(320g) Parametrical Sensibility Analysis of Reynolds Stress Model in a Coaxial and Confined Jet Flow

The objective of this study is to
investigate the parametric sensibility of the Reynolds Stress Model, with a
version proposed by Speziale, Sarkar and Gatski in relation to the C_µ,
C_ε-1
and C_ε-2 parameters, for a confined coaxial jet flow at different velocity
ratios. The numerical results were compared with experimental data, which were
obtained by a two-dimension particle image velocimetry system (2D-PIV), in the fully
developed flow region. The experimental and numerical results were evaluated at
two different axial positions (L/D=25 and L/D=37.5) in terms of axial mean
velocity and turbulence kinetic energy. The results indicated that changing the
C_µ parameter in 30% above its default value, the RSM-SSG
model represents more precisely
the velocity field in the flow.

1.       
INTRODUCTION

Confined and coaxial jet flows are found in
several industrial applications such as jet pumps, burners, ejectors, among
others. In confined jets the entrainment of sufficient mass from surroundings
is strictly related to the vorticial structures of the flow which may vary
according to the velocity ratio, R_U = U_out/U_in,
where U_in is the jet velocity and U_out is the co-flow
velocity (DECKER et al. 2011). In order to understand the flow behavior
and the mixture process in coaxial jet flows several authors developed
experimental and numerical studies to investigate the influence of the inlet
conditions for coaxial jets. Ahmed and Sharma (2000) investigated the turbulent
mixing of two coaxial and confined jets by means of LASER Doppler velocimetry
system. The authors made experiments to investigate the velocities ratio effect
between the two streams. Lin (1998) studied a confined swirling coaxial jet
modeling evaluating the influence of grid density and turbulence models. Mahmoud
et al., (2010) proposed a numerical study of an axisymmetric turbulent
jet discharging into co-flowing stream with R_U ranging between 0 and
4.5. The standard k?e model and the Reynolds Stress Model were applied. The authors
observed that both turbulence models are valid to predict the average and
turbulent flow sizes. Decker et al. (2011) presented numerical studies
using four RANS models to investigate the behavior of a confined coaxial jet in
the region of development flow. In order to add a contribution to the coaxial
jet flow analysis, this study proposes the investigation of the turbulence
viscosity parameter (C_µ) and its dissipation rate parameters
(C_ε-1 and C_ε-2) by means of a parametric analysis at different operational
conditions. The results are compared with experimental data and conclusions
about the better parameters values are made.

2.     
METHODOLOGY

 
2.1.      
Experimental Setup

In the test facility showed in Figure 1, a
Pitot tube (A) is connected to a differential pressure transmitter in order to
measure the mass flow ratio in the know transversal area. As the mass flow
ratio inside the chamber is the same in the measurement section, the inlet mean
velocity of the gas phase in the chamber (U_out) can be determined.
This velocity is controlled by a Programmable Logical Controller coupled to the
radial ventilator located at the end of test facility (B), which is also
responsible for maintaining the entire system under negative pressure. The jet
velocity (U_in) is provided by a compressed air system, which is
connected to a relief valve and a flow meter (C). The measurements are obtained
in the Plexiglass chamber (D) for different axial positions from the nozzle by
means of a particle image velocimetry (PIV) system (E). In order to measure the
gas flow velocity, TiO₂ particles were used due to its ability to
follow the gas flow (Stokes number << 1). The TiO₂ particles
are loaded in the flow system by an ejector located in the inlet region (F).

Figure 1 ? Test Facility.

 
2.2.      
Operational and Geometrical Conditions

In the test facility, experiments were
realized for two different initial velocities in the jet and in the chamber,
which are presented in Table 1. This setup provides four different velocities
ratios, which are presented in Table 2.

Table 1: Initial velocities in the jet and in the chamber.

Table 2:
Velocities ratios.

The experiments were developed at 25 °C.
The PIV measurements were taken in the same horizontal plane, as showed in
Figure 2. The measurement region is 510 mm length x 110 mm width, which is
subdivided in six sections with 90 mm length x 110 mm width (Figure 2). The first
(S1) and last (S2) coordinate sections are presented in Table 3, with the
others sections. After calibration of the 2D-PIV system, 1000 frames were taken
in the measuring region with a time step of 150 µs. Thus, two different axial
positions were selected to investigate the radial profiles in terms of mean
velocity and turbulence kinetic energy. These positions are located at L/D=25 and
L/D=37.5. The geometrical conditions are presented in Figure 2, where D is the
nozzle diameter.

Figure 2 ? Geometrical conditions and measurement region.

Table 3 ?
Sections for the experimental measurements.

  2.3.      Numerical
Simulations

The objective of this study is to
investigate the behavior of RSM-SSG model in a confined coaxial jet flow for
different velocity ratios, changing the default values of some parameters of
the model. In this way, the numerical simulations were performed varying the C_µ,
C_ε-1
and C_ε-2 parameters in +30% and ?30% of its default values.

In order to achieve
this objective, an experimental design of three factors at three levels was
performed, which is presented in Table 4.

Table 4 ?
Design of experiments.

The numerical simulations were conducted by
a CFD commercial package, the FLUENT 13. The geometrical grid used in these
simulations consists in approximately 291,640 hexahedral elements. The advection
scheme used in the simulations was High Resolution due to the strong convective
component of the gas transport. The convergence criterion for all cases was 10^?4
in the residual norm. The iterations were solved with a time step size of 10^?4
s, totalizing 5 seconds of real time simulation.

The boundary
conditions for physical frontiers of the coaxial confined jet flow are:

·         
Inlet (Chamber and Jet): It is adopted uniform and constant properties for the gas flow with
an initial velocity condition.

·         
Outlet: Constant
pressure with continuity conditions for all flow properties.

·         
Wall: No-slip
conditions and wall logarithm function for the turbulent properties.

3.     
RESULTS AND DISCUSSIONS

The numerical results of the axial mean
velocities were compared with experimental data and analyzed by means of a
criteria known as integrated absolute value of the error (IAE), where the set-point
is the experimental data. The simulations results for the axial mean velocity
are presented in Table 5.

Table 5 ? Value of the errors determined by IAE criterion for the
axial mean velocity.

In the Table 5 it is possible to observe
that the results to the simulations 1, 10, 23 and 27 are closer to the
experimental data in relation to the default results (simulation 14) than the
others simulations. These four results are selected to be analyzed in graphical
form in terms of mean axial velocity profiles and turbulence kinetic energy
profiles, as seen in Figure 3 and in Figure 4, respectively, for two different
axial positions.

Figure 3 ? Axial mean velocity profiles
for two different axial positions.

In Figure 3 it
is possible to observe that the best numerical result is obtained when the C_µ
parameter is set to +30% to its default value and the two other parameters are
fixed in default values (blue line). Extending this analysis, Figure 4 presents
the turbulence kinetic energy profiles. For both axial positions it is possible
to observe that the simulation with the default values parameters presented better
result, however the simulation result which the C_µ parameter is
adjusted in +30% to default value is also close to the experimental data,
mainly at the L/D=37.5.

Figure 4 ?
Turbulence kinetic energy profiles for two different axial positions.

These 27
numerical simulations were also performed for the others velocities ratios and
the results obtained were similar to those previously presented.

4.     
CONCLUSIONS

The 27 simulation results are compared with
PIV experimental data and the results showed that the best is obtained when the
C_µ parameter is modified default value (0.09) to a value 30%
above, i.e., for 0.117. These results indicate that the parametric sensibility
analysis is a tool that can be used to determine the best fit for model
parameters analysis.  

REFERENCES

Decker, R.K.; Buss,
L.; Wiggers, V.R.; Noriler, D.; Reinehr, E.L.; Meier, H.F.; Martignoni, W.P.;
Mori, M., (2011), Numerical Validation of a Coaxial and Confined Jet Flow,
Chemical Engineering Transactions, 24, 1459-1464.  

Lin C.A., (1998),
Modeling a confined swirling coaxial jet. Center for Turbulence Research,
Annual Research Briefs.

Mahmoud H., Kriaa
W., Mhiri H., Le Palec G. and Bournot P., (2010), A numerical study of a
turbulent axisymmetric jet emerging in a co-flowing stream, Energy Conversion
and Management, 51, 2117?2126.