# Coaxial stable jets loaded with particles

Authors: Hishida et. al.

Type: Experimental

Status:

Description

## Description

We study the axisymmetrical injection of an air flow laden with particles in a coaxial flow of lower velocity. The jet is vertical and two kinds of particles are considered (similar diameter but different density). The test-case and the experimental data are taken from [1]%$^{1}$%, itself taken from [2].

Figure 1 shows the domain and the main dimensions can be found in Table 1. A particle-laden air flow is injected from the central pipe and an air flow without particles is injected from the external annular pipe.

 domain diameter length 60 mm 300 mm injector diameter 13 mm
Table 1 - Domain dimensions

## Flow Parameters

Flow parameters are extracted from [1].

• density : %$\rho = 1.18 kg.m^{-3}$%
• dynamic viscosity : %$\mu = 1.8 \times 10^{-5} kg.m^{-1}.s^{-1}$%
• specific heat capacity : %$Cp = 1219 J.K^{-1}.kg^{-1}$%
• reference velocity : %$U_0 = 1.0 m.s^{-1}$%

Figure 1 - Domain geometry

### Particles parameters

As flow parameters, particles characteristics are taken from [1]. Two kinds of particles have been used, they have a different density. For heavy particles the name "case 1" will be used and "case 2" for light particles. The particles parameters are given in Table 2.

 Case 1 Case 2 average diameter 64.4%$\mu m$% 80.1%$\mu m$% density 2590%$kg.m^{-3}$% 280%$kg.m^{-3}$%

Table 2 - Particles parameters

### Inlet conditions

Inlet conditions are taken from [2] in order to be identical to the value found in the inlet measurement files and on the different cut plane %$^{1}$%. Numerical values in Tables 3 to 8 correspond to : Axial and radial velocities as well as their fluctuation, for air and for the particles. Particle mass flux are also found in these tables. For flow computation, turbulence inlet condition is required. Following [1], the turbulent energy is calculated from :

%$k=\frac {1} {2}(2u_r '^{2}+ u_z '^{2})$%

and the rate of dissipation from :

%$\epsilon=\frac{C_\mu k^{3/2}}{l_m}$%

where %$C_\mu=0.09$% and %$l_m=0.03l$%, %$l$% being the internal diameter of the pipe or the external annular section width. For case 1, shear measurements are known. It is used for calculation with a second order model.

Some values from tables found in [2] have been modified to account for the symmetry conditions in the domain and its dimensions (to facilitate interpolation in the code).

• For air inlet conditions, case 1 (table 3), the line corresponding to -1 mm was removed (redundant with line at 1 mm by symmetry), the radial velocity ant the shear stress at 0 mm was fixed to 0. An additional line was added at 30 mm, by keeping the same values as the one found at 13 mm (except for the radial velocity which is zero).
• For particle inlet conditions, case 1 (table 4), the line at -8mm was used at 8 mm (changing the sign of the radial velocity), a line was added at 0 mm (taking the value of the variables at 0.2 mm except for the radial velocity which is zero) and a line was added at 6.5 mm (main inlet radius) taking the values found at 6.2 mm.
• For inlet particle mass flow, case 1 (table 5), the line at -0.4 mm was used at 0.4 mm, a line at 0 mm was added with the same value².
• For air inlet conditions, case 2 (table 6), two were added at 0 mm and 30 mm using the closest value of measurement points, except for the radial velocity which is fixed to zero.
• For particle inlet conditions, case 2 (table 7), the radial velocity at 0 mm is zero. The maximal value is kept at 7 mm, even if it's not totally coherent with what was done for the mass flux (what is relevant is to make sure that the mass flux is zero at the internal edge of the injector).
• For inlet particle mass flux, case 2 (table 8), the null value at 7 mm is 6.5 mm.

 Radial coordinates Axial velocity Radial velocity Axial velocity fluctuations Radial velocity fluctuations Shear stress %$mm$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% %$m^{2}.s^{-2}$% 0 29.181 0.032 0.944 0.992 0.000 1 28.714 0.045 1.150 1.059 0.087 2 27.969 0.050 1.476 1.192 0.249 3 26.623 0.149 1.669 1.409 0.248 4 25.518 -0.011 1.739 1.421 0.465 5 23.471 0.076 2.267 1.626 0.576 6 19.470 0.639 2.725 2.266 1.234 7 15.085 -0.459 1.484 0.803 -0.119 8 15.482 -0.461 0.263 0.312 -0.004 9 15.575 -0.259 0.192 0.239 -0.004 10 15.685 -0.357 0.164 0.247 -0.002 11 15.653 -0.373 0.174 0.257 -0.001 12 15.654 -0.354 0.168 0.282 -0.001 13 15.623 0.355 0.152 0.331 0.002 30 15.623 0.000 0.152 0.331 0.002
Table 3 - Air inlet conditions - Case 1

 Radial coordinates Axial velocity Radial velocity Axial velocity fluctuations Radial velocity fluctuations %$mm$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% 0.0 23.314 0.000 1.577 1.028 0.2 23.314 0.005 1.577 1.028 0.8 23.333 0.039 1.507 0.985 1.2 23.263 0.105 1.493 1.116 2.2 23.550 -0.006 1.543 1.063 3.2 23.429 -0.187 1.685 1.050 4.2 23.149 -0.137 1.776 1.026 5.2 22.846 -0.010 1.834 0.897 6.2 22.430 0.029 1.948 0.843 6.5 22.430 0.029 1.948 0.843
Table 4 - Particle inlet conditions - Case 1

 Radial coordinates Mass flow %$mm$% %$kg.m^{-2}.s^{-1}$% 0.0 15.400 0.4 15.400 0.6 15.270 1.6 13.280 2.6 11.110 3.6 9.107 4.6 7.831 5.6 6.811 6.5 0.0624
Table 5 - Inlet particle mass flow - Case 1

 Radial coordinates Axial velocity Radial velocity Axial velocity fluctuations Radial velocity fluctuations %$mm$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% 0.0 29.74 0.000 1.166 0.940 0.4 29.74 0.014 1.166 0.940 1.4 29.25 -0.011 1.341 1.004 2.4 28.19 -0.032 1.679 1.186 3.4 26.87 -0.094 1.810 1.302 4.4 25.33 -0.099 1.920 1.420 5.4 23.02 0.004 2.679 1.716 6.4 19.61 0.644 2.932 2.389 7.4 14.73 -0.0336 1.025 0.560 8.4 15.45 -0.289 0.220 0.297 9.4 15.51 -0.355 0.180 0.275 10.4 15.54 -0.358 0.165 0.200 11.4 15.58 -0.349 0.170 0.206 12.4 15.58 -0.257 0.165 0.199 14.4 15.58 -0.257 0.169 0.190 16.4 15.58 -0.244 0.172 0.230 18.4 15.58 -0.196 0.169 0.237 20.4 15.58 -0.140 0.165 0.245 22.4 15.58 -0.116 0.172 0.244 24.6 15.58 -0.054 0.163 0.240 26.4 15.58 -0.009 0.164 0.247 30.0 15.58 0.000 0.164 0.247
Table 6 - Air inlet conditions - Case 2

 Radial coordinates Axial velocity Radial velocity Axial velocity fluctuations Radial velocity fluctuations %$mm$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% %$m.s^{-1}$% 0 28.07 0.000 2.092 0.640 1 27.87 -0.002 2.067 0.651 2 27.60 -0.004 1.971 0.632 3 26.95 -0.010 1.971 0.644 4 25.77 0.022 2.156 0.649 5 24.14 0.059 2.394 0.628 6 21.20 0.128 3.018 0.633 7 18.89 1.083 3.082 0.707
Table 7 - Particle inlet conditions - Case 2

 Radial coordinates Mass flow %$mm$% %$kg.m^{-2}.s^{-1}$% 0.0 2.006 1.0 1.842 2.0 1.549 3.0 1.256 4.0 1.018 5.0 0.980 6.0 0.800 6.5 0.000
Table 8 - Inlet particle mass flux - Case 2

%$^{1}$% For an undetermined reason, inlet data in [1] do not match the values found in the figures of the same document. For inlet boundary conditions and for comparisons between calculation and measurements, downstream data files from an older validation cases were used [2], they correspond to figures found in [1].

%$^{2}$% In the results we present, this line was not added, the value at the points located at a radius smaller than 0.4 mm was calculated by extrapolating the values found at 0.4 mm and 0.6 mm. This has no effect of the results since in the 2D mesh, just one inlet face centre is concerned (and it's close to 0.4 mm)

## Reference Publications

[1] Fifth Workshop on Two-Phase Flow Predictions - Specifications for Test Cases, LSTM Erlangen,March 19-22, 1990.

[2] Minier J.P., Ouraou M., Module diphasique lagrangien du code ESTET : calculs de validation etapplications industrielles, Rapport EDF, HI-81/01/027/A, 2001.

## Results

Simulation results available for this case:
Code Version Author Restrictions
Code_Saturne 2.0-beta2 M. Guillaud AccessEDFGroup
Number of topics: 1

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Topic revision: r67 - 2013-04-10 - 16:30:10 - AminRasam
CfdTm Web
12 Dec 2019

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