Abstract

A convective fluid flow in air could be regulated if the physical process were better understood. Temperature and velocity measurements are required in order to obtain a proper characterization of a convective fluid flow. In this study, we show that a classical schlieren system can be used for simultaneous measurements of temperature and velocity in a convective fluid flow in air. The schlieren technique allows measurement of the average fluid temperature and velocity integrated in the direction of the test beam. Therefore, in our experiments we considered surfaces with isothermal conditions. 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 by using optical flow techniques. The algorithm implemented analyzes motion between consecutive schlieren frames to obtain a tracked sequence and finally velocity fields. The proposed technique was applied to measure the temperature and velocity fields in natural convection of air due to unconfined and confined heated rectangular plates.

© 2013 Optical Society of America

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References

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  1. Graham O. Hughes and Ross W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech. 40, 185–208 (2008).
    [CrossRef]
  2. J. A. Schetz and A. E. Fuhs, Handbook of Fluid Dynamics and Fluid Machinery: Experimental and Computational Fluid Dynamics (Wiley, 2009), Vol. 2.
  3. 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]
  4. V. P. Tregub, “A color schlieren method,” J. Opt. Technol. 71, 785–790 (2004).
    [CrossRef]
  5. 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]
  6. E. M. Popova, “Processing schlieren-background patterns by constructing the direction field,” J. Opt. Technol. 71, 572–574 (2004).
    [CrossRef]
  7. 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]
  8. 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]
  9. S. Garg and L. N. Cattafesta, “Quantitative schlieren measurements of coherent structures in a cavity shear layer,” Exp. Fluids 30, 123–134 (2001).
    [CrossRef]
  10. 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]
  11. W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).
  12. G. S. Settles, Schlieren and Shadowgraph Technique (Springer, 2001).
  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. Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
    [CrossRef]
  22. A. Martínez-González, J. A. Guerrero-Viramontes, and D. Moreno-Hernández, “Temperature and velocity measurement fields of fluids using a schlieren system,” Appl. Opt. 51, 3519–3525 (2012).
    [CrossRef]
  23. E. D. Iffa, A. Rashid, A. Aziz, and A. S. Malik, “Velocity field measurement of a round jet using quantitative schlieren,” Appl. Opt. 50, 618–625 (2011).
    [CrossRef]
  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 Measurement, R. J. Goldstein, ed. (Taylor & Francis, 1996), pp. 451–508.
  26. B. K. P. Horn and B. G. Schunck, “Determining optical flow,” J. Artificial Intelligence Res. 17, 185–203 (1981).
    [CrossRef]

2012 (1)

2011 (2)

E. D. Iffa, A. Rashid, A. Aziz, and A. S. Malik, “Velocity field measurement of a round jet using quantitative schlieren,” Appl. Opt. 50, 618–625 (2011).
[CrossRef]

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[CrossRef]

2009 (2)

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]

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]

2008 (1)

Graham O. Hughes and Ross W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech. 40, 185–208 (2008).
[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)

1989 (1)

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

1981 (1)

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” J. Artificial Intelligence Res. 17, 185–203 (1981).
[CrossRef]

1936 (1)

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

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]

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]

Auclair, F.

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[CrossRef]

Aziz, A.

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]

Dossman, Y.

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[CrossRef]

Floor, J. W.

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[CrossRef]

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]

Fuhs, A. E.

J. A. Schetz and A. E. Fuhs, Handbook of Fluid Dynamics and Fluid Machinery: Experimental and Computational Fluid Dynamics (Wiley, 2009), Vol. 2.

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 Measurement, R. J. Goldstein, ed. (Taylor & Francis, 1996), pp. 451–508.

Gollahalli, S. R.

Griffin, D.

Griffiths, Ross W.

Graham O. Hughes and Ross W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech. 40, 185–208 (2008).
[CrossRef]

Guerrero-Viramontes, J. A.

A. Martínez-González, J. A. Guerrero-Viramontes, and D. Moreno-Hernández, “Temperature and velocity measurement fields of fluids using a schlieren system,” Appl. Opt. 51, 3519–3525 (2012).
[CrossRef]

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]

Horn, B. K. P.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” J. Artificial Intelligence Res. 17, 185–203 (1981).
[CrossRef]

Hughes, Graham O.

Graham O. Hughes and Ross W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech. 40, 185–208 (2008).
[CrossRef]

Iffa, E. D.

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]

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.

Kuehn, T. H.

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

Malik, A. S.

Martínez-González, A.

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 Visualization, 2nd ed. (Academic, 1987).

Moreno-Hernández, D.

A. Martínez-González, J. A. Guerrero-Viramontes, and D. Moreno-Hernández, “Temperature and velocity measurement fields of fluids using a schlieren system,” Appl. Opt. 51, 3519–3525 (2012).
[CrossRef]

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]

Paci, A.

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[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]

Rashid, A.

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]

Schetz, J. A.

J. A. Schetz and A. E. Fuhs, Handbook of Fluid Dynamics and Fluid Machinery: Experimental and Computational Fluid Dynamics (Wiley, 2009), Vol. 2.

Schunck, B. G.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” J. Artificial Intelligence Res. 17, 185–203 (1981).
[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 Technique (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]

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]

Annu. Rev. Fluid Mech. (1)

Graham O. Hughes and Ross W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech. 40, 185–208 (2008).
[CrossRef]

Appl. Opt. (3)

Exp. Fluids (4)

Y. Dossman, A. Paci, F. Auclair, and J. W. Floor, “Simultaneous velocity and density measurements for an energy based approach to internal waves generated over a ridge,” Exp. Fluids 51, 1013–1028 (2011).
[CrossRef]

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

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]

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

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. Artificial Intelligence Res. (1)

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” J. Artificial Intelligence Res. 17, 185–203 (1981).
[CrossRef]

J. Opt. Technol. (2)

Meas. Sci. Technol. (4)

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]

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]

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]

Other (6)

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 Measurement, R. J. Goldstein, ed. (Taylor & Francis, 1996), pp. 451–508.

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

G. S. Settles, Schlieren and Shadowgraph Technique (Springer, 2001).

J. A. Schetz and A. E. Fuhs, Handbook of Fluid Dynamics and Fluid Machinery: Experimental and Computational Fluid Dynamics (Wiley, 2009), Vol. 2.

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.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of a parallel-light Z-type schlieren system used for calibrated schlieren and optical flow.

Fig. 2.
Fig. 2.

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

Fig. 3.
Fig. 3.

Flow chart for temperature and velocity fields calculations in a Z-type schlieren system.

Fig. 4.
Fig. 4.

Instantaneous schlieren images and temperature fields. A, An instantaneous schlieren image for unconfined fluid flow; B, calculated temperature field from case A; C, an instantaneous schlieren image for confined fluid flow; D, calculated temperature field from case C.

Fig. 5.
Fig. 5.

Average temperature fields using 100 schlieren images for unconfined (left) and confined (right) fluid flow.

Fig. 6.
Fig. 6.

Instantaneous schlieren images at different points in time. From the left to the right: first frame, second frame and resulting velocity vector plot; unconfined (top) and confined (bottom) fluid flow.

Fig. 7.
Fig. 7.

A, E, Images of data derived from the analysis of original schlieren; B, F, temperature analysis; C, G, velocimetry field vectors; D, H, temperature and velocimetry field vectors of the same region of interest. Images are for unconfined (top) and confined (bottom) fluid flows.

Equations (10)

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

dds(nmdr⃗ds)=nm,
εξ=ζ2ζ1nmξdz,
ρx=ρx=δxf2hk,
T=ρ0ρT0=n01nm1T0,
ρ(x)=ρ0+1f2hKζ1ζ2δxdx.
dIdt=0,
Ixu+Iyv+It=0,
un+1=u¯nIx[Ixu¯n+Iyv¯n+It]/(α2+Ix2+Iy2)vn+1=v¯nIy[Ixu¯n+Iyv¯n+It]/(α2+Ix2+Iy2),
u¯i,j,k=16{ui1,j,k+ui,j,+1,k+ui+1,j,k+ui,j1,k}+112{ui1,j1,k+ui1,j+1,k+ui+1,j+1,k+ui+1,j1,k}v¯i,j,k=16{vi1,j,k+vi,j,+1,k+vi+1,j,k+vi,j1,k}+112{vi1,j1,k+vi1,j+1,k+vi+1,j+1,k+vi+1,j1,k},
Ix14{Ii,j+1,kIi,j,k+Ii+1,j+1,kIi+1,j,k+Ii,j+1,k+1Ii,j,k+1+Ii+1,j+1,k+1Ii+1,j,k+1}Iy14{Ii+1,j,kIi,j,k+Ii+1,j+1,kIi,j+1,k+Ii+1,j,k+1Ii,j,k+1+Ii+1,j+1,k+1Ii,j+1,k+1}It14{Ii,j,k+1Ii,j,k+Ii+1,j,k+1Ii+1,j,k+Ii,j+1,k+1Ii,j+1,k+Ii+1,j+1,k+1Ii+1,j+1,k}.

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