This document summarizes a presentation given at the 50th AIAA Aerospace Science Meeting on large eddy simulation (LES) studies of reacting and non-reacting transverse jets in supersonic crossflow. The presentation discusses the numerical methodology used, including the compressible flow solver and direct quadrature method of moments (DQMOM) combustion model. Results are presented for non-reacting and reacting jet in supersonic crossflow cases, including comparisons to experimental data. Key flow features like shock structures and vortical structures are analyzed.

1. 50th AIAA Aerospace Science Meeting Nashville, Tennessee January 10th, 2012
Acknowledgements
Texas Advanced Computing Center
Large Eddy Simulation based Studies of
Reacting and Non-reacting Transverse Jets
in Supersonic Crossflow
Shaun Kim a,b Pratik Donde a Venkat Raman a
Kuo-Cheng Lin c Campbell Carter d
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
a b c d

2. data have shown that this is not a reali
free-stream, plume overexpansion do
Motivation 354
Subsequently, Champigny and Lacau
supersonic cross-flow. TheirS. K. stru
S. Kawai and flow Lel
Crossflow
Jet
• Combustion inside hypersonic engine requiresetmixing of an und
Figure 1. Schematics of the transverse injection
crossflow (Ben-Yakar al. 2006; Gruber, Nejad,
optimization due to short residence time Figure 1
turing flows with complex shocks and contact surfaces a
eddying motions present in high Reynolds number flowf
The Champigny–Lacau model has
• Jet in supersonic crossflow exhibits complex flow upstream separation zone created fro
In the present study, an under-expanded sonic jet inj
is numerically simulated by using layer interaction also g
shock/boundary a high-order low dis
features; shock-turbulence interactions, 3D vortical
difference scheme (Lele the crossflow, but turns downstre
into 1992) and spatial filtering (Gait
structures capture the physicsreferred to as the barrel shock. The ba
of the supersonic turbulent mixing. R
capturing schemes the high-wavenumber biased artificia
of plume moves downstream. A se
vortices moving downstream along th
2005) and diffusivity (Fiorina & Lele 2007) are simpli
and stretched grid originating from the& Lele 2007) to se
framework (Kawai boundary layer p
• Supersonic combustion modeling is crucial to predict examines this near field mean flow stru
objective of this paper is to develop further insights into
chemical reaction characteristics the supersonic jet mixing. Comparisons between the L
data (Santiago & Dutton 1997) are also performed for v

3. Outline
• Jet in supersonic crossflow (JISC)
• Numerical methodology
- Compressible flow solver
- Direct quadrature method of moments (DQMOM)
• Result and discussions
- Non-reacting jet in supersonic crossflow
- Reacting jet in supersonic crossflow

4. flowfield that makes it difficult to quantify its effect on forces and moments. In the past, some res
suggested that the jet can be properly represented by a solid cylinder of given transverse length in in
Jet in Supersonic Crossflow
data have shown that this is not a realistic representation. Such a model does not include plume exp
free-stream, plume overexpansion downstream or the horseshoe vortex surrounding the jet arou
Subsequently, Champigny and Lacau5 gave a detailed explanation of the flow phenomena pres
354 supersonic cross-flow. TheirS. K. structure model is shown in Fig. 1.
S. Kawai and flow Lele
crossflow (Ben-Yakar et al. 2006; Gruber, Nejad, ChenChampigny-Lacau
Figure 1. Schematics of the transverse injection of an under-expanded jet into a supersonic
& Dutton 1995).
Figure 1. Champigny and Lacau flow structure model.5
• Jet/crossflow interaction creates complex 3D vortical
turing flows with complex shocks and contact surfaces and the 3-D broadband turbulent
The Champigny–Lacau model has found widespread acceptance currently. Amongst the flow fea
eddying motions present in high Reynolds number flows.
structures
In the present study, an under-expanded sonic jet injected bow a supersonic crossflow the approaching bounda
upstream separation zone created from a into shock interaction with
is numerically simulated by using layer interaction also generatesand dissipative compactshock. As the jet exits, it i
shock/boundary a high-order low dispersive a shock, or separation
difference scheme (Lele the crossflow, but turns downstream because of 2000) to properly a shock forms around th
into 1992) and spatial filtering (Gaitonde & Visbal this interaction and
• Shock-turbulence interaction
capture the physicsreferred to as the barrel shock. The barrel shock is terminated with a Mach disk and wake vortices a
of the supersonic turbulent mixing. Recently developed discontinuity-
capturing schemes the high-wavenumber biased artificial viscosity (Cook formed aft2004, jet plume with the so-c
of plume moves downstream. A secondary shock is & Cabot of the
2005) and diffusivity (Fiorina & Lele 2007) are simplified and extended to curvilinear model describes the hors
vortices moving downstream along the surface. The Champigny–Lacau
and stretched grid originating from the& Lele 2007) to separation upstream of the jet main
framework (Kawai boundary layer perform the simulation. The between the -shock region. Th
• Highly unsteady flow field
objective of this paper is to develop further insights into the 3-D complex flow physics and moments.
examines this near field mean flow structure and their effects on forces of
the supersonic jet mixing. Comparisons between the LES results and the experimental

5. UTCOMP : Compressible Flow Solver
• Large-eddy simulation (LES) captures unsteady flow
motion in turbulence with large length scale
• Flow in subfilter scale needs closure
- Dynamic Smagorinsky model is used for closing convective
terms
• High numerical scheme : 5th order WENO
• MPI based parallelization

6. ied. The rate of mixing depends on the coefficient
Direct quadrature method of moments
C / that appears in the definition of the mixing time
scale (Eq. (5)). Figure 5 shows the time-averaged
(DQMOM)
absolute difference between the abscissas normal-
ized by the mean scalar values. When the mixing
coefficient is doubled in value, the peaks are pulled
• Joint PDF of thermochemical composition variables is
towards the mean, which is reflected in the lower
normalized value. This plot also shows that there
is significant evolved using DQMOM method
variation in the abscissas with the
maximum OH variation being around four times
the mean value. Since these fluctuations occur in
the shear• Developed forany given time, combustion by Koo et al.
layer, it is likely that at supersonic
the weight associated with the Combustion Institutes, 2011)
(Proceedings ofpeaks. of the peaks is
one
much higher than the other This will reduce Fig. 7. Instantaneous snapshots of OH mass fraction for
the impact of the temperature difference between (top) high inlet temperature and (bottom) low inlet
temperature cases.
Supersonic reacting jet Supersonic cavity-stabilized flame

7. Results and Discussion
• Non-reacting Jet in Supersonic Crossflow
• Reacting Jet in Supersonic Crossflow

8. Non-reacting Jet in Supersonic Crossflow
• Sonic jet in Mach 2 crossflow
• Momentum ratio = 1.52
• Compared with the experiment from Air Force Research
Laboratory (AFRL) by Lin et al. (Journal of Propulsion and Power,
2010)
Crossflow Jet
Air C2H4
M = 2.0 M = 1.0
ρ = 0.65 kg/m3 ρ = 2.504 kg/m3
T = 167 K T = 287.5 K
p = 31 kPa p = 213.8 kPa
δ = 6.4 mm d = 4.8 mm

9. Computational details
24d
• 17 million grid cells over
31d x 8d x 24d 8d
computational domain
- 15y+ x 1.5y+ x 15y+ near wall 31d
• Spatial discretization
- Flow : 5th order WENO | Scalar : 3rd order QUICK
• Crossflow simulated separated as boundary layer
• Periodic boundary condition in spanwise direction
• Computed with 480 processors for 36 hours

10. Flow Evolution of Non-reacting JISC
C2H4
Density gradient magnitude
Ma

11. Flow Evolution of Non-reacting JISC
C2H4
Density gradient magnitude
Ma

12. Comparison with the Experiment
LES Experiment
C2H4 on symmetric plane
x/d x/d
x/d=5 x/d=25 x/d=5 x/d=25
y/d y/d y/d y/d
C2H4 at x/d=5 and x/d=25
z/d z/d z/d z/d
Wall PSP
Wall pressure distribution
x/d x/d

13. Comparison with the Experiment
LES Experiment
y/d y/d
C2H4 on symmetric plane
x/d=5 x/d x/d=5 x/d
z/d z/d
y/d y/d
C2H4 at x/d=5 and x/d=25
Wall PSP
Wall PSP
x/d=25 x/d=25
Wall pressure distribution x/d x/d
z/d x/d z/d x/d

14. Comparison with the Experiment
LES Experiment
C2H4 on symmetric plane
x/d x/d
x/d=5 x/d=25 x/d=5 x/d=25
y/d y/d y/d y/d
C2H4 at x/d=5 and x/d=25
z/d z/d z/d z/d
Wall PSP
Wall pressure distribution
x/d x/d

15. Shock Structures in JISC
Bow shock
Reflected shock
λ-shock
Barrel shock
Recirculation zones Expansion fan Mach disk
• Most of jet fluid passes through windward side of
barrel shock and Mach disk

16. suggested that the jet can be properly represented by a solid cylinder of given tra
Shock Structures in JISC
data have shown that this is not a realistic representation. Such a model does no
free-stream, plume overexpansion downstream or the horseshoe vortex surrou
Subsequently, Champigny and Lacau5 gave a detailed explanation of the flo
354 supersonic cross-flow. TheirS. K. structure model is shown in Fig. 1.
S. Kawai and flow Lele
Bow shock
Reflected shock
λ-shock
Barrel shock
crossflow (Ben-Yakar et al. 2006; Gruber, Nejad, ChenChampigny-Lacau
Figure 1. Schematics of the transverse injection of an under-expanded jet intoMach disk
Expansion fan a supersonic
& Dutton 1995).
Figure 1. Champigny and Lacau flow structure mo
turing flowsUnderexpandedand contact surfaces and the 3-D barrel shock
• with complex shocks jet in crossflow creates broadband turbulent
The Champigny–Lacau model has found widespread acceptance currently. A
eddying motions present in high Reynolds number flows.
and Mach disk
In the present study, an under-expanded sonic jet injected bow a supersonic crossflow the a
upstream separation zone created from a into shock interaction with
is numerically simulated by using layer interaction also generatesand dissipative compactshock.
shock/boundary a high-order low dispersive a shock, or separation
difference scheme (Lele the crossflow, but turns downstream becausethethis interaction and a sho
• Common1992) and structures are visible Visbal 2000) to properly
into shock spatial filtering (Gaitonde & in of result
capture the physicsreferred to as the barrel shock. The barrel shock is terminated with a Mach disk
of the supersonic turbulent mixing. Recently developed discontinuity-

17. Vortical Structures in JISC

18. Vortical Structures in JISC
agn itude
m
ient
grad
Density

19. Vortical Structures in JISC

20. Vortical Structures in JISC
C2H4 = 0.8
Q-criterion vorticity
with contour of C2H4

21. Vortical Structures in JISC

22. Vortical Structures in JISC
C2H4 = 0.8 Vortical structure
• Boundary layer thickening is seen in the shock-boundary
layer interaction
• Jet/crossflow interaction creates vortical structures
• Interaction of vortical structures is closely related to efficient
mixing in the near field

23. Vortical Structures in JISC

24. Vortical Structures in JISC

25. Vortical Structures in JISC
Long streak of
streamwise vorticity

26. Vortical Structures in JISC
x/d = 5
x/d = 0
Long streak of
streamwise vorticity
x/d = 3
x/d = 5
0
LES Experiment

27. Results and Discussion
• Non-reacting Jet in Supersonic Crossflow
• Reacting Jet in Supersonic Crossflow

28. Reacting Jet in Supersonic Crossflow
• Sonic jet in Mach 3.38 crossflow
• Momentum ratio = 1.4
• Compared with the experiment by Ben-Yakar et al.
(Physics of Fluids, 2006)
Crossflow Jet
Air C2H4
M = 3.38 M = 1.0
ρ = 0.0846 kg/m3 ρ = 7.02 kg/m3
T = 1290 K T = 263 K
p = 32.4 kPa p = 550 kPa
δ = 0.75 mm d = 2 mm

29. Computational details
24d
• 15 million grid cells over
21d x 10d x 24d 10d
computational domain
- 60y+ x 2y+ x 60y+ near wall 21d
• Periodic boundary in spanwise direction
• LES-DQMOM methodology for combustion modeling
- Reduced 13 species C2H4-air mechanism
• Computed with 820 processors for 72 hours

30. 026101-9 Transverse jets in supersonic crossflows
Shock Structures Comparison
LES Experiment
026101-6 Ben-Yakar, Mungal, and Hanson
Instantaneous
Time-averaged
• Shock structure is highly unsteady dueschlieren imagefeatures coherent structures
FIG. 5. An example to flapping s exposure time for
injection case. While the unsteady
with 3
motion at the windward sideaged tothe some of the weak shocks such as upstream separat
of zero, barrel shock
wave and downstream recompression wave are emphasized.

31. Flow Evolution of Reacting JISC
Mixture Fraction
Temperature (K)

32. Flow Evolution of Reacting JISC
Mixture Fraction
Temperature (K)

33. Flow Evolution of Reacting JISC
t1 0.5 flow
t2
residence time
Mixture Fraction
Temperature (K)
OH

34. Flow Evolution of Reacting JISC
0.5 flow
residence time

35. Flow Evolution of Reacting JISC
0.5 flow
residence time
• Mixing depends on much larger coherent motions
• Low Reynolds number in crossflow cause the mixing
process to be “tearing up” rather than effective
turbulent mixing

36. Flow Configuration
• Difference in flow configuration between non-reacting
and reacting jet
• Reacting case had thinner boundary layer thickness
(shock tunnel)
Non-reacting Reacting
J 1.52 1.4 ± 0.1
Rejet ~420,000 ~480,000
Reδ ~190,000 ~3,000
δ 1.33 D 0.375 D
Ujet 325 m/s 315 m/s

37. Time-averaged Mixing Properties
• Entrainment heavily depends on large coherent motion
• Inefficient mixing quality in the near field (mixture
fraction RMS ~ 0.5)
• Flow residence time much smaller than ignition time
delay

38. Conclusions
• LES captures unsteady motion of jet in supersonic
crossflow accurately
• Flow structures in JISC were studied
• LES-DQMOM methodology was used to study
supersonic combustion with multivariate ethylene-air
reaction mechanism
• Reacting case did not have enough near field mixing
• No flame stabilization was found in the reacting case

39. Questions
Large Eddy Simulation based Studies of
Reacting and Non-reacting Transverse Jets
in Supersonic Crossflow
Shaun Kim a,b Pratik Donde a Venkat Raman a
Kuo-Cheng Lin c Campbell Carter d
a b c d