Numerical Investigation of a Hydropower Tunnel: Estimating Localised Head-Loss Using the Manning Equation

Abstract

The fluid dynamics within a water tunnel is investigated numerically using a RANS approach with the k-ε turbulence model. The computational model is based on a laser scan of a hydropower tunnel located in Gävunda, Sweden. The tunnel has a typical height of 6.9 m and a width of 7.2 m. While the average cross-sectional shape of the tunnel is smooth the local deviations are significant, where some roughness elements may be in the size of 5 m implying a large variation of the hydraulic radius. The results indicate that the Manning equation can successfully be used to study the localised pressure variations by taking into account the varying hydraulic radius and cross-sectional area of the tunnel. This indicates a dominant effect of the tunnel roughness in connection with the flow, which has the potential to be used in the future evaluation of tunnel durability. ANSYS-CFX was used for the simulations along with ICEM-CFD for building the mesh.

Experimental and Numerical Determination of the Head Loss of a Pressure Driven Flow through an Unlined Rock-Blasted Tunnel

“…One of the main objectives of the numerical study was to investigate the applicability of methods that can also be used by practitioners. Our results confirm the conclusions of [30] that it is possible to calibrate a computationally efficient model for a specific target value (here: head loss between two specific cross sections). We will further investigate the applicability of the numerical model with data from three other tunnels, which were acquired in the framework of the present research project.…”

“…Localized pressure variations due to the variation in hydraulic diameter and cross-sectional areas could be predicted. On the other hand, Andersson et al [30] commented critically on the performance of the model to capture the head loss at larger cross sections, which is in line with the results presented above. Finally, another possible reason for the observed deviations between the numerical simulations and the scale model may be associated with uncertainties from the scale model.…”

“…However, a detailed investigation of this issue was beyond the scope of the study and these empirical coefficients were not tuned in the calibration process. We further note that the study carried out by [30] revealed the applicability of the k-ε model for modelling the flow in an unlined tunnel. Localized pressure variations due to the variation in hydraulic diameter and cross-sectional areas could be predicted.…”

“…A further possibility to investigate the flow features and hydraulic losses in conduits is by means of computational fluid dynamics (CFD) which has become more and more popular because of the increased computer power over time. Simulations carried out by [30] using a computational grid derived from terrestrial laser scanning (TLS) data of a hydropower-tunnel and a 3D-modelling approach based on the Reynolds-averaged Navier-Stokes (RANS) equations with the k-ε turbulence model showed the possibility to study local pressure variations due to a complex tunnel geometry. A similar conclusion was reported based on the numerical simulations of physical scale model experiments by [29].…”

Error analysis of hydraulic radius evaluation in hydraulic calculation

“…Recently, with the development of the compute, it is possible to use the hydraulic radius directly in calculation and some researchers start to pay attention to the error of replacing the hydraulic radius by depth, some primary analysis of to the error characteristic have been done [6][7] and some academician take hydraulic radius directly without replacing in their calculation [8] . Recently, a new and improved definition of hydraulic radius for closed conduits flowing partially full is presented to determine the channel discharge and friction slope of uniform flow [9] .Some results indicate that the Manning equation can successfully be used to study the localised pressure variations by taking into account the varying hydraulic radius and cross-sectional area of the tunnel [10] . But sometimes it is difficult to get the accurate geometry of the crosssections, so it is necessary to research on value-taking errors of hydraulic radius, which may give directions to practical application.…”