Study of the fluid film vaporization in the interface of a mechanical face seal

Tribology International 92 (2015) 84–95

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Study of the fluid film vaporization in the interface of a mechanical face seal F. Migout, N. Brunetière n, B. Tournerie Institut Pprime, CNRS-Université de Poitiers-ISAE ENSMAa, Department GMSC, SP2MI, Bd Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France

art ic l e i nf o

a b s t r a c t

Article history: Received 24 February 2015 Received in revised form 27 April 2015 Accepted 27 May 2015 Available online 7 June 2015

This paper presents numerical simulations of the effect of an increase in feeding temperature on a mechanical seal operating with water. A transient numerical model using the homogeneous fluid theory was developed to analyze the vaporization of the fluid film in a mechanical seal interface. Heat transfer in the contiguous solids and faces deformations are considered. After a validation of the model by comparison with experiments, a parametric study is presented. For moderate temperature rise, the vaporization of the fluid in the contact has no significant effect on the seal performance. However, above a temperature threshold, the mechanical seal can exhibit unstable behavior which can be detrimental for its life expectancy. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Mechanical face seal Phase change Numerical simulation Infrared thermography

1. Introduction Mechanical seals are composed of a rotating ring sliding versus a static one. The interface between these two elements ensures the sealing of the fluid in the process. A lubricating film formed with the sealed fluid is generally generated between the seal faces, avoiding wear and reducing friction. The film connects the high pressure and high temperature zone to the atmosphere. If the temperature of the sealed fluid or of the film reaches the atmospheric saturation temperature, phase change will occur in the sealing interface. This situation can lead to severe oscillations, known as ‘puffing’, which can be detrimental for the seal life expectancy (wear and leakage [1]). Orcutt [2] was one of the first researchers to experimentally study vaporization in a mechanical seal interface. He used a seal composed of a rotating transparent disc and carbon seal ring fed in water by the inner radius. He made visualizations of the interface and temperature measurement by means of a pyrometer. He observed, in some cases, torque and leakage fluctuations accompanied by an oscillation of the liquid boundary radial location. On the other hand, he demonstrated that vaporization can be beneficial to limit temperature and reduce friction torque. He explained that this is due to the enhanced hydrostatic pressure generated by the vaporization. According to Orcutt, the non-liquid zone is composed of vapor with drops of liquid water. More recent works [3,4] confirm the existence of a radial non-liquid zone in the

n

Corresponding author. Tel.: þ 33 549 496 531; fax: þ 33 549 496 504. E-mail address: [email protected] (N. Brunetière).

http://dx.doi.org/10.1016/j.triboint.2015.05.029 0301-679X/& 2015 Elsevier Ltd. All rights reserved.

interface. However, there is no certainty on the nature of the fluid: pure vapor or a mixture of liquid and vapor. Accordingly, two approaches have been adopted to model the vaporization of the fluid between the faces of a mechanical seal. If the leakage is small enough, the liquid is assumed to turn instantaneously to vapor at a given radius [5]. Otherwise, it is necessary to consider a continuous boiling where the mass fraction of vapor in the fluid varies gradually from 0 to 1 [6]. This second method is obviously more accurate but more complicated. Moreover, modeling vaporization in sealing necessitates considering heat transfer with solids, transient effects, dynamic behavior and turbulence and inertia effects in the case of high Reynolds number values. Many authors have considered the steady-state problems which are simpler to solve from the heat transfer point of view. Hughes et al. [5] considered semi-infinite solids, obtaining thus an analytical solution for heat transfer. Lebeck [7] was certainly one of the first to use numerical simulations for heat transfer. These allow a more accurate prediction of the surfaces temperature. Etsion and Pascovici [8] used an analytical heat transfer method which works for an asymmetrical situation. Recently, Wang et al. [9] presented simulation results for a wavy tapered seal in steady-state operation. To deal with transient thermal problems encountered, for example, during puffing, Hughes et al., [10] extended the semiinfinite solids approach, whereas Blasbalg and Salant preferred to use the fin theory [11]. The coupling of fluid solids with an accurate numerical transient heat transfer model has yet not been performed. Several authors [5–8] studied phase change in steady state and demonstrated that the opening force due to the fluid pressure in the interface, when plotted versus the film thickness, can exhibit

F. Migout et al. / Tribology International 92 (2015) 84–95

Nomenclature _ m ε

T m a b B C Cf E Et F h hi i k M m N n p P qi r ℜ r S Se t T u Vri Vzi

(kg s  1) Mass flow Strain tensor Dimensionless temperature rise (Pa s) Dynamic viscosity (Pa m6 mol  2) Van der Waals constant (m3 mol  1) Van der Waals constant Balance ratio (J m  3 K  1) Specific heat of solids (N m) Friction torque (Pa) Elasticity modulus (W K  1) Thermal efficiency of solids (N) Force (m) Film thickness (m) Height of surface i (J kg  1) Enthalpy (W m  1 K  1) Thermal conductivity of solids (kg mol  1) Molar mass (kg) Stator mass (rad K  1) Thermal rotation rates of solids Refraction index (Pa) Pressure (W) Power (W m  2) Heat flux from solid i (m) Radial coordinate (J mol  1 K  1) Perfect gas constant (m) Radius (m2) Sealing interface area Sealing number (s) Time (K) Temperature (m) Height variation due to deformation (m s  1) Radial velocity of surface i (m s  1) Axial velocity of surface i

an unstable zone. This means that this force can increase with the film thickness, leading to an opening of the seal. This unstable zone can be avoided by increasing the closing force or the balance ratio of the seal, as experimentally shown by Rhodes et al., [12]. According to Lebeck and Chiou [13], the seal faces profile also controls the appearance of puffing. In dynamic approaches, the authors considered the mass of the floating ring [14,15] and the squeeze of the film in more advanced simulations [11,16]. This type of model allows the simulation of puffing (oscillation of the film thickness) as well as the opening of the seal. In the case of an opening or high operating speed, the fluid flow can be turbulent and fluid inertia effects can become significant. Moreover, because of the low sound speed of the liquid–vapor mixture, the flow can be choked. Several authors [17–19] have studied this problem and highlight the effect of centrifugal inertia and choked flow on the fluid force and the leakage of the seal. Vaporization can occur not only in pure liquids but also in liquid mixtures. Harrison and Watkins [20] reported severe failures on seals operating with crude oil when the amount of water content increases. The problems were ascribed to vaporization of the lubricating film. Etsion and Pascovici [21] made an attempt to study this problem with a simplified approach. They demonstrated that phase change takes place more easily in the mixtures than with pure liquids constituting the mixture. The aim of the present paper is to study phase change in waterlubricated seals with an advanced numerical model. As done by Yasuna and Hughes [22], the fluid film is described by a continuous

85

Vθi (m s  1) Circumferential velocity of surface i z (m) Axial coordinate z2 (m) Axial displacement of the stator Δh (m) Film thickness difference Δr (m) Radial width of a control volume ΔR (m) Seal width ΔT ¼Tm–Tf (K) Averaged temperature rise α (K  1) Thermoviscous coefficient λ Vapor mass fraction λ (K  1) Thermal expansion coefficient ν Poisson ratio ρ (kg m  3) Density υ (m) Light wave length ω (rad s  1) Rotor angular velocity index v l W, w E, e P o c a f f tot m o i 0 1 2

Vapor Liquid West node, west boundary East node, east boundary Current node Opening Closing Atmospheric Sealed fluid Friction Total Mean Outer Inner Initial Rotor Stator

boiling model but is coupled to an accurate unsteady numerical heat transfer model. Moreover, the mass of the ring and the squeeze effect are considered. The simulation results are compared to measurements obtained on a dedicated test rig. The objective of this work is to obtain a stability map of a seal when the sealed fluid temperature and the balance ratio of the seal are varied. This type of simulation has not been done before.

2. Theoretical model 2.1. Geometrical configuration The problem is assumed to be axisymmetrical. The stator height, h2, the rotor height, h1, and the film thickness h are thus only a function of time and local radius (Fig. 1a): 8 > < h1 ðr; t Þ ¼ h10 ðr Þ þ u1 ðr; t Þ h2 ðr; t Þ ¼ h20 ðr Þ þ u2 ðr; t Þ þ z2 ðt Þ > : hðr; t Þ ¼ h ðr; t Þ  h ðr; t Þ 2

ð1Þ

1

In these expressions, hi0 is the initial face profile, u is the thermal deformation and z2 the axial position of the stator. The surfaces are assumed to be smooth and fully separated by the fluid.

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Fig. 1. (a) Fluid film model (b) Control volume model and (c) Dynamic model.

The velocity components of the seal surfaces are 8 V ðr; t Þ ¼ 0 > < r1 V θ1 ðr; t Þ ¼ r ωðt Þ > : V ðr; t Þ ¼ ∂h1 ðr;t Þ z1

ð2Þ

2.3. Governing equations

∂t

8 V ðr; t Þ ¼ 0 > < r2 V θ2 ðr; t Þ ¼ 0 > : V ðr; t Þ ¼ ∂h2 ðr;t Þ z2

ð3Þ

∂t

2.2. Fluid properties The fluid is assumed to be a homogeneous mixture of liquid and vapor. It is thus assumed that:  The surface tension of bubbles or drops is neglected.  The pressure of the liquid and vapor phases is the same.  The liquid and vapor phases move at the same velocity.

ρ

ρv

ρl

ð4Þ

where λ is the vapor mass fraction which can vary continuously from 0 (full liquid) to 1 (full vapor). The enthalpy i of the mixture is given by [24]:   i ¼ λ:iv þ 1  λ il ð5Þ Several expressions [24] can be found in the literature for the viscosity of the mixture. Saadat and Flint [23] compared predictions and measurements of pressure in a two-phase flow thrust bearing and found that the best formula is: 1

μ

¼ λ:

1

μv

  1 þ 1λ :

μl

The governing equations for the fluid are written in a control volume (Fig. 1b). The fluid characteristics are assumed to be uniform in each control volume. It means that the pressure, density, vapor mass fraction and temperature are constant across the film thickness. Thus, the fluid temperature and the seal faces temperature are equal. The control volume is a ring of mean radius r, width Δr and height h. The continuity equation on this control volume is: ∂  _ w m _ e ¼0 ρh 2π r Δr þ m ∂t

ð6Þ

The enthalpy and viscosity of the liquid and vapor are described by the laws given in [25,26] as well as the density of the liquid. The density of the vapor is given by the van der Walls law:    ρ2 M p þ a v2  b ¼ ℜT ð7Þ ρv M

ð8Þ

If the inertia of the fluid is neglected, the mass flow is an explicit function of the pressure gradient: _ ¼ρ m

These are strong assumptions, but they greatly simplify this complex problem. The results of Saadat and Flint [23] show that it is a reasonable choice. Assuming a homogeneous fluid mixture of liquid and vapor, the density ρ of the mixture can be expressed in this way [24]:  1 1 1  ¼ λ: þ 1  λ :

where a and b are the van der Walls coefficients of water, M the molar mass of water and R the perfect gas constant. This is a third order polynomial in ρ which is solved by Cardan's method.

π r ∂p h3 μ ∂r 6

ð9Þ

The enthalpy of the fluid is obtained by solving the energy equation:   ∂p ∂ _ _ ∂t ρih :2π r Δr  mw iw þ me ie  2π r Δrh ∂t ¼

μr2 ω2 h

  :2π r Δr  q1 þ q2 :2π r Δr

ð10Þ

q1 and q2 are heat fluxes between the film and solids. Since fluid inertia is assumed to be neglected, the kinetic energy contribution has been removed from the energy Eq. (10). In the solids, the local governing equations are used. The heat transfer equation is:  2  ∂T ∂ T 1 ∂T ∂2 T þ 2 ¼0 ð11Þ ρC k 2 þ ∂t r ∂r ∂z ∂r where k and C are the thermal conductivity coefficient and the specific heat of the solid. The solids displacements u are computed from the thermoelasticity equations:   E E ε λE 1 tr ε þ div ð12Þ  T ¼0 1  2ν ð1  2νÞð1 þ νÞ ð1 þ νÞ where the strain tensor is defined in this way:  2

ε ¼ 1 ∇u þ∇t u



ð13Þ

Here, Ε, η and λ are respectively the Young's modulus, Poisson's ratio and the thermal expansion coefficient of the solid.

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The axial position of the floating ring (Fig. 1c) is governed by Newton's law: 2

F o F c ¼ m

d z2 dt 2

ð14Þ

In this equation, Fc and Fo are respectively the closing and opening forces applied to the seal ring and m the mass of the stator. The opening force is the integral of the fluid pressure on the sealing area S which tends to separate the seal faces: Z F o ¼ pdS ð15Þ

Fig. 2. Discretization of the fluid film.

S

The closing force can be expressed in this way: h i F c ¼ S pf B þ pa ð1 BÞ þ F s

ð16Þ

where pf and pa are the pressure of the sealed fluid and the atmosphere respectively and B the balance ratio of the seal. Fs is a secondary force due to springs or the secondary seal. In this study this force is set to zero. 2.4. Numerical solution For all the transient equations, an implicit scheme is used. This means that all the spatial derivatives are evaluated at time t, whereas the temporal derivative is computed in this way:   ∂F ∂R F ðt Þ  F t  Δt ∂R þ  ð17Þ þ ðt Þ ∂t ∂x ∂x Δt The fluid film is divided into a number of adjacent control volumes of width Δr. A half-control volume is used at the inner and outer radii as shown in Fig. 2. The mass flow can be expressed from the pressure of the neighbor nodes:

π r w pP  pW h w 3 μw Δr 6 3 π r e pE  pP he _ e ¼ ρe m μe Δr 6

_ w ¼ ρw m

ð18Þ

In these equations, the radius, viscosity, density and film thickness are calculated at the boundary between the adjacent cells. This is just the average of the values at the neighbor nodes. By introducing these equations in the continuity equation of each control volume, a tridiagonal system is obtained. The pressure at the inner and outer radii are replaced by their values (pf or pa). An iterative process is necessary to obtain the local pressure since the density of the fluid is dependent on the pressure. To solve the energy equation, it is necessary to know the mass flow at the boundaries, Ri and Ro, of the domain. Knowing the pressure and density in each control volume and the mass flow between the control volumes, the mass flow at the boundaries can be expressed: _ i ¼m _ e m

∂  ρ h π r Δr ∂t

_ wþ _ o ¼ m m

∂  ρh π r Δr ∂t

ð19Þ ð20Þ

An upwind scheme is used for the transported enthalpy in the energy equation: _ w ÞiW þ ½1  signðm _ w ÞiP iw ¼ signðm _ e ÞiP þ ½1  signðm _ e ÞiE ie ¼ signðm

ð21Þ

This formulation takes account of the flow direction. For the half-control volume at the inlet, the entering enthalpy is the enthalpy of the sealed fluid. Thus the calculated enthalpy at the first node is different from the sealed fluid enthalpy.

Fig. 3. Finite element model of the solids and boundary conditions.

A previously developed finite element module is used to calculate the temperature and displacement of the solids. In the present work, a convection condition is applied on the wetted surfaces, whereas surfaces in contact with the atmosphere are assumed to be insulated (Fig. 3). The convection coefficient is based on Becker's correlation [27]. For the heat transfer, the two solids are included in a single model to have an automatic partition of the heat flux at the interface. Moreover, it is also possible to impose the temperature of nodes located at the interface. In this case, the heat flux is computed. The resulting temperature is used to determine the displacement of each solid. To avoid a rigid solid displacement, an arbitrary node has an imposed axial displacement equal to zero. Note that only the thermal deformations are considered in this paper. Mechanical deformations were assumed to be negligible because of the low pressure values used in this work. The coupling of the energy equation with the heat transfer model is done in this way. In a full liquid zone, where the pressure and temperature are known from a previous iteration, the enthalpy is calculated. Thus it is possible to determine the heat flux between the film and the solids: 

   q1 þ q2 ¼  ∂t∂ ρih : þ m_ w2iwπ rΔmr_ e ie þ 2π r Δrh∂p ∂t þ

μ r 2 ω2 h

ð22Þ

From the heat flux, the temperature at the interface is obtained by the heat transfer model. It is thus possible to update the enthalpy, etc. If the temperature at a given node is higher than the saturation temperature, the fluid is thus a mixture of liquid and vapor. Thus at this node the saturation temperature is imposed in the heat transfer model and the heat flux is computed. Let us assume that the fluid flow is outward. Thus the enthalpy at the last liquid node is known. Thus it is possible to compute the enthalpy

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of the first mixture node using the computed flux:     1 μ r 2 ω2 ∂ :2π r Δr  q1 þ q2 :2π r Δr  ρih :2π r Δr ie ¼ _e m ∂t h  ∂p _ w iw þ2π r Δrh þ m ∂t

ð23Þ

Using Eq. (5), it is possible to compute the vapor mass fraction λ since the saturated liquid and vapor enthalpy are known. This is done for each node in the mixture zone. If λ is higher than 1, then the fluid is assumed to be fully vapor. The same procedure as for a fully liquid zone is used. To obtain the distance between the seal faces, it is necessary to solve the dynamic Eq. (14). The acceleration term is approximated in this way:     2 z2 ðt Þ  2z2 t  Δt þ z2 t  2Δt d z2 ð t Þ  ð24Þ dt 2 Δt 2 Because of the strong coupling between the fluid force Fo and the opening force, the Newton method is used to find the new value of the stator position z2. The general solution procedure is presented in Fig. 4. It is a quite complicated process with several loops. The first one is to obtain the pressure and density of the fluid using the continuity equation. The second loop is to obtain the temperature of the fluid and solids and the state of the fluid (liquid, mixture vapor). This is the most complicated part with mixed boundary conditions for the solids depending on the fluid state. Next, the faces deformations are computed and the axial dynamic behavior is considered. Then the film thickness is updated. This process is repeated for each time step until the end time is reached. The convergence on variables is done in this way: ‖F new  F old ‖ rε ‖F old ‖

ð25Þ

The convergence constraint is lower than or equal to 10  6 depending on the variable. Moreover, a relaxation process is used when updating the variables.

3. Comparison with experiments Before using the model, it is important to validate it by comparison with experiments. A special test rig has been used for the purpose of validation (Fig. 5). It is an inner pressurized seal composed of a rotating carbon ring and a transparent sapphire disc. This disc is pressed on the carbon ring with a controllable closing force by means of a piston and pressurized air (Fig. 5b). The air piston and thus the sapphire disc are able to tilt in order to be perfectly aligned with the rotating ring. An infrared camera was used to observe the seal interface (Fig. 5a) and to obtain a thermogram of the interface. After a specific treatment, it is possible to obtain the temperature distribution of the top surface of the carbon ring [28]. For that, it is necessary to know the emissivity of the carbon face and the transmissivity of the sapphire. A CCD camera was also used to observe the interface lit by a monochromatic light source. The objective of this observation was to obtain the film thickness by interferometry. In the case of two-phase flow, the variation of the refraction index when water turns to vapor was expected to modify the interference fringes distribution. However, this measurement did not give satisfying results because of the difficulty in observing the fringes during rotation. To ensure a full fluid film between the surfaces, the carbon ring is initially tapered using a conical expander (Fig. 5b). The taper angle is adjusted by modifying the tightening torque of the screws which fasten the conical expander on the shaft. The initial taper of the sealing interface can be measured by interferometry (Fig. 6a).

Fig. 4. Solution procedure.

Fringes on the image correspond to lines of constant film thickness. The thickness difference Δh between two fringes is given by:

Δh ¼

υ

n h io sin ðπ =4Þ 2n cos arcsin n

ð26Þ

where υ ¼ 600 nm is the light wavelength, n the refraction index of the media and π/4 is the angle of the incident light. If the media in the sealing interface is air or vapor, n ¼1 and Δh¼0.42 mm. When it is liquid water n is 1.33 and Δh¼ 0.266 mm. When the water circulating in the system heats the solids, the taper angle is increased because of the difference in thermal expansion of the materials. Moreover, the maximum height of the carbon ring is not at the outer radius but 1 mm inward from the boundary (Fig. 6a). For the simulations, the surface has been modeled by a parabola having its maximum 1 mm from the outer radius and leading to a 4.5 mm initial height difference between the inner and outer radii. Note that a slight waviness is visible on Fig. 6 (non axisymmetrical lines close to the outer radius). But the height variations are small

F. Migout et al. / Tribology International 92 (2015) 84–95

89

Table 2 Characteristics of the seal rings.

Fig. 5. Experimental device (a) general view–(b) scheme.

Material

Carbon ring

Sapphire disc

Density ρ (kg m  3) Thermal conductivity k (W m  1 K  1) Specific heat C (J Kg  1 K  1) Young's modulus E (GPa) Poisson's ratio ν Thermal expansion coefficient λ (10  6 K  1) Inner radius (m) Outer radius (m) Height (m)

1800 10 470 20 0.2 4 0.0345 0.0415 0.018

3980 24.15 761 444.5 0.212 5.83 0.017 0.043 0.01

Fig. 7. Comparison of theroretical and experimental temperature profiles for different values of the closing force (balance ratio B).

Fig. 6. Carbon ring profile (a) Interferometry–(b) Model.

Table 1 Operating conditions of the tested seal. Parameter

Value

Fluid at inner radius Fluid temperature Fluid pressure pf Atmosphere pressure pa Rotating speed ω Balance ratio

Water 117 1C 0.342 MPa 0.1 MPa 1500 rpm 0.75–0.9

compared to the taper induced height variations. The axisymmetric assumption used in the model is validated in this case. The tests were performed in steady-state conditions at a constant feeding pressure and temperature and constant speed. The operating conditions during the experiments are presented in

Fig. 8. Images of the interface at different balance ratio values.

Table 1. The seal rings properties are described in Table 2. Each experiment was repeated three times. The values used for the comparison are the average of the three measurements. The variations of the parameters during the three tests are

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F. Migout et al. / Tribology International 92 (2015) 84–95

materialized by an error bar, which is different from the uncertainty. Temperature profiles were recorded at different values of the closing force (i.e., different values of the balance ratio) and compared to the simulation results in Fig. 7. Note that each measured temperature profile is the average of a 5 s movie. Thus possible circumferential temperature variations are averaged. Let us first comment on the theoretical results. At low load (B¼0.75), the fluid is partially vaporized, leading to an outlet temperature equal to the saturation temperature (about 98 1C), which tends to cool the contact compared to the inlet temperature. If the balance ratio is increased from 0.75 to 0.84, the temperature at the outlet remains constant, whereas the temperature in the contact decreases. This is because the mass flow decreases, thus reducing the amount of hot fluid entering the interface. This tendency is theoretically and experimentally obtained. However, the outlet measured temperature is higher than the atmospheric saturation temperature. According to the simulations, the width of the area where sharp temperature decreases to the atmospheric saturation temperature take place is about 0.15 mm. The size of the pixel being higher than this value, it has not been possible to capture such temperature variation at the outlet. If the load is increased again, the viscous friction is raised, allowing the complete vaporization of the fluid at the outlet. The temperature thus increases above 100 1C at the outlet of the fluid film. This tendency is also experimentally observed. Fig. 8 presents images obtained with the CCD camera at different balance ratios. The change in gray level at the outlet confirms a change in the nature of the fluid at the outer radius. However, it is difficult to obtain more quantitative information from these pictures. The average interface temperature as well as the outlet temperature are presented as a function of the balance ratio in Fig. 9. To be in line with experiments, the outlet temperature is the temperature at radius r¼ 41.2 mm, which is 0.3 mm from the exact outer radius. The average and outlet temperature values obtained by measurements and simulation first decrease when the balance ratio is increased, reaching a minimum, and then increase with B. Once again, similar tendencies are observed, but the magnitude of the temperature variations in experiments is lower than in simulations. A temperature shift of about 3 K is observed between the measurements and simulation. This could be due to uncertainties on the optical material properties, temperature measurement and operating conditions.

The thermal power exchanged at the interface of the seal is the sum of power dissipated by viscous friction and the difference in mass flow of enthalpy: _ ðii  io Þ Pf ¼ C f ω þ m

ð27Þ

where Cf is the viscous friction torque. On the experimental test rig the thermal power is measured by the difference in temperature between the fluid entering and exiting the test cell and the fluid mass flow circulating in the cell mc. This measured power includes the interface thermal power Pf as well as the thermal power Pe exchanged with the environnement: _ c C p ðT out T in Þ ¼ P tot ¼ P f þ P e m

ð28Þ

where Cp is the heat capacity of the liquid water. The problem is that Pe is unknown and difficult to determine. However, since the rotation speed, fluid temperature and room temperature are constant during the tests, it is assumed that Pe is constant. It is thus possible to eliminate this term by comparing the power variation:   ð29Þ ΔP f ¼ P tot ðBÞ  minðP tot Þ ¼ P f ðBÞ  min P f The measured and calculated power variations are compared in Fig. 10. A good agreement is obtained. The dissipated power first decreases when the balance ratio is raised, leading to a temperature reduction in the contact. The power variation reaches a minimum and increases with B as the temperature in the interface. The differences between simulated and measured temperature values can have several origins. First the model is not a perfect description of the real situation. Some residual waviness and

Fig. 10. Power variation in the contact as a function of the balance ratio.

Table 3 Characteristics of the seal components. Material 3

Fig. 9. Average face temperature and outlet temperature (r¼ 41.2 mm) as a function of the balance ratio.

Density ρ (kg m ) Thermal conductivity k (W m  1 K  1) Specific heat C (J Kg  1 K  1) Young's modulus E (GPa) Poisson's ratio ν Thermal expansion coefficient λ (10  6 K  1) Inner radius (m) Outer radius (m) Height (m)

Carbon stator

SiC rotor

1800 10 470 20 0.2 4 0.029 0.033 0.008

3100 150 670 400 0.17 4.3. 0.028 0.037 0.007

F. Migout et al. / Tribology International 92 (2015) 84–95

misalignment could breakdown the assumption on axisymmetry. The displacement of the solids is not as simple as described by the model which neglects mechanical deformation. Some non-linear effects can come from the assembly technic used for the test rig elements (conical expander, screws, etc). The heat transfer coefficient on the wetted surface has been approximated by an empirical law [27]. It is known that this coefficient is actually not uniformly distributed along the surfaces [29]. On the other hand, temperature measurements need a number of optical parameters which are difficult to determine [28]. Moreover, it is assumed that the transparent disk is at a uniform temperature to solve the radiometric problem [28]. This assumption has a little effect when the disk emissivity is very low for example when it is made of calcium fluoride as in [28]. In the case of sapphire, it is a stronger assumption because of its higher emissivity. It could thus affect temperature measurements. However, even if the results are not perfectly correlated, the model is able to capture the unusual behavior experimentally observed. It confirms the validity of the present approach. Moreover, these results show the necessity to use a continuous boiling model. Indeed, a discrete boiling model cannot predict an outlet temperature equal to the saturation temperature.

91

Table 4 Operating conditions. Parameter

Value

Outer pressure Inner pressure (atmosphere) Fluid Fluid temperature Rotating speed (rad/s) Balance ratio B

1.1 MPa 0.1 MPa Water 90–185 1C 500 0.7–0.9

4. Parametric study In this section, the influence of the water inlet temperature will be analyzed. The design parameters of the studied seal are presented in Table 3 and its operating conditions are given in Table 4. For this study, the rotation speed as well as the fluid pressure are kept constant at 500 rad/s and 1 MPa (relative to atmosphere) respectively. Different values of the balance ratio of the seal are used. During simulations, the sealed fluid temperature is increased stepwise from 90 to 185 1C. A step of 5 1C is applied every 25 s. The mesh and boundary conditions are presented in Fig. 11. The walls wetted by water are submitted to a convection condition based on Becker's correlation [27]. 75 nodes are used in the radial direction to capture the sharp pressure and temperature variations observed during vaporization.

Fig. 11. Configuration, mesh and boundary conditions used in the parametric study.

4.1. Results for B ¼0.8 In this section, the results obtained when the balance ratio B is equal to 0.8 are detailed. Fig. 12 presents the radial distribution of fluid in the seal interface as a function of time when the sealed fluid temperature is varied. In the dimensionless radius scale, 0 corresponds to the inlet and 1 to the outlet. At low water temperature, that is to say 90 1C, the viscous dissipation is not high enough to turn the liquid water into vapor. The fluid film is fully liquid. When the water temperature is increased, the fluid first turns to mixture at the outlet. If the temperature increases again, the fluid is entirely transformed into vapor at the outlet. When the water temperature reaches 170 1C, some temporal oscillations are observed. Their magnitude increases if the water temperature is set to 175 1C. It has not been possible to reach higher temperature values because of convergence problems. As experimentally observed, instabilities or puffing corresponds to an oscillation of the liquid limit. Fig. 13 presents the evolution of the minimum film thickness, friction torque and mass flow. A sharp increase in film thickness and in mass flow magnitude is obtained when two-phase flow occurs in the sealing interface. Indeed, the change in fluid density due to phase change enhances the hydrostatic load generation as explained by Orcutt [2]. It is obviously associated with a decrease in torque. When the sealed fluid temperature continues to increase, the film thickness and the mass flow increase whereas the torque value decreases. This torque evolution has been experimentally observed by Lebeck and Chiou [13]. More

Fig. 12. Evolution of the liquid mixture vapor radial distribution with time and evolution of the sealed fluid temperature.

significant variations are obtained just before the appearance of instabilities. It can be seen that there is a large interval of twophase safe operation before oscillations take place. Fig. 14a) presents radial pressure profiles for different sealed fluid temperatures. When the film is fully liquid (T¼90 1C), the pressure profile decreases smoothly from the inlet to the outlet. When mixture or vapor occurs at the outlet, a sharp pressure gradient is observed due to the kinematic viscosity rapid change. It is thus possible to generate a load even with a parallel surface, as discussed by Orcutt [2]. Temperature variations in the sealing interface are presented in Fig. 14b) for different feeding fluid temperature values. When the fluid is completely liquid (T¼90 1C), a usual temperature rise is observed with a maximum value close to the outlet. This is due to higher friction resulting from thinner film at the inner radius and to the increased

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Fig. 14. Radial distributions for different feeding temperature values: (a) fluid pressure–(b) temperature variations.

cooled by convection. In the last case, the lowest temperature is observed in the contact. In this case, the cooling due to phase change is more efficient than convection. In the three images, the maximum temperature is obviously located in the contact because of viscous friction.

Fig. 13. Temporal evolution of the (a) minimum film thickness, (b) friction torque and (c) mass flow.

distance to the surfaces, where the seal is cooled by convection. When the fluid temperature is increased, the temperature first remains similar but with a lower magnitude. This is due to the lower viscosity of water with higher temperature and cooling provided by phase change. When the temperature is raised to 165 1C, the cooling due to phase change is high enough to decrease the contact temperature to below the sealed fluid temperature. When the fluid is fully vaporized (close to the inner radius), its temperature can rise again. Some examples of temperature variations in the solids are presented in Fig. 15. For T¼ 90 1C and 125 1C, the lowest temperatures are observed along the wall wetted by the sealed fluid, which ensures the rings are

4.2. Instabilities for B ¼0.8 Fig. 16 shows a more detailed view of the parameters evolution when oscillations are observed (i.e., T¼ 170 1C). These results have been recomputed with a smaller time step (0.01 s) to capture the frequency of the oscillations. The oscillations period is about 0.17 s at the end of the simulation. The minimum film thickness variations are 25% of its mean value, leading to more significant mass flow oscillations. The magnitude of the temperature variations is, however, small (about 1 K) but involves significant heat flux variations because of the speed of oscillations. Fig. 17 shows the evolution of the pressure profile during one oscillation period. The maximum pressure variation at one point is 0.08 MPa, which is significant compared to the outlet atmospheric pressure.

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Fig. 16. Temporal evolution of the (a) temperature and friction torque and (b) film thickness and mass flow in the case of instabilities.

Fig. 15. Temperature variations in the solids for different feeding temperature values: (a) T ¼ 90 1C, (b) T ¼ 125 1C, (c) T ¼ 165 1C.

4.3. Parametric study The same computation has been performed for B varying from 0.7 to 0.9. Fig. 18 summarizes the results obtained. For each temperature and balance ratio combination, the behavior of the seal is given. As indicated in the previous section, the film can be fully liquid, liquid–vapor mixture at the outlet, vapor at the outlet or unstable. Note that the saturation temperature at the outlet (98 1C for 0.1 MPa) and at the inlet (186 1C for 1.1 MPa) is indicated in the figure. For the lowest temperature value, the film is fully liquid whatever the balance ratio. For low balance ratio values, a smooth transition from liquid to mixture and then vapor is obtained when the water temperature rises. This is not observed for high balance ratio values where the film is thinner, thus enhancing the vaporization of water. The appearance of oscillations shifts to higher

Fig. 17. Radial pressure profiles at different time steps during instabilities.

temperature values when the balance ratio is increased. Note that for B¼0.9, no oscillatory behavior was observed. Rhodes et al. [12] found that unstable behavior can be avoided using a high balance ratio, which is in agreement with our work. In the case of liquid films, it is possible to express the balance ratio as a function of the mean film thickness hm and of the seal

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Fig. 19. Dimensionless load as a function of the dimensionless film thickness for stable cases.

Fig. 18. Map of the seal response.

coning angle B¼

βΔR 4hm

β [30]:

þ 0:5

ð30Þ

where ΔR is the seal width. Eq. (30) is presented in Fig. 19. This curve corresponds to a stable behavior for which the film thickness increases when the load decreases. All the steady-state simulation results have also been reported in Fig. 20. Note that in the present work the coning angle is due to the thermal deformation of the seal faces. At low water temperature (T¼ 90 1C), the numerical results are in close agreement with Eq. (30) because of the liquid film. When the film is composed of two phases, the equilibrium film thickness is higher than for a fully liquid film. When the fluid temperature is 95 1C, there is a change in slope corresponding to the transition from mixture to full vapor outlet. At higher temperature this change disappears and a lower static stiffness is obtained (larger film variations with load). Beyond a temperature threshold (135 1C), the film thickness curve slope exhibits a sign change. Thus a given film thickness can be reached for two different load values (or balance ratio). However, this situation does not necessarily correspond to an unstable situation, as discussed in previous papers [5–8] where only steady-state simulations were performed. Brunetière and Apostolescu [30] showed that the dimensionless temperature rise in a liquid lubricated mechanical seal is a function of a dimensionless thermal loading parameter, the sealing number Se: T¼

Se

ð31Þ

TexpT

The sealing number is [30]:

ω2 ðRo þ Ri Þ2 α2 ðB 0:5Þ

Se ¼ μ

Et N

S

ð32Þ

where Et and N are the seal ring thermal efficiency and thermal rotation rates. α is the thermoviscous coefficient based on the Reynolds viscosity law. The dimensionless temperature rise is: T ¼ αΔT

ð33Þ

Eq. (31) is presented in Fig. 20, together with the numerical results. For low water temperature, the film is liquid and a reasonable agreement is obtained between the analytical solution and simulations. When phase change appears in the fluid film, the temperature deviates from that predicted by Eq. (31). Indeed, the appearance of

Fig. 20. Dimensionless temperature rise as a function of the sealing number Se for stable cases.

mixture or vapor tends to increase the film thickness, thus reducing the viscous dissipation. In addition, a significant amount of energy is used to vaporize water, which limits the temperature rises. When the water temperature is increased, the deviation between the numerical results and the analytical curves rises. For high feeding temperature values, negative temperature variations can be obtained because of vaporization, which is obviously not possible with viscous liquid film. The oscillations occur in regions where the dimensionless temperature curves tend to be vertical. This would suggest that instabilities take place when a small amount of Se variation leads to significant temperature variations.

5. Conclusion In this paper, the effect of a temperature increase on a mechanical seal working with water has been analyzed using a

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transient numerical model. This axisymmetrical model considers phase change using a homogeneous fluid description. It is coupled to a transient finite element solid model including heat transfer and deformation. This model was first successfully compared with experiments. It was found that the contact temperature can first decrease when the applied load is increased. The model is able to capture this particular behavior which is unusual and mainly due to vaporization. A parametric study was carried out for a range of balance ratios. The fluid temperature was gradually raised for each balance ratio value. The results of the parametric study show that there exists a large interval of safe operation with a two-phase flow in the fluid film. At high water temperatures, instabilities are observed. The appearance of these oscillations can be shifted to higher temperature values by using a higher balance ratio. Moreover, the appearance of phase change can significantly reduce the sealing interface temperature. References [1] Lymer A. An engineering approach to the selection and application of mechanical seals. In: Proceedings of the 4th international conference on fluid sealing, BHRA. 1969. p. 239–246. [2] Orcutt F. An Investigation of the operation and failure of mechanical face seals. J Lubr Technol 1969;91:713–25. [3] Cicone T, Pascovici M, Frêne J, Tournerie B. Visualization of vaporization in very thin films with application to mechanical face seals. 2nd World Tribol Congr 2001, Abstracts of papers, ISBN3-901657-08-8, Vienna, Austria, Sept. 03-07, p.195. [4] Wang T, Huang W, Liu X, Li Y, Wang Y. Experimental study of two-phase mechanical face seals with laser surface texturing. Tribol Int 2014;72:90–7. [5] Hughes W, Winowich N, Birchk M, Kennedy W. Phase change in liquid face seals. J Lubr Technol 1978;100:74–80. [6] Hughes W, Chao N. Phase change in liquid face seals–II–isothermal and adiabatic bounds with real fluids. J Lubr Technol 1980;102:350–9. [7] Lebeck A. A mixed friction hydrostatic face seal model with phase change. J Lubr Technol 1980;102:133–8. [8] Etsion I, Pascovici M. Phase change in a misaligned mechanical face seal. J Tribol 1996;118:109–15. [9] Wang T, Huang W, Liu Y, Liu X, Wang Y. A homogeneous phase change model for two-phase mechanical seals with three-dimensional face structures. J Tribol 2014;136:041708–11.

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[10] Basu, P & Hughes, W. Thermal instability in two phase face seals. In: Proceedings of the 11th international conference on fluid sealing. 1987. p. 423–441. [11] Blasbalg D, Salant R. Numerical study of two-phase mechanical seal stability. Tribol Trans 1995;38:791–800. [12] Rhodes D, Hill R, Wensel R. Reactor coolant shaft seal stability during station blackout. EG&G Idaho 1987, NUREG/CR-4821, EGG-2492, AECL-9342, 57 pages. [13] Lebeck, A & Chiou, B. Two-phase mechanical face seal operation: experimental and theoretical observations. In: Proceedings of the 11th turbomachinery symposium. 1982. p. 181–188. [14] Beeler R, Hughes W. Dynamics of two-phase face seals. ASLE Trans 1984;27: 146–153. [15] Salant R, Blasbalg D. Dynamic behavior of two-phase mechanical seals. Tribol Trans 1991;34:122–30. [16] Yasuna J, Hughes W. Squeeze film dynamics of two-phase seals. J Tribol 1992;114:236–47. [17] Hughes, W & Beeler, R. Turbulent two-phase flow in ring and face seals. In: Proceedings of the 9th international conference on fluid sealing, BHRA. 1981. p. 185–202. [18] Basu P, Hughes W, Beeler R. Centrifugal inertia effects in two-phase face seals. ASLE Trans 1987;30:177–86. [19] Beatty P, Hughes W. Turbulent two-phase flow in face shaft seals. J Tribol 1987;109:91–9. [20] Harrison, M & Watkins, R. Evaluation of forties mail oil line pump seals. In: Proceedings of the 10th international conference on fluid sealing. 1984. p. 1–16. [21] Etsion I, Pascovici M. Vaporization in face seals operating with liquid mixtures. Tribol Trans 1997;40:694–700. [22] Yasuna J, Hughes W. A continuous boiling model for face seals. J Tribol 1990;112:266–74. [23] Saadat N, Flint W. Expressions for the viscosity of liquid/vapour mixtures: predicted and measured pressure distributions in a hydrostatic bearing. IMechE, J, J Eng Tribol 1996;210:75–9. [24] Wallis G. One-Dimensional Two-Phase Flow. New York: Mc Graw-Hill; 1969. [25] Pezzani P. Propriétés Thermodynamiques de l'Eau. Les Techniques de l'Ingénieur 1992;W120:1–11. [26] Perrot P. Propriétés Thermodynamiques de l'Eau. Les Techniques de l'Ingénieur 2006;K585:1–20. [27] Becker K. Measurement of convective heat transfer from a horizontal cylinder rotating in a tank of water. Int J Heat Mass Transf 1963;6:1053–62. [28] Reungoat, D & Tournerie, B. Temperature measurement by infrared thermography in a lubricated contact: radiometric analysis. In: Proceedings of the eurotherm seminar 42: quantitative infrared thermography. Editions Européennes Thermique et Industrie. 1994. [29] Brunetière N, Modolo B. Heat transfer in a mechanical face seal. Int J Therm Sci 2009;48:781–94. [30] Brunetière N, Apostolescu A. A simple approach to the thermoelastohydrodynamic behavior of mechanical face seals. Tribol Trans 2009;52:243–55.