What Is a Labyrinth Seal?

Labyrinth seal refers to a seal with many zigzag cells between rotating parts and fixed parts to reduce leakage. It is the ideal labyrinth runner model.

There are many zigzag chambers between rotating parts and fixed parts to reduce leakage

The function of a fluid passing through a maze to reduce its flow is called a "maze effect". For liquids, there are hydrodynamic effects, including hydraulic friction and stream contraction effects; for gases, there are thermodynamic effects, that is, the thermal conversion of gas due to compression or expansion in a maze; in addition, there is a "breathing effect" "Wait. The labyrinth effect is a comprehensive response to these effects, so the labyrinth seal mechanism is very complicated. ^[1]

Labyrinth Seal Friction Effect

When the leaking liquid flows in the maze, the friction caused by the viscosity of the liquid reduces the flow rate and reduces the flow (leakage). In simple terms, the friction and local friction of the fluid along the flow path constitute the friction effect. The former is related to the length and cross-section of the channel, and the latter is related to the number of bends and the geometry of the maze. Generally, when the flow path is long, the corners are sharp, and the tooth tip is high, the resistance is large, the differential pressure loss is significant, and the leakage is reduced. ^[1]

Maze-sealed streamer contraction effect

As the fluid passes through the labyrinth slit, it will shrink due to the influence of inertia, and the cross section of the flow beam will be reduced. Let the aperture area be A, then the minimum area of the stream after shrinkage is

Here

Is the shrinkage factor. At the same time, the velocity of the gas after passing through the orifice also changes. Set the ideal flow velocity to U. The actual flow velocity is smaller than U, so

Is the velocity coefficient, then the actual velocity

for:

=

Therefore, the flow Q through the orifice is: Q =

Where

= (flow coefficient) ^[1]

The flow coefficient of the labyrinth slit is related to the shape of the gap, the shape of the tooth top and the roughness of the wall surface. For non-compressible fluid, it is also related to Reynolds number; for compressive fluid, it is also related to pressure ratio and Mach number. At the same time, it also affects the flow state before the slit. Therefore, in a complex type of maze, the flow coefficient of one slit cannot be regarded as the flow coefficient of all slits. According to the test, the flow coefficient of the first stage is smaller, and the flow coefficient of the slit after the second stage is larger. Generally, the flow coefficient is usually 1. However, the flow coefficient of the tines is smaller than 1, which is about 0.7, and the flow coefficient of the round teeth is close to 1, usually taking = 1, and the calculated leakage is too large. ^[1]

Thermodynamic effect of labyrinth seal

An ideal labyrinth flow channel model is a series of annular backlashes and interdental cavities. The flow of gas through each backlash and interdental cavity can be described as follows: At the entrance of the gap, the gas state is

,

Starting from zero, the closer the gas is to the inlet, the more the airflow contracts and accelerates. Not far behind the smallest gap, the airflow gains the maximum speed. When entering the cavity, the flow velocity section suddenly expands and a strong airflow is formed in the cavity. Vortex. From an energy point of view, the pressure energy of the airflow is converted into kinetic energy before and after the gap. At the same time, when the temperature decreases (the enthalpy value h decreases) and the gas enters the circular chamber between the two teeth at high speed, the volume suddenly expands to produce a severe vortex. As a result of the eddy current friction, most of the kinetic energy of the airflow is converted into thermal energy, which is absorbed by the airflow in the chamber to increase the temperature, and the enthalpy returns to the value before entering the gap, and only a small part of the kinetic energy still enters at a residual speed. For the next gap, repeat the above process step by step. ^[1]

Labyrinth seal ventilation effect

In an ideal maze, it is thought that the kinetic energy of the airflow passing through the slit in the expansion chamber becomes all thermal energy. That is, it is assumed that the asymptotic velocity at the next slit is equal to zero, but this is only true when the expansion chamber is extremely wide and extremely long. In a general through-maze, since the airflow passing through the slit can only diffuse to one side, the energy conversion of velocity energy (kinetic energy) to thermal energy cannot be sufficiently performed in the expansion chamber, and there is a part of the gas velocity on the side of the smooth wall It does not decrease or only slightly decreases, and directly flows over the top of each tooth to the low-pressure side, and this passing phenomenon is called "breathing effect". ^[1]