Study on the Unsteady Flow of the Approach Channel’s Entrance

Abstract

The entrance of shiplock’s approach channel always exist a mixing shear layer caused by the shear mixing layer, where is the junction of main river flow and the quiescent water of the approach channel. The flow structure of the turbulent mixing area presented as large-scale vortices frequently and periodically. And the fluctuations of the water surface and velocity induced by the separation of vortices may threat the navigation conditions, which should be considered during the engineering designing. The existing studies regard the mixing shear layer as steady flow and only take care of the average shear velocity, which may underestimate the harm of the shear flow. In this work, RNG k-ε model and LES model were adoped to study the hydraulic characteristics of the entrance. The vortex characteristics and the influence on the water level and velocity were analyzed. Results shown that LES model had better precision than RNG k-ε model in the unsteady characteristics. Then further studies about the recirculation flow were performed with LES model, The length and period of the recirculation flow was studied. It found that the vortex was generated at the upstream of shear zone, and then transferred with the recirculate flow until it was collapsed. All the above provide references for hydraulic characteristics of the entrance.

1 Introduction

The entrance of port and lock approach is a junction of quiescent water and flow water, where is a turbulent mixing shear flow and circulation flow always exist (Kimura and Hosoda 1997). The flow structure of the entrance caused by turbulent mixing behave as large-scale vortexes generated frequently and periodically. The separation of large-scale vortexes causes the water surface and velocity fluctuation at the entrance and the approach channel, which affects the flow stability in the approach channel and threat to the safety of navigation (Sauida 2016). Many scholars have focus the flow characteristics. For example, Liu (1995) studied the mixing zone at the entrance of the dead end and its recirculation characteristics with physical experiment, and explored the flow structure and mechanism of the entrance area. Li et al (2005) studied the flow conditions in the entrance area of the lower approach channel of the Gezhouba shiplock. The results shown that the flow velocity and direction of the recirculation flow at the entrance were extremely unstable, and the flow presented a periodic characteristic, which was similar to the oscillatory flow and had a significant influence on the navigation. Zhou et al. (2005) summarized the results of physical model test and prototype observation of some shiplocks in China, and analyzed the wave and discharge variation at the entrance caused by wind or the water releasing of nearby hydraulic engineering. The results shown that the fluctuation presented as short wave, and the period is less than 5 s with the amplitude could be reached more than 1 m. In addition, many scholars have used numerical models to study the hydraulic characteristics of the entrance area, such as transverse flow velocity, longitudinal flow velocity, recirculation velocity, and so on. However, existing studies mainly focusing on the flow structure and average flow filed of the entrance, in meanwhile ignored the unsteady characteristics of the vortex. Therefore, it is necessary to conduct further study on the vortex characteristics of the entrance, to explore the influence of unsteady characteristics on the approach channel.

The large eddy simulation (LES) and RNG k - ε turbulence model were used to study the flow characteristics in the entrance area. The flow field and periodic characteristics obtained by the two numerical simulation methods are compared and analyzed. In addition, the hydraulic characteristics of the recirculation zone in the entrance were discussed.

2 Simulation Model

RANS k - ε model and LES model were used to simulate the flow field of approach channel and its entrance respectively.

2.1 RANS k-ε Model

The control equations of RANS k - ε model can be expressed as (Girimaji 2006):

$$ \frac{\partial k}{{\partial t}} + u_{j} \frac{\partial k}{{\partial x_{j} }} = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\frac{{\nu_{t} }}{{\sigma_{k} }} + \nu } \right)\frac{\partial k}{{\partial x_{j} }}} \right] + G - \varepsilon $$

(1)

$$ \frac{\partial \varepsilon }{{\partial t}} + u_{j} \frac{\partial \varepsilon }{{\partial x_{j} }} = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\frac{{\nu_{t} }}{{\sigma_{\varepsilon } }} + \nu } \right)\frac{\partial \varepsilon }{{\partial x_{j} }}} \right] + C_{1\varepsilon } \frac{\varepsilon }{k}G - C_{2\varepsilon } \frac{{\varepsilon^{2} }}{k} $$

(2)

where, ρ is fluid density, t is time, u_j is the velocity vector in j direction, k is turbulent kinetic energy, ε is turbulent dissipation rate, σ_ij is the Kronecker function, the stress component is δ_ij, ν_t is eddy viscosity, p is the pressure term. The other parameters are presented as:

$$ \begin{aligned} \tau_{ij} & = 2\left( {\nu + \frac{{k^{2} }}{\varepsilon }} \right)\sigma_{ij} - \frac{2}{3}k\delta_{ij} , \, \sigma_{ij} = \frac{1}{2}\left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }}} \right), \, \nu_{t} = C_{d} \frac{{k^{2} }}{\varepsilon } \\ G & = 2\nu_{t} \sigma_{ij} \frac{{\partial u_{i} }}{{\partial x_{j} }}, \, C_{d} = 0.09, \, C_{1\varepsilon } = 1.44, \, C_{2\varepsilon } = 1.92, \, \sigma_{k} = 1.0, \, \sigma_{\varepsilon } = 1.3 \\ \end{aligned} $$

(3)

2.2 LES Model

In this work, Smagorinsky-Lilly dynamic model was used to solve the subgrid stress τ_ij, and the coefficients are obtained dynamically in the calculation process, rather than a pre-given value. Two filtering factors were introduced in the model, namely, grid filtering factor Δ and test filtering factor Δ. Generally, the value of test filtering factor is twice of the grid filtering factor. Then the subgrid stress was expressed with eddy viscosity model (Sagaut, P. 2006):

$$ \tau_{ij} - {{\delta_{ij} \tau_{kk} } \mathord{\left/ {\vphantom {{\delta_{ij} \tau_{kk} } 3}} \right. \kern-\nulldelimiterspace} 3} = - 2C\overline{\vartriangle }^{2} \left| {\overline{S}} \right|\overline{S}_{ij} $$

(4)

in which, $\overline{S} = \sqrt {2\overline{S}_{ij} \overline{S}_{ij} }$, $\overline{S}_{ij} = \frac{1}{2}\left( {\partial {{\overline{u}_{i} } \mathord{\left/ {\vphantom {{\overline{u}_{i} } {\partial x_{j} + \partial {{\overline{u}_{j} } \mathord{\left/ {\vphantom {{\overline{u}_{j} } {\partial x_{i} }}} \right. \kern-\nulldelimiterspace} {\partial x_{i} }}}}} \right. \kern-\nulldelimiterspace} {\partial x_{j} + \partial {{\overline{u}_{j} } \mathord{\left/ {\vphantom {{\overline{u}_{j} } {\partial x_{i} }}} \right. \kern-\nulldelimiterspace} {\partial x_{i} }}}}} \right)$, $\overline{\vartriangle } = 2\vartriangle$, C is a coefficient and is considered to be constant between the two filter factors. The least square method was used to calculate the C value, as:

$$ C = {{L_{ij} M_{ij} } \mathord{\left/ {\vphantom {{L_{ij} M_{ij} } {\left( {2M_{ij} M_{ij} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2M_{ij} M_{ij} } \right)}} $$

(5)

where L_ij is calculated as:

$$ {{L_{ij} = \overline{{\overline{u}_{i} \overline{u}}}_{j} - \overline{{\overline{u}}}_{i} \overline{{\overline{u}_{i} }} M_{ij} } \mathord{\left/ {\vphantom {{L_{ij} = \overline{{\overline{u}_{i} \overline{u}}}_{j} - \overline{{\overline{u}}}_{i} \overline{{\overline{u}_{i} }} M_{ij} } {\left( {2M_{ij} M_{ij} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2M_{ij} M_{ij} } \right)}} $$

(6)

$$ M_{ij} = - 2\left( {\overline{\vartriangle }^{2} \left| {\overline{{\overline{S}}} } \right|\overline{{\overline{S}}}_{ij} - \overline{\vartriangle }^{2} \overline{{\left| {\overline{S}} \right|\overline{S}_{ij} }} } \right)$$

(7)

2.3 Mesh and Boundary Conditions

The experiment of Kimura and Hosoda (1997) was used for model validation. The experiment was carried at a rectangular channel with a dead end of the length and width both 15 cm (B = L = 15 cm), the width of the rectangular channel is 10 cm, the bottom slope is 1: 500, and the water depth is 1 cm.

The structured mesh was used in numerical model. In order to capture the flow structure at the entrance, the refined mesh was adopted at the entrance. The minimum mesh size is 1.25 mm, and the number of mesh elements was 1138491. The velocity of inlet of main channel was 25.5 cm/s, and the outlet was set as pressure boundary. The free surface was treated by VOF method. The central difference scheme was used to solve the convection diffusion equations. The second-order implicit method was used to calculate the transient term, and the time step was set as 0.001 s. When the residual errors were less than 1 × 10⁻⁵, the calculation was considered as stable.

Besides the condition of approach channel L = 15 cm, another 4 conditions had been presented to study the influence of length on the characteristics of recirculation flow, with L = 30 cm, 45 cm, 60 cm and 75 cm respectively, as shown in Table 1 (Fig. 2).

Fig. 1.

Experiment model of in Kimura and Hosoda (1997)

Fig. 2.

Mesh of calculated zone

Table 1. Simulation conditions

3 Results

3.1 Validation

The average flow velocities in the x direction of T0–T1 section (as shown in Fig. 1) calculated by RNG model and LES model are shown in Fig. 3. It can be seen that the time-average results of two models both close to the experiment results. For the instantaneous flow fields at three points a, b and c (the location as shown in Fig. 1), it can be seen that the instantaneous variation of flow velocity calculated by LES model also consistent with the experiment results. And the lowest order oscillation period of flow velocity is about 1 s. It was accorded with the calculation results of the wave period of approach channel $T = {{2L} \mathord{\left/ {\vphantom {{2L} {\left( {n\sqrt {gh} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {n\sqrt {gh} } \right)}}$ (n = 1, 2, 3…). Meanwhile the results calculated by RNS model were only agree with the experiment results in amplitude, but failed with the period. The lowest order oscillation period of RNS model was about 2 s, which did not meet the variation of instantaneous flow field in the approach channel.

So with the RNG k-ε model, only the time-averaged characteristics of the flow field can be obtained. The results of LES model are agree with the experiment results which measured by Particle Image Velocimetry (PIV). With LES model, the spatial-temporal random distribution characteristics of the flow velocity can be captured, including the swing of the jet axis and the distribution of the vortex. The calculation results of LES model are more accurate than the RNG k-ε model in the recirculation zone of the entrance area (Fig. 4).

Fig. 3.

Comparison of time-averaged velocity distributions along T0–T1

Fig. 4.

Comparison of temporal variations in velocity in x-direction

3.2 Flow Characteristics

LES model was used to study the flow conditions of the approach channel under five conditions with different length of approach channels, as shown in Table 1.

3.2.1 Length of Recirculation Zone

In this work, the flow velocity greater than 1 cm/s was considered as effective zone when determined the recirculation zone. The length of recirculation zone was found equal the length of approach channel when the channel length smaller than 30 cm. if the length of approach channel larger than 45 cm, the length of recirculation was keep consistent with value of 25 cm, as shown in Fig. 5 and Fig. 6.

Fig. 5.

The velocity field of recirculation zone in typical condition. (a) Condition C-2, (b) Condition C-3.

Fig. 6.

Length of recirculation flow in different conditions

3.2.2 Period of Recirculation Zone

Results show that the water level on the T1-T0 axis in the recirculation zone maintained unchanged, and the water depth at the two sides of T1-T0 axis increases and decreases alternately. The period of recirculation zone of condition C-1 is 1.0 s, and 1.6 s in all the other conditions, which in accordance with the results of the recirculation flow length, as shown in Fig. 7.

Fig. 7.

Velocity variation at c point in typical conditions (condition of C-2) (a) velocity u at x axis, (a) velocity v at y axis (c) depth h

3.2.3 Vortex of the Entrance

The shear zone at the entrance of mainstream and approach channel is an area of vortex generation and collapse. The results shown that the vortex generated at the upstream corner, then transferred with the flow to the downstream and the approach channel, and collapsed at last. The velocity and water level fluctuation in the recirculation zone were shown in Fig. 8.

Fig. 8.

Vorticity distribution at different time

4 Conclusions

The flow characteristics of approach channel were studied with numerical model in this work, and the RNG k-ε and LES models were compared with Kimura and Hosoda (1997). The results showed that both of the two models could be used to study the time-average flow field at the recirculation zone of entrance. However, the simulation results of RNG k-ε model has ignored the eddy details, and cannot accurately presented the periodic characteristics of flow velocity and water level oscillation in the recirculation zone. Meanwhile, the results of LES model has a good precision for the simulation of velocity and water level fluctuation, as well as the period characteristics of recirculation zone. The LES model was adopted for the further studies of the effects of approach channel length on the recirculation zone. And the results shown that the vortex generates at the shear zone of entrance, and causes the period change in the oscillation of flow velocity and water surface, the length and period of the recirculation region is mainly decide by the dimensional parameters of approach channel and the flow conditions. All the above provide references for hydraulic characteristics of the entrance.