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Application of Modified Log-Wake Law in Open-Channel Flows Junke Guo Dept. of Civil Engineering, University of Nebraska email@example.com Pierre Y. Julien Dept. of Civil Engineering, Colorado State University firstname.lastname@example.org
CONTENTS • Overview • Background • Hypothesis • Test with flume data • Application in the Mississippi River • Conclusions EWRI 2006, Omaha, NE
OVERVIEW • Topic: Velocity profile model in open-channel flows • What we know:The log law; the log-wake law • What we observe: (1) The velocity dip phenomenon; (2) the effect of roughness • What is the gap:(1) What we know cannot model the velocity dip phenomenon; (2) it is difficult to account for roughness for transitional regime. • What we propose:We will show you a modified log-wake law that can model the velocity dip phenomenon in hydraulically smooth, transitional and complete rough turbulent flows. EWRI 2006, Omaha, NE
BACKGROUND • Similarities: pipe, boundary layer, and open-channel flow • The log law • In the early 1930s, it was proposed for pipes and boundary layers. • In the late 1930s, Keulegan showed it works for open-channels. • The log-wake law • In 1956, Coles proposed it for pipes and boundary layers. • In 1980s, Coleman, Nezu and Rodi, and Graf showed that it works for open-channels. EWRI 2006, Omaha, NE
Problem The log-wake law cannot predict the velocity dip phenomenon observed in most open channel flows! Can the log-wake law be modified? EWRI 2006, Omaha, NE
BACKGROUND (cont.) • The modified log-wake law • In 2003 and 2005, Guo and Julien proposed a modified log-wake law for turbulent pipe and boundary layer flows. • The wake strength P:the effects of pressure-gradient in pipes or convective inertia in boundary layers. • The last term corrects the log law velocity gradient to be zero at the maximum velocity. EWRI 2006, Omaha, NE
BACKGROUND (cont.) • Test with pipe data (Guo and Julien 2003) EWRI 2006, Omaha, NE
BACKGROUND (cont.) • Test with boundary layer data(Guo et al. 2005) EWRI 2006, Omaha, NE
Questions Can we apply the modified log-wake law to open-channel flows? Is there any advantage to do so? EWRI 2006, Omaha, NE
HYPOTHESIS • Turbulent velocity profiles in open-channel flows can be described by the modified log-wake law (MLWL). where y0 is a virtual bed and it is much less than water depth h. EWRI 2006, Omaha, NE
HYPOTHESIS (cont’) • The virtual bed includes the effects of Reynolds number and roughness size. EWRI 2006, Omaha, NE
TEST WITH FLUME DATA SETS • Data sources: • Coleman (1986) • Lyn (1986) • Kironoto and Graf (1994) • Sarma et al. (2000) • Data analysis: • Determine the maximum velocity and its position. • Assume k = 0.41 and fit data to determine the wake strength P. • Plot the modified log-wake law with experimental data. EWRI 2006, Omaha, NE
Comparison with Coleman’s data EWRI 2006, Omaha, NE
Comparison with Lyn’s data EWRI 2006, Omaha, NE
Comparison with Kironoto and Graf’s data EWRI 2006, Omaha, NE
Comparison with Sarma’s data EWRI 2006, Omaha, NE
Test results – Answers to our questions • The MLWL CAN well fit experimental velocity profiles in open-channel flows. • The MLWL has an advantage that can replicate the velocity dip phenomenon near the free surface. • However, unlike pipe or boundary layers flows, a universal wake strength does not exist. EWRI 2006, Omaha, NE
APPLICATION IN MISSISSIPPI RIVER • The modified log-wake law can be applied to fit measured velocity profiles in the Mississippi River. EWRI 2006, Omaha, NE
SUMMARY AND CONCLUSIONS • The modified log-wake law (MLWL) can be applied to describe turbulent velocity profiles in open-channel flows. • The MLWL consists of three terms: • The log law that represents the effect of the bed. • The wake law that represents the effects of gravity, secondary flows, and roughness. • The cubic correction term near the maximum velocity. • Unlike pipe or boundary layer flows, A universal wake strength may never exist for open-channel flows. EWRI 2006, Omaha, NE
SUMMARY AND CONCLUSIONS (cont’) • The MLWL compares very well with flume data from Coleman (1986), Lyn (1986), Kironoto and Graf (1994) and Sarma et al. (2000). In particular, it can well model the velocity dip phenomenon near the free surface. • The MLWL has been successfully tested with a Mississippi River velocity profile measurements. EWRI 2006, Omaha, NE