The Eighth Asia-Pacific Conference on Wind Engineering,
December 10–14, 2013, Chennai, India
NUMERICAL INVEST
TIGATION OF WIND FORCES AND
D STROUHAL
FREQUENCIES OF SECONDARY HYPERBOLOID RE
EFLECTOR
Eswaran M1, R K Verma, G.R. Reddy, R. K. Singh and K.K. Vaze
Reactor safety divvision, Bhabha Atomic Research Centre, Mumbai, 4000085.
1
Correesponding author email: [email protected]
ABSTRACT
In this work, flow around the seconndary hyperboloid reflector is studied by numerical soolutions of the unsteady
Navier-Stokes equations. The compputed wind load is applied on the central tower to find
f
its deflection. For
validation, a simple two tandem cyylinders under the wind load is investigated for a certain range of values of
spacing ratio (L/D). These results are
a compared with few previously published results and
a good agreement is
found. After the validation of prresent numerical procedure, the forces (drag and lift) and the Strouhal
frequencies of solar secondary hypeerboloid reflector are determined for operational (40 km
m/hr) and survival (160
km/hr) wind speeds. Analysis has also
a
been done to find out the deflections due to winnd load. The computed
wind loads are applied on the Seconndary hyperboloid and central tower.
Keywords: Secondary reflector; Tandem
T
cylinders; Strouhal frequency; Vortex shedding; Lift and drag
force; Wind loads.
Introduction
Solar energy has attrracted more attention during the recent yeears, is a form of
sustainable energy. Today thee great verity of solar technologies for electtricity generation is
available and among many, the
t application of reflector in large sizes is employed in many
systems. The amount of solarr radiation entering the aperture of a collector depends on the
local solar energy potential. Application
A
of reflectors for solar heating andd solar power plant
improved in the recent years. Most of the solar power plants installed with reflectors are on
flat terrain and they may be suubjected to some environmental problems. One
O of the problems
for such a large reflector is their stability to track the sun very accurrately (Naeeni and
Yoghoubi, 2007). Solar therm
mal power plants are a gifted alternative to covver significant parts
of growing energy demand. The
T Fig. 1 shows the schematic diagram of typical molten salt
type solar power plant. In thiss concept, the central tower has a secondary hyperboloid mirror
surrounded by heliostats. The sunrays from all the heliostats are refleccted downwards by
hyperboloid to a ground baseed receiver which absorbs the solar radiationn and transfers to a
molten salt steam generating system.
s
The steam is then used to run a turbinne generator system
as in a conventional power plaant.
Wind forces play a siignificant role in design and operation of large reflectors and
need for satisfactory estimatees of these forces are becoming increasinglyy evident (Cohen et
al., 2006). Studies of wind looads on structure and boundary layer over different bodies such
as buildings (Huang and Cheen, 2007), hills, towers (Armitt, 1980), arch roof, automobiles,
heliostat (Pfahl and Uhlemannn, 2011), parachute, and dish are extensive both
b
experimentally
and theoretically. Converselyy, wind flow around parabolic and hyperboliic shapes is rare. In
engineering, fluid forces andd Strouhal numbers are the primary factorss considered in the
design of structures subjecteed to cross flow, e.g., chimney stacks, tubbe bundles in heat
Proc. of the 8th Asia-Pacific Conference on Wind Engineering – Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds)
c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: 978-981-07-8011-1
Copyright doi:10.3850/978-981-07-8012-8 p8
691
Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
exchangers, overhead power cables, bridge piers, stays, chemical reaction towers, power
plant towers, offshore platforms and adjacent skyscrapers.
IS 875 Part 3 provides force coefficient for most structural shapes. This coefficient when
multiplied by design wind pressure and effective area of structure provides wind load on
structures. Since IS 875 Part 3 does not provide force coefficient for hyperboloid surface,
CFD analysis has been performed to find out the forces due to wind loads on hyperboloid
surface. Shedding frequencies has also been obtained by CFD analysis. Hyperbolic reflector
is a little more than quarter segment of full hyperboloid. In this work, flow around the
secondary hyperboloid reflector is studied and computed wind load is applied on the central
tower to find its deflection. After the validation of simple tandem cylinder case, the forces
(drag and lift) and the Strouhal frequencies of solar secondary hyperboloid reflector are
determined for operational (40 km/hr) and survival (160 km/hr) wind speeds. Analysis has
also been done to find out the deflections due to wind load. The computed wind loads are
applied on the secondary hyperboloid and central tower.
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Fig. 1. Solar power plant
Fig. 2 Secondary hyperboloid reflector
Numerical Methodology
Governing equations
Based on the Navier-stokes time averaged equations and using Bousssinesq approximation
for Reynolds stresses, differential equations governing viscous turbulent flow field can be
written as
∂ρ
+ div( ρX ) = 0
(1)
∂t
∂ ( ρu )
∂p
+ div( ρXu ) = div( μ eff gradu ) −
∂t
∂x
∂p
∂ ( ρv )
+ div( ρXv) = div( μ eff gradv) −
∂y
∂t
(2)
(3)
where ρ is the fluid density, μ eff the effective viscosity, X the mean flow velocity field, p
the pressure and u, v are the mean components of flow field in the x and y directions,
respectively. In the present CFD model, the RNG k–İ turbulence scheme presented by
Yakhot et al. (1992) is used. This scheme differs from the standard k–İ turbulence scheme in
that it includes an additional sink term in the turbulence dissipation equation to account for
non-equilibrium strain rates and employs different values for the model coefficients. The
RNG turbulence model is more responsive to the effects of rapid strain and streamline
curvature, flow separation, reattachment and recirculation than the standard k– ε model
(Jeong et al., 2002). Thus, the turbulence of flow field is expressed in turbulence kinetic
energy (k) and dissipation rate ( ε ), using following equations,
&
∂ ( ρk )
+ div ( ρu k ) = div (Γk gradk ) + G − ρε
∂t
692
(4)
Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
c μη 3 (1 − η / η 0 ) ε 2
&
∂ ( ρε )
ε
ε2
+ div( ρuε ) = div(Γε gradε ) + c1 G −
ρ
c
−
2
∂t
k
k
k
1 + βη 3
G = μ T (u ij + u ji )u ij ;
with
μ t = ρC μ
k2
ε
;
(5)
μ eff = μ + μ t
(6)
where Γk = μ + (μt / σ k ) and Γε = μ + (μt / σ ε ) are diffusion coefficients for k and ε ,
respectively. Here, μ , μ t , σ k and σ ε are the molecular viscosity, turbulent viscosity, turbulent
Prandtl number and turbulent Schmidt number respectively. The primary coefficients of the
RNG model are provided by Yakot et al. (1986). The coefficients used in the turbulent
models cμ , c1 , c2 and η 0 values are 0.085, 1.42, 1.68 and 4.38 respectively. The 4th and 5th
terms in Eq. 5 represent the shear generation and viscous dissipation of ε . The extra term in
Eq.5 employs the parameter η , which represents the ratio of characteristics time scales of
turbulence and the mean flow fields, defined by η = Sk / ε . It can be shown that η is a function
of generation of dissipation of k and can be written as:
η = c μ (G / ρε )
(7)
The standard k − ε model along with Boussinesq equation, performs well for the
broad range of engineering problems, however in the problems which include unbalanced
effects, etc., finally this model reaches to responses which are over diffused, i.e., the μt
values predicted by this model will be large.
Computational domain and boundary conditions
Numerical simulation of wind flow around the secondary hyperboloid reflector (Fig.
2) is studied. The fluid is assumed incompressible. As there is no free surface, the body
forces can be ignored. Secondary hyperboloid reflector is placed in a 120 r2 x 64 r2
rectangular domain, in which the bottom corner of reflector is located 36 r2 from the inlet
boundary, where r2 denotes the maximum distance from x axis to reflector in y direction as
shown in Fig. 3. In the present CFD model, the RNG k–İ turbulence scheme presented by
Yakhot et al. (1992) is used. This scheme differs from the standard k–İ turbulence scheme in
that it includes an additional sink term in the turbulence dissipation equation to account for
non-equilibrium strain rates and employs different values for the model coefficients. The
RNG turbulence model is more responsive to the effects of rapid strain and streamline
curvature, flow separation, reattachment and recirculation than the standard k– ε model
(Jeong et al., 2002).
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ϯϮƌϮ
LJ
ƌϭ
ϯϲƌϮ
ƌϮ
dž
ϯϮƌϮ
&ƌĞĞ^ůŝƉ
Fig.3 Computational domain.
At the inlet, the Dirchlet boundary conditions are applied (u=U, v=0, k = 2( I * U ref ) 2 3
and ε = c μ3 4 (k 3 2 ) l , where Uref and I is the free stream velocity and turbulent intensity, and l
=0.007L, where L is the diameter of the computational domain of flow).The pressure is
prescribed at a point at the inlet. At the outlet, the Neumann-type conditions are employed (
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
∂u ∂x = 0 , ∂v ∂x = 0 , ∂k ∂x = 0 and ∂ε ∂x = 0 ). No slip boundary condition is applied at the
boundary of a fixed cylinder, i.e., velocity components on the boundaries zero ( u = 0 , v = 0 ).
The top and bottom boundaries of the computational domain are considered as symmetry
boundary to negate the propagation wall effects inside the domain over the time period.
Grid generation and discretization
In this study, non uniform staggered Cartesian grid is used and the enclosed area of
reflector is refined with respect to other areas of the flow field. Boundary layers have also
been created around the solid boundary. In such a grid, the velocity components (u and v) are
calculated for the points located on the main control volume surfaces, i.e., the staggered
points, while pressure, kinetic energy and dissipation rate of turbulent energy (p, k and ε ) are
calculated for the points located on the main grid. The flow close to a solid wall is for a
turbulent flow, is very different compared to the free stream. This means that the assumptions
used to derive the k − ε model are not valid close to walls. So that wall functions are used to
describe the flow at the walls. This corresponds to the distance from the wall and structure
where the logarithmic layer meets the viscous sub-layer. The normal distance from the
structure boundary to the wall boundary, yw is automatically computed from y w+ = ρμt y w / μ ,
where μ t = C μ1 4 k is the friction velocity. The y w+ value is kept within recommended range of
30 -150, to satisfy the log law. Spatial discretization is performed using second order upwind
scheme and temporal discretization is performed based on second order implicit method
which causes much less damping and is thereby more accurate. A Finite volume based
commercial solver is used for solving RANS and turbulent equations. The well known SemiImplicit Method for Pressure-Linked Equations Consistent (SIMPLEC) numerical algorithm
is employed for the velocity–pressure coupling.
Fig.4 Grid arrangement
Fig.5 Boundary layers around the cylinder.
Results and discussion
The dimensionless flow parameters are defined as follows,
, C L = 2 FL
C D = 2 FD
2
2
ρU L
ρU L
[1]
where FL and FD denote lift and drag forces on the reflector per unit length, respectively. The
ρ and U denote the fluid density in kilogram per unit volume and free stream flow velocity
in meter per second. Dimensionless flow parameters are also given by
Re =
f L
ρUL
tU
, St = v , T =
μ
U
L
[2]
where Re is the Reynolds number, St is the Strouhal number, T is the dimensionless time, μ is
the fluid viscosity, L is the characteristic length (i.e., r2 for flow over hyperboloid and
cylinder diameter for flow over tandem cylinders), t is the time in second at each time step
and fv is the frequency of vertex shedding which can be calculated from the oscillating
frequency of lift force.
Flow over tandem cylinders –Validation
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
Flow around two tanddem cylinders provides a good model to understand the physics
of flow around multiple cyylindrical structures. In order to better unnderstand the flow
characteristics and wake inteerference, initially, simple tandem cylinder arrangement cases
were analysed and comparedd with Slaouti and stansby (1992) and Meneeghini et al. (2001)
results and for high Reynoldds number, compared with Moriya et al. (20002), Dehkordi et al.
(2011) results. The present ressults are very closely matching with their experimental results
and numerical results. Fig. 6 shows the notations for staggered configuration.
c
The
investigation is performed in the range of L/D ratio with zero staggered anngle (Į), where Į is
the angle between the free-strream flow and the line connecting the centerss of the cylinders, L
is the gap width between the cylinders,
c
and D is the diameter of a cylinder..
Fig.6 Notation for stagggered
configuration.
Fig. 7 Streamline plot for tandeem cylinder Į =0˚
and L/D =3.00
Flow around two tanddem cylinders of identical diameters is in genneral classified into
three main regimes (Zdravkovvich, 1987; Alam and Zhou, 2007) (i) the extended-body regime
(L/D < 0.7), (ii) the reattachm
ment regime (L/D = 0.7 to 3.5), (iii) the co-sheedding regime (L/D
> 3.5). Fig. 7 shows the streaamline plot for tandem cylinder Į =0˚ and L/D
L/ =3.0, where the
shear layers separated from thhe upstream cylinder reattach on the downstream cylinder and
the flow in the gap is still insiignificant. If increase the L/D ratio further thhen the shear layers
roll up alternately in the gap between
b
the cylinders and thus the flow in thee gap is significant.
Table 1. Comparisonns of flow parameter for two tandem cylinders at Į =0˚.
Parametric
Results
Cylinder
Re =200 and
T/D =2
Re=200 and
T/D =3
UC
DC
UC
DC
Re=2.2 × 104
and T/D =2
UC
DC
Mean Drag Coefficient
Slaouti and
Meneghini
Present
Stansby
et al. (2001)
(1992)
0.89
1.03
1.064
-0.163
-0.21
-0.17
0.87
1.0
1.069
-0.158
-0.16
-0.08
Moriya et
Dehkordi et
al, 2002*
al, 2011
1.05
0.95
1.0
-0.20
-0.40
-0.17
Strouhaal Frequency
Meneghini
Slaoouti and
Staansby
et al.
Present
(11992)
(2001)
0.14
0
0.13
0.13
0.14
0
0.13
0.13
0.146
N
NA
0.125
0.146
N
NA
0.125
Dehkordi
Moriiya et al,
2
2002
et al, 2011
0.15
0
0.140
0.155
0.15
0
0.140
0.155
UC= Upstream cylinder; DC = Downstream cylinder; *Values are taken from Ghadiri
G
et al, 2011.
Strouhal number is a significant feature of fluid which has a stroong dependence on
both Reynolds number and spacing.
s
This non-dimensional number, speccify how cylinders
response to hydrodynamic foorces and when their oscillation frequency reeaches to the point
near natural frequency whichh can lead to damage of the structure. Therebby, comparisons of
the Strouhal numbers and mean
m
drag coefficients in the present work with
w other data are
presented for Re = 200 in Tabble 1. Table 1 shows comparisons of flow tw
wo tandem cylinders
at Re =200 and Į =0˚, Re =100000 and Į =0˚and Re =2.2 × 104 and Į =0˚. It
I can be seen from
Table 1 that the negative draag has completely eliminated in the co-sheddding regime while
increasing the L/D ratio. The reattachment
r
of upstream shear layer onto thee second cylinder is
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
observed. Due to this, negative drag is found on the downstream cylinder which results from
the pressure difference between front and back sides of this cylinder. Frequency of the vertex
shedding is calculated from the oscillation frequency of lift force.
Flow over the secondary hyperboloid reflector
In this work, the calculations are made for three wind directions and the two velocities
say operational wind speed (40 km/hr) and survival wind speed (160 km/hr). The wind
directions are taken as follows, wind flow in positive x direction (case 1), wind flow in
negative x direction (case 2), wind flow in positive z direction (case 3). The x, y and z
directions are correspondence to Fig. 2. Since case 1 and 2 computational domains are almost
similar except the wind direction for case 3 the shape of the object is changed accordingly.
Vortex shedding is an oscillating flow that takes place when a fluid flows past a bluff body at
certain velocities, and it is depending to the size and shape of the body and Reynolds number
of fluid flow. If the structure is not mounted rigidly and vortex shedding frequency matches
the resonance frequency of the structure, the structure can start to resonate, vibrating with
harmonic oscillations driven by the energy of the flow.
Wind direction
Fig.7 Pressure contour for case 1 at
operational wind speed at tU L =250.
Fig.6 Velocity contour for case 1 at
operational wind speed at tU L =250.
Wind direction
Wind direction
Secondary vortex
Primary vortex
Fig. 8 Velocity contour at tU L =250, case1
with operational wind speed
Fig. 9 Streamline diagram at tU L =250,
case1 with operational wind speed
Wind flow in positive x direction (case 1)
In this case, operational and survival wind velocities are taken to find the forces and
shedding frequency. Velocity and pressure contours and streamline diagram at operational
wind speed are depicted in Figures 8-12. The velocity and pressure fluctuations in the wake
region create an oscillating flow in rear of the structure. Drag is generated by the difference in
velocity between the solid object and the fluid. Fig 8 shows the velocity magnitude contour.
Fig. 9 shows the streamline diagram. It is found that the one primary and one secondary
vortex are formed behind the structure for all the cases. The shedding frequency has been
calculated from lift force fluctuations. The velocity at x and y components are shown in Fig
10 – 11. For case 1, the region above the structure has a positive pressure, while the just
behind the structure holds the negative u velocity. Alternate convective shedding rolls have
been observed from u and v contours. The velocity values are depicted in the respective place
in the picture itself. And coefficient of pressure is showed in pressure contour as shown in Fig
12.
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
Ͳ Ϭ͘ϬϭϲŵͬƐ
ϭϯ͘ϲŵͬƐ
ϯ͘ϬϯϰŵͬƐ
ͲϬ͘ϴϳϱϱŵͬƐ
ϲ͘ϳϱŵͬƐ
ͲϮ͘ϵϯϵŵͬƐ
ϳ͘ϮŵͬƐ
ϭϰ͘ϰϵŵͬƐ
Fig.10 Velocity at x component (u) contour for
case 1 at operational wind speed at tU L =250.
Ͳ ϰ͘ϳϱϴ
ϯ͘ϳϰŵͬƐ
Ͳϭ͘ϮϯϭŵͬƐ
Ͳϯ͘ϳϭϵŵͬƐ
ϭϬ͘ϵŵͬƐ
ϭϰ͘ϭϯŵͬƐ
ϱ͘ϭϲϳŵͬƐ
Ͳϯ͘ϳϰŵͬƐ
Fig.11 Velocity at y component (v) contour for
case 1 at operational wind speed at tU L =250
Wind direction
ƉсϬ͘Ϭϱϴ
ƉсϬ͘ϬϮϴϮ
ƉсͲϬ͘ϴϵ
ƉсͲϬ͘ϴϵϲ
Fig.12 Pressure contour for case 1 at operational wind speed at tU L =250
Fig. 13 shows the drag and lift coefficients fluctuations over non-dimensional time.
From these fluctuations the average coefficients are calculated. Wind speeds are varied
between operational and survival wind speeds, and strouhal number have been calculated and
illustrated as dimensional form in Fig. 14. Drag and lift forces are increasing while increasing
the wind velocity. However, the lift force is increasing sharply compared to drag force. The
structural first mode frequency has been calculated as 1.02 Hz, as shown in Fig. 14 the wind
velocity corresponds to structure frequency is 100 KM/HR. So that, the plant can be operated
upto 81 KM/HR after including safety margin of 25% with structure frequency. If the wind
shedding frequency matches with tower structural frequency (i.e., 1.02 Hz), the structure can
start to resonate, vibrating with harmonic oscillations driven by the energy of the flow and
subsequently, deflection will be increased in the tower.
1.8
-0.52
-0.56
Resonance region of higher mode
Shedding Frequency in Hz
CL
-0.60
-0.64
-0.68
-0.72
0.68
0.64
cD
Fundamental Frequency of Structure (1.02 Hz)
1.6
0.60
1.4
1.2 + 25 %
Resonance region of first mode
1.0
0.8
- 25 %
0.6
0.4
Safe region for
plant operation
0.2
0.56
0.52
0.0
0
50
100
150
200
250
300
40
Non-dimentional time(tU/L)
Fig.13 Drag and lift force coefficients at
operational wind speed for case 1.
60
80
100
120
140
160
Wind Velocity in km/hr
Fig.14 Shedding frequency with wind velocity
for case 1
Wind flow in negative x direction (case 2)
In this analysis, the wind direction is considered in negative x direction as shown in
Fig. 2. The streamline plots for operational and survival wind speeds are shown at T =250 in
Figs. 15 and 16. These streamline plots show the primary and secondary vortices. Different
recirculation regions can be found on the leeward side of the hyperboloid reflector. The
shape of the primary vortex is slightly more in the survival wind speed. Compare to
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
operational speed, the secondary vortex size is also more fluctuating with respect to time at
survival wind speed. The force coefficients and Strouhal number are shown in Table 1.
Wind direction
Wind direction
Fig. 16 Streamline plot at survival wind speed
at tU L =250
Fig. 15 Streamline plot at operational wind
speed and tU L =250
Wind flow in positive z direction (case 3)
While compare to the previous cases, the case 3 computational domain and shape of
the object is dissimilar. Here the 2D cut section is taken from the y – z coordinate of
hyperboloid. Since wind directions are similar in both directions, i.e., positive and negative z
direction. The drag, lift coefficients and Strouhal number for this case are shown in Table 7.2.
The Strouhal number is calculated from the first mode frequency. Since the shape of the
reflector guides the wind flow around structure, it holds low pressure coefficient around the
reflector. So that, case 3 shedding frequency is relatively low. The wind force on the reflector
increases sharply while the wind speed increases. When the flow direction is in positive x
direction (Case 1), then the lift force is negative. That means the lift force on structure is
acting towards ground. Flow direction is in negative x direction (case 2), now situation is just
opposite. i.e., the lift force is acting opposite to gravity.
Table 7.2: Force coefficients and Strouhal numbers
Sl. No
CASE 1
CASE 2
CASE 3
Operational (40 km/hr)
CD
CL
St
0.668
- 0.68
0.158
0.49
0.29
0.1893
0.374
-0.668
0.081
Survival (160 km/hr)
CD
CL
St
0.625
-0.64
0.1615
0.4818 0.2897
0.19158
0.332
-0.62
0.092
Using the above coefficient, total wind load on secondary reflector has been calculated for
three cases.
Structural analysis
Finite element analysis has been performed to find out the structural frequencies.
Analysis has also been done to find out the deflections due to wind load. Table 2 shows the
frequencies and mass participation factors in dominant modes. Hyperboloid has been
designed as a truss structure as per IS 800. Structural tubes of different sizes have been used
as truss member to reduce deflections under dead weight and wind loads. Depth of truss has
been optimized and is 600mm. Truss member has been optimized to reduce weight of
hyperboloid structure. This hyperboloid is supported on three towers. Height of the tower is
45m. Base of the tower is 7×7 m and top is 1.5×1.5m. Tower has been designed to ensure
fundamental frequency beyond 1 Hz. Pre-stressed cables have been used to limit the
deflections in hyperboloid reflecting surface. A secondary hyperboloid and central tower has
been designed as a truss structure as per IS Table 3 shows deflections in secondary
hyperboloid due to wind loads acting on structure. Figures 17 and 18 show deformed shape
due to survival wind load for case 1.
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
Table 2: Frequencies and Participation Factors
X-direction
Y-direction
Z-direction
S. No.
Frequency
(Hz)
1.
1.02
*MPF
182.33
**%MP
54.15
MPF
-3.54
%MP
0.02
MPF
0.19
%MP
-
2.
1.04
3.30
0.02
213.36
74.12
-21.04
0.72
3.
1.70
125.87
25.80
0.78
-
3.64
0.02
4.
1.92
-3.69
0.02
47.60
3.69
113.80
21.08
4.84
-31.04
1.57
0.25
-
0.63
-
5.
Note: MPF- *Mass Participation Factors, **%MP-Percentage Mass Participation
Table 3: Maximum Deflections in Secondary Hyperboloid
Wind speed
Operational
Survival
Maximum Deflections
Case 1
Case 2
Case 3
9.5
8.75
6.56
108
89
108
Fig. 17 Deformed Shape of central tower due to
survival wind load for case1. (Dead Loads +
Imposed Loads + Wind Loads)
Case 1
11.63
186
Bending stress
Case 2
Case 3
11.06
11.19
177
179
Fig. 18 Deformed shape of support frames of
reflector due to wind load for case1. (Dead
Loads + Imposed Loads + Wind Loads).
Conclusions
The solar power plant secondary reflector has been taken for analysis against wind
load. Drag and lift forces are evaluated under operational (40 km/hr) and survival (60 km/hr)
wind speeds. Since IS 875 Part 3 does not provide force coefficient for hyperboloid surface,
CFD analysis has been performed to find out the forces due to wind loads on hyperboloid
surface. Shedding frequencies has also been obtained by CFD analysis. The wind directions
are also varied to find these parameters. Here, the forces and vortex shedding frequency is
increasing while increasing the wind velocity. From above work, the following conclusions
are drawn.
1. Fundamental frequency of the structure is 1.02 Hz, which is quite away from
shedding frequency estimated by CFD analysis. Also IS 800 recommends frequency
more than 1.0 Hz to avoid wind oscillation. If the wind shedding frequency matches
with tower structural frequency (i.e., 1.0 Hz), the structure can start to resonate,
vibrating with harmonic oscillations driven by the energy of the flow and
subsequently, deflection will be increased in the tower.
2. Since IS 875 Part 3 does not provide force coefficient for hyperboloid surface, CFD
analysis has been performed to find out the forces due to wind loads on hyperboloid
surface.
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
3. From Fig. 7.16, it can be observed that the wind velocity corresponds to structural
fundamental frequency 1.02 Hz is 105 km/hr, considering resonance frequency band
of ±25% the wind velocity up to which plant can be operated is ~80 km/hr.
4. Drag and lift forces are increasing while increasing the wind velocity. However, the
lift force is increasing sharply compared to drag force (Figure 7.15). When the flow
direction is in positive x direction (case 1), then the lift force is negative. That means
the lift force on structure is acting towards ground. When flow direction is in negative
x direction (case 2), the lift force is acting opposite to gravity (Table 8.1).
5. The shape of the reflector guides the wind flow around structure while wind flowing
from positive z direction, it holds low pressure coefficient around the reflector
resulting relatively low shedding frequency (Table 7.2).
The calculated stresses are found within acceptable limit for both operational and
survival wind speeds. This study can be extended by finding the suitable drag minimization
techniques to avoid the resonance matching.
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