Uniform Channel Flow Research Articles

Motion blur treatment utilizing deep learning for time-resolved particle image velocimetry

A new method is hereby presented to reduce motion blur induced error of time-resolved particle image velocimetry. The Monte-Carlo method (MCM) was applied to synthetic images to quantify the error due to blurred particle images. As the size of the streaks grew, it caused large errors in estimating displacements and increased the frequency of outliers beyond 20% for some cases. The mean displacement error was also about 0.2 – 0.55 px, which is larger than the nominally accepted PIV uncertainty of 0.1 px. A novel deblur filter (i.e., the generator) using a generative adversarial network (GAN) was developed, using 1 million synthetic images. The generator was verified using unlearned data from the MCM. The frequency of outliers, which was originally higher than 20% for the worst case, decreased to about 6%, and the displacement error was reduced to less than 0.3 px. The generator was applied to actual experimental images of a synthetic jet that had image blur and resulted in a substantial reduction of outliers. We also checked the performance of the generator in a uniform channel flow, and found that the deblurred images resulted in less PIV velocity error, and was closer to the results from the sharp images than those from the blurry images.Graphic abstract

Three-Dimensional Velocity Distribution in Straight Smooth Channels Modeled by Modified Log-Law

Time-average velocity distribution in steady and uniform channel flows is important for fundamental research and practical application as it is always three-dimensional (3D), regardless of channel geometry. However, its determination has predominantly been carried out by using complex numerical software, even for the simplest geometry such as rectangular channels. The log-law was developed initially for circular pipe flows, where a single shear velocity is used to normalize the velocity (u+) and its distance (y+). Tracy and Lester found that the performance of the log-law can be extended to express velocity profiles in rectangular channels when the global shear velocities (gRS)0.5 and (ghS)0.5 are used to normalize the measured velocity u and its distance y. This study extends this discovery from the channel central line to the corner regions, and its general form of log-law was found to be valid even in trapezoidal or triangular open channels or closed ducts. This modified log-law can produce good agreement with the measured velocity with an average error of less than 5%. Therefore, this study provides a simple and reliable tool for engineers and researchers to estimate the velocity contours in straight and smooth channel flows.

Development of in/outflow boundary conditions for MPM simulation of uniform and non-uniform open channel flows

This paper describes the development and application of inflow and outflow boundary conditions (BCs) for the material point method (MPM) in order to simulate fluid flow problems. This corresponds to velocity and pressure controlled BCs. Due to the coupled Lagrangian and Eulerian description of the fluid motion in MPM it is necessary to add and remove material points, with appropriate kinematic properties, to and from the computational domain. The newly-developed BCs have been used to simulate uniform open channel flow and the phenomenon of free overfall in open channels, which is transient conditions leading to non-uniform flow due to a sudden bed level drop. It is shown that the numerical results predict well the flow geometry including end depth ratio, pressure distribution and accelerations, therefore the velocities and displacements.

Manning’s formula and Strickler’s scaling explained by a co-spectral budget model

Manning’s empirical formula in conjunction with Strickler’s scaling is widely used to predict the bulk velocity$V$from the hydraulic radius$R_{h}$, the roughness size$r$and the slope of the energy grade line$S$in uniform channel and pipe flows at high bulk Reynolds numbers. Despite their importance in science and engineering, both Manning’s and Strickler’s formulations have waited for decades before finding a theoretical explanation. This was provided, for the first time, by Gioia & Bombardelli (Phys. Rev. Lett., vol. 88, 2002, 014501), labelled as GB02, using phenomenological arguments. Perhaps their most remarkable finding was the link between the Strickler and the Kolmogorov scaling exponents, the latter pertaining to velocity fluctuations in the inertial subrange of the turbulence spectrum and presumed to be universal. In this work, the GB02 analysis is first revisited, showing that GB02 employed severalad hocscaling assumptions for the turbulent kinetic energy dissipation rate and, although implicitly, for the mean velocity gradient adjacent to the roughness elements. The similarity constants arising from the GB02 scaling assumptions were presumed to be independent of$r/R_{h}$, which is inconsistent with well-known flow properties in the near-wall region of turbulent wall flows. Because of the dependence of these similarity constants on$r/R_{h}$, this existing theory requires the validity of the Strickler scaling to cancel the dependence of these constants on$r/R_{h}$so as to arrive at the Strickler scaling and Manning’s formula. Here, the GB02 approach is corroborated using a co-spectral budget (CSB) model for the wall shear stress formulated at the cross-over between the roughness sublayer and the log region. Assuming a simplified shape for the spectrum of the vertical velocity$w$, the proposed CSB model (subject to another simplifying assumption that production is balanced by pressure–velocity interaction) allows Manning’s formula to be derived. To substantiate this approach, numerical solutions to the CSB over the entire flow depth using different spectral shapes for$w$are carried out for a wide range of$r/R_{h}$. The results from this analysis support the simplifying hypotheses used to derive Manning’s equation. The derived equation provides a formulation for$n$that agrees with reported values in the literature over seven decades of$r$variations. While none of the investigated spectral shapes allows the recovery of the Strickler scaling, the numerical solutions of the CSB reproduce the Nikuradse data in the fully rough regime, thereby confirming that the Strickler scaling represents only an approximate fit for the friction factor for granular roughness.

Baroclinic instability of axially symmetric flow over sloping bathymetry

Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical two-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Non-zero barotropic flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

Theoretical analysis and numerical simulation of mechanical energy loss and wall resistance of steady open channel flow

The mechanical energy loss and the wall resistance are very important in practical engineering. These problems are investigated through theoretical analysis and numerical simulation in this paper. The results are as follows. (1) A new mechanical energy equation for the total flow is obtained, and a general formula for the calculation of the mechanical energy loss is proposed. (2) The general relationship between the wall resistance and the mechanical energy loss for the steady channel flow is obtained, the simplified form of which for the steady uniform channel flow is in consistent with the formula used in Hydraulics deduced by π theorem and dimensional analysis. (3) The steady channel flow over a backward facing step with a small expansion ratio is numerically simulated, and the mechanical energy loss, the wall resistance as well as the relationship between the wall resistance and the mechanical energy loss are calculated and analyzed.

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

Micro diffuser flow modeling for cold gas propulsion systems

AbstractThe use of highly diluted and hypersonic gas flow is in the scope of application of cold gas thrusters for space applications. Satellites and small spacecrafts are navigated to their orbital trajectory with these nozzles. Inside these propulsion systems high density gradients are dominating the efficiency and the thrust steering behavior of the propulsion systems.Micro flows in the transient regime between free molecular flow and continuous flow are not able to be computed with trustworthy results by using a continuous model with no‐slip boundary conditions. Therefore boundary slip‐velocity models are used for modeling the reduced wall shear stress. Molecular shear stresses decrease the molecular mean velocity near the wall. With a Knudsen number depending slip‐velocity model the effective shear stress is computed by the mean gradient of the velocity profile near the wall.In the present study a trans‐sonic nozzle flow is computed by using a calibrated velocity slip model what depends on the Knudsen number. The Knudsen numbers are lower the Kn=1 at the nozzle neck of the propulsion system. The results are compared with simulation results of a uniform channel flow and computations of the corresponding no‐slip approach. The differences in the hypersonic region are following discussed. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Accurate vertical profiles of turbulent flow in z‐layer models

AbstractThree‐dimensional hydrodynamic z‐layer models, which are used for simulating the flow in rivers, estuaries, and oceans, suffer from an inaccurate and often discontinuous bottom shear stress representation, due to the staircase bottom. We analyze the governing equations and clearly show the cause of the inaccuracies. Based on the analysis, we present a new method that significantly reduces the errors and the grid dependency of the results. The method consists of a near‐bed layer‐remapping and a modified near‐bed discretization of the k − ε turbulence model. We demonstrate the applicability of the approach for uniform channel flow, using a schematized two‐dimensional vertical model and for the flow over a bottom sill using the Delft3D modeling system.

Flume experimental evaluation of the effect of rill flow path tortuosity on rill roughness based on the Manning–Strickler equation

Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v=kStR2/3I1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughness which is in conflict with the assumptions of (sectional) uniform channel flow and constant channel roughness of the Manning–Strickler equation.The objective of this study is to evaluate the effect of rill morphology on roughness and hence to assess the Manning–Strickler roughness coefficient (kSt) by rill morphological data. A laboratory experiment was set up to analyse rill hydraulics and roughness of I.) Free Developed Rill (FDR) flows and II.) Straight Constrained Rill (SCR) flows in the flume. The flume experiment generated Manning–Strickler roughness coefficients (kSt) between 22m1/3s−1 and 44m1/3s−1 reflecting a potential area of the roughness parameter uncertainty. It was found that FDR experiments generated significantly lower kSt values compared to SCR experiments, because skin and local friction effects in the FDR experiments were more efficient reducing flow velocity probably due to higher energy dissipation. Rill flow path tortuosity (Tort) was used to describe the rill morphology of the experiments and correlation statistics between Tort and kSt identified considerable explanatory capacity of rill flow path tortuosity on rill roughness. The flume study demonstrated that a regression model between Tort and kSt can be used to assess local friction effects of unconfined rill morphologies and hence to reduce the area of uncertainty of the Manning–Strickler roughness parameter.

Comments on the separation efficiency of asymmetrical flow field-flow fractionation in channels of constant channel and crossflow velocities leading to constant separation efficiency

It is shown theoretically that a claim in the literature about the overall separation efficiency of asymmetrical flow FFF channels being improved by geometries that permit a uniform channel flow velocity throughout the channel length is untrue.

A two-dimensional lattice Boltzmann model for uniform channel flows

In this paper a novel two-dimensional lattice Boltzmann model (LBM) is developed for uniform channel flows. The axial velocity is solved from a momentum diffusion equation over the cross-sectional plane. An extrapolation boundary condition is also introduced to enhance the no-slip boundary in the momentum equation. This boundary treatment can also be applied to LBM simulations of other diffusion processes. The algorithm and boundary treatment are validated by simulations of steady Poiseuille and pulsatile Womersley flows in circular pipes. The numerical convergence and accuracy are comparable to those of existing models. Moreover, comparison with general three-dimensional lattice Boltzmann simulations demonstrates the advantages of our two-dimensional model, including lower computational resource requirements (memory and time), easier boundary treatment for arbitrary cross-sectional shapes, and no velocity constraint. These features are attractive for practical applications with uniform channel flows.

Nonlinear Mixing Length Model for Prediction of Secondary Currents in Uniform Channel Flows

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated.

Liquid–granular channel flow dynamics

The paper tackles some important issues regarding the dynamics of mixtures of grains and water, on the basis of a series of experiments on uniform channel flows of non-cohesive particles and water. Precise measurements of the granular concentration, temperature, velocity, normal and shear stresses are presented. The experiments show the existence of an unstable stratification of collisional and frictional regimes, and, with reference to the time integrated variables, to a relatively smooth transition between the two regimes. The experimental data were interpreted following Bagnold's theory and the kinetic theories. Finally, the paper presents and discusses global relationships in uniform flow condition among depth-integrated parameters (slope, solid and liquid average concentrations, average velocity, water and grains flow depth).

Momentum Exchange in Straight Uniform Compound Channel Flow

Transverse exchange of momentum between the channel and the floodplain in straight uniform compound channel flow is considered in this paper. This process results in the so-called “kinematic effect,” a lowering of the total discharge capacity of a compound channel compared to the case where the channel and the floodplain are considered separately. The mechanisms responsible for the momentum exchange are considered. The transverse shear stress in the mixing region is modeled using a newly developed effective eddy viscosity concept, that contains: (1) the effects of horizontal coherent structures moving on an uneven bottom, taking compression and stretching of the vortices into account and (2) the effects of the three-dimensional bottom turbulence. The model gives a good prediction of the transverse profiles of the streamwise velocity and the transverse shear stress of the flood channel facility experiments. Characteristic features of the lateral profile of the eddy viscosity are also well predicted qualita...

Flow of a visco-plastic fluid in a channel of slowly varying width

We develop an asymptotic solution for the Poiseuille flow of a Bingham fluid along a two-dimensional channel of slowly varying width, for the case of small amplitude width variation, h . We show that an asymptotic solution with an intact unyielded plug region can be found for h less than a critical value h c ∼ O ( δ ) , where δ is the aspect ratio (channel half-width to wavelength of the variation). Our method involves no form of relaxation of the exact Bingham model. We provide upper and lower estimates for h c . The function h c / δ shows little variation with δ ≪ 1 , and exhibits a maximum in Bingham number, B , at around B ≈ 5 . There is a small variation in the true plug speed from that of the uniform channel flow. At small B the perturbed plug moves slightly slower than that in the uniform channel, whereas at large B the true plug moves faster than the uniform channel flow. Finally, we consider the structure of the flow for h ∼ O ( 1 ) , for which the plug has broken.

On establishing uniform channel flow with tail gate

On establishing uniform channel flow with tail gate

On establishing uniform channel flow with tail gate

Steady uniform flow is a basic reference condition for hydraulic analyses of water surface profiles, resistance, velocity and pressure distributions, and channel geometry effects for open-channel flows. In laboratory experiments uniform flow is often generated by adjusting tail and entrance gates such that the flow depth remains constant along the channel. This note shows that the constant depth criterion is necessary, but insufficient, to obtain a true uniform flow for which cross-sectional flow velocity and stress distributions should also remain unchanged for a short reach around the measurement section.

On establishing uniform channel flow with tail gate

Steady uniform flow is a basic reference condition for hydraulic analyses of water surface profiles, resistance, velocity and pressure distributions, and channel geometry effects for open-channel flows. In laboratory experiments uniform flow is often generated by adjusting tail and entrance gates such that the flow depth remains constant along the channel. This note shows that the constant depth criterion is necessary, but insufficient, to obtain a true uniform flow for which cross-sectional flow velocity and stress distributions should also remain unchanged for a short reach around the measurement section.

Investigation of bed shear stresses subject to external turbulence

The fluctuating bed shear stress has largely been investigated only for uniform channel flows and boundary layers. In practical engineering, the flow conditions are often modified due to the presence of various hydraulic structures. To what extent the modification affects the known characteristics of the bed shear stress is not clear. This study presents experimental results of the bed shear stress fluctuations, which are obviously subjected to external turbulence generated by superimposing artificial structures in the open channel flows. The statistical analysis of the measurements shows that the probability density function of the bed shear stress can be described by the lognormal function. Some associated relations concerning higher-order moments, skewness and kurtosis, which are derived from the lognormal function, are further compared with the experimental data. Physical implication of the skewed probability density distribution is finally discussed.