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The comparison of the calculated streamlines of the gas flow with those
The comparison of the calculated streamlines of the gas flow with those
obtained from the integration of the measured axial velocity shows that
obtained from the integration of the measured axial velocity shows that
the flow field is predicted reasonably well for both conditions (Figure 10).
the flow field is predicted reasonably well for both conditions
([[Evaluation_AC3-12#figure10|Figure 10]]).
The most obvious difference is that the  axial  extension  of  the
The most obvious difference is that the  axial  extension  of  the
central recirculation bubble is predicted to be larger at the  top  and
central recirculation bubble is predicted to be larger at the  top  and
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|[[Image:AC3-12_fig10.png|700px]]
|[[Image:AC3-12_fig10.png|700px]]
|-
|-
|align="center" width=650px|'''Figure 10:''' Measured and calculated gas-phase streamlines  (the  upper parts of each figure corresponds to  the  calculations  and  the  lower parts show the measurements); (a) Case 1; (b) Case 2.
|align="center" width=650px|'''Figure 10:''' Measured and calculated gas-phase streamlines  (the  upper parts of each figure corresponds to  the  calculations  and  the  lower parts show the measurements); (a) Case 1; (b) Case 2.
|}
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The measured cross-sectional profiles of the three velocity  components
The measured cross-sectional profiles of the three velocity  components
are compared with the  calculations  in  Figure 11 for  Case 2. The
are compared with the  calculations  in  [[Evaluation_AC3-12#figure11|Figure 11]] for  Case 2.
The
agreement is very good, except for the  tangential  velocity  which  is
agreement is very good, except for the  tangential  velocity  which  is
under-predicted in the region downstream  of  the  location  where  the
under-predicted in the region downstream  of  the  location  where  the
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jets and within the recirculation at the edge of the pipe expansion  (z = 52 mm),
jets and within the recirculation at the edge of the pipe expansion  (z = 52 mm),
the agreement  is  reasonably  good  for  the  cross-sections
the agreement  is  reasonably  good  for  the  cross-sections
further downstream. Similar results have been obtained for swirl Case 1
further downstream. Similar results have been obtained for swirl Case 1
which was summarized in  a  previous  publication  (Sommerfeld  et al. 1992).
which was summarized in  a  previous  publication  ([[References_AC3-12#10|Sommerfeld  ''et al.'' 1992]]).


<div id="figure11"></div>
<div id="figure11"></div>
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|[[Image:AC3-12_fig11.png|700px]]
|[[Image:AC3-12_fig11.png|700px]]
|-
|-
|align="center" width=650px|'''Figure 11:''' Comparison between measurements and numerical calculations for the gas-phase in Case 2: (a) axial mean velocity; (b)  radial  mean velocity; (c) tangential mean velocity; (d) turbulent kinetic energy.
|align="center" width=650px|'''Figure 11:''' Comparison between measurements and numerical calculations for the gas-phase in Case&nbsp;2: (a) axial mean velocity; (b)  radial  mean velocity; (c) tangential mean velocity; (d) turbulent kinetic energy.
|}
|}


The measured and calculated particle mean velocities and the associated
The measured and calculated particle mean velocities and the associated
velocity fluctuations are compared in Figure 12 and 13 again  for  case
velocity fluctuations are compared in
2. All mean velocity components are  generally  well-predicted,  except
[[Evaluation_AC3-12#figure12|Figures&nbsp;12]] and [[Evaluation_AC3-12#figure13|13]]
for the radial velocity which is predicted to be positive at z = 315 mm
again  for  case&nbsp;2.
All mean velocity components are  generally  well-predicted,  except
for the radial velocity which is predicted to be positive at z&nbsp;=&nbsp;315&nbsp;mm
(i.e. the particles move towards the wall) whereas the experiments show
(i.e. the particles move towards the wall) whereas the experiments show
negative velocities. This implies that in the experiment the  particles
negative velocities. This implies that in the experiment the  particles
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The particle velocity fluctuations are more or less under-predicted for
The particle velocity fluctuations are more or less under-predicted for
all three velocity components, which presumably is caused by the under-
all three velocity components, which presumably is caused by the under-prediction
prediction of the gas-phase turbulent kinetic  energy  in  the  initial
of the gas-phase turbulent kinetic  energy  in  the  initial
region of flow development (Figure 11(d)). This  is  demonstrated  in
region of flow development
Figure 12(b) for  the  fluctuation  of  the  axial  particle  velocity
([[Evaluation_AC3-12#figure11|Figure&nbsp;11(d)]]).
component.
This  is  demonstrated  in
[[Evaluation_AC3-12#figure12|Figure&nbsp;12(b)]]
for  the  fluctuation  of  the  axial  particle  velocity component.


<div id="figure12"></div>
<div id="figure12"></div>
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|[[Image:AC3-12_fig12.png|700px]]
|[[Image:AC3-12_fig12.png|700px]]
|-
|-
|align="center" width=650px|'''Figure 12:''' Comparison  of  measured  and  calculated  axial  particle velocity profiles: (a) mean particle velocity (m/s); (b) mean  particle velocity fluctuation (m/s), Case 2.
|align="center" width=650px|'''Figure 12:''' Comparison  of  measured  and  calculated  axial  particle velocity profiles: (a) mean particle velocity&nbsp;(m/s); (b) mean  particle velocity fluctuation&nbsp;(m/s), Case&nbsp;2.
|}
|}


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|[[Image:AC3-12_fig13.png|700px]]
|[[Image:AC3-12_fig13.png|700px]]
|-
|-
|align="center" width=650px|'''Figure 13:''' Comparison of measurements and  calculations:  (a)  radial particle velocity (m/s); (b) tangential particle velocity (m/s),  Case 2.
|align="center" width=650px|'''Figure 13:''' Comparison of measurements and  calculations:  (a)  radial particle velocity&nbsp;(m/s); (b) tangential particle velocity&nbsp;(m/s),  Case&nbsp;2.
|}
|}


The calculated particle mass flux shows very good  agreement  with  the
The calculated particle mass flux shows very good  agreement  with  the
experiments in the initial region just downstream of the inlet,  namely
experiments in the initial region just downstream of the inlet,  namely
at z = 52 mm, and further downstream at z = 315 (Figure 14(a)). In  the
at z&nbsp;=&nbsp;52&nbsp;mm, and further downstream at z&nbsp;=&nbsp;315
([[Evaluation_AC3-12#figure14|Figure&nbsp;14(a)]]).
In  the
intermediate region, where the particles  rebound  from  the  wall  and
intermediate region, where the particles  rebound  from  the  wall  and
interact again with the central recirculation bubble (see  Figure 7),
interact again with the central recirculation bubble
(see  [[Test_Data_AC3-12#figure7|Figure&nbsp;7]]),
some differences between the experiments and predictions  are  observed
some differences between the experiments and predictions  are  observed
in the near-wall region. At z = 155 and 195 mm, the measurements show a
in the near-wall region. At z&nbsp;=&nbsp;155 and 195&nbsp;mm, the measurements show a
relatively narrow layer of particles near the  wall  with  the  maximum
relatively narrow layer of particles near the  wall  with  the  maximum
being directly at the wall. The  calculations  show  a  slightly  wider
being directly at the wall. The  calculations  show  a  slightly  wider
particle layer with a maximum in the particle mass flux  located  at  a
particle layer with a maximum in the particle mass flux  located  at  a
radial position of 65 mm, which might result from the assumptions  made
radial position of 65&nbsp;mm, which might result from the assumptions  made
in the particle-wall collision model.
in the particle-wall collision model.


A sensitive study, by using different  normal  restitution  ratios  and
A sensitivity study, by using different  normal  restitution  ratios  and
wall friction coefficients in the particle-wall collision model,  shows
wall friction coefficients in the particle-wall collision model,  shows
that their influence on the particle mass flux distribution at z = 155
that their influence on the particle mass flux distribution at z&nbsp;=&nbsp;155
and 195 mm is not too strong (Figure 15). A  reduction  in  the  normal
and 195&nbsp;mm is not too strong ([[Evaluation_AC3-12#figure15|Figure&nbsp;15]]).
A  reduction  in  the  normal
restitution ratio from 0.8 to 0.6 gives a  slightly  narrower  particle
restitution ratio from 0.8 to 0.6 gives a  slightly  narrower  particle
layer with a more pronounced maximum  closer  to  the  wall.  When  the
layer with a more pronounced maximum  closer  to  the  wall.  When  the
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In the publications of Sommerfeld et al.  (1992)  additional  numerical
In the publications of [[References_AC3-12#10|Sommerfeld ''et&nbsp;al.'' (1992)]] additional  numerical
results for the swirl Case 1 may be  found.  Details  on  measured  and
results for the swirl Case 1 may be  found.  Details  on  measured  and
calculated  particle  size-velocity  correlations  are  presented  in
calculated  particle  size-velocity  correlations  are  presented  in
Sommerfeld and Qiu (1993).
[[References_AC3-12#11|Sommerfeld and Qiu (1993)]].
 
<div id="figure15"></div>
{|align="center"
|[[Image:AC3-12_fig15.png|700px]]
|-
|align="center" width=650px|'''Figure 15:''' Measured and calculated axial particle mass flux  at  z&nbsp;=&nbsp;115 and 195&nbsp;mm for different parameters in the wall collision model: &#9651;,&nbsp;with lift force, e&nbsp;=&nbsp;0.8, &mu;&nbsp;=&nbsp;0.3; &#9674;,&nbsp;with lift force, e&nbsp;=&nbsp;0.6,  &mu;&nbsp;=&nbsp;0.3; &#10033;,&nbsp;without lift force, e&nbsp;=&nbsp;0.8, &mu;&nbsp;=&nbsp;0.3; &#9633;,&nbsp;experiment, Case&nbsp;2.
|}
 
The test case particle-laden swirling flow (here Case 1) was also  used
for validation of "in-house" codes at the '''5th  Workshop  on  Two  Phase Flow Predictions'''
([[References_AC3-12#9|Sommerfeld and Wennerberg 1991]]). It should  be  noted
that in all the graphs shown below, the swirling Case&nbsp;1 described above
is named Case&nbsp;3. Several groups have participated in these calculations
and the results may be found in the Workshop Proceedings,  including  a
description of the numerical methods applied.
 
Most of  the  calculations  were  performed  with  the  two-dimensional
Euler/Lagrange approach (e.g. Azevedo/Pereira,  Milojevic,  Wennerberg,
Berlemont, Blümcke  and  Ando/Sommerfeld).  Regarding  the  fluid  flow
mostly the standard k-&epsilon; turbulence model was  used,  some  participants
adapted however the model  constants  (i.e.  Blümcke).  Moreover,  some
contributions were based on the application of algebraic stress  models
in order to predict the stress components of the fluid, which were also
used for the particle tracking (e.g. Berlemont and Wennerberg). The two-fluid
approach was only applied by Simonin also using a k-&epsilon;  turbulence
model. The fluctuating motion of the dispersed phase was linked to  the
continuous phase  turbulence  through  analytic  correlations
([[References_AC3-12#7|Simonin&nbsp;1991]]).
 
Some results of the test case calculations for Case&nbsp;1 (in  the  figures
named Case 3) are shown below
([[Evaluation_AC3-12#figure16|Fig.&nbsp;16]] to [[Evaluation_AC3-12#figure23|23]]),
revealing that there  is
a noticeable scatter of the calculations  performed  by  the  different
groups. The mean velocities for gas and  particle  phase  are  captured
reasonably well, but all components of the fluctuating  velocities  are
generally considerably under-predicted, for both gas and particles.  In
the numerical calculation  of  the  particle  mass  flux  profiles  the
critical issue is the prediction of  the  correct  penetration  of  the
particles into the central recirculation region.  At  the  end  of  the
recirculation region mostly the particle mass flux is  under-predicted.
Surprisingly, the profiles of the particle  number  mean  diameter  are
captured quite well by most of the computations.
 
<div id="figure16"></div>
{|align="center"
|[[Image:AC3-12_fig16.png|700px]]
|-
|align="center" width=650px|'''Figure 16:''' Measured and  calculated  axial  gas-phase  mean  velocity profiles presented at the 5th Workshop on Two-Phase  Flow  Predictions, Case&nbsp;1.
|}
 
<div id="figure17"></div>
{|align="center"
|[[Image:AC3-12_fig17.png|700px]]
|-
|align="center" width=650px|'''Figure 17:''' Measured  and  calculated  axial  gas-phase  rms  velocity profiles presented at the 5th Workshop on Two-Phase  Flow  Predictions, Case&nbsp;1.
|}
 
<div id="figure18"></div>
{|align="center"
|[[Image:AC3-12_fig18.png|700px]]
|-
|align="center" width=650px|'''Figure 18:''' Measured and calculated tangential gas-phase mean velocity profiles presented at the 5th Workshop on Two-Phase  Flow  Predictions, Case&nbsp;1.
|}
 
<div id="figure19"></div>
{|align="center"
|[[Image:AC3-12_fig19.png|700px]]
|-
|align="center" width=650px|'''Figure 19:''' Measured  and  calculated  axial  particle  mean  velocity profiles presented at the 5th Workshop on Two-Phase  Flow  Predictions, Case&nbsp;1.
|}
 
<div id="figure20"></div>
{|align="center"
|[[Image:AC3-12_fig20.png|700px]]
|-
|align="center" width=650px|'''Figure 20:''' Measured  and  calculated  axial  particle  rms  velocity profiles presented at the 5th Workshop on Two-Phase  Flow  Predictions, Case&nbsp;1.
|}
 
<div id="figure21"></div>
{|align="center"
|[[Image:AC3-12_fig21.png|700px]]
|-
|align="center" width=650px|'''Figure 21:''' Measured and  calculated  tangential  particle-phase  mean velocity profiles presented at  the  5th  Workshop  on  Two-Phase  Flow Predictions, Case&nbsp;1.
|}
 
<div id="figure22"></div>
{|align="center"
|[[Image:AC3-12_fig22.png|700px]]
|-
|align="center" width=650px|'''Figure 22:''' Measured and calculated particle mass flux in the  stream-wise  direction  presented  at  the  5th  Workshop  on  Two-Phase  Flow Predictions, Case&nbsp;1.
|}
 
<div id="figure23"></div>
{|align="center"
|[[Image:AC3-12_fig23.png|700px]]
|-
|align="center" width=650px|'''Figure 23:''' Measured and  calculated  particle  mean  number  diameter presented at the 5th Workshop on Two-Phase Flow Predictions, Case&nbsp;1.
|}


<br/>
<br/>
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{{ACContribs
{{ACContribs
| authors=Martin Sommerfeld
| authors=Martin Sommerfeld
| organisation=Martin-Luther-Universitat Halle-Wittenberg
| organisation=Martin-Luther-Universität Halle-Wittenberg
}}
}}
{{ACHeader
{{ACHeader_ref
|area=3
|area=3
|number=12
|number=12

Latest revision as of 16:30, 11 February 2017

Front Page

Description

Test Data

CFD Simulations

Evaluation

Best Practice Advice

References

Particle-laden swirling flow

Application Challenge AC3-12   © copyright ERCOFTAC 2013

Comparison of Test Data and CFD

A rather good agreement between the experiments and predictions was obtained for gas and particle phase in both swirling cases considered. The comparison of the calculated streamlines of the gas flow with those obtained from the integration of the measured axial velocity shows that the flow field is predicted reasonably well for both conditions (Figure 10). The most obvious difference is that the axial extension of the central recirculation bubble is predicted to be larger at the top and downstream ends for both cases. The predicted width of the central recirculation bubble and the extension of the recirculation at the edge of the pipe expansion are in good agreement with the measured results.

AC3-12 fig10.png
Figure 10: Measured and calculated gas-phase streamlines (the upper parts of each figure corresponds to the calculations and the lower parts show the measurements); (a) Case 1; (b) Case 2.

The measured cross-sectional profiles of the three velocity components are compared with the calculations in Figure 11 for Case 2. The agreement is very good, except for the tangential velocity which is under-predicted in the region downstream of the location where the recirculation bubble has its largest radial extension. Although, the turbulent kinetic energy of the gas phase is considerably under- predicted in the initial mixing region between the primary and annular jets and within the recirculation at the edge of the pipe expansion (z = 52 mm), the agreement is reasonably good for the cross-sections further downstream. Similar results have been obtained for swirl Case 1 which was summarized in a previous publication (Sommerfeld et al. 1992).

AC3-12 fig11.png
Figure 11: Comparison between measurements and numerical calculations for the gas-phase in Case 2: (a) axial mean velocity; (b) radial mean velocity; (c) tangential mean velocity; (d) turbulent kinetic energy.

The measured and calculated particle mean velocities and the associated velocity fluctuations are compared in Figures 12 and 13 again for case 2. All mean velocity components are generally well-predicted, except for the radial velocity which is predicted to be positive at z = 315 mm (i.e. the particles move towards the wall) whereas the experiments show negative velocities. This implies that in the experiment the particles move on average away from the wall. Although, it might be expected that the numerical results in the near-wall region are very sensitive with respect to the modelling of the wall collision process, it was found that a variation in the normal restitution ratio and the friction coefficient in the three-dimensional inelastic collision model did not result in considerable changes in the velocity profiles. The scattering of the numerical results in the core region downstream of the location, where the central recirculation bubble has its largest radial extension is a result of the low number of collected particles, since the majority of the particles have already moved out of the core region.

The particle velocity fluctuations are more or less under-predicted for all three velocity components, which presumably is caused by the under-prediction of the gas-phase turbulent kinetic energy in the initial region of flow development (Figure 11(d)). This is demonstrated in Figure 12(b) for the fluctuation of the axial particle velocity component.

AC3-12 fig12.png
Figure 12: Comparison of measured and calculated axial particle velocity profiles: (a) mean particle velocity (m/s); (b) mean particle velocity fluctuation (m/s), Case 2.
AC3-12 fig13.png
Figure 13: Comparison of measurements and calculations: (a) radial particle velocity (m/s); (b) tangential particle velocity (m/s), Case 2.

The calculated particle mass flux shows very good agreement with the experiments in the initial region just downstream of the inlet, namely at z = 52 mm, and further downstream at z = 315 (Figure 14(a)). In the intermediate region, where the particles rebound from the wall and interact again with the central recirculation bubble (see Figure 7), some differences between the experiments and predictions are observed in the near-wall region. At z = 155 and 195 mm, the measurements show a relatively narrow layer of particles near the wall with the maximum being directly at the wall. The calculations show a slightly wider particle layer with a maximum in the particle mass flux located at a radial position of 65 mm, which might result from the assumptions made in the particle-wall collision model.

A sensitivity study, by using different normal restitution ratios and wall friction coefficients in the particle-wall collision model, shows that their influence on the particle mass flux distribution at z = 155 and 195 mm is not too strong (Figure 15). A reduction in the normal restitution ratio from 0.8 to 0.6 gives a slightly narrower particle layer with a more pronounced maximum closer to the wall. When the particle lift force is switched off in the calculations, the particle layer becomes wider with a less pronounced maximum in the mass flux distribution near the wall. This also shows that the particle lift force due to rotation is only important in the near-wall region, where high rotational velocities are induced by the wall collision. Since the particles lag behind the air flow in the near-wall region, the direction of the lift force is directed towards the centreline. From these results, one may conclude that the particle motion in the near- wall region might also be affected by electrostatic forces, although the Plexiglas test section was carefully grounded.

AC3-12 fig14.png
Figure 14: Comparison of measurements and calculations: (a) stream-wise particle mass flux (kg/m2s); (b) particle number mean diameter (μm), Case 2.

In the publications of Sommerfeld et al. (1992) additional numerical results for the swirl Case 1 may be found. Details on measured and calculated particle size-velocity correlations are presented in Sommerfeld and Qiu (1993).

AC3-12 fig15.png
Figure 15: Measured and calculated axial particle mass flux at z = 115 and 195 mm for different parameters in the wall collision model: △, with lift force, e = 0.8, μ = 0.3; ◊, with lift force, e = 0.6, μ = 0.3; ✱, without lift force, e = 0.8, μ = 0.3; □, experiment, Case 2.

The test case particle-laden swirling flow (here Case 1) was also used for validation of "in-house" codes at the 5th Workshop on Two Phase Flow Predictions (Sommerfeld and Wennerberg 1991). It should be noted that in all the graphs shown below, the swirling Case 1 described above is named Case 3. Several groups have participated in these calculations and the results may be found in the Workshop Proceedings, including a description of the numerical methods applied.

Most of the calculations were performed with the two-dimensional Euler/Lagrange approach (e.g. Azevedo/Pereira, Milojevic, Wennerberg, Berlemont, Blümcke and Ando/Sommerfeld). Regarding the fluid flow mostly the standard k-ε turbulence model was used, some participants adapted however the model constants (i.e. Blümcke). Moreover, some contributions were based on the application of algebraic stress models in order to predict the stress components of the fluid, which were also used for the particle tracking (e.g. Berlemont and Wennerberg). The two-fluid approach was only applied by Simonin also using a k-ε turbulence model. The fluctuating motion of the dispersed phase was linked to the continuous phase turbulence through analytic correlations (Simonin 1991).

Some results of the test case calculations for Case 1 (in the figures named Case 3) are shown below (Fig. 16 to 23), revealing that there is a noticeable scatter of the calculations performed by the different groups. The mean velocities for gas and particle phase are captured reasonably well, but all components of the fluctuating velocities are generally considerably under-predicted, for both gas and particles. In the numerical calculation of the particle mass flux profiles the critical issue is the prediction of the correct penetration of the particles into the central recirculation region. At the end of the recirculation region mostly the particle mass flux is under-predicted. Surprisingly, the profiles of the particle number mean diameter are captured quite well by most of the computations.

AC3-12 fig16.png
Figure 16: Measured and calculated axial gas-phase mean velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig17.png
Figure 17: Measured and calculated axial gas-phase rms velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig18.png
Figure 18: Measured and calculated tangential gas-phase mean velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig19.png
Figure 19: Measured and calculated axial particle mean velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig20.png
Figure 20: Measured and calculated axial particle rms velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig21.png
Figure 21: Measured and calculated tangential particle-phase mean velocity profiles presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig22.png
Figure 22: Measured and calculated particle mass flux in the stream-wise direction presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.
AC3-12 fig23.png
Figure 23: Measured and calculated particle mean number diameter presented at the 5th Workshop on Two-Phase Flow Predictions, Case 1.




Contributed by: Martin Sommerfeld — Martin-Luther-Universität Halle-Wittenberg

Front Page

Description

Test Data

CFD Simulations

Evaluation

Best Practice Advice

References


© copyright ERCOFTAC 2013