3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. I: Numerical Model

A general-purpose numerical method is developed for solving the full three-dimensional (3D), incompressible, unsteady Reynolds-averaged Navier-Stokes (URANS) equations in natural river reaches containing complex hydraulic structures at full-scale Reynolds numbers. The method adopts body-fitted, chimera overset grids in conjunction with a grid-embedding strategy to accurately and efficiently discretize arbitrarily complex, multiconnected flow domains. The URANS and turbulence closure equations are discretized using a second-order accurate finite-volume approach. The discrete equations are integrated in time via a dual-time-stepping, artificial compressibility method in conjunction with an efficient coupled, block-implicit, approximate factorization iterative solver. The computer code is parallelized to take full advantage of multiprocessor computer systems so that unsteady solutions on grids with 106 nodes can be obtained within reasonable computational time. The power of the method is demonstrated by applying it to simulate turbulent flow at R ? 107 in a stretch of the Chattahoochee River containing a portion of the actual bridge foundation located near Cornelia, Georgia. It is shown that the method can capture the onset of coherent vortex shedding in the vicinity of the foundation while accounting for the large-scale topographical features of the surrounding river reach.     

3D CFD Predictions and Experimental Comparisons of Pressure Drop in a Ball Valve at Different Partial Openings in Turbulent Flow

A three dimensional computational fluid dynamics model, using the STAR-CD software, has been developed to simulate fluid flow in a commonly used flanged ball valve at different partially open settings. The Reynolds number (Re) range for the flow simulations was varied between 105 and 106 to simulate a variety of flow conditions. Each flow Re number is studied with three open positions for the valve, i.e., fully open, two-thirds open, and one-third open. The simulation was used to calculate two important parameters used in characterizing the flow properties in a typical valve namely the loss coefficient, K, and the flow coefficient, Cv. An attempt was also made to compare some of the simulation results with experimental data and available American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) data on valves. The simulations agree reasonably well with recently published experimental results and indicate that in most cases the K factor is independent of Re. The ASHRAE data for K factor values showed similar trends to the simulation but with lower values as it was only reported for gates valves. The Cv values show strong increases with the degree of valve opening and lesser influence by the Re number variations in the range studied     

Installation of Torpedo Anchors: Numerical Modeling

Torpedo anchors are used as foundations for mooring deep-water offshore facilities, including risers and floating structures. They are cone-tipped cylindrical steel pipes ballasted with concrete and scrap metal and penetrate the seabed by the kinetic energy they acquire during free fall through the water. A mooring line is usually connected at the top of the anchor. The design of such anchors involves estimation of the embedment depth as well as short-term and long-term pullout capacities. This paper describes the development of a computational procedure that leads to prediction of torpedo-anchor embedment depth. The procedure relies on a computational fluid dynamics (CFD) model for evaluation of the resisting forces on the anchor. In the model, the soil is represented as a viscous fluid and the procedure is applied to axially symmetric penetration of the seabed. The CFD approach provides estimates of not only the embedment depth but the pressure and shear distributions on the soil-anchor interface and in the soil.     

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

Numerical Investigation into Secondary Currents and Wall Shear in Trapezoidal Channels

This paper presents the use of computational fluid dynamics (CFD) to determine the distribution of the bed and sidewall shear stresses in trapezoidal channels. The impact of the variation of the slant angle of the side walls, aspect ratio, and composite roughness on the shear stress distribution is analyzed. The shear stress data can be directly output from the CFD models at the boundaries, but they can also be derived using the Guo and Julien equations for the average bed and side wall shear stresses. These equations compute the shear stress as a function of three components; gravitational, secondary flows, and interfacial shear stress, and are hence used to gauge the respective merits of the different components of wall shear. The results show a significant contribution from the secondary currents and internal shear stresses on the overall shear stress at the boundaries. This work also extends previous work of the authors on rectangular channels.     

Numerical Evaluation of Wind Flow over Complex Terrain: Review

This paper reviews the current state of the art in the numerical evaluation of wind flow over different types of topographies. Numerical simulations differing from one another by the type of numerical formulation followed, the turbulence model used, the type of boundary conditions applied, the type of grids adopted, and the type of terrain considered are summarized. A comparative study among numerical and experimental (both wind tunnel and field) existing works establishing the modifications of wind flow over hills, escarpments, valleys, and other complex terrain configurations demonstrates generally good predictions on the upstream but problematic predictions on the downstream areas of the complex terrain. Comparisons are also made with provisions of the current wind standards as well as with speed-up values calculated using guidelines derived from theoretical models.     

Numerical Simulation of Groundwater Flow with Gradually Increasing Heterogeneity due to Clogging

Well injection replenishes depleting water levels in a well field. Observation well water levels some distance away from the injection well are the indicators of the success of a well injection program. Simulation of the observation well response, located a few tens of meters from the injection well, is likely to be affected by the effects of nonhomogeneous medium, inclined initial water table, and aquifer clogging. Existing algorithms, such as the U.S. Geological Survey groundwater flow software MODFLOW, are capable of handling the first two conditions, whereas time-dependent clogging effects are yet to be introduced in the groundwater flow models. Elsewhere, aquifer clogging is extensively researched in theory of filtration; scope for its application in a well field is a potential research problem. In the present paper, coupling of one such filtration theory to MODFLOW is introduced. Simulation of clogging effects during “Hansol” well recharge in the parts of western India is found to be encouraging.     

Modeling 3D Supercritical Flow with Extended Shallow-Water Approach

Despite the three-dimensional (3D) nature of the flow, the classical shallow-water equations are often used to simulate supercritical flow in channel transitions. A closer comparison with experimental data, however, often shows large discrepancies in the height and pattern of the shock waves that increase with the Froude number. An extension to the classical shallow-water approach is derived considering higher-order distribution functions for pressure and horizontal and vertical velocities, therefore taking nonhydrostatic pressure distribution and vertical momentum into account. The approach is applied to highly supercritical flow in a channel contraction (F0 = 4.0), a channel junction (F0 ≈ 4.5 for both branches), and a channel expansion (F0 = 8.0). Specific problems of such flows—wetting and drying of computational cells and wave breaking due to steep free-surface gradients—are discussed and solved numerically. The solutions with the extended approach are compared both with experimental data and classical shallow-water computations, and the influence of the additional terms considering the 3D nature of such flows is illustrated.     

Three-Dimensional CFD Predications and Experimental Comparison of Pressure Drop of Some Common Pipe Fittings in Turbulent Flow

A three-dimensional computational fluid dynamics (CFD) model has been constructed to simulate fluid flow in two commonly used pipe fittings: An elbow and a T-joint using the STAR-CD code. A k-ε Chen model suitable for high Re numbers flows was used for that purpose. Two flow configurations were used for the T-joint. In the first, the flow enters through the middle leg of the fitting; and in the second, the flow enters from one of the ends and exits from the other two outlets. The Re number for the flow simulations was varied between 0.78×105 and 1.56×105 to simulate a variety of flow conditions with approximately six uniformly distributed values of Re numbers chosen between these limits. The velocity profile indicated some flow reversal regions near the inner radius and some high velocity regions near the outer radius downstream of the elbow. Pressure profiles showed significant changes from a high value on the outer radius to a low one on the inner radius. The T-joint flow case into the center leg showed recirculation regions immediately downstream of the elbows, and high velocity values just downstream from the stagnation zone. The pressure profile for that arrangement showed significant pressure gradients across the flow area before the flow splits into the two legs. For the straight leg inflow case, the velocity shows flow reversals in the 90° bend and the pressure drop is large along the 90° bend as opposed to the straight leg. The simulation uses a flow split of 50–50 between those legs. The simulations agree reasonably well with recently published experimental results. For the T-joint and with the flow introduced through the straight branch (T-joint-Inlet Case B), the difference in pressure drop for the straight run and branch flow was 7.76% and 18.38%, respectively. For the elbow, the difference was 8.1% lower than the experiment. Comparisons were also made with values supplied by the ASHRAE Handbook for K values, i.e., minor loss factors.     

External Iterative Coupling Strategy for Surface-Subsurface Flow Calculations in Surface Irrigation

Coupling the unsteady open-channel flow equations of surface irrigation with the equation of variably saturated porous media flow is a computationally complex problem because of the dependence of infiltration on surface-flow depths. Several models of this coupled process have been developed, all of which solve the surface and subsurface flow iteratively at each time step of the surface-flow solution. This study presents an alternative strategy, in which stand-alone surface and subsurface-flow models are used to conduct the calculations sequentially and iteratively at the time level of the irrigation event. At each iteration, the subsurface-flow results are computed using the surface-flow depths generated by the surface-flow model at the current iteration. Infiltration results computed at selected computational nodes are fitted to an empirical infiltration function, and then fed back to the surface-flow model. The proposed strategy, labeled external iterative coupling, was prototyped for border and basin irrigation systems using the WinSRFR and HYDRUS-1D models. The proposed procedure produced irrigation performance results comparable to those generated with an internally coupled model, even when using a single representative location to calibrate the empirical infiltration equation used by the surface-flow model. In comparison with models that iterate at each time step, the proposed coupling strategy reduces the computational effort and improves convergence. The approach provides a practical alternative for coupling existing and future surface and subsurface flow models.     

Accuracy Order of Crank–Nicolson Discretization for Hydrostatic Free-Surface Flow

Application of Crank–Nicolson (CN) discretization to the hydrostatic (or shallow-water) free-surface equation in two-dimensional or three-dimensional Reynolds-averaged Navier–Stokes models neglects a second order term. The neglected term is zero at steady state, so it does not appear in steady-state accuracy analyses. A new correction term is derived that restores second-order accuracy. The correction is significant when the amplitude of the surface oscillation is within two orders of magnitude of the water depth and the barotropic Courant–Friedrichs–Lewy (CFL) stability condition is less than unity. Analysis shows that the CN accuracy for an unforced free-surface oscillation is degraded to first order when the barotropic CFL stability condition is greater than unity, independent of whether or not the new correction term is applied. The results indicate that the semi-implicit Crank–Nicolson method, applied to the hydrostatic free-surface evolution equation, is only first-order accurate for the time and space scales typically used in lake, estuarine, and coastal ocean studies.     

Coherent Structure Dynamics in Turbulent Flows Past In-Stream Structures: Some Insights Gained via Numerical Simulation

Large-scale coherent vortical structures in natural streams and rivers dominate flow and transport processes and impact the stability of stream banks, the diversity and abundance of organisms, and the quality of running waters in aquatic ecosystems. Thus, understanding and being able to model the dynamics of energetic coherent structures in such flows at ecologically relevant scales are crucial prerequisites for developing a science-based ecosystem restoration framework. We review recent progress toward the development of coherent-structure-resolving (CSR) computational fluid dynamics techniques, based on hybrid URANS/LES modeling strategies, for simulating turbulent flows in open-channels with hydraulic structures. CSR simulations of the turbulent horseshoe vortex (THSV) past bed-mounted piers explained the physical mechanism leading to the experimentally documented bimodal velocity fluctuations of the vortex and underscored the importance of the Reynolds number as a key parameter governing the THSV dynamics. Simulations of high Reynolds number flows past surface-piercing, groynelike structures in open channels revealed the complexity of the recirculating region at the upstream face of the groyne, underscored the interaction of the flow in this region with the energetic shear layer shed from the point of separation at the upstream side wall, and demonstrated the importance of flow depth in the vorticity dynamics of such flows. The paper also identifies areas for future work and modeling challenges that need to be addressed for the computational tools to be able to accurately predict flow and transport processes in real-life aquatic environments.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.     

Three-Dimensional Numerical Modeling of Initial Mixing of Thermal Discharges at Real-Life Configurations

A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.     

Numerical Simulation of Equal and Opposing Subcritical Flow Junctions

This study presents measured and computational results of a flow pattern at a junction with equal and opposing flows in the upstream channel that collide and turn 90° into the branch channel. The computational results are obtained using a two-dimensional, depth-averaged model with the k-ε turbulent closure scheme. The aim is to predict the recirculation zones that form as the flow turns into the branch channel. The simulated depth and velocity profiles in the upstream main and the downstream branch channels are found to compare well with the measurements made in the physical model for various inlet Froude numbers and width ratios of the main channel to the branch channel. The absolute relative error between the measured and computed contraction coefficient, a measure of the recirculation zone size, is less than 4.7%. The computational model is then used to develop curves for the contraction coefficient for various inlet Froude numbers and ratios of main channel width to the branch channel width for design purposes.     

Steady and Unsteady Simulations of Turbulent Flow and Transport in Ultraviolet Disinfection Channels

The effects of unsteadiness in the turbulent flow through a staggered array of circular cylinders, modeling an ultraviolet disinfection system, are studied by means of solutions of the two-dimensional Reynolds-averaged Navier–Stokes equations incorporating the standard k–? turbulence model. Time averaging is applied to the unsteady solution, and the time-averaged characteristics are compared with a solution where a steady flow is a priori assumed, as well as with time-averaged measurements. Differences between the predictions of time-averaged and the steady-flow models are found to be largest in the entrance region of the array, and to decline in importance in the downstream direction. Comparison with measurements indicate that, while the time-averaged unsteady model predictions exhibited better agreement in some respects, the turbulent kinetic energy remained substantially underpredicted. Predictions of head losses through the array are also discussed.     

Laminar Pipeline Flow of Wastewater Sludge: Computational Fluid Dynamics Approach

A computational fluid dynamics (CFD) technique applied to laminar flow of wastewater sludge in horizontal, circular pipes is presented. The technique employs the Crank-Nicolson finite difference method in conjunction with the variable secant method, an algorithm for determining the pressure gradient of the flow. Head loss (pressure drop) and velocity profile are predicted using the technique. Numerical predictions of head loss and velocity profile for several combinations of flows, pipe sizes, and sludge solids concentrations are compared to exact analytical values, derived from the theory of laminar flow of Bingham-plastic fluids. The predicted values are in good agreement with the exact values. Comparisons are also made to head loss values for municipal wastewater sludge from the literature. The CFD technique has several advantages over the analytical calculations, including ease of use, time efficiency, and the ability to readily change boundary conditions, flow geometry, and the rheological model for the shear stress.     

Errors in Acoustic Doppler Profiler Velocity Measurements Caused by Flow Disturbance

Acoustic Doppler current profilers (ADCPs) are commonly used to measure streamflow and water velocities in rivers and streams. This paper presents laboratory, field, and numerical model evidence of errors in ADCP measurements caused by flow disturbance. A state-of-the-art three-dimensional computational fluid dynamic model is validated with and used to complement field and laboratory observations of flow disturbance and its effect on measured velocities. Results show that near the instrument, flow velocities measured by the ADCP are neither the undisturbed stream velocity nor the velocity of the flow field around the ADCP. The velocities measured by the ADCP are biased low due to the downward flow near the upstream face of the ADCP and upward recovering flow in the path of downstream transducer, which violate the flow homogeneity assumption used to transform beam velocities into Cartesian velocity components. The magnitude of the bias is dependent on the deployment configuration, the diameter of the instrument, and the approach velocity, and was observed to range from more than 25% at 5?cm from the transducers to less than 1% at about 50?cm from the transducers for the scenarios simulated.     

Computational Fluid Dynamics Study of a Noncontact Handling Device Using Air-Swirling Flow

The vortex gripper is a recently developed pneumatic noncontact handling device that takes advantage of air-swirling flow to cause upward lifting force and that thereby can pick up and hold a work piece placed underneath without any contact. It is applicable where, e.g., in the semiconductor wafer manufacturing process, contact should be avoided during handling and moving in order to minimize damage to a work piece. For the purpose of a full understanding of the mechanism of the vortex gripper, a computational fluid dynamics (CFD) study was conducted in this paper, and at the same time, experimental work was carried out to measure the pressure distribution on the upper surface of the work piece. First, three turbulence models were used for simulation and verified by comparison with the experimental pressure distribution. It is known that the Reynolds stress transport model (RSTM) can reproduce the real distribution better. Then, on the basis of the experimental and numerical result of RSTM, an insight into the vortex gripper and its flow phenomena, including flow structure, spatial velocity, and pressure distributions, and an investigation into the influence of clearance variation was given.