Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected]) 303 6.3 Dynamic Seals 6.3.1 Classification of Seals Seals are broadly classified as liquid and gas seals according to the working fluid used in the system. The most common working fluids are water, air, nitrogen, Triflurobromomethane (CBrF 3 ), liquid oxygen, liquid hydrogen etc. In addition, they can be categorized as static and dynamic seals. Static seals are used where the two surfaces do not move relative to one another. Gasket-type seals are static seals (Fig. 1). Dynamic seals are used where sealing takes place between two surfaces having relative movement viz. rotary, reciprocating, and oscillating. The main focus of the present paper is on rotary seals. It has wide variety of applications in high-speed, high-pressure and cryogenic temperature conditions of aviation and space industries such as in turbine stages, turbo-pumps, compressors, gear boxes, etc. Rotary seals can be subdivided into two main categories as clearance seals and contact seals. Clearance seals are circumferential non-contacting seals (Fig. 2a). In contact seals, the contact is formed by positive pressure, while in the case of clearance seals; they operate with positive clearance (no rubbing contact). The most commonly used material for dynamic seals (especially for rotary seals) are stainless steel, bronze, aluminium, nickel-based alloys, Polytetrafluroethane etc. Fig. 2(a) shows a typical rotary seal with the clearance exaggerated. Rotary seals based on geometry can be classified as (i) Ungrooved plain seals (or Smooth annular seals): (a) Straight (Fig. 2b), (b) Tapered (Fig. 2c) and (c) Stepped (Fig. 2d). In geometry they are similar to journal bearings but the clearance/radius ratio is as low as two times and as high as ten times (or more) large to avoid rotor/stator contact. (ii) Grooved/Roughened surface seals: (a) Porous surface seals (b) Labyrinth seals (Figs. 3(a-d)), (c) Helically grooved / Screw seals (d) Circular hole or triangular patterns seals and (e) Honeycomb patterns seals (Fig. 4). These seals are used in centrifugal and axial compressors and pumps and in turbines. Different internal surface patterns of seals are shown in Fig. 5. (iii) Contact seals: (a) Brush seals (Fig. 6a) (b) Face seals and (c) Lip seals (Fig. 6b)) Because of rubbing, these seals are used commonly in low speed pumps, or where the working fluid can act as a coolant. Contact seals provide much lower leakage rates than either of non-contact seals (Adams, 1987), however, the latter can operate at very high speed and pressure conditions. (iv) Floating-ring oil seals: The ring whirls or vibrates with the rotor in the lubricating oil, but does not spin. They are used in high-pressure multi-stage centrifugal compressors.
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Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
303
6.3 Dynamic Seals
6.3.1 Classification of Seals
Seals are broadly classified as liquid and gas seals according to the working fluid used in the system.
The most common working fluids are water, air, nitrogen, Triflurobromomethane (CBrF 3 ), liquid
oxygen, liquid hydrogen etc. In addition, they can be categorized as static and dynamic seals. Static
seals are used where the two surfaces do not move relative to one another. Gasket-type seals are static
seals (Fig. 1). Dynamic seals are used where sealing takes place between two surfaces having relative
movement viz. rotary, reciprocating, and oscillating. The main focus of the present paper is on rotary
seals. It has wide variety of applications in high-speed, high-pressure and cryogenic temperature
conditions of aviation and space industries such as in turbine stages, turbo-pumps, compressors, gear
boxes, etc. Rotary seals can be subdivided into two main categories as clearance seals and contact
seals. Clearance seals are circumferential non-contacting seals (Fig. 2a). In contact seals, the contact is
formed by positive pressure, while in the case of clearance seals; they operate with positive clearance
(no rubbing contact). The most commonly used material for dynamic seals (especially for rotary seals)
are stainless steel, bronze, aluminium, nickel-based alloys, Polytetrafluroethane etc. Fig. 2(a) shows a
typical rotary seal with the clearance exaggerated. Rotary seals based on geometry can be classified as
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Numerical simulation results and discussion
In this subsection, numerical results of dynamic coefficients of seals are presented for the rotor speed
up to 50,000 rpm. The input data are taken as mentioned in Table 4.1.
Table 4.1. Input data for numerical simulation of dynamic coefficients of seals
Length of the seal 11, 22, 33 and 44 mm
Radius of the seal 22 mm
Clearance of the seal 0.2 and 0.4 mm
Dynamic viscosity of water at 32 oC 0.8×10-6 m2/s
Entrance loss coefficient 0.5
Inlet pressure 3, 6, 16, 41, 81 bar
Seal exit pressure 1 bar
Speed of the rotor 1 to 50,000 rpm
Seals dynamic coefficients are dependent on speeds, seal dimensions and pressure differences. The
stiffness (kd and kc), damping (cd and cc) and mass (md) coefficients are presented for various speeds
(ω), pressure differences (∆P) and ratios L/D.
Figures 4.3 to 4.15 show the variation of the direct and cross-coupled stiffness and damping and direct
inertia coefficients with respect to the speed up to 50000 rpm, for different values of clearances (0.2
and 0.4 mm), L/D ratios (0.25, 0.50, 0.75 and 1.00) and pressure differences (2, 5, 15, 40 and 80 bar).
The effects of these variables on seal dynamic coefficients are discussed in detail in following
sections.
Effect of rotational speeds and pressure differences
Direct stiffness coefficients increase with increase in the pressure difference (Figure 4.3). At low-
pressure differences (2 and 5 bars), the direct stiffness coefficient becomes negative as shown in
Figure 4.3. The direct stiffness coefficient reaches maximum nearly at 5000 rpm and then slowly
declines as shown in Figure 4.3. The cross-coupled stiffness linearly increases with the rotor speed
and also increases with the pressure difference (Figure 4.4). The direct damping coefficient increase
slightly to the speed, however, it increases with the pressure difference (Figure 4.5). The cross-
coupled damping increases linearly with the speed but, insensitive to the pressure difference (Figure
4.6). The direct inertia coefficient increases sharply with the rotor speed and it is almost insensitive to
the pressure difference (Figure 4.7).
Effect of L/D ratios
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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L/D ratio has significant effect on rotor dynamic coefficients of seals. The direct stiffness increases
with the increase in L/D ratio. For L/D= 1.00, after reaching a maximum value nearly to 8000 rpm it
starts declining and becomes negative with increase in the rotor speed. At L/D=0.25, the direct
stiffness coefficient always has positive values (Figure 4.8). The cross-coupled stiffness and the direct
and cross-coupled damping coefficients increase with the increase in L/D ratio as shown in Figures
4.9-4.10.
Effect of seal clearances
Doubling the clearance show a huge drop in the direct stiffness and damping coefficients, while
increasing speeds up to 50,000 rpm. The drop in the cross-coupled stiffness and damping and direct
inertia coefficients with increase in clearance is also significant (Figures 4.13-4.15).
Figure 4.3. Direct stiffness coefficients for C=0.2 mm, L/D=0.25 and ∆P=2 to 80 bar.
Figure 4.4. Cross-coupled stiffness coefficients for C=0.2 mm, L/D=0.25, ∆P=2 to 80 bar.
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Figure 4.5. Direct damping coefficients for C=0.2 mm, L/D=0.25, ∆P=2 to 80 bar.
Figure 4.6. Cross-coupled damping coefficients for C=0.2 mm, L/D=0.25, ∆P=2 to 80 bar.
Figure 4.7. Direct inertia coefficients for C=0.2 mm, L/D=0.25, ∆P=2 to 80 bar.
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Figure 4.8. Direct stiffness coefficients for C=0.2 mm, ∆P=40 bar, L/D=0.25-1.00.
Figure 4.9. Cross-coupled stiffness coefficients for C=0.2 mm, ∆P=40 bar, L/D=0.25-1.00.
Figure 4.10. Direct damping coefficients for C=0.2 mm, ∆P=40 bar, L/D=0.25-1.00
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Figure 4.11. Cross-coupled damping coefficients for C=0.2 mm, ∆P=40 bar, L/D=0.25-1.00
Figure 4.12. Direct inertia coefficients for C=0.2 mm, ∆P=40 bar, L/D=0.25-1.00
Figure 4.13. Direct and cross-coupled stiffness coefficients for ∆P=40 bar, L/D=0.25, C=0.2 & 0.4
mm.
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Figure 4.14. Direct and cross-coupled damping coefficients for ∆P=40 bar, L/D=0.25, C=0.2 & 0.4
mm.
Figure 4.15. Direct inertia coefficients for ∆P=40 bar, L/D=0.25, C=0.2 and 0.4 mm.
Basic governing equations to obtain dynamic coefficients of the smooth-annular turbulent seals (i.e.
smooth seals) are explained briefly. Dynamic coefficients are calculated from the bulk flow theory for
a seal dimension and effects of rotor speeds, seal dimensions and operation conditions on dynamic
coefficients of seals are presented and discussed in detail.
6.3.3 Fluid-Film Dynamic Force Equations
A model of a typical annual (or clearance) seal is shown in Fig. 2(a). The geometrical shape of a
clearance seal is similar to that of a hydrodynamic bearing; however, they are different in the
following aspects. To avoid contact between a rotor and a stator, the ratio of the clearance to the shaft
radius in seals is made few times (2 to 10 times) larger than that of hydrodynamic bearings. The flow
in seals is turbulent and in hydrodynamic bearings it is laminar. Therefore, unlike hydrodynamic
bearing, one cannot use the Reynolds equation for analysis of seals. When a rotor vibrates, a reaction
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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force of the fluid in the seal acts on the rotor. In case of a small vibration around the equilibrium
position, the fluid force can be linearized on the assumption that deflections and x y∆ ∆ are small.
The general governing equations of fluid-film forces on seals, which has small oscillations relative to
the rotor, is given by the following linearized force-displacement model (Childs et al., 1986)
xy xy xyx xx xx xx
y yx yx yxyy yy yy
k c mf k c mx x x
f k c mk y c y m y
∆ ∆ ∆ − = + + ∆ ∆ ∆
(2)
where fx and fy are fluid-film reaction forces on seals in x and y directions. k, c, m represent the
stiffness, damping and added-mass coefficients, subscripts: xx and, yy represent the direct and xy and
yx represent the cross-coupled terms, respectively. These coefficients vary depending on the
equilibrium position of the rotor (i.e. magnitude of the eccentricity), rotational speed, pressure drop,
temperature conditions etc. The off-diagonal coefficients in equation (2) arise due to fluid rotation
within the seal and unstable vibrations may appear due to these coefficients. Equation (2) is applicable
to liquid annular seals. But for the gas annular seals, the added-mass terms are negligible. For small
motion about a centered position (or with very small eccentricity) the cross-coupled terms are equal
and opposite (e.g., kxy = -kyx = kc and cxy = -cyx = cc) and the diagonal terms are same (e.g., kxx = kyy = kd
and cxx = cyy = cd) (Childs et al., 1986). Considering these relationships and neglecting the cross-
coupled added-mass terms, equation (2) takes the following form
0
0
x d c d c d
y dc d c d
f k k c c mx x x
f mk k y c c y y
∆ ∆ ∆ − = + + − ∆ − ∆ ∆
(3)
where subscripts: d and c represent direct and cross-coupled, respectively. The RDPs largely affect the
performance of the turbomachineries as they lead to serious synchronous and sub-synchronous
vibration problems. Whirl frequency ratio, f = kc /(cdω ) is a useful non-dimensional parameter for
comparing the stability properties of seals. For circular synchronous orbits, it provides a ratio between
the destabilizing force component due to kc and the stabilizing force component due to cd. In
experimental estimation of RDPs of seals, these coefficients (of equation (2) and (3)) are determined
with the help of measured vibrations data from a seal test rig.
The more recent textbooks on rotor dynamics include information on rotor dynamic characteristics of
rotary seals. Vance (1988), Childs (1993), Krämer (1993), Rao (2000), Adams (2001) and Tiwari et
al. (2005) provide a good introductory treatments of seal dynamics.
References:
Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])
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Dr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati, ([email protected])