NSWC/WOL TR 76-155 



If A = AMIN , then (At/T) = (TPOS - t ) /T + 1/2 (BIO] 

 C n-1 n FC c n-l n 



The parameter (At/T) locates positive phase cut-off in 

 terms of bubble oscillation cycles. "Zero" is taken as the last 

 expansion occurring during the positive phase. Using (At/T) _, } the 

 starting radius for the final oscillation at lowered pressure was 

 then selected from the approximate values listed in Table B-l. 



Phase Shift Correction . The effect of the negative 



pressure phase is often limited by its short duration relative to 



the bladder period of oscillation. Thus, it is also necessary to 



account for the phase shift which occurs upon surface cut-off. This 



was done by adding a time correction to the duration, At of the 

 1 ^ neg, 



negative pressure phase. Using the parameter (At/T) computed 

 from Equation 11 or 12, this correction was approximated as follows: 



If <_(At/T) £ 0.1, then Phase Corr = (Bll) 



If 0.1 < (At/T)__ < 0.5, then Phase Corr = -(t - TPOS) (B12) 

 — PC — ' c 



n 



If 0.5 <_ (At/T) <_ 1.0 ; then Phase Corr = TPOS - t (B13) 



c n-l 



where t is the time at which AMIN would have occurred had not 



c n 

 surface cut-off intervened. (Since this subsequent minimum depends 



B-6 



