Measurements of Hydraulic Fluid Propertied at High Pressures 2012 Intl Journal of Fluid Power

8/12/2019 Measurements of Hydraulic Fluid Propertied at High Pressures 2012 Intl Journal of Fluid Power

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International Journal of Fluid Power 13 2012) No. 2pp . 51-59

MEASURING AND MODELLING HYDRAULIC FLUID DYNAMICSAT HIGH PRESSURE - ACCURATE AND SIMPLE APPROACHJuho-Pekka Karjalainen Reijo Karjalainen and Kaievi Huhtala

Tampere University of Technology TUT),Departm ent of Intelligent Hydrau lics and Automation IHA).P.O.Box 589, FIN-33101, Tampere, Finlandjuho-pekka. [email protected],[email protected], kaievi. [email protected]

AbstractDynamic properties of hydraulic fiuids have to be taken into account in ever increasing fiuid power applications.The main reasons are increasing accuracy demands in control and modelling, as well as increasing operating pressureand temperature ranges. Moreover, the already wide spectrum of different hydraulic fiuids is also expanding all thetime.However, information on dynamic hydraulic fiuid behavior is still very difficult to be obtained. On the other hand,existing fiuid models tend to be either too inaccurate, or at least highly non-generic for most practical applications.This article introduces simple, yet accurate approaches for measuring and predicting the most important dynamicfluid parameters: bulk modulus, density and speed of sound in fiuid. The methods are basically applicable to any stan-dard hydraulic fiuid, without any extra system-related constraints, at least at the presented conditions. The studied pres-sure range reaches 1500 bar, and the temperatures cover a normal operating range of industrial applications. Examplesof both measured and predicted results for selected commercial hydraulic fiuids are given. The results have also been

found to be in excellent agreement with existing reference data.Keywords: adiabatic, bulk modulus, density, dynamics, high-pressure, hydraulic tluid, isothermal, measuring, modelling, second order polynomial,speed of sound

1 IntroductionMost fiuid power engineers agree on hydraulic fiuidbeing one of the most important components in everyfiuid power system. In addition to e.g., lubrication, heattransfer and contamination control, fiuid is first and

foremost the power transmitting medium. Therefore, itmight be even argued that fiuid is the most importantsingle component.Possibly, fiuid properties have not been as signifi-cant design parameters in former applications as theyare today. Therefore, there is very limited or no reli-able, measured information on fiuid behavior availablefor system designers - especially at pressure levelsover 300 bar, or for different types of hydraulic fluids.However, operating pressures have been increasingthroughout the fiuid power field. Moreover, the selec-tion of different hydraulic fiuids is increasing all thetime - mineral oil based fiuids are being replaced e.g.,

with vegetable oil or synthetic ester based fluids.Therefore, fiuid parameter variation has become an

On the other hand, it would be important to have use-ftil tools for predicting different fiuid parameters. Thereare a number of models also for fluid parameters, butunfortunately they usually fall into two different catego-ries.Some models are too simplified and therefore inac-curate. Other models might possibly be accurate, butthey are impossible to use in practice, due to the parame -terization, which assumes information, which is verydifficult or usually even impo ssible to find. Both of thesekinds of models are, in effect, as useil from a systemdesig ner s point of view as no fiuid model at all.

In this article, the effects of pressure, temperatureand fiuid type on dynamic fluid parameters are studied.An accurate, yet simple and cost effective approach formeasuring the most important dynamic fiuid parametersis presented, and a method for predicting the observedbehavior in a very generalized manner is suggested - thefiuid parameters being speed of sound in a fiuid, fluiddensity and fluid bulk modulus. The presented pressure


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Juho-Pekka Karjalainen. Reijo Karjalainen and Kalevi Huhtala

2 Measuring Method2 1 Reference Metho ds

There are many reported methods for measuringdifferent dynamic fiuid parameters. A short overviewof the most typical reference methods is given in thefollowing. Reference methods have also been surveyedin K arjalainen 201lb) .2.1.1 Bulk Modulus

In Gho lizadeh 2011), a relatively thorough litera-ture survey was recently performed concentrating par-ticularly on fluid bulk modulus measurement. Gholi-zadeh 2011) also creditably explains how there arefour different definitions for fluid bulk modulus - itcan be either secant or tangent, and isothermal or adia-hatic. Which value of bulk modulus should be used inwhich cases is a somewhat controversial subject. Thisarticle will not focus on that part, some discussion mayhe found e.g., in Gholizade h 2011) and its references,also in Karjalainen 201lh) .

As it is also stated in Gholizadeh 2011), the mosttypical ways to measure fiuid bulk modulus are basedon using some kind of fiuid compressing device, or ondefining the speed of sound in a fluid. Using compres-sion e.g. ASTM -D6793-02) leads usually to isother-mal secant bulk moduli, whereas speed of sound meth-ods are expected to lead to adiahatic tangent values. Ofcourse, there are certain relationships between differentdefinitions of bulk moduli, which might allow defininganother values hased on another. However, for exam-ple, heat capacity factors are not commonly availablefor many hydraulic fiuids.Using compressing devices, the reached pressureranges are usually reported higher, evidently even up to690 MPa. However, compression methods may bequite sensitive to errors, e.g., due to unexpected struc-tural compliances of the measuring device. Moreover,compression methods are more expensive and difficultto apply in many situations e.g., when studying newand unknown fluids.

2.1.2 Speed of Sound in FluidIn Gholizadeh 2011 ), also the mo st tjrpical ways tomeasure speed of sound in fluid were surveyed. Forexample, an ISO standard ISO 15086-2:2000) presentstwo possible methods. However, these methods areknown to be tested more specifically at pressure levelsunder 500 bar. Therefore, elevated pressure levelspresent many challenges to the equipment depictede.g., in the standard. In particular, producing continu-ous pressure fiuctuation at high pressures may be diffi-cult and very expensive. It is also worth mentioningthat the possihle viscosity range of measured fluids willbe narrowed, if e.g., a hydraulic pump is used for pro-

ducing the demanded pressure fluctuation. Some otherpossible aspects needed to be considered with continu-ous pumping have been discussed e.g., in Karjalainen

2.1.3 DensityAlso in Gholizadeh 2011), an inclusive survey ofdensity measuring methods was given. Most of thedensity measuring methods are hased on some speciallaboratory equipment which is not that commonlyusually available for an average fluid power engineer.

Moreover, this kind of equipment may be quite expen-sive. One such accurate and commercially availabledevice, vibrating tube densitometer, is e.g., based onmeasuring oscillation periods inside a fiuid filled tube.On the other hand, density may be defined e.g., frommass of a fluid and using a similar type of com pressiondevice as used in defining isothermal bulk modulus.2 2 The Studied Measuring Method

One possibility of defining all the three parameterswith the same system is given in Karjalainen 201lh) .The measuring system consists of typical fluid powercomponents and is relatively easy and cost effective tohuild. It is also easy to maintain which is a benefit,particularly when dealing with previously unknownfluids or operating conditions. The method is based onmeasuring speed of sound in fiuid directly, fluid den-sity and bulk modulus may be determined iteratively.This article is based on the described method.2.2.1 The Studied Measuring System for Speed ofSound

A schematic picture ofthe studied measuring systemfor speed of sound in a fluid line is shown in Fig. 1. Pressure intensifier2 Hydraulic cyiinder3 Measuring pipe4 Heat resistance5 Gear pump6 Separate tank7 Pressure reiief vaive

Fig. 1: The schematic picture of the studied measuringsystemA closed, straight, fluid filled measuring pipe ispressurized with a pneumatically driven single-pistonpump, which acts as a pressure intensifier. The high-pressure measuring pipe is enclosed in an outer, oil-filled low-pressure pipe for temperature control circu-lation. With a PID controller, the temperature of theactual measuring pipe can be maintained accuratelyindependent of possible changes e.g., in room tempera-ture. Oil temperature is measured at the both ends ofthe measuring pipe. The temperature circulation is

driven with a simple gear pump. The pressure reliefvalve in the measuring line is a safety valve, whichremains closed in normal operation.


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Measuring andModelling H ydraulic Fluid Dynamics a tHigh PressureAccurate andSimple Approach

by knocking a hydraulic cylinder. Two fast piezo-electric pressure transducers record the pressure waveat two points, at known distanee from eaeh other. Witheross-eorrelation algorithm, the delay of the pressurewave propagation can be found from the phase shift ofthe two pressure transients. And since pressure wave istraveling at a speed of sound in a fluid line, this willlead to the effective value of the speed of sound.The removal of the effeet of system compliances isexplained in Seetion 2.2.3. After that, following aniterative procedure (explained in Section 2.2.2) it willlead to the desired values of speed of sound in fluid,adiabatic tangent fluid bulk modulus, and fluid density.The reliability of this non-standard measuring systemhas been justified in detail in Karjalainen (201lb).

The repeatability of measuring pressure wave propa-gation has been found to be excellent. Figure 2 shows anexample scatter of three consecutive measurements(tl -13) with Shell Tellus VG 46 mineral hydraulic oil at40C temperature. The dashed line represents a secondorder p ial fltting of the reported delay. The maximumerror in repeatability at the same operating pressure isone sample period - in this case only 20 [i swith 50 kHzsampling rate. During the testing phase ofthe measuringsystem the repeatability in normal operation has beenfound to be within one sample period even with statis-tically larger investigation.Delay [ms]

1.50 ~Tellus ISO VG 46

1.50

1.401.30

1.20

1.10C

Fig. 2:

- tlA t2X t3

Delay

T= 4O C500 11Pressure [ba r] 0 00 1500

Example of the repeatabil i ty of measuring pressurewave delay in a minera l hydraulic oi l .

Unlike e.g., in (ISO 15086-2:2000), Johnston(1991), Kojima (2000) and Yu (1994), this methoddocs not have a hydraulic pump for producing pressurefluetuation. Therefore, this approach has certain advan-tages.The viscosity range of a measured fluid is not solimited. With the presented system, fluids with kine-matie viscosities of - 1100 cSt have been measuredsuccessfully. Moreover, temperature can be controlledmore easily when there is no volumetric flow throughthe measuring line.

Basically, the presented method does not make anyrestrictions for measuring temperatures. Of course,some method of eooling the system is needed for lowertemperatures. Moreover, fluid should be in such a statein the measuring pipe that a detectable pressure tran-sient can still be produced with the cylinder. The stud-ied pressure range so far has reached 1500 bar. How-

2.2.2 The Iterative Procedure for Bulk Modulus andDensityThe originally used iteration procedure for fluidbulk modulus and density was published e.g., in Kar-jalainen (2005, 2006, 2007, 2009, 2011a) leading to asystematic 1 - 2 referenced maximum error at pres-

sure range of 1500 bar (Karjalainen, 2011b; Kuss,1976). However, the proeedure was slightly revised toits flnal form in Karjalainen (2011b) leading to e.g.,referenced maximum error of density of less than0.5 (Karjalainen, 201 1b; Kuss, 1976). The revisionprocess has been explained in detail in Karjalainen(2011b). The revised flnal iteration procedure is pre-sented in the following.Onee a speed of sound in the fluid line is measuredaecording to Section 2.2.1, there are two equations,Eq. 1 (Merritt, 1967) and Eq. 2 (Karjalainen, 2011b;Garbacik, 2000) for iterative determination of effectiveadiabatie tangent bulk modulus and fluid density. As

already mentioned in Seetion 2.1.1, the heat eapacityfactors in Eq. 2 might be difficult to find for everyfluid. Therefore, also an estimated equation Eq. 3 (Kar-jalainen, 2011b) may be used instead of Eq. 2 withgood accuracy in practice. The ratio of the fluid heatcapacity factors has been replaced with an estimate thatisothermal tangent bulk modulus is approximately200 MPa smaller than the corresponding adiabatictangent value. In practice, this is a fair assumptionaccording to e.g., Hodges (1996) and Borghi (2003).The results of this study have been dcflned using theestimate equation, with the above reported aecuracy.(1 )

P.=

P,, = Pa,,,,. ^

(2)

(3)The iteration proeedure should be started at the at-mospheric pressure, or close to it, and the first valuesfor effective bulk modulus and density are received.

After that, all the preeeding effective bulk moduli, aswell as the presently iterated effective bulk modulus,should be summed in either of the used equations Eq. 2or Eq. 3. Presented mathematically the above wouldmean:

= meanwhere the value B j is the eurrently iterated adiabaticvalue of the effective bulk modulus at the pressure inquestion. All the other values are received from thepreceding pressure steps.The size of eonseeutive pressure steps can e.g., fol-low normal pressure steps of these kinds of measure-ments. In Karjalainen (201 lb) it has been shown thatthis will lead to similarly good accuracy than by using


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2.2.3 The Removal of System CompliancesAs in this studied case, the measuring line shouldbe designed to have no dead volumes. Moreover, themeasuring line should be de-aerated with thoroughfiushing. In this study, the fiushing of the system wasperformed at a pressure level of over 1000 bar. Withthe above conditions, system compliances can be esti-mated very well with equations Eq. 4 and Eq. 5 Kar-jalainen, 2011b; Merritt, 1967) for a rigid thick-walledpipe.

1 [-/.i , -D-c

B =-Br B fr

(4)

(5)

3 Measurem ent ResultsEight different commercial hydraulic fiuids wereselected for this study. Speed of sound in fiuid, adia-batic tangent fiuid bulk modulus and fiuid density weremeasured according to Chapter 2. The studied pressurerange was 100 - 1500 bar which covers e.g., state-of-artcommon rail injection pressures. The studied tempera-ture range of 40 - 70C was selected to cover the nor-mal range of industrial fiuid power applications. Theselected fiuids and the received results are presented inthe following.

3 1 The Selected FluidsDifferent commercial fiuids were selected to coverthe most typical spectrum of the hydraulic fiuids beingused at the moment - water had to be abandoned at thisstage e.g., due to possible rusting problems. Waterviscosity would not have been a problem. Differentbase fiuids were selected for finding out whether itwould affect the fiuid dynamics. The effect of viscositygrades and additives were researched by selecting dif-ferent mineral oil based fiuids.

Table 1: The fiuid characteristics of the studied hy-draulic fiuids Karjalainen 201 lb )ISO' ^iKia rt it /cd t lLiJil chari ic icr i i t l la data

Fluid

Sl i d l TL ' l l us \ ( i . i :S M I T d l u s S V U . l i .S I K 1 I T C I I U S T X V ( ; 4 6Cum SAE low-.10Shell Rimu b .vJO \ ' ( iK -Shcll ai ibiauu n fluidS-936.'iShell Nlurel lcHF-EV-1 6a i m g l l ; C r i r a : O i l V 4 6

Viscosil)'

i tSl l4h- I1) 12.616

46.3

Viscosityr ioo

[cSl]5 46 , ' 'S.411..11

1.\9 8928

Dcas i l ycorT t c i i onuxlikitrnt(u)|kg(m'T))

0 6 50.650.650.650.650.680.650.63

as standard industrial hydraulic fiuids. Shell Tellus TXis basically the same fiuid as the previous ones, but ithas viscosity index enhancing additives. Comet SAEand Shell Rimula are diesel engine motor oils. ShellCalibration fiuid is a standard calibration fiuid usede.g., in injection motors. Shell Naturelle HF-E is asynthetic ester fiuid, and Comet ECO Pine is pine oilbased natural ester fiuid.3 2 Speed of Sound in Fluid

The measured speeds of sound are presented inFig. 3 and 4. As it can be seen, only calibration fiuidstands out, clearly having the lowest value for speed ofsound. All the other fiuids present somewhat similarabsolute values regardless of different base fiuids,viscosity grades or additives. In practice, the trend ofspeed of sound behavior will not change between thefiuids or temperatures. In fact, the measurements arefollowing uniform second order polyno mials Kar-jalainen, 2 009; 201 lb) - this discovery has been usedin defining the prediction method of Section 4.3.

Measured Speed of Sound

500 750 1000Pressure [bar ]

Tellus VG32 Tellus VG4eTe l lusTX_VG46 Comet_SAE10w-30 R imu laX30_VG93 Calibration fluid+ HF-E VG46- Pine oil VG46I T=40*C

Fig 3 : The measured speeds of sound in the studied hy-draulic fluids at 40C

MeasuredSpeed of Sound


Tellus VG32 T ellus VG46t TellusTX_VG46- Comet_SAE10w 30 R imu laX30_VG93 Calibration fluid+ HF.E VG46-P ine o i l VG46

T= 70 C

Fig 4: The measured speeds of sound in the studied hy-draulic fluids at 70CSpeed of sound in fiuid is known to set the upperlimit for the fastest possible frequency response Smith, 1960). However, it does not necessarily meanthat the fastest possible response could be used in prac-tice it might even lead to unstable control response.

Moreover, in sections 3.3 and 3.4 it is shown that thereare significant differences in bulk moduli and densitiesbetween fiuids with similar measured speeds of sound.


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Measuring and Modelling Hydraulic Fluid Dynamics at High Pressure - Accurate and Simple Approach

3 3 Adiabatic Tangent Bulk ModulusThe measured adiabatic tangent bulk moduli arepresented in figures 5 and 6. It can be seen that the pineoil has the highest bulk modulus. Also the HF-E fluidhas a bit higher bulk modulus than the studied mineraloils.The calibration fluid has the lowest bulk mo dulus,

whereas the other five mineral oils are presentinghighly similar behavior - despite different viscositygrades or additives. Therefore, base fluid would seemto have the biggest effect on fluid s bulk modulus.Measured Bulk Modulus

5tXJ 75 0 1000Pressure (ba r) T=40*C

Fig 5: The measured adiabatic tangent bulk moduli in thestudied hydraulic fluids at 40CMeasured Bulk Modulus


U5 0

* Tellus VG32 Tellus VG4eiTellusTX_VG46XComet_SAEtOw.30i :RimulaX30_VG93 Cal ibration f luid

T= 70 CFig 6: The measured adiabatic tangent bulk moduli in thestudied hydraulic fluids at 70C

There are differences in absolute values betweenthe fluids - definitely big enough to affect certain ap-plications. However, the trend of the bulk modulusbehavior will not change between the fluids or tem-peratures. Again, the measurements are following uni-form second order polynomials (Karjalainen, 2009;2011b) - this discovery has been used in defining theprediction m ethod of Section 4.1 .3 4 Density

The measured densities of the studied fluids arepresented in figures 7 and 8. The absolute values mayvary significantly between the fluids. However, the fivefluids (Tellus VG 32, Tellus VG 46, Tellus TX, CometSAE, Rimula x30) having highly similar mineral oilbase fluid are forming one group. Pine oil has the high-est density, followed by the HF-E fluid. Calibrationfluid clearly has the lowest density. Based on the re-

Densi ty|kg/m31

98 0 -Measured Density

500 750 1000Pressure {bar]

* Tellus VG32 Tellus VG46A TellusTX_VG46. Comet_SAE10w.30 RimulaX30_VG93 Cal ibration f luid+ HF.E VG46- Pine oil VG46

T=40'C

Fig 7: The measured densities of the studied hydraulicfluids at 40CMeasured Density

BOO 7 5 0 1 0 0 0Pressure [bar]

Te l lus VG32 T e l lus VG4e1 Tel lusTX_VG46xComet_5AE10w.30> RimulaX30,VG93 Calibration fluid.f HF-EVG4e-Pine oi l VG46

T= 70 C

Fig. 8: The measured densities of the studied hydraulicfluids at 70CSimilar to speed of sound and bulk modulus, thetrend of the density behavior will not change between

the fluids or temperatures. Also these measurementsare following uniform second order polynomials (Kar-jalainen, 2009; 2011b) - this discovery has been usedin defining the prediction method of Section 4.2.

4 Prediction MethodAs mentioned in the introduction, there are differentmodels also for dynamic fluid parameters. However,the existing models are usually too simplified and inac-curate, or the models require parameters, which cannotbe realized in practice. On the other hand, the high-pressure behavior of hydraulic fluid dynamics is stillquite an unknown research area. Even any measureddata is very rare for pressure levels over 300 bar -especially when the fluid is not mineral oil based.Quite simple prediction m ethod has been developedat IHA for speed of sound in fluid, fluid bulk modulusand fluid density. As stated in Chapter 3, measure-ments seem to follow a uniform second order polyno-mial trend. Therefore, with simple second order poly-nomials it is possible to predict the dynamic fluid be-havior. Furthermore, the most important aspect withthis method is that the parameterization is possible for

any standard hydraulic fluid - only ISO standardizedfluid characteristics is needed. The actual developmentof the models has been explained more in detail in


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Juho-Pekka Karjalainen, Reijo Karjalainen and Kaievi Huhtala

70C and up to 1500 bar, with many different types offluids. In Chapter 5 of this article, the received predic-tion accuracy is demonstrated. More results have beenreported in Karjalainen (2011b). When the operatingconditions clearly differ from the presented ones somerestrictions may occur with the presented equations.This is discussed in Section 4.4. Further research is inprogress for narrowing down these restrictions.4 1 Bulk Modulus Model

According to the second order polynomials fitted tomeasured data, the second and first order terms may beesfimated quite well for the best fit. The constant termis a fiuid and temperature dependent factor. The equa-tion for fluid tangent bulk m odulus is given in Eq. 6(Karjalainen, 201 lb). The pressure is expressed in [bar]and bulk modulus in [MPa].- +\.2- (6)

The constant term of the second order model ofadiabatic tangent bulk modulus can be estimated usingEq. 7 (Borghi, 2003; Karjalainen, 2011b). Eq. 8 (Bor-ghi, 2003; Karjalainen, 2011b) may be used for iso-thermal tangent bulk modulus. All the parameters ofthe constant term equations can be found for any stan-dard hydraulic fiuid. The kinematic viscosity at atmos-pheric pressure and 20C may e.g., be calculated withthe well-known Walther equation (Hodges, 1996). Inthese equations, kinematic viscosity is expressed in[cSt] and temperature in [C].=0 1 [1.57 + 0.1510 20-r417

10 20-r435

7

8

4 2 Density ModelThe first version of the density model was alreadypublished in Karjalainen (2009, 2011a). However, thesecond and first order terms of the model were slightlyrevised in Karjalainen (201 lb). The first version can beexpected to lead to an additional systematic maximumftjll scale error of about 1 - 2 , and the model pre-sented in this article should be used instead for betteraccuracy.Also for fluid density model, the second and firstorder polynomial terms may be estimated for the bestfit, at the presented temperature range. The constantterm is a fluid and temperature dependent factor. Theequation for fluid density is given in Eq. 9 (Kar-jalainen, 2011b). Pressure is expressed in [bar] anddensity in [kg/m^].

p(p,T)= -\-\0- -p +0.QS6-p +C (p^,.T) ^5^For the constant term, there is a commonly usedprocedure for finding a density value at atmospheric

density correction coefficients a are listed e.g., in(ASTM/IP) and Hodges (1996). For the studied fiuidsthe coefficients are also listed in Table 1. In Eq. 10,temperature is expressed in [C], a in [kg/(m^-C)] anddensity in [kg/m^].

4 3 Speed of Sound ModelAs with bulk modulus and density, the second andfirst order terms of speed of sound model have beenselected for the best fit. The constant term is a tempera-ture and fluid dependent factor. The equation for speedof sound in fiuid is given in Eq. 11 (Karjalainen, 2009;201 la; 201 lb). Pressure is expressed in [bar] and speedof sound is expressed in [m/s].c(p,T)=-0.000\ p +0.4S-p +C, p^,,T) (11)The constant term of speed of sound equation can

be calculated from the previously presented constantterms of fluid tangent bulk modulus (Eq. 7 or Eq. 8)and density (Eq. 10), using also the previously pre-sented Eq. 1. Combined, this will lead to Eq. 12 (Kar-jalainen, 2009; 201 la; 201 lb).

(12)4 4 Current Restrictions

The presented temperature range covers 40 - 70C.Further research has been also performed for ternpera-ture range of 20 - 130C. Based on first results with theexpanded temperature range, the density equation (Eq.9) may be modified for a better accuracy by giving somesimple temperature relation for the first order term. Itwould seem clear that the first order term slightly in-creases with increasing temperature - the effect of whichis insignificant with the presented range of 40 - 70C.The speed of sound and bulk modulus models would notseem to be that affected by temperature.However, some further research has also been madeusing mineral oil and petrol based fluids with densitiesas high as 1000 kg/m^. With these fiuids the constant

terms of speed of sound and bulk modulus modelsmight need some kind of simple density related factor.It would seem that with high-density fiuids there is asystematic uniform shift between the measured andpredicted values - the predicted ones being somewhatlower than the actually measured ones. Same kind ofbehavior could also be discovered with the pine oilstudied for this article - the results and received model-ling accuracies of the pine oil are given more in detailin Karjalainen (201 lb).Fluid behavior at temperatures below 0C willclearly need more research, but in theory the basic fluidbehavior should remain unchanged with fluids de-

signed for lower temperatures. Fluid behavior at pres-sures over 1500 bar will be researched in near future -it is possible that elevated pressure will slightly modify


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Measuring and Modelling Hydraulic Fluid Dynamics at High Pressure- Accurate and Simple Approach

5 Prediction ResultsIn the following, the measured results of Chapter 3are compared to the prediction results, which werereceived with the equations of Chapter 4. Due to thelength of the material to be considered, only the resultsof Shell Tellus VG 46 are shown graphically in thisarticle. Shell Tellus VG 46 was selected due to its gen-erally well-known hehavior. More results can be foundin Karjalainen (2011b). Nevertheless, the receivedmodelling errors for all the eight studied fiuids aregiven in Section 5.4.

5.1 Speed of Sound in FluidFigure 9 illustrates the comparison of measuredspeeds of sound in the selected Shell Tellus VG 46mineral hydraulic oil (data points) with the predictedones (continuous lines), at 40C and 70C . With visualexamination, the prediction seems to perfomi well atthe presented operating range. There are no significantuniform shift errors, and the predicted polynomialsclearly follow the measurements. The values for mod-elling errors are given in Table 2, in Section 5.4. Possi-ble restrictions of the presented model were discussedin Section 4.4.

5.2 Adiabatic Tangent Bulk Mod ulusFigure 10 shows the comparison of measured adia-batic tangent bulk moduli of the selected Shell TellusVG 46 mineral hydraulic oil (data points), with thepredicted ones (continuous lines), at 40C and 70C.

As it can he seen, the prediction method performs verywell at the presented operating range. The modellingerrors are given in Tahle 2, in Section 5.4. Possihlerestrictions of the presented model were discussed inSection 4.4.5.3 Density

Figure 11 represents a comparison of measureddensities of the selected Shell Tellus VG 46 mineralhydraulic oil (data points) with the predicted ones (con-tinuous lines), at 40C and 70C. Again with visualinspection, the prediction performs well at the pre-sented operating range. The modelling errors are alsogiven in Tahle 2, in Section 5.4. Possible restricfions ofthe presented model were discussed in Section 4.4.

2000 T -1900 Speed of soundTellus VG 46 ~

Measured@40CPredicted(5)40C

A Measured@70C- Predicted @70C

500 1000 1500

3400

2900Bulk ModulusTellus VG 4 6

Measured@40CPredicted@40C

Measured@70CPredicted(a)70C

500 1000Pressure [bar]

1500

Fig. 10: The comparison of measured and predicted adia-batic tangent bulk moduli of Shell Tellus VG 46, at40C and 70C

1

930 -

910900 -890 880870

830 -{

Density

A ') 500 1000

Pressure [bar)

Measured@40CPredicted@40C

A Measured@70C Predicted@70C

1500

Fig. 11: The comparison of measured and predicted densi-ties of Shell TellusV 46 at 40C and 70C5.4 Modelling Error

The modelling errors hetween the predictionmethod of Chapter 4 and the measurement results ofChapter 3 are listed in Table 2, for all the eight studiedfluids. The average modelling errors in Tahle 2 havebeen calculated as percentages from the maximumvalue of the fluid parameter at 1500 bar pressure (fromfull scale, FS ).Apart from few exceptions, all the studied full scaleerrors are within two percent. The results are excellent,especially keeping in mind the universally applicahlenature ofthemodels.

Table 2: The average predicfion errors of the secondorder polynomial models

FluidTellus VG 32Tellus SVG 46Tellus TX VG 46Comet SAE lOW-30Rimula i30 VG 93Calibrt, fluid S.9365Naturel ls HF-Eve 46ECO Pine O il VG 45

Bulk modulus40C

FSI%11.20. 60. 81.01.21.71.84.2

7 0 ^FS|%12. 81.11.51.52. 44 .01.74. 3

D e n s i t y40 "C

FS1%0.20.20.20. 20. 00. 30.10. 2

70CFS

(% |0. 70. 30. 40. 30.61.00.40.3

Speed of sound40C

FSl%l1.01.10. 91.61.70.90. 61.1

70CFS[%11.50.90.80.91.81.71.02.4


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Juho-Pekka Karjalainen, Reijo Karjalainen and Kalevi Huhtala

even this much tighter condition of error evaluationgives an error under five percent.When the operating conditions clearly change fromthe presented ones, some modifleations to the pre-sented models may be needed for aehieving similaraccuracy - this was discussed in Section 4.4.

ing system. Also, results with water should be testedthere is quite good referenee data available for waterdynamies.

Nomenclature6 Conclusions

In this article, simple yet accurate methods formeasuring and predicting the most important dynamichydraulic fluid parameters were introduced. The fluidparameters; speed of sound in fluid, adiabatie tangentbulk modulus and density; were studied at the normaloperating temperatures of industrial fluid power sys-tems. The studied pressure range was up to 1500 bar.These methods were applied to eight different com-mercial hydraulic fluids. It was shown that at the pre-sented conditions both the measuring system and theprediction method performed very well.

Based on the results, the studied fluids were com-pared in terms of dynamic fluid behavior. It is quiteevident that base fluid has the dominant effect on thesefluid parameters. Viscosity grade or additives did notseem to have any signiflcant impact. Practically, all thestudied fluids were discovered to behave similarly interms of changing temperatures. Moreover, all the fluidswere presenting similar pressure trends. However, sig-nificant differences in absolute values were recordedbetween the fluids at the same operating eond itions.The experimental results of e.g., fluid bulk modulimight seem to be counterintuitive. For example, it maybe surprising that the slope of bulk modulus has beendiscovered to reduce as pressure is increased, when itcould be expected to even increase due to increasingmolecular forces of a compressed fluid. The actualphysics behind this phenomenon would clearly needmore researeh which is beyond the scope of this article.However, similar reducing trend in speed of soundmeasurements at elevated pressures has also been dis-covered in e.g., Beyer (1998), where speed of sound indiesel fuels was discovered to follow deereasing fourthorder polynomials. Moreover as stated in S ection 2.2.2,

the measured densities of this artiele have been foundto be in excellent agreement with referenees even innumerical values. These will give additional eonfi-dence also to the experimental diseoveries and observa-tions oft isartiele.Future work is already in progress for expandingthe operating range of the measuring system. Pressurelevel will be raised up to about 2500 bar. The tempera-ture range has already been raised up to 130C, resultswill be published later. In addition, research on ex-panding the presented prediction models to cover awider operating range with similar aecuracy has beenstarted. At this stage, it would not seem to demand any

major modifieations - naturally these future modifica-tions will not affect the results of this artiele at the

effB. ff.

ccB(Patni )c ( P a t m )

D(Patm )

LPP-* atmTA

Patm.T

Atm,15i

Hitm.20l

Effective bulk modulusEffeetive adiabatic bulkmodulusFluid bulk modulusPipe bulk modulusSpeed of soundConstant term of tangent bulkmodulusConstant term of speed ofsoundConstant term of fluid density

[Pa][Pa][Pa][Pa][m/s][Pa][m/s][kg/m^]

Fluid heat capacity factor at [-]constant pressureFluid heat capacity factor at [-]constant volumePipe inner diameter [m]Pipe outer diameter [m]Modulus of elastieity [ a]Measuring pipe length [m]Pressure [ a]Atmospheric pressure [ a]Temperature [C]Density correction coefflcient [kg/m -C]Pois son s ratio for hydrau lic [-]pipe materialDensity at meas ured pressure [kg/m^]and temperatureDensity estimate at meas ured [kg/m^]pressure and temperatureDensity at atm. pressure and at [kg/m^]temperature TDensity at atm. pressure and at [kg/m^]15C temperatureKinem atic viscosity at atm. [mVs]pressure and temperature of2O C


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Measuring and M odelling Hydraulic Fluid Dynamics at High Pressure - Accurate and Simple Approach

ReferencesASTM-D6793-02. 2002. Standard Test Method forDetermination of Isothermal Secant and TangentBulk Modulus. USA: ASTM. (5 p.)ASTM/IP.Petroleum Measurement Table 53.Beyer, T. 1998. The Measurement of Diesel FuelProperties at High Pressure. M.Sc.(Tech.) thesis.Georgia Institute ofT echnology.USA. (141 p.)Borghi M. Bussi C Milani M. and Paltrinieri F.2003.A Numerical Approach to the Hydraulic Flu-ids Properties Prediction. Proceedings of SICFP'O3,pp. 715 - 729. Tampere University of Technology.Finland.Garbacik A. and Stecki J.S. 2000. Developments inFluid Power Control of Machinery and Manipula-tors.Fluid Power Net publication, pp. 227 - 257.Gholizadeh H. Burton R. and Schoenau G.2011.Fluid Bulk Modulus: A Literature Survey. Interna-tional Joumal of Fluid Power, Vol. 12, No. 3, pp.5 - 15.Hodges, P. 1996. Hydraulic Fluids. London: Arnold.(167 p.)ISO 15086-2:2000. 2000. Hydraulic Fluid Power De-termination of the Fluid-borne Noise Characteris-tics of Components and Systems -Part 2 (27 p.)Johnston D. N. and Edge, K. A. 1991. In-situ Meas-urement of the Wavcspced and Bulk Modulus in

Hydraulic Lines. Proc.I.Mech.E., Part 1, Vol. 205,pp 191 - 197.Karjalainen J. - P. K arjalainen R. H uhtala K .and Vilenius M.2005. The Dynamics of HydraulicFluids - Significance, Differences and Measuring.Proceedings of PTMC 2005, pp. 437 - 450. Univer-sity of Bath. UK .Karjalainen J. - P. Karjalainen R. H uhtala K.and Vilenius M.2006. High-pressure Properties ofHydraulic Fluids - Measuring and Differences.Proceedings of PTM C 20 06, pp. 67 - 79. University

of Bath. UK.Karjalainen J. - P. K arjalainen R. H uhtala K .and Vilenius M. 2007. Fluid Dynamics - Com-parison and Discussion on System-related Differ-ences. Proceedings of SICFP'O7, pp. 371 - 381.Tampere U niversity of Technology. Finland.Karjalainen J. - P. Ka rjalainen R. Huh tala K.and Vilenius M. 2009. Second Order PolynomialModel for Fluid Dynamics in High Pressure. Pro-ceedings of ASME DSCC 2009. Hollywood, CA.USA. (7 p.)Karjalainen J. - P. Ka rjalainen R. H uhtala K.and Vilenius M. 2011a. Comparison of Measuredand Predicted Dynamic Properties of Different

Karjalainen J. -P.2 1 lb. High-Pressure Properties ofHydraulic Fluid Dynamics and Second Order Poly-nomial Prediction Method. Dr.(Tech.) thesis. Tam-pere University ofTechnology.Finland. (164 p.)Kojima E. and Yu J. 2000. Methods for Measuringthe Speed of Sound in the Fluid in Fluid Transmis-

sion Pipes. SAE Technical Paper 2000-01-2618.Society of Automotive Engineering, Inc. (10 p.)Kuss E. 1976. pVT-Daten bei hohen Drcken.DGMK- Forschungsbericht, 4510/1975. (69 p. +appendixes)Merritt H. E. 1967. Hydraulic Control Systems.USA: John Wiley & Sons Inc. (358 p.)Smith jr. L. H. Peeler R. L. andBernd L. H. 1960.Hydraulic Fluid Bulk Modulus - Its Effect on Sys-tem Performance and Techniques for PhysicalMeasurement. N FPA P ublication. (19 p.)Yu, J., Chen, Z. and Lu, Y. 1994. The Variation of OilEffective Bulk Modulus with Pressure in HydraulicSystems. Transactions ASM E, Joum al of Dynam icSystems, Measurement & Control, Vol. 116, pp.146- 150.

. luho-Pekka KarjalainenBorn in August 1978. Received his Dr. Tech.degree from Tampere University of Tech-nology (Finland) in 20 1 . He is currentlyworking as a research fellow in the Depart-ment of Intelligent Hydraulics and Automa-tion (IHA) of the university. His primaryresearch fields are hydraulic fluid dynamics,different hydraulic fluid types and fluideffects on fluid power applications.

Reijo KarjalainenBorn in February 1952. Received his Lie.Tech. degree from Tampere University ofTechnology (Finland) in 1996. He is cur-rently working as a laboratory manager inthe Department of Intelligent Hydraulics andAutomation (IHA) of the university. Hisprimary research fields are testing andanalysis of different hydraulic fluid typesand different test equipment designs for fluidpower applications.

Kalevi HuhtalaBorn in August 1957. Received his Dr. Tech.degree from Tampere University of Teeh-nology (Finland) in 1996. He is currentlyworking as a professor in the Department ofIntelligent Hydraulics and Automation (IHA)of the university. He is also head of depart-ment. His primary research flelds are intelli-gent mobile machines and diesel enginehydraulics.


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Measurements of Hydraulic Fluid Propertied at High Pressures 2012 Intl Journal of Fluid Power