Performance Criteria of Pulse-Jet Propellers 



elements characterize its dynamics. For many purposes a rather detailed 

 knowledge of both distributions spatial as well as temporal will be necessary. 



In the present context however we may introduce the mean thrust 



T, = f J J- S,, dS„ dt (1) 



, 1/ f S ^ •'■' ''- - ' vi'' ' 



and the mean power 



/ /-^c S,, dS, dt (2) 



f 



1/ f s 



of the propeller acting as the frequency f as the basic measures of its overall 

 performance. 



Introducing further the propeller translation advance speed v^ in the 

 fluid, we may immediately establish the principle ,...,• 



T, V, < P \^ (3) 



for the reaction power of the propeller due to the velocity field induced by the 

 propeller at its own location. Once again we are facing a serious problem, since 

 it is in general apparently difficult to define the advance speed in question. 



The part of the system's boundary passing through the fluid may now be 

 divided into two parts Sj and Sj, the inlet and the outlet section, respectively, 

 the definition of the dividing line being another problem to be solved in any par- 

 ticular case. With the appropriate choice of normals the mean volume flows 



Qi = f J J ^i dSj dt (4) 



1/ f Sj 



through the sections are both positive and, according to the principle of conser- 

 vation of matter, equal: 



Qp = Qi = Q ■ (5) 



The general conservation principle for any quantity included in the boundary of 

 the system may be put in the form 



FLj - FLi = FL + PR (6) 



expressing the fact that the mean net outflow of the quantity over the fluid bound- 

 aries equals its mean inflow FL over the other part of the boundary and its mean 

 production PR in the boundary of the system, the mean storage in the boundary 

 being zero due to the periodicity, see Fig. 2. 



Application of this prinicple to the momentum flows 



Mie = f / / (P ^. ^n, + S, J aS^ dt (7) 



l/f Si 



results in the momentum principle 



M2, - Ml, = T , (8) 



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