Abstract

This study employs rainbow schlieren deflectometry (RSD) to characterize the unsteady, supersonic/subsonic exhaust plume of a rotating detonation combustor (RDC). First, RSD images are analyzed to quantify the frequency and strength of flow oscillations and their relationship to the detonation wave. Secondly, a three-dimensional (3D) tomographic algorithm is used to obtain the local 3D density field across the whole region of interest (ROI). The tomographic analysis relies upon wave rotation to infer projection data of the 3D exhaust plume at multiple view angles using a single RSD camera system and was previously validated using phantom data from computational fluid dynamics analysis of an RDC. The annular RDC operated on methane and 2/3 O2–1/3 N2 oxidizer mixture is equipped with a converging nozzle to pressurize the combustion chamber. The product flow exiting the nozzle throat expands across an unoptimized conical aerospike attached to the center body of the RDC. RSD images provide a temporal resolution of 369 ns and spatial resolution of 100 μm in a 6.4 mm high and 25.6 mm wide ROI of the exhaust plume. A rainbow filter is calibrated to convert hue in color schlieren images into deflection angle data. These data are used to characterize the unsteady flow oscillations that show excellent agreement with PCB pressure probe measurements acquired inside the combustion chamber. Tomographic analysis yields a 3D local density field that shows distinct features, consistent with published numerical simulations of the RDC exhaust plume. For the first time, this work demonstrates the ability of high-speed nonintrusive RSD diagnostics to acquire whole-field density measurements in an operational RDC. Such data would be valuable to validate high-fidelity numerical simulations and gain a further understanding of the exhaust flow to help with RDC-turbine integration. Further improvements to the RSD hardware and analysis procedures would enhance present capabilities to ultimately infer other thermodynamic properties such as temperature and pressure from density measurements.

References

1.
Bach
,
E.
,
Thethy
,
B. S.
,
Edgington-Mitchell
,
D.
,
Rezay Haghdoost
,
M.
,
Oliver Paschereit
,
C.
,
Stathopoulos
,
P.
, and
Bohon
,
M. D.
,
2022
, “
Kiel Probes for Stagnation Pressure Measurement in Rotating Detonation Combustors
,”
AIAA J.
,
60
(
6
), pp.
3724
3735
.10.2514/1.J061061
2.
Naples
,
A.
,
Hoke
,
J.
,
Battelle
,
R.
, and
Schauer
,
F.
,
2019
, “
T63 Turbine Response to Rotating Detonation Combustor Exhaust Flow
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p.
021029
.10.1115/1.4041135
3.
Stevens
,
C. A.
,
Fotia
,
M.
,
Hoke
,
J.
, and
Schauer
,
F.
,
2015
, “
Comparison of Transient Response of Pressure Measurement Techniques With Application to Detonation Waves
,”
AIAA
Paper No. 1102.10.2514/6.1102
4.
Merzkirch
,
W.
,
2012
,
Flow Visualization
, Academic Press Inc., Orlando, F
L
.
5.
Tobias
,
J.
, and
Agrawal
,
A. K.
,
2021
, “
Time Resolved Flow Field in the Radial Plane of an Aerospike Integrated With a Rotating Detonation Combustor
,”
AIAA
Paper No. 3675.10.2514/6.3675
6.
Tobias
,
J.
,
Agrawal
,
A. K.
, and
Paxson
,
D. E.
,
2022
, “
Experimental and Computational Analysis of a Rotating Detonation Combustor
,”
AIAA
Paper No. 1879.10.2514/6.1879
7.
Agrawal
,
A. K.
,
Talukdar
,
S.
,
Langner
,
D.
, and
Gupta
,
A.
,
2023
, “
Flow Characterization of a Rotating Detonation Combustor Integrated With Various Convergent Nozzles
,”
AIAA
Paper No. 1295.10.2514/6.1295
8.
Langner
,
D.
,
Gupta
,
A.
,
Talukdar
,
S.
, and
Agrawal
,
A. K.
,
2023
, “
Multi-Wave Operation of a Radial Rotating Detonation Engine With Integrated Aerospike
,”
AIAA
Paper No. 0578.10.2514/6.0578
9.
Journell
,
C. L.
,
Gejji
,
R. M.
,
Walters
,
I. V.
,
Lemcherfi
,
A. I.
,
Slabaugh
,
C. D.
, and
Stout
,
J. B.
,
2020
, “
High-Speed Diagnostics in a Natural Gas–Air Rotating Detonation Engine
,”
J. Propul. Power
,
36
(
4
), pp.
498
507
.10.2514/1.B37740
10.
Tobias
,
J.
,
Depperschmidt
,
D.
,
Welch
,
C.
,
Miller
,
R.
,
Uddi
,
M.
,
Agrawal
,
A. K.
, and
Daniel
,
R.
,
2019
, “
OH* Chemiluminescence Imaging of the Combustion Products From a Methane-Fueled Rotating Detonation Engine
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p. 021021.10.1115/1.4041143
11.
Athmanathan
,
V.
,
Braun
,
J.
,
Ayers
,
Z. M.
,
Fugger
,
C. A.
,
Webb
,
A. M.
,
Slipchenko
,
M. N.
,
Paniagua
,
G.
,
Roy
,
S.
, and
Meyer
,
T. R.
,
2022
, “
On the Effects of Reactant Stratification and Wall Curvature in Non-Premixed Rotating Detonation Combustors
,”
Combust. Flame
,
240
, p.
112013
.10.1016/j.combustflame.2022.112013
12.
Rankin
,
B. A.
,
Richardson
,
D. R.
,
Caswell
,
A. W.
,
Naples
,
A. G.
,
Hoke
,
J. L.
, and
Schauer
,
F. R.
,
2017
, “
Chemiluminescence Imaging of an Optically Accessible Non-Premixed Rotating Detonation Engine
,”
Combust. Flame
,
176
, pp.
12
22
.10.1016/j.combustflame.2016.09.020
13.
Nair
,
A. P.
,
Lee
,
D. D.
,
Pineda
,
D. I.
,
Kriesel
,
J.
,
Hargus
,
W. A.
, Jr
,
Bennewitz
,
J. W.
,
Danczyk
,
S. A.
, and
Spearrin
,
R. M.
,
2020
, “
MHz Laser Absorption Spectroscopy Via Diplexed RF Modulation for Pressure, Temperature, and Species in Rotating Detonation Rocket Flows
,”
Appl. Phys. B
,
126
(
8
), p.
138
.10.1007/s00340-020-07483-8
14.
Agrawal
,
A.
, and
Wanstall
,
C. T.
,
2018
, “
Rainbow Schlieren Deflectometry for Scalar Measurements in Fluid Flows
,”
J. Flow Visualization Image Process.
,
25
(
3–4
), pp.
329
357
.10.1615/JFlowVisImageProc.2018028312
15.
Albers
,
B. W.
, and
Agrawal
,
A. K.
,
1999
, “
Schlieren Analysis of an Oscillating Gas-Jet Diffusion Flame
,”
Combust. Flame
,
119
(
1–2
), pp.
84
94
.10.1016/S0010-2180(99)00034-6
16.
O'Meara
,
B.
,
Bedick
,
C.
, and
Ferguson
,
D. H.
,
2018
, “
Experimental Investigation of a Shock Wave Using Calibrated Schlieren Images
,”
AIAA
Paper No. 2018-4686.10.2514/6.2018-4686
17.
Miller
,
R.
,
Tobias
,
J.
,
Depperschmidt
,
D.
,
Bell
,
K.
,
Langner
,
D.
, and
Agrawal
,
A. K.
,
2019
, “
Rainbow Schlieren Imaging of Density Field in the Exhaust Flow of Rotating Detonation Combustion
,”
AIAA
Paper No. 2019-4380.10.2514/6.2019-4380
18.
Dille
,
K. J.
,
Frederick
,
M. D.
,
Slabaugh
,
C. D.
, and
Heister
,
S. D.
,
2024
, “
Rotating Detonation Combustor Performance Informed Through a Novel Megahertz-Rate Stagnation Pressure Measurement
,”
Phys. Fluids
,
36
(
2
), p. 026127.10.1063/5.0195465
19.
Gupta
,
A.
,
Langner
,
D.
,
Miller
,
R.
,
Sawaya
,
S.
, and
Agrawal
,
A. K.
,
2023
, “
Imaging Exhaust Flow of Radial RDE Using Rainbow Schlieren Deflectometry
,”
AIAA
Paper No. 2023-2391.10.2514/6.2023-2391
20.
Kak
,
A. C.
, and
Slaney
,
M.
,
2001
,
Principles of Computerized Tomographic Imaging
, IEEE Press, New York.
21.
Agrawal
,
A. K.
,
Butuk
,
N. K.
,
Gollahalli
,
S. R.
, and
Griffin
,
D.
,
1998
, “
Three Dimensional Rainbow Schlieren Tomography of a Temperature Field in Gas Flows
,”
Appl. Opt.
,
37
(
3
), pp.
479
485
.10.1364/AO.37.000479
22.
Hartmann
,
U.
, and
Seume
,
J. R.
,
2016
, “
Combining ART and FBP for Improved Fidelity of Tomographic BOS
,”
Meas. Sci. Technol.
,
27
(
9
), p.
097001
.10.1088/0957-0233/27/9/097001
23.
Nicolas
,
F.
,
Todoroff
,
V.
,
Plyer
,
A.
,
Le Besnerais
,
G.
,
Donjat
,
D.
,
Micheli
,
F.
,
Champagnat
,
F.
,
Cornic
,
P.
, and
Le Sant
,
Y.
,
2016
, “
A Direct Approach for Instantaneous 3D Density Field Reconstruction From Background-Oriented Schlieren (BOS) Measurements
,”
Exp. Fluids
,
57
(
1
), pp.
1
21
.10.1007/s00348-015-2100-x
24.
Grauer
,
S. J.
,
Unterberger
,
A.
,
Rittler
,
A.
,
Daun
,
K. J.
,
Kempf
,
A. M.
, and
Mohri
,
K.
,
2018
, “
Instantaneous 3D Flame Imaging by Background-Oriented Schlieren Tomography
,”
Combust. Flame
,
196
, pp.
284
299
.10.1016/j.combustflame.2018.06.022
25.
Amjad
,
S.
,
Karami
,
S.
,
Soria
,
J.
, and
Atkinson
,
C.
,
2019
, “
Assessment of Three-Dimensional Turbulent Density Measurements From Tomographic Background-Oriented Schlieren (BOS)
,”
13th International Symposium on Particle Image Velocimetry
,
Munich, Germany
, July
22
24
.https://athene-forschung.unibw.de/128737?sortfield0=authors&sortfield1=&show_id=128815&liststyle=text
26.
Atkinson
,
C.
,
Amjad
,
S.
, and
Soria
,
J.
,
2017
, “
A Tomographic Background-Oriented Schlieren Method for 3D Density Field Measurements in Heated Jets
,”
11th Asia-Pacific Conference on Combustion
,
Sydney, Australia
, Dec.
10
14
.https://research.monash.edu/files/334151819/262797539_oa.pdf
27.
Gupta
,
A.
,
Bell
,
K.
,
Bogdanowicz
,
E. F.
, and
Agrawal
,
A. K.
,
2024
, “
Schlieren-Based Methodology for Tomographic Reconstruction of 3D Density Field in RDE Exhaust
,”
AIAA
Paper No. 2024-2035.10.2514/6.2024-2035
28.
Schwer
,
D.
, and
Kailasanath
,
K.
,
2012
, “
Modeling Exhaust Effects in Rotating Detonation Engines
,”
AIAA
Paper No. 3943.10.2514/6.3943
29.
Faris
,
G. W.
, and
Byer
,
R. L.
,
1988
, “
Three-Dimensional Beam-Deflection Optical Tomography of a Supersonic Jet
,”
Appl. Opt.
,
27
(
24
), pp.
5202
5212
.10.1364/AO.27.005202
30.
Song
,
Y.
,
Zhang
,
B.
, and
He
,
A.
,
2006
, “
Algebraic Iterative Algorithm for Deflection Tomography and Its Application to Density Flow Fields in a Hypersonic Wind Tunnel
,”
Appl. Opt.
,
45
(
31
), pp.
8092
8101
.10.1364/AO.45.008092
31.
Al-Ammar
,
K.
,
Agrawal
,
A.
,
Gollahalli
,
S. R.
, and
Griffin
,
D.
,
1998
, “
Application of Rainbow Schlieren Deflectometry for Concentration Measurements in an Axisymmetric Helium Jet
,”
Exp. Fluids
,
25
(
2
), pp.
89
95
.10.1007/s003480050211
32.
Butuk
,
N. K.
,
1997
, “
Fluid Flow Diagnostics Using Rainbow Schlieren Imaging and Computer Tomography
,”
The University of Oklahoma
, Norman, OK.
33.
Guo
,
Z.
,
Song
,
Y.
,
Yuan
,
Q.
,
Wulan
,
T.
, and
Chen
,
L.
,
2017
, “
Simultaneous Reconstruction of 3D Refractive Index, Temperature, and Intensity Distribution of Combustion Flame by Double Computed Tomography Technologies Based on Spatial Phase-Shifting Method
,”
Opt. Commun.
,
393
, pp.
123
130
.10.1016/j.optcom.2017.02.043
34.
Zhang
,
B.
,
He
,
Y.
,
Song
,
Y.
, and
He
,
A.
,
2009
, “
Deflection Tomographic Reconstruction of a Complex Flow Field From Incomplete Projection Data
,”
Opt. Lasers Eng.
,
47
(
11
), pp.
1183
1188
.10.1016/j.optlaseng.2009.06.007
35.
Zhang
,
B.
,
Wu
,
Z.
, and
Zhao
,
M.
,
2015
, “
Deflection Tomographic Reconstructions of a Three-Dimensional Flame Structure and Temperature Distribution of Premixed Combustion
,”
Appl. Opt.
,
54
(
6
), pp.
1341
1349
.10.1364/AO.54.001341
36.
Faris
,
G. W.
, and
Byer
,
R. L.
,
1987
, “
Beam-Deflection Optical Tomography
,”
Opt. Lett.
,
12
(
2
), pp.
72
74
.10.1364/OL.12.000072
37.
Gardiner
,
W.
, Jr
,
Hidaka
,
Y.
, and
Tanzawa
,
T.
,
1981
, “
Refractivity of Combustion Gases
,”
Combust. Flame
,
40
, pp.
213
219
.10.1016/0010-2180(81)90124-3
You do not currently have access to this content.