Large-Eddy Simulation of High Reynolds Number Turbulent Flow Past a Square Cylinder

Flow past a square cylinder at a Reynolds number of 21,400 has been studied numerically using the large-eddy simulation technique. A dynamic subgrid-scale stress model has been used for the small scales of turbulence. The time- and span-averaged axial and transverse velocities in the downstream of the cylinder are in good agreement with the experimental results. The distribution of turbulent normal and shear stresses is also well predicted. The coherent and incoherent components of turbulent fluctuations at some specified phases have been separated and their relative magnitudes downstream of the cylinder have been compared. The comparison shows more coherence in the near wake than the far wake, while the coherent and incoherent components are of comparable magnitude in the far wake. The far wake shows irregular phase-averaged structures.     

Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models

The standard k?ω turbulence model and two versions of blended k?ω/k?ε models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended.     

Thermistor Chain Data Assimilation to Improve Hydrodynamic Modeling Skill in Stratified Lakes and Reservoirs

Results from a three-dimensional hydrodynamic model of a stratified lake show that the computed structure of the pycnocline changed rapidly due to numerical diffusion, thus altering the vertical mixing dynamics and introducing a positive feedback that quickly drives model predictions off course. To negate the numerical diffusion a pycnocline filtering method is proposed that assimilates high-resolution thermistor chain data and adaptively adjusts to minimize the discrepancy between observed and computed temperatures. The adaptive pycnocline filter ensures that the computed temperature gradients in the metalimnion at the position of the thermistor chain remain within the bounds of the measured values so the computation preserves the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of the lake.     

Effect of Transitions on Flow past a Square Cylinder at Low Reynolds Number

Numerical simulations have been performed for three-dimensional flow past a square cylinder. The cylinders are placed normal to the incoming uniform flow. The results are based on higher order spatial and temporal discretization. The computations are carried out for a range of Reynolds number (100-325). The flow is found to be two-dimensional at R = 160 while it becomes three-dimensional at R = 163.5. Both Mode-A and Mode-A* are observed to be quite prominent and distinct at R = 175 though they are present in a range of Reynolds number. The spanwise wavelength for Mode-A is higher than at R = 250 where finer-scale structures are observed called Mode-B. The decay rate for primary vortices in Mode-A* is the fastest and it is the lowest for Mode-B. The magnitude of secondary vortices of Mode-A* is quite high compared to Mode-A, but of comparable magnitude to Mode-B. The effect of transitions on the instantaneous flow and root mean square fluctuations are quite significant while the time-averaged flow does not show any noticeable variation.     

Turbulence Modeling of Flows over Circular Spillways

To predict the characteristics of flows over circular spillways, a turbulence model based on the Reynolds stress model (RSM) is presented. Circular spillways are used to regulate water levels in reservoirs. The flow over the spillway is rapidly varied with highly curvilinear streamlines. The isotropic eddy-viscosity models such as k-ε models are based on the Boussinesq eddy viscosity approximation that assumes the components of the turbulence Reynolds stress tensor linearly vary with the mean rate of strain tensor. Hence, they cannot very precisely predict the characteristics of flows over the spillway. On the other hand, the non-isotropic turbulence models such as the turbulence Reynolds stress models (RSM) that calculate all the components of the Reynolds stress tensor can accurately predict the characteristics of these flows. The k-ε models and RSM were applied in the present study to obtain the flow parameters such as the pressure and velocity distributions as well as water surface profiles. The previously published experimental results were used to validate the simulation predictions. For flow over a circular spillway, RSM appears to properly validate the characteristics of the flow under various conditions in the field, without recourse to expensive experimental procedures.     

Recirculating Flow in Oscillatory U-Tubes

Wastewater treatment facilities often experience undesirable oscillations in water surface elevations due to the potential of unsteady outlet flow. Self-induced oscillations, particularly those generated by the geometry and flow conditions of treatment facilities with a U-tube component, are of particular interest. This study focuses on the U-tube component of an existing wastewater treatment facility where oscillations of constant amplitude and period were observed shortly after the facility was operational. It is assumed that an oscillating U-tube manometer represents this problem, and a numerical model was developed to predict the amplitude and period of the oscillations using Newton’s second law of motion and momentum analysis. A 1-to-4.88-scale physical model of the existing facility was constructed and tested. Numerical model results show good agreement with measured oscillatory characteristics of the existing facility and the physical model.     

Reynolds Stress and Bed Shear in Nonuniform Unsteady Open-Channel Flow

Expressions for the Reynolds stress and bed shear stress are developed for nonuniform unsteady flow in open channels with streamwise sloping beds, assuming universal (logarithmic) velocity distribution law and using the Reynolds and continuity equations of two-dimensional open-channel flow. The computed Reynolds stress distributions are in agreement with experimental data.     

Determination of Boundary Shear Stress and Reynolds Shear Stress in Smooth Rectangular Channel Flows

A method for computing three-dimensional Reynolds shear stresses and boundary shear stress distribution in smooth rectangular channels is developed by applying an order of magnitude analysis to integrate the Reynolds equations. A simplified relationship between the lateral and vertical terms is hypothesized for which the Reynolds equations become solvable. This relationship has the form of a power law with an exponent of n = 1, 2, or infinity. The semiempirical equations for the boundary shear distribution and the distribution of Reynolds shear stresses are compared with measured data in open channels. The power-law exponent of 2 gave the best overall results while n=infinity gave good results near the boundary.     

Reynolds Stress in Open Channel Flow with Upward Seepage

Nonuniform-unsteady flow in open channels with streamwise sloping beds having uniform upward seepage is theoretically analyzed. Expressions for the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic law of velocity profile due to upward seepage, and using the Reynolds and continuity equations of two-dimensional open channel flow. The computed Reynolds stress profiles are in agreement with the experimental data.     

Formulas for Friction Factor in Transitional Regimes

This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse’s experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows.     

Direct Numerical Simulation of Turbulent Flow in a Square Duct: Analysis of Secondary Flows

A direct numerical simulation of turbulent flow in a square duct was performed for a Reynolds number based on bulk streamwise velocity and duct height equal to 4,440. The mechanism by which secondary flows are generated in a square duct was investigated. Two counterrotating secondary flows occur around the duct corner. These secondary flows were found to play a key role in momentum transfer between the corner and center of the duct. A conditional quadrant analysis was performed in the local maximum and minimum regions of the wall shear stress in order to characterize the pattern of the mean secondary flows.     

Turbulent Bed Shear Stress under Symmetric and Asymmetric Waves: Experimental and Numerical Results

A new instrument built to directly measure the bottom shear stress under different conditions of periodic waves is presented. Similar to classical Taylor’s cylindrical viscosimeter, the instrument is formed by two concentric cylinders, and the space between them is filled with water. The internal cylinder is fixed whereas the external cylinder, with a specific roughness, rotates following a given unsteady velocity time history. The shear stress at the outer cylinder wall is measured by using a torque meter. Both monochromatic and sawtooth-shaped waves have been tested, and the experimental shear stress time histories were compared with the results obtained from a numerical model.     

Depth-Averaged Shear Stress and Velocity in Open-Channel Flows

Turbulent momentum and velocity always have the greatest gradient along wall-normal direction in straight channel flows; this has led to the hypothesis that surplus energy within any control volume in a three-dimensional flow will be transferred toward its nearest boundary to dissipate. Starting from this, the boundary shear stress, the Reynolds shear stress, and the velocity profiles along normal lines of smooth boundary may be determined. This paper is a continuous effort to investigate depth-average shear stress and velocity in rough channels. Equations of the depth-averaged shear stress in typical open channels have been derived based on a theoretical relation between the depth-averaged shear stress and boundary shear stress. Equation of depth mean velocity in a rough channel is also obtained and the effects of water surface (or dip phenomenon) and roughness are included. Experimental data available in the literature have been used for verification that shows that the model reasonably agrees with the measured data.     

Fluctuations of Turbulent Bed Shear Stress

With the assumption that the bed shear stress fluctuates in a lognormal fashion, the probability density function (PDF) of the standardized bed shear stress is derived as a function of the relative shear stress intensity. The PDF is more skewed with larger relative intensities, but approaches a Gaussian function when the relative intensity is small. The computed PDF agrees well with the reported experimental data for flows over a smooth boundary. The higher-order moments of the bed shear stress, skewness, and kurtosis, are shown analytically to be also dependent on the relative intensity. The theoretical dependencies are then compared to a number of measurements available in the literature. The Reynolds number effect on the relative intensity is also discussed.     

Bubbly Two-Phase Flow in Hydraulic Jumps at Large Froude Numbers

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-averaged void-fraction data highlight a rapid deaeration of the jump roller. The results suggest that the hydraulic jumps are effective aerators and that the rate of detrainment is comparatively smaller at the largest Froude numbers.     

Omission of Critical Reynolds Number for Open Channel Flows in Many Textbooks

During the analysis of an open channel flow experiment, students were asked to determine whether the flow was laminar or turbulent. The array of answers highlighted the different information carried in fluid mechanics textbooks. It was noted that approximately 50% of the books did not mention the fact that the critical Reynolds number would be different in open channels as compared to circular pipes flowing full.     

Timescale Behavior of the Wall Shear Stress in Unsteady Laminar Pipe Flows

Based on two-dimensional (2D) flow model simulations, the effects of the radial structure of the flow (e.g., the nonuniformity of the velocity profile) on the pipe wall shear stress, τw, are determined in terms of bulk parameters such as to allow improved 1D modeling of unsteady contribution of τw. An unsteady generalization, for both laminar and turbulent flows, of the quasi-stationary relationship between τw and the friction slope, J, decomposes the additional unsteady contribution into an instantaneous energy dissipation term and an inertial term (that is, based on the local average acceleration-deceleration effects). The relative importance of these two effects is investigated in a transient laminar flow and an analysis of the range of applicability of this kind of approach of representing unsteady friction is presented. Finally, the relation between the additional inertial term and Boussinesq momentum coefficient, is clarified. Although laminar pipe flows are a special case in engineering practice, solutions in this flow regime can provide some insight into the behavior of the transient wall shear stress, and serve as a preliminary step to the solutions of unsteady turbulent pipe flows.     

Laboratory Measurements of Flow and Turbulence in Discontinuous Distributions of Ligulate Seagrass

Turbulent flow characteristics were investigated in laboratory flume studies of a ligulate plant canopy interrupted by a gap representing discontinuities observed in seagrass prairies. The reliability of velocity measurements obtained using an acoustic Doppler velocimeter within the canopy was shown using specifically designed experiments. In relatively fast flow (mean velocity 5.5?cm?s?1), the mean flow profile was logarithmic above the canopy, had an inflection point near its top, and uniformly low values within it. Within the gap, a recirculation cell formed. Reynolds stress maxima were approximately coincident with the mean flow inflection point. Quadrant analysis revealed an ejection-dominated upper layer, a sweep-dominated region around the top of the canopy and within the gap, and no dominant quadrant within the canopy. In slower flow (mean velocity 1.7?cm?s?1) the plants were quasiemergent and the flow fields more uniform. Sweeps similarly dominated the region near the top of the canopy and within the gap. In both flows, autocorrelation of longitudinal velocity fluctuations showed a Lagrangian time scale maximum at the downstream end of the gap.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.