A Feasibility Study of Fiber-Film Probes forCharacterisation of Cavitation Dynamics in

a Rocket Engine Turbopump InducerOliver Jia-Richards

Massachusetts Institute of Technologyoliverjr@mit.edu

Zoltan S. SpakovszkyMassachusetts Institute of Technology

zolti@mit.edu

ABSTRACTOne of the main challenges in characterising the dynam-ics of a rocket engine turbopump inducer is the measure-ment of mass flow fluctuations during forced responsetesting. Historically, such measurements have been takenthrough a spatially averaged mass flow measurement farupstream of the inducer with an electromagnetic flowmeter or laser Doppler velocimetry. Fiber-film probesare proposed to take local, unsteady velocity measure-ments in a rocket engine turbopump inducer test setup.This work shows that a fiber-film probe is capable of tak-ing local, unsteady velocity measurements in an inducerinlet flow during cavitation and has sufficient signal-to-noise ratio to measure velocity profiles in the presenceof back flow. Experiments were run the Aerospace Cor-poration’s inducer test facility with the MIT inducer inorder to assess a fiber-film probe’s performance. Thiswork takes the first steps towards performing forced re-sponse inducer experiments with local, unsteady velocitymeasurements.

1 INTRODUCTIONCavitation is the formation of vapour bubbles when thestatic pressure of a liquid drops below its vapour pres-sure. This corresponds to regions of the flow of highvelocity, such as over the suction surface of a turbopumpblade. As the flow progresses along the blade chord thepressure will increase. This causes the vapour bubble tocollapse and can fatigue the blades.

To avoid cavitation in the main turbopump, an induceris introduced upstream in order to provide an initial pres-sure rise. The inducer is subjected to cavitation undernominal operating conditions but is designed to with-stand the fatigue. However, cavitation in the inducer stillhas detrimental effects on the performance and life ofa rocket engine and can potentially lead to vibration

instabilities [1]. One instability of interest results whenthe formation and collapse of vapour bubbles results inunattenuated fluctuations in the fuel mass flow and pres-sure. These fluctuations can cause further fluctuationsin the thrust that is produced by the rocket engine. Thevariance in produced thrust can excite the longitudinalvibrations of the vehicle structure [2]. This type of in-stability is nicknamed POGO as the rocket mimics thejumping toy [3] and can lead to mechanical failure ofthe entire rocket vehicle [4].

To assess POGO instability, the dynamics of the rocketengine turbopump inducer need to be characterised. Thisis done through forced response experiments where thepressure and mass flow fluctuations are measured up-stream and downstream of the inducer [1]. From thesemeasurements a transfer matrix for the inducer can becreated [2] and the effect of the inducer on the fuel flowcan be assessed.

One of the open challenges in determining the transfermatrix elements is measuring fluctuations in the massflow due to the violent nature of the inlet flow. Someof the most recently published efforts [5, 6] used elec-tromagnetic flow meters and laser Doppler velocimetry(LDV) to take a bulk mass flow measurement externally.These methods are limited in that they can only measurebulk flow properties such as cavitation surge. Effects ofother, two-dimensional, forms of cavitation in an inducersuch as rotating cavitation, alternate blade cavitation,and higher order cavitation cannot be captured.

Further limitations on these methods are caused bythe location of the measurement plane in the inducerinlet duct. The nature of these measurement techniquesforces them to take measurements far upstream (greaterthan two inducer radii) of the inducer leading edge. Theupstream influence of the inducer and any cavitation is

greatly attenuated far upstream. As a result the fluctua-tions that these methods are trying to measure will bemasked by noise.

LDV has another limitation that is unique to its method-ology. In order to measure the flow velocity the test liq-uid is seeded with small particles. While typically nota problem the seeding can act as nucleation sites. Thiscan cause "fake" cavitation in the inducer and alter anytests done under cavitation conditions.

Outside of attempting to measure fluctuations in theinducer inlet flow, the combination of a wedge probeand total head probe has been used to for steady velocitymeasurements in an inducer test setup such as axialand swirl velocity profiles [7]. The static pressure andflow direction are acquired through a radial traversewith the wedge probe. A second radial traverse withthe total head probe is required in order to measurethe total pressure and therefore allow the flow velocityto be calculated. Since two separate measurements arerequired to measure a single value, any inconsistenciesin the inducer test setup, such as hystersis, will skew thetest data. The two measurement requirement also meansthat this method cannot be extended to take unsteadyflow properties and is limited to steady flow propertiessuch as velocity profiles.

A new method for taking velocity measurements withhigh response capability and minimal intrusion is re-quired. This work investigates using a fiber-film probeto take local, steady and unsteady, velocity measure-ments and assesses its ruggedness and signal-to-noiseratio. A fiber-film probe will allow for local velocitymeasurements close to the inducer face and thereforedoes not share the limitations seen in [5] and [6]. Thiswill allow for characterisation of a rocket engine turbop-ump inducer’s dynamics in a forced response experimentunder all forms of cavitation as well as observations into various phenomena in the inlet flow. In turn, this willlead to a characterisation of the effects of cavitation onthe upstream and downstream mass flow fluctuationsand result in the ability to assess POGO instability.

1.1 Scope of PaperA pilot study is conducted to demonstrate that a fiber-film probe is capable of providing such measurements aswell as being able to measure steady properties of the in-let flow. Specifically, the work performed demonstratesthe following capabilities:

(1) In situ calibration using pre-existing test facilityhardware

(2) Local, unsteady velocity measurements in a cav-itating inducer

(3) Sufficient signal-to-noise ratio to measure veloc-ity profiles in the presence of backflow

(4) Characterisation of inlet flow uniformity

2 TECHNICAL APPROACHFiber-film, or hot-film, anemometry takes advantage ofthe convective cooling over a thin (2 µm), heated filmto measure the local flow velocity. Assuming the fluidmedium and temperature are constant, the heat flowflux of the film via convective cooling is controlled bythe local flow velocity and film temperature. Therefore,by measuring the power input required to maintain theprobe at a certain temperature the flow velocity can becalculated. Since for a metal the resistance is propor-tional to the temperature, this amounts measuring thepower required to maintain the resistance of the probe.

The resistance of the probe is measured through aWheatstone bridge. The probe and a known resistor formone leg of the bridge and two other known resistors formthe other leg. By measuring the voltage difference be-tween the two legs the resistance of the probe, and there-fore the temperature, can be determined. The voltagedifference between the two legs is then passed througha servo amplifier which then feeds back into the bridgein order to balance it. By measuring the power the servoamplifier delivers to rebalance the bridge the convectivecooling on the film and therefore the local flow veloc-ity can be determined. Since the film length is small (3mm) relative to the inducer radius (76 mm) this mea-surement can be approximated as a point measurementin the inducer inlet duct.

For all of the experiments a DANTEC DISA Type56C17 CTA Bridge and DISA Type 56C01 CTA Unitwere used in combination with a DANTEC 55R11 straight,heavy coating, fiber-film probe and a DANTEC 55H21straight, 235 mm long probe support to take velocitymeasurements. A picture of the fiber-film probe can beseen in Figure 1.

In order to characterise the fiber-film probe in an in-ducer inlet flow, the probe was placed in the AerospaceCorporation’s inducer test facility with the MIT inducer.The flow coefficient and cavitation number of the inletflow were varied in order to impose different conditionsin the inlet flow and on the fiber-film probe. The flow

Figure 1: DANTEC 55R11 straight, heavy coating,fiber-film probe.

coefficient (Φ) is a non-dimensional representation ofthe flow velocity and the cavitation number (σ ) is a non-dimensional representation of the difference betweenthe flow’s static pressure and vapour pressure. Both aredefined as follows:

Φ =u

(rOD − rID )Ω(1)

σ =p − pvapour12ρ (rt ipΩ)2

(2)

where u is the axial velocity of the inducer inlet flow, pis the static pressure of the fluid, pvapour is the vapourpressure of the test fluid, ρ is the density of the test fluid,rOD is the outer radius of the analysis area, rID is theinner radius of the analysis area, and Ω is the rotationalvelocity of the inducer. Unless otherwise specified theouter diameter is the inducer tip radius (rOD = rt ip ) andthe inner diameter is zero (rID = 0). A full analysis ofthe flow coefficient and cavitation number combinationand corresponding inlet conditions for the same testsetup used in this work can be found in [8].

The test facility used was the Aerospace Corpora-tion’s Inducer Test Facility in El Segundo, California.A schematic of the test facility can be seen in Figure 2.

Figure 2: Schematic of The Aerospace Corpora-tion’s inducer test facility [8].

This test facility uses water for the test fluid and allowsfor the flow coefficient and cavitation number of the inletflow to be individually set. The inducer itself is housedin the instrumentation section of the test facility. Forthe experiments the MIT inducer, representative of theSpace Shuttle main engine low-pressure oxidiser pumpinducer, was used. The fiber-film probe was insertedinto the inlet flow through a flange just upstream of theinstrumentation section.

Figure 3 shows a numerical calculation of the inletflow conditions in the test facility for the same test setupused in this work [8]. A pictorial representation of thefiber-film probe is shown in the approximate location ofthe measurement plane used for this work. A Swagelokfitting and Teflon ferrule provided a seal between theprobe support and instrumentation section flange. The fit-ting can be loosened without fully breaking the seal andallows for the probe to be manually traversed throughthe inlet duct. This allows measurements to be taken atvarying radial positions so as to determine the velocityprofiles and the radial distribution of unsteady effects.

The location of the measurement plane was set bythe location of pre-existing ports in the instrumentationsection upstream flange. Due to the time required tomanufacture a new instrumentation section it was notpossible to add new ports and change the location ofthe measurement plane. The measurement plane was2.28 inducer tip radii away from the inducer leadingedge. As the pressure fluctuations decay exponentiallythe strength of the velocity fluctuations caused by blade

Figure 3: MIT inducer with numerical calculationsfor the inducer inlet flow [8] and approximate loca-tion of the fiber-film probe.

passing, rotating cavitation, alternate blade cavitation,and higher order cavitation were attenuated to the pointthat they could not be measured. However, the measure-ment location allows for measurement of the effects ofcavitation surge as well as measurement of velocity pro-files which is sufficient to demonstrate the capabilitiesof a fiber-film probe. This also eliminates the risks asso-ciated with placing the probe in the most violent regionof the inlet flow.

3 FIBER-FILM PROBE CALIBRATIONIn order to take velocity measurements in the inducerinlet duct the fiber-film probe and anemometer had to becalibrated. Due to the lack of an available water tunnel,the fiber-film probe calibration had to be done in situ.The strategy was to calibrate the probe by equating thevolume flow measured by a flow meter in the inducertest facility to a time integrated voltage profile measuredthrough a radial traverse with the fiber-film probe.

To produce the voltage profiles five voltage measure-ments were taken from the centreline of the inlet ductto the wall at a spacing of 0.25 radii. Due to physicalrestrictions, the measurement near the wall was taken at0.95 radii from the centreline. A fifth degree polynomialfit was created using the five measurements to generatean approximate continuous representation of the volt-age profile. Four such voltage profiles were created atflow coefficients 0, 0.07, 0.085, and 0.10 referenced tothe inlet area (rOD = rt ip , rID = rhub ) in order to pro-vide a wide spread of data as well as focused data nearthe nominal operating flow coefficient (0.083) of theinducer.

After generating the profiles the following equationwas solved for each flow coefficient:

V =

∫ R

02πrv (E)dr (3)

where V is the measured volume flow, R is the inducerinlet duct radius, and v is the local flow velocity as afunction of the measured voltage E.

In order to solve Equation 3 an equation for the flowvelocity as a function of the measured voltage had tobe manually selected. For simplicity a basic two termpower relation was chosen:

v = A + BEn (4)

where A, B, and n are the calibration coefficients for theprobe and need to be solved for. Since there are threeunknown coefficients but four profile measurements apseudo least-squares fit was performed. An initial valueof n was selected and Equation 3 was solved exactly forflow coefficients of 0 and 0.10. This allowed for A and Bto be solved for and an estimate of the volume flow forthe flow coefficients of 0.07 and 0.085 to be calculated.The error of this estimated volume flow compared tothe volume flow measured by the flow meter allowedfor the chosen value of n to be adjusted until the sum ofsquare errors was minimised. When solved the resultingcalibration coefficients are A = −0.0022, B = 9.26∗10−4and n = 6.98.

To validate the resulting calibration it was comparedto typical calibration curves for fiber-film probes as de-scribed in [9]. The methods used in [9] to produce thecalibration curves us a different calibration function thanthe one used in this work. The calibration function isbased on King’s law:

E2 = C + Dvn′

(5)

where E is the measured voltage, v is the flow velocity,andC,D, andn′ are calibration coefficients. When fittingour calibration equation to the King’s law equation weobtain n′ 0.3. Typical values of n′ as reported by [9] are0.25-0.3 for water velocities of less than 0.2 m/s and0.4-0.45 for velocities in the range 0.5-4 m/s. Thereforethe calibration for the fiber-film probe is consistent withthe data in the literature.

3.1 Problems with CalibrationDrifts over time in the velocity measurement were ob-served. This resulted in a few minor, but noticeable, dis-crepancies in the velocity measurements depending on at

what time during the testing they were taken. The mostsignificant changes in voltage measurement occurred af-ter the anemometer was power cycled. Despite attemptsto mitigate this effect by leaving the anemometer on atall times after calibration, a drift of approximately 0.2 Vin the voltage measurement was still present.

For future testing an accurate measurement of the ve-locity is required. There are two likely causes of thedrift in calibration. One would be the temperature ofthe water in the test facility. Since the measurement ofthe fiber-film probe is based on cooling, fluctuationsin the water temperature can have significant impactson the cooling and therefore on the measurements. An-other possible explanation is the anemometer as the mostsignificant changes occurred after the anemometer waspower cycled. The anemometer used in this work is oldand damage seen by the anemometer over the years orduring shipment could cause it to be unreliable.

4 LOCAL, UNSTEADY VELOCITYMEASUREMENTS

The calibration of the fiber-film probe allows for local,unsteady velocity measurements to be taken. Initial anal-ysis was conducted using the velocity measurementstaken for the calibration of the probe. A segment ofone of the measurements can be seen in Figure 4. Thismeasurement was taken at the centreline of the initialflow for a flow coefficient of 0.10 referenced to the inletarea. The data shows noise in the local flow coefficientmeasurement with an amplitude of approximately 0.004for a mean local flow coefficient of 0.0942. The spikesin the power spectral density for this measurement areat intervals of 120Hz. This would indicate that a signifi-cant portion of the noise in the velocity measurement isdue to the electrical connection. Like the issues seen inSection 3.1 this may be due to the anemometer unit.

The far upstream location of the fiber-film probe meansthat it is unable to measure the effects of inducer bladepassing, rotating cavitation, alternate blade cavitation,or higher order cavitation. However, since cavitationsurge causes a one dimensional, planar oscillation thefiber-film probe was capable of measuring the velocityfluctuations. Figure 5 shows the local velocity measure-ment taken at the centreline of the inducer inlet flow fora flow coefficient of 0.06 and a cavitation number of0.0292.

An analysis of the power spectral density reveals thatthese fluctuations occur at a frequency of approximately

Figure 4: Local flow coefficient measurement andpower spectral density for a flow coefficient of 0.10.

0.1 of the rotor frequency, consistent with the data in[8]. This matches a visual inspection of the local flowcoefficient measurement. These fluctuations caused bycavitation surge also far overpower the electrical noisedemonstrating the high signal-to-noise ratio of the fiber-film probe. Figure 6 shows an optical and velocity mea-surement taken during cavitation surge demonstratingthe ability to take simultaneous optical and velocity mea-surements.

These measurements demonstrate the capability of thefiber-film probe to take local, unsteady velocity measure-ments, a capability required to be able to dynamicallycharacterise an inducer. The major contributor to noisein the measurement is electrical noise. This problemmay be easily fixed by simply using a more modernanemometer or improving the electrical isolation of themeasurement system. Since the aim of this project was to

Figure 5: Local flow coefficient measurement andpower spectral density of cavitation surge.

assess the feasibility of how the fiber-film probe wouldperform neither of these proposals were explored.

5 AXIAL AND SWIRL VELOCITY PROFILESBy manually traversing the fiber-film probe and timeaveraging the unsteady velocity measurement, flow pro-files can be constructed. Figure 7 shows flow coefficientprofiles taken during the calibration of the fiber-filmprobe along with error bars representing one standarddeviation of error due to noise. We can see that the noiseincreases closer to the inlet duct wall. This is most likelydue to an introduction of a swirl component to the inletflow that becomes more significant closer to the wall.

For each of the points taken in Figure 7 the probe wasplaced perpendicular to the axial direction as the flow isassumed to be approximately axial. However, the probeis sensitive to flow parallel to the film and therefore any

Figure 6: Simultaneous optical and velocity mea-surement of cavitation surge.

component in the swirl direction will also be picked up,albeit at a lower sensitivity, and influence the velocitymeasurement.

This can be seen more clearly at lower flow coef-ficients where a backflow region is introduced to theinlet flow. The backflow region is flow that is flowingupstream and opposite to the bulk mass flow. This iscaused by tip leakage flow where the pressure differencebetween the suction surface and pressure surface of theblades pushes fluid around the inducer blade tip andback into the inlet duct. Since this flow was previouslyattached to the inducer blade it has picked up a swirlcomponent to its velocity. At lower flow coefficient thiseffect becomes more noticeable.

Figure 8 shows the raw local flow coefficient mea-sured for an overall flow coefficient of 0.04, a highlyloaded condition. Two profiles are show: one where theprobe is placed perpendicular to the axial direction andanother where the probe is placed perpendicular to the

Figure 7: Flow coefficient profiles taken for calibra-tion of the fiber-film probe.

swirl direction. The local flow coefficient correspondingto the swirl flow coefficient increases towards the inletduct wall, as expected. However, the swirl flow coeffi-cient at the centreline is not zero. This is due to the factthat the probe is still sensitive parallel to the film andtherefore is still picking up the purely axial flow.

This indicates that the measurements taken are notactually the true axial or swirl local flow coefficients anda correction needs to be implemented. The correctionimplemented here is the one suggested in [9] and isoften reffered to as Jørgensen’s equation. It defines thefollowing relationship between the perpendicular andparallel flow coefficients:

Φ2e = Φ2

N + k2Φ2

T (6)

Where Φe is the effective flow coefficient, the one mea-sured by the fiber-film probe, ΦN is the true flow co-efficient perpendicular to the probe, and ΦT is the trueflow coefficient parallel to the probe. k is a sensitivitycoefficient that is unique to each probe and needs to bedetermined experimentally.

Due to the lack of an available water tunnel the calcu-lation for k, like the probe calibration, had to be donein situ. It is assumed that the velocity measured at thecentreline in Figure 8 is truly axial. This means thatΦT = 0 and a value for k can be determined based onthe measurements taken with the probe perpendicularto the axial and swirl directions. For the probe used inthis work k = 0.303. This is consistent with the valuespresented in [9].

Figure 8: Raw local flow coefficient measurementstaken at a flow coefficient of 0.040 with the fiber-filmprobe perpendicular to the axial direction (blue) andswirl direction (red).

When this correction is applied to the data in Figure8 the resulting corrected local flow coefficient can beseen in Figure 9. A second manual correction was alsoapplied to define the two axial local flow coefficientmeasurements nearest to the duct wall to be negative.This is impossible to measure with the fiber-film probeas the probe itself has no knowledge of the flow direction.This correction was determined based on the results ofFigure 8 as the local flow coefficient starts to increasenear the duct wall opposite the effect expected from thepresence of a boundary layer.

These measurements demonstrate that a fiber-filmprobe has sufficient signal-to-noise ratio such that avelocity profile can be measured even in the presence ofback flow. They also demonstrate techniques for measur-ing the individual components of the inlet flow velocity.Such capability is valuable as it allows insight into theinducer inlet flow. It also means that a single probe canbe used for both unsteady velocity measurements as wellas steady measurements such as flow profiles.

6 ANALYSIS OF FLOW UNIFORMITYFurther analysis of the flow profiles shown in Figure7 show increased non-uniformity in the flow profile asflow coefficient is increased. Table 1 shows the flownon-uniformity for each flow coefficient where flow non-uniformity is defined as the percent increase in local flowcoefficient from the centreline to the 0.75 radial position.

Figure 9: Corrected flow profiles in the axial (blue)and swirl (red) directions taken at a flow coefficientof 0.040.

Table 1: Flow Profile Non-Uniformity Analysis

Flow Coefficient Flow Non-Uniformity (%)0.070 11.30.085 17.70.100 22.4

A steady increase in non-uniformity is observed as flowcoefficient is increased.

This trend is opposite what would be expected. Asflow coefficient is decreased tip leakage flow is increased.This creates a region of back flow in the inlet duct andthe expectation is that this region of back flow would in-crease the non-uniformity seen in the flow profile. How-ever, it may be the case that this region of back flow isactually causing the flow profile to be more uniform.

A potential explanation for this phenomena is thatthe back flow region creates bloackage and therefore afavourable pressure gradient in the inlet duct. The de-crease in area for the forward flowing axial flow meansthat the static pressure of the flow will decrease. To seethe effect of the favourable pressure gradient on flownon-uniformity examine the one dimensional, incom-pressible, and inviscid momentum equation:

du

u= −

dp

ρu2(7)

The fluid in the wake has a lower velocity but experi-ences the same pressure gradient. Therefore, the frac-tional change in velocity is larger for fluid in the wake.As a result, any variance in the flow profile will be atten-uated causing the flow profile to become more uniformas the flow passes through a favourable pressure gradient.As the flow coefficient is decreased and the back flowregion is increased the pressure gradient will becomemore favourable. This results in greater attenuation ofany non-uniformity in the flow profile and greater uni-formity in the inlet flow following the trend observed inthe experimental data.

7 CONCLUSIONThis work constitutes the first steps towards perform-ing forced response experiments with local unsteadyvelocity measurements in a rocket engine turbopumpinducer. A fiber-film probe is demonstrated to be capa-ble of taking local unsteady velocity measurements in acavitating inducer, a necessary requirement for dynamiccharacterisation of the inducer. It is also shown that afiber-film probe has sufficient signal-to-noise ratio tomeasure velocity profiles in the presence of back flow.This provides a proper foundation for future work toevaluate a fiber-film probe’s capability to measure theeffects of rotating cavitation, alternate blade cavitation,and higher order cavitation.

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