experimental identification of fluid thin film dynamic...

Experimental Identification of Fluid Thin FilmDynamic Coeicients for Space Propulsion TurboPumpsPascal Jolly1*, Olivier Bonneau1, Mihaı Arghir1, Romain Gauthier2, Jerome Dehouve3

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

Abstractrough an application example, a test rig dedicated to the measurement of rotordynamic coef-cients for thin uid lm components, as encountered in liquid Rocket Engine Turbopump, ispresented. Low viscosity uids (as cryogenic uids), leads to thin lm ows with high Reynoldsnumber. Tests are performed with a Reynolds similitude, using warm water and a component’snominal diameter about ten times larger than the prototype (for bearings and seals). Typical resultsare presented for a front shrouded centrifugal pump impeller, using various kinds of eye-packingseals and a vaned diuser. All the tests have been operated with a centered position of the rotor. Forvarious rotor speeds, experimental data (displacements, forces, pressures, owrate, temperatures,torque) have been recorded for steady-state static case and dynamic excitations (frequency rangefrom 20 to 80 Hz in 10 Hz increments). First, the performance curves are discussed. en, theidentied dynamic coecients are presented.[?]KeywordsTest Rig — Dynamic Coecients — Turbopump — Impeller1Institut Pprime CNRS, Universite de Poitiers, ISAE ENSMA, Poitiers, France2ARIANE GROUP, Vernon, France3CNES DLA, Evry, France*Corresponding author: [email protected]

INTRODUCTIONIn order to estimate vibration levels caused by uid-structuralinteractions, designers of turbopumps can use rotordynamicmodels, where input parameters for each component actingon the rotor (bearings, seals, impellers) consist in linearizeddynamic coecients. In the case of thin uid lm compo-nents (like labyrinth seals and uid bearings), uid inertiaeect is signicant and it is good to validate theoretical simu-lations against experimental results. A consortium of Frenchcompanies (CNES, ASL, EDF R&D, ALSTOM) together withCNRS (French Scientic Research Center) and the Universityof Poitiers have built a test rig specially dedicated to the ex-perimental analysis of these uid components. is test rignamed BALAFRE (”BAnc LAmes Fluides a haut nombre deREynolds”) measures the displacements induced by dynamicexcitations and the resulting uid lm responses. ese mea-surements enable the identication of the dynamic behavior(stiness, damping and added mass) of uid bearings, seals orimpellers. e paper describes the test rig and some typicalresults obtained for a centrifugal impeller.

1. TEST FACILITYe test rig BALAFRE (BAnc LAmes Fluides a haut nombrede REynolds) is dedicated to the identication of dynamicforce coecients of thin uid lm components of high speedrotating machines. ese components oen use a low viscos-

ity process uid as lubricant (in cryogenic applications forexample). erefore, the ow in the thin uid lm exhibitshigh Reynolds numbers. In order to reproduce experimen-tally these high Reynolds numbers regimes, the test rig useshot water as lubricant (temperatures limited to 50°C), inletpressure as high as 45 bar and tested components can have anominal diameters up to 350 mm. ese conditions lead toaxial and circumferential Reynolds number up to 105. etest rig is mainly composed of a test cell, an electric motor,a hydraulic system (with pumps, tanks, lters and valves)and a Programmable Logic Controller associated with DAQdevice. A cross section view of the test cell is shown in Figure1, where the tested component (an annular seal in the presentconguration) is overhung mounted at the le end of a ro-tating sha 7 . e rotor and the stator of the annular sealare respectivelly indicated as 1 and 2 . is design givesa great modularity to the test cell, where various kinds ofcomponents have benn mounted : seals, hydrostatic bearingsand impellers.

e whole test rig is pressurized at 5 bar. is means thatan annular seal can have a maximum pressure dierence of40 bar between the upstream and the downstream (discharge)chambers. e necessary ow rate (up to 120m3/h) is deliv-ered by two centrifugal pumps driven by electrical motorswhose total power is 330 kW. e maximum sha speed (6000rpm) is obtained with a three-phase asynchronous motor of180 kW. A double conical hydrostatic thrust bearing is lo-

Experimental Identification of Fluid Thin Film Dynamic Coeicients for Space Propulsion Turbo Pumps — 2/7

Figure 1. Cross sectional view of the test rig

cated close to the test component. It has many roles: rst itmust guide the rotation of the sha and support the staticaxial load (which can reach as much as 200 kN) generatedby the 40 bar pressure dierence between the two faces ofthe annular seal. Its second role is to transmit the excitationsimposed by the 8 piezoelectric actuators mounted four byfour along two planes. e housing of the bearing is linkedto the frame via a hollow tube 6 designed to be very stiaxially and exible in the radial direction. e rst naturalfrequency of the bending mode of the sha is 460 Hz; thetwo rst natural frequencies of the torsional modes are 14 Hzand 269 Hz. e double conical hydrostatic thrust bearing isprovided with 2x6 recesses and orice restrictors [1] and isfed with water at 150 bar. e average uid lm thicknessin the two parts of the bearing is about 40 µm and the axialand radial stinesses are larger than 109 N/m.1. e outletow from both the tested component and the double conicalhydrostatic thrust bearing is discharged in the test rig andthen returns to a water tank of 5m3 via several hoses andpipes. Dynamic displacements are applied to the rotor by 8piezoelectric shakers, mounted 4 by 4 in the forward and inthe rear plane of the double conical hybrid bearing. e max-imum dynamic displacements are ±100 µm with a frequencyrange from 20 to 200 Hz, corresponding to dynamic loads of20 kN per axis2. e housing 2 of the tested component isxed on a rigid part 3 which is mounted on the test rig’sframe 5 via three piezoelectric force transducers (Kistler9167) 4 each one being able to measure three components,in a range [−20 kN ; 20 kN]. eir stinesses are respectively4.6x109 N/m and 1.67x109 N/m in directions Z and X,Y. Foreach axis, the proportional error is ≤ ±1 % and the hysteresisis ≤ 2 %, both for the full scale output. e three sensorsconstitute a force balance. e rst natural frequency of the

1e stinesses of the double conical hydrostatic thrust bearing are highcontrary to those of the tested component in order to lower the power ofthe shakers

2e power of the shakers is set to a percentage of their total power.erefore, the obtained amplitudes of displacements of the rotor depend onthe direct stinesses of the tested component

axial mode of the stator assembly (housing and force sensors)is 280 Hz. e two rst natural frequencies of the bendingmode are 370 Hz and 520 Hz. e housing is equipped with6 eddy current proximity probes (Bently Nevada 3300 XL8mm), positioned three by three in the front and rear plane(for an annular seal or a hydrostatic bearing). eir linearityerror is ≤ 5 %. ese sensors measure the relative displace-ments between the rotor and the housing. erefore, theposition of the rotor center in the two planes as well as theradial clearance can be deduced. Before each test, a dedicatedpart, having an outside diameter that ts exactly the hous-ing’s inside diameter, is used to calibrate simultaneously theresponse (gain and oset) of the 6 displacement sensors. Mis-alignment of the rotor can also be obtained knowing that thetwo measuring planes are equidistant from the housing mid-plane. ree accelerometers are also mounted on the housingenabling the measurement of its absolute movements.

2. DYNAMICCOEFFICIENTS IDENTIFICATION

In many works, known orbiting motions are imposed tothe impeller (whirling motion is produced by an eccentricdrive mechanism) and resulting hydrodynamic forces aremeasured [2, 3, 4]. According to a mass-damping-stinessmodel, implying that the hydrodynamic force matrix |A| isquadratic with in ω/Ω (whirl motion speed to sha speedratio), rotordynamic coecients matrices are then obtainedfrom a least squares t. In [5], measurements are performedusing a hydraulic exciter to impose transient excitations (upto 50 Hz) to the impeller in one direction of motion (verticaltranslation). In [6], an experimental apparatus equipped withactive magnetic bearings is used to measure uid lm forceswhile imposing a whirling orbit to impellers.

Here, the dynamic displacements of the rotor imposed bythe shakers generate uid forces that the housing transmits tothe piezoelectric force transducers (acting like high stinesssprings). For lateral displacements of the rotor along vecxand vecy axes of the coordinate system dened in Figure1, the equations of the fundamental principle of dynamicsapplied to the housing with respect to the center of the com-ponent O are:

m Üx = − fx +

3∑k=1

f bkx

m Üy = − fy +3∑

k=1f bky

(1)

where f and f bk are respectively the uid lm forces andthe forces measured by the k th sensor of the force balancewhile the subscript x and y denote their directions. For anexcitation frequency in the range 20 to 120 Hz, the accelera-tions of the housing can be neglected [7], and eq. 1 can be


simplied as:fx =

3∑k=1

f bkx

fy =3∑

k=1f bky

(2)

Introducing the small perturbation hypothesis, uid lmforces can be described by linear dynamic coecients (sti-ness K , damping C and added mass M) or impedances Z . Inthe frequency domain (aer applying the Fourier transform),the uid lm forces and the displacements of the rotor arewrien as follows:

Fx = ZxxX + ZxyY

Fy = ZyxX + ZyyY(3)

e unknown impedances Zxx , Zxy , Zyx and Zyy arefound by using two linearly independent excitations (denotedby the superscripts 1 and 2) consisting in lateral vibrationsobtained by successively exciting the piezoelectric shakersin two orthogonal directions and with the same phase forthe front and rear planes. e impedances are computed byinverting the displacement matrix as follows:

[Zxx Zxy

Zyx Zyy

]=

[F1x F2

x

F1y F2

y

] [X1 X2

Y 1 Y 2

]−1(4)

e stiness, damping and added mass matrices of coe-cients are calculated from the real and imaginary part of thecorresponding impedances as follows:

Ki j − Mi jω

2 = <[Zi j (ω)

]jωCi j = =

[Zi j(ω)

] (5)

with [i j] = [xx; xy; yx; yy]. Equation 5 shows that inorder to enable the identication of constant dynamic co-ecients, the real part of the impedance must describe aparabola and its imaginary part must describe a straightline. In order to perform a curve ing by the least squareprocedure, the impedances are calculated for a signicantnumber of excitation frequencies ω. An example of the realand the imaginary parts of the impedance used during theidentication3 is shown in Figure 2.

e uncertainty in Ki j and Ci j is respectively estimatedto ±15 % and ±30 %.

3. TESTED IMPELLERSTwo types of centrifugal impellers were tested: open (un-shrouded) and closed (front shrouded). Although the testimpeller was designed to work with a cryogenic uid, wa-ter was used as working uid. Figure 3 gives a schematic

3Example corresponds to a sealing component at Ω = 50 , Hz

Figure 2. Curve ing of impedance’s real and imaginaryparts for identication as a function of ω(Hz) in abscissa

view of the test cell with an open type impeller. Both testswere conducted with a vaned diuser. e owrate of waterpassing through the diuser is measured by a Venturi owrate meter located at the outlet of the volute. e leakagebetween the back shroud and the casing is therefore esti-mated since the inlet owrate is also measured. For the opentype impeller, 7 congurations were tested, consisting inchanging the pressure loss downstream of the volute casing.For the closed type impeller, 6 congurations were tested,as listed in Table 1, dened by a combination of 3 types ofeye-packing seal with 2 types of front casing (smooth andtextured). In the present case, the 6 eddy current proxim-ity probes are positioned by three, respectively to measureradial and axial displacements of the impeller relatively tothe casing. e tests were performed by imposing only twotranslation degrees of freedom, from a centered position andwithout misalignment.

4. TESTS CONDITIONSAll the tests have been operated with a centered position ofthe rotor. For each rotor speedΩ, experimental data (displace-ments, forces, pressures, owrates, temperatures, torque) arerecorded for steady-state static case and dynamic excitations.e tests have been performed according to the following


Table 1. Tested Combinations of eye-packing seal and frontcasing

Conguration Name Eye Packing Seal Front Casing

AS-S Annular Seal SmoothFS-S Face Seal SmoothLS-S Labyrinth Seal SmoothAS-T Annular Seal TexturedFS-T Face Seal TexturedLS-T Labyrinth Seal Textured

Figure 3. Cross sectional view of the test rig set up for anopen type impeller

conditions :

• Rotor speed Ω: 2000, 3000, 4000 and 5000 rpm,• Excitations frequencies ω: 20, 30, 40, 50, 60, 70, and 80

Hz,• Water Inlet pressure Ps : 6 bar,

5. RESULTS AND DISCUSSIONIn the present paper, only results corresponding to the closedtype impeller are presented. Ariane Group has proceededto many CFD simulations, using FINE™/Turbo, in order toobtain the performance curves as well as rotordynamic coef-cients.

5.1 Performance curvese open impeller has been tested rst in order to nd thepressure loss to install downstream of the volute casing inorder to reach a given ow rate at 4000 rpm (Design Point).en, the closed impeller has been tested with the pressureloss obtained previously. For all the tests, the ow coecientφ is of the order of 0.15. Figure 4 shows the performancecurves, for each combination listed in Table 1, where thepressure rise is dened as the dierence between the inletpressure of the impeller and the outlet pressure of the diuser.Pressure and owrate at design point are used to normalized

Figure 4. Performance curves in centered position

the corresponding data. e conguration LS−T , that corre-sponds to the combination of an labyrinth seal as eye-packingseal and a textured front casing, beer ts the reference curve,as well as the conguration AS − T . Both cases show that atextured casing helps to bring points closer to the referencecurve and therefore improve impeller’s eciency.

5.2 Rotordynamic Coeicientse present experimental dynamic coecients are madenondimensional as follows [8].

Dimensionless stiness coecients K∗i j =

Ki j

πρr2b22Ω2

Dimensionless damping coecients C∗i j =Ci j

πρr2b22Ω(6)

where ρ = mass density of pumped liquid, r2 = impellerouter (discharge) radius and b2 = impeller discharge widthincluding impeller side plate.

For various sha speeds, Figures 5 show the evolutionof the four term K∗i j of the stiness matrix for the 6 testedcongurations. In rotordynamics, for seals and impellers, theassumption of skew-symmetric coecient matrices (K, Cand M) is stated to be suited [9]. However, some theoreti-cal results in [10] are in contradiction with this. Secondly,many authors agree that, for most large impellers, the directstiness coecients are negatives4 and included in the range[−2, 5;−4, 2] [8, 9]. As a rst observation, present experimen-tal results do not provide equal values for the direct stinesscomponents, at least at low rotational speed. Moreover, atΩ = 2000 rpm, Kxx is always negative except for the con-guration AS − T . is conguration provides the higherlevels of direct stinesses when the two congurations withthe face seal provide very low or negative ones. A closedimpeller is therefore able to provide positive direct stinesses

4As explained in [11], direct stiness coecients produce a radial forcedirected inward and collinear with the rotor deection vector. If the coe-cients are negatives, the direction of the fore reverses (outward)


beyond a rotating speed and some kinds of eye-packing seals.As a second observation, the normalized stinesses are of theorder of one or several tens: this is higher than those above-mentioned and of the same order as in [12], obtained for anopen-impeller. e normalized cross coupling stinesses aremore in accordance with the assumption that Kxy = −Kyxand their amplitude decrease with increasing Ω. e cong-urations with a textured front casing provide lower valuesof the cross coupled stiness than the smooth one, showingthe benet of this design.

e normalized damping coecients are almost constantin the range of rotating speeds. e higher direct damping isprovided by the conguration LS − T and the higher crosscoupled damping is provided by the conguration FS − S.According to the above results, a closed impeller should beequipped with an annular seal and the front casing shouldbe textured.5

6. CONCLUSIONA test rig dedicated to the identication of rotordynamiccoecients is presented. A set of results obtained for aclosed-impeller are used to demonstrate the test rig gives,researchers and industrial supporting partners, the ability tomeasure stiness and damping matrices for uid lm compo-nents as used in a liquid Rocket Engine Turbopump. In orderto increase its possibilities, through a French Governmentprogram, the test rig is being modied in order to:

• perform long duration tests,• test components fed with air.

Regarding the dynamic behavior of the present shroudedimpeller, positive values of direct stinesses and higher levelsof damping can be obtained by using a textured front casing.e annular seal is the most appropriate for this impellerwhile the face seal is not.

ACKNOWLEDGMENTSe authors are grateful to Centre National d’Etudes Spa-tiales (CNES) and to ARIANE GROUP for using the test rigBALAFRE and for their agreement to present this experi-mental work. is work was partially funded by the FrenchGovernment program “Investissements d’Avenir” (EQUIPEXGAP, reference ANR-11-EQPX-0018).

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[3] Y. Yoshida, Y. Tsujimoto, D. Yokoyama, H. Ohashi, andKano F. Rotordynamic uid force moments on anopen-type centrifugal compressor impeller in precess-ing motion. International Journal of Rotating Machinery,7(4):237–251, 2001.

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[5] U. Bolleter, A. Wyss, I. Welte, and R. Sturchler. Measure-ment of hydrodynamic interaction matrices of boilerfeed pump impellers. ASME. J. Vib., Acoust., 109(2):144–151, 1987.

[6] M. Uchiumi, N. Nagao, Y. Yoshida, and M. Eguchi. Com-parison of rotordynamic uid forces between closed im-peller and open impeller. In Proceedings of ASME. FluidsEngineering Division SummerMeeting, Rio Grande, PuertoRico, July 8–12, 2013.

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[8] M. A. Corbo and S. B. Malanoski. Pump rotordynamicsmade simple. In Proceedings of the Fieenth Interna-tional Pump Users Symposium, Turbomachinery Labora-tory Texas A M University, College Station, Texas, pages167–204, 1998.

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[10] D.R. Adkins and C.E. Brennen. Analyses of hydro-dynamic radial forces on centrifugal pump impellers.ASME. J. Fluids Eng., 110(1):20–28, 1988.

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[12] N. Nagao, M. Eguchi, M. Uchiumi, and Y. Yoshida. Ro-tordynamic forces acting on a centrifugal open impellerin whirling motion by using active magnetic bearing.Progress in Propulsion Physics, 4:445–456, 2013.


Figure 5. Dimensionless Measured Stiness Coecients K∗i j according to the 6 tested congurations


Figure 6. Dimensionless Measured Damping Coecients C∗i j according to the 6 tested congurations

experimental identification of fluid thin film dynamic...

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