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Three-Dimensional Nozzle Design for Maximum Thrust. Volume I. Theoretical Development and Results.

AD878642

Publication Date	1970
Personal Author	Snyder, L. E.; Thompson, H. D.
Page Count	180
Abstract	The problem of designing three-dimensional (nonaxisymmetric) supersonic nozzles which produce the maximum axial thrust for a prescribed upstream flow field, mass flow rate, exit lip shape and position, and ambient pressure was formulated and numerically solved. The formulation was written to consider a three-dimensional, supersonic, isoenergetic, homentropic flow of a perfect gas. The axial thrust and mass flow rate were written as integrals over a control surface which was constrained to pass through the exit lip of the nozzle. The functional to be maximized was formed by summing the integral equation for the axial thrust and the integral equation for the mass flow rate times a Lagrange multiplier. The fixed length and fixed ambient pressure constraints were imposed by substitution into the variational problem. The numerical solution technique was programmed for the CDC 6500 computer. The results confirm that the three-dimensional optimal nozzles designed using this technique are significantly better than three-dimensional nozzles that have identical initial conditions and have comparable overall dimensions. Furthermore, the results show that two-dimensional or axisymmetric methods are not adequate for designing three-dimensional optimum nozzles. (Author)
Keywords	Supersonic nozzles Three dimensional flow Thrust Optimization Calculus of variations Design Rocket nozzles Supersonic combustion ramjet engines Exhaust nozzles
Source Agency	Non Paid Delimited ADS
NTIS Subject Category	46B - Fluid Mechanics
Corporate Authors	Purdue Univ Lafayette Ind Jet Propulsion Center
Document Type	Technical Report
Title Note	Technical rept.
NTIS Issue Number	197624
Contract Number	F33615-67-C-1068

Three-Dimensional Nozzle Design for Maximum Thrust. Volume I. Theoretical Development and Results.

Three-Dimensional Nozzle Design for Maximum Thrust. Volume I. Theoretical Development and Results.
AD878642

Publication Date	1970
Personal Author	Snyder, L. E.; Thompson, H. D.
Page Count	180
Abstract	The problem of designing three-dimensional (nonaxisymmetric) supersonic nozzles which produce the maximum axial thrust for a prescribed upstream flow field, mass flow rate, exit lip shape and position, and ambient pressure was formulated and numerically solved. The formulation was written to consider a three-dimensional, supersonic, isoenergetic, homentropic flow of a perfect gas. The axial thrust and mass flow rate were written as integrals over a control surface which was constrained to pass through the exit lip of the nozzle. The functional to be maximized was formed by summing the integral equation for the axial thrust and the integral equation for the mass flow rate times a Lagrange multiplier. The fixed length and fixed ambient pressure constraints were imposed by substitution into the variational problem. The numerical solution technique was programmed for the CDC 6500 computer. The results confirm that the three-dimensional optimal nozzles designed using this technique are significantly better than three-dimensional nozzles that have identical initial conditions and have comparable overall dimensions. Furthermore, the results show that two-dimensional or axisymmetric methods are not adequate for designing three-dimensional optimum nozzles. (Author)
Keywords	Supersonic nozzles Three dimensional flow Thrust Optimization Calculus of variations Design Rocket nozzles Supersonic combustion ramjet engines Exhaust nozzles
Source Agency	Non Paid Delimited ADS
NTIS Subject Category	46B - Fluid Mechanics
Corporate Authors	Purdue Univ Lafayette Ind Jet Propulsion Center
Document Type	Technical Report
Title Note	Technical rept.
NTIS Issue Number	197624
Contract Number	F33615-67-C-1068