scholarly journals A Novel Analytical Method for Evaluating the Characteristics of Hydraulic Jump at a Positive Step

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2005
Author(s):  
Milad Mohammadi ◽  
Mohammad Nazari-Sharabian ◽  
Moses Karakouzian
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Hydraulic Jump ◽  
Rectangular Channel ◽  
Theoretical Models ◽  
Energy Dissipation Rate ◽  
Flow Depth ◽  
Jump Length ◽  
Positive Step

We present a new method to evaluate the hydraulic jump characteristics in a horizontal rectangular channel with a positive step. We considered the flow curvature effect and the free surface’s small rise at the A-type hydraulic jump’s end. First, we present a novel method to give jump length estimation based on the similarity of the jump and the turbulent wall-jet, considering the pressure gradient. Then, considering the jump as a curvilinear flow and using a one-dimensional momentum equation, we present an accurate expression for the conjugate flow depth regarding the initial Froude number and step height. Finally, we compute the jump’s energy dissipation rate. Compared to the theoretical models for conjugate flow depth in a hydraulic jump, the proposed equation in this study fit the experimental data better, even for high steps and large initial Froude numbers. However, for low Froude numbers (F1 < 5), the equation was less accurate in estimating the jump length. Regarding the jump’s energy dissipation rate, the results agreed well with the experimental data from previous investigations. However, it is noted that the increased energy dissipation rate dwindled in larger Froude numbers.

scholarly journals Study on the Best Depth of Stilling Basin with Shallow-Water Cushion

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1801
Author(s):  
Qiulin Li ◽  
Lianxia Li ◽  
Huasheng Liao
Keyword(s):  
Energy Dissipation ◽  
Shallow Water ◽  
Froude Number ◽  
Flow Regime ◽  
Dissipation Rate ◽  
Hydraulic Jump ◽  
Energy Dissipation Rate ◽  
Main Stream ◽  
Stilling Basin ◽  
Key Factor

The depth of the stilling basin with shallow-water cushion (SBSWC) is a key factor that affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the water cushion is considered as ‘shallow’ has not been stated clearly by far, and only conceptual description is provided. Therefore, in order to define the best depth of SBSWC and its relationship between the Froude number at the inlet of the stilling basin, a large number of experiments were carried out to investigate SBSWC. First of all, 30 cases including five different Froude numbers and six depths were selected for which large eddy simulation (LES) was firstly verified by the experiments and then adopted to calculate the hydraulic characteristics in the stilling basin. Finally, three standards, based on the flow regime of hydraulic jump, the location of the main stream and the energy dissipation rate, were proposed to define the best depth of SBSWC. The three criteria are as follows: (1) a complete hydraulic jump occurs in the basin (2) the water cushion is about 1/10–1/3 deep of the stilling basin, and (3) the energy dissipation rate is more than 70% and the unit volume energy dissipation rate is as high as possible. It showed that the best depth ratio of SBSWC (depth to length ratio) was between 0.1 and 0.3 and it also indicated the best depth increased with the increase in Froude number. The results of the work are of significance to the design and optimizing of SBSWC.

scholarly journals SPH Simulation of Hydraulic Jump on Corrugated Riverbeds

2019 ◽  
Vol 9 (3) ◽  
pp. 436 ◽  
Author(s):  
Shenglong Gu ◽  
Fuping Bo ◽  
Min Luo ◽  
Ehsan Kazemi ◽  
Yunyun Zhang ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Hydraulic Jump ◽  
Numerical Study ◽  
Energy Dissipation Rate ◽  
Vortex Pattern ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Smoothed Particle ◽  
Sph Simulation

This paper presents a numerical study of the hydraulic jump on corrugated riverbed using the Smoothed Particle Hydrodynamics (SPH) method. By simulating an experimental benchmark example, the SPH model is demonstrated to predict the wave profile, velocity field, and energy dissipation rate of hydraulic jump with good accuracy. Using the validated SPH model, the dynamic evolvement of the hydraulic jump on corrugated riverbed is studied focusing on the vortex pattern, jump length, water depth after hydraulic jump, and energy dissipation rate. In addition, the influences of corrugation height and length on the characteristics of hydraulic jump are parametrically investigated.

scholarly journals Criterion for analyzing experimental data on eddy diffusion coefficients

2014 ◽  
Vol 32 (6) ◽  
pp. 581-588 ◽  
Author(s):  
M. N. Vlasov ◽  
M. C. Kelley
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Heat Transport ◽  
Transport Coefficient ◽  
Dissipation Rate ◽  
Lower Thermosphere ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Cooling Rates ◽  
Eddy Heat Transport

Abstract. Problems exist in estimating the eddy heat transport coefficient, Keh, from experimental data. These problems are due to uncertainty in determining the turbulent energy dissipation rate and to the uncertainty of Keh dependence on the energy dissipation rate. In this paper, a new criterion for estimating the eddy heat transport coefficient is suggested. This criterion is based on the effect of eddy turbulence on the energy budget of the upper mesosphere and lower thermosphere. The calculations show high cooling around and above the Keh peak for Keh values inferred from experimental data. The cooling rates are much higher than cooling rates corresponding to the temperature given by the MSIS-E-90 model or to temperatures measured during the experiments. The main contribution to high cooling rates is due to the term with eddy heat conduction, which strongly depends on the Keh gradient. According to our results, the heating/cooling values below the Keh peak altitude correspond to the temperature given by the MSIS-E-90 model, but at the peak and above, the cooling rates are larger by a factor of 2–3 than the rates corresponding to the temperatures. This means that the Keh values in the peak and above may be overestimated. Application of this criterion to the Turbulent Oxygen Mixing Experiment (TOMEX) data shows that eddy diffusions inferred from observing chemical tracers in TOMEX are strongly overestimated.

The spectrum of a turbulent passive scalar in the viscous–convective range

1990 ◽  
Vol 217 ◽  
pp. 203-212 ◽  
Author(s):  
J. Qian
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Energy Dissipation Rate ◽  
Average Value ◽  
Variation Approach ◽  
Spectrum Function

The closed equations of isotropic turbulence, obtained by the method of non-equilibrium statistical mechanics and a perturbation-variation approach (Qian 1983, 1985, 1988), are applied to the study of the spectrum dynamics of a turbulent passive scalar in the viscous–convective range. Batchelor's k−1 spectrum is further confirmed. Moreover the effective average value of the least principal rate of strain γ in Batchelor's spectrum function is theoretically evaluated and it is found that γ−1 = C(ν/ε)½ with C = 2√5. Here ν is the kinematic viscosity, and ε is the energy dissipation rate. This prediction is in agreement with experimental data reported by Grant et al. (1968) and Williams & Paulson (1977).

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

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