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STUDY OF THE INFLUENCE OF THE SPECIFIC SPEED COEFFICIENT ON THE COUNTER-ROTOR STAGE
29.11.2023 00:22
[3. Технічні науки]
Автор: Olexandr Kulikov, Post graduade student,Sumy State University, Sumy; Olexandr Ratushnyi, PhD in Engineering Sciences, Teaching Assistant, Sumy State University, Sumy
ORCID: 0000-0001-7222-8766 Olexandr Kulikov
ORCID: 0000-0002-3525-0953 Olexandr Ratushnyi
Centrifugal pumps make up a broad class of pumps. Liquid pumping or the head created by them occurs due to the rotational movement of one or more impellers. The large number of different types of centrifugal pumps manufactured for different purposes can be reduced to a small number of basic types. This difference in the constructive development of which is dictated mainly by the peculiarities of the use of pumps and the mechanical requirements imposed on them.
Each pump has two main parts: impeller, which drives the liquid into a rotational motionand the pump casing, which directs the liquid to the impeller and brings out it from it with increased pressure. The impeller is installed on the shaft (with supports in bearings), which is driven by the motor through an elastic or rigid coupling.
Impellers and the pump unit as a whole are classified primarily by specific speed coefficient ns.
where, n - the rotation frequency of the impeller.
Q - capacity.
H - head.
The speed coefficient characterizes the efficiency, the shape of the flow part, ratio of geometric parameters and the form of pump characteristics. That is, to calculate the dimensions of the impeller, namely: outer diameter D2, entrance diameter D1 and exit width b2 you must first find the specific speed coefficient ns. Depending on what characteristics we want to obtain from the impeller, the value will also depend ns.
With lower specific speed coefficient and large blade installation angles, more blades are used. Thus, the choice of the number of blades should be related to the angle at the exit from the impeller and the speed coefficient. In some cases ns=40-60 it is advisable to use open-type impellers. This is explained by the fact that the distance between the cover and the main disc is insufficient for casting blades of the desired shape. In turn, the use of semi-open or open impellers significantly reduces efficiency.
In the flow part, the liquid moving along the channels of the impeller transfers mechanical energy from the drive side, which is converted into flow energy: kinetic - due to an increase in absolute speed and potential - in the form of increased pressure. In the spiral outlet, the kinetic energy of the liquid flow is partially converted into potential energy (into pressure).
The contra-rotating effect works as follows. For ease of perception, the impeller and blade disc is delivered to a distance “а” (fig.1). Velocity vectors and their components are given for the axisymmetric flow scheme and conditions wl = -wll (the gratings rotate in opposite directions with the same angular velocity). In addition, at the entrance to the first grid, selected conditions without circulating leakage. At the same time, it is worth noting that if this condition is met for the first grid (vu1=0) it is easy to provide thanks to the design of the supply inlet, but provide the condition vu3=0 at the entrance to the second grid will be much more difficult. This can be achieved only thanks to the appropriate combination of geometric and kinematic parameters of both the first and second lattices [1,2].
The flow at the entrance to the second grid is coming out of the first. It has a significant moment (twist), created by the first grid (vu2∙r2). Simultaneously, its direction is opposite to the second grid’s rotation direction.. And although the vector v3̅ does not create twists (vu3=0), a twist vu2∙r2 is the real negative circulation at the entrance to the second grid [1,2].
Figure 1 - Flow kinematics in counter-rotor centrifugal grids
It should also be noted that the second grid's blades move towards the current coming from the first grid, changing its momentum in a very short time. And this, according to the moment theorem, causes a sharp increase in the force of interaction between the solid surface of the blade and the current that attacks it. This, obviously, leads to a significant increase in the intensity of the energy transfer process. Considering the working process of the contra-rotating blade system and, first of all, the work of the second grid, an assumption arises that the first grid, created at the entrance to the second flow with significant negative circulation Г2, thus provides an intense contra-rotating for the blades of the second rotor (they actively interact). This flow’s kinetic energy quickly passes into the state of pressure energy, which resembles the working process in hydraulic machines of the active principle of the action (for example, in jet bucket turbines) [1,2].
Maximum efficiency centrifugal pump was achieved for ns=150-250. Figure 2 shows the dependence η = f(ns, Q)
Figure 2 - Dependence of efficiency of the coefficient of speed and feed.
In the process of designing any bladed machine, it is necessary to establish the relationship between the main working parameters of the machine (capacity and head) and geometric dimensions, the shape of the blades, frequency of rotation of the impeller. And if everything is clear with centrifugal pumps of the traditional type, then returning to counter-rotor type pumps, many questions arise.
It was investigated that the use of the counter-rotor effect in pumps significantly increases their head characteristics, but in turn the efficiency decreases. It is possible to ensure an increase in efficiency in the counter-rotor stages not only by influencing the change in the angle of installation of the blades, but also on the flow part and changing the specific speed coefficient. To study the dependence of the pressure-energy parameters on the speed coefficient, two counter-rotor stages with different configurations of blade grids were calculated.
The object of the research was the impeller of the pump CNS-180/1900 behind which was a bladed counter-rotor disk. In general, several studies have been conducted with two types of bladed discs (fig.1) to find the point with the highest efficiency values. Geometric dimensions, such as the diameter of the entrance to the impeller D1, overall diameter of the impeller D2, the diameter of the entrance to the blade disc D3 and overall diameter of the blade disc D4 remained unchanged in all studies. It should be noted that the geometric dimensions of the counter-rotor stage are as follows: outer diameter of the impeller D2=302mm; outer diameter of the blade disc D4=410mm; the gap between the working elements of the step 2mm; blade disc height h=52mm [3].
A normal impeller has the following characteristics: head Н=138m., power N=82 kW, efficiency η=0,82% capacity Q=180 m3/h. These are the pressure-energy characteristics of the wheel at maximum efficiency. Зlet's find the speed coefficient using formula (1).
As we can see, the speed coefficient for a conventional impeller is equal to ns=61
In the counter-rotary stage after the impeller, a blade disk was added to increase the head of the stage. It should be noted that for the calculation of the speed coefficient, the frequency of rotation of the working bodies is taken into account. The rotation frequency of the impeller and the blade disc are equal 3000 rpm relative to the pump casing or observer. When determining the speed coefficient separately for the impeller, we take the rotation frequency 3000 rpm., and for a blade disc 6000 rpm. This can be explained by the fact that when determining the speed coefficient, it is necessary to take the frequency of rotation relative to the liquid, and not the pump casing.
In multistage pumps, on the example of pumps CNS, the liquid leaves the impeller with a large twist of flow, after which it enters the diffuser, which leads the liquid to the next impeller with minimal losses and ensures an axisymmetric flow of liquid without twist. That is, there will be no twisting of the fluid flow at the entrance to the next impeller, as in all other impellers. In the counter-rotor stage, the process of fluid energy transfer is more complicated. At the entrance in front of the impeller, there will be no twisting of the fluid flow. After exiting the impeller, the liquid enters the blade disc with a certain amount of energy and flow twist equal to the frequency of rotation of the impeller. At the entrance to the blade disk, to its rotation frequency, it is necessary to additionally add the twist of the liquid that came out of the impeller. Thus, the frequency of rotation of the blade disk relative to the pump casing is 3000 rpm, but relative to the flow that came out of the impeller, in order to maintain the energy balance in the system, it is necessary to take 6000 rpm.
The first study of the counter-rotary stage was conducted with a capacity Q =172 m3/h (fig.3a). This feed corresponds to the optimal operating mode of the basic impeller. Based on the results of the research, head and energy characteristics of the first stage were obtained: head Н=412m., power N=292 kW, efficiency η=0,66%. Of them, the head of the impeller is separate Н=156m., and the blade disk Н=256m. Let's calculate the speed coefficients separately for the impeller and blade disk
As you can see, the speed coefficient has slightly decreased compared to the base stage. But if in pumps of the CNS type all the stages are the same, then in the counter-rotor pump, the stages, as we can see, have different configurations. Therefore, it will be appropriate to find the average value of the speed coefficient.
According to these values, it can be said that on average the speed coefficient has slightly increased.
The second study of the counter-rotary stage was carried out with a capacity Q =271 m3/h (fig.3b). With this feed, the highest efficiency of the first counter-rotor stage was obtained. Based on the results of the study, the following characteristics were obtained for the first stage with increased capacity: head Н=359m., power N=341 kW, efficiency η=0,78%. Of them, the head of the impeller is separate Н=131m., and the blade disk Н=268m. Let's calculate the speed coefficients separately for the impeller and blade disk.
Figure 3 – Fluid flow in the first counter-rotor stage
a) at nominal flow b) at increased feed.
The next study was carried out for a counter-rotary stage of a different configuration without changing the capacity (fig.4a). According to the results of the study, the following characteristics of the second stage were obtained: head Н=368m., power N=322 kW, efficiency η=0,56%. at Q =180 m3/h. Of them, the head of the impeller is separate Н=132m., and the blade disk Н=236m. Let's calculate the speed coefficients separately for the impeller and blade disk.
As you can see, the speed coefficients has increased slightly compared to the base stage. This happened due to a change in the blade grid, which in turn affected the characteristics of the step.
The average value of the speed coefficient.
The last study of the counter-rotary stage was carried out with a feed Q =432 m3/h (fig.4b). With this head, the highest efficiency of the second counter-rotor stage was obtained. Based on the results of the study, the following characteristics were obtained for the second stage with increased head: head Н=256m., power N=358 kW, efficiency η=0,84 Of them, the head of the impeller is separate Н=101m., and the blade disk Н=155m. Let's calculate the speed coefficients separately for the impeller and blade disk.
Figure 4 – Fluid flow in the second counter-rotor stage
a) at nominal flow b) with increased head.
Based on the obtained data, the following conclusions can be drawn. Firstly, due to the blade disk, the stage is able to create a much higher head and, in addition, to pump almost twice as much liquid, while having a good efficiency. Secondly, analyzing Figure 2, it is possible to increase the speed coefficient of the counter-rotor stage, as a result of which we will get a much higher efficiency based on the studies of the first and second stages with increased heade. As we can see, when the stage is working with small capacity, the impeller is underloaded. This causes vortex formation in the blade chambers and reduces the efficiency (Fig. 3a, 4a). This phenomenon occurs due to the fact that rarefaction is created at the entrance to the blade disk. At increased capacity, the liquid completely fills the inter-blade chambers, which causes the liquid flow to stabilize.
According to Figure 2, the best value of efficiency was obtained in stage, the speed coefficient of which was as close as possible to 150. As we can see, to such a stage (Fig. 4b) the flow of liquid between the blade chambers is stable and without vortex formations. There is a local increase in speed at the entrance to the blade disc due to the narrowing of the flow. In the future, by changing the design of the blades and the blade disc, it is possible to achieve better pressure-energy parameters.
References
1. Numerical study of the centrifugal contra rotating blade system / A. A. Kulikov et al. Journal of Physics: Conference Series. 2021. Vol. 1741. P. 012008. URL: https://doi.org/10.1088/1742-6596/1741/1/012008.
2. Effect of Impeller Trimming on the Energy Efficiency of the Counter-Rotating Pumping Stage / I. Pavlenko et al. Applied Sciences. 2023. Vol. 13, no. 2. P. 761. URL: https://doi.org/10.3390/app13020761.
3. Impact of the Closed, Semi-Opened, and Combined Contra-Rotating Stages on Volume Loss Characteristics / O. Kulikov et al. Journal of Engineering Sciences. 2022. Vol. 9, no. 1. P. D6–D13. URL: https://doi.org/10.21272/jes.2022.9(1).d2.
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