Leakage flows

Figure 4-112. Effect of leakage flow across the tips of rotating blades.

To maintain maximum sealing effieieney, it is essential that the labyrinth lands maintain sharp edges in the direetion of the flow. This requirement is similar to that in orifiee plates. A sharp edge provides for maximum vena eontraeta effeet, and lienee maximum restrietion for the leakage flows. (Figure 13-22.)... 

If leakage flow-rate Qieak is laminar, then... 

Control Valve - Double-seated control valves are considered to pass sufficient leakage flow that equipment blocked in by such valves need not be provided with thermal expansion protection. 

A factor is often required in this equation to allow for eccentricity of the screw in the barrel. Typically this increases the leakage flow by about 20%. 

For many practical purposes sufficient accuracy is obtained by neglecting the leakage flow term. In addition the pressure gradient is often considered as linear so... 

The other case is where the pressure at the end of the extruder is large enough to stop the output. From (4.9) with <2 = 0 and ignoring the leakage flow... 

The operating point for an extnider/die combination may also be determined from equations (4.9) and (4.12) - ignoring leakage flow... 

An analysis of the flow behavior which is more or less confirmed by numerical simulations is presented by Leblanc. " The total flow in an internal mixer (tangential type) can be divided into a laminar, circulating flow which is pushed by the rotor tip, an axial directed flow, as an effect of the helix angle between axis and rotor wing and a leakage flow between rotor tip and mixing chamber waU (refer to Figure 35.6), or... 

Generally, the absolute magnitude of Q is not as important as the ratio leak rate to the total flow rate Qieaf/QtotJ. The leakage rate given by Equation (5.4) is the volume flow rate at the temperature and pressure of the leakage flow, and must be corrected to standard conditions for comparison with reactant feed rates. The total required flow rate of fuel or air to the stack is proportional to the stack current, which increases with the electrochemically active area and is inversely proportional to the cell area specific resistance (R"). 

Rowell and Finlayson described leakage flow through the flight clearance as flow between two parallel plates [7]. The rate of energy dissipation between the flight lands and the barrel wall is given by Eq. 7.82. This dissipation is considered to be the same as that for barrel rotation, and it is provided in the literature [9]. 

Potente, H., Effen, N., and Liu, ]., Throughput Calculation with Considerations of Leakage Flow on Injection Molding Plasticizing Units, Polym. Eng. ScL, 36, 1557 (1996)... 

The leakage-flow of non-contact gap and labyrinth seals can be considerable, and must be recycled internally. It should be noted that labyrinth compressors use this type of seal on the rods, also. 

Figure 4.8 also presents an analytical solution for the screw characteristic curve of a single screw extruder with leakage flow effects. The discrepancies between analytical solution and experimental results arise due to the fact that the screw curvature, the flight angle and the fillet radii are not included in the analytical model. The analytical solution given by Tadmor and Klein [27] was used. 

This assumption is not fully valid since, due to die flight clearance, there is leakage flow over the flight of die... 

Standpipes are used in the gas-solid circulating flow systems in which a cyclone-standpipe-valve configuration for the separation and reintroduction of particles, as shown in Fig. 8.18, is constantly encountered. The satisfactory operation of the cyclone-standpipe system depends on a small leakage flow of gas up the standpipe. A simple method to estimate... 

The validity of Eq. (8.95) is subjected to the condition that n + wp is less than the terminal velocity of the particles. Equation (8.95) further indicates the condition at which the leakage flow of gas downward along the standpipe occurs when... 

The typical pressure profile of the standpipe and the valve is shown in Fig. 8.18. As can be seen in the figure, the pressure head over the standpipe Aps, in the absolute sense, is equal to the sum of the overall pressure head, Apt, and the pressure drop over the valve, Ap0. From Eq. (8.92), the particle volume fraction in the standpipe can be estimated from the measured height of the bulk particles. Thus, given the particle mass flow rate, the leakage flow of gas in the standpipe can be estimated from Eq. (8.95). 

Example 8.3 In an operation of gas-solid circulating flow in a cyclone-standpipe-valve system, the particles are 100 p.m glass beads with a density of 2,500 kg/m3. The particle volume fraction in the standpipe is 0.55. The gas is air with a viscosity of 1.8 x 10-5 kg/m s and a density of 1.2 kg/m3. The particle mass flow is 70 kg/m2 s. The height of solids in the standpipe is 1.4 m. The total pressure head over the standpipe and valve is 4,500 Pa. Estimate the leakage flow of air in the standpipe. If the particle volume fraction at minimum fluidization is 0.5 and the area ratio of valve opening to pipe cross section is 0.6, what is the orifice coefficient of this valve ... 

Thus, the interstitial velocity of leakage flow of air is estimated from Eq. (8.95) as... 

The minus sign means that the leakage flow of air is directed downward. 

For a fluidized standpipe, the drag force of particles balances the pressure head as a result of the weight of solids. If the Richardson and Zaki form of equation (Eq. (8.55)) is proposed for the drag force, derive an expression for the leakage flow of gas in this standpipe. Discuss the effect of particle size on the leakage flow assuming all other conditions are maintained constant. 

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