NSWC/WOL TR 76-155 



APPENDIX B 



METHOD FOR CALCULATING GAS BLADDER RESPONSE 

 TO EXPLOSION PRESSURE WAVE 



Figure 2.3.2 sketched the way we approximated the explosion 

 pressure signature by a sequence of pressure steps in order to 

 calculate the bladder response by means of the equations developed 

 in Appendix A. Appendix B gives the details of the procedure. 



Boundary Condition at Pressure Jumps . Step changes in the 



outside water pressure from p to p , , occurring at half-period 

 c ^n ^n+1 ^ c 



intervals change the equilibrium pressure P of the oscillating 

 bubble flow (equal to the outside pressure p ) . Since the oscillatory 

 system described by Equation Al has finite mass, neither A nor A can 

 change impulsively, i.e., 



A A = (Bl) 



and 



A A = (B2) 



for all pressure jumps. And, thus for pressure jumps occurring at 

 extrema where A=0 , only the equilibrium pressure P„ can change. 



Let A be the maximum or minimum bubble radius at the 

 c 

 n 



time of the pressure jump p to p , , . If A is greater than the 

 t- j f t- n ^n+1 c 3 



n 



new equilibrium radius* A , , , the new oscillation begins at maximum 



n+1 



* _ 



The equilibrium radius A is the at-rest radius which corresponds to the 



equilibrium pressure E, (= p , the outside pressure). A is calculated 



^ n n 



from p using Equation B6, below. 



B-l 



