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HYDROSTATIC MECHANISM OF A WAVY-TILT-DAM MECHANICAL SEAL

Wei Liu, Ying Liu, Jingjing Zhai, Weifeng Huang and Yuming WangState Key Laboratory of Tribology, Tsinghua University, Beijing, China

E-mail: [email protected]

ICETI 2012-J1138_SCINo. 13-CSME-67, E.I.C. Accession 3525

ABSTRACTA theoretical model is developed to study the hydrostatic mechanism of the WTD seal in this paper. Theinfluences of structure parameters on the seal performance are studied under different rotor speed and sealedpressure. The results show that the existence of waves will impair the hydrostatic effect in the radial di-rection and promote the hydrostatic effect in the circumferential direction. The taper β1 will dominate theperformance of the WTD seal under the stable working condition when there is no cavitation occurs.

Keywords: mechanical seal; wave; wavy-tilt-dam; hydrostatic; hydrodynamic.

MÉCANISME HYDROSTATIQUE D’UN JOINT D’ÉTANCHÉITÉONDULÉ D’UN BARRAGE INCLINÉ

RÉSUMÉDans cet article, un modèle théorique est développé pour étudier le mécanisme hydrostatique d’un jointd’étanchéité ondulé d’un barrage incliné. Les influences des paramètres de la structure sur la performancedu joint sont étudiées sous différentes vitesse du rotor et de la pression du joint de scellement. Les résultatsdémontrent que la présence d’ondes aura des impacts sur l’effet hydrostatique dans la direction radiale etfavorisera l’effet hydrostatique dans la direction circonférentielle. La pente β1 dominera la performance dujoint d’étanchéité ondulé sous un mode de fonctionnement stable quand il n’y a pas de cavitation.

Mots-clés : joint mécanique ; onde ; joint d’étanchéité ondulé de barrage incliné ; hydrostatique ; hydro-dynamique.

807Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

NOMENCLATURE

Fb fluid force imposes on the stator ring’s back (N)Fclose closing force (N)Fs spring force (N)Fopen opening force (N)G1 gravity of the stator ring (N)h film thickness (µm)ha amplitude of the wave at outer radius (µm)hi film thickness at inner radius (µm)ht height of the radial angle at outer radius (µm)k the number of wavinessn rotational velocity of the rotor (rpm)p film pressure distribution (MPa)pi inner pressure (MPa)po outer pressure (MPa)∆p differential pressure (MPa)Q leakage (m3/h)r radial coordinate (m)Rd dam radius (m)Ri inner radius (m)Ro outer radius (m)Vθ fluid velocity in the circumferential direction (m/s)z axial coordinate (m)

Greek symbolsα ratio of waviness to taperθ circumferential coordinate (rad)β1 radial angle on the stator face (µrad)ω angular velocity of the rotor (rad)µ viscosity of water (Pa·s)

1. INTRODUCTION

Comparing with the contact mechanical face seals, the non-contact mechanical face seals with differentstructure on the face have being proved to be less energy consumption and long lifetime. The stability ofmechanical seals in the pumps or the compressors is essential for the process industry. Therefore a goodstructure of the seal face is required to ensure the performance of the seal.

The non-contact and non-leakage mechanical seal with multiple lobe grooves on the face was developedby Etsion [1] in 1984, since then, many theoretical and experimental literatures have been published [2].Lai [3] described the development of the spiral groove liquid mechanical seals later. Gabriel [4] discussedthe fundamentals of spiral groove non-contacting face seals, proved the spiral groove seal had better perfor-mance. Wang conducted several studies on the spiral groove seal that used in oil field [5,6] and gas field [7].Liu [8] designed the main parameters for double spiral grooves face seal. Peng analysis the spiral groovedry gas seal with an inner annular groove [9] and with goose-grooves [10].

Laser surface texturing (LST) has gained an increasing interest in recent years as a means for enhanc-ing tribological performance of sealing faces. Etsion [11] developed the first model for LST mechanicalseals based on circle micro dimples. Since then, a large volume of theoretical and experimental work waspublished on various aspects of LST liquid and gas seals by Etsion’s group [12–14]. Peng’s group [15, 16]investigated both the hydrostatic and the hydrodynamic effects of the LST seals.

To get a better idea of how hydrodynamic effect works in seals and to establish some limiting values of

808 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

various parameters, Lebeck conducted several studies on the wave face seals. The results showed that theminimum film thickness depended on both the wave amplitude and the number of waves [17]. Laboratorytests were carried out by Young [18, 19], who found that under a wide range of operating conditions, thetested seals produced low friction, low leakage and low wear. Liu [20] analyzed the effect of structureparameters on a wavy-tilt-dam (WTD) seal under different operating parameters.

However, many of the researchers mentioned above focused solely on the analysis of hydrodynamic me-chanical seal [21], like the spiral groove seals, the LST seals, or on the face seals with waves and radialtaper, the mechanism of these seals, especially WTD seal was not clearly described. Therefore, it is nec-essary to reveal the mechanism of the WTD seal and investigate the structural parameters to provide betterperformance.

In addition, most of the researchers only focused on the hydrodynamic effect of the waves, without con-sidering the hydrostatic effect of the WTD seals. Liu [20] has pointed that under stable working conditionif there is no cavitation the WTD seal works as a hydrostatic seal, but just fixing the initial film thicknessto analyze the influence of the structure and operating parameters. In this article, to reveal the hydrostaticmechanism of WTD seal shown in Figs. 1 and 2, a theoretical model is developed. The balancing filmthickness under which the opening force of the seal is equal to the closed force, the leakage of the WTDseal are studied. Additionally, the investigation of the structural parameters of the WTD seal has been doneunder different operating parameters.

2. MATHEMATICAL MODEL

2.1. Geometry ModelThe equation of film thickness is deduced according to the geometric model shown in Fig. 2:

h(r,θ) =

{hi, r ≤ Rd

hi +(r−Rd)(1−α coskθ) tanβ1, r > Rd(1)

β1 = ht/(Ro −Rd) (2)

Dimensionless parameter α is defined as ratio of waviness to taper shown in Eq. (3):

α = ha/ht (3)

In Eq. (1), h(r,θ) represents the film thickness; hi is the film thickness at inner radius Ri; β1 is the taper onthe stator face in Eq. (2); ht is the height of the taper at outer radius Ro; Rd represents the dam radius; ha isthe amplitude of the wave at Ro. The value of α is 0 ≤ α ≤ 1, when α = 0, it means there is no wave on theface, and α = 1 means ha is equal to the height of the taper at outer radius. Hence, the hydrodynamic effectof the film is separated with hydrostatic effect by α .

2.2. Kinematic ModelIn this article, the seal is supposed to operate in laminar flow, without phase changing in the lubricant film.For incompressible fluid, Reynolds equation is

∂

∂ r

(rh3

12µ

∂ p∂ r

)+

1r

∂

∂θ

(h3

12µ

∂ p∂θ

)=

ωr2

∂h∂θ

(4)

where ω stands for the angular velocity of the rotor, and µ is the viscosity of the fluid. Vr and Vθ are thefluid velocity in the radial and circumferential directions, calculated by

Vr =1

2µ

∂ p∂ r

(z2 − zh) (5a)


Fig. 1. WTD seal face.

Fig. 2. WTD seal structure.

Vθ =1

2µ

∂ p∂θ

(z2 − zh)+ωrzh

(5b)

2.3. Boundary ConditionsAs reported in bearing studies, the Reynolds boundary condition provides accurate results for load supporteven when cavitation occurs [17]. In this article, the Reynolds cavitation boundary condition is used in orderto simplify the calculating process. At the outer and inner radius, the boundary pressure is po and pi, seeEq. (6a). The periodic condition is given in (6b).

p(Ri,θ) = pi, p(Ro,θ) = po (6a)

p(r,θ) = p(r,θ +2π/k) (6b)

2.4. Performance ParametersThe opening force of the seal should be equal to the closing force, so the balancing film thickness willvaries with different structures. The performance parameters of the seal are as follows:


Table 1. Parameters of the WTD mechanical seal and the fluid.Item ValueOuter pressure po (MPa) 5Inner pressure pi (MPa) 0Differential pressure ∆p = po − pi (MPa) 5Outer radius Ro (m) 0.15125Inner radius Ri (m) 0.14025Dam radius Rd (m) 0.14245Viscosity of water at 50◦C µ (Pa·s) 549.4×10−6

Rotational velocity of the rotor n (rpm) 1500Closing force (N) 36949

Opening force:

Fopen =∫ 2π

0

∫Ri

Ro prdrdθ (7)

Closing force:Fclose = Fb +Fs +G1 (8)

where Fb is the fluid force imposes on the stator ring’s back; Fs is the spring force; G1 is the gravity of thestator ring.

Leakage:

Q =∫ 2π

0

∫ h

0rVrdzdθ (9)

3. RESULTS AND DISCUSSION

The main geometric parameters of the WTD seal and working conditions are shown in Table 1. The param-eters will be constant unless they are investigated.

3.1. Influence of Geometrical ParametersFrom Eq. (5), it can be found that the Vθ will change with the number of k, the larger k is, the larger Vθ willbe, which will result in the hydrostatic effect in the circumferential direction. Figure 3a is the film thickness.Figure 3b shows Vθ on the plane of the middle height of the film thickness in which the number of wave kis 1 and the rotor speed is zero. Supposing the anticlockwise direction is positive, in this figure we can seethat the fluid flow from the hmax to the hmin area in two different directions, hence causing the hydrostaticforce in the circumferential direction. This hydrostatic effect will inevitably increase with k.

3.1.1. Influence of β1The variation in minimum film thickness, which represents the balancing position of the seal, and leakagewith β1 are shown in Fig. 4. The minimum film thickness is augment with increasing β1. Because when taperangle β1 becomes larger, the hydrostatic effect in the radial direction becomes more evident. The openingforce should be equal to the closing force, so the balancing film thickness increases. Under the same β1,when β1 is less than 300 µrad, the film thickness and leakage increase when α increases, this is because thatthe hydrostatic effect in the radial direction is not obvious due to small value of β1. In this situation, whenα is larger, the hydrostatic effect in circumferential direction is more effective. On the contrary, when β1is larger than 300 µrad, the minimum film thickness and Q are down with up of α . The result is that the


Fig. 3. Film thickness, Vθ distribution when k = 1, n = 0: (a) film thickness, (b) Vθ distribution.

Fig. 4. Variation in performance parameters with β1 under different α: (a) minimum film thickness, (b) leakage.

integrative hydrostatic effect in circumferential and radial direction decreases, which means the waves onseal face will weaken the hydrostatic performance.

As we know from Eq. (9), Q is related to the triple of h, so Q increases exponentially with β1. Due to thedecreases of the total film thickness, Q decreases when α increases under large angle.

Influence of kThe performance of the WTD seal varies with the k can be seen in Fig. 5. When α is equal to 0, there isno wave on the seal face except the radial taper, which means under this condition, the seal is a hydrostaticseal. The balancing film thickness keeps constant. The minimum film thickness of the WTD seal with smallα has large balancing film thickness, which will result in the large Q. This is because when α is small, theexistence of waves will not influence the opening force obviously, which is the same as the result shownin Fig. 4. But when α is close to 1, the effect of waves will be more notable. It is shown in Fig. 3 thatthe hydrostatic effect in the circumferential direction will augment with increasing k, hence the openingforce will increase, and so are the minimum film thickness and leakage. Although the waves will impair


Fig. 5. Variation in performance parameters with k under different α: (a) minimum film thickness, (b) leakage.

Fig. 6. Variation in performance parameters with n under different α: (a) minimum film thickness, (b) leakage.

the hydrostatic effect in the radial direction, the leakage will decrease as well, as shown in Fig. 5b. Thestructure parameters of the WTD seal β1, k and α should be considered simultaneously. For example,considering the need of cooling, the leakage should not be zero in some practical using. If the leakage isrequired to be 15 liter per hour, for the proper structure value we will have β1 = 650 µrad, α = 1, k isapproximately 9.

3.2. Influence of Operating Parameters3.2.1. Influence of nIt is well known that the performance of the hydrostatic mechanical seal with radial taper will not be affectedby the rotor speed n. This principle is proved in Fig. 6 with α = 0. The performance of the WTD sealnearly remains the same when α is less than 0.5. However, when α is close to 1, the minimum filmthickness hi and leakage Q are all increased with increasing n. There appears no cavitation in the fluidfilm now, and the wave in one period is a cosine wave, so the pressure decreases in the divergence areawill neutralize the pressure increases in the convergence area, resulting in the hydrodynamic effect of the


Fig. 7. Variation in performance parameters with ∆p under different α: (a) minimum film thickness, (b) leakage.

WTD seal being zero [22]. From Eq. (5), it is obvious that the curves increase only because the increasein Vθ , the fluid flows from the peak of the film thickness to the valley will result in more hydrostatic effectin the circumferential direction due to the kinetic energy plus with rotor speed. Hence, the performance ofthe WTD seal will be affected by the rotor speed, which is a big difference from the traditional hydrostaticmechanical seals.

3.2.2. Influence of ∆ pAs shown in Fig. 7, the performance of the WTD seal varies with ∆p. When α is less than 0.5, hi and Qincrease the same as with α = 0, which implies that the seal is now a totally hydrostatic seal. When α isclose to 1, hi firstly decreases and then increases with ∆p. Because when ∆p is small (here it is less than 2MPa), cavitation occurs in the fluid film, which will cause the hydrodynamic force. The WTD seal worksas a hydrodynamic seal, the opening force is bigger than the WTD seal with small α so hi becomes larger.With ∆p increasing, cavitation hardly appears in the film, the WTD seal turns out to be a hydrostatic sealagain, and the curves trend are all the same. In the cases discussed here, no cavitation occurs (except forthe region shown in Fig. 7b). Thus, all results are valid except for the leakage results in the cavitated regionshown in Fig. 7b. Q will increase linearly with ∆p due to the large film thickness.

4. CONCLUSION

1. If there is no cavitation occurs in the fluid film during the stable working condition, the WTD sealworks as a hydrostatic mechanical seal. The existence of waves on the seal face will impair thehydrostatic effect in the radial direction. However, the hydrostatic effect will be promoted in thecircumferential direction due to the waves.

2. The structure parameter β1 will dominate the hydrostatic effect in the radial direction under the stableworking condition, meanwhile, the hydrostatic effect in the circumferential direction will increasewith the increase of k and α , especially when α is close to 1.

3. The hydrostatic effect in the circumferential direction will increases due to the kinetic energy pluswith rotor speed. The total hydrostatic effect will also increases with increasing ∆p.


ACKNOWLEDGEMENTS

This work was supported by the National Basic Research Program of China (973) (Grant No.2009CB724304), the National Natural Science Foundation of China (Grant No. 50975157) and the Na-tional Science and Technology Support Plan (Grant No.2011BAF09B05).

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