Experimental study of the effect of velocity slip and mass loading on the modification of grid-generated turbulence in gas–solid particles flows

Full text

169
Proc. Estonian Acad. Sci. Eng., 2005, 11, 2, 169–180
Experimental study of the effect of velocity slip
and mass loading on the modification
of grid-generated turbulence in
gas–solid particles flows
Medhat Hussainov, Alexander Kartushinsky, Ylo Rudi, Igor Shcheglov
and Sergei Tisler
Laboratory of Multiphase Media Physics, Tallinn University of Technology, Akadeemia tee 23A,
12618 Tallinn, Estonia; aeromeh@online.ee
Received 4 May 2004
Abstract. Experimental data on the effects of the velocity slip and mass loading on a grid-
generated turbulence in gas–solid particles flow are presented. Glass beads (700 m) were used as
the dispersed phase. Velocities of both phases were measured with a Laser Doppler Anemometer.
Turbulence decay curves, obtained for different grids, show that particles enhance turbulence for
small grids and attenuate it for the large ones. Turbulence enhancement and attenuation are
intensified with the increase of the flow mass loading. The particles effect on turbulence changes
from turbulence attenuation for a small velocity slip to its enhancement for a large velocity slip. A
criterion for the evaluation of turbulence modification in gas–solid particles flow is proposed.
Key words: gas–solid particles flow, grid-generated turbulence, turbulence modification, mass
loading ratio, velocity slip.
1. INTRODUCTION
The effect of solid particles on turbulence has been a prime issue of many
experimental studies during last decades. New results about the dependence of
turbulence on both the ratio between the particle size and the Euler turbulence
length-scale E
L and the particle Reynolds number p
R
e were obtained in [1,2].
Later on, the dependence of the attenuation of the turbulent energy on the particle
mass loading was established in [3]. The data were classified into two groups: the
first group consisted of light particles with low Stokes numbers E,St based on
the Euler turbulence time scale E
T with a weak dependence of the turbulence

170
attenuation on the mass loading; the second one consisted of heavy particles with
more sharp dependence of the turbulence attenuation on the mass loading.
However, the influence of particles on turbulence, depending on the Stokes
number, is still an open issue. For instances, the authors of [4] found that the
turbulence attenuation for a given mass loading depends weakly on the Stokes
number; on the contrary, the authors of [3] found a considerable increase of the
turbulence attenuation with the increase of E.St Therefore experiments with
various Reynolds and Stokes numbers of the particles would clarify the effect of
particles on turbulence.
The grid-generated turbulence is an appropriate subject to study the effect of
particles on the turbulence modification since, first, it is well studied theoretically
and experimentally for the single-phase flow and, secondly, there are no
complicating factors for analysis such as non-uniformity of the flow fields or the
influence of the confining surfaces. Besides, it is easy to vary the Stokes number
by changing only the grid parameters. However, experimental investigation of
the grid-generated turbulence in gas–solid particles flows is complicated, first of
all due to large transverse dimension of the flow that results in high mass flow of
particles and also because of the difficulties in optical probing. Problems
concerning entering of particles into the flow make the task even more
complicated. Because of that, there is a lack of experimental studies concerning
the grid-generated turbulence in two-phase flows. The papers [5–7] are among the
few papers devoted the given problem. For example, while studying the effect of
the air bubbles on the turbulence intensity behind a grid, the authors of [5]
observed both attenuation and enhancement of the turbulence for a wide range of
the energy spectrum of the liquid phase. The grid-generated turbulence in a water
flow, loaded by 655 m plastic or glass particles, was investigated in [6]. Here
the mean flow velocity was 1 m/s and the Reynolds number ,
M
R
e calculated for
the grid mesh size ,M was 15 600. A short section of the initial period of the
turbulence decay for 15 33,XM was studied (X is the streamwise
coordinate counted down the stream behind the grid). It was found that the light
plastic particles caused an increase of the longitudinal component of the turbulent
energy, but heavy glass particles decreased the transversal component of the
latter. It should be noted that experimental results on the effect of particles on
turbulence in the water flow are hardly comparable with similar ones obtained for
the air flow, because in case of the water flow the same values of the mass
loading of the flow by the same particles can be obtained for the volume con-
centration of particles of 3 orders of magnitude higher than in air. As numerous
investigations have shown, the character and the amount of change of the
turbulence by particles in many respects depend on both the volume con-
centration and the mass loading. Unfortunately, no much attention has been paid
to similar studies in gas–solid particles flows until now. As an exception,
paper [7] can be mentioned, where the effect of 120 and 480 m glass beads on
the decay of the grid-generated turbulence in the downward air flow was studied.
It was found that 120 m particles with p13Re decreased turbulence, whereas

171
480 m particles with p170Re increased it. However, these experiments were
conducted for only one type of the grid. Thus the parameters of the initial
turbulence were not varied and it was not possible to reveal their influence on the
turbulence modification in the case of the two-phase flow.
Thus experimental investigations of the effect of parameters of the initial
turbulence as well as of the velocity slip and flow mass loading on the turbulence
of the gas phase of flow are needed. This study tries to fill partly this gap.
2. EXPERIMENTAL CONDITIONS
The experiments were carried out in a vertical two-phase open-loop wind
channel with a closed test section described in detail in [8]. The instantaneous
velocities of the tracer particles and particles of the dispersed phase were
measured with a Laser Doppler Anemometer (LDA) [9]. Glass beads of the
density p2500 kg/m3 with a diameter of 700 m were used as the
dispersed phase. A gravity acceleration device was used. This device allowed to
obtain the required velocity slip for high values of the mass loading ratio of the
flow. Three different grids were used (Table 1, where d is the diameter of the
grid rods and S is the solidity of the grid).
The grid Reynolds number ,
M
R
e which is calculated as
MuM
Re (1)
for the given mean gas flow velocity 9.5u m/s was 3040, 6333 and 10 133,
respectively. Here is the kinematic viscosity of gas.
The investigation of the influence of the velocity slip on turbulence was
carried out for the positive velocity slip, i.e. when particles lagged the gas. The
velocity slip was set only by the preliminary acceleration of particles before their
entering into the flow, without changing the parameters of the particles or of the
initial single-phase flow.
The influence of the flow mass loading æ on turbulence was explored for the
range of æ from 0 to 1 (kg dust)/(kg air). The mass flow of the dispersed phase
was measured by the isokinetic sampling technique [10] and on-line monitored by
the Laser Concentration Measurer [11].
Table 1. Parameters of the grids
M, mm M/d S
4.8 2.53 0.487
10 2.50 0.490
16 4.00 0.360

172
3. RESULTS
Figure 1 shows decay curves of the turbulence 22
rms
uu ( rms
u is the root
mean square value of the gas fluctuation velocity) behind different grids in the
single- and two-phase flow for the mass loading of 0.14 (kg dust)/(kg air). The
velocity slip rs
uuu was about 4 m/s (s
u is the mean particles velocity). As
follows from Fig. 2, the pronounced turbulence enhancement by particles is
observed for the grids 4.8M and 10 mm, while for the grid 16M mm the
turbulence attenuation takes place. The character of the turbulence attenuation
Fig. 1. Decay curves behind different grids.
Fig. 2. The turbulence intensity vs the flow mass loading at X = 450 mm.
X/M
(rms
/uu )2 single-phase; M = 4.8 mm two-phase; M = 4.8 mm
single-phase; M = 10 mm two-phase; M = 10 mm
single-phase; M = 16 mm two-phase; M = 16 mm
æ, kg/kg
rms
u
u, %
M = 4.8 mm
M = 16 mm

173
Table 2. Constants of the decay curves of different grids
M, mm C A
4.8; single-phase flow 20.09 2.62
4.8; two-phase flow 17.59 –0.01
10; single-phase flow 18.80 0.91
10; two-phase flow 18.0 3.15
16; single-phase flow 29.28 5.63
16; two-phase flow 30.57 6.04
behind the grids agrees with the well-known behaviour of the decay curves in
grid-generated turbulent flows described in [12]:
2
2
rms
,
uX
CA
M
u (2)
where C and A are coefficients according to Table 2.
Experimental results (Fig. 2) show that increase in the mass loading of the
flow results in the intensification of the additional turbulence generation for the
grid 4.8M mm and in the attenuation of the turbulence for the grid
16M mm. As it can be seen from Fig. 2, the turbulence intensity depends
linearly on the mass loading at least up to 1 (kg dust)/(kg air).
Most interesting are the results concerning the turbulence modification by
particles with various velocity slip (Fig. 3). The influence of the velocity slip on
turbulence is distinctly apparent in case of the grid 16M mm. The turbulence
attenuation is observed for this grid for small velocity slip, while for large slip
(larger than 3.5 m/s) the character of the particles effect changes to the opposite,
i.e. the turbulence enhancement takes place. Thus for the given experimental
conditions for 16M mm, the velocity slip determines the character of the
particles effect. The turbulence enhancement by particles with larger values of
the velocity slip was observed also for the grids 4.8M and 10 mm.
The turbulence structure of a single-phase flow behind the grid is determined
by such flow parameters as the mean flow velocity ,u the grid mesh size M and
the ratio Md [12]. The character of the particles effect on turbulence of the gas
phase in the two-phase flow depends both on the turbulence parameters of the
initial single-phase and the parameters of the dispersed phase, such as diameter
, the material density p, the flow mass loading ,æ the particle Reynolds
number p
R
e and the Stokes number E.St In order to analyse the experimental
results, the experimental parameters of the single- and two-phase flows at the
location 50XM along the flow axis are presented in Table 3. In Table 3 the
following notations are used:
the Euler integral turbulence time scale E
E,
L
Tu (3)
the Kolmogorov turbulence time scale
1/4
3
K,t (4)

174
K is the Kolmogorov turbulence length scale, k is the turbulence kinetic
energy and is the dissipation rate of the turbulence kinetic energy.
Table 4 shows the parameters of the dispersed phase. The change of the
turbulence intensity by the particles Ch is calculated according to [1]:
TP F
F
()
100,Ch (5)
Fig. 3. The turbulence intensity vs the velocity slip at the location X = 365 mm. Heavy dash lines
denote the turbulence intensity for different grids in the single-phase flow.
Table 3. Experimental parameters of the single- and two-phase (bold) flows at the location
X/M = 50 M, mm
Parameter 4.8 10 16
2.51 10–2 5.11 10–2 7.47 10–2
E,T s 2.53 10–2 5.03 10–2 7.40 10–2
1.61 10–3 2.28 10–3 3.28 10–3
K,t s 1.54 10–3 2.18 10–3 3.32 10–3
1.55 10–4 1.85 10–4 2.22 10–4
K, m 1.52 10–4 1.81 10–4 2.23 10–4
9.54 10–3 1.96 10–2 2.41 10–2
E,L m 1.01 10–2 2.01 10–2 2.35 10–2
1.45 10–1 1.47 10–1 1.04 10–1
k, m2/s2 1.61 10–1 1.59 10–1 1.01 10–1
5.786 2.876 1.394
, m2/s3 6.364 3.162 1.360
rms
u
u, %
M = 4.8 mm
M = 10 mm
M = 16 mm
r
u, m/s

175
where TP and F are the turbulence intensities of the two-phase and single-
phase flow, respectively; is calculated from Eq. (2) as follows:
rms .
uu (6)
The volume concentration of the dispersed phase is calculated as
p,
s
æu
u (7)
where is the material density of gas.
p
R
e is the particle Reynolds number:
r
p,
u
Re (8)
p is the particle response time and K
St is the Stokes number based on the
Kolmogorov turbulence time scale K.t The ratio of the interparticle distance
and the particle diameter is determined according to [13] as
1/3 1.
6 (9)
As it can be seen from Table 4, the diameter of the particles used in experi-
ments is substantially smaller than the energy-containing eddies E
(0.08).L
Therefore, according to [1], only the turbulence attenuation should take place.
However, the experimental data do show both turbulence attenuation and
enhancement. At the same time, the increasing of the turbulence attenuation for
16M mm or reducing of the turbulence enhancement for 4.8M and 10 mm
Table 4. The parameters of the dispersed phase
M, mm
Parameter 4.8 10 16
,Ch % 5.31 4.05 – 1.70
,æ kg/kg 1.4 10–1 1.4 10–1 1.4 10–1
1.35 10–4 1.19 10–4 1.15 10–4
r,u m/s 4.4 3.7 3.5
p
Re 2.0533 102 1.7267 102 1.6333 102
,
p s 3.76 3.76 3.76
K
St 2.45 103 1.73 10 1.13 103
E
St 1.49 102 7.48 101 5.08 101
1.472 101 1.541 101 1.559 101
K, 4.50 3.78 3.16
E
L 7.34 10–2 3.57 10–2 2.90 10–2

176
that were observed in experiments, are in agreement with the general concept of
the turbulence attenuation by the particles with decreasing ratio of E.L
Let us analyse the experimental results using the diagram presented in
Fig. 4 [14], which exhibits the domains of the particles effect on the turbulence
modification depending on the interparticle distance, related to as well as to
the Stokes numbers E
St and K.St The shaded area in the given diagram cor-
responds to the given experimental flow conditions and shows the turbulence
enhancement by particles that should occur.
Another criterion of the particles effect on turbulence, suggested in [15], is the
particle Reynolds number p,
R
e which determines the velocity slip. Figure 5
shows the dependence of the turbulence on p.
R
e This plot also demonstrates that
the turbulence attenuation takes place up to p175,Re and turbulence is
enhanced for p175.Re
Fig. 4. The map of the flow regimes in particle-laden flows [14]; p is the volume fraction of
particles: p
pNV V (N is the number of particles, p
V is volume of a particle and V is the
volume occupied by particles and fluid).
Particles
enhance
production
Negligible
effect on
turbulence
Particles
enhance
dissipation
p
One-way
coupling Two-way
coupling Fou
r
-way
coupling
Dilute
suspension Dense
suspension

177
Fig. 5. The change of the turbulence intensity by particles vs p
Re for the grid 16M mm at the
location 365X mm.
The criterion p
R
e reflects the influence of the averaged velocities of the gas
and particles and does not consider the turbulence parameters of the initial single-
phase flow. Therefore, it is necessary to choose a criterion that would consider
turbulence of the initial single-phase flow. The turbulence Reynolds number
L,
R
e determined by the Euler turbulence length-scale E
L and the fluctuating
velocity of gas rms
u as
rms E
L,
uL
Re (10)
can be accepted as such a criterion.
Let us clarify in what way the conditions of turbulence of the initial single-
phase flow, which is characterized by L,
R
e affect the particles influence on
turbulence in the two-phase flow. It is evident that the portion of energy,
supplemented by particles owing to the shedding of vortices, decreases with the
increase of the turbulent energy of the initial single-phase flow. At the same time,
according to [1], the particles effect moves towards the turbulence attenuation
with the growth of the eddy size E
L of the initial single-phase flow. This implies
that the particles effect Ch is in inverse proportion to L
R
e that was verified by
experimental data (Fig. 6).
It seems logical to unify both criteria, p
R
e and L,
R
e into a single generaliz-
ing criterion pL
.
R
eRe This approach is a development of the Crowe’s
criterion [1], since the ratio pL E srms
()(
||
)Re Re L u u u considers the
velocity characteristics of gas and particles in addition to Crowe’s parameter
E.L Thus the introduced criterion enables one to consider the combined
influence of the parameters of the dispersed phase and of the initial single-phase
flow on the turbulence of the carrier phase of the two-phase flow. Based on the
Ch, %
Rep

178
processing of the experimental data, obtained with the fixed mass loading for
different grids at various velocity slips in different cross-sections of the flow, the
dependence of the change of the turbulence intensity on the ratio pL
R
eRe is
obtained (Fig. 7). As Fig. 7 shows, all experimental data are fitted by the curve,
which shows the point of transition from the turbulence attenuation to its
enhancement at pL
0.4.Re Re Based on linear dependence of the change of the
turbulence intensity by particles on the mass loading, stretch or shrink of this
curve in vertical direction, depending on the flow mass loading, can be expected.
Fig. 6. The change of the turbulence intensity by particles vs L
Re for different values of .
p
Re
Fig. 7. The change of the turbulence intensity by particles vs pL
Re Re for the flow mass loading
0.14æ (kg dust)/(kg air).
p
Re = 221...227
p
Re = 208...217
p
Re = 97...126
Ch, %
ReL
Ch, %
Rep /ReL

179
4. CONCLUSIONS
Experimental investigations of the effect of the velocity slip and of the mass
loading on the grid-generated turbulence in a gas–solid particles flow have been
carried out. The velocity slip was achieved by preliminary acceleration of
particles before their entering the flow, when the parameters of the gas and
dispersed phases were invariable. The obtained results allow to draw the follow-
ing conclusions:
the 700 m glass beads may attenuate or enhance the turbulence, depending
on the parameters of turbulence of the initial single-phase flow;
the velocity slip determines the particles effect on turbulence for the grid
16M mm for the given experimental conditions; the turbulence attenuation
is observed for small velocity slips, whereas enhancement takes place for the
velocity slips larger than 3.5 m/s;
the ratio pL
R
eRe is proposed as the criterion for considering the combined
influence of the parameters of the dispersed phase and the initial single-phase
flow on the turbulence of the carrier phase of the two-phase flow;
pL
0.4Re Re is the critical value for the given experimental conditions that
determines the influence of particles on turbulence; at pL
0.4Re Re the
turbulent energy is attenuated and at pL
0.4Re Re it is enhanced;
the particles effect on turbulence depends linearly on the mass loading up to
the loading of 1 (kg dust)/(kg air).
REFERENCES
1. Gore, R. A. and Crowe, C. T. Effect of particle size on modulating turbulent intensity.
Int.
J. Multiphase Flow
, 1989,
15
, 279–285.
2.
Hetsroni, G. Particles-turbulence interaction. Int. J. Multiphase Flow, 1989, 15, 735–746.
3.
Kulick, J. D., Fessler, J. R. and Eaton, J. K. On the Interaction between Particles and
Turbulence in a Fully-developed Channel Flow in Air. Thermosciences Division, Depart-
ment of Mech. Eng., Stanford University, Rep. No. MD-66, Stanford, California, 1993.
4.
Squires, K. D. and Eaton, J. K. Particle response and turbulence modification in isotropic
turbulence. Phys. Fluids A, 1990, 2, 1191–1203.
5.
Lance, M. and Bataille, J. Turbulence in the liquid phase of a uniform bubbly air-water flow.
J. Fluid Mech., 1991, 222, 95–118.
6.
Schreck, S. and Kleis, S. J. Modification of grid-generated turbulence by solid particles.
J. Fluid Mech., 1993, 249, 665–688.
7.
Stojanovic, Z., Chrigui, M., Sadiki, A., Dreizler, A., Gei , S. and Janicka, J. Experimental
investigation and modeling of turbulence modification in a dilute two-phase turbulent flow.
In Proc. 10th Workshop on Two-Phase Flows Predictions. Merseburg, 2002, 52–60.
8.
Hussainov, M., Kartushinsky, A., Rudi, Ü., Shcheglov, I., Kohnen, G. and Sommerfeld, M.
Experimental results of turbulence modulation by rough solid particles in a grid-generated
flow. Proc. Estonian Acad. Sci. Eng., 2000, 6, 217–229.
9.
Hussainov, M., Kartushinsky, A., Rudi, Ü., Shcheglov, I., Kohnen, G. and Sommerfeld, M.
Experimental investigation of turbulence modulation by solid particles in a grid-generated
vertical flow. Int. J. Heat Fluid Flow, 2000, 21, 365–373.
10.
Laats, M. K. and Frishman, F. A. Assumptions used for the calculation of the two-phase
turbulent jet. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1970, No. 2, 186–191 (in Russian).

180
11.
Hussainov, M., Kartushinsky, A., Mulgi, A., Shcheglov, I. and Tisler, S. Properties of solid
particle distribution in two-phase laminar boundary layers of various shapes and particle
sedimentation. Proc. Estonian Acad. Sci. Phys. Math., 1994, 43, 237–249.
12.
Hinze, J. O. Turbulence. McGraw-Hill, New York, 1975.
13.
Kenning, V. M. and Crowe, C. T. On the effect of particles on carrier phase turbulence in gas-
particle flows. Int. J. Multiphase Flow, 1997, 23, 403–408.
14.
Elghobashi, S. Particle-laden turbulent flows: direct simulation and closure models. Spec.
No. “Computational Fluid Dynamics for the Petrochemical Process Industry” (Olie-
mans, R. V. A., ed.). Appl. Sci. Res., 1991, 48, 301–314.
15.
Hetsroni, G. Particles-turbulence interaction. Int. J. Multiphase Flow, 1989, 15, 735–746.
Tahkefaasi kiirusliku nihke ja masskoormatuse mõju
hindamine võreturbulentsi modifitseerumisele
dispersses vooluses
Medhat Hussainov, Alexander Kartušinski, Ülo Rudi, Igor Štšeglov
ja Sergei Tisler
Eksperimentide läbiviimisel kasutati dispersse faasi moodustamiseks sfäärilisi
klaasosakesi suurusega 700 µm, gaasi ja tahkete osakeste kiirusi mõõdeti laser-
dopplermeetodiga. Turbulentsi sumbumiskõverad fikseeriti ruudukujuliste aken-
dega võre taga, kusjuures võreakna suurused olid 4,8, 10,0 ja 16,0 mm. Nagu
katsed näitasid, sumbus turbulents väikeste (4,8 ja 10,0 mm) võreakende puhul
aeglasemalt kui samade parameetritega gaasivooluse puhul. See tõendab turbu-
lentsi täiendavat genereerimist tahkete osakeste poolt. Samas põhjustasid osake-
sed turbulentsi sumbumist suure (16,0 mm) võreakna puhul. Dispersse vooluse
masskoormatuse suurendamisel võimendus osakeste mõju vooluse võreturbulent-
sile mõlemal juhul. Faasidevahelise kiirusliku nihke mõju uurimisel dispersse
vooluse turbulentsile nihkekiiruste vahemikus 0–5 m/s täheldati nii dispersse
vooluse turbulentsi sumbumist kui ka genereerumist. Eksperimentaalsete and-
mete baasil määrati kriteriaalne parameeter, mis võimaldab arvestada dispersse
faasi ja ühefaasilise lähtevooluse parameetrite mõju dispersse vooluse turbulent-
sile.