Population growth has led to a significant increase in demand for water resources. The scarcity of surface water has made tapping into available groundwater resources essential. This article presents a study focusing on water pumping using a less cumbersome wind system with improved efficiency. This is achieved by eliminating the power electronics interface and its control, which in turn removes harmonics generated by the static converter and requires less maintenance. The simulation results are compared with those from similar systems that include the power electronics bay.
In recent years, computational fluid dynamics has been increasingly used in the development of various types of rotating machines. In the case of water turbines and pumps, a large number of researches have been published recently, related to the use of different numerical methods for prediction of efficiency, cavitation characteristics and different dynamic phenomena. For basic analysis an accurate result near the optimal operating regime is sufficient, but for detailed analysis the numerical analyses in the wider field of operating conditions are necessary. Thus, some otherwise known physical phenomena that occur in the part-load and full-load regime may be encountered. In these areas, due to the nature of the flow, various non-stationary phenomena occur that are dominant for such operating regimes. This paper presents the problems that arise if only stationary results are taken into account, and some recommendations for avoiding subsequent problems in the operation of centrifugal pumps.
Cavitation is an essential problem that occurs in all kinds of pumps. This cavitation contributes highly towards the deterioration in the performance of the pump. In industrial applications, it is very vital to detect and decrease the effect of the cavitation in pumps. Using different techniques to analysis and diagnose cavitation leads to increase in the reliability of cavitation detection. The use of various techniques such as vibration and acoustic analyses can provide a more robust detection of cavitation within the pump. In this work therefore, focus is put on detecting and diagnosing the cavitation phenomenon within a centrifugal pump using vibration and acoustic techniques. The results obtained from vibration and acoustic signals in time and frequency domains were analysed in order to achieve better understanding regarding detection of cavitation within a pump. The effect of different operating conditions related to the cavitation was investigated in this work using different statistical features in time domain analysis (TDA). Moreover, Fast Fourier Transform (FFT) technique for frequency domain analysis (FDA) was also applied. Furthermore, the comparison and evaluation system among different techniques to find an adequate technique incorporating for accuracy and to increase the reliability of detection and diagnosing different levels of cavitation within a centrifugal pump were also investigated.
Complicated system of forces acts on the rotor of multi-stage centrifugal pump under its exploitation. Axial force is the biggest one for pumps with one-side inlet wheels. This force in many constructions of pumps is balanced by special automatic balancing device (ABD). This device consists of an unloading disk rigidly fixed on the shaft and a non-rotating supporting disk. The corresponding surfaces of these elements form cylindrical and face throttles arranged in series divided with the unloading chamber. Automatic operation of such devices is caused by the interdependence of hydrodynamic characteristics in cylindrical and face throttles. The middle gap value of cylindrical throttle is one of the main characteristics determining the pressure in the chamber and the ABD flow-rate value. The middle gap can increase due to erosive wear under pump operating, and it can result in negative impact on ABD operating. In this work, the intensity of erosion wear is considered as a function of middle velocity of flow and the coefficient of material wear. The middle velocity of flow in the cylindrical throttle is obtained by solving equations of turbulent fluid flow motion jointly with continuity equation. It allows one to determine the changes of the middle gap of cylindrical throttle in time and to estimate the influence of such changes on static and flow-rate characteristics of the ABD.
PL
Podczas pracy wielostopniowej pompy na jej wirnik oddziałuje złożony układ sił. W pompach posiadających wirnik z jednostronnym wlotem największą wartość uzyskuje siła osiowa. W większości spotykanych rozwiązań równoważenie tej siły odbywa się za pomocom specjalnego elementu konstrukcyjnego – tarczy odciążającej. Tarcza obraca się razem z wałem współpracując ze stałymi pierścieniami. Przestrzeń między tymi elementami tworzy układ dławiący. Jeśli wystąpi przemieszczenie wirnika w stronę wlotu, to wzrastające ciśnienie wywoła powstanie siły odsuwającej tarczę. Istotne znaczenie ma rozkład ciśnienia w układzie dławiącym. Występująca zdolność samoregulacji tarczy odciążającej zależy od charakterystyki hydrodynamicznej układu dławiącego. Grubość szczeliny cylindrycznego dławika może powiększać się podczas pracy pompy w wyniku erozyjnego zużycia powierzchni uszczelnienia. W opracowaniu intensywność zużycia uzależniono od średniej prędkości w szczelinie oraz współczynnika zużycia materiału. Wartość średniej prędkości uzyskano w wyniku rozwiązania układu równań ruchu cieczy w szczelinie oraz równania ciągłości. Takie podejście pozwoliło wyznaczyć grubość szczeliny dławika w funkcji czasu i oszacować jej wpływ na charakterystyki tarczy odciążającej.
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In petroleum and mine industries, the centrifugal pumps were used for transferring solid particles with water. This method is preferable to other methods because of its user friendly and economic issues. In this article by selecting a proper pump and designing test circuit,we conducted hydraulic tests for water and water mixture with solid particles. For this purpose, an experimental set-up of centrifugal pump with only water and water with solid particles was developed. Then by analyzing the test results and efficiency equation, optimal coefficients of head loss is provided to improve the pump efficiency during hydraulic transmission of solids. The experimental results of power consumption, head, and pressure difference measurements in solid-liquid systems are presented. The experimental set-up results are compared with simulation and numerical one, which show a good agreement with them. It reveals that by adding the solid particles and increasing the fluid density up to 15%, the consumed power increases by about 20%, which result in dropping the efficiency of hydraulic system up to 6%. Finally, the optimal components for developed cycle presented for evaluation the various configuration and hydraulic analysis of pure flow and flow with solid particles in various applications to enhance the most achievable efficiency.
The pump performance and occurrence of cavitation directly depends on different operating conditions. To cover a wide range of operation conditions for detecting cavitation in this work, investigations on the effect of various suction valve openings on cavitation in the pump were carried out. In order to analyse various levels of cavitation in different operation conditions, the effect of the decrease in the inlet suction pressure of the centrifugal pump by controlling the inlet suction valve opening was investigated using this experimental setup. Hence, the acoustic and pressure signals under different inlet valve openings and different flow rates, namely, 103, 200, 302 l/min were collected for this purpose. A detailed analysis of the results obtained from the acoustic signal was carried out to predict cavitation in the pump under different operating conditions. Also, the acoustic signal was investigated in time domain through the use of the same statistical features. The FFT technique was used to analyse the acoustic signal in the frequency domain. In addition, in this work an attempt was made to find a relationship between the cavitation and noise characteristics using the acoustic technique for identifying cavitation within a pump.
Centrifugal pumps are used for different applications that include pressure boosting, wastewater, water supply, heating and cooling distribution and other industrial processes. This paper presents theoretical and experimental investigations of mechanical vibrations of a centrifugal pump. The flow in this pump, which induces pressure pulsations and mechanical vibrations, have been monitored. Vibration measurements and data collection (overall vibrations levels and frequency spectrum) were extracted from the system. In addition, one of the methods used to study vibration amplitudes for this pump is forced response analysis. To study and analyze the pump system, the finite element analysis software (ANSYS) was applied. Depending on the analysis performed and investigations outcomes, the system natural frequency coincides with the vane-pass frequency (VPF) hazardously. To attenuate the system’s vibration, a vibration control element was used. The vibration levels were reduced by a factor of 2 for a tuned element as obtained from a forced harmonic response analysis of the pump system with absorber. It is shown that the inserted element allows the centrifugal pump to work in a safe operating range without any interference with its operation.
The small number of available complete modern pump characteristics makes the safety analysis of nuclear and conventional power plants based on the characteristics made over half a century ago of specific speeds nq = 24.6,147.1 and 261.4. The aim of the paper is to check sensitivity of the power plant system response for different complete pump characteristics–modern and available from older tests for nq = 24.6, 147.1 and 261.4. It has been shown that Suter’s characteristics for modern pumps give a different response to the pumping system of a power plant in break down than those used so far.
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Wyjaśniono problem pracy pompy poza zalecanym zakresem, wymaganymi warunkami napływu cieczy do króćca ssawnego i w konsekwencji ulegania awarii przez 2-strumieniową pompę wirową. Przedstawiono zagadnienie zwiększonego poziomu drgań, niewłaściwej konfiguracji zabudowy rurociągu ssawnego oraz zastosowanej armatury. Zilustrowano sposób diagnozowania i rozwiązywania problemu, który po wdrożeniu w docelowym miejscu pracy potwierdził słuszność wprowadzonych rozwiązań konstrukcyjnych.
EN
The issue of a pump operation beyond its recommended range and required flow conditions to the suction flange and consequently failure of double suction axially split centrifugal pump was explained. The increased vibration level, improper configuration of the suction pipeline and used hydraulics were presented. It was also illustrated how to diagnose and solve a problem which after implementation at the target workplace has confirmed the correctness of implemented design solutions.
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Multistage centrifugal pumps with variable speed drives are currently widely used in a variety of industrial and commercial applications. However, there are limitations to defining the efficiency of variable speed drive pumps. As an alternative method, energy saving rates can be evaluated with flow patterns and mean duty cycles. Computational fluid dynamics (CFD) is being used as a good tool to understand this and is less time consuming in terms of analyzing performances the experimental method. Research attention was focused on the energy saving rates of a multistage centrifugal pump for variable flow with variable speed drive through numerical and experiment methods. For this investigation Reynolds-averaged Navier-Stokes (RANS) equations were discretized by the finite volume method and a two equations SST model was used to account for three dimensional steady state flows. In the experimental system, an experimental set-up of a variable flow system was made to obtain energy saving rates and computational results were validated. The energy saving rates of the pumps depend on the flow patterns and specific mean duty cycles on which the machine or system operates. Mean duty cycles were divided into different flow operating conditions and a weighting for the mean value was given for each segment according to interval time. The pump system was operated at 50_70% of maximum flow rates. The energy saving rates were obtained from input power through CFD simulation and experimentally, and the mean duty cycle was obtained from flow patterns in the field of the pump. Energy saving rates were evaluated as a function of mean duty cycle and input power of the system operation. The total energy consumed for the constant speed drive was 25,922 kWh and for the variable speed drive pump was 17,687 kWh through CFD. The total annual energy saving rates were annually 33.81% through computational and 31.77% through experimental method with the variable speed drive system when compared to the constant speed drive system.
Wykorzystując algorytm zaproponowany we wcześniejszym artykule rzedstawiono wybór uszczelnienia czołowego pompy wirowej do przesyłania wody. Zebranie danych początkowych umożliwiła ankieta, którą producenci uszczelnień zwykle zamieszczają na stronie internetowej. Dla określonych warunków pracy wybrano uszczelnienie czołowe z obracającą się obudową, osadzone wewnątrz kadłuba z hydraulicznym odciążeniem. Kolejny krok polegał na sprawdzeniu granicznych wartości parametrów eksploatacyjnych uszczelnienia jak ciśnienie, temperatura i prędkość obrotowa z uwzględnieniem zastosowanych materiałów i cieczy.
EN
Using the algorithm proposed in the earlier paper a selection of face seal for the water transportation pump is presented. Data necessary for the selection can be found in manufacturer's website for seals. A front-facing seal with the rotating housing, mounted inside the hull with hydraulic relief was selected for given operating conditions. The next step was to check limits for seal operating parameters such as pressure, temperature and rotational speed with respect to materials and solutions used. The presented analysis and seal selection was of a simplified character.
Cavitation is a common cause of failure in centrifugal pumps. Because of interaction of several mechanical parts and fluid, the vibration signal of a centrifugal pump is complicated. In this paper, the vibrations of a transparent-casing centrifugal pump are studied. Three states are studied experimentally: no cavitation, limited cavitation and developed cavitation. Each case was also confirmed by visually inspecting the cavitation bubbles. The vibrations of the pump was acquired by using an accelerometer that was attached to the casing. Discrete wavelet transform (DWT) analysis and empirical mode decomposition (EMD) are used to extract classification features from the acquired signals. Using these features, an artificial neural network (ANN) successfully diagnosed the cavitation condition of the pump. Finally, EEMD is also implemented. The results showed the success of EMD and DWT in cavitation diagnosis. The output of EEMD does not show significant change comparing to EMD.
W artykule opisano schemat typowego układu pompowego i pokazano jego statyczne i dynamiczne charakterystyki, istotne przy komputeryzacji ich pomiaru. Przedstawiono skomputeryzowane stanowisko badawcze do wyznaczania podstawowych charakterystyk statycznych i dynamicznych pompy wirowej i rurociągu. Oprogramowanie wspomagające pomiary umożliwia wyznaczenie parametrów energetycznych pompy na podstawie zmierzonych wielkości fizycznych. Stanowisko ułatwia pomiary i opis krzywych rozwoju kawitacji, a także wyznaczenie pełnej charakterystyki kawitacyjnej pompy. Opracowana karta pomiarowa pozwala na ocenę zgodności parametrów nominalnego punktu pracy z parametrami katalogowymi wg obowiązującej normy dla przyjętej klasy maszyny. Przedstawione skomputeryzowane stanowisko badawcze dedykowane jest do pomiarów odbiorczych pomp odśrodkowych.
EN
In the paper it is described a schema of typical pump system and it is shown its static and dynamic characteristics which are essential in the process of computerization measurements of the characteristics. Compurized test stand for operational measurements has been presented. The article describes the basic static and dynamic characteristics of a centrifugal pump and pipeline Software aiding measurements make possible to determine pump parameters on the basis of measured physical quantities. Test-stand is labour-saving for measurements, description of cavitational development curves and determination of cavitational pump characteristics. Elaborated measurement card makes possible to compare working point with catalogue parameters.
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The performance of pumps are influenced by many factors among which the geometric configuration of the volute. The role of the volute in a centrifugal pump is the transformation of the kinetic energy into pressure with a minimum of losses. The volute is a pump element which is difficult to modify. It must be able to be adapted to impeller with different dimensions. The objective of this work is to investigate by numerical simulation the Von Mises stress distribution and displacements in volutes of different dimension in diameters and width of a centrifugal pump. The study is carried out using finite element method on a three dimensional configuration using ABAQUS code. Only a few attempts of numerical analyses of the mechanical behavior of volute are made. This element plays an important role in the pump adaptation for a given operating conditions by adjusting its dimensions. This activity is conditioned by a good understanding of 418 Belbachir, S., Allali, A., Lousdad, A. E. and Benguediab, M. the design process of the volutes. The obtained results show the modifications of the diameter and the width of the volute have an effect on the values of Von Mises’ stresses and on the displacements. The stresses and displacements reach their maximum with increasing diameters and are inversely for the increase in the width. These dimensional modifications can act indirectly on the clearance at the bec and also on the clearance between the volute exit and the impeller. These are functional clearances which allow the determination of the operating characteristics of centrifugal pumps. With these results substantial improvement on the pump design can be made.
Spectral analysis is the key tool for the study of vibration signals in rotating machinery. In this work, the vibration analysis applied for conditional preventive maintenance of such machines is proposed, as part of resolved problems related to vibration detection on the organs of these machines. The vibration signal of a centrifugal pump was treated to mount the benefits of the approach proposed. The obtained results present the signal estimation of a pump vibration using Fourier transform technique compared by the spectral analysis methods based on Prony approach.
PL
Analiza widma jest kluczowym narzędziem badania sygnałów dotyczących wibracji w maszynach wirujących. W niniejszej pracy proponuje się analizę wibracji dla oceny stanu technicznego tych maszyn w ramach utrzymania prewencyjnego, bazującą na detekcji wibracji ich poszczególnych elementów. Przydatność i korzyści zaproponowanego podejścia zostały ocenione podczas badania pompy odśrodkowej. Uzyskane wyniki przedstawiają estymację sygnałów wibracji pompy z wykorzystaniem transformaty Fouriera w porównaniu z przeprowadzoną analizą widma z zastosowaniem modelu Prony’ego.
This article presents a process for developing a simplified model of a centrifu-gal pump impeller in a CAD environment. Developing a virtual object involved modeling an impeller of a pump both in working condition and with one of the blades damaged. The resonant frequency magnitudes obtained as the result of the analysis of the model were compared with the results obtained in the measurements carried out on a real object. The measurements and simulations were carried out on a pump before and after the damage to the impeller. In order to verify the developed model, particular elements of the model were weighed and then compared with the corresponding masses of the corresponding elements obtained from the virtual object.
PL
W artykule zaprezentowano proces tworzenia uproszczonego modelu wirnika pompy wirowej w środowisku oprogramowania CAD. Konstruowanie obiektu wirtualnego obejmowało modelowanie wirnika pompy sprawnej oraz z symulowanym uszkodzeniem jednej z łopatek. Porównano wyniki częstotliwości rezonansowych uzyskanych w wyniku analizy modelu z uzyskanymi w trakcie pomiarów na rzeczywistym obiekcie. Pomiary i symulacje przeprowadzono na pompie przed i po uszkodzeniu wirnika. W celu weryfikacji sporządzonego modelu poszczególne elementy pompy poddano ważeniu i porównano z masami odpowiednich elementów uzyskanych z obiektu wirtualnego.
The full cavitation model is increasingly applied in the cavitating flow simulation and the cavitation performance prediction of a centrifugal pump to improve or optimize its hydraulic design. Since the model involves surface tension and non-condensable gas content, it can be potentially applied in predicting cavitation behaviour of a centrifugal pump when handling viscous oils that possess different surface tension and gas content than water. However, the model has not been validated extensively against experimental incipient cavitation and NPSHr (net positive suction head required) data so far. In the paper, the cavitation performance of an experimental centrifugal pump is investigated using the CFD code and the full cavitation model when pumping water. The incipient cavitation number-flow rate curve and head-NPSHa (net positive suction head available) relationship are established and compared with experimental observations. The relationship between the head and integrated vapour-liquid volume ratio in the impeller is argued. The influence of the non-condensable gas content and turbulence model on the head-NPSHa curve is clarified. The cavity pattern predicted is compared with the visualized one. The computational methods adopted and the results achieved here can be useful for the cavitation performance prediction of a centrifugal pump in engineering.
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W artykule przedstawiono nową konstrukcję zatapialnego agregatu pompowego, który dzięki wprowadzonym oryginalnym rozwiązaniom w układzie przepływowym uzyskuje wysoką sprawność. Agregat posiada szereg zabezpieczeń, które wyłączają silnik w uzasadnionych sytuacjach i chronią przed dalszymi uszkodzeniami. Przedstawiono analizę różnych parametrów pracy agregatu pompowego, których przekroczenie może być zagrożeniem dla agregatu i powinno być przyczyną jego wyłączenia czasowego lub trwałego przez układ czujników i sterownik współpracujący z wyłącznikiem.
EN
The paper presents new construction of submersible pump, which obtains high efficiency thanks to original solutions of flow channels. The submersible pump has several safety devices which turn off electric engine in explained situations and protect against next damages. The paper includes an analysis of various parameters of pump’s work, which transgression could become a danger for submersible pump. In case of the danger the security system turns off the engine temporally or permanently.
Objective: The paper deals with the experimental investigations of the vibrations of the centrifugal fire pump with a hidden defect. The aim of the work is to identify the vibrational symptoms which accompany the operation of a fire pump with a defect (unfastened shaft in a bearing seat). This information is applicable for the technical diagnostics of the fire pumps in operation. Project and methods: The research consisted in a set of experimental tests of a centrifugal pump installed on the active fire engine. The experiments were carried out with the application of the measurement system “Ultra-V-I”. The system has a valid certificate of state metrological certification, issued in Ukraine, and allows to make measurements of vibration acceleration of the investigated object. All signals were spectrally analysed. The Fast Fourier Transform (FFT) was used for these procedures. A spectral analysis for transient regimes of vibrations was carried out with the application of short-time Fourier transform. Results: The changes in the spectrum and orientation of vibrations fire pump with the mentioned type of defect were identified. The analysis of the spectra of vibrations at the frequency of excitation of 2000 rpm in the vertical direction shows strong domination of 7 harmonic (233 Hz). Besides, the spectrum involves first (33.3 Hz), third (99 Hz) and fourth (133 Hz) harmonics of rotor rotation. However, the most important phenomenon consists in the presence of fraction harmonics in the spectrum, which in turn indicates system nonlinearities caused by loosening and contact impacts. These harmonics are 0.5 and 3.5 harmonics of rotor rotation (16.5 Hz and 116.6 Hz). A quantitative comparison shows that the largest vibration level is observed in the axial direction and the smallest one is observed in the horizontal direction. The comparison of vibrations of the defected and non-defected fire pumps shows that the defect makes an axial direction weaker and it leads to increasing axial vibration acceleration up to 80%. Vibrations in other directions are approximately the same in case of defected and non-defected pumps. Changes in the orientation angle of the vibrations ellipse trajectory were identified. Conclusions: The information about vibrational symptoms of the analysed type of hidden defect is useful in fire pumps technical diagnostics. This method will improve the quality of systems technical check-ups as well as their preventive maintenance. This in turn will contribute to the decrease in the amount of firefighting equipment left standing idle due to untimely repair works as well as prevent sudden failures of the utilised pumps.
PL
Cel: W artykule omówiono badania eksperymentalne wibracji pompy odśrodkowej, w której stwierdzono ukrytą wadę. Celem pracy jest określenie charakterystyk drgań mechanicznych, które towarzyszą pracy pompy z defektem (luz w gnieździe łożyska). Wiedza ta ma zastosowanie dla diagnostyki stanu technicznego użytkowanej pompy pożarniczej. Projekt i metody: Omawiana analiza polegała na wykonaniu szeregu testów eksperymentalnych na odśrodkowej pompie pożarniczej zamontowanej w uruchomionym samochodzie pożarniczym. Eksperymenty przeprowadzono z wykorzystaniem systemu pomiarowego „Ultra-V-1”, posiadającym ważny państwowy certyfikat metrologiczny wydany na Ukrainie i pozwalającym na wykonanie pomiarów przyspieszenia wibracji badanego urządzenia. Wszystkie sygnały poddano analizie widmowej z wykorzystaniem szybkiej transformacji Fourier. Analiza widmowa dla przebiegów przejściowych wibracji była dokonana przy użyciu krótko-czasowej transformaty Fouriera. Wyniki: Określono zmiany w widmie i kierunku wibracji pompy pożarniczej z danym typem defektu. Analiza widmowa wibracji przy częstotliwości wzbudzenia na poziomie 2000 obrotów na minutę w kierunku pionowym wykazuje silną dominację siódmej harmonicznej (233Hz). Ponadto w widmie obecne są pierwsza (33,3 Hz), trzecia (99 Hz) i czwarta (133 Hz) harmoniczne obrotu wirnika. Niemniej jednak najważniejszym odnotowanym zjawiskiem jest obecność dodatkowych składowych harmonicznych w spektrum dla niskich częstotliwości, co wskazuje na nieliniowość systemu, spowodowaną poluzowaniami i oddziaływaniami kontaktowymi. Są to harmoniczne 0,5 i 3,5 częstotliwości obrotu wirnika (16,5 Hz i 116,6 Hz). Na podstawie analizy porównawczej stwierdzono, iż największy poziom wibracji ma miejsce w kierunku osiowym, a najmniejszy – w kierunku horyzontalnym. Porównanie wibracji pompy pożarniczej z defektem i bez defektu wykazało, że defekt osłabia kierunek osiowy, a to powoduje zwiększenie przyśpieszenia drgań osiowych do 80%. Wibracje o innych kierunkach były zbliżone do siebie w przypadku pomp sprawnych i z uszkodzeniem. W toku badań zauważono zjawisko zmiany kąta orientacji trajektorii eliptycznej drgań. Wnioski: Przeprowadzone badania dotyczące analizy zmian drgań mechanicznych pompy odśrodkowej z ukrytym defektem. Otrzymane wyniki mogą zostać wykorzystane w procedurach diagnostyki technicznej pomp gaśniczych. Wykorzystanie tej metodyki badawczej przyczyni się do polepszenia przeglądów technicznych i zabiegów profilaktycznych, co z jednej strony wpłynie na zmniejszenie zastoju będącego skutkiem przeprowadzania prac naprawczych w nieodpowiednim czasie, a z drugiej strony pozwoli zapobiegać nagłym awariom użytkowanych pomp.
The unsteady flow fields in a centrifugal pump at the shut-off condition (SOC) are simulated by the Unsteady Reynolds Averaged Navier-Stokes (URANS) approach. To improve simulation accuracy and assign the boundary condition, special 3D models are made. Three-dimensional URANS equations are solved on high-quality unstructured grids with the shear stress transport turbulence model by using the computational fluid dynamics (CFD) code CFX-11.0. Furthermore, the numerical simulation results are validated by particle image velocimetry (PIV) measurements. The main goal of the study is, on one hand, the validation of the numerical procedure proposed, and on the other hand, the detailed analysis of the unsteady inner flow field distribution and pressure fluctuation in the centrifugal pump at SOC. In addition, the head of the pump at SOC is predicted based on CFD results. The flow analysis indicates that there exists two eddies in each impeller flow passage, and the velocity at the volute diffusion part is very low. The amplitudes of pressure fluctuation at ƒr (impeller rotation frequency) and 3ƒr dominate in the impeller, while the pressure fluctuation at ƒb (blade passing frequency) is dominant in the volute.
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