1 Reduction in turbulence -induced non- linear dynamic vibration using tuned liquid damper TLD

2025-04-28 0 0 704.17KB 6 页 10玖币
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Reduction in turbulence-induced non-linear dynamic vibration using tuned liquid
damper (TLD)
Ananya Majumdar1, Biplab Ranjan Adhikary1 and Partha Bhattacharya1
1Department of Civil Engineering, Jadavpur University, Kolkata-700032, India
ABSTRACT
In the present research work, an attempt is made to develop
a coupled non-linear turbulence-structure-damper model in a
finite volume-finite difference (FV-FD) framework. Tuned
liquid damper (TLD) is used as the additional damping system
along with inherent structural damping. Real-time simulation of
flow-excited bridge box girder or chimney section and the
vibration reduction using TLD can be performed using the
developed model. The turbulent flow field around a structure is
modeled using an OpenFOAM transient PISO solver, and the
time-varying drag force is calculated. This force perturbs the
structure, causing the sloshing phenomena of the attached TLD,
modeled using shallow depth approximation, damping the
flow-induced vibration of the structure. The structural motion
with and without the attached TLD is modeled involving the
FD-based Newmark-Beta method using in-house MATLAB
codes. The TLD is tuned with the vortex-shedding frequency of
the low-Reynolds number flows, and it is found to be reducing
the structural excitation significantly. On the other hand, the
high-Reynolds number turbulent flow exhibits a broadband
excitation, for which by tuning the TLD with few frequencies
obtained through investigations, a good reduction in vibration
is observed.
Keywords: Turbulence-structure interaction, tuned liquid
damper, finite difference, OpenFOAM.
1. INTRODUCTION
Turbulence proves its’ prominent presence in our
surroundings, which can adversely affect the important
structures like bridges, high-rise buildings or chimneys. The
excessive flow-induced vibration even leads to collapse. One of
such an iconic example is Tacoma bridge collapse and a very
recent, the under-construction bridge collapse in Sultangunj,
India on 29th April 2022.
In order to reduce the turbulence-excited structural motion
it is important to properly model the flow field surrounding the
structure. Next, the structural motion is to be estimated with and
without a TLD attached to it.
To obtain the desired reduction in the excitation level of the
structure, several active and passive damping techniques are
used by researchers and engineers. One of the widely used
passive damping instruments is TLD, which is essentially tuned
to the first fundamental frequency [1,2] or first two fundamental
frequencies [3] of the vibrating structure for the best damping
experience. In the case of harmonic excitation and non-
deterministic forcing with a prominent frequency value, the
TLD is tuned to the excitation frequency [4]. In case of
turbulent flow, the behavior of TLD and possible tuning
frequency is not studied yet.
2. LITERATURE REVIEW AND OBJECTIVE
Many researchers have investigated the flow past bluff body
for different Reynolds numbers (Re) using numerical [5] or
experimental techniques [6-8]. The Strouhal number (St) and
drag coefficient (C) are evaluated and reported. Structural
excitation due to any random forcing is estimated using the FD-
based non-linear Newmark-Beta method in time domain [4].
The sloshing behavior of TLD and resulting structural response
reduction is estimated numerically and/or experimentally [1-4]
using harmonic or random earthquake ground acceleration.
However, the coupled non-linear model to capture the
turbulence-induced structural motion and its reduction using
TLD is non-existent.
Therefore, in the present research work, an attempt is made
to develop a numerical FV-FD-based non-linear model that will
estimate the turbulence forcing, and simultaneously at each
time step, it will capture the sloshing-induced base shear
produced by the TLD liquid at the TLD-structure junction,
eventually producing additional damping to the SDOF system.
3. METHODOLOGY
The entire work is subdivided into two subsections, each
consisting of modelling a part of the full solution technique.
a) Modelling the turbulent flow-field past a rigid obstacle
and estimation of the drag force applied to it.
b) Using the time-varying turbulent forcing to estimate
the structural response at each time step with and
without attached TLD.
3.1 Turbulence past a rigid obstacle
Unsteady or transient simulation for isotropic turbulence is
performed using Large Eddy Simulation (LES), which
essentially works based on filter operation. Eddies larger than a
certain length scale, typically in the order of the grid size, are
fully resolved. The smaller eddies are modelled using a sub-grid
scale model. As the turbulence is considered to be isotropic,
only the size of these smaller eddies becomes important, not the
shape. Once the mean velocity field is computed by the RANS
model, the fluctuating velocity component (u) can
conceptually be estimated by subtracting time-averaged mean
velocity U
, from instantaneous velocity, U. This fluctuating
velocity is then used to calculate the turbulent kinetic energy
(k) per unit mass, as k =
uu. If all the fluctuating
components in three directions are considered, the Reynolds
stress tensor can be estimated (per unit density) in symmetric
2
matrix form, and in 3D and 2D domains the resolved kinetic
energy becomes
k =
1
2
[(u)
+ (v)
+ (w)
] (1)
k =
1
2
[(u)
+ (v)
]
(2)
The amount of the remaining kinetic energy is termed sub-grid
scale kinetic energy, k, and calculated by a sub-grid eddy
viscosity model. In the present study, the Smagorinsky-Lilly
model is used, where an additional stress term () is applied
to break down the eddies larger than the mesh size because
molecular viscosity is not sufficiently strong to do so. This
stress term can be derived by applying filtering operation on
compressible Navier-Stokes equations as follows:

+
(
)

= 0 (3)
(
)
 +
(
)

=

+
 +
(4)
This sub-grid stress  is modelled using Eq. (5)
 = 2
2
3
 (5)

=
1
2

+


1
3



(6)
Assuming the profile to be linear within the viscous
sublayer, and obeying the 1/7th power law in the outside region,
the wall function is formulated as described by Germano et al.
(1991).
()=
 <11.8
8.3()/  >11.8
(7)
where non-dimensionalized velocity (U) and wall distance
() are given as
=
,=
(8)
Lilly (1966) proposed a value for the Smagorinsky constant
C as 0.173, considering turbulence to be homogeneous and
isotropic, which is true for a shear-free turbulent event far from
any wall. However, modern CFD codes typically use different
values of C for near-wall turbulent events. In the present wall-
function approach (SLWF) Smagorinsky-Lilly constant, C is
considered as 0.1 to determine the sub-grid scale kinematic
eddy viscosity.
In the Pressure-Implicit with Splitting of Operators (PISO)
algorithm, steady-state flow problems can be solved using the
LES model with a pressure corrector.
The coefficient of drag is given by
=
1
2
2
(9)
FD: Drag Force, A: Projected area
3.2 Sloshing of tuned liquid damper (TLD)
At any point wave height is h. Assuming shallow wave
theory to be valid and no point of time wave is reaching the tank
top, partial differential equations for the sloshing motion of
liquid can be written as [4],

+

+

= 0
1
21 (10)


+


+


()+

= 0
(11)
Where, u is the displacement of the structure at any point of
time, thus, displacement of the TLD liquid surface, as it is
attached to the structure.  is the rotational displacement, h
is the wave height at location x and time t, v is the particle
velocity at location x and time t. The boundary conditions are
given by:
(0, )=(,)= 0
(12)
Initial conditions: At the starting of time (t = 0) steady state
condition is considered,
(, 0)=; (. 0)= 0
(13)
Non-dimensional slope of the energy gradient line is written as,
=

(14)
The wall shear stress at the base of the tank, is given by,
=

, 0.7 (15)
=

, > 0.7
(16)
is the forcing frequency, =
; is the absolute
viscosity of fluid, here water. Sloshing force (F) acting on the
walls of the water tank is given by:
= 0.5(
)+
(17)
,: Wave height w.r.t bottom of the tank at the right and left
wall of the tank. : Density of fluid, here water.
The sloshing frequency of the tank liquid is given as,
= 1
2
tanh(
)
(18)
= Fundamental natural frequency of liquid sloshing
L = Tank length
3.3 Solving non-linear partial differential equations
The non-linear partial differential equations used to
describe tuned liquid damper system discussed in the previous
section are solved in iterative finite difference technique. Any
general function f can be written as,
=+(1)

+

2
(19)
The function can be velocity (v), wave height (h), or slope of
the energy gradient line (S). In this numerical approach space
derivatives are estimated as,


=


2
(20)
for a particular time step.  is the element dimension. ‘i’ is the
node number. Time derivatives are estimated as,
摘要：

1Reductioninturbulence-inducednon-lineardynamicvibrationusingtunedliquiddamper(TLD)AnanyaMajumdar1,BiplabRanjanAdhikary1andParthaBhattacharya11DepartmentofCivilEngineering,JadavpurUniversity,Kolkata-700032,IndiaABSTRACTInthepresentresearchwork,anattemptismadetodevelopacouplednon-linearturbulence-str...

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