To calculate the heat a dry-running seal generates, multiply the net load pressing the faces together by the friction coefficient of the face pair in dry contact and by the sliding speed at the mean face diameter. It is the same product used for a seal running in liquid, but two of its inputs change once the film is gone: the load loses some or all of its hydraulic part, and the friction coefficient becomes a dry value.
With the faces dry, all of the face heat comes from the face materials rubbing, and there is no liquid to carry it away. The face heat calculation for liquid service, with the flush flow it sizes, is covered separately.
Step 1: Find the Face Load With No Liquid Film
With no liquid film between the faces, the load pressing them together is the spring force plus whatever pressure still acts across the faces, and in a drained seal chamber it is the spring force alone. The face contact pressure comes from the same equation as in liquid service:
pc = Δp × (B − K) + psp
- pc: face contact pressure, in MPa.
- Δp: pressure differential across the seal faces, in MPa.
- B: the seal’s balance ratio, from its drawing.
- K: pressure drop coefficient, the share of Δp that acts to open the faces.
- psp: spring pressure, the spring force at working length divided by the face area, in MPa.
When the seal chamber has drained, Δp is zero and the contact pressure equals the spring pressure.
When gas or vapour is still under pressure in the chamber, keep the hydraulic term, but do not treat the liquid benchmark K = 0.5 as a constant. For a gas film between parallel seal faces, K is about 0.50 only when the sealed pressure is close to the outside pressure, and it rises with the pressure ratio to roughly 0.64 to 0.70 once the gas flow chokes. A higher K means a lighter face load, so for parallel faces K = 0.5 errs toward more heat.
Multiply the contact pressure by the face area to get the face load:
F = pc × A
A = π × (Do² − Di²) / 4
Do and Di are the outer and inner diameters of the face contact in mm, so A comes out in mm² and the face load F in N.
Step 2: Pick a Friction Coefficient for Dry Contact
Use a dry friction coefficient measured for your face pair: in a dry ring-on-ring test, carbon graphite against sintered silicon carbide ran at a mean of about 0.25 to 0.3, against the 0.07 that API 682 assigns to lubricated faces.
Uncoated silicon carbide against itself is far worse: in the same test the pair cracked the upper ring and the run was stopped after 100 seconds.
We have not found a published dry friction value for carbon against tungsten carbide. For that pair, ask the seal maker for a measured figure rather than borrowing the silicon carbide one.
Step 3: Calculate the Heat
Turn the face load, friction coefficient and speed into heat in two steps, first the running torque and then the power:
Tr = F × f × Dm / 2000
H = Tr × N / 9550
Tr is the running torque in N·m, F the face load in N from Step 1, f the dry friction coefficient from Step 2, Dm the mean face diameter (Do + Di) / 2 in mm, N the shaft speed in rpm, and H the heat in kW.
Some published versions multiply contact pressure, sliding speed and friction coefficient with no face area. That product is heat per square metre of face, not watts; multiply it by the face area to get the seal’s heat load.
A published analysis works the dry case through for the inboard seal of a cartridge double seal, with faces of 37.4 mm OD and 31 mm ID and a face area of 343.64 mm². Running dry with pressure still on the faces, at a contact pressure of 0.242 MPa and a friction coefficient of 0.1689 measured on a tribometer for resin-impregnated carbon against silicon carbide, the example seal’s running torque is 0.240 N·m. At 3000 rpm, the example seal’s dry faces generate 0.0754 kW, about 75 W.
Treat the result as an order of magnitude.
Nearly all of the heat flows into the two face rings, shared between them roughly in proportion to their thermal conductivities.
Calculating Heat for a Seal Built to Run Dry
For a contacting seal built to run dry, such as an agitator seal or a dry containment seal, the calculation is the same three steps with the dry coefficient of its face pair; for a non-contacting dry gas seal, the friction term applies only until the faces lift off.
Calculate with the pressure and speed the seal sees in dry service, and check them against the maker’s dry rating.
Once a dry gas seal passes its lift-off speed, the heat comes from shearing the gas film, which the load × friction × speed product does not describe. If the gas film fails, the faces rub and the seal is back in the dry-contact case of Steps 1 to 3.