Fluid and Thermal Induced Vibration in Thin Slender Tube

Abstract

Thin beam and thin walled circular tubes are widely found in various structural engineering applications. For example, satellites, rockets where the propellant is transferred through connecting pipe lines, micro heat exchanger pipe used in refrigeration and air conditioning system, air craft fuel ducts, etc. Invariably the structure experiences fluid load due to inertia effect of the fluid, thermal loads due to heat conduction and convection and dynamic loads due to inertia effect of the structural element. The pipelines conveying high velocity internal flow may experience severe flow induced vibration due to fluid pipeline interaction. Therefore response of the pipe to fluid load and inertia load is very important for the safe design and operation. The present study is focused on the dynamic response of slender cantilever pipe oriented in the horizontal and vertical direction conveying air at different pressure. The objective of this work is to formulate the equation of motion using Newtonian’s approach and finite element solution of this equation that helps to study the effect of boundary conditions, flow velocity, fluid pressure on the free vibration characteristics of the cantilevered pipe conveying air. The FORTRAN codes are written based on the finite element formulation. This code is validated with problems reported in archival journals. The experimental set-up was fabricated in the laboratory and experiments were conducted to study the response of the cantilever tube in horizontal and vertical orientation at different lengths, conveying air with different pressure. Certain important observations which are concluded from this work are (i) increasing the length of cantilever tube will increase the amplitude of transverse displacement and decrease the fundamental frequency of tube, irrespective of its orientation and (ii) increasing the pressure will increase amplitude of transverse response of cantilever tube and but the frequency remains same. These experimental observations are compared with the numerically obtained results. To understand the thermally induced oscillations, it is essential to solve the heat transfer and structural problems simultaneously by coupling the temperature distribution and the structural displacement. The second order linear differential equation of motion with damping and thermal load as forcing function is presented. In the present study, spatial and time variation of convection that arises due to motion of beam is interpreted based on the physical understanding of the nature of air currents that are established due to motion of tube. Thus, the forced convective heat transfer coefficient is computed using Reynold’s number, Prandlt number and Nusselt number. Fourth order Runge-Kutta method is used to determine the transient response of the tube being subjected to heat source. The dynamic response of the tube is studied for various heating rates and different diameters of tube. The analysis showed that the rate of vibration is governed by the natural frequency of the tube and convective heat transfer coefficient. The displacement histories, which were initiated due to initial displacement, with the passage of time exhibited an initial decrease in the displacement and gradually increased to a maximum value depending on the heating rate and the magnitude of the sustained oscillations, were governed by the fact that the heat removed by convection balance the internal heating. Experimental studies were also carried out on thermally induced vibration of internally heated cantilever tube with tip mass and cantilevered U-tube with and without tip mass. The experimental results on the displacement response are found to agree reasonably well with the theoretical results. The important observations from the study conducted were, lowering the heating rate leading to larger time to attain steady state amplitude and vice- versa and also there exists a threshold heating rate to produce thermal induced motion for the tube. According to available literature, combined effect of fluid flow and thermal effect on the vibration of pipe has not been studied rigorously. In the present work, experimental and theoretical study of fluid and thermal induced vibration has been carried out on thin tube. The experiments are conducted for different end mass, length of the tube as well as the air passing through the tube at different temperature and pressure. The natural frequencies are calculated theoretically using finite element formulation and compared with the experimental results. It is observed from the study that the increase in pressure tends to increase the frequency due to increase in stiffness and increase in temperature tends to decrease the frequency due to softening effect of tube.