Analysis approach
In this study we seek to apply CFD simulation to obtain the forces originated by the flow in a submerged tunnel, especially the dynamic component of the vertical force. In the dimensioning of these structures, this load must be considered together with the contributions due to traffic, self-weight, etc.
Computational fluid dynamics allows the equations governing the movement of the fluid to be solved numerically, thus obtaining the pressure field and the tangential stresses on the structure. In order to evaluate the dynamic component, the analysis carried out is of the transient type.
First, we study a base case with a single cylinder modelling a single tunnel, for which experimental data are available in known literature references. The case we want to analyse has a high Reynolds number of about 40 million.
Preparation of CFD models
To perform the analyses we use a pseudo-2D model that we solve in the Cradle ScFlow software. The water domain around the tunnel must be extended sufficiently to minimise the influence of the model boundary conditions on the structure.
A mesh must then be generated that can capture the effects of the boundary layer and the general behaviour of the fluid. The following pictures show the domain used and a detail of the mesh:
The water flow enters the domain on the left-hand side at a velocity imposed as a function of the Reynolds number to be studied, and exits freely on the other surfaces of the far field.
CFD simulation results
With CFD simulation we can see the wakes in the flow generated by the tunnel, and we can measure the dynamic effect of the forces generated.
These analyses allow us to obtain parameters of interest such as the dimensionless Strouhal number or the average of the Lift and Drag coefficients. The following graph shows the result obtained for the vertical forces.
These results fit well with the experimental data obtained from the literature on reference dynamics. For the Strouhal number, a less turbulent case is tested, with Reynolds 10000, and the Reynolds 40 million case, obtaining in both cases results that agree with the experimental results in the range of precision indicated in the literature.
Studies with additional configurations
Once the methodology has been validated, we proceed to the study of other configurations of interest. We begin this phase by analysing the case of two parallel tunnel lines, as could be the case to implement the two directions of traffic circulation. The contours of the tunnels are separated by a distance equal to one fourth of the diameter.
The vertical force obtained does not present such a clearly defined sinusoidal shape as in the initial case, so we proceed to perform a Fourier analysis to find the main contributions of the response obtained. The image shows the analysis carried out for the front tunnel.
Finally, we studied the effect of including both tunnels in an ellipse-shaped envelope, in order to smooth the effect of the flow on the structure. By studying the pressure field and the forces on the structure we found that for small angles of incidence the desired effect is achieved, but for steeper angles of incidence of the flow the behaviour is less desirable.
In particular, a low-pressure zone appears in the upper front part, which produces somewhat higher forces than in the initial case in the direction opposite to the initial flow.
