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207 (2006).
[CrossRef]

Proc. Inst. Mech. Eng. Part C (1)

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mech. Eng. Part C 211, 55–76 (1997).
[CrossRef]

Other (7)

M. Raffel, C. E. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide2nd ed. (Springer, 2007).

R. J. Adrian, “Bibliography of Particle Image Velocimetry using imaging methods: 1917–1995,” TAM Report 817 (University of Illinois at Urbana-Champaign, 1996).

M. A. Kegerise and G. S. Settles, “Schlieren image-correlation velocimetry and its application to free-convection flows,” in Proceedings of the Ninth International Symposium on Flow Visualization, G. M. Carlomagno and I. Grant, eds. (2000), paper 380.

W. Merzkirch, Flow Visualization2nd ed. (Academic, 1987).

G. S. Settles, Schlieren and Shadowgraph Techniques, 1st ed. (Springer, 2001).

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972).

R. J. Goldstein and T. H. Kuehn, “Optical system for flow measurement: shadowgraph, schlieren, and interferometric techniques,” in Fluid Mechanics MeasurementR. J. Goldstein, ed. (Taylor and Francis, 1996), pp. 451–508.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of a parallel-light z-type schlieren system used for calibrated schlieren and particle image velocimetry.

Fig. 2.
Fig. 2.

Calibration curves of measured intensity across pixels (n, m).

Fig. 3.
Fig. 3.

Flow chart for fields calculations in z-type schlieren system.

Fig. 4.
Fig. 4.

Image of the experimental flow for simultaneous schlieren and PIV measurement. A shape distortion of the 50 μm polystyrene latex particles with a knife edge at a cutoff of approximately 60%. One part of the particles is suppressed, making PIV analysis difficult.

Fig. 5.
Fig. 5.

A–D, example schlieren pattern results with different temperatures (22 °C, 28 °C, 32 °C, and 34 °C); E–H, contour plots of temperature fields for the same temperatures as above.

Fig. 6.
Fig. 6.

Typical images of particles for PIV measurement (in this case, obtained in the z-type schlieren system). Images A and B are separated by 1/15s, which contain particles 50 μm in size.

Fig. 7.
Fig. 7.

Displacement of particles found by the PIV method. Images obtained from the schlieren system at temperatures of A, 22 °C; B, 28 °C; C, 31 °C; and D, 34 °C; driven by the natural convection of water provoked by a heated rectangular plate.

Fig. 8.
Fig. 8.

Images of data derived from the analysis of A, the original schlieren image acquired with the system; B, temperature analysis; C, velocimetry field vectors; and D, temperature and velocimetry field vectors of the same region of interest.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

dds(nmdr⃗ds)=nm,
εξ=ζ2ζ1nmξdz,
ρx=ρx=δxf2hk,
T=ρ0ρ,T0=n01nm1T0.
I(n,m)Δx=I(n,m)ξI(n,m)0,
I(n,m)δx=I(n,m)pI(n,m)0.
δx(n,m)=Δx,whereΔxcorresponds to the conditionmin|I(n,m)δxI(n,m)Δx|.
ρ(x)=ρ0+1f2hKζ1ζ2δxdx.

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