THE INFLUENCE OF MUDDY WATER FLOW IN PIPELINES ON THE OPERATING EFFICIENCY OF PUMPS AND CHANGES IN HYDRAULIC PARAMETERS

УДК 621.67

Abstract

This study investigates the hydraulic and energy-related challenges associated with transporting sediment-laden water at pumping stations on the Amu Darya River and its irrigation systems. Increased water turbidity affects hydraulic parameters, raises energy consumption, and reduces the efficiency and reliability of pumping equipment. The influence of suspended sediments on flow characteristics and pump performance is analyzed using energy conservation principles and hydraulic flow theory. Mathematical relationships for calculating hydraulic losses in sediment-water mixtures are presented, with particular emphasis on critical flow velocity required to prevent sediment deposition and ensure stable pipeline operation. A comparative analysis of pipeline head characteristics for clean and sediment-laden water is carried out through an engineering example. The results show that sediment concentration significantly increases hydraulic resistance, head losses, and electricity consumption. Calculations for a turbidity level of 5% confirm additional energy demand compared to clean-water operation. The findings can be applied to improve pumping station energy efficiency, optimize operating conditions, and enhance the reliability of irrigation water supply systems.

Аннотация

В данной статье исследуются гидравлические и энергетические проблемы, возникающие при транспортировке нанососодержащих водных потоков на насосных станциях реки Амударья и в связанных с ней оросительных системах. Повышенная мутность воды оказывает влияние на гидравлические параметры, увеличивает энергопотребление и снижает эффективность и надежность насосного оборудования. Влияние взвешенных наносов на характеристики потока и работу насосов анализируется на основе закона сохранения энергии и положений гидравлической теории течения. Представлены математические зависимости для расчета гидравлических потерь в водно-наносных смесях, особое внимание уделено критической скорости потока, необходимой для предотвращения осаждения наносов и обеспечения устойчивой работы трубопроводов. Выполнен сравнительный анализ напорных характеристик трубопроводов при транспортировке чистой и нанососодержащей воды. Результаты показывают, что увеличение концентрации наносов приводит к росту гидравлического сопротивления, потерь напора и расхода электроэнергии. Полученные выводы могут быть использованы для повышения энергоэффективности насосных станций и надежности оросительных систем.

Keywords: muddy flow, pumping station, hydraulic resistance, pressure pipeline, head loss, critical velocity, energy consumption, irrigation system.

Ключевые слова: мутный поток, насосная станция, гидравлическое сопротивление, напорный трубопровод, потери напора, критическая скорость, потребление энергии, ирригационная система.

Introduction

In our republic, one of the known problems is the high concentration of sediment in the water flow at many pumping stations that take water from the Amu Darya and its associated irrigation facilities. A high content of sediment particles negatively affects the hydraulic parameters of the flow in the water intake section and internal flow passages of the pump, leads to an increase in hydraulic resistance at the inlet of pressure pipelines, causes additional loads and increased vibrations in the pump, and results in a decrease in the pump’s water delivery efficiency [1].

When pumping muddy flow (a mixture of sediment particles and water) through pressure pipelines using pumps, additional energy consumption is required. The main reasons for this are the increase in hydraulic resistance and the increase in the density of the muddy flow [1].

Main body. The pressure pipeline is defined by coordinates at points 1 and 2, and the energy of the muddy flow passing through the cross-sectional areas located at a certain distance from each other can be expressed using the energy conservation equation as follows [2] (Figure 1).

Figure 1. Diagram for determining the change in muddy flow energy between two points of the water flow

1- point: Q_s.p·ρ_s.p·/2 + Q_w·ρ_w·/2 + Q_m.f·ρ_m.f·g·z₁

2- point: Q_s.p·ρ_s.p·/2 + Q_w·ρ_w·/2 + Q_m.f·ρ_m.f ·g·z₂                                  (1)

where, Q_s.p , ρ_s.p ,  are the flow rate, density, and velocity of sediment particles; Q_w, ρ_w,  are the flow rate, density, and velocity of water; Q_m.f,  ρ_m.f,  are the flow rate, density, and velocity of the muddy flow; z₁ and z₂ are the geometric parameters that determine the potential energy of the flow at points 1 and 2.

Thus, in equation (1), the sum of the first and second terms represents the kinetic energy of the muddy flow, while the third term represents its potential energy. This equation accounts for the fact that, due to the large hydraulic size of the sediment particles and the frontal resistance acting on them, their velocity differs from that of the water flow (<).

Moreover, the movement of the muddy flow from point 1 to point 2 occurs due to the energy supplied by the pump, and a portion of this energy is spent to overcome frictional forces (viscous forces). It is known that this energy is also used to raise the temperature of the flow from t₁ at point 1 to t₂ at point 2. Taking this factor into account, equation (1) can be written in the following form:

Q_s.p·ρ_s.p·/2+Q_w·ρ_w·/2+Q_m.f·ρ_m.f·g·z₁+Q_m.f·ρ_m.f·g· t₁·с_m.f/M

Q_s.p·ρ_s.p·/2+Q_w·ρ_w·/2+Q_m.f·ρ_m.f·g·z₂ +Q_m.f·ρ_m.f·g· t₂·с_m.f/M                          (2)

where M is the mechanical equivalent of the heat I generated in overcoming the viscous force, and с_m.f  is the specific heat capacity of the muddy flow.

The work done to overcome the frictional force can be expressed as follows [3].

W_f.f = I/M = Q_m.f·ρ_m.f·g·с_m.f (t₂ – t₁)/M                                     (3)

For this case, the law of conservation of energy can be written in the following form:

Q_s.p·ρ_s.p·/2+Q_w·ρ_w·/2+Q_m.f·ρ_m.f·g·z₂ +Q_m.f·ρ_m.f·g· t₂·с_m.f/M – W_f.f + I/M +

+ Q_m.f(р₂ –р₂) = Q_s.p·ρ_s.p·/2+Q_w·ρ_w·/2+Q_m.f·ρ_m.f·g·z₁+Q_m.f·ρ_m.f·g· t₁·с_m.f/M              (4)

Dividing the left and right sides of this equation by Q_m.f ·ρ_m.f ·g and taking (2.3) into account, we can write (4) as follows.

(1 – q)/2g + q·/2g +z₁ + p₁/ ρ_m.f·g +h_g.q=(1 – q)/2g+q·/2g +z₂+p₂/ ρ_m.f·g (5)

бунда q = Q_s.p·ρ_s.p/Q_m.f ·ρ_m.f; 1 – q = Q_w·ρ_w/ Q_m.f ·ρ_m.f;  h_f = W_f.f/ Q_m.f ·ρ_m.f ·g

From equation (5), it is possible to determine the head loss that occurs when pumping muddy mixtures, which is important for identifying the optimal operating modes of pumps.

h_f =(1 – q)/2g+q·/2g +z₂+p₂/ ρ_m.f ·g – (1 – q)/2g –q·/2g – z₁ – p₁/ρ_m.f ·g (6)

This equation shows that, during the transportation of muddy flow, the change in the value of h_f  relative to clean water mainly depends on the amount of sediment particles in the flow and on the density of the muddy flow, which varies under their influence.

In equation (6), determining the velocity of sediment particles is a rather complex problem. The solution to this problem is given in [4] based on the following equation.

      (7)

where ; ρ_p is the density of a sediment particle with added (associated) mass, ρ_p =ρ_s.p + К_p·ρ_w, К_p is the added mass coefficient, which is equal to 0.5 for a spherical sediment particle; S is the distance between the cross sections with coordinates defined by points 1 and 2 along the pipeline; d is the diameter of the spherical sediment particle.

If the pipe diameter does not change over the distance S, then, due to the negligible difference, it can be assumed that  

For the pumping of muddy mixtures, the head loss h_f in horizontally installed pressure pipelines for finely dispersed (particle size 0.05–0.15 mm) and coarsely dispersed (particle size 0.15–1.5–2.0 mm) hydro-mixtures is addressed in [5], where recommendations are provided for determining the values of specific hydraulic resistance in pipelines.

For example, for finely dispersed hydro-mixtures, the following formula is proposed.

                                            (8)

where i_m.f and i_w are the values of specific hydraulic resistance in the pipeline for muddy flow and clean water, respectively; ρ_s.p and ρ_w are the densities of the sediment particles and water; с_z is an empirical coefficient depending on the amount of sediment particles: if the particle size is less than 0.7 mm and their concentration does not exceed 5–6%, then с_z = 1.0; in general, с_z varies within the range 0.85–1.15; δ is the volumetric concentration of sediment particles, which is determined by the following formula.

δ =(ρ_m.f – ρ_w)/(ρ_s.p – ρ_w)                                                    (9)

For the pumping of coarsely dispersed muddy flows, it is recommended to determine the specific hydraulic resistance of the head loss using the following formula [5,6].

                                  (10)

where с₁ is a coefficient that accounts for the pipe diameter, с₁ = 0.3–0.4 for pipe diameters

D=150–900 mm, с₁ = 0.5–0.6 for pipe diameters D=100–125 mm, с₁ = 1.5–1.6 for pipe diameters D = 63–100 mm, θ is the hydraulic size of the particles with diamete d_nom, а is the relative density coefficient of the sediment particles, which is determined by the following formula.

а =(ρ_s.p– ρ_w)/ρ_w,                                                (11)

In pump station pressure pipelines, sections installed with an upward incline are encountered more frequently than horizontal sections. For such pipelines, when pumping muddy water, it is recommended to determine the specific hydraulic resistance using the following formula [5].

i_m.f = i_w(1+a·δ)    When Fr_a >10                                   (12)

    When 1 <Fr_a <10               (13)

where  Fr_a is the Froude number of the muddy flow, which is determined as follows:

                                                   (14)

In muddy water flows in pipelines, there is a concept called the critical velocity of the flow, which is considered the velocity at which the head loss is minimized and is close to the threshold value at which sediment particles may settle. This velocity can be determined using the following formula [5,6].

                                           (15)

For coarsely dispersed muddy flows in a horizontal pipeline, the critical velocity can be determined using the following formula [5,6].

                                   (16)

The graphs showing the dependence of the hydraulic resistance coefficients on the flow velocity for muddy flows in a horizontal pipeline are presented in Figure 2 [7].

Figure 2. Graphs of the dependence of the specific hydraulic resistance coefficient on the flow velocity in horizontal pressure pipelines.

1, 2, 3, 4 – graphs of i_m.f  vs. for muddy flows with densities ρ₁< ρ₂ < ρ₃< ρ₄; 5 – graph of i_s vs.  for clean water.

As can be seen from the graphs, as the density of the muddy flow increases, the values of the hydraulic resistance coefficient also increase, and their minimum values (indicated as point B on the graphs) correspond to the critical velocity of the flow, which has been confirmed by both theoretical and experimental studies [7].

At flow velocities corresponding to the range between points A and B shown on the graphs, sediment settling may occur; therefore, the probable velocity values are taken within the range between points B and C.

For example, the D1250–65 pump delivers a muddy flow with a flow rate of Q=0,28 m³/s through a pressure pipeline with a diameter of D =0,4 m, a length of L=150 m, and an upward incline of 25°, to a height of Н_G = 22 m. In this pipeline, we determine the limiting flow velocity  and the specific hydraulic resistance coefficient i_l.о.

Sediment particle density ρ_s.p =2000 kg/m³, water density ρ_w =1000 kg/m³, muddy flow density ρ_m.f =1050 kg/m³, mean particle diameter d_nom= 0.5 mm, hydraulic size θ =5.24 sm/s [6].

To determine how this condition affects the pump’s operating mode, we calculate the pipeline system head characteristics for both clean water and muddy flow, and then represent them on the pump performance curve. For this, the pipeline head characteristic  Н = H_G + k·Q²  is calculated for different values of Q in both cases, and the graph is plotted (Figure 3).

In the above equation, the value of k is calculated.

k_w = ΔН_w/ Q² =2,19/0,28²=27,93

k_m.f = ΔН_m.f/ Q² =3,09/0,28²=39,41

Thus:

ΔН_w =27,93 Q  ;          ΔН_m.f =39,41Q²

Н_w = H_G + k_w·Q²  = 22 +27,93 Q² ;

Н_m.f = H_G + k_w·Q²  = 22 +39,41Q²

The results of the calculations are presented in Table 2.

Table 2. Results of the calculations

Based on the results presented in Table 2, we plot the pipeline system head characteristic curves.

Figure 3. Graphs of the pipeline system head characteristics for the D1250–65M–O pump

Conclusion

 The results of the calculations show that when pumping muddy flow, the specific hydraulic resistance coefficient in the pressure pipeline increased by 41%, which caused the pump flow rate to decrease from 0.28 m³/s to 0.265 m³/s. To assess the impact on energy consumption, the electrical energy is calculated as:

Е_w = 9,81·Q_w·H_w·T/η_w = 9,81·0,28·23,3·500/0,8 =40000 kW·h    

where the pump operating time is taken as Т=500 h.

During this period, the pump delivers V = Q_w · Т · 3600 = 0,28·500·3600 =504000 m³ of water. According to the requirements, the pump must deliver the same volume of water even if it is muddy, and for this, it will consume the following amount of electrical energy.

Thus, when pumping muddy water with sediment particles making up 5%, according to the calculations above, this can lead to an additional electricity consumption of 690 kWh.

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