Pressure drop accelerating tube

Divide the exchanger tube into sections and calculate the pressure drop section-by-section up the tube. Use suitable methods for the sections in which the flow is two-phase. Include the pressure loss due to the fluid acceleration as the vapour rate increases. For a horizontal reboiler, calculate the pressure drop in the shell, using a method suitable for two-phase flow. 

Draft Tube Pressure Drop. The pressure drop across the draft tube, AP2 3, is usually similar to that across the downcomer, APj 4, in magnitude. Thus, for a practical design basis, the total pressure drop across the draft tube and across the downcomer can be assumed to be equal. In most operating conditions, the pressure drop at the bottom section of the draft tube has a steep pressure gradient due primarily to acceleration of the solid particles from essentially zero vertical velocity. The acceleration term is especially significant when the solid circulation rate is high or when the draft tube is short. 

The pressure drop inside the draft tube is more complicated because it involves acceleration of solid particles from essentially zero vertical velocity. However, the model for calculating the pressure drop in vertical pneumatic conveying lines suggested by Yang (1977) can be applied. The acceleration length can be calculated from numerical integration of the following equation. 

Numerically integrate Eq. (11) to obtain the particle acceleration length and Eq. (15) to obtain the pressure drop across the draft tube, AP2 3. 

In most of the work reported in the literature it is assumed that the wetted tube over which the pressure drop is measured is sufficiently long that such entry effects can be neglected. No account is taken of the waves at the film surface, or of the fact that they may move faster than the mean surface velocity of the film, and the energy lost or gained by the gas stream in accelerating or decelerating the liquid surface near the inlet is also neglected. 

During the flow of the streams through the accelerating tubes, several factors may lead to pressure drop along the path. These factors include friction between the gas flow and the inside wall of the tube, acceleration of the particles, collisions of particles on the wall and between particles etc. For convenience, the pressure drop through the accelerating tube can be considered to consist of two constituents caused by gas flow and particles, respectively, -Apx.d and -Apdc p, which are discussed separately below. 

Similar to the calculation of pipe-resistance, the pressure drop caused by the gas flow passing through the accelerating tube, -ApXd, can be represented by... 

The pressure drop resulting from the movement of particles can be determined by an energy balance. The overall energy balance round the flow of suspension inside the accelerating tube is written as... 

On the other hand, the collisions of particles on the inside wall of the tube and between particles also result in a certain pressure drop, which is denoted by -Apac>p2. Some researchers let it be a fraction of the pressure drop caused by pure airflow [67] however, it would be more convenient and reasonable to correlate it with that resulting from the acceleration of the particles, -ApaCiPi, because the factors affecting the two kinds of collision are the same as those for —Ap ac.pi. In this way, we have... 

The pressure drops between Points A and C, between Points A and C, between Points A and B, and between Points A and B , denoted by -ApAC, -ApA C, -ApAB, and -A/Evb, respectively, are measured with inclined U-shape tubes filled with colored kerosene. The average of -ApAB and -ApA B- is taken as the pressure drop through the accelerating pipes, while that of -Ap v and -ApA c as the overall pressure drop across the impinging stream contactor, -ApT. Consequently, there should be... 

The power of 0.000118 in Eq. (4.20) implies that the effect of Rea on is very small, so that A.d can be considered to be independent of Re.d in the range of practical interest, and a constant of 0.0214 is taken for A.d. Since the pressure drop due to pure airflow passing through the accelerating tube occupies only a very small fraction of the total across the contactor while the values for A, obtained from the curves of versus Red given in Ref. [20] can also be used directly for calculation without significant error. 

It is clear from Fig. 4.5 that the data for ,c>p are considerably concentrated over 85% of the values are in the range 4.3 to 6.2, and the average value is 5.34. This fact indicates that ,c>p can be considered to remain essentially constant and that, consequentially, Eq. (4.11) describes well the pressure drop behavior due to the acceleration and collisions of the particles. Therefore the combined consideration of the two kinds of collisions, i.e., the collisions of particles on the wall and between particles, is reasonable and feasible. It should be noted that, as described by Eqs. (4.5) and (4.6), for a given impinging velocity u0, the velocity of particles at the outlet of the accelerating tube depends on the length of the tube Lac, the particles to gas mass flow rate ratio and the mean diameter of particles dv. Therefore Eq. (4.11) actually... 

The derivation of Eq. (44c) assumes no acceleration along the axis of the capillary. This is not true at both ends of the capillary where the rate of flow is much faster inside the tube than outside. Thus the pressure drop, AP, is not caused entirely by the viscous resistance of the fluid and a portion of it is attributed to the velocity of the flow according to the well-... 

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