- Email: [email protected]
Flow and deposition measurement of foam beads in a closed re-circulating wind tunnel for snowdrift modelling
Journal Pre-proof Flow and deposition measurement of foam beads in a closed re-circulating wind tunnel for snowdrift modelling Ganesh Kumar, Ajay Gairola, Aditya Vaid PII:
S0955-5986(19)30341-3
DOI:
https://doi.org/10.1016/j.flowmeasinst.2019.101687
Reference:
JFMI 101687
To appear in:
Flow Measurement and Instrumentation
Received Date: 26 August 2019 Revised Date:
25 October 2019
Accepted Date: 29 December 2019
Please cite this article as: G. Kumar, A. Gairola, A. Vaid, Flow and deposition measurement of foam beads in a closed re-circulating wind tunnel for snowdrift modelling, Flow Measurement and Instrumentation (2020), doi: https://doi.org/10.1016/j.flowmeasinst.2019.101687. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
1
Flow and deposition measurement of foam beads in a closed re-circulating
2
wind tunnel for snowdrift modelling Ganesh Kumara*, Ajay Gairolab, Aditya Vaida
3 a
Snow and Avalanche Study Establishment, Defence Research and Development Organization, Himparisar, Plot no-01, Sector-37A, Chandigarh, PIN-160036, India b Indian Institute of Technology (IIT), Roorkee, Uttarakhand, PIN-247667, India
4 5 6 7 8
ABSTRACT
9
A facility was created for flow and deposition measurement of foam beads (Expanded
10
Polystyrene) in a closed re-circulating wind tunnel to model the snowdrift experimentally.
11
The geometrical and flow similarities between the model (foam beads) and prototype
12
(snow) particles were established for the wind tunnel experiments. The wind tunnel was
13
instrumented with the electronic regulator, anemometer and newly developed flux
14
measuring sensors along with a data logger to carry out the experiments for different
15
simulated terrain conditions. An array of optical sensors for measurement of foam beads
16
flux was calibrated with the known quantity of the material and used to find the flux
17
variation with wind speed inside the tunnel. All three modes of drifting transportation
18
namely creeping, saltation and suspension could be observed through the transparent
19
acrylic wall for data collection. The threshold velocity of foam bead movement was 4.05
20
m/s in the horizontal section and same was 2.7 m/s in the inclined section at an angle of
21
30° downward (a critical angle of avalanche starting zone). The process of snow
22
deposition by the snow fence was simulated with the foam beads deposition around the
23
scaled model (1:50) of a snow fence in the wind tunnel. The experiments helped to find a
24
flow measuring technique for light drifting material like foam beads and the modelling of
25
drifting snow.
26
Keywords: Similarity; Snowdrift; Wind tunnel; Modelling; Foam beads.
27
*
Corresponding Author Email: [email protected] 1
28
1. Introduction
29
The naturally precipitated snow is redistributed by the wind causing the problems like
30
blockage of highway, invisibility and avalanche occurrence in the snowbound area [1]. When
31
the wind speed exceeds its threshold shear velocity, snow particles eject from the snow
32
surface. Snow is mainly transported by three modes namely creeping, saltation and
33
suspension [2]. In the creeping process, the snow particles move on the snow surface. After
34
gaining the energy from wind, the snow particles are energized and subsequently influence
35
other particles to move in the saltation stage. The extra drag on the particles changes their
36
trajectories significantly and they erode more particles from the snow surface. At the last
37
mode of transportation, particles are suspended in air and at this stage, snow particles are
38
transported to a larger distance.
39
The tedious and time-consuming study of a snowdrift in the real scenario is simplified
40
by using wind tunnel experiments and numerical modelling techniques. The experiments had
41
been carried out with natural snow and its simulated materials in the wind tunnel. Lee et al.
42
[3] and Clifton et al. [4] had used the natural snow for their wind tunnel experiments. Other
43
researchers [5–8] had also used real snow for modelling of the snowdrift in the wind tunnel.
44
Alhajraf [9], Durand et al.[10] and Gauer [11] had applied numerical modelling methods for
45
snowdrift simulation. Tominaga [12] showed the potential of Computational Fluid Dynamics
46
(CFD) technique in the modelling of the snowdrift. Most of the researchers working in the
47
snowdrift area had used scaled models and particles of different materials like sand, clay and
48
sawdust. Y. Anno used activated clay particles as a substitute for natural snow in the wind
49
tunnel experiments and found the effects of snow fence geometry on the snowdrift [13]. He
50
found the two-dimensional distribution of clay particles using image processing and
51
introduced simulation of the drift geometry of snow. Isyumov and Mikitiuk employed bran as
52
simulant material in the wind tunnel tests to simulate the snowdrift formation on the lower 2
53
level of a two-level roof at different wind velocities [14]. Kind carried out experiments on
54
wind tunnel with sand and snow to simulate the transport mechanics [15]. Flaga et al. had
55
used grinded Styrofoam to model deposition pattern and drifted snow load over the structures
56
in the wind tunnel [16]. Zhou et al. simulated the redistribution of snow loads on a stepped
57
flat roof in a wind tunnel test using particles like saw wood ash, medium-density polyfoam
58
and silica sand [17]. The wind tunnel tests using these different kinds of particles were
59
performed with nearly identical dimensionless wind velocity and dimensionless time to
60
ensure comparability of test results. The snow threshold velocity in the wind tunnel was
61
measured by Clifton et al. and they found that the threshold shear velocity depends on snow
62
density and particle size [4].
63
Wind tunnel experiments have been carried out by scientists recently for the
64
experimental simulations of blowing and drifting snow. They have tested the snow fence
65
model in the wind tunnel to improve its performance for controlling the drifting snow.
66
Naaim-Bouvet carried out extensive wind tunnel experiments using the image-processing
67
technique to determine the total transport rate [19]. These measurements are being used for
68
development and testing of numerical snowdrift model. Almost all the results of the wind
69
tunnel are based on a rectangular or square section of the wind tunnel. Hence, an attempt was
70
made to design a closed re-circulating wind tunnel (4 m length, 0.2 m diameter and 1.74 m
71
height) with experimental space of 2 m length for carrying out experiments with low-density
72
material like foam beads in the laboratory. It has the advantage of using the same material for
73
the repeatability of the experiment. The acrylic transparent wall of the wind tunnel facilitates
74
visual observation and sufficient strength to the structure. This facility has helped to
75
investigate a light material like foam bead for snowdrift modelling. The deposition pattern of
76
foam beads around a scaled model of snow fence has been observed in the wind tunnel. The
3
77
results of wind tunnel have been compared with the observations made at Banihal Top
78
(Jammu and Kashmir, India) which experiences high snowdrift activities.
79
2. Foam beads and other materials used for the snowdrift modelling
80
The numerical method is going to be popular with the increase of computational capability of
81
the computer. However, it requires high skill and its validation requires the results of wind
82
tunnel experiments and field experimental data. It is also difficult and tedious task to work
83
with snowdrift experimentally in the snowfield. The researchers have worked with sand, clay
84
soil, sawdust and bran to simulate the snowdrift in the wind tunnel. These materials have
85
comparatively high densities and they require high wind speed for their transportation in the
86
wind tunnel. Authors were looking for a more suitable material for drifting snow simulation.
87
The foam bead (Extended Polystyrene) has low density (average bulk density of 50 kg/m3)
88
closer to freshly precipitated snow. The real snow has the limitation of its storage,
89
maintenance and its availability only during the winter season at some places. Some stimulant
90
materials used in the wind tunnel by the researchers are illustrated in Table-1.
91
Table -1
92
Materials used for modelling of snowdrift
93 Ser no
Material
1
Sand
2.
Bulk density (kgm-3)
Angle of repose (°)
1250-2000
34
Sawdust
290-400
43
3.
Rice bran
287
25
4.
Snow
18-420
35-80
5.
Clay soil Foam beads
650
40-45
50
38
6. 94
4
Researchers Xuanyi Zhou et al. [17], Florence Naaim-Bouvet and Mohamed Naaim [18] Naaim et al. [20], Xuanyi Zhou et al. [21] lsyumov, N. and Mikitiuk, M. [14] Andrew Clifton et al. [4], Hiroshi Sakamoto [7] Yutaka Anno [13] Authors of the present paper
95
Snow particles stick to other particles to form a bigger snow particle due to their
96
cohesiveness and sintering. The opposite electrostatic charges are generated among foam
97
beads due to abrasion and rubbing with each other. It was observed that two foam beads were
98
sticking with each other (two or more) sometimes. The availability of foam beads of small
99
size (1x10-3 m to 10x10-3 m) in large quantity and low density at economical rate has
100
motivated to carry out experiments with them for the simulation study of drifting snow in the
101
wind tunnel. Similarity criteria between snow and foam beads flow were established for snow
102
modelling (more discussed in the next section). They have one limitation that foam beads
103
eject less number of particles in compare to snow particles in the saltation layer. Instead of
104
its close density and characteristic with snow particle, the flow mechanism of foam beads and
105
its application in snowdrift modelling have not been studied previously. Hence a study was
106
made to simulate the snowdrift deposition pattern with foam beads.
107
3. Similarity of the foam beads flow and snowdrift
108
Wind tunnel test, due to its accessibility for easy control and systematic study, is regarded as
109
an important research method. Snowdrift wind tunnel simulation requires geometric,
110
kinematic and dynamic similarities to be established between model and prototype. The
111
study on physical modelling of snowdrift was carried out with foam beads in a closed re-
112
circulating wind tunnel. The similarities of particle density, the wind field and flow around
113
the snow fence (structure) had been observed. These similarities are the basic requirements in
114
wind tunnel experiments [17]. The similarity characteristics between snow (prototype) and
115
foam beads (model) are illustrated in Table-2.
116
5
117
Table 2
118
Similarity characteristics of prototype and model
Ser. No.
1.
Prototype
Model
(Snow)
(Foam bead)
(A) Particle Dia., D (x10-3 m)
0.15-2.0
1.5
(B) Particle Density, ρp (kg/m3)
50-700
100
(C) Bulk Density, ρ (kg/m3)
18-420
50
0.15-0.36
0.25
(A) Height, H(m)
4
0.08
(B) Porosity (%)
50
50
(C) Width, B (m)
4
0.08
Type
Similarity Parameter
Particles
(D) Threshold Shear Velocity, (m/s)
2.
Snow Fence
119 120
3.1 Geometrical Similarity
121
Geometrical similarity requires an equivalence of the ratio of the geometric dimension to
122
characteristic dimension between the model and prototype as mentioned in Eq. (1)
123
=
(1)
124
where l is the linear dimension, L is characteristic length and subscripts 'm' and 'p' refer to
125
model and prototype respectively. The geometrical similarity of the snow fence model and
126
prototype had been achieved. Spherical foam beads (model) were used for the experiments
127
whereas most of the snow particles (prototype) are found in the shape of a hexagonal prism.
128
This dissimilarity between foam beads and snow did not affect the results. The size and
129
density similarities between them facilitated the use of foam beads for simulation in the wind
130
tunnel. The geometrical similarity was established for the foam beads and snow particles with
131
the length scales close to 1:1. The deposition pattern in the wind tunnel was observed around 6
132
the scaled model (1:50) of the snow fence. The deposition pattern around the snow fence
133
depends on its height and porosity. The height and the extension of the deposition pattern due
134
to the snow fence were compared on a dimensionless scale by dividing them with the height
135
of the structure. Use of the dimensionless scale nullifies the effect of the scaling factor (1:50)
136
on the result of the deposition pattern due to the same porosity(50 %) of the prototype and
137
the model.
138
3.2 Similarity of the wind field
139
The similarity of the wind field around the model and prototype is required in physical
140
modelling. The foam beads begin to move after exceeding threshold wind speed. The
141
kinematic similarity parameter for wind velocity has been established with Eq. (2) given by
142
Y. Anno (1984) [22]
143
=
(2)
144
where is the wind speed at maximum structure height and is threshold shear velocity.
145
The surface roughness height is proportional to
146
particle flow depends on the Reynolds number in
147
148
field in the wind tunnel [23].
149
∗
. The surface-roughness height in the
form. It was reported that the value of
always satisfies Eq. (3) for the particle flow to ensure dynamic similarity of the flow
≥ 30
(3)
150
where is the acceleration of gravity and ν is the kinematic viscosity which is equal to 1.45 x
151
10-5 m2/s for air. The value of the Roughness-height Reynolds number for the foam bead flow
152
is 54 which satisfies the criteria of dynamic similarity of the flow field in the wind tunnel.
7
153
The aerodynamic roughness height under saltation conditions [24] could be expressed as Eq.
154
(4)
155
156
where ρ is the air density, which in the present study has been taken as 1.2 kg/m3. ρp is the
157
particle density and l is the characteristic length.
158
3.3 Similarity of movement of particles
159
The movement of particles is initiated by the wind force. Froude number, which is the ratio of
160
inertial force and gravitational force, has a significant role in particle transportation. The
161
similarity of movement of particles is achieved with Froude numbers of model and prototype
162
expressed by Eq. (5)
163
164
where is the threshold shear velocity, dp is the particle diameter and ρ is the air density.
165
Gravity force is important for the settlement of blowing snow and the trajectory of ejected
166
particles. For the saltation, the similarity of the trajectory of the particle is defined by the Eq.
167
(6)
168
169
where is the velocity at maximum structure height, l is the characteristic length and
170
other symbols are as mentioned above. Zhou [17] reported that the ratio of drag force to
171
inertial force should satisfy Eq. (7)
172
=
! "ρ #
"ρ
%$
=
(4)
! "ρ #
=
"ρ
%$=
(5)
(6)
(7)
8
173
where &' is the settling velocity of the particles.
174
3.4 Similarity of Deposition
175
The similarity of deposition depends on the size and shape of particles. The foam beads have
176
a uniform size of 1.5x 10-3 m. A higher degree of angle of repose is better for the similarity of
177
prototype and model. The similarity of deposition [21] is found with the help of the angle of
178
repose and it is given by Eq. (8)
179
(θ)m= ( p
(8)
180
where θ is the angle of repose in the still state of the particles. A similar angle of repose is
181
difficult to achieve when modelling particles are used in a snowdrift test [13]. This problem
182
did not occur in the simulation with foam beads. The foam beads bounce off if they are
183
dropped from a height and may give a different angle of deposition. The angle of repose for
184
foam beads is obtained by dropping foam beads on a circular disc gently and measuring the
185
angle of the conical shape of their deposition. The average angle of repose for foam beads is
186
38° which lies in the range of angle of repose of snow 35° to 80° [2,25]. It provided the
187
advantage over the simulant materials used by previous researchers. The physical
188
characteristics of the snowdrift prototype had been taken from the literature [18,26] for the
189
modelling.
190 191
The similarity parameters of prototype snowdrift and model foam bead flow were analyzed and have been illustrated in Table-3.
192
9
193
Table-3
194
Similarity parameters of snowdrift (prototype) and foam bead flow (model) in the wind tunnel
Description
Similarity of the wind field Similarity of the ejection process
Similarity of particle trajectory
Similarity of Deposition
Physical Meaning
Similarity parameters
Snowdrift (Prototype)
)U∗ ) +
Foam Bead flow (Model)
1.34e-6 – 1.873e-5
9.56e-4
-
54
0.004-2.166
0.05
29.94-71.867
36.4
10.78
9.1
)1
3.034
106.79
&'
&'
0.2-0.5
0.4
0.018-0.046
0.044
θ
35-80
38
Aerodynamic roughness height of saltating particles ,
Roughness-height Reynolds number
0 ≥ 30 2 /
) )1 − ρ 3
Froude number of particle trajectory in the ejection process Similarity parameter of wind velocity Velocity at maximum structure height (m/s) Froude Number of particle trajectory in the saltation process Settling velocity of the particles (m/s) Ratio of drag force and inertial force
)1 − ρ +
Angle of Repose (°)
195 196
A snow particle ejects more snow particles from the surface after impacting it in the
197
saltation process. This process of particles ejection by the impact of other particles is rare in
198
saltation of foam beads. The strong separation of their flow is also observed. This results in a
199
larger value of the roughness height of foam beads
200
The settling velocity &' for snow varies from 0.2 m/s to 0.5 m/s considering the
201
heterogeneity of the snow particles [27]. The ratio of drag force and inertial force
202
snow ranges from 0.018 to 0.046 for the above range of settling velocity of snow. Thus, the
203
settling velocity (0.4 m/s) and the value of
4%
10
∗
as compared to the snow particles.
4%
for
(0.044) for foam beads lies well within the
204
range for snow particles. Y. Anno (1984) pointed out that Froude Number had a minimal
205
influence on the final pattern of redistribution of snow [22] and so the similarity parameter of
206
5 " 6
207
and the model are well established for the experiments with the foam beads in the wind
208
tunnel.
209
4. Experimental setup and methodology
210
A closed re-circulating wind tunnel 4m in length was designed and built in-house to carry out
211
the experiments for the modelling of a snowdrift with foam beads. The acrylic transparent
212
circular tube (diameter 0.2 m and thickness 0.005 m) which enables the visual observation of
213
drifting activities was used in the fabrication of the wind tunnel. The whole setup was divided
214
into three sections namely horizontal, inclined and vertical (Fig. 1) resembling different
215
terrain slopes for the experimental simulations. The horizontal section had the main test space
216
for simulation study of deposition pattern and observation of foam beads transportation under
217
the wind force. Foam beads having the spherical shape of average diameter 0.0015 m and
218
average bulk density of 50 kg/m3 had been used as simulants in the wind tunnel. An exhaust
219
fan (blade diameter 0.6 m and 1400 rpm) was fitted coaxially with the horizontal section to
220
produce the wind speed up to 14 m/s for the movement of foam beads in the wind tunnel. Anemometer
221 222 223
Mass Flux Instrument
Horizontal section
Duct for feeding foam beads
224
Vertical section
225
Data logger and processor
226
for foam beads could be relaxed. Thus, the similarity relations between the prototype
Exhaust fan
Inclined section
227 228
Fig. 1. A closed re-circulating wind tunnel
11
229 230
Fig. 2. Two-dimensional drawing of the wind tunnel system and exhaust fan location
231
The optical sensors, exhaust fan and flow rate controller are placed in the horizontal section
232
(Fig. 2). This section had provision to fix the fence model in the flow path and to monitor the
233
flow pattern around the model through the transparent wall. A scaled model of snow fence
234
(1:50) with the thickness of 1.5x10-3 m and 50 % porosity was used to simulate the storage
235
capacity of the snow fence (Fig. 3).
236
The flow of foam beads was caused by the wind force in the wind tunnel. The foam
237
beads creep over the layer of particle surface and suspend in the air under higher wind speed
238
of more than 6 m/s. The forces acting on a snow particle are (1) weight W; (2) aerodynamic
239
drag FD; (3) aerodynamic lift FL; (4) magnus lift FM; (5) electrical force FE [28] (Fig. 4).
240 241 Snow Fence Model 242 243 244
Fixture for the model
245 246 247
Fig. 3. Fitting of Snow Fence Model in the Wind Tunnel
12
248 249
Fig. 4. Schematic presentation of forces acting on suspended foam bead (weight W; aerodynamic drag
250
FD; aerodynamic lift FL; magnus lift FM; electrical force FE)
251
Similar forces act on the suspended foam beads and on the snow particles. The inclined
252
section had provision to change the slope of the surface for the experiments by changing the
253
height of the coaxial vertical section. The foam beads were flown upward due to wind force
254
in the vertical section. When wind force on a foam bead exceeds the sum of gravity and drag
255
force, it suspends inside the vertical section. The magnitude of static charge on the foam bead
256
is in the order of 23.87µCkg-1 which is in the range of the electrostatic charge +72µCkg-1 to
257
-208 µCkg-1 on the snow particle [29]. The electrostatic and magnus forces acting on the
258
foam beads were found to be in the range of 2x10-6 N to 5.6 x10-6 N which are negligible in
259
comparison to the wind force (0.03N) and so these forces were not taken into consideration in
260
this paper.
261
The wind tunnel was instrumented with a wind sensor and a mass flow rate sensor
262
along with a data logger. The data logger was provided with a wireless communication
263
system to transfer the raw data to a receiver which could be attached to a personal computer
264
(PC) up to a distance of 500 m. The observed data were analyzed with the help of the
265
LabVIEW programmable software to obtain mass flux variation with time and velocity. The
13
266
complete wind tunnel setup was fitted on a wooden platform, which had three supports for its
267
stability and smooth functioning during the experiments.
268
4.1 Measurement of wind speed
269
A hot-wire anemometer (Testo model no 435-4) had been used to measure the wind velocity
270
in the wind tunnel. The anemometer has wind velocity measuring range from 0 to 20 m/s
271
with an accuracy of ±0.03 m/s. It was placed near the starting point of the horizontal section.
272
The electronic regulator attached with an exhaust fan controls the wind speed in the wind
273
tunnel. The maximum wind speed achieved with the exhaust fan fitted at the end of the
274
horizontal section was 14 m/s which lies within the measuring range of the anemometer. The
275
cross-sectional area of the experimental space was the same and symmetrical which helped to
276
measure the wind speed in the closed wind tunnel with an anemometer conveniently.
277
Initially, the wind profiles were measured without the foam beads in the wind tunnel.
278
The wind velocity was measured at every 0.01m height from the surface of the wall to the
279
centerline of the wind tunnel (Fig. 5). It provided the wind profile in the wind tunnel and the
280
wind profile was compared with the field data.
281 282 283
Fig. 5. Schematic diagram of the wind tunnel wall and positions of the anemometer
284
14
285
4.2 Measurement of mass flux
286
A new mass flux measuring instrument based on the principle of opacity technique was
287
introduced in the middle part of the horizontal section in the wind tunnel. The instrument was
288
developed on the basis of the cotton mass flow measurement technique [30]. The
289
transportation of foam beads occurs due to the wind force produced by the exhaust fan. The
290
foam beads were made to pass through the sensing device installed in two rows. A sheet of
291
Infrared rays (IR) was used to illuminate the flow of particles passing through the measuring
292
space. The data loggers were programmed to provide the mass flow rate according to light
293
attenuation due to foam beads. The transmitted light flux was sensed by an array of optical
294
sensors. The IR radiation reaching the optical sensor was attenuated by the passage of the
295
particles in its path. The instrument measures denseness of optical obstruction.
296
The denseness was proportional to the area occupied by particles in the flow path.
297
When there was high particle density, the lesser light passed through it. The measurement of
298
particle flow was proportional to total area obstructed by all the particles in the optical path.
299
The measurement was sampled at a high frequency (1000 Hz). The measurement was
300
essentially the optical intensity measurement in an analogue form that was integrated with
301
respect to time. The data were processed to get the mass flow rate in the wind tunnel with
302
respect to the wind speed.
303
4.3 Field experimental setup
304
There is a permanent observatory for the collection of metrological data at Banihal Top,
305
Jammu and Kashmir (J & K), India. For the study of snowdrift and performance of snow
306
fence, a FlowCapt along with Automatic Weather Station (AWS) and snow fences (height 3.5
307
m and 4.0 m) had been installed at the experimental site. The wind speed is measured with a
308
15
AWS
FlowCapt
309 310
Fig. 6. FlowCapt and AWS installed at the snowfield observatory
311
propeller based wind anemometer (Young Model 05103 wind monitor) attached to AWS
312
(Fig. 6). The deposition pattern around the snow fence was measured with the help of
313
avalanche probing rods, measuring tapes, snow mast and scales at the experimental site [31].
314
A FlowCapt is an automatic acoustic-based instrument for snow flux rate measurement in the
315
snowfield area. It is used for snowdrift assessment and research work [1,32–34]. The snow
316
mass flux rate was measured at the experimental site to compare with the wind tunnel
317
experiment.
318
5. Results and discussion
319
The experimental site observes high snowdrift activities as the average wind velocity in a
320
month is near to the threshold velocity of the snow. The data of the wind speed, mass flux
321
and particles deposition pattern were collected at the field observatory. Similar data were also
322
found during the experiments in the wind tunnel for the comparison and snowdrift modelling.
323
The turbulent wind flow pattern in the wind tunnel was also consistent with the field flow.
16
324
5.1 Metrological observations and wind speeds
325
The maximum snow precipitation occurs in the winter season between December and March
326
at the field experimental site. The maximum wind speed up to 39 m/s has been observed at
327
the experimental site (Banihal Top, Jammu and Kashmir, India). The prevalent direction of
328
the wind is southwest (SW) at the site during the snowstorm and it helps to get the orientation
329
of the snow fence. The summary of temperature, wind speed and standing snow from
330
December 2010 to March 2016 observed at the experimental site are illustrated in Table- 4.
331
Table 4
332
Summary of the metrological data observed at Banihal top, Jammu and Kashmir, India Average Min Temp (°°C) -3.7 -7.8 -5 -1.6 -4.5 -8.9 -5.6 -1.9 -4.5 -6.9 -3.9 0.2
Average Dry Bulb Temp (°°C) -0.7 -6.5 -3.7 0.9 -2.7 -7.3 -4.2 -0.1 -3.4 -6.1 -3 1.4
Average Standing Snow (x10-2 m) 58.5 89.7 173.1 123 15.7 128.8 298.1 197.7 59.9 100 132.2 77.4
Average Wind Speed (m/s) 2.39 4.42 6.14 7.39 6.42 5.19 5.78 6.86 7.81 8.19 5.83 7.22
Maximum Wind Speed (m/s) 10.1 12.8 13.9 15.2 9.6 12.9 11.1 12.0 16.4 15.8 13.4 16.2
Prevalent Direction of the Wind
Dec 2010 Jan 2011 Feb 2011 Mar 2011 Dec 2011 Jan 2012 Feb 2012 Mar 2012 Dec 2012 Jan 2013 Feb 2013 Mar 2013
Lowest Min Temp (°°C) -7.0 -11.0 -8.0 -5.5 -8.0 -14.0 -8.0 -8.0 -7.5 -11.0 -7.0 -5.0
Dec 2013 Jan 2014 Feb 2014 Mar 2014 Dec 2014 Jan 2015 Feb 2015 Mar 2015
-8.5 -10.5 -9.0 -5.5 -6.5 -10.0 -8.5 -7.5
-3.7 -7.7 -5.5 -3.1 -3.4 -5.2 -4.4 -2.7
-1.9 -6.2 -4.5 -1.8 0 -3.5 -2.5 -0.5
39.1 128 204 238 0 25.9 121 253.2
5.39 6.58 5.78 6.83 5.47 6.14 5.94 6.00
13.6 11.1 14.7 13.1 11.2 10.7 11.1 11.8
NE S SW SW NE NE SW S
Dec 2015 Jan 2016 Feb 2016 Mar 2016
-10.0 -8.5 -8.5 -5.5
-4.7 -4.9 -3 -0.5
-2.9 -3 -1.2 1.4
30.7 12.7 38 29
6.22 6.39 5.50 4.92
11.3 11.7 12.9 10.3
ENE E E SW
Month-Year
17
NE NE SW SW NE S SW SW NE S SW NE
333
The wind velocities along the flow direction were measured between the surface and the
334
centre of the tunnel without the foam beads in the tunnel. The threshold velocity of foam
335
beads was found by observing the movement of a foam bead under a gradual increase in wind
336
speed. Its value was 4.05 m/s which lies in the range of threshold wind speed of dry snow
337
particles 4-11 m/s [35]. In the case of the inclined surface (30º), the threshold velocity of
338
foam beads was 2.7 m/s due to their granularity and the action of gravitational force on them.
339
5.2 Turbulence characteristics
340
The atmospheric boundary layer condition of turbulent flow is defined by the logarithmic
341
wind profile. The logarithmic wind profile at the height z is given by Eq (9) [4] 7 =
342
∗ 8
;
ln ;
(9)
<
343
where ∗ is the shear velocity, = = 0.41 is called the Von Karman Constant and z0 is the
344
roughness height. The value of z0 depends on the geometry of the snow surface. In the
345
present paper, the value of z0 is 0.0015 m which lies in the range of its value (0.0001 m to
346
0.005m) [4,36,37]. The value of ∗ for the field is 0.56 m/s. It was found that the wind
347
velocity pattern in the wind tunnel closely followed the wind velocity pattern of the
348
atmospheric boundary layer in the field (Fig.7). 1.4 Field
Height (h/H)
1.2 Wind tunnel
1 0.8 0.6 0.4 0.2 0 0.1
349 350
1 Wind velocity (U/U(H))
Fig. 7. Variation of dimensionless wind velocity with the dimensionless height
18
10
351
The turbulent kinetic energy (TKE) in the turbulence flow is defined by the half the sum of
352
the square of standard deviations of the velocity components (Eq. 10).
353 354
B EEEEEEE D A = C (10) D EEE . Where C = C − CE is the difference between local velocity( C ) and the mean velocity C
A 7 at height z
355
The turbulent kinetic energy
356
modelled as Eq (11) [38]
357 358
A 7 = FGB +H 7 + 7J + G (11) where the constants cB = −0.6035 and c = 1.7934 for shear velocity U∗ = 0.511 m/s for
359
for the atmospheric boundary layer is
the atmospheric boundary layer. Zhou et. al. (2016) [21] considered the value of cB =
360
−0.064 and c = 0.588 for U∗ = 0.35 m/s for the wind tunnel. The values of U∗ for the field
361
and the wind tunnel are 0.56 m/s and 0.35 m/s respectively in the present paper. The
362
constants of the turbulent kinetic energy are found statistically and so same values of
363
constants were used in the present paper due to relatively close values of U∗ for the field and
364
the wind tunnel. The relation between the dimensionless turbulent kinetic energy (A/A and
365
dimensionless height is depicted in Fig 8. It is found that the turbulent kinetic energy (A/A
366
for the field and the wind tunnel at h/H greater than 0.75 are very close ( Fig.8). Wind Tunnel 1.4
Field
Height (h/H)
1.2 1 0.8 0.6 0.4 0.2 0 0.8
0.9
1
1.1
1.2
1.3
Turbulent Kinetic Energy (k/kH) 367 368
Fig. 8. Variation of dimensionless turbulent kinetic energy with the dimensionless height
19
Wind Tunnel 1.4
Field
Height (h/H)
1.2 1 0.8 0.6 0.4 0.2 0 6
8
10
12
14
16
Turbulent Intensity (%)
369 370
Fig. 9. Variation of turbulence intensity with the dimensionless height
371
The turbulent intensity is another characteristic of a turbulence flow. It is defined as is the
372
EEE . . ratio of the standard deviation of fluctuating wind velocity to the mean wind velocity C
373
The turbulent intensity R 7 at the height z is obtained with the wind velocity and turbulent
374
kinetic energy using Eq (12)
R 7 =
375
J.SB ;
FA 7
(12)
376
It was found that the turbulence intensities are 10.7% and 10.0 % at the height of AWS (h/H
377
= 0.75) and at h/H = 0.75 in the wind tunnel respectively (Fig. 9). Thus, the turbulence
378
characteristics for the field and the wind tunnel are consistent.
379
The wind profile at different locations 0.5 m, 1.5 m, 2.5 m and 3.5 m were observed
380
in the horizontal section of the empty wind tunnel (Fig. 10). It was found that the wind
381
velocity at the centre of the tunnel was increased with the distance from the inlet location and
382
the boundary layer depth were also increased. The velocity was increased by 0.06 m/s in 3m
383
distance and so the flow in the wind tunnel was considered uniform throughout the
384
experimental space.
20
Vertical height from wall (m)
0.12 0.50 m distance 0.1 1.50 m distance 0.08
2.50 m distance
0.06 0.04 0.02 0
385
0.1
1 Wind velocity (m/s)
10
386
Fig. 10. Wind flow profiles in the horizontal section of the wind tunnel
387
The characteristics of turbulence flow in the wind tunnel and at the field observatory were
388
found similar in nature from the above graphs. The wind profiles for both conditions (Fig. 7)
389
were matched except one data near the wall having more kinetic energy for the snow (Fig.8).
390
The turbulent intensities in both conditions are matched near the wall but deviations for wind
391
tunnel and field were increased up to 1.5 % with the height (Fig.9). Modelled turbulence
392
quantities show the same behaviour as the field data which is important to have the same flow
393
characteristics in the wind tunnel. Variation in the magnitude is well within the modelling
394
constraints (less than 1.5%) and this is quite low in comparison to the inherent variation that
395
the field data is subject to.
396
5.3 Mass flux of particles
397
The snow mass flux was measured with FlowCapt in the snowfield. A sample of mass flux
398
with wind speed is shown in Fig. 11. The drifting of snow was observed above the wind
399
speed of 7 m/s. The mass flux rate varies with the surface condition and the wind speed in the
400
field. The maximum snow flux rate of 31.2 x10-3 kgm-2s-1 is observed at 18 m/s wind speed
401
with the FlowCapt.
21
Average wind velocity
35
Mass Flux
30
20
25 15
20
10
15 10
5
5
0
0 0
402
Mass flux (kgm-2 s-1)x10-3
Average wind velocity (ms-1)
25
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
Time (hours)
403
Fig. 11. Snow mass flux measured with FlowCapt and average wind speed at the experimental site
404
The foam beads were placed in the wind tunnel through the duct provided in the horizontal
405
section. The foam beads were kept flat with the help of forced wind by running the fan and
406
switching it off before the initiation of the experiment. The wind speed in the tunnel was
407
increased slowly and gradually with the electronic regulator. The foam beads, initially, roll
408
over the surface like creeping of snow particles and later they suspend in the air under high
409
wind speed (more than 6 m/s). The wind velocity was measured at the centreline of the
410
cross-section of the tube by the anemometer. The mass flow rate of foam beads with respect
411
to wind speed was calibrated by measuring the known quantity of foam beads and the wind
412
velocity. The result has validated the concept of the mass flux proportionality with wind
413
speed for the design of the optical instrument.
414
The mass flux rate of snow particles and foam beads were observed with respect to
415
the wind velocity (Fig. 12). The mass fluxes of snow and foam beads were proportional to the
416
cubic of wind speed with a coefficient of determination (R2) in order of 0.9. It is in line with
417
the Bagnold’s observation for the mass flux rate of sand [39]. It was observed that the trend
418
line of mass flux rate of foam beads and that of snow are parallel for the low wind speed. 22
Snow
Mass flux (kgm-2 s-1)x 10-3
35
Foam Beads
30 25 20 15 10 5 0 0
5
10
15
20
25
Average wind velocity (ms-1) 419 420
Fig. 12. Mass flux variation with wind speed
421
The abrupt change in mass flux rate of snow results from the fact that the large-sized particles
422
are also drifted at the higher wind speed (more than 15 m/s).
423
5.4 Particles deposition pattern
424
At the initial stage of transportation, foam beads were passed through the bottom gap of the
425
model like creeping of snow. At higher wind speed aerodynamic entrainment occurred and
426
they left the surface to flow with the wind. The foam beads were obstructed by snow fence
427
model in their way and they deposited around the model of snow fence. Their deposition
428
pattern was measured by placing graph paper on the other side of the tunnel wall. The
429
experiments were also carried out with snow fence models of different heights (6 x10-2 m and
430
7x10-2 m) and porosities (0 and 25%). The blocking ratio of the model was found to be about
431
7.64% which is acceptable as per the literature [40]. The mass flux data for the field and the
432
wind tunnel were more similar and proportional at the wind speed of 10 m/s. The height of
433
the deposited foam beads was maximum at the wind speed of 8 m/s in the wind tunnel.
434
Hence, these two wind speeds have been considered for the validation of results.
23
435
The observations of snow deposition pattern on the leeward side of snow fences
436
(height 4 m and 3.5 m with porosity 50 %) in the field were taken for model validation in the
437
wind tunnel. The non-dimensional deposition patterns of snow and foam beads are found by
438
dividing the deposition height by the height of the structure (H) (Fig. 13). The deposition
439
pattern around the model changed at different wind speeds due to obstruction and vortices
440
generated on the leeward side due to the presence of the model. With the increase of wind
441
speed, the clearance gap and the distance from the structure to the maximum height was
442
increased. However, there was a reduction of the deposition height in the wind tunnel.
443
The similarity between the deposition patterns of foam beads in the wind tunnel and
444
snow in the field was observed through the experiments. The storage capacity of the snow
445
fence model was lower at a higher wind speed of 10 m/s. The nature of the deposition pattern
446
of foam beads at lower wind speed was much closer to that of snow around snow fence in
Deposition height / H
1.2 1 0.8 0.6 0.4 0.2 0 0
5
10
15
Distance from structure / H Foam beads deposition around model in the wind tunnel at 8 m/s Foam beads deposition around model in the wind tunnel at 10 m/s Snow deposition around snow fence height 3.5 m in the field Snow deposition around snow fence height 4.0 m in the field
447 448
Fig. 13. Deposition pattern of foam beads and snow around the model and the snow fence
24
20
Snow Fence
Snow Rime
Snow Deposition
449 450
Fig. 14. Snow riming on snow fence at the experimental site
451
the field. The height and position of the nose of the deposition pattern for the foam beads
452
were reduced and shifted to the leeward side respectively. The snow deposition pattern
453
around snow fence of the height 4m was found comparatively higher than that for the model
454
and snow fence of height 3.5m. Due to the snow riming (Fig. 14), the porosity of the snow
455
fence of height 4m at the experimental site was reduced and it contributed for getting more
456
snow on the leeward side of the snow fence. The snow deposition pattern in the field depends
457
on the weather condition and snow fence characteristics along with snow riming over them.
458
6. Conclusion
459
The modelling of drifting snow has been attempted using the numerical method and
460
experimental technique in the wind tunnel to solve the problems of snow cornice formation,
461
blockage of highways due to snowdrift and avalanche hazards. Authors used the foam beads
462
(Expanded Polystyrene) as a simulant material in the re-circulating closed wind tunnel for the
463
snowdrift modelling as it has low density (50 kgm-3) like freshly precipitated snow and is
464
economically available. Geometric, kinematic and dynamic similarity parameters for the
465
particles and wind field were determined to carry out wind tunnel experiments with foam
466
beads. Turbulent kinetic energy and turbulence intensity measured at AWS height resembled
467
the values at the corresponding height by similitude inside the test section. Further, the mass 25
468
flow rate of foam beads was measured with a newly developed optical-based instrument in
469
the horizontal section of the wind tunnel to establish its relation with the wind speed. It was
470
found that the mass flow rate of foam beads and snow were proportional to the cubic of wind
471
speeds. The deposition pattern of foam beads around the model structure (1:50) at the wind
472
speeds 8 m/s and 10 m/s were validated with the snow deposition around the snow fence in
473
the field. The facility may be further utilized for investigation of other light materials for
474
aeolian phenomena and to improve the performance of a snow fence.
475
Acknowledgements
476
Authors are grateful to the Director, Snow and Avalanche Study Establishment (SASE),
477
Defence Research and Development Organization, India for his support and providing the
478
facility for this paper. The construction of the wind tunnel was funded by SASE under the
479
built-up project. Authors also want to acknowledge scientists and all other technical persons
480
involved in wind sensors installation and collection of the wind data at the experimental site
481
Banihal Top, Jammu and Kashmir, India.
482
References
483
[1]
484
M. Lehning, C. Fierz, Assessment of snow transport in avalanche terrain, Cold Reg. Sci. Technol. 51 (2008) 240–252. doi:10.1016/j.coldregions.2007.05.012.
485
[2]
S.M. David Peter, Avalanche handbook, 1977. doi:10.1016/0148-9062(77)90015-8.
486
[3]
S.J. Lee, K.C. Park, C.W. Park, Wind tunnel observations about the shelter effect of
487
porous fences on the sand particle movements, Atmos. Environ. 36 (2002) 1453–1463.
488
doi:10.1016/S1352-2310(01)00578-7.
489
[4]
A. Clifton, J.D. Rüedi, M. Lehning, Snow saltation threshold measurements in a
490
drifting-snow wind tunnel, J. Glaciol. 52 (2006) 585–596.
491
doi:10.3189/172756506781828430.
492
[5]
F. Naaim-Bouvet, M. Naaim, J.L. Michaux, Snow fences on slopes at high wind speed: 26
493
Physical modelling in the CSTB cold wind tunnel, Nat. Hazards Earth Syst. Sci. 2
494
(2002) 137–145. doi:10.5194/nhess-2-137-2002.
495
[6]
M. Liu, Q. Zhang, F. Fan, S. Shen, Experiments on natural snow distribution around
496
simplified building models based on open-air snow-wind combined experimental
497
facility, J. Wind Eng. Ind. Aerodyn. 173 (2018) 1–13.
498
doi:10.1016/j.jweia.2017.12.010.
499
[7]
H. Sakamoto, M. Moriya, K. Takai, Y. Obata, Development of a New Type Snow
500
Fence with Airfoil Snow Plates to Prevent Blowing-Snow Disasters : Part 1 ,
501
Evaluation of Performance by Blowing-Snow Simulation in a Wind Tunnel, J. Nat.
502
Disaster Sci. 23 (2001) 1–11.
503
[8]
M. Guala, C. Manes, A. Clifton, M. Lehning, On the saltation of fresh snow in a wind
504
tunnel: Profile characterization and single particle statistics, J. Geophys. Res. Earth
505
Surf. 113 (2008) 1–13. doi:10.1029/2007JF000975.
506
[9]
S. Alhajraf, Computational fluid dynamic modeling of drifting particles at porous
507
fences, Environ. Model. Softw. 19 (2004) 163–170. doi:10.1016/S1364-
508
8152(03)00118-X.
509
[10] Y. Durand, G. Guyomarc’h, L. Mérindol, J.G. Corripio, Improvement of a numerical
510
snow drift model and field validation, Cold Reg. Sci. Technol. 43 (2005) 93–103.
511
doi:10.1016/j.coldregions.2005.05.008.
512 513 514
[11] P. Gauer, Numerical modeling of blowing and drifting snow in Alpine terrain, J. Glaciol. 47 (2001) 97–110. doi:10.3189/172756501781832476. [12] Y. Tominaga, Computational fluid dynamics simulation of snowdrift around
515
buildings : Past achievements and future perspectives, Cold Reg. Sci. Technol. (2017)
516
0–1. doi:10.1016/j.coldregions.2017.05.004.
517
[13] Y. Anno, Modelling a snowdrift by means of activated clay particles, Ann. Glaciol. 6
27
518 519 520 521 522 523
(1985) 48–52. [14] N. Isyumov, M. Mikitiuk, Wind Tunnel Model Tests of Snow Drifting on a Two-Level Flat Roof, J. Wind Eng. Ind. Aerodyn. 36 (1990) 893–904. [15] R.J. Kind, Mechanics of Aeolian Transport of Snow and Sand, J. o[ Wind Eng. Ind. Aerodyn. 36 (1990) 855–866. [16] A. Flaga, G. Kimbar, P. Matys, A new approach to wind tunnel similarity criteria for
524
snow load prediction with an exemplary application of football stadium roof, 5th Eur.
525
African Conf. Wind Eng. EACWE 5, Proc. (2009).
526
[17] X. Zhou, J. Hu, M. Gu, Wind tunnel test of snow loads on a stepped flat roof using
527
different granular materials, (2014) 1629–1648. doi:10.1007/s11069-014-1296-z.
528
[18] F. Naaim-Bouvet, M. Naaim, Snowdrift modelling in a wind tunnel: vertical and
529 530 531 532 533 534
horizontal variation of the snow flux, Ann. Glaciol. 26 (1998) 212–216. [19] F. Naaim-Bouvet, M. Naaim, Snowdrift modeling in a wind-tunnel: vertical and horizontal variation of the snow flux, Ann. Glaciol. 26 (1998) 212–216. [20] M. Naaim, F. Naaim-Bouvet, H. Martinez, Numerical simulation of drifting snow: erosion and deposition models, Ann. Glaciol. 26 (1998) 191–196. [21] X. Zhou, S. Qiang, Y. Peng, M. Gu, Wind tunnel test on responses of a lightweight
535
roof structure under joint action of wind and snow loads, Cold Reg. Sci. Technol. 132
536
(2016) 19–32. doi:10.1016/j.coldregions.2016.09.011.
537 538 539 540
[22] Y. Anno, Requirements for modeling of a snowdrift, Cold Reg. Sci. Technol. 8 (1984) 241–252. [23] F. Naaim-Bouvet, Comparison of Requirements for Modeling Snowdrift, Surv. Geophys. 16 (1995) 711–727.
541
[24] X. Zhou, L. Kang, M. Gu, L. Qiu, J. Hu, Numerical simulation and wind tunnel test for
542
redistribution of snow on a flat roof, Jnl. Wind Eng. Ind. Aerodyn. 153 (2016) 92–105.
28
543 544 545 546 547 548
doi:10.1016/j.jweia.2016.03.008. [25] O. Abe, Shear strength and angle of repose of snow layers including graupel, Ann. Glaciol. 38 (2004) 305–308. doi:10.3189/172756404781815149. [26] X. Zhou, G. Ming, Numerical Simulation of Snow Drift on the Surface of a large- span Roof Structure, Fourth Int. Symp. Comput. Wind Eng. (2006) 889–892. [27] X. Zhou, L. Kang, X. Yuan, M. Gu, Wind tunnel test of snow redistribution on flat
549
roofs, Cold Reg. Sci. Technol. 127 (2016) 49–56.
550
doi:10.1016/j.coldregions.2016.04.006.
551 552 553 554 555
[28] N. Huang, J. Zhang, Simulation of snow drift and the effects of snow particles on wind, Model. Simul. Eng. 2008 (2008) 1–6. doi:10.1155/2008/408075. [29] D.S. Schmidt, J.D. Dent, R.A. Schmidt, Charge-to-mass ratio of individual blowingsnow particles, Ann. Glaciol. 26 (1998) 207–211. [30] J.A. Thomasson, D.A. Pennington, H.C. Pringle, E.P. Columbus, S.J. Thomson, R.K.
556
Byler, Cotton mass flow measurement: experiments with two optical devices, Appl.
557
Eng. Agric. 15 (1999) 11–17.
558 559 560
[31] G. Kumar, Performance of snow fence at Banihal Top in Himalayan region, J. Cold Reg. Eng. 29 (2015). doi:10.1061/(ASCE)CR.1943-5495.0000088. [32] C. Amory, A. Trouvilliez, H. Gallée, V. Favier, F. Naaim-Bouvet, C. Genthon, C.
561
Agosta, L. Piard, H. Bellot, Comparison between observed and simulated aeolian snow
562
mass fluxes in Adélie Land, East Antarctica, Cryosphere. 9 (2015) 1373–1383.
563
doi:10.5194/tc-9-1373-2015.
564
[33] C. Jaedicke, Acoustic snowdrift measurements: Experiences from the FlowCapt
565
instrument, Cold Reg. Sci. Technol. 32 (2001) 71–81. doi:10.1016/S0165-
566
232X(01)00017-9.
567
[34] A. Trouvilliez, F. Naaim-Bouvet, C. Genthon, L. Piard, V. Favier, H. Bellot, C.
29
568
Agosta, C. Palerme, C. Amory, H. Gallée, A novel experimental study of aeolian snow
569
transport in Adelie Land (Antarctica), Cold Reg. Sci. Technol. 108 (2014) 125–138.
570
doi:10.1016/j.coldregions.2014.09.005.
571
[35] L. Li, J.W. Pomeroy, S. Canada, S. Canada, Estimates of Threshold Wind Speeds for
572
Snow Transport Using Meteorological Data, J. Appl. Meteorol. 36 (1997) 205–213.
573
doi:10.1175/1520-0450(1997)036<0205:EOTWSF>2.0.CO;2.
574
[36] M. Lehning, F. Naaim, M. Naaim, B. Brabec, J. Doorschot, Y. Durand, G.
575
Guyomarc’H, J.L. Michaux, M. Zimmerli, Snow drift: Acoustic sensors for avalanche
576
warning and research, Nat. Hazards Earth Syst. Sci. 2 (2002) 121–128.
577
doi:10.5194/nhess-2-121-2002.
578
[37] J.D. Holmes, Wind Loading of Structures, Second, Taylor and Francis, London, 2007.
579
[38] Y. Yang, M. Gu, S. Chen, X. Jin, New inflow boundary conditions for modelling the
580
neutral equilibrium atmospheric boundary layer in computational wind engineering, J.
581
Wind Eng. Ind. Aerodyn. 97 (2009) 88–95. doi:10.1016/j.jweia.2008.12.001.
582 583 584 585
[39] R.A. Bagnold, The Physics of Blown Sand and Desert Dunes, London : Chapman and Hall, 1941. [40] C.K. Choi, D.K. Kwon, Wind tunnel blockage effects on aerodynamic behavior of bluff body, Wind Struct. An Int. J. 1 (1998) 351–364. doi:10.12989/was.1998.1.4.351.
586
30
Highlights of the Research Paper (1) Foam beads (Expanded Polystyrene) as simulant material for snowdrift particles (2) Similarity relations between model and prototype for modelling (3) A technique to measure the flow rate of foam beads with optical sensors (4) Measurement of flow and threshold velocity of foam beads (5) Modelling of deposition pattern of snow around the snow fence
S0955-5986(19)30341-3
DOI:
https://doi.org/10.1016/j.flowmeasinst.2019.101687
Reference:
JFMI 101687
To appear in:
Flow Measurement and Instrumentation
Received Date: 26 August 2019 Revised Date:
25 October 2019
Accepted Date: 29 December 2019
Please cite this article as: G. Kumar, A. Gairola, A. Vaid, Flow and deposition measurement of foam beads in a closed re-circulating wind tunnel for snowdrift modelling, Flow Measurement and Instrumentation (2020), doi: https://doi.org/10.1016/j.flowmeasinst.2019.101687. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
1
Flow and deposition measurement of foam beads in a closed re-circulating
2
wind tunnel for snowdrift modelling Ganesh Kumara*, Ajay Gairolab, Aditya Vaida
3 a
Snow and Avalanche Study Establishment, Defence Research and Development Organization, Himparisar, Plot no-01, Sector-37A, Chandigarh, PIN-160036, India b Indian Institute of Technology (IIT), Roorkee, Uttarakhand, PIN-247667, India
4 5 6 7 8
ABSTRACT
9
A facility was created for flow and deposition measurement of foam beads (Expanded
10
Polystyrene) in a closed re-circulating wind tunnel to model the snowdrift experimentally.
11
The geometrical and flow similarities between the model (foam beads) and prototype
12
(snow) particles were established for the wind tunnel experiments. The wind tunnel was
13
instrumented with the electronic regulator, anemometer and newly developed flux
14
measuring sensors along with a data logger to carry out the experiments for different
15
simulated terrain conditions. An array of optical sensors for measurement of foam beads
16
flux was calibrated with the known quantity of the material and used to find the flux
17
variation with wind speed inside the tunnel. All three modes of drifting transportation
18
namely creeping, saltation and suspension could be observed through the transparent
19
acrylic wall for data collection. The threshold velocity of foam bead movement was 4.05
20
m/s in the horizontal section and same was 2.7 m/s in the inclined section at an angle of
21
30° downward (a critical angle of avalanche starting zone). The process of snow
22
deposition by the snow fence was simulated with the foam beads deposition around the
23
scaled model (1:50) of a snow fence in the wind tunnel. The experiments helped to find a
24
flow measuring technique for light drifting material like foam beads and the modelling of
25
drifting snow.
26
Keywords: Similarity; Snowdrift; Wind tunnel; Modelling; Foam beads.
27
*
Corresponding Author Email: [email protected] 1
28
1. Introduction
29
The naturally precipitated snow is redistributed by the wind causing the problems like
30
blockage of highway, invisibility and avalanche occurrence in the snowbound area [1]. When
31
the wind speed exceeds its threshold shear velocity, snow particles eject from the snow
32
surface. Snow is mainly transported by three modes namely creeping, saltation and
33
suspension [2]. In the creeping process, the snow particles move on the snow surface. After
34
gaining the energy from wind, the snow particles are energized and subsequently influence
35
other particles to move in the saltation stage. The extra drag on the particles changes their
36
trajectories significantly and they erode more particles from the snow surface. At the last
37
mode of transportation, particles are suspended in air and at this stage, snow particles are
38
transported to a larger distance.
39
The tedious and time-consuming study of a snowdrift in the real scenario is simplified
40
by using wind tunnel experiments and numerical modelling techniques. The experiments had
41
been carried out with natural snow and its simulated materials in the wind tunnel. Lee et al.
42
[3] and Clifton et al. [4] had used the natural snow for their wind tunnel experiments. Other
43
researchers [5–8] had also used real snow for modelling of the snowdrift in the wind tunnel.
44
Alhajraf [9], Durand et al.[10] and Gauer [11] had applied numerical modelling methods for
45
snowdrift simulation. Tominaga [12] showed the potential of Computational Fluid Dynamics
46
(CFD) technique in the modelling of the snowdrift. Most of the researchers working in the
47
snowdrift area had used scaled models and particles of different materials like sand, clay and
48
sawdust. Y. Anno used activated clay particles as a substitute for natural snow in the wind
49
tunnel experiments and found the effects of snow fence geometry on the snowdrift [13]. He
50
found the two-dimensional distribution of clay particles using image processing and
51
introduced simulation of the drift geometry of snow. Isyumov and Mikitiuk employed bran as
52
simulant material in the wind tunnel tests to simulate the snowdrift formation on the lower 2
53
level of a two-level roof at different wind velocities [14]. Kind carried out experiments on
54
wind tunnel with sand and snow to simulate the transport mechanics [15]. Flaga et al. had
55
used grinded Styrofoam to model deposition pattern and drifted snow load over the structures
56
in the wind tunnel [16]. Zhou et al. simulated the redistribution of snow loads on a stepped
57
flat roof in a wind tunnel test using particles like saw wood ash, medium-density polyfoam
58
and silica sand [17]. The wind tunnel tests using these different kinds of particles were
59
performed with nearly identical dimensionless wind velocity and dimensionless time to
60
ensure comparability of test results. The snow threshold velocity in the wind tunnel was
61
measured by Clifton et al. and they found that the threshold shear velocity depends on snow
62
density and particle size [4].
63
Wind tunnel experiments have been carried out by scientists recently for the
64
experimental simulations of blowing and drifting snow. They have tested the snow fence
65
model in the wind tunnel to improve its performance for controlling the drifting snow.
66
Naaim-Bouvet carried out extensive wind tunnel experiments using the image-processing
67
technique to determine the total transport rate [19]. These measurements are being used for
68
development and testing of numerical snowdrift model. Almost all the results of the wind
69
tunnel are based on a rectangular or square section of the wind tunnel. Hence, an attempt was
70
made to design a closed re-circulating wind tunnel (4 m length, 0.2 m diameter and 1.74 m
71
height) with experimental space of 2 m length for carrying out experiments with low-density
72
material like foam beads in the laboratory. It has the advantage of using the same material for
73
the repeatability of the experiment. The acrylic transparent wall of the wind tunnel facilitates
74
visual observation and sufficient strength to the structure. This facility has helped to
75
investigate a light material like foam bead for snowdrift modelling. The deposition pattern of
76
foam beads around a scaled model of snow fence has been observed in the wind tunnel. The
3
77
results of wind tunnel have been compared with the observations made at Banihal Top
78
(Jammu and Kashmir, India) which experiences high snowdrift activities.
79
2. Foam beads and other materials used for the snowdrift modelling
80
The numerical method is going to be popular with the increase of computational capability of
81
the computer. However, it requires high skill and its validation requires the results of wind
82
tunnel experiments and field experimental data. It is also difficult and tedious task to work
83
with snowdrift experimentally in the snowfield. The researchers have worked with sand, clay
84
soil, sawdust and bran to simulate the snowdrift in the wind tunnel. These materials have
85
comparatively high densities and they require high wind speed for their transportation in the
86
wind tunnel. Authors were looking for a more suitable material for drifting snow simulation.
87
The foam bead (Extended Polystyrene) has low density (average bulk density of 50 kg/m3)
88
closer to freshly precipitated snow. The real snow has the limitation of its storage,
89
maintenance and its availability only during the winter season at some places. Some stimulant
90
materials used in the wind tunnel by the researchers are illustrated in Table-1.
91
Table -1
92
Materials used for modelling of snowdrift
93 Ser no
Material
1
Sand
2.
Bulk density (kgm-3)
Angle of repose (°)
1250-2000
34
Sawdust
290-400
43
3.
Rice bran
287
25
4.
Snow
18-420
35-80
5.
Clay soil Foam beads
650
40-45
50
38
6. 94
4
Researchers Xuanyi Zhou et al. [17], Florence Naaim-Bouvet and Mohamed Naaim [18] Naaim et al. [20], Xuanyi Zhou et al. [21] lsyumov, N. and Mikitiuk, M. [14] Andrew Clifton et al. [4], Hiroshi Sakamoto [7] Yutaka Anno [13] Authors of the present paper
95
Snow particles stick to other particles to form a bigger snow particle due to their
96
cohesiveness and sintering. The opposite electrostatic charges are generated among foam
97
beads due to abrasion and rubbing with each other. It was observed that two foam beads were
98
sticking with each other (two or more) sometimes. The availability of foam beads of small
99
size (1x10-3 m to 10x10-3 m) in large quantity and low density at economical rate has
100
motivated to carry out experiments with them for the simulation study of drifting snow in the
101
wind tunnel. Similarity criteria between snow and foam beads flow were established for snow
102
modelling (more discussed in the next section). They have one limitation that foam beads
103
eject less number of particles in compare to snow particles in the saltation layer. Instead of
104
its close density and characteristic with snow particle, the flow mechanism of foam beads and
105
its application in snowdrift modelling have not been studied previously. Hence a study was
106
made to simulate the snowdrift deposition pattern with foam beads.
107
3. Similarity of the foam beads flow and snowdrift
108
Wind tunnel test, due to its accessibility for easy control and systematic study, is regarded as
109
an important research method. Snowdrift wind tunnel simulation requires geometric,
110
kinematic and dynamic similarities to be established between model and prototype. The
111
study on physical modelling of snowdrift was carried out with foam beads in a closed re-
112
circulating wind tunnel. The similarities of particle density, the wind field and flow around
113
the snow fence (structure) had been observed. These similarities are the basic requirements in
114
wind tunnel experiments [17]. The similarity characteristics between snow (prototype) and
115
foam beads (model) are illustrated in Table-2.
116
5
117
Table 2
118
Similarity characteristics of prototype and model
Ser. No.
1.
Prototype
Model
(Snow)
(Foam bead)
(A) Particle Dia., D (x10-3 m)
0.15-2.0
1.5
(B) Particle Density, ρp (kg/m3)
50-700
100
(C) Bulk Density, ρ (kg/m3)
18-420
50
0.15-0.36
0.25
(A) Height, H(m)
4
0.08
(B) Porosity (%)
50
50
(C) Width, B (m)
4
0.08
Type
Similarity Parameter
Particles
(D) Threshold Shear Velocity, (m/s)
2.
Snow Fence
119 120
3.1 Geometrical Similarity
121
Geometrical similarity requires an equivalence of the ratio of the geometric dimension to
122
characteristic dimension between the model and prototype as mentioned in Eq. (1)
123
=
(1)
124
where l is the linear dimension, L is characteristic length and subscripts 'm' and 'p' refer to
125
model and prototype respectively. The geometrical similarity of the snow fence model and
126
prototype had been achieved. Spherical foam beads (model) were used for the experiments
127
whereas most of the snow particles (prototype) are found in the shape of a hexagonal prism.
128
This dissimilarity between foam beads and snow did not affect the results. The size and
129
density similarities between them facilitated the use of foam beads for simulation in the wind
130
tunnel. The geometrical similarity was established for the foam beads and snow particles with
131
the length scales close to 1:1. The deposition pattern in the wind tunnel was observed around 6
132
the scaled model (1:50) of the snow fence. The deposition pattern around the snow fence
133
depends on its height and porosity. The height and the extension of the deposition pattern due
134
to the snow fence were compared on a dimensionless scale by dividing them with the height
135
of the structure. Use of the dimensionless scale nullifies the effect of the scaling factor (1:50)
136
on the result of the deposition pattern due to the same porosity(50 %) of the prototype and
137
the model.
138
3.2 Similarity of the wind field
139
The similarity of the wind field around the model and prototype is required in physical
140
modelling. The foam beads begin to move after exceeding threshold wind speed. The
141
kinematic similarity parameter for wind velocity has been established with Eq. (2) given by
142
Y. Anno (1984) [22]
143
=
(2)
144
where is the wind speed at maximum structure height and is threshold shear velocity.
145
The surface roughness height is proportional to
146
particle flow depends on the Reynolds number in
147
148
field in the wind tunnel [23].
149
∗
. The surface-roughness height in the
form. It was reported that the value of
always satisfies Eq. (3) for the particle flow to ensure dynamic similarity of the flow
≥ 30
(3)
150
where is the acceleration of gravity and ν is the kinematic viscosity which is equal to 1.45 x
151
10-5 m2/s for air. The value of the Roughness-height Reynolds number for the foam bead flow
152
is 54 which satisfies the criteria of dynamic similarity of the flow field in the wind tunnel.
7
153
The aerodynamic roughness height under saltation conditions [24] could be expressed as Eq.
154
(4)
155
156
where ρ is the air density, which in the present study has been taken as 1.2 kg/m3. ρp is the
157
particle density and l is the characteristic length.
158
3.3 Similarity of movement of particles
159
The movement of particles is initiated by the wind force. Froude number, which is the ratio of
160
inertial force and gravitational force, has a significant role in particle transportation. The
161
similarity of movement of particles is achieved with Froude numbers of model and prototype
162
expressed by Eq. (5)
163
164
where is the threshold shear velocity, dp is the particle diameter and ρ is the air density.
165
Gravity force is important for the settlement of blowing snow and the trajectory of ejected
166
particles. For the saltation, the similarity of the trajectory of the particle is defined by the Eq.
167
(6)
168
169
where is the velocity at maximum structure height, l is the characteristic length and
170
other symbols are as mentioned above. Zhou [17] reported that the ratio of drag force to
171
inertial force should satisfy Eq. (7)
172
=
! "ρ #
"ρ
%$
=
(4)
! "ρ #
=
"ρ
%$=
(5)
(6)
(7)
8
173
where &' is the settling velocity of the particles.
174
3.4 Similarity of Deposition
175
The similarity of deposition depends on the size and shape of particles. The foam beads have
176
a uniform size of 1.5x 10-3 m. A higher degree of angle of repose is better for the similarity of
177
prototype and model. The similarity of deposition [21] is found with the help of the angle of
178
repose and it is given by Eq. (8)
179
(θ)m= ( p
(8)
180
where θ is the angle of repose in the still state of the particles. A similar angle of repose is
181
difficult to achieve when modelling particles are used in a snowdrift test [13]. This problem
182
did not occur in the simulation with foam beads. The foam beads bounce off if they are
183
dropped from a height and may give a different angle of deposition. The angle of repose for
184
foam beads is obtained by dropping foam beads on a circular disc gently and measuring the
185
angle of the conical shape of their deposition. The average angle of repose for foam beads is
186
38° which lies in the range of angle of repose of snow 35° to 80° [2,25]. It provided the
187
advantage over the simulant materials used by previous researchers. The physical
188
characteristics of the snowdrift prototype had been taken from the literature [18,26] for the
189
modelling.
190 191
The similarity parameters of prototype snowdrift and model foam bead flow were analyzed and have been illustrated in Table-3.
192
9
193
Table-3
194
Similarity parameters of snowdrift (prototype) and foam bead flow (model) in the wind tunnel
Description
Similarity of the wind field Similarity of the ejection process
Similarity of particle trajectory
Similarity of Deposition
Physical Meaning
Similarity parameters
Snowdrift (Prototype)
)U∗ ) +
Foam Bead flow (Model)
1.34e-6 – 1.873e-5
9.56e-4
-
54
0.004-2.166
0.05
29.94-71.867
36.4
10.78
9.1
)1
3.034
106.79
&'
&'
0.2-0.5
0.4
0.018-0.046
0.044
θ
35-80
38
Aerodynamic roughness height of saltating particles ,
Roughness-height Reynolds number
0 ≥ 30 2 /
) )1 − ρ 3
Froude number of particle trajectory in the ejection process Similarity parameter of wind velocity Velocity at maximum structure height (m/s) Froude Number of particle trajectory in the saltation process Settling velocity of the particles (m/s) Ratio of drag force and inertial force
)1 − ρ +
Angle of Repose (°)
195 196
A snow particle ejects more snow particles from the surface after impacting it in the
197
saltation process. This process of particles ejection by the impact of other particles is rare in
198
saltation of foam beads. The strong separation of their flow is also observed. This results in a
199
larger value of the roughness height of foam beads
200
The settling velocity &' for snow varies from 0.2 m/s to 0.5 m/s considering the
201
heterogeneity of the snow particles [27]. The ratio of drag force and inertial force
202
snow ranges from 0.018 to 0.046 for the above range of settling velocity of snow. Thus, the
203
settling velocity (0.4 m/s) and the value of
4%
10
∗
as compared to the snow particles.
4%
for
(0.044) for foam beads lies well within the
204
range for snow particles. Y. Anno (1984) pointed out that Froude Number had a minimal
205
influence on the final pattern of redistribution of snow [22] and so the similarity parameter of
206
5 " 6
207
and the model are well established for the experiments with the foam beads in the wind
208
tunnel.
209
4. Experimental setup and methodology
210
A closed re-circulating wind tunnel 4m in length was designed and built in-house to carry out
211
the experiments for the modelling of a snowdrift with foam beads. The acrylic transparent
212
circular tube (diameter 0.2 m and thickness 0.005 m) which enables the visual observation of
213
drifting activities was used in the fabrication of the wind tunnel. The whole setup was divided
214
into three sections namely horizontal, inclined and vertical (Fig. 1) resembling different
215
terrain slopes for the experimental simulations. The horizontal section had the main test space
216
for simulation study of deposition pattern and observation of foam beads transportation under
217
the wind force. Foam beads having the spherical shape of average diameter 0.0015 m and
218
average bulk density of 50 kg/m3 had been used as simulants in the wind tunnel. An exhaust
219
fan (blade diameter 0.6 m and 1400 rpm) was fitted coaxially with the horizontal section to
220
produce the wind speed up to 14 m/s for the movement of foam beads in the wind tunnel. Anemometer
221 222 223
Mass Flux Instrument
Horizontal section
Duct for feeding foam beads
224
Vertical section
225
Data logger and processor
226
for foam beads could be relaxed. Thus, the similarity relations between the prototype
Exhaust fan
Inclined section
227 228
Fig. 1. A closed re-circulating wind tunnel
11
229 230
Fig. 2. Two-dimensional drawing of the wind tunnel system and exhaust fan location
231
The optical sensors, exhaust fan and flow rate controller are placed in the horizontal section
232
(Fig. 2). This section had provision to fix the fence model in the flow path and to monitor the
233
flow pattern around the model through the transparent wall. A scaled model of snow fence
234
(1:50) with the thickness of 1.5x10-3 m and 50 % porosity was used to simulate the storage
235
capacity of the snow fence (Fig. 3).
236
The flow of foam beads was caused by the wind force in the wind tunnel. The foam
237
beads creep over the layer of particle surface and suspend in the air under higher wind speed
238
of more than 6 m/s. The forces acting on a snow particle are (1) weight W; (2) aerodynamic
239
drag FD; (3) aerodynamic lift FL; (4) magnus lift FM; (5) electrical force FE [28] (Fig. 4).
240 241 Snow Fence Model 242 243 244
Fixture for the model
245 246 247
Fig. 3. Fitting of Snow Fence Model in the Wind Tunnel
12
248 249
Fig. 4. Schematic presentation of forces acting on suspended foam bead (weight W; aerodynamic drag
250
FD; aerodynamic lift FL; magnus lift FM; electrical force FE)
251
Similar forces act on the suspended foam beads and on the snow particles. The inclined
252
section had provision to change the slope of the surface for the experiments by changing the
253
height of the coaxial vertical section. The foam beads were flown upward due to wind force
254
in the vertical section. When wind force on a foam bead exceeds the sum of gravity and drag
255
force, it suspends inside the vertical section. The magnitude of static charge on the foam bead
256
is in the order of 23.87µCkg-1 which is in the range of the electrostatic charge +72µCkg-1 to
257
-208 µCkg-1 on the snow particle [29]. The electrostatic and magnus forces acting on the
258
foam beads were found to be in the range of 2x10-6 N to 5.6 x10-6 N which are negligible in
259
comparison to the wind force (0.03N) and so these forces were not taken into consideration in
260
this paper.
261
The wind tunnel was instrumented with a wind sensor and a mass flow rate sensor
262
along with a data logger. The data logger was provided with a wireless communication
263
system to transfer the raw data to a receiver which could be attached to a personal computer
264
(PC) up to a distance of 500 m. The observed data were analyzed with the help of the
265
LabVIEW programmable software to obtain mass flux variation with time and velocity. The
13
266
complete wind tunnel setup was fitted on a wooden platform, which had three supports for its
267
stability and smooth functioning during the experiments.
268
4.1 Measurement of wind speed
269
A hot-wire anemometer (Testo model no 435-4) had been used to measure the wind velocity
270
in the wind tunnel. The anemometer has wind velocity measuring range from 0 to 20 m/s
271
with an accuracy of ±0.03 m/s. It was placed near the starting point of the horizontal section.
272
The electronic regulator attached with an exhaust fan controls the wind speed in the wind
273
tunnel. The maximum wind speed achieved with the exhaust fan fitted at the end of the
274
horizontal section was 14 m/s which lies within the measuring range of the anemometer. The
275
cross-sectional area of the experimental space was the same and symmetrical which helped to
276
measure the wind speed in the closed wind tunnel with an anemometer conveniently.
277
Initially, the wind profiles were measured without the foam beads in the wind tunnel.
278
The wind velocity was measured at every 0.01m height from the surface of the wall to the
279
centerline of the wind tunnel (Fig. 5). It provided the wind profile in the wind tunnel and the
280
wind profile was compared with the field data.
281 282 283
Fig. 5. Schematic diagram of the wind tunnel wall and positions of the anemometer
284
14
285
4.2 Measurement of mass flux
286
A new mass flux measuring instrument based on the principle of opacity technique was
287
introduced in the middle part of the horizontal section in the wind tunnel. The instrument was
288
developed on the basis of the cotton mass flow measurement technique [30]. The
289
transportation of foam beads occurs due to the wind force produced by the exhaust fan. The
290
foam beads were made to pass through the sensing device installed in two rows. A sheet of
291
Infrared rays (IR) was used to illuminate the flow of particles passing through the measuring
292
space. The data loggers were programmed to provide the mass flow rate according to light
293
attenuation due to foam beads. The transmitted light flux was sensed by an array of optical
294
sensors. The IR radiation reaching the optical sensor was attenuated by the passage of the
295
particles in its path. The instrument measures denseness of optical obstruction.
296
The denseness was proportional to the area occupied by particles in the flow path.
297
When there was high particle density, the lesser light passed through it. The measurement of
298
particle flow was proportional to total area obstructed by all the particles in the optical path.
299
The measurement was sampled at a high frequency (1000 Hz). The measurement was
300
essentially the optical intensity measurement in an analogue form that was integrated with
301
respect to time. The data were processed to get the mass flow rate in the wind tunnel with
302
respect to the wind speed.
303
4.3 Field experimental setup
304
There is a permanent observatory for the collection of metrological data at Banihal Top,
305
Jammu and Kashmir (J & K), India. For the study of snowdrift and performance of snow
306
fence, a FlowCapt along with Automatic Weather Station (AWS) and snow fences (height 3.5
307
m and 4.0 m) had been installed at the experimental site. The wind speed is measured with a
308
15
AWS
FlowCapt
309 310
Fig. 6. FlowCapt and AWS installed at the snowfield observatory
311
propeller based wind anemometer (Young Model 05103 wind monitor) attached to AWS
312
(Fig. 6). The deposition pattern around the snow fence was measured with the help of
313
avalanche probing rods, measuring tapes, snow mast and scales at the experimental site [31].
314
A FlowCapt is an automatic acoustic-based instrument for snow flux rate measurement in the
315
snowfield area. It is used for snowdrift assessment and research work [1,32–34]. The snow
316
mass flux rate was measured at the experimental site to compare with the wind tunnel
317
experiment.
318
5. Results and discussion
319
The experimental site observes high snowdrift activities as the average wind velocity in a
320
month is near to the threshold velocity of the snow. The data of the wind speed, mass flux
321
and particles deposition pattern were collected at the field observatory. Similar data were also
322
found during the experiments in the wind tunnel for the comparison and snowdrift modelling.
323
The turbulent wind flow pattern in the wind tunnel was also consistent with the field flow.
16
324
5.1 Metrological observations and wind speeds
325
The maximum snow precipitation occurs in the winter season between December and March
326
at the field experimental site. The maximum wind speed up to 39 m/s has been observed at
327
the experimental site (Banihal Top, Jammu and Kashmir, India). The prevalent direction of
328
the wind is southwest (SW) at the site during the snowstorm and it helps to get the orientation
329
of the snow fence. The summary of temperature, wind speed and standing snow from
330
December 2010 to March 2016 observed at the experimental site are illustrated in Table- 4.
331
Table 4
332
Summary of the metrological data observed at Banihal top, Jammu and Kashmir, India Average Min Temp (°°C) -3.7 -7.8 -5 -1.6 -4.5 -8.9 -5.6 -1.9 -4.5 -6.9 -3.9 0.2
Average Dry Bulb Temp (°°C) -0.7 -6.5 -3.7 0.9 -2.7 -7.3 -4.2 -0.1 -3.4 -6.1 -3 1.4
Average Standing Snow (x10-2 m) 58.5 89.7 173.1 123 15.7 128.8 298.1 197.7 59.9 100 132.2 77.4
Average Wind Speed (m/s) 2.39 4.42 6.14 7.39 6.42 5.19 5.78 6.86 7.81 8.19 5.83 7.22
Maximum Wind Speed (m/s) 10.1 12.8 13.9 15.2 9.6 12.9 11.1 12.0 16.4 15.8 13.4 16.2
Prevalent Direction of the Wind
Dec 2010 Jan 2011 Feb 2011 Mar 2011 Dec 2011 Jan 2012 Feb 2012 Mar 2012 Dec 2012 Jan 2013 Feb 2013 Mar 2013
Lowest Min Temp (°°C) -7.0 -11.0 -8.0 -5.5 -8.0 -14.0 -8.0 -8.0 -7.5 -11.0 -7.0 -5.0
Dec 2013 Jan 2014 Feb 2014 Mar 2014 Dec 2014 Jan 2015 Feb 2015 Mar 2015
-8.5 -10.5 -9.0 -5.5 -6.5 -10.0 -8.5 -7.5
-3.7 -7.7 -5.5 -3.1 -3.4 -5.2 -4.4 -2.7
-1.9 -6.2 -4.5 -1.8 0 -3.5 -2.5 -0.5
39.1 128 204 238 0 25.9 121 253.2
5.39 6.58 5.78 6.83 5.47 6.14 5.94 6.00
13.6 11.1 14.7 13.1 11.2 10.7 11.1 11.8
NE S SW SW NE NE SW S
Dec 2015 Jan 2016 Feb 2016 Mar 2016
-10.0 -8.5 -8.5 -5.5
-4.7 -4.9 -3 -0.5
-2.9 -3 -1.2 1.4
30.7 12.7 38 29
6.22 6.39 5.50 4.92
11.3 11.7 12.9 10.3
ENE E E SW
Month-Year
17
NE NE SW SW NE S SW SW NE S SW NE
333
The wind velocities along the flow direction were measured between the surface and the
334
centre of the tunnel without the foam beads in the tunnel. The threshold velocity of foam
335
beads was found by observing the movement of a foam bead under a gradual increase in wind
336
speed. Its value was 4.05 m/s which lies in the range of threshold wind speed of dry snow
337
particles 4-11 m/s [35]. In the case of the inclined surface (30º), the threshold velocity of
338
foam beads was 2.7 m/s due to their granularity and the action of gravitational force on them.
339
5.2 Turbulence characteristics
340
The atmospheric boundary layer condition of turbulent flow is defined by the logarithmic
341
wind profile. The logarithmic wind profile at the height z is given by Eq (9) [4] 7 =
342
∗ 8
;
ln ;
(9)
<
343
where ∗ is the shear velocity, = = 0.41 is called the Von Karman Constant and z0 is the
344
roughness height. The value of z0 depends on the geometry of the snow surface. In the
345
present paper, the value of z0 is 0.0015 m which lies in the range of its value (0.0001 m to
346
0.005m) [4,36,37]. The value of ∗ for the field is 0.56 m/s. It was found that the wind
347
velocity pattern in the wind tunnel closely followed the wind velocity pattern of the
348
atmospheric boundary layer in the field (Fig.7). 1.4 Field
Height (h/H)
1.2 Wind tunnel
1 0.8 0.6 0.4 0.2 0 0.1
349 350
1 Wind velocity (U/U(H))
Fig. 7. Variation of dimensionless wind velocity with the dimensionless height
18
10
351
The turbulent kinetic energy (TKE) in the turbulence flow is defined by the half the sum of
352
the square of standard deviations of the velocity components (Eq. 10).
353 354
B EEEEEEE D A = C (10) D EEE . Where C = C − CE is the difference between local velocity( C ) and the mean velocity C
A 7 at height z
355
The turbulent kinetic energy
356
modelled as Eq (11) [38]
357 358
A 7 = FGB +H 7 + 7J + G (11) where the constants cB = −0.6035 and c = 1.7934 for shear velocity U∗ = 0.511 m/s for
359
for the atmospheric boundary layer is
the atmospheric boundary layer. Zhou et. al. (2016) [21] considered the value of cB =
360
−0.064 and c = 0.588 for U∗ = 0.35 m/s for the wind tunnel. The values of U∗ for the field
361
and the wind tunnel are 0.56 m/s and 0.35 m/s respectively in the present paper. The
362
constants of the turbulent kinetic energy are found statistically and so same values of
363
constants were used in the present paper due to relatively close values of U∗ for the field and
364
the wind tunnel. The relation between the dimensionless turbulent kinetic energy (A/A and
365
dimensionless height is depicted in Fig 8. It is found that the turbulent kinetic energy (A/A
366
for the field and the wind tunnel at h/H greater than 0.75 are very close ( Fig.8). Wind Tunnel 1.4
Field
Height (h/H)
1.2 1 0.8 0.6 0.4 0.2 0 0.8
0.9
1
1.1
1.2
1.3
Turbulent Kinetic Energy (k/kH) 367 368
Fig. 8. Variation of dimensionless turbulent kinetic energy with the dimensionless height
19
Wind Tunnel 1.4
Field
Height (h/H)
1.2 1 0.8 0.6 0.4 0.2 0 6
8
10
12
14
16
Turbulent Intensity (%)
369 370
Fig. 9. Variation of turbulence intensity with the dimensionless height
371
The turbulent intensity is another characteristic of a turbulence flow. It is defined as is the
372
EEE . . ratio of the standard deviation of fluctuating wind velocity to the mean wind velocity C
373
The turbulent intensity R 7 at the height z is obtained with the wind velocity and turbulent
374
kinetic energy using Eq (12)
R 7 =
375
J.SB ;
FA 7
(12)
376
It was found that the turbulence intensities are 10.7% and 10.0 % at the height of AWS (h/H
377
= 0.75) and at h/H = 0.75 in the wind tunnel respectively (Fig. 9). Thus, the turbulence
378
characteristics for the field and the wind tunnel are consistent.
379
The wind profile at different locations 0.5 m, 1.5 m, 2.5 m and 3.5 m were observed
380
in the horizontal section of the empty wind tunnel (Fig. 10). It was found that the wind
381
velocity at the centre of the tunnel was increased with the distance from the inlet location and
382
the boundary layer depth were also increased. The velocity was increased by 0.06 m/s in 3m
383
distance and so the flow in the wind tunnel was considered uniform throughout the
384
experimental space.
20
Vertical height from wall (m)
0.12 0.50 m distance 0.1 1.50 m distance 0.08
2.50 m distance
0.06 0.04 0.02 0
385
0.1
1 Wind velocity (m/s)
10
386
Fig. 10. Wind flow profiles in the horizontal section of the wind tunnel
387
The characteristics of turbulence flow in the wind tunnel and at the field observatory were
388
found similar in nature from the above graphs. The wind profiles for both conditions (Fig. 7)
389
were matched except one data near the wall having more kinetic energy for the snow (Fig.8).
390
The turbulent intensities in both conditions are matched near the wall but deviations for wind
391
tunnel and field were increased up to 1.5 % with the height (Fig.9). Modelled turbulence
392
quantities show the same behaviour as the field data which is important to have the same flow
393
characteristics in the wind tunnel. Variation in the magnitude is well within the modelling
394
constraints (less than 1.5%) and this is quite low in comparison to the inherent variation that
395
the field data is subject to.
396
5.3 Mass flux of particles
397
The snow mass flux was measured with FlowCapt in the snowfield. A sample of mass flux
398
with wind speed is shown in Fig. 11. The drifting of snow was observed above the wind
399
speed of 7 m/s. The mass flux rate varies with the surface condition and the wind speed in the
400
field. The maximum snow flux rate of 31.2 x10-3 kgm-2s-1 is observed at 18 m/s wind speed
401
with the FlowCapt.
21
Average wind velocity
35
Mass Flux
30
20
25 15
20
10
15 10
5
5
0
0 0
402
Mass flux (kgm-2 s-1)x10-3
Average wind velocity (ms-1)
25
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
Time (hours)
403
Fig. 11. Snow mass flux measured with FlowCapt and average wind speed at the experimental site
404
The foam beads were placed in the wind tunnel through the duct provided in the horizontal
405
section. The foam beads were kept flat with the help of forced wind by running the fan and
406
switching it off before the initiation of the experiment. The wind speed in the tunnel was
407
increased slowly and gradually with the electronic regulator. The foam beads, initially, roll
408
over the surface like creeping of snow particles and later they suspend in the air under high
409
wind speed (more than 6 m/s). The wind velocity was measured at the centreline of the
410
cross-section of the tube by the anemometer. The mass flow rate of foam beads with respect
411
to wind speed was calibrated by measuring the known quantity of foam beads and the wind
412
velocity. The result has validated the concept of the mass flux proportionality with wind
413
speed for the design of the optical instrument.
414
The mass flux rate of snow particles and foam beads were observed with respect to
415
the wind velocity (Fig. 12). The mass fluxes of snow and foam beads were proportional to the
416
cubic of wind speed with a coefficient of determination (R2) in order of 0.9. It is in line with
417
the Bagnold’s observation for the mass flux rate of sand [39]. It was observed that the trend
418
line of mass flux rate of foam beads and that of snow are parallel for the low wind speed. 22
Snow
Mass flux (kgm-2 s-1)x 10-3
35
Foam Beads
30 25 20 15 10 5 0 0
5
10
15
20
25
Average wind velocity (ms-1) 419 420
Fig. 12. Mass flux variation with wind speed
421
The abrupt change in mass flux rate of snow results from the fact that the large-sized particles
422
are also drifted at the higher wind speed (more than 15 m/s).
423
5.4 Particles deposition pattern
424
At the initial stage of transportation, foam beads were passed through the bottom gap of the
425
model like creeping of snow. At higher wind speed aerodynamic entrainment occurred and
426
they left the surface to flow with the wind. The foam beads were obstructed by snow fence
427
model in their way and they deposited around the model of snow fence. Their deposition
428
pattern was measured by placing graph paper on the other side of the tunnel wall. The
429
experiments were also carried out with snow fence models of different heights (6 x10-2 m and
430
7x10-2 m) and porosities (0 and 25%). The blocking ratio of the model was found to be about
431
7.64% which is acceptable as per the literature [40]. The mass flux data for the field and the
432
wind tunnel were more similar and proportional at the wind speed of 10 m/s. The height of
433
the deposited foam beads was maximum at the wind speed of 8 m/s in the wind tunnel.
434
Hence, these two wind speeds have been considered for the validation of results.
23
435
The observations of snow deposition pattern on the leeward side of snow fences
436
(height 4 m and 3.5 m with porosity 50 %) in the field were taken for model validation in the
437
wind tunnel. The non-dimensional deposition patterns of snow and foam beads are found by
438
dividing the deposition height by the height of the structure (H) (Fig. 13). The deposition
439
pattern around the model changed at different wind speeds due to obstruction and vortices
440
generated on the leeward side due to the presence of the model. With the increase of wind
441
speed, the clearance gap and the distance from the structure to the maximum height was
442
increased. However, there was a reduction of the deposition height in the wind tunnel.
443
The similarity between the deposition patterns of foam beads in the wind tunnel and
444
snow in the field was observed through the experiments. The storage capacity of the snow
445
fence model was lower at a higher wind speed of 10 m/s. The nature of the deposition pattern
446
of foam beads at lower wind speed was much closer to that of snow around snow fence in
Deposition height / H
1.2 1 0.8 0.6 0.4 0.2 0 0
5
10
15
Distance from structure / H Foam beads deposition around model in the wind tunnel at 8 m/s Foam beads deposition around model in the wind tunnel at 10 m/s Snow deposition around snow fence height 3.5 m in the field Snow deposition around snow fence height 4.0 m in the field
447 448
Fig. 13. Deposition pattern of foam beads and snow around the model and the snow fence
24
20
Snow Fence
Snow Rime
Snow Deposition
449 450
Fig. 14. Snow riming on snow fence at the experimental site
451
the field. The height and position of the nose of the deposition pattern for the foam beads
452
were reduced and shifted to the leeward side respectively. The snow deposition pattern
453
around snow fence of the height 4m was found comparatively higher than that for the model
454
and snow fence of height 3.5m. Due to the snow riming (Fig. 14), the porosity of the snow
455
fence of height 4m at the experimental site was reduced and it contributed for getting more
456
snow on the leeward side of the snow fence. The snow deposition pattern in the field depends
457
on the weather condition and snow fence characteristics along with snow riming over them.
458
6. Conclusion
459
The modelling of drifting snow has been attempted using the numerical method and
460
experimental technique in the wind tunnel to solve the problems of snow cornice formation,
461
blockage of highways due to snowdrift and avalanche hazards. Authors used the foam beads
462
(Expanded Polystyrene) as a simulant material in the re-circulating closed wind tunnel for the
463
snowdrift modelling as it has low density (50 kgm-3) like freshly precipitated snow and is
464
economically available. Geometric, kinematic and dynamic similarity parameters for the
465
particles and wind field were determined to carry out wind tunnel experiments with foam
466
beads. Turbulent kinetic energy and turbulence intensity measured at AWS height resembled
467
the values at the corresponding height by similitude inside the test section. Further, the mass 25
468
flow rate of foam beads was measured with a newly developed optical-based instrument in
469
the horizontal section of the wind tunnel to establish its relation with the wind speed. It was
470
found that the mass flow rate of foam beads and snow were proportional to the cubic of wind
471
speeds. The deposition pattern of foam beads around the model structure (1:50) at the wind
472
speeds 8 m/s and 10 m/s were validated with the snow deposition around the snow fence in
473
the field. The facility may be further utilized for investigation of other light materials for
474
aeolian phenomena and to improve the performance of a snow fence.
475
Acknowledgements
476
Authors are grateful to the Director, Snow and Avalanche Study Establishment (SASE),
477
Defence Research and Development Organization, India for his support and providing the
478
facility for this paper. The construction of the wind tunnel was funded by SASE under the
479
built-up project. Authors also want to acknowledge scientists and all other technical persons
480
involved in wind sensors installation and collection of the wind data at the experimental site
481
Banihal Top, Jammu and Kashmir, India.
482
References
483
[1]
484
M. Lehning, C. Fierz, Assessment of snow transport in avalanche terrain, Cold Reg. Sci. Technol. 51 (2008) 240–252. doi:10.1016/j.coldregions.2007.05.012.
485
[2]
S.M. David Peter, Avalanche handbook, 1977. doi:10.1016/0148-9062(77)90015-8.
486
[3]
S.J. Lee, K.C. Park, C.W. Park, Wind tunnel observations about the shelter effect of
487
porous fences on the sand particle movements, Atmos. Environ. 36 (2002) 1453–1463.
488
doi:10.1016/S1352-2310(01)00578-7.
489
[4]
A. Clifton, J.D. Rüedi, M. Lehning, Snow saltation threshold measurements in a
490
drifting-snow wind tunnel, J. Glaciol. 52 (2006) 585–596.
491
doi:10.3189/172756506781828430.
492
[5]
F. Naaim-Bouvet, M. Naaim, J.L. Michaux, Snow fences on slopes at high wind speed: 26
493
Physical modelling in the CSTB cold wind tunnel, Nat. Hazards Earth Syst. Sci. 2
494
(2002) 137–145. doi:10.5194/nhess-2-137-2002.
495
[6]
M. Liu, Q. Zhang, F. Fan, S. Shen, Experiments on natural snow distribution around
496
simplified building models based on open-air snow-wind combined experimental
497
facility, J. Wind Eng. Ind. Aerodyn. 173 (2018) 1–13.
498
doi:10.1016/j.jweia.2017.12.010.
499
[7]
H. Sakamoto, M. Moriya, K. Takai, Y. Obata, Development of a New Type Snow
500
Fence with Airfoil Snow Plates to Prevent Blowing-Snow Disasters : Part 1 ,
501
Evaluation of Performance by Blowing-Snow Simulation in a Wind Tunnel, J. Nat.
502
Disaster Sci. 23 (2001) 1–11.
503
[8]
M. Guala, C. Manes, A. Clifton, M. Lehning, On the saltation of fresh snow in a wind
504
tunnel: Profile characterization and single particle statistics, J. Geophys. Res. Earth
505
Surf. 113 (2008) 1–13. doi:10.1029/2007JF000975.
506
[9]
S. Alhajraf, Computational fluid dynamic modeling of drifting particles at porous
507
fences, Environ. Model. Softw. 19 (2004) 163–170. doi:10.1016/S1364-
508
8152(03)00118-X.
509
[10] Y. Durand, G. Guyomarc’h, L. Mérindol, J.G. Corripio, Improvement of a numerical
510
snow drift model and field validation, Cold Reg. Sci. Technol. 43 (2005) 93–103.
511
doi:10.1016/j.coldregions.2005.05.008.
512 513 514
[11] P. Gauer, Numerical modeling of blowing and drifting snow in Alpine terrain, J. Glaciol. 47 (2001) 97–110. doi:10.3189/172756501781832476. [12] Y. Tominaga, Computational fluid dynamics simulation of snowdrift around
515
buildings : Past achievements and future perspectives, Cold Reg. Sci. Technol. (2017)
516
0–1. doi:10.1016/j.coldregions.2017.05.004.
517
[13] Y. Anno, Modelling a snowdrift by means of activated clay particles, Ann. Glaciol. 6
27
518 519 520 521 522 523
(1985) 48–52. [14] N. Isyumov, M. Mikitiuk, Wind Tunnel Model Tests of Snow Drifting on a Two-Level Flat Roof, J. Wind Eng. Ind. Aerodyn. 36 (1990) 893–904. [15] R.J. Kind, Mechanics of Aeolian Transport of Snow and Sand, J. o[ Wind Eng. Ind. Aerodyn. 36 (1990) 855–866. [16] A. Flaga, G. Kimbar, P. Matys, A new approach to wind tunnel similarity criteria for
524
snow load prediction with an exemplary application of football stadium roof, 5th Eur.
525
African Conf. Wind Eng. EACWE 5, Proc. (2009).
526
[17] X. Zhou, J. Hu, M. Gu, Wind tunnel test of snow loads on a stepped flat roof using
527
different granular materials, (2014) 1629–1648. doi:10.1007/s11069-014-1296-z.
528
[18] F. Naaim-Bouvet, M. Naaim, Snowdrift modelling in a wind tunnel: vertical and
529 530 531 532 533 534
horizontal variation of the snow flux, Ann. Glaciol. 26 (1998) 212–216. [19] F. Naaim-Bouvet, M. Naaim, Snowdrift modeling in a wind-tunnel: vertical and horizontal variation of the snow flux, Ann. Glaciol. 26 (1998) 212–216. [20] M. Naaim, F. Naaim-Bouvet, H. Martinez, Numerical simulation of drifting snow: erosion and deposition models, Ann. Glaciol. 26 (1998) 191–196. [21] X. Zhou, S. Qiang, Y. Peng, M. Gu, Wind tunnel test on responses of a lightweight
535
roof structure under joint action of wind and snow loads, Cold Reg. Sci. Technol. 132
536
(2016) 19–32. doi:10.1016/j.coldregions.2016.09.011.
537 538 539 540
[22] Y. Anno, Requirements for modeling of a snowdrift, Cold Reg. Sci. Technol. 8 (1984) 241–252. [23] F. Naaim-Bouvet, Comparison of Requirements for Modeling Snowdrift, Surv. Geophys. 16 (1995) 711–727.
541
[24] X. Zhou, L. Kang, M. Gu, L. Qiu, J. Hu, Numerical simulation and wind tunnel test for
542
redistribution of snow on a flat roof, Jnl. Wind Eng. Ind. Aerodyn. 153 (2016) 92–105.
28
543 544 545 546 547 548
doi:10.1016/j.jweia.2016.03.008. [25] O. Abe, Shear strength and angle of repose of snow layers including graupel, Ann. Glaciol. 38 (2004) 305–308. doi:10.3189/172756404781815149. [26] X. Zhou, G. Ming, Numerical Simulation of Snow Drift on the Surface of a large- span Roof Structure, Fourth Int. Symp. Comput. Wind Eng. (2006) 889–892. [27] X. Zhou, L. Kang, X. Yuan, M. Gu, Wind tunnel test of snow redistribution on flat
549
roofs, Cold Reg. Sci. Technol. 127 (2016) 49–56.
550
doi:10.1016/j.coldregions.2016.04.006.
551 552 553 554 555
[28] N. Huang, J. Zhang, Simulation of snow drift and the effects of snow particles on wind, Model. Simul. Eng. 2008 (2008) 1–6. doi:10.1155/2008/408075. [29] D.S. Schmidt, J.D. Dent, R.A. Schmidt, Charge-to-mass ratio of individual blowingsnow particles, Ann. Glaciol. 26 (1998) 207–211. [30] J.A. Thomasson, D.A. Pennington, H.C. Pringle, E.P. Columbus, S.J. Thomson, R.K.
556
Byler, Cotton mass flow measurement: experiments with two optical devices, Appl.
557
Eng. Agric. 15 (1999) 11–17.
558 559 560
[31] G. Kumar, Performance of snow fence at Banihal Top in Himalayan region, J. Cold Reg. Eng. 29 (2015). doi:10.1061/(ASCE)CR.1943-5495.0000088. [32] C. Amory, A. Trouvilliez, H. Gallée, V. Favier, F. Naaim-Bouvet, C. Genthon, C.
561
Agosta, L. Piard, H. Bellot, Comparison between observed and simulated aeolian snow
562
mass fluxes in Adélie Land, East Antarctica, Cryosphere. 9 (2015) 1373–1383.
563
doi:10.5194/tc-9-1373-2015.
564
[33] C. Jaedicke, Acoustic snowdrift measurements: Experiences from the FlowCapt
565
instrument, Cold Reg. Sci. Technol. 32 (2001) 71–81. doi:10.1016/S0165-
566
232X(01)00017-9.
567
[34] A. Trouvilliez, F. Naaim-Bouvet, C. Genthon, L. Piard, V. Favier, H. Bellot, C.
29
568
Agosta, C. Palerme, C. Amory, H. Gallée, A novel experimental study of aeolian snow
569
transport in Adelie Land (Antarctica), Cold Reg. Sci. Technol. 108 (2014) 125–138.
570
doi:10.1016/j.coldregions.2014.09.005.
571
[35] L. Li, J.W. Pomeroy, S. Canada, S. Canada, Estimates of Threshold Wind Speeds for
572
Snow Transport Using Meteorological Data, J. Appl. Meteorol. 36 (1997) 205–213.
573
doi:10.1175/1520-0450(1997)036<0205:EOTWSF>2.0.CO;2.
574
[36] M. Lehning, F. Naaim, M. Naaim, B. Brabec, J. Doorschot, Y. Durand, G.
575
Guyomarc’H, J.L. Michaux, M. Zimmerli, Snow drift: Acoustic sensors for avalanche
576
warning and research, Nat. Hazards Earth Syst. Sci. 2 (2002) 121–128.
577
doi:10.5194/nhess-2-121-2002.
578
[37] J.D. Holmes, Wind Loading of Structures, Second, Taylor and Francis, London, 2007.
579
[38] Y. Yang, M. Gu, S. Chen, X. Jin, New inflow boundary conditions for modelling the
580
neutral equilibrium atmospheric boundary layer in computational wind engineering, J.
581
Wind Eng. Ind. Aerodyn. 97 (2009) 88–95. doi:10.1016/j.jweia.2008.12.001.
582 583 584 585
[39] R.A. Bagnold, The Physics of Blown Sand and Desert Dunes, London : Chapman and Hall, 1941. [40] C.K. Choi, D.K. Kwon, Wind tunnel blockage effects on aerodynamic behavior of bluff body, Wind Struct. An Int. J. 1 (1998) 351–364. doi:10.12989/was.1998.1.4.351.
586
30
Highlights of the Research Paper (1) Foam beads (Expanded Polystyrene) as simulant material for snowdrift particles (2) Similarity relations between model and prototype for modelling (3) A technique to measure the flow rate of foam beads with optical sensors (4) Measurement of flow and threshold velocity of foam beads (5) Modelling of deposition pattern of snow around the snow fence