First Multiflow Conference on the Turbulent-Nonturbulent Interface
School of Aeronautics, Madrid SP. 25-26 October 2012
Superlayer Contributions to the Mixture Fraction Pdf in a
Turbulent Round Jet Flow
Markus Gampert, Philip Schaefer & Norbert Peters
Institute for Combustion Technology, RWTH Aachen, Templergraben 64, Aachen, Germany
[email protected]
The outer boundary of a turbulent jet flow is characterized by turbulent regions adjacent to non-turbulent
ones. In analogy to [1], we will refer to the region in which the scalar signal changes from turbulent to
laminar as the scalar superlayer. The present study focuses on the footprint this superlayer leaves in the
scalar pdf as well as on the scaling of the superlayer thickness by means of an experimental investigation of
the mixture fraction field Z of a turbulent jet flow.
The experiments were performed in a co-flowing turbulent jet facility, which consists of a center tube
with an internal diameter of 12 mm. Propane is fed through the center tube and CO2 was chosen as co-flow
gas. The Reynolds number based on jet exit conditions was varied between 3, 000 and 18, 440 and the scalar
fields were acquired using high-speed two-dimensional Rayleigh scattering imaging.
Figure 1(a) shows an examplary planar measurement of the mixture fraction field and (b) the profile
of Z through the centerline in y-direction and fixed z = 0 at x/d=10 and Reλ = 83. One observes three
regions in the signal, one of which belongs to the turbulent part of the flow (A), while the second one (B)
describes the scalar superlayer, where the value of the mixture fraction drops from the turbulent to the outer
flow value. In the third part (C), one observes this outer flow with Z = 0. Furthermore, a length scale δ is
introduced, indicating that the extension of the superlayer can be described by a characteristic thickness.
(a)
(b)
1
C
B
0.3
0
-0.3
0 0.2 0.4 0.6 0.8 0.9
d
0.6
Z
z/d
0.8
Z
A
0.4
-2
C
B
-1
y/d
0
1
A
0.2
0
-2
-1
y/d
0
1
Figure 1: Sample instantaneous mixture fraction fields illustrating the different regions of the flow field inner turbulent flow(A), superlayer(B) and outer coflow(C): (a) Instantaneous mixture fraction field with a
single superlayer, (b) Centerline variation of the mixture fraction corresponding to Fig. (a).
Since combustion occurs in the vicinity of the stoichiometric mixture fraction, which is around Z =
0.06 for typical fuel/air mixtures, it is expected to take place largely within the superlayer. Therefore,
profound understanding of this part of the flow is essential for an accurate modeling of turbulent nonpremixed combustion. To this end, we use a composite model developed by [2] for the pdf P (Z) which
takes into account the different contributions from the fully turbulent as well as the superlayer part of the
flow. A very good agreement between the measurements and the model was observed over a wide range of
axial and radial locations, see fig. 2 for two examples.
Measured pdf
Composite pdf
Turbulent part
Superlayer part
Beta pdf
3
pdf
2.5
2
1.5
(b)
Measured pdf
Composite pdf
Turbulent part
Superlayer part
Beta pdf
8
6
pdf
(a)
1
4
2
0.5
0
0
0.2
0.4
Z
0.6
0.8
0
0
1
0.2
0.4
0.6
0.8
1
Z
Figure 2: Comparison between measured and approximated pdfs at x/d = 10 and Reλ = 83 (a) r̃ = 0.120
(b) r̃ = 0.155.
Further, we detect the location of the superlayer following [3] and investigate the profile of the mixture
fraction in the superlayer normal direction to analyze its spatial extension δ, where we observe a steep scalar
drop across the superlayer. Da Silva and co-workers (e.g. [4]) postulated for the thickness of the superlayer
−1/2
in the presence of a mean shear a scaling according to δ/L ∼ ReL , where ReL is a Reynolds number
based on the integral scale L, which translates into δ/L ∼ Re−1
λ . The resulting values are shown in Fig. 3
over the local Taylor based Reynolds number Reλ and confirm this relation, meaning δ ∝ λ .
0.8
δ/L
0.6
~Re-1
λ
0.4
60
Re λ
100
140
Figure 3: Scaling of the non-dimensional thickness of the scalar superlayer δ/L as a function of the Taylorbased Reynolds number Reλ
References
[1]
[2]
[3]
[4]
S. Corrsin and A. L. Kistler, NACA Report 1244, (1955).
E. Effelsberg and N. Peters, Combust. Flame 50, 351–360 (1983).
R. R. Prasad and K. R. Sreenivasan, Exp. Fluids 7, 259–264 (1989).
C. B. da Silva and R. R. Taveira, Phys. Fluids 22, 121702 (2010).