Abstract

Rapid-double-exposure, diffuse-illumination holography is evaluated analytically and experimentally as a flow visualization method for time-varying shock waves. Conditions are determined that minimize the distance (localization error) between the surface or curve of interference-fringe localization and the shock surface. Treated specifically are the cases of shock waves in a transonic compressor rotor for which there is laser anemometer data for comparison and shock waves in a flutter cascade.

© 1981 Optical Society of America

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References

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  1. J. Winckler, Rev. Sci. Instrum. 19, 307 (1948).
    [Crossref] [PubMed]
  2. R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).
  3. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 284.
  4. A. J. Decker, “Fringe Localization Requirements for Three-Dimensional Flow Visualization of Shock Waves in Diffuse-Illumination, Double-Pulse Holographic Interferometry,” NASA TP-1868, to be published.
  5. D. R. Boldman, A. E. Buggele, “Wind Tunnel Tests of a Blade Subjected to Midchord Torsional Oscillation at High Subsonic Stall Flutter Conditions,” NASA TM-78998 (1978).
  6. A. J. Strazisar, R. V. Chima, “Comparison Between Optical Measurements and a Numerical Solution of the Flow Field in a Transonic Axial Flow Compressor Rotor,” AIAA Paper 80-1078 (June1980).
  7. W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Gaseous Density Fields,” NASA TN-2693 (1952).
  8. A. J. Strazisar, J. A. Powell, Proceedings of the Joint Fluids Engineering Gas Turbine Conference and Products Show, B. Lakshminarsyana, P. Runstadler, Eds. (American Society of Mechanical Engineers, New York, 1980), pp. 165–176; to be published in ASME J. Eng. Power.

1978 (1)

D. R. Boldman, A. E. Buggele, “Wind Tunnel Tests of a Blade Subjected to Midchord Torsional Oscillation at High Subsonic Stall Flutter Conditions,” NASA TM-78998 (1978).

1974 (1)

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

1952 (1)

W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Gaseous Density Fields,” NASA TN-2693 (1952).

1948 (1)

J. Winckler, Rev. Sci. Instrum. 19, 307 (1948).
[Crossref] [PubMed]

Boldman, D. R.

D. R. Boldman, A. E. Buggele, “Wind Tunnel Tests of a Blade Subjected to Midchord Torsional Oscillation at High Subsonic Stall Flutter Conditions,” NASA TM-78998 (1978).

Buchele, D. R.

W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Gaseous Density Fields,” NASA TN-2693 (1952).

Buggele, A. E.

D. R. Boldman, A. E. Buggele, “Wind Tunnel Tests of a Blade Subjected to Midchord Torsional Oscillation at High Subsonic Stall Flutter Conditions,” NASA TM-78998 (1978).

Chima, R. V.

A. J. Strazisar, R. V. Chima, “Comparison Between Optical Measurements and a Numerical Solution of the Flow Field in a Transonic Axial Flow Compressor Rotor,” AIAA Paper 80-1078 (June1980).

Decker, A. J.

A. J. Decker, “Fringe Localization Requirements for Three-Dimensional Flow Visualization of Shock Waves in Diffuse-Illumination, Double-Pulse Holographic Interferometry,” NASA TP-1868, to be published.

Heflinger, L. O.

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

Howes, W. L.

W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Gaseous Density Fields,” NASA TN-2693 (1952).

Kobayashi, R. J.

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

Powell, J. A.

A. J. Strazisar, J. A. Powell, Proceedings of the Joint Fluids Engineering Gas Turbine Conference and Products Show, B. Lakshminarsyana, P. Runstadler, Eds. (American Society of Mechanical Engineers, New York, 1980), pp. 165–176; to be published in ASME J. Eng. Power.

Strazisar, A. J.

A. J. Strazisar, J. A. Powell, Proceedings of the Joint Fluids Engineering Gas Turbine Conference and Products Show, B. Lakshminarsyana, P. Runstadler, Eds. (American Society of Mechanical Engineers, New York, 1980), pp. 165–176; to be published in ASME J. Eng. Power.

A. J. Strazisar, R. V. Chima, “Comparison Between Optical Measurements and a Numerical Solution of the Flow Field in a Transonic Axial Flow Compressor Rotor,” AIAA Paper 80-1078 (June1980).

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 284.

Ware, T. C.

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

Winckler, J.

J. Winckler, Rev. Sci. Instrum. 19, 307 (1948).
[Crossref] [PubMed]

Wuerker, R. F.

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

NASA CR-121264 (1)

R. F. Wuerker, R. J. Kobayashi, L. O. Heflinger, T. C. Ware, “Application of Holography to Flow Visualization within Rotating Compressor Blade Row,” NASA CR-121264 (1974).

NASA TM-78998 (1)

D. R. Boldman, A. E. Buggele, “Wind Tunnel Tests of a Blade Subjected to Midchord Torsional Oscillation at High Subsonic Stall Flutter Conditions,” NASA TM-78998 (1978).

NASA TN-2693 (1)

W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Gaseous Density Fields,” NASA TN-2693 (1952).

Rev. Sci. Instrum. (1)

J. Winckler, Rev. Sci. Instrum. 19, 307 (1948).
[Crossref] [PubMed]

Other (4)

A. J. Strazisar, J. A. Powell, Proceedings of the Joint Fluids Engineering Gas Turbine Conference and Products Show, B. Lakshminarsyana, P. Runstadler, Eds. (American Society of Mechanical Engineers, New York, 1980), pp. 165–176; to be published in ASME J. Eng. Power.

A. J. Strazisar, R. V. Chima, “Comparison Between Optical Measurements and a Numerical Solution of the Flow Field in a Transonic Axial Flow Compressor Rotor,” AIAA Paper 80-1078 (June1980).

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 284.

A. J. Decker, “Fringe Localization Requirements for Three-Dimensional Flow Visualization of Shock Waves in Diffuse-Illumination, Double-Pulse Holographic Interferometry,” NASA TP-1868, to be published.

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Figures (10)

Fig. 1
Fig. 1

Fringe-localization variables in rapid-double-exposure holography.

Fig. 2
Fig. 2

Fringe-localization variables for a time-varying shock wave.

Fig. 3
Fig. 3

Holography in a single-stage compressor test facility.

Fig. 4
Fig. 4

Reference coordinates for a compressor rotor.

Fig. 5
Fig. 5

Surface-localized fringe pattern associated with passage shock wave in rotating transonic compressor rotor.

Fig. 6
Fig. 6

Comparison of shock position from laser anemometry with fringe position from rapid-double-exposure holography–data recorded near stall at 100% speed.

Fig. 7
Fig. 7

Shock positions calculated from fringe position for two extremes of view in Table I.

Fig. 8
Fig. 8

Diffuse-illumination holography in a three-blade flutter cascade.

Fig. 9
Fig. 9

Reference coordinates for computing fringe localization in a flutter cascade.

Fig. 10
Fig. 10

Surface-localized fringe pattern associated with one state of a shock wave in a flutter cascade.

Tables (1)

Tables Icon

Table I Direction Cosines Defining Extremes of Viewing Perspective In Measuring Fringe Position

Equations (44)

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z = - f · K x z d z - i ^ · f d z ,
z = - f · K y z d z - j ^ · f d z
r = r f + k k z ( z - z )
r = r r + k k z z .
K x = ( k y 3 + k z 2 , - k x k y , - k x k z ) ,
K y = ( - k x k y , k x 2 + k z 2 , - k y k z ) ,
g 1 ( r ) = 0
g 2 ( r ) = 0.
R 1 = r f + k k z ( Z 1 - z )
R 2 = r f + k k z ( Z 2 - z ) ,
f ( r ) = Δ N 2 ( r ) g 2 ( r ) δ [ g 2 ( r ) ] - Δ N 1 ( r ) g 1 ( r ) δ [ g 1 ( r ) ] ,
z = Δ N 2 ( R 2 ) g 2 ( R 2 ) · K x Z 2 k · g 2 ( R 2 ) - Δ N 1 ( R 1 ) g 1 ( R 1 ) · K x Z 1 k · g 1 ( R 1 ) Δ N 2 ( R 2 ) i ^ · g 2 ( R 2 ) k · g 2 ( R 2 ) - Δ N 1 ( R 1 ) i ^ · g 1 ( R 1 ) k · g 1 ( R 1 ) ,
z = Δ N 2 ( R 2 ) g 2 ( R 2 ) · K y Z 2 k · g 2 ( R 2 ) - Δ N 1 ( R 1 ) g 1 ( R 1 ) · K y Z 1 k · g 1 ( R 1 ) Δ N 2 ( R 2 ) j ^ · g 2 ( R 2 ) k · g 2 ( R 2 ) - Δ N 1 ( R 1 ) j ^ · g 1 ( R 1 ) k · g 1 ( R 1 ) .
g 2 ( r ) = g 1 ( r t ) ,
r t = γ ¯ ¯ · r + d ,
γ ¯ ¯ = ( 1 0 - α 0 1 0 α 0 1 ) ,
d = ( 0 , 0 , - R c α ) ,
g 1 ( r ) = g ( r ) = 0.
g 2 ( r ) = g ( r t ) = t g ( r t ) · γ ¯ ¯ ,
R 1 = R ,
R t = γ ¯ ¯ · R 2 + d ,
z = Δ N ( R t ) t g ( R t ) · γ ¯ ¯ · K x Z 2 k · t g ( R t ) · γ ¯ ¯ - Δ N ( R ) g ( R ) · K x Z 1 k · g ( R ) Δ N ( R t ) i ^ · t g ( R t ) · γ ¯ ¯ k · t g ( R t ) · γ ¯ ¯ - Δ N ( R ) i ^ · g ( R ) k · g ( R ) ,
z = Δ N ( R t ) t g ( R t ) · γ ¯ ¯ · K y Z 2 k · t g ( R t ) · γ ¯ ¯ - Δ N ( R ) g ( R ) · K y Z 1 k · g ( R ) Δ N ( R t ) j ^ · t g ( R t ) · γ ¯ ¯ k · t g ( R t ) · γ ¯ ¯ - Δ N ( R ) j ^ · g ( R ) k · g ( R ) .
g ( R t ) = 0 ,
g ( R ) = 0.
Δ m = 1 - Δ N ( R ) Δ N ( R t ) .
z = Z 1 + [ K x · g ( R ) ] [ k · g ( R ) ] d Z 2 d α | α = 0 [ i · g ( R ) ] - k x [ k · g ( R ) ] 2 Z 1 Δ m α [ i · g ( R ) ] D x
z = Z 1 + [ K y · g ( R ) ] [ k · g ( R ) ] d Z 2 d α | α = 0 [ j ^ · g ( R ) ] - k y [ k · g ( R ) ] 2 Z 1 Δ m α [ j ^ · g ( R ) ] D y
D x = Δ m α [ k · g ( R ) ] + k · g ( R ) i ^ · g ( R ) [ i ^ · d d α t g ( R t ) | α = 0 ] - [ k · d d α t g ( R t ) | α = 0 ] - [ k · g ( R ) · Ω ¯ ¯ ] + [ k · g ( R ) ] [ j ^ · g ( R ) · Ω ¯ ¯ ] i ^ · g ( R )
D y = Δ m α [ k · g ( R ) ] + k · g ( R ) j ^ · g ( R ) [ j ^ · d d α t g ( R t ) | α = 0 ] - [ k · d d α t g ( R t ) | α = 0 ] - [ k · g ( R ) · Ω ¯ ¯ ] + [ k · g ( R ) ] [ j ^ · g ( R ) · Ω ¯ ¯ ] j ^ · g ( R ) ,
Ω ¯ ¯ = ( 0 0 - 1 0 0 0 1 0 0 ) .
z = i = 0 5 A i y i
k x , k y g 2 ( R 2 ) z ,             g 1 ( R 1 ) z ,             g 2 ( R 2 ) y ,             g 1 ( R 1 ) y
z - Z 1 = Z 2 - Z 1 1 - Δ N 1 ( R 1 ) Δ N 2 ( R 2 ) g 1 ( R 1 ) / x g 2 ( R 2 ) / x k · g 2 ( R 2 ) k · g 1 ( R 1 ) ,
z - Z 1 = Z 2 - Z 1 1 - Δ N 1 ( R 1 ) Δ N 2 ( R 2 ) g 1 ( R 1 ) / y g 2 ( R 2 ) / y k · g 2 ( R 2 ) k · g 1 ( R 1 ) ,
z - Z 2 = Z 1 - Z 2 1 - Δ N 2 ( R 2 ) g 2 ( R 2 ) / x Δ N 1 ( R 1 ) g 1 ( R 1 ) / x k · g 1 ( R 1 ) k · g 2 ( R 2 ) ,
z - Z 2 = Z 1 - Z 2 1 - Δ N 2 ( R 2 ) g 2 ( R 2 ) / y Δ N 1 ( R 1 ) g 1 ( R 1 ) / y k · g 1 ( R 1 ) k · g 2 ( R 2 ) .
X - X 1 = k x k z ( z - Z 1 )
X - X 2 = k x k z ( z - Z 2 ) ,
k · g 2 ( R 2 ) k · g 1 ( R 1 )
k · g 1 ( R 1 ) k · g 2 ( R 2 ) .
Δ N 1 ( R 1 ) Δ N 2 ( R 2 )
Δ N 2 ( R 2 ) Δ N 1 ( R 1 ) .
g 1 ( R 1 ) x / g 2 ( R 2 ) x

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