Numerical Simulation of the Lock-In Effect of a Fixed-Fixed Tube in Cross Flow

Abstract

This paper deals with the development of a numerical calculation code that is able to simulate the three-dimensional flow through a heat exchanger tube bundle and therefore allows a coupled calculation of fluid-structure interaction between the flow and the tube bundle. The incompressible flow field is calculated by a Navier-Stokes solver using a first-order power law scheme, a SIMPLEC algorithm to calculate the pressure and velocity correction fields, and a line-by-line Gauss-Seidl tridiagonal algorithm to solve the linearised system of equations. The transient parts of the Navier-Stokes equations are discretised by a second-order forward finite differencing scheme. The turbulence is examined with the aid of a large-eddy turbulence model. The transient fluid forces acting on the tubes are calculated by integration of all local flow pressure values on the surfaces of the tubes. As an example a single fixed-fixed cylinder in a flow channel is considered using the structural calculation part already developed as well as the new flow field and flow forces subroutines. The time series of the tube's motion and the fluid forces acting on the tube are analysed by Fourier's transformation. The lock-in effect occurring when the vortex shedding frequency approaches the first natural frequency of the tube can be excellently demonstrated by varying the inflow velocity over a wide range of Reynolds numbers.