The cavitation phenomenon in the flow zone distributor bodyspool valve.

Balasoiu, Victor ; Bordeasu, Ilare ; Popoviciu, Mircea Octavian 等

1. INTRODUCTION

The hydraulic resistance describe hydraulic system elements with diverse functional role, and the diversity of type construction assures the purpose for their role. The majority of hydraulic resistance works by strangle the flow vein . From this reason the cavitation phenomena can occurs during with increasing speed and the different pressure values in different points of the hydraulic resistance.

For studying the cavitation regime in hydraulic resistance distributor body-spool valve, the research had focus to determine energetic spectrum of analyse cavitation effect among the hydraulic distribution apparatus (Anton 1985).

In a series of anatomization Numachi broach the problem of cavitation inside Venturi tubes and inside the diaphragm to determine the cavitation start moment ,by using the relation:

[[sigma].sub.inst] = [p.sub.i] - [p.sub.d]/[DELTA]p = ([p.sub.i] - [p.sub.d])/([rho][v.sup.0.sub.2]/2) (1.a)

Where: [p.sub.i] pressure on the strangled section, [p.sub.d] the vaporization pressure of the liquid, [v.sub.0] the reference medium speed to input. The initiation and the development of the cavitation inside the hydraulic servo valve with cylindrical spool valve is possible due to local flowing conditions, which can occurs by increasing the speed and lowering the pressure and it is characterized through the cavitation coefficient (Raszga 1998, Gerald 1994, Toshiuki et al. 1993,)

Numachi, starting from the definition relation of the flow rate coefficient, he determine by experimental the coefficient :

[C.sub.k] = [Q.sub.k] [square root of 1 - [m.sub.2]]/[pi]/4 d 2/2 [square root of 2g ([p.sub.1k] - [p.sub.2k])/[gamma]] (2)

Where: [C.sub.k]--flow rate coeficient in cavitation regime, [Q.sub.k]--flow rate in cavitation conditions, [p.sub.1k], [p.sub.2k] input and output pressure in cavitations. In figure 1, is presented the variation of the flow coefficient versus the cavitation coeficient.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The spool-valve distributor its characterized by Martin and Wiggert (Anton 1985) as being made of several hydraulic resistance, which works at high pressure and increasing speed. The most important is high speed jet with circular form, which appears at the exit of adjusting slit through cylindrical room and the exit circuit of apparatus.(Fig 2). If the jet is free for small apertures and two-dimensional flow model, it will reach to a value for flow coefficient Cd of 0.673, and a 69[degrees] in ratio with spool-valve axis, calculated by McCloy and Martin in 1973 (Raszga 1998).

In distributors with cylinder spool-valves can be notice two types of incipient cavitation correlated to free or attached jet. In case of attached jet can be notice a cavitation development along wall and the cavitation bubbles appears due to increased friction tension near to wall, that leads to a liquid break and appearance of new liquid-gas interface.

The development of cavitation in distributors with cylindrical spool-valve can be identified by recording dynamical values, which are pulsating pressure in the exit room of circular jet, which represent a different noise from the turbulent jet, to be distinguished in energetic spectrum of measured values. (Martin et al., 1981) due to development conditions of phenomenal and assumed measurements for experimental appliance. The type of cavitation that appear is developed cavitation, not a gas cavitation that appears in other author's works incriminated. Point out the presence of dissolved air in 10% has a reduced effect due to short time of existence of cavity in case of cavitation implosion. But they are responsible whit forming of air bubble with high dimensions which can affect system dynamics.

2. GENERAL EXPRESSION OF CAVITATION COEFFICIENT FOR CONTROL VALVES

If we consider the structure of hydraulic trace for a distributor with cylindric spool-valve, in maximum speed assumption, respective lower pressure, appears near to minimal section of trace from the adjusting slit area. (Point M from fig.3) Making use by cavitation coefficient of distribution section, ratio to input section we obtain:

[[sigma].sub.corp0] = [[sigma].sub.D0] = ([V.sup.2.sub.max]/[V.sup.2.sub.0] --1) + ([h.sub.p0m])/[[V.sup.2.sub.0]/2g] (3)

The energetic loses therm can be write starting from the equation of energy transfer, to take into account that the hydraulic loses are preponderant due to perturbation of speed field. Reference to entrance section we obtain cavitation coefficient for distributor:

[[sigma].sub.D0] = ([V.sup.2.sub.max]/[V.sup.2.sub.0] - 1) + ([h.sub.p0M])/([V.sup.2.sub.0]/2g) = ([V.sup.2.sub.max]/[V.sup.2.sub.0] - 1) + [??]0M (4)

Reporting the difference of pressure between in and out (1.a) , we take input section as reference:

[[sigma].sup.*.sub.inst0] = [p.sub.0] - [p.sub.v]/[DELTA][p.sub.02] (1.b)

[[sigma].sup.*.sub.D0] = [rho][V.sup.2.sub.0]/2[DELTA][p.sub.02][([V.sub.max]/[V.sub.0]) - 1 + [[zeta].sub.0M]] (5)

for output section considered as reference, relation (5) becam:

[[sigma].sup.*.sub.D2] = [rho][V.sup.2.sub.2]/2[DELTA][p.sub.02][([V.sub.max]/[V.sub.2]) - 1 - [[zeta].sub.M2]] (6)

Reporting to section "x", relation becam: :

[[sigma].sup.*.sub.Dx] = [rho][V.sup.2.sub.x]/2[DELTA][p.sub.02][([V.sub.max]/[V.sub.x]) - 1 + [[zeta].sub.xM]] (7)

Similar to cavitation coefficient (Raszga 1998), (Toshiuki et all. 1993) the local loosing coefficient signify the energetic looses which emerge on trace of the hydraulic distributor with cylindrical spool valve, due to strong perturbation geometrical structure of the speed field of the inner hydraulic trace. The major loose it take place in adjusting slit area with x opening. At the slit output appears a drown annular jet in the exit room ("A" or "2") .In fig. 4 is represented the spectrum of current lines on the all considered domain, and in fig. 5 we have represented a detailed flow structure in adjusting split area. Inquiring the energy transfer equation between section "0" and "f" the local energetic losses coefficient Z0M that appear on hydraulic trace with cylindrical spool valve becomes:

[[zeta].sub.M2/0] = ([p.sub.f] - [p.sub.2])/([rho][V.sup.2.sub.0]/2) - [K.sup.2.sub.0]/[K.sup.2.sub.2] + (1/[C.sup.2.sub.c])([K.sup.2.sub.0]/[x.sup.2]) (8)

The reserved cavitation coefficient in all matters of connote, marking out the difference between cavitation coefficient of installation and the cavitation coefficient of device (apparatus)--hydraulic distributor. Long time as the value of reserved cavitation coefficient is positive , the regime of work remain cavitation free.

In the moment when the value of reserved cavitation coefficient is null, the working cavitation regime is incipient, and in one point from the hydraulic trace the pressure drops enough to make possible the air bubble emerge, and the liquid break and the gas vapour development is high enough. In this working regime and only now, the value of cavitation coefficient of device is equally numeric with value of cavitation coefficient of the distributor, although they differ as analytic relations. From analytic point of view, the characterization of free cavitation regime of incipient, developed and industrial cavitation and super cavitation it is realised. Practical knowledge of coefficients values is difficult by using local values characteristic flowing field through distributor spool valve.The all definition for cavitation coefficient ,in particular for distributor with cylindrical spool valve ,was started from rigorous definition of cavitation regime and cavitation coefficient.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

3. CONCLUSION

Elaborated documentation about studied phenomenon--the cavitation phenomenon in the hydraulic distributor--spool valve, allow knowledge from theoretical research and experimental, and offer the based elements for extend knowledge of phenomenon. To accentuate the existence of cavitation phenomenon inside the acting hydraulic installation, which works usually with mineral oil, and especially in case of distributor with spool valve, it was accomplished by experimental way and deduced with numerical way by using calculus software with method of finite element.

Correlation of experimental result by Martin and Wiggert (1981) with indicated numerical results by (Gerald C, 1994), (Toshiyuki H. et al. 1993), (Anton, 1985). To determine an analytic numerical relation even approximated it is necessary if we want to describe the initiation and cavitation phenomenon effect in operation of the distributors with spool valve.

ACKNOWLEDGMENTS

The present work has been supported from the National Univ. Research Council Grant CNCSIS--IDEI nr.35/ 68 / 2007.

4. REFERENCES

Anton, I. (1985), Cavitation, Vol II, Ed. Academiei Romaniei, Bucuresti,

Gerald, C.F., Wheatley. P.O.,(1994), Applied numerical Analysis, Edition Hardcover, ISBN:13.9780201565539, pp.536

Raszga, C., (1998).. The Cavitation of phenomenal in the distribution of cilynder sertar, Doctoral Degree Thesis,

Toshiuki, H., Cheng, P., Hayashi, S. (1993) Numerical Analysis of Transient Flow Through a Spool Valve, Reports. Inst. Fluid Sciences, Tohoku Univ, pp.123-133, ISSN:0916287

Martin, C.S., Medlarz, S., Wiggert,D.C., Brennen, C. (1981), Cavitation Inception in Spool Valves, Journal Fluids Engineering, ASME, Vol 103 (4), pp564-576, ISSN: 00982-202.