Junke Guo

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Eddy viscosity and complete log-law for turbulent pipe flow at high Reynolds numbers

Journal of Hydraulic Research, 2016

ABSTRACT Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles... more ABSTRACT Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles' log-wake law for which the wake component is purely empirical. This research innovates Coles' wake law with another log-function, and thus combines the log- and the wake-laws into a single (complete) log-law, for which the von Kármán constant (0.39) is the only fit parameter. Specifically, the symmetrical velocity distribution about the centreline requires a symmetrical eddy viscosity model which is approximated by a quartic polynomial, leading to a complete log-law including the effects of the bottom and top walls as well as their interactions. The complete log-law is confirmed with data from both smooth and rough pipes; it also results in an accurate and explicit friction law for smooth pipe flow. Furthermore, the complete log-law is preliminarily tested with data from channels and boundary layers; the quartic eddy viscosity may be extended for ice-covered river flow in future studies.

Discussion of "The Albert Shields Story

Journal of Hydraulic Engineering, 1997

The Log-Law of the Wall in the Overlap from a Functional Equation

Journal of Engineering Mechanics

Application of General Unit Hydrograph Model for Baseflow Separation from Rainfall and Streamflow Data

Journal of Hydrologic Engineering

General and Analytic Unit Hydrograph and Its Applications

Journal of Hydrologic Engineering, 2022

Second Log-Wake Law from Pipe Symmetry and its Applications in Symmetric and Antisymmetric Channel Flows

Journal of Hydraulic Engineering, 2020

AbstractThe velocity distribution of turbulent pipe flow is often described by the Coles log-wake... more

Maximum Shear-Stress Method for Stable Channel Design

Journal of Hydraulic Engineering, 2020

AbstractStable channel design is important for conveying water among stakeholders in a safe and c... more

Exact Solution for Depth of Impact Crater into Granular Bed

Journal of Engineering Mechanics, 2018

AbstractWhen a sphere impacts a granular bed such as a sand bed, the penetration depth is often d... more

General Mean Velocity Distribution Law for Smooth-Wall Plane Couette Flow

Journal of Engineering Mechanics, 2018

AbstractPlane Couette flow between two parallel smooth walls is one of the classic wall-bounded s... more

Exact Solution for Asymmetric Turbulent Channel Flow with Applications in Ice-Covered Rivers

Journal of Hydraulic Engineering, 2017

AbstractAsymmetric turbulent channel flow, such as ice-covered river flow, is a century-old probl... more

Scour, Flooding, and Inundation

Public Roads, 2010

The FHWA hydraulics R&D program conducts advanced and applied research to mitigate disaster r... more

Turbulent velocity profiles in clear water and sediment- laden flows

Thesis Colorado State University Source Dai B 59 05 P 2330 Nov 1998 237 Pages, Nov 1, 1998

Turbulent velocity profiles in pipes and open-channels are studied. The purpose is to find a suit... more Turbulent velocity profiles in pipes and open-channels are studied. The purpose is to find a suitable velocity profile for the entire boundary layer, particularly near the water surface, and to study the effects of sediment suspension on the model parameters. A modified log-wake law is proposed. It consists of three parts: a log term, a wake term, and a linear term. Physically, the log term reflects the inertia effect, the wake term reflects the large scale turbulent mixing, and the linear term reflects the upper boundary condition. In open-channels, the log term reflects the effect of the bed, the wake term reflects the effect of the side-walls, and the linear term reflects the wind shear at the water surface. For pipes, the new law contains two universal constant: the von Karman constant kappa0=0.406 and the wake strength Omega0=3.2. For narrow open-channels, the velocity profile equation is similar to that in pipes except that the wake strength Omega0 decreases with the width-depth ratio. For wide open-channels, the wake term may be neglected. The modified log-wake law then reduces to a log-linear law. The von Karman constant kappa0 is still 0.406. The water surface shear stress is considered through the parameter lambda0 which is about a constant 0.065 for a smooth bed at small relative roughness, but increases with the relative roughness in very rough beds. The modified log-wake law is also valid in sediment-laden flows. Sediment affects the velocity profile in two different ways: concentration and density gradient. Both reduce the von Karman constant /kappa . However, both have little effect on the wake term and the linear term. The new law compares quite well with over 100 experimental velocity profiles in pipes and open-channels. The correlation coefficients r are always over 0.99.

Turbulent velocity distribution with dip phenomenon in conic open channels

Journal of Hydraulic Research, 2014

ABSTRACT Conic open-channel flow as occurs in sub-drains, sewers, and culverts is computed by Man... more ABSTRACT Conic open-channel flow as occurs in sub-drains, sewers, and culverts is computed by Manning's or Darcy's resistance equations for the cross-sectional average velocity only. Yet, fish passage culvert design requires the cross-sectional velocity distribution, which is proposed in this paper based on two hypotheses: (i) centreline velocity distribution follows the conventional log-law with a cubic deduction near the water surface; (ii) cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law but neglecting the squared sine function. These hypotheses result in a novel and simple velocity distribution model without any fitting parameter. Its graphical interpretation for the elliptic, parabolic, and hyperbolic channels indicates reasonable velocity contours with dip phenomenon. Further, it agrees well with circular pipe data related to the average shear velocity, velocity-dip position, centreline and cross-sectional velocity distributions. A potential application includes fish passage culvert design by specifying a low velocity zone near the wall.

Applied Mathematical Model for Turbulent Boundary Layers

World Environmental and Water Resource Congress 2006, 2006

We present a complete analytical model for mean velocity profile in turbulent boundary layers. Th... more We present a complete analytical model for mean velocity profile in turbulent boundary layers. The model integrates the conventional log-wake law and the Barenblatt power (scaling) law in the intermediate region so that it includes the effects of the Reynolds number. Furthermore, it includes the effects of the wall and the boundary layer edge so that the model can describe the entire turbulent boundary layer mean velocity profile analytically. The model has been confirmed with recent laboratory experimental data of Osterlund. Introduction The mean velocity profile in turbulent boundary layers is usually described by the log law or the log-wake law (Coles 1956). Barenblatt et al. (2002, 2004) challenged this conventional argument and triggered hot debates on this classical subject. They claimed that the mean flow in wall-bounded turbulent flow has a persistent dependence on the Reynolds number, and that the well known logarithmic law of the wall is invalid. They believed that a Reynolds number dependent power (scaling) law better describes velocity profiles in wall-bounded flows. In particular, zero-pressure-gradient boundary layer flows follow two sharply separated power laws (Barenblatt et al. 2002). Others (Osterlund et al. 2000, Zanoun et al. 2003, Bushmann and Gad-El-Hak 2003) defended the classical logarithmic law by doing experiments and various analyses. All the discussions are limited to the overlap layer. Our studies (Guo and Julien 2003, Guo et al. 2005) showed that both the conventional log-wake law and the Barenblatt power law have merits and weaknesses. Both laws are intermediate asymptote and are not valid near the wall and near the boundary layer edge, except that Barenblatt's two power laws (Barenblatt et al. 2002) are not smoothly connected. Nevertheless, the log-wake law is simpler, and the power law includes the effects of the Reynolds number and is more realistic. Integrating the conventional log-wake law and the Barenblatt power law and considering the effects of the wall and the upper boundary layer edge, we in this paper propose an applied mathematical model for zero-pressure-gradient turbulent boundary layers. Referring to Fig. 1, we divide a boundary layer flow into two regions: the inner and Copyright ASCE 2006 World Environmental and Water Resources Congress 2006 outer regions; or five layers: the laminar sublayer, the transition layer, the overlap layer, the wake layer, and the layer of the upper boundary layer edge. We first introduce the laws in the inner and the outer regions, respectively. We then match them to result in a complete velocity profile model that satisfies all physical requirements. 10 0 10 1 10 2 10 3 10 4 0 5 10 15 20 25 30 35 yu * /ν u/ u * laminar layer transition layer overlap layer wake layer edge layer Inner region

Bridge Scour Design and Protection

Substructure Design, 2014

Modified Log-Wake Law in Smooth Rectangular Open-Channels

Advances in Hydraulics and Water Engineering, 2002

A modified log-wake law is proposed to describe turbulent velocity profiles in smooth rectangular... more A modified log-wake law is proposed to describe turbulent velocity profiles in smooth rectangular open-channels. The new law consists of three components: a log term, a wake term, and a free surface term. The log term reflects the channel bed effect and predominates in terms of velocity magnitude; the wake term expresses the sidewall effect and can be neglected near the channel bed; and the free surface term satisfies the free surface boundary conditions. The modified log-wake law contains six parameters: (1) the von Karman constant κ ≈ 0.42; (2) the wake strength Π = κ; (3) the bed shear velocity u * b ; (4) the sidewall shear velocity u * w ; (5) the maximum velocity u max or the integration constant A; and (6) the velocity gradient at the upper boundary. The analysis clearly shows that the wake function results from sidewall effects. The modified log-wake law can replicate the velocity dip phenomenon in narrow channels at width-depth ratios less than 5. When the width-depth ratio exceeds 5, the maximum velocity occurs at the free surface. Finally, the modified logwake law compares very well with Coleman's, Lyn's and Muste and Patel's experimental data.

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Semi-analytical model for temporal clear-water scour at prototype piers

Journal of Hydraulic Research, 2014

The temporal pier scour process was studied extensively for laboratory scale but remains poorly u... more The temporal pier scour process was studied extensively for laboratory scale but remains poorly understood for prototype piers. This research presents a novel semi-analytical solution for temporal clear-water scour at prototype piers with arbitrary initial scour conditions, by integrating the fundamental mass conservation law and the empiricism from previous studies. The proposed solution includes the conventional power-, log- and exponential laws for the initial, growth and decay phases, respectively, in a single model agreeing with recent high-quality data for long durations and prototype scour with a determination coefficient higher than 0.98. The results show that (i) temporal pier scour process is described by two basic parameters: characteristic time tc and equilibrium scour depth η∞; and (ii) the proposed solution may be useful for data correction in relation to η∞ and for real-time bridge scour monitoring during floods. Yet, its predictive power depends on the predictability of tc and η∞, indicating a future research need.

Sidewall and non-uniformity corrections for flume experiments

Journal of Hydraulic Research, 2014

ABSTRACT Studying open channel flow and sediment transport in narrow flumes under non-uniform flo... more ABSTRACT Studying open channel flow and sediment transport in narrow flumes under non-uniform flow conditions, both sidewall and non-uniformity corrections are required for bed-shear stress. This research first reviews conventional predictive methods for bed-shear stress, including the flow-depth method, the hydraulic radius method and Einstein's sidewall correction. It then presents a novel procedure for sidewall and non-uniformity corrections based on a recent cross-sectional velocity distribution model. These methods are compared with data from the log-law under uniform and non-uniform, sub- and supercritical flow conditions, indicating that (i) the flow-depth and the hydraulic radius methods specify the upper and lower bounds for bed-shear stress; (ii) although Einstein's procedure causes a paradox for smooth flumes, it agrees with data from rough beds; and (iii) the proposed is better than Einstein's for subcritical flow, but the latter has advantage for supercritical flow. As an application, sediment inception under non-uniform flow conditions is also discussed.

Modeling Hydroplaning and Effects of Pavement Microtexture

Transportation Research Record, 2005

Hydroplaning on wet pavement occurs when a vehicle reaches a critical speed and causes a loss of ... more Hydroplaning on wet pavement occurs when a vehicle reaches a critical speed and causes a loss of contact between its tires and the pavement surface. This paper presents the development of a three-dimensional finite volume model that simulates the hydroplaning phenomenon. The theoretical considerations of the flow simulation model are described. The simulation results are in good agreement with the experimental results in the literature and with those obtained by the well-known hydroplaning equation of the National Aeronautics and Space Administration (NASA). The tire pressure-hydroplaning speed relationship predicted by the model is found to match well the one obtained with the NASA hydroplaning equation. Analyses of the results of the present study indicate that pavement microtexture in the 0.2-to 0.5-mm range can delay hydroplaning (i.e., raise the speed at which hydroplaning occurs). The paper also shows that the NASA hydroplaning equation provides a conservative estimate of the hydroplaning speed. The analyses in the present study indicate that when the microtexture of the pavement is considered, the hydroplaning speed predicted by the proposed model deviates from the speed predicted by the smooth surface relationship represented by the NASA hydroplaning equation. The discrepancies in hydroplaning speed are about 1% for a 0.1-mm microtexture depth and 22% for a 0.5-mm microtexture depth. The validity of the proposed model was verified by a check of the computed friction coefficient against the experimental results reported in the literature for pavement surfaces with known microtexture depths.

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Bridge pressure flow scour at clear water threshold condition

Transactions of Tianjin University, 2009

Bridge pressure flow scour at clear water threshold condition is studied theoretically and experi... more Bridge pressure flow scour at clear water threshold condition is studied theoretically and experimentally. The flume experiments reveal that the measured scour profiles under a bridge are more or less 2-dimensional; all the measured scour profiles can be described by two similarity equations, where the horizontal distance is scaled by the deck width while the local scour by the maximum

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