ANALYSIS OF FLOW DYNAMICS IN WATER INTAKE STRUCTURES USING THE K-Ε TURBULENCE MODEL

ABSTRACT

This study investigates the velocity distribution in forebays by applying the Reynolds-Averaged Navier-Stokes (RANS) model. The forebay is divided into three distinct sections to analyze flow characteristics more effectively. Each section's velocity profiles were examined under varying flow conditions, revealing significant differences in flow behavior. In section 1-1, the maximum flow speed reached 0.61 m/s, while in section 2-2, it was observed at 0.53 m/s. Notably, section 3-3 exhibited the highest recorded speed of 0.8 m/s, demonstrating a sharp increase in velocity at a specific distance from the wall. The findings highlight the impact of flow distribution on sedimentation processes, underscoring the importance of optimizing water intake structures for enhanced hydraulic performance.

АННОТАЦИЯ

В этом исследовании изучается распределение скорости в передовых бассейнах с применением модели Рейнольдса-усредненного Навье-Стокса (RANS). Передовой бассейн разделен на три отдельных участка для более эффективного анализа характеристик потока. Профили скорости каждого участка были исследованы при различных условиях потока, что выявило значительные различия в поведении потока. В участке 1-1 максимальная скорость потока достигла 0,61 м/с, в то время как в участке 2-2 она наблюдалась на уровне 0,53 м/с. Примечательно, что участок 3-3 показал самую высокую зарегистрированную скорость 0,8 м/с, что свидетельствует о резком увеличении скорости на определенном расстоянии от стенки. Результаты подчеркивают влияние распределения потока на процессы седиментации, подчеркивая важность оптимизации водозаборных сооружений для улучшения гидравлических характеристик.

Keywords: flow rate, pumping station, k-ε-model, numerical simulation, pre-chamber.

Ключевые слова: скорость потока, насосная станция, k-ε-модель, численное моделирование, аванкамера.

1. INTRODUCTION

In recent years, because of global climate change in the region, water consumption in major rivers has decreased by 53% per capita over the past 30 years, and water scarcity has increased in many countries [1]. According to the UN classification, Uzbekistan is among the countries experiencing water scarcity; the future water balance of its resources is affected by the rapid melting of glaciers that form the main rivers of the region, other aspects of climate change, as well as the growing needs of the population for water resources and industrial development [2].

Taking this into account, a concept for the development of the water sector of the Republic of Uzbekistan for 2020-2030 was developed [3]. Today, pumping stations are widely used in agriculture and water supply to cultivated fields; in this regard, one can also see the works of Mamajonov, Glovatsky, and others [4,5]. Forebays of pumping stations face several problems when using them to supply water to agricultural land. When studying the processes in the forebays and analyzing the scientific works of Shakirov, Nosirov, Alikulov, and many other researchers [6-11], it became  known that a decrease in the efficiency of the forebays, flow turbidity, and incorrect velocity distribution occurs due to the uneven occurrence of the flow distribution and direct dependence on cavitation processes in the pump.

However, operational challenges such as turbulent flows, non-uniform velocity distributions, and sediment deposition can significantly impact the performance and lifespan of pumping equipment. Numerical simulation, particularly using computational fluid dynamics (CFD), provides a powerful method for analyzing and optimizing flow conditions in forebay. Among various turbulence modeling approaches, the k-ε turbulence model combined with the Reynolds-Averaged Navier-Stokes (RANS) equations has gained prominence due to its balance between computational cost and accuracy in predicting turbulent flow characteristics (Launder & Spalding, 1974; Rodi, 1980)[12,13].

The RANS approach involves decomposing the instantaneous velocity into mean and fluctuating components, which allows for the modeling of turbulent flow fields through averaged quantities. The k-ε model, widely used for simulating turbulence in hydraulic applications, introduces two additional transport equations for the turbulent kinetic energy (k) and its dissipation rate (ε). These parameters help predict flow separation, velocity profiles, and energy losses in complex flow domains such as pumping station forebay (Versteeg & Malalasekera, 2007; Wilcox, 1993)[14,15]. By utilizing these models, engineers can investigate various configurations of forebay designs, including the implementation of flow straighteners, screens, or baffles to reduce vortex formation and ensure a uniform flow distribution (Zhou et al., 2019; Mohammadi & Pironneau, 1994)[16,17].

The use of CFD with the RANS/k-ε approach has been demonstrated to be effective in evaluating flow patterns and sediment transport within pumping station forebay. For example, Zhou et al. (2019) used the k-ε model to simulate flow disturbances in a forebay, resulting in optimized arrangements of guide vanes that significantly reduced turbulence intensity. Similarly, studies by Ramesh et al. (2020) and Wu et al. (2021) have shown the potential of CFD for predicting sediment deposition patterns, allowing for the design of effective sediment management strategies that prevent clogging and erosion of pumping equipment[18].

In conclusion, the numerical simulation of flow movement in the forebays of pumping stations using the RANS/k-ε approach serves as a robust method for optimizing hydraulic performance. By enabling detailed analysis of flow behavior and sediment dynamics, it facilitates the development of efficient designs and maintenance practices for pumping station forebays.

2. MATERIALS AND METHODS

2.1. Model Description

Currently, the k-ε turbulence model, grounded in the three-dimensional Navier-Stokes equations, is extensively employed for numerically solving hydrodynamic process problems. This model is among the most widely utilized RANS models, addressing two equations related to the kinetic energy of turbulence (k) and its dissipation (ε). It is particularly effective for tackling various engineering challenges and is noted for its advantageous balance between precision and computational efficiency.

Where; 1- channel, 2- water supply channel, 3- fotebay, 4- gate, 5- water intake, chamber, 6- suction pipe of the pump.

The core formulation of the Navier-Stokes equations comprises the mass and momentum conservation equations, which collectively define how a fluid behaves in both space and time.

The Continuity equation expressed as follows:

                                                                             (1)

The motion equation is given by:

                                  (2)

Where :   represent the velocity components in each direction, ​denote the coordinate components; fluid density, pressure, effective viscosity coefficient - gravitational acceleration;

The inlet boundary is defined at the culvert entrance, designed as a mass flow inlet to mitigate computational errors stemming from uneven grid density distribution. The outlet boundary is positioned at the discharge pipe of the forebay, configured as a static pressure outlet. Wall functions are applied to manage all solid wall surfaces. Due to slight variations in water level, the free surface is considered under the premise of a rigid cover.

2.2 Turbulence model. Water flow at a pumping station is typically characterized by high Reynolds number turbulence, especially in the bay, where sidewall outflows and significant backflows are common. The two-equation k-interaction model is often deemed more suitable. Thus, the RNG k-adhesion model is used for simulating the flow pattern at the forebay's front. To determine effective viscosity, turbulent eddy viscosity must first be calculated using a k-ε turbulence model, which incorporates turbulence kinetic energy (k) and its dissipation rate (ε). This model accounts for turbulent viscosity and mean flow circulation, making it suitable for complex flows with significant curvature, such as side inlet flows[24].

                              (3)

                           (4)

From formula (3) presented above

Where is created from turbulent kinetic energy, represented as:

 calculated by the following equation:

Constants and functions of the k-e model are given in articles [17-18].

3. RESULTS AND DISCUSSION

Suboptimal flow distribution in water intake structures can lead to the occurrence of vortices and sedimentation processes. In this investigation, experiments were carried out with inlet flow velocities 0.8 m/s, referred Figure 2. The primary flow demonstrated significant velocity at the cross-section corresponding to the width of the receiving chamber. As the flow progressed, countercurrents began to emerge in areas extending 5 meters on either side of the forebay. This development resulted in the establishment of vortex flows, highlighting the complexities of flow dynamics within the system and the potential impacts on sediment transport and deposition.

The forebay is divided into three sections along the length (Figure 2), with the width of section 1-1 measuring l = 2.6 meters. Analyzing the velocity distribution (Figure 3), the maximum flow speed at the center reaches 0.61 m/s, while the speed measured 1.1 meters from the wall decreases to 0.1 m/s. This reduction in speed is primarily attributed to the effects of reverse flow. Section 2-2 (Figure 4) has a width of b2 = 4.10 meters. The maximum flow speed at this location is 0.53 m/s. Near the shore, the speed increases to 0.05 m/s. At this velocity, sedimentation occurs rapidly in the forebay.  In section 3-3 (Figure 5), the flow characteristics vary slightly; notably, the highest speed measured at the center is 0.8 m/s, and a sharp increase in speed is observed from 0.3 m/s at a distance of 1.7 meters from the wall.

4. CONCLUSIONS

This research offers an in-depth examination of the flow behavior within the forebay of a pumping station, employing the k-ε turbulence model in conjunction with advanced numerical simulation methods. The findings reveal notable flow instabilities near the suction pipe, with velocity variations observed to reach up to 20% from the desired operational benchmarks. Variability in flow uniformity poses significant risks to the efficacy and safety of the pumping system.

In summary, this study lays a robust groundwork for future investigations, emphasizing the need for a systematic exploration of various flow rectification strategies, thorough experimental validation, and extensive comparative studies to determine best practices in hydraulic engineering. This approach aims to promote the design of efficient coastal pumping stations while ensuring that velocity fluctuations remain below 5% to improve operational dependability.

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