Pressure drop through accelerating tube

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. 

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... 

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... 

Thus, the sub-total pressure drop due to the suspension flow passing through the accelerating tube is written as... 

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. 

The coefficient f depends on the Reynolds number for flow within the tube. In laminar flow, the Hagen-Poiseuille law can be applied. In turbulent flow the Blasius equation is used. The main difficulty is the evaluation of water pressure drop during transition boiling. The pressure drop consists of three components friction (APf), acceleration (APJ and static pressure (APg). In once-through horizontal tubes boiler APg=0. The Lockard-Martinelli formulation is used to estimate the friction term. 

Now consider the rapid expansion of a supercritical fluid through the expansion nozzle depicted in Figure 3, which is in use in our laboratory and is similar to those typically reported in the literature (19,20). A tapered inlet (usually 120° angle) is followed by a cylindrical capillary section in which L/D typically ranges from 3 to 6000. Given the comparatively low viscosity of a supercritical fluid, the effects of acceleration and friction on the pressure are weak at the low flow speeds that exist upstream of the nozzle in the process tubing. Consequently, the pressure drop up to this point is small. However, when the fluid passes into the tapered inlet section of a typical RESS nozzle, the slow expansion gradually turns rapid. If, to simplify analysis, we subdivide the process into an isobaric part followed by a rapid expansion, the question of where the rapid expansion truly starts must be addressed. 

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