Turbulent Flows in Non-Uniform Open Channels : Experimental Measurements and Numerical Modelling

Investigations into the turbulent flows in uniform and nonuniform open channels by previous researchers have demonstrated the requirement and importance of understanding the turbulence structures and energy losses due to irregularity in non-uniform open channels. Responding to this requirement, the turbulent flow in one special non-uniform open channel has been studied both experimentally and numerically. This non-uniform open channel was designed so that its width and bed level vary while its cross-sectional area below the water surface keeps constant. An upstream uniforzn open channel is attached to the non-uniform open channel to establish fully developed turbulent flow conditions. A downstream uniform channel is also attached for control of water depth and downstream flow condition. The experimental study consisted of measurements of turbulent velocity field with a LDV (Laser Doppler Velocimetry) and measurements of boundary shear stress (BSS) with Roving Preston tubes in the experimental channel. Turbulent velocity components in the longitudinal and vertical directions were measured with the LDV in forward scattering mode and the laser beams were focused from the channel side wall into the water. Turbulent velocity components in the longitudinal and transverse directions were measured with the LDV in back scattering mode and the laser beams are focused from above the water surface into the water. Both the forward scattering mode measurements and the back scattering mode measurements were taken at two cross sections in the upstream uniform open-channel and at twelve cross sections in the nonuniform open channel. Obtained data include mean longitudinal velocity U, transverse velocity V, vertical velocity W, turbulence intensities u^2,v^2,w^2, and Reynolds shear stresses -uv and -uw. The chief results of these measurements are: 1) There is no separation of flow in the nonuniform open channel. 2) As flow passes from wider and shallower section to narrower and deeper section, it responds as though it experiences contraction in horizontal planes and expansion in vertical planes. The reverse occurs as flow passes from narrower and deeper section to wider and shallower section; 3) The secondary currents in the nonuniform open channel are combinations of the effects of pure contraction and expansion of channel boundaries and the effects of the vortex kind secondary currents; 4) Turbulence intensities in the non-uniform open channel show similar distribution patterns to that in the uniform open-channel but their magnitudes change due to the change of channel shape; 5) Negative values of the Reynolds shear stresses, -uw, appear at the free surface and may extend to a large depth below the free surface in the nonuniform open channel. Boundary shear stresses in the experimental channel were measured with Roving Preston tubes. The use of the Roving Preston tubes was preceded with calibrations of themselves in air pipe flow and calibrations of a special pressure transducer in air and in water. Delicate measurement procedures were designed for measurements of BSS in the nonuniform open channel. The BSS were measured at one cross section in the uniform open-channel and at twelve cross sections in the nonuniform open channel. The chief results of these measurements are: 1) The irregularity of the nonuniform open channel significantly affects the distribution of the BSS but the total shear force has little change; 2) The effect of the secondary currents on the BSS is very similar to the effect of secondary currents on the ESS in uniform open channel; 3) The irregularity in the non-uniform open channel does not cause extra energy loss since there is no flow separation. The numerical study made use of a FEM (finite element method) commercial package FIDAP to simulate the turbulent flows in the experimental channel. These simulations are carried out with Speziale's eddy-viscosity anisotropic k-Epsilon model, the standard k-Epsilon model, and the RNG model. With each model, simulations were undertaken for four consecutive uniform channels of 5 m length so that fully developed turbulent flow conditions were established before entering into the simulation of flow in the non- uniform channel. In all simulations the free surfaces were fixed. Simulation results include U, V, W, k, and Epsilon. For turbulent flow in the uniform channel, only Speziale's model is capable of predicting qualitatively correct secondary currents. For turbulent flow in the non-uniform open channel, all three models gave similar simulation results. The calculated distribution patterns of U and W are in agreement with measurements except near the free surface but differences exist in magnitude. None of the three models was capable of modelling the transverse velocity V in the nonuniform open channel correctly. Further simulations are necessary with movable free surface and better boundary condition for the energy dissipation rate s in order to achieve better agreement with the experimental values, especially near the free surface