Abstract

This paper utilizes the background oriented schlieren (BOS) technique to measure the velocity field of a variable density round jet. The density field of the jet is computed based on the light deflection created during the passage of light through the understudy jet. The deflection vector estimation was carried out using phase-based optical flow algorithms. The density field is further exploited to extract the axial and radial velocity vectors with the aid of continuity and energy equations. The experiment is conducted at six different jet-exit temperature values. Additional turbulence parameters, such as velocity variance and power spectral density of the vector field, are also computed. Finally, the measured velocity parameters are compared with the hot wire anemometer measurements and their correlation is displayed.

© 2011 Optical Society of America

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References

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  1. M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).
  2. D. Calluaud and L. David, “Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block,” Exp. Fluids 36, 53–61 (2004).
    [CrossRef]
  3. http://www.dantecdynamics.com/Default.aspx?ID=653
  4. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).
  5. G. E. A. Meier, “Hintergrund schlierenmessverfahren,” Deutsche Patentanmeldung, DE 199 42 856 A1 (1999).
  6. S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.
  7. G. S. Settles, “Recent developments in schlieren and shadowgraph techniques,” in Proceedings of 14th International Symposium on Flow Visualization (2010), paper ISFV14-IL-2.
  8. W. L. Howes, “Rainbow schlieren,” NASA TP-2166 (1983).
  9. W. L. Howes, “Rainbow schlieren and its applications,” Appl. Opt. 23, 2449–2460 (1984).
    [CrossRef] [PubMed]
  10. X. Xiao, I. K. Puri, and A. K. Agrawal, “Temperature measurements in steady axisymmetric partially premixed flames by use of rainbow schlieren deflectometry,” Appl. Opt. 41, 1922–1928 (2002).
    [CrossRef] [PubMed]
  11. R. P. Satti, P. S. Kolhe, S. Olcmen, and A. K. Agrawal, “Miniature rainbow schlieren deflectometry system for quantitative measurements in microjets and flames,” Appl. Opt. 46, 2954–2962 (2007).
    [CrossRef] [PubMed]
  12. A. F. Ibarreta and C. J. Sung, “Flame temperature and location measurements of sooting premixed Bunsen flames by rainbow schlieren deflectometry,” Appl. Opt. 44, 3565–3575 (2005).
    [CrossRef] [PubMed]
  13. F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.
  14. F. Klinge, “Fluid flow rate determining method, involves tracing spatial offset of density variations based on images taken at different times, and determining local flow rate of fluid from offset and interval of times,” German patent DE102006047286 (2008).
  15. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
    [CrossRef]
  16. H. Liu, R. Chellappa, and A. Rosenfeld, “Fast two-frame multiscale dense optical flow estimation using discrete wavelet filters,” J. Opt. Soc. Am. A 20, 1505–1515 (2003).
    [CrossRef]
  17. D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
    [CrossRef]
  18. J. Magarey and N. Kingsbury, “Motion estimation using a complex-valued wavelet transform,” IEEE Trans. Signal Process. 46, 1069–1084 (1998).
    [CrossRef]
  19. E. Goldhahn and E. J. Seume, “The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field,” Exp. Fluids 43, 241–249 (2007).
    [CrossRef]
  20. J. E. Bridges and M. P. Wernet, “Effect of temperature on jet velocity spectra,” NASA/TM-2007-214993 (2007).
  21. R. Cook and T. DeRose, “Wavelet noise,” ACM Trans. Graphics 24, 803–811 (2005).
    [CrossRef]
  22. B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
    [CrossRef]
  23. E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
    [CrossRef]
  24. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [CrossRef] [PubMed]
  25. N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
    [CrossRef]
  26. J. H. W. Lee and V. H. Chu, Turbulent Jets and Plumes—A Lagrangian Approach (Kluwer, 2003).
    [CrossRef]

2010 (2)

G. S. Settles, “Recent developments in schlieren and shadowgraph techniques,” in Proceedings of 14th International Symposium on Flow Visualization (2010), paper ISFV14-IL-2.

E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
[CrossRef]

2008 (2)

B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
[CrossRef]

F. Klinge, “Fluid flow rate determining method, involves tracing spatial offset of density variations based on images taken at different times, and determining local flow rate of fluid from offset and interval of times,” German patent DE102006047286 (2008).

2007 (4)

E. Goldhahn and E. J. Seume, “The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field,” Exp. Fluids 43, 241–249 (2007).
[CrossRef]

J. E. Bridges and M. P. Wernet, “Effect of temperature on jet velocity spectra,” NASA/TM-2007-214993 (2007).

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

R. P. Satti, P. S. Kolhe, S. Olcmen, and A. K. Agrawal, “Miniature rainbow schlieren deflectometry system for quantitative measurements in microjets and flames,” Appl. Opt. 46, 2954–2962 (2007).
[CrossRef] [PubMed]

2005 (2)

2004 (3)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

D. Calluaud and L. David, “Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block,” Exp. Fluids 36, 53–61 (2004).
[CrossRef]

F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.

2003 (2)

2002 (1)

2001 (1)

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

1999 (1)

G. E. A. Meier, “Hintergrund schlierenmessverfahren,” Deutsche Patentanmeldung, DE 199 42 856 A1 (1999).

1998 (3)

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.

J. Magarey and N. Kingsbury, “Motion estimation using a complex-valued wavelet transform,” IEEE Trans. Signal Process. 46, 1069–1084 (1998).
[CrossRef]

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

1994 (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
[CrossRef]

1991 (1)

D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
[CrossRef]

1984 (1)

1983 (1)

W. L. Howes, “Rainbow schlieren,” NASA TP-2166 (1983).

Agrawal, A. K.

Atcheson, B.

B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
[CrossRef]

Aziz, A. R. A.

E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
[CrossRef]

Barron, J. L.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
[CrossRef]

Beauchemin, S. S.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
[CrossRef]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Bridges, J. E.

J. E. Bridges and M. P. Wernet, “Effect of temperature on jet velocity spectra,” NASA/TM-2007-214993 (2007).

Calluaud, D.

D. Calluaud and L. David, “Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block,” Exp. Fluids 36, 53–61 (2004).
[CrossRef]

Chellappa, R.

Chu, V. H.

J. H. W. Lee and V. H. Chu, Turbulent Jets and Plumes—A Lagrangian Approach (Kluwer, 2003).
[CrossRef]

Cook, R.

R. Cook and T. DeRose, “Wavelet noise,” ACM Trans. Graphics 24, 803–811 (2005).
[CrossRef]

Dalziel, S. B.

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.

Dam, N. J.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

David, L.

D. Calluaud and L. David, “Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block,” Exp. Fluids 36, 53–61 (2004).
[CrossRef]

DeRose, T.

R. Cook and T. DeRose, “Wavelet noise,” ACM Trans. Graphics 24, 803–811 (2005).
[CrossRef]

Fleet, D. J.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
[CrossRef]

D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
[CrossRef]

Goldhahn, E.

E. Goldhahn and E. J. Seume, “The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field,” Exp. Fluids 43, 241–249 (2007).
[CrossRef]

Heidrich, W.

B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
[CrossRef]

Howes, W. L.

Hughes, G. O.

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.

Huisman-Kleinherenbrink, P. M.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

Ibarreta, A. F.

Iffa, E. D.

E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
[CrossRef]

Ihrke, I.

B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
[CrossRef]

Jenkin, M.

D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
[CrossRef]

Jepson, A. D.

D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
[CrossRef]

Kingsbury, N.

J. Magarey and N. Kingsbury, “Motion estimation using a complex-valued wavelet transform,” IEEE Trans. Signal Process. 46, 1069–1084 (1998).
[CrossRef]

Kirmse, T.

F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.

Klinge, F.

F. Klinge, “Fluid flow rate determining method, involves tracing spatial offset of density variations based on images taken at different times, and determining local flow rate of fluid from offset and interval of times,” German patent DE102006047286 (2008).

F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.

Kolhe, P. S.

Kompenhans, J.

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.

Lee, J. H. W.

J. H. W. Lee and V. H. Chu, Turbulent Jets and Plumes—A Lagrangian Approach (Kluwer, 2003).
[CrossRef]

Liu, H.

Magarey, J.

J. Magarey and N. Kingsbury, “Motion estimation using a complex-valued wavelet transform,” IEEE Trans. Signal Process. 46, 1069–1084 (1998).
[CrossRef]

Malik, A. S.

E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
[CrossRef]

Meier, G. E. A.

G. E. A. Meier, “Hintergrund schlierenmessverfahren,” Deutsche Patentanmeldung, DE 199 42 856 A1 (1999).

Olcmen, S.

Puri, I. K.

Raffel, M.

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

Rodenburg, M.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

Rosenfeld, A.

Satti, R. P.

Settles, G. S.

G. S. Settles, “Recent developments in schlieren and shadowgraph techniques,” in Proceedings of 14th International Symposium on Flow Visualization (2010), paper ISFV14-IL-2.

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

Seume, E. J.

E. Goldhahn and E. J. Seume, “The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field,” Exp. Fluids 43, 241–249 (2007).
[CrossRef]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Stoffels, G. G. M.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

Sung, C. J.

Sutherland, B. R.

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.

ter Meulen, J. J.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

Tolboom, R. A. L.

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Wereley, S. T.

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

Wernet, M. P.

J. E. Bridges and M. P. Wernet, “Effect of temperature on jet velocity spectra,” NASA/TM-2007-214993 (2007).

Willert, C. E.

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

Xiao, X.

ACM Trans. Graphics (1)

R. Cook and T. DeRose, “Wavelet noise,” ACM Trans. Graphics 24, 803–811 (2005).
[CrossRef]

Appl. Opt. (4)

CVGIP: Image Underst. (1)

D. J. Fleet, A. D. Jepson, and M. Jenkin, “Phase-based disparity measurement,” CVGIP: Image Underst. 53, 198–210(1991).
[CrossRef]

Exp. Fluids (4)

E. Goldhahn and E. J. Seume, “The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field,” Exp. Fluids 43, 241–249 (2007).
[CrossRef]

D. Calluaud and L. David, “Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block,” Exp. Fluids 36, 53–61 (2004).
[CrossRef]

B. Atcheson, W. Heidrich, and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren,” Exp. Fluids 46, 467–477 (2008).
[CrossRef]

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, and J. J. ter Meulen, “Imaging of an underexpanded nozzle flow by UV laser Rayleigh scattering,” Exp. Fluids 24, 93–101 (1998).
[CrossRef]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

IEEE Trans. Signal Process. (1)

J. Magarey and N. Kingsbury, “Motion estimation using a complex-valued wavelet transform,” IEEE Trans. Signal Process. 46, 1069–1084 (1998).
[CrossRef]

Int. J. Comput. Vis. (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77(1994).
[CrossRef]

J. Eur. Opt. Soc. Rap. Pub. (1)

E. D. Iffa, A. R. A. Aziz, and A. S. Malik, “Concentration measurement of injected gaseous fuel using quantitative schlieren and optical tomography,” J. Eur. Opt. Soc. Rap. Pub. 5, 10029 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (11)

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry A Practical Guide, 2nd ed.(Springer, 2007).

J. H. W. Lee and V. H. Chu, Turbulent Jets and Plumes—A Lagrangian Approach (Kluwer, 2003).
[CrossRef]

F. Klinge, T. Kirmse, and J. Kompenhans, “Investigation of the density and velocity distribution of a wing tip vortex by means of stereoscopic background oriented schlieren method (BOS) and stereoscopic particle image velocimetry (PIV),” in 12th International Symposium on Application of Laser Techniques to Fluid Mechanics (2004), paper 1249.

F. Klinge, “Fluid flow rate determining method, involves tracing spatial offset of density variations based on images taken at different times, and determining local flow rate of fluid from offset and interval of times,” German patent DE102006047286 (2008).

J. E. Bridges and M. P. Wernet, “Effect of temperature on jet velocity spectra,” NASA/TM-2007-214993 (2007).

http://www.dantecdynamics.com/Default.aspx?ID=653

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

G. E. A. Meier, “Hintergrund schlierenmessverfahren,” Deutsche Patentanmeldung, DE 199 42 856 A1 (1999).

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland, “Synthetic schlieren,” in Proceedings of 8th International Symposium on Flow Visualization (1998), paper 62.

G. S. Settles, “Recent developments in schlieren and shadowgraph techniques,” in Proceedings of 14th International Symposium on Flow Visualization (2010), paper ISFV14-IL-2.

W. L. Howes, “Rainbow schlieren,” NASA TP-2166 (1983).

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Figures (13)

Fig. 1
Fig. 1

Two levels of CDWT [15].

Fig. 2
Fig. 2

Algorithm for displacement vector estimation.

Fig. 3
Fig. 3

Velocity and the normal vector of an elemental area.

Fig. 4
Fig. 4

(a) Model for axisymmetric jet’s frontal view. (b) Cross-sectional area of a jet along a plane perpendicular to the jet axis.

Fig. 5
Fig. 5

BOS experimental setup.

Fig. 6
Fig. 6

Centerline density distribution of different exit temperatures and their respective trend lines.

Fig. 7
Fig. 7

Centerline velocity decay at different jet-exit temperatures.

Fig. 8
Fig. 8

Axial velocity distribution of the jet at 473 K .

Fig. 9
Fig. 9

(a) Axial velocity and (b) the tangential velocity profile of a heated jet.

Fig. 10
Fig. 10

Vorticity vector of the injected hot air at 473 K .

Fig. 11
Fig. 11

Velocity variance v i v ¯ i / U o (a) axial velocity (b) tangential velocity.

Fig. 12
Fig. 12

PSD of the axial velocity at T = 473 K .

Fig. 13
Fig. 13

Percentage COV between BOS and hot wire anemometry readings of velocity decay at 302 and 323 K .

Tables (1)

Tables Icon

Table 1 COV of Different Velocity Parameters

Equations (21)

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

I x δ x + I y δ y + I t δ t = 0.
ε ( θ , s ) = d d s l n ( t , s ) d t ,
n ' ( x , y ) = 0 π q ( s ) * ε ( θ , s ) d θ ,
q ( s ) = Q ( k ) e i 2 π k s d k ,
n 1 = G ρ ,
T = ρ o ρ T o = n o 1 n 1 T o ,
/ t V ρ d v = s ρ V . d S ,
/ t V ρ d v = s ρ V . n d s .
V z = V . n = V n cos α .
/ t V ρ r d r d θ d z = ρ V z r d r d θ .
/ r θ ( / t V ρ r d r d θ d z ) = / r θ ( s ρ V n r d r d θ ) .
( / t ( ρ r ) ) d z = ρ V n r .
V z = ( / t ( ρ r ) ) d z ρ r .
( ρ V z ) / t + V r ( ρ V z ) / r + V z ( ρ V z ) / z = P / z ,
p = ρ R T .
V r = ( ( p / z ) + ( ρ V z ) / t + V z ( ( ρ V z ) / z ) ( ρ V z ) / r ) .
( ) r = ( ) t f 1 + ( ) t + 1 f 1 ( ) r = ( ) t f 1 + ( ) t + 1 f 1 ( ) t = ( ) t f 3 + ( ) t + 1 f 3 } ,
V i ( X , t ) = u i ( X , t ) U i ( X ) ,
U i ( X ) = 1 T t = 0 t = T u i ( X , t ) d t .
G v k v k ( f ; X ) = 1 T t = 0 t = T v k v k ¯ ( τ ; X ) e i ω τ d τ .
COV = ( U ¯ BOS ) 2 ( U ¯ HWA ) 2 U HWA × 100 % ,

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