PSI - Issue 32

R. Tsvetkov et al. / Procedia Structural Integrity 32 (2021) 209–215

212

4

R. Tsvetkov et al./ Structural Integrity Procedia 00 (2021) 000 – 000

(4      − , (2 1) (4 2 1) i i i    −   − + )

(7)

K

=

i

i

i

i

(

) ( ) 2 / 8

 is the dimensionless angular frequency of liquid oscillations in the i- th connecting

where

i i R =     

segment. In the case of Poiseuille flow friction coefficient K is equal to 1. Initial conditions are defined as follows:

0 , i i h h V V H H = = = , i i i i 0

0

.

(8)

The system of equations (1) – (4) for independent variables h̃ i , Ṽ i and H̃ i , supplemented by initial conditions (6), was solved using the Matlab software. Let's consider kinematic excitation that corresponds to the initial condition (8), where the height of the liquid column in the i - sensor at the initial moment is equal to h̃ 0 tank - Δ h̃ i . Such a disturbance is associated with an instantaneous change in the position of the vessel or with the adding liquid to the vessel. An important characteristic of the oscillatory process is the attenuation (stabilization) time T̃ which corresponds to the interval required to restore the equilibrium of the liquid after its disturbance. It can be described by the relation: where h̃ end is the height of the liquid column at final moment t̃ (in this case h̃ end =1), ε is specified accuracy. 3. The results of numerical experiments Based on the mathematical model (1) – (7), a numerical parametric analysis of dynamic processes in HLS caused by a change in the liquid level in one vessel was carried out. Fig. 2 shows the scheme of the multipoint HLS that contains 4 sensors and one storage tank, united by the connecting hoses. The length L between the sensors may be varied. Usually, L is equal to the distance between the load-bearing structural elements, which is fixed for a particular structure. L is usually varied from several meters to hundred meters. The ratio of the diameters of the measuring unit and the connecting hose r / R can be chosen arbitrarily in numerical experiments. The radius of measuring vessels is determined by the design of the liquid level sensor. , h t T   −     +     end h h h , end i h (9)

Fig. 2. Layout of the HLS sensors on the structure columns.