Insights and methodologies in wall-bounded turbulent channel flows

Abstract

Wall-bounded channel flows are of massive interest to civil and environmental engineers due to their immense application for water supply and management. This dissertation addresses five key aspects of turbulent channel flows relevant to practicing engineers, laboratory researchers, fluid scientists, and consultants leveraging computational fluid dynamics for modeling turbulent flows. In the first study, a device was developed and tested to enable Particle Image Velocimetry (PIV) for free surface flows. Measuring flows reliably requires that illumination provided by the laser sheet remains undisturbed. In open channel flows, introducing the laser sheet from the free surface can be necessary as the bed may be optically opaque. An oscillating free surface can further complicate maintaining an undisturbed laser sheet. This research has shown that the disturbance of the laser sheet, when introduced from the free surface, can be mitigated by introducing an improvised device called an optical coupler. The effect of the coupler on the measured velocity field was systematically studied using independent Laser Doppler Anemometer (LDA) measurements. The effect of the coupler on the measured velocity field was confined to its vicinity near the surface of the flow. The mean flow profile remains largely unaffected. Additionally, appropriate material for fabricating the coupler has been recommended by studying the relative performance of a glass and acrylic coupler. While the glass coupler measurements were closer to the undisturbed flow profile, the durability and ease of handling an acrylic coupler make it a viable alternative. The second study is focused on ensuring fully developed flow in short laboratory flumes. Ensuring a fully developed flow is essential for any experimental or modeling study that involves wall-bounded flows. Flow development in pipes has been extensively studied, and empirical relationships have been widely published. Recently, similar studies on open channels have revealed that the entrance length in laboratory flume is ≈ 100h, where h is the depth of the flow. Such a prescription renders most laboratories unfit for experimental work. Further, the inlet configuration in the flume can also hamper flow development, even after the length requirements are met. In this study, we develop a methodology to obtain developed flow in short channels by modifying the inlet and tripping the boundary layer. Further, we also provide a robust, rapid test to confirm if the flow is fully developed using Direct Numerical Simulation (DNS) datasets. The proposed method is validated using flume experiments for flows with friction Reynolds number Reτ ∼ 1500−3000. Against the current prescription, we show that it is possible to obtain fully developed profiles within a distance of ≈ 20h from the inlet. In the next (third) study, we leverage the DNS data for closed channel flow for a range of friction Reynolds Number (Reτ ∼ 180 − 5000) to develop a new One Point Friction Velocity Method (OPFVM) to calculate friction velocity U∗ in terms of free-surface velocity Um, flow depth h and kinematic viscosity ν for smooth wall-bounded flows. In contrast to prevalent methods that require several cumbersome near-boundary measurements to obtain friction velocity, the OPFVM relies on a single easy-to-measure free-surface velocity measurement. The formulation obtains friction velocity for a closed channel flow (CCF) DNS regime with Reτ = 10049 and on four open channel flow (OCF) DNS regimes with Reτ ∼ 180 − 2000. The same formulation was then experimentally verified in our laboratory. To avoid being prescriptive, a sensitivity analysis was performed to determine the permissible variation in Um to restrict the error in estimated U∗ to 2%. The relationship between the depth-averaged velocity Ub and the maximum free-stream velocity Um is also explored using the DNS datasets and an approximate relationship between Ub and Um is proposed. With advances in remote sensing technology that enables free-stream velocity measurements, this method extends the potential to measure even the friction velocity remotely. Computational Fluid Dynamics (CFD) is an essential tool for analyzing fluid flows. The k − ϵ model is a turbulence model used in Raynold-Averaged Navier-Stokes simulations to close the Reynolds stress terms. The empirical constants used in k − ϵ model were obtained using experiments conducted at low Reynolds numbers several decades ago. In this study, we revisit the turbulent viscosity parameter Cµ, based on the stress-intensity ratio c2 = |uw|k. Here, |uw| and k are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a-priori comparisons, we find that the widely accepted value of Cµ = 0.09, does not agree with the latest DNS and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging c2 in the equilibrium region, where the production (P) of k is within 10% of the dissipation rate(ϵ), and consequently, c4 ≈ Cµ. We evaluate flows up to friction Reynolds number Reτ ≈ 10000 and find that with increasing Reτ, Cµ approaches a value of 0.06, which is 50% lower than the prevalent value of 0.09. Finally, we perform an a-priori test with the new (proposed) value of Cµ = 0.06 to show that the estimated turbulent viscosity νT for wall-bounded flows is in much closer agreement with the exact (DNS) values than when νT is estimated using Cµ = 0.09. The final study develops a new scaling law for wall-bounded turbulent flows. This formulation eliminates all arbitrary constants and depends only on physical parameters, namely, the free-stream velocity Um, the friction velocity U∗, the kinematic viscosity ν, and the distance from the wall z. This is a significant step towards describing the velocity profile using these pertinent parameters.