© Strojni{ki vestnik 46(2000)8,538-548 © Journal of Mechanical Engineering 46(2000)8,538-548 ISSN 0039-2480 ISSN 0039-2480 UDK 621.67:534.83:681.892 UDC 621.67:534.83:681.892 Pregledni znanstveni ~lanek (1.02) Review scientific paper (1.02) Analiza obratovalnega hrupa in vibracij okrova radialne ~rpalke Radial Pump Operating Noise and Casing-Vibration Analyses Andrej Predin - Mitja Kastrevc - Ignacijo Bilu{ V prispevku je podana teoretična in eksperimentalna študija dinamičnih tekočinskih vibracij in hrupa. Eksperimentalne meritve so izvedene na enostopenjski radialni črpalki, ki obratuje s čisto hladno vodo. Pri različnih obratovalnih režimih (vrtilnih frekvencah rotorja) so izvedene meritve naslednjih obratovalnih karakteristik: dusilna krivulja, pretok - izkoristek, pretok - obratovalni hrup in pretok -amplituda vibracij okrova. Rezultati meritev so podani v časovnem in frekvenčnem prostoru. © 2000 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: črpalke radialne, hrup črpalk, meritve vibracij, minimiranje hrupa) This paper surveys theoretical and experimental studies of fluid-dynamic vibration and noise. The experimental measurements were carried out on a radial one-stage pump which operates with clean cold water. Several experimental measurements on the operating characteristics such as capacity-head, capacity-efficiency, capacity-operating noise and capacity-pump casing vibration amplitudes under different operating regimes (different impeller speed) were performed. Measurement results are given in time and frequency domains. © 2000 Journal of Mechanical Engineering. All rights reserved. (Keywords: radial pumps, pump noise, vibration measurements, noise minimization) 0 UVOD Obratovalni hrup in vibracije okrova sodobnih črpalk morajo biti minimalni. V ta namen moramo reducirati vse vire. Obratovalni hrup in vibracije okrova so posledica pulzirajočih tokovnih veličin na izstopu iz rotorja. Hrup se sprošča vedno, ko imamo opravka z relativnim gibanjem dveh tekočin (kavitacija - voda in para) ali tekočine in trdne stene (lopatice). Značilni viri hrupa črpalk vsebujejo časovno spremenljiv sistem sil, ki delujejo na eno ali več komponent črpalke. Hrup je rezultat reakcije tekočine na omenjene sile in vsiljenega nihanja teles, ki so v stiku s tokom. Vibracije okrova in njegovih mirujočih ter gibajočih se delov so posledica tokovno vzbujenih vibracij teles v ustaljenem ali pulzirajočem in turbulentnem toku. Pri tokovno vzbujenih vibracijah je prav tako treba upoštevati tudi različne vibracijske oblike kakor pri nihajočih trdnih telesih. Pulzacija toka na izstopu iz rotorja je posledica nepopolnosti rotorja in še posebej relativnega vrtinčnega toka v posameznem rotorskem kanalu, ki je pri obratovanju zunaj preračunske točke (točka največjega izkoristka) še močnej ši in povzroča nepravilni natok 0 INTRODUCTION Modern pumps are expected to have their op-erating noise and casing vibrations minimized. In this way the noise and vibration pollution of the surround-ings are reduced. The operating noise and casing vibra-tions of radial pumps are a consequence of the pulsating fluid flow properties at the impeller exit. Noise may be emitted whenever there is a relative motion of two fluids (cavitation – water and vapour) or a fluid and a solid surface (blades, vanes). Typical sources of noise from pumps involve a time-varying system of forces affecting one or more components of the pump. Noise results from the fluid’s reactions to this force as well as from the forced vibration of structures in contact with the flow. The vibration of the pump casing and its static and dynamic (moving) parts are a consequence of the flow-induced vibration of solid structures in stationary or pulsating and turbulent flow. Therefore, the subject of flow-induced vibrations must also consider the vibration of structures of a single mode or of many modes as well. The pulsating flow at the impeller exit is the result of impeller imperfec-tions, especially, of the relative flow whirl in an individual impeller channel. The whirl increases by shifting the op-erating mode out of the optimum regime (out of the best VH^tTPsDDIK stran 538 A. Predin - M. Kastrevc - I. Bilu{: Analiza obratovalnega hrupa - Operating Noise Analses v rotorske in vodilne kanale. Tako nastane neustaljeni pulzacijski turbulentni tok, ki povzroča vibracije okrova. Moč opisanih tokovnih pulzacij v posameznih obratovalnih režimih (obratovanje pri majhnih, pod optimalnih pretokih) se spreminja. Odvisna je od natočnega kota na rotorske lopatice, ki se spreminja v odvisnosti od pretoka in/ali vrtilne frekvence. Študija hidravličnih lastnosti črpalke je zasnovana na modelu črpalke, na katerem so opazovane vibracije okrova in hrup v odvisnosti od vrtilne frekvence. Pri meritvah so določeni tudi različni mehanizmi tokovnih motenj. Za minimizacijo hrupa in vibracij moramo vedeti, da se te povečujejo s povečanjem vrtilne frekvence rotorja in tudi kadar je obratovalni pretok ali obratovalna točka črpalke zunaj točke največjega izkoristka. Hrup in vibracije okrova so minimalne, ko črpalka obratuje z optimalnim pretokom, ki je največkrat kar preračunski pretok. Če pa želimo dosegati zahtevano črpalno višino in pretoke pri manjših vrtilnih frekvencah rotorja, morajo biti izstopne hitrosti toka večje. Te lahko dosežemo le s povečanjem izstopnega kota rotorskih lopatic ali s povečanjem izstopnega premera rotorja. Na žalost sta oba postopka omejena s trdnostjo materiala in kavitacijskimi problemi. Zaradi tega je za minimizacijo hrupa in vibracij priporočena standardna tridimenzionalna metoda optimizacije med vrtilno frekvenco rotorja, izstopnim kotom rotorskih lopatic in izstopnim premerom rotorja. efficiency point – BEP), and causes the irregular loading of the impeller and guide-vane channels. As a result, the non-stationary pulsating and turbulent flow that causes the casing vibrations is created. The intensity of the flow pulsations in some particular pump regimes (operating with small under-optimum capacities) is changed. It de-pends on the angle of flow attack to the impeller blade that is changed by the operating capacity or/and by changing the impeller speed. The study of pump hydraulics behaviour is based on the pump-scale model in which the noise and casing vibrations observed for a given configuration as a function of the impeller speed are tested. With meas-urements, the particular disturbance mechanisms are determined. For minimizing the pump operating noise and casing vibrations it is necessary to know that the noise intensity and pump-casing vibration amplitudes increase as the impeller speed increases. They also in-crease when the operating capacity, or pump operating point is out of the BEP. The minimum noise intensity and pump casing vibration amplitudes exist when the pump operates at optimum capacity, that is in most cases the pump design capacity. However, if we want to sat-isfy the required head and capacity with a smaller impeller speed, the flow velocities at the impeller exit must be larger. This can only be achieved by increasing the impeller-blade exit angle or by increasing the impeller-exit diameter. Unfortunately, both approaches are limited by impeller material strength and by cavitation problems. For these reasons the classic 3D optimisation plan of the impeller speed, the blade’s exit angle and the impeller-exit diameter for the minimization of the pump operating noise and casing vibration are recommended. 1 DIMENZIJSKA ANALIZA NASTAJANJA ZVOKA 1 DIMENSIONAL ANALYSIS OF SOUND GENERATION Za analizo tokovno vzbujenih motenj razdelimo tok na časovno povprečno in oscilirajočo komponento (Reynoldsov postopek). V skladu s tem je lokalna hitrost v določeni točki definirana kot vsota povprečne vrednosti in trenutnega odmika od tega časovnega povprečja. Hitrost v točki tekočinskega toka je tako predstavljena z: The first feature of flow-induced disturbance to note is that flow is generally usefully regarded as a mean plus a fluctuating part (Reynolds’ idea). There-fore, the local velocity at a particular point may be regarded as a superposition of an average value and an instantaneous fluctuating part. Thus the velocity at a point in the fluid flow may be described by: U =U + u(x,y,z,t) (1), kje sta - Upovprečna vrednost in u(x,y,z,t)- njena oscilirajoča vrednost, ki je odvisna od časa in lege v toku in jo poenostavljeno lahko določimo kot: where U is the average value and u(x,y,z,t) is the unsteady value which depends on time and location in the flow, and can be determined in a simplified way as: 2(t) = - 0 u2(t)dt J kjer je t - opazovan časovni trenutek. V dinamično podobnih tokovih, pri katerih je zahtevana enakost tako amplitude kakor faze, ostane zveza med silami in premiki nespremenjena, kar je pri primerjavi modela s prototipom upoštevamo v razmerju: (2), 0 0 where t0 is the observation time. In similar dynamic flows, this requires the relationship of both the magnitude and the phase, among forces and motions to remain fixed, for example in a model-to-full-size comparison, the ratio: A. Predin - M. Kastrevc - I. Bilu{: Analiza obratovalnega hrupa - Operating Noise Analses u(t) U (3), ki je nespremenljivo, ne glede na vrednost U, ta pomeni stopnjo hitrostnih spremeb glede na povprečno hitrost [1] in [2]. Da bi lahko bilo zgornje razmerje nespremenljivo, morajo biti v ravnotežju tudi različne napetosti, ki delujejo na tekočinske delce. Ponavadi je to kombinacija vztrajnostnih in viskoznih sil, katerih razmerje je definirano z Reynoldsovim številom. Zgoraj omenjena podobnost je zelo pomembna, saj je vzbujevalna tlačna napetost, označena s p, ki vzbuja hrup ali vibracije v danem toku v neposrednem razmerju: is a constant, regardless of the value of U , that is, the distribution of velocity fluctuation’s scales on the mean velocity, [1] and [2]. For maintenance of this constancy through the flow, the balance of the various types of stress that act on fluid particles must also be main-tained. Generally these are the combinations of the inertial and viscous stress and a measure of the ratio of the inertial to viscous stress in the flow is the Reynolds number. The above-mentioned similitude is important because of the exciting stress, denoted here by p , that produces sound or vibration in a given type of flow which is in direct proportion as: r0U2 (4), kjer pomenita: r0 - gostoto tekočine, pd- dinamični tlak. Sorazmernost velja tako dolgo, dokler sta sorazmerni tudi povprečna in oscilirajoča komponenta hitrosti. Ker sta napetosti, ki povzročata hrup in vibracije sorazmerni dinamičnemu tlaku pd, lahko le-tega privzamemo za merilo moči vzbujanja. Merilo ujemanja hidrodinamičnih ali aerodinamičnih gibanj in hitrosti delčkov glede na hitrost širjenja zvoka je Machovo število, ki pomeni razmerje med hidrodinamično hitrostjo in hitrostjo zvoka. Reynoldsovo in Machovo število predstavljata relativen pomen vztrajnostnih, viskoznih in tlačnih napetosti v tekočini. Za dinamično in akustično podobnost modela in prototipa morata biti poleg podobne geometrijske zato enaki tudi vrednosti Reynoldsovega in Machovega števila. 1.1 Stopnja zvočnega tlaka Osnovna merjena veličina zvoka v določeni točki je tlak p. Ker je zvok dinamični pojav je tudi akustično vzbujen tlak časovno spremenljiva veličina. Običajno merilo akustičnega tlaka je njegova časovno povprečena kvadratna vrednost: where r0 is the fluid mass density and pd is the dynamic pressure. The proportionality may hold as long as the fluctuating velocity and the mean velocity are also proportional. Since the sound- and vibration-pro-ducing stresses are proportional to pd , this can be taken as a measure of the intensity of the magnitude of the excitation. A measure of the matching of fluid iner-tial motions of hydrodynamics or aerodynamics and the particle velocities related to the propagation of sound is the Mach number, which expresses the ratio of the hydrodynamic velocity to the acoustic particle velocity. The Reynolds and Mach numbers express the relative importance of inertial, viscous, and compressive stress in the fluid. Fluid dynamics and acoustic similitude therefore ideally require, in addition to similar geometries, equal values of Reynolds and Mach numbers for model and prototype. 1.1 Sound pressure level The principal measured property of sound is the pressure (p) at a point. Since sound is a dynamic phenomenon, the acoustically induced pres-sure is also a time-varying quantity. The measure of acoustic pressure that is conventionally reported is the time average of a pressure squared, that is: T /2 - j pt) dt (5) s časovnim povprečjem enakim nič, p = 0, ki je v preprosti zvezi z intenziteto in stopnjo jakosti zvoka. Stopnja zvočnega tlaka je določena z: -T /2 with the time average equal to zero, p =0 . This is sim-ply related to sound intensity and power levels. The sound pressure level is determined from the above as: L = 10log(p2 /p2 (6), kjer je p = 2 . 10-5 N/m2, ali 20 mPa za zvok v plinih, in 106 N/m2, ali 1 mPa za zvok v kapljevinah. Če obravnavamo širjenje zvoka na močnostni bazi, je stopnja moči zvoka podana z: . where pref = 2 10-5 is N/m2, or 20 mPa for sound in gases, and 10-6 N/m2, or 1 mPa for a sound in liquids. Generally, if the sound transmission is considered on a power basis, the sound power level is defined as: 10log(P /Pref (7), VBgfFMK stran 540 A. Predin - M. Kastrevc - I. Bilu{: Analiza obratovalnega hrupa - Operating Noise Analses kjer sta P - moč zvoka, prenesena prek določene površine in P f - referenčna veličina, ponavadi enaka 10 12 W. MoČ zvoka, prenesenega prek krogelne površine A tvori točkast izvor, ki je v naslednji zvezi z zvočnim tlakom: where P is the sound power transmitted across a speci-fied surface and Pref is a reference quantity convention-ally taken as 10-12 W. The sound power radiated across a spherical surface of the area As, forms an omni-direc-tional source that is related to the sound pressure as: Ln = L +10log ( p2 A lr 0c0Pj (8), kjer je c0 - hitrost zvoka. Intenzivnost zvoka lahko določimo iz: LI = 10log where c0 is the acoustic speed. The sound intensity level may be found from: (9), kjer je zveza akustične intenzivnosti s povprečno kvadratno vrednostjo tlaka definirana kot: where the acoustic intensity is related to the mean-square pressure by: p2 I= r0c0 (10) in / = 10 12 W/m2. Akustična intenzivnost je dejansko vektorska veličina. Če je dovolj daleč od vira, je njena smer normalna na krogelno površino, ki točkasti izvor obdaja. Smer I je na dovolj veliki oddaljenosti, torej radialno iz središča izvora. V črpalki veljajo med dimenzijskimi parametri naslednje zveze: tipske hitrosti tlačna razlika Dp oc r D2n2s and / = 10 12 W/m2. The acoustic intensity is a vector property. However, far enough from the source the acoustic energy intensity across a spherical surface surrounding the source is directed normal to the surface. Therefore in the far field the direction of/is radial from the acoustic centre of the source. In a pump the following relationships apply between dimensional parameters: the tip speed UT