Numerical simulation of free cross-shaped jet/Laisvos kryzmines sroves skaitinis imitavimas.
Meslem, A. ; Dia, A. ; Beghein, C. 等
1. Introduction
The lobed nozzles are commonly used under very high Reynolds number
in aeronautics and combustion applications for thrust improvement and
noise reduction [1-3]. Under low or moderate Reynolds numbers for HVAC
applications, the analysis of lobed nozzle and orifice jets shows that
large streamwise structures generated by the lip of the lobed diffuser
are present and control the ambient air induction [4-7]. The previous
experimental studies provided some knowledge on the physical phenomena
at the origin of their particular performance. An innovative concept for
optimized air diffusion in buildings using passive control of air jet
through lobed diffusers was also proposed [8, 9]. This concept reposes
on the idea of relatively costless and simple modifications of the exit
boundary geometry of classical existing diffusers. At each elementary
cross-shaped orifice of a perforated panel diffuser, large scale
structures develop in the orifice troughs and control air induction in
the jet near field [4, 9]. The perforated panel flow induction depends
heavily on elementary orifice geometry parameters and designing optimal
orifice geometry by experimental means alone is quite expensive due to
the wide range of parameters involved. Computational Fluid Dynamics
(CFD) based methods represents a better alternative to experimental
methods in the case of optimization studies. Reynolds-Averaged
Navier-Stokes (RANS) equation solvers were used routinely for the
analysis of aeronautic and aerospace systems. Passive controlled engine
exhaust nozzles were numerically analyzed at high exit Reynolds number
in terms of their performance quantities and noise reduction [10-15].
RANS models replace all turbulent fluid dynamic effects with a
turbulence model. When they have been successful in calculating thrust,
noise prediction is not as satisfactory. In fact, despite significant
work to improve RANS-based methods they seem to have limitations to
accurately predict the turbulent fluid structures that cause jet noise
and mixing in high Reynolds number flows with significant
three-dimensionality [13]. For six lobed circular nozzle at exit
Reynolds number of 5.5x[10.sup.4], Nathan et al. [15] found that
numerical simulations using four widely employed turbulence models among
them Shear-Stress Transport (SST) k[omega] turbulence model--agree
reasonably well with the Particle Image Velocimetry (PIV) measurements
in terms of streamwise vorticity and spanwise vorticity. However, the
turbulent kinetic energy is over predicted.
In our case, the Reynolds number is lower and the diffuser geometry
optimization is based on the mean flow characteristics such as jet
volumetric flow rate and jet expansion.
In this study the flow dynamics of isothermal, turbulent
cross-shaped free jet is investigated both numerically and
experimentally. Numerical and experimental results are compared to
assess the capability and limits of the turbulence model SST k[omega] to
provide near field orifice lobed jet characteristics at moderate
Reynolds number.
2. Experimental campaign
The air jet is generated using a cross-shaped orifice (Fig. 1). The
equivalent diameter based on the orifice exit area is [D.sub.e] = 10 mm.
The air blowing facility consists of an axial miniature fan placed
inside one meter long metallic pipe of 0.16 m diameter. A convergent
duct placed at the end of the pipe ensures the reduction of the
turbulence level at the jet exit. A honeycomb structure is positioned
just upstream of the convergent duct. The initial Reynolds number based
on the maximum exit velocity and on the equivalent diameter [D.sub.e] is
around 4000 (Table 1).
Two-dimensional Dantec PIV is used to measure longitudinal
distribution of flow streamwise velocity in the Major Plane (MP) and
minor Plane (mP) defined in Fig. 1. The system is made up of a 200 mJ
dual Yag laser, a synchronizer, a high-sensitivity CCD camera of 4000 x
2672 [pix.sup.2] resolution and the Dynamic Studio software for data
acquisition, processing and post processing. The lasers emit 532 nm
wavelength pulse light, the thickness of the light sheet is about 1 mm.
The acquisition frequency of the PIV system is 1 Hz and a total of 500
image couples were acquired. The jet was seeded with small olive oil
droplets, 1 to 2 [micro]m in diameter, provided by a liquid seeding
generator. It is assumed that tracer particle sliding is negligible. The
calibrated image gives a spatial resolution of 40.6 [micro]m per pixel
which corresponds to a 162.3 x 108 [mm.sup.2] field of view. Images are
processed through an adaptive multigrid correlation algorithm handling
the window distortion and the sub-pixel window displacement. The
prediction-correction method is validated for each grid size when the
signal to noise ratio of the correlation is above a threshold of 1.1. In
average, less than 1% of the vectors are detected as incorrect. These
incorrect vectors are corrected by using a bilinear interpolation
scheme. The final size of the interrogation windows gives a spatial
resolution of 0.49 mm.
[FIGURE 1 OMITTED]
The obtained velocity field is extended from the jet exit to X =
15.5[D.sub.e] in the longitudinal direction. The obtained mean
streamwise velocity field is shown in Figs. 3 (1a) and (1b) using
isovalues (color map) representation.
The velocity fields in transverse planes (YZ) at different axial
positions 0.5[D.sub.e] [less than or equal to] x [less than or equal to]
5[D.sub.e] are obtained using time-resolved stereoscopic PIV
measurements (the mean streamwise velocity contours are plotted in Fig.
5). The PIV system is composed of two Phantom V9 cameras of 1200 x 1632
[pixels.sup.2] and a Nd: YLF NewWave Pegasus laser of 10 mJ energy and
527 nm wavelength. The acquisition frequency of the PIV system is 500 Hz
for a maximal image window. In each plane, a number of 1000 image
couples were acquired. The two cameras are mounted on a traversing
system with an angle of 45[degrees] to the normal position of the light
sheet plane of the laser. The lenses are separated from the camera in
order to shift the CCD-chip plane with respect to the lens plane, in the
way that the Scheimpflug conditions are satisfied. The calibrated image
gives a spatial resolution of 60 um per pixel which corresponds to a 98
x 72 [mm.sup.2] field of view. Images are processed through an adaptive
multi-grid correlation algorithm handling the window distortion and the
sub-pixel window displacement. The prediction-correction method is
validated for each grid size when the signal to noise ratio of the
correlation is above a threshold of 1.1. In average, less than 3% of the
vectors are detected as incorrect. The final grid is composed of 16 x 16
[pixels.sup.2] size interrogation windows with 50% overlapping leading
to a spatial resolution of 0.39 mm. The same liquid seeding generator as
for the classical PIV measurements was used. More details about the
time-resolved stereoscopic PIV technique are given by [7].
3. Computational details
The flow considered in this study is weakly turbulent, and a
turbulent model is thus required for the computation of the flow. Of the
various models that are available, the widely used RANS Shear Stress
Transport (SST) k[omega] turbulence model [16] has been chosen.
The computational domain (Fig. 2, a) is composed of two parts
separated by the orifice plate having 1.5 mm in thickness. The upstream
part and the downstream part of the domain have the dimensions of 10 x
10 x 10[D.sub.e] and 30 x 10 x 10[D.sub.e] respectively. The inlet
boundary conditions for the simulation are given at the inlet plane of
the upstream part of the domain. On this plane a uniform velocity of
0.00728 m/s and a turbulence intensity of 2% are specified. Owing to the
symmetry of the problem, just one quarter of the flow is modeled. The
other boundary conditions are mentioned in the Fig. 2.
The numerical analysis is performed using a finite volume based
solver StarCCM+Version 5.04. The SIMPLE algorithm is used for
pressure-velocity coupling. The flow variables are calculated on a
collocated grid. A second order upwind scheme is used to calculate the
convective terms in the equations. A grid size of 1.4 million regular
Cartesian nonuniform cells has been considered for the investigation.
This grid is highly refined in the orifices plane (see Fig. 2, b). The
values of y+ for the first gridline off the surfaces of the plate are
less than 4 which is acceptable for the low Reynolds number formulation
of the considered model.
[FIGURE 2 OMITTED]
4. Results and discussion
The jet inlet conditions (i.e. flow characteristics at the orifice)
are given in Table 1 for the measured flow and the simulated flow
respectively. Mean characteristics of the initial boundary layers are
given in Table 2. The values of the shape factor H for MP and mP suggest
that the initial boundary layers are laminar in the two cases (real and
simulated flows). However, the values of the initial momentum thickness
([[theta].sub.0]) and the initial displacement thickness
([[delta].sup.*]) in the real flow are greater than the ones obtained
for the calculated flow.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The MP and mP streamwise mean velocity isocontours given in Fig. 3,
show that the global behaviour of the simulated flow is similar to the
real one. Jet contraction in the MP and jet expansion in the mP, between
X = 0.5[D.sub.e] and X = 3[D.sub.e], are due to the axis-switching
phenomenon [4, 17]. However, the model overpredicts jet potential core
length. Potential core length overestimation is also visible on the
streamwise maximum velocity evolution (Fig. 4). Acceptable predicted
values are obtained beyond X = 8[D.sub.e] position.
In Fig. 5, streamwise velocity contours in the jet near field are
given at different flow transverse planes. The axis-switching which
occurs between X = 0 and X = 3[D.sub.e] is well predicted by the model
with a slight lead in its prediction.
[FIGURE 6 OMITTED]
Even if the model predicts the axis-switching phenomenon, the
isocontours comparison reveals that the spatial distribution of the flow
is not perfectly predicted by the model: the inner contours are tight
and contraction/expansion in the MP/mP is more pronounced than in
reality. In order to quantify the gap of the model prediction in the
flow spatial distribution, we represent in Fig. 6 the jet thicknesses
evolutions in the MP and the mP, given by U = 0.5 [U.sub.m] and U = 0.1
[U.sub.m] positions, where [U.sub.m] is the maximum velocity at the
considered streamwise position X. The flow spreading thicknesses
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] in the two planes, confirm the
slight advance of the model in predicting the crossover phenomenon.
Theses curves also confirm the pronounced character of axis-crossover.
What is relevant however to note is the very good prediction of the
average radius [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (Fig.
7) based on the transverse flow area [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII].
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
The average radius [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] based on the transverse flow area [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] is less well predicted for 4[D.sub.e] [less than
or equal to] X [less than or equal to] 5[D.sub.e]. This suggests that
the induction phenomenon is correctly reproduced by the model, but
mixing of the induced air and the jet air, is not perfectly reproduced.
This explains the poor prediction of the decay of the axial velocity
(Fig. 4). The tightening of the inner contours of the axial velocity
observed previously (Fig. 5) is another consequence of the deficit model
prediction of the mixing.
As expected, prediction of the volumetric flow rate defined in this
study by Q = [integral] U dS |[sub.U>0.15m/s] is quite satisfactory
(Fig. 8). The satisfactory comparison of the global jet expansion, given
by jet flow area (Fig. 8, a), and the one of the jet volumetric flow
rate (Fig. 8, b), suggest considering mean jet velocity, given by
[U.sub.mean] (X) = Q (X) / [S.sub.Flow] (X), where [S.sub.Flow] =
[integral] dS |[sub.U>0.15m/s] as a more reliable quantity of the
model prediction of the jet streamwise velocity evolution (Fig. 9). As
shown in Fig. 9, except for the first point at X = 0.5[D.sub.e], the
mean jet velocity [U.sub.mean] is well predicted by the model.
Evolutions of the integral of turbulence kinetic energy k along the
X-axis from the numerical and the experimental transverse fields are
given in Fig. 10. The turbulence kinetic energy increases with the axial
distance for both experimental and simulated flows. However, as found by
Nathan et al. [15], the SST k[omega] model overpredics turbulent values.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
5. Conclusion
This study allowed assessing the capability and the limits of the
turbulence model SST k[omega] to provide the orifice lobed flow
characteristics at moderate Reynolds number. The numerical results are
compared to experimental measurements. The axis-switching phenomenon of
the jet which occurs between X = 0 and X = 3[D.sub.e] is well predicted
by the model. Mean characteristics of the initial boundary layers are
lower than reference values. Turbulent kinetic energy is over predicted.
The flow expansion in the minor plane and flow contraction in the major
plane are more pronounced and the potential core length is overestimated
generating a delay on the streamwise maximum velocity decay. However,
satisfactory predictions of the flow transverse area and its volumetric
flow rate are observed and lead to good predictions of the streamwise
evolutions of "mean flow radius" and "mean flow
velocity".
Consequently, the most notable conclusion of the present study is
that the simulation approach using two-equation turbulence model SST
k[omega] can successfully predict many significant features about the
orifice lobed jet at moderate Reynolds number. The well predicted
quantities will be used for designing optimal geometrical parameters of
the lobed orifice for HVAC application.
Received March 07, 2011
Accepted June 13, 2012
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A. Meslem *, A. Dia *, C. Beghein *, A. Ammar *, I. Nastase **, M.
El Hassan *
* LEPTIAB, Universite de La Rochelle, Pole Sciences et Technologie,
La Rochelle, France, E-mail: ameslem@univ-lr.fr
** CAMBI, Technical University of Civil Engineering, Bucharest,
Romania, E-mail: ilinca.nastase@cambi.ro
cross ref http://dx.doi.org/10.5755/j01.mech.18.4.2328
Table 1
Exit conditions
Method [Q.sub.0], [U.sub.0mean] [U.sub.0m]
[m.sup.3]/s m/s m/s
PIV 3.47 x 4.42 6.41
[10.sup.-4]
SST k[omega] 3.06 x 3.90 5.36
Model [10.sup.-4]
Method [U.sub.0mean] [U.sub.0]
[D.sub.e]/v [D.sub.e]/v
PIV 2815 4063
SST k[omega] 2484 3414
Model
0: initial
m: maximum
Table 2
Initial boundary layer characteristics in the
major and minor planes at X = 0.1[D.sub.e]
Method Boundary [delta] [[theta] H = [[delta]
*/ .sub.0]/ .sup.*]/
[D.sub.e] [D.sub.e] [[theta].sub.0]
PIV MP 0.216 0.051 4.45
mP 0.197 0.038 5.23
SST MP 0.100 0.027 3.67
k[omega]
Model mP 0.053 0.014 3.38
MP: major plane; mP: minor plan; [[delta].sup.*]: displacement
thickness; [[theta].sub.0]: momentum thickness
