Three-Dimensional Nozzle Design for Maximum Thrust. Volume I. Theoretical Development and Results
Report Number: AFAPL TR 70-79 Volume 1
Author(s): Snyder, Lynn E,, Thompson, H. Doyle
Corporate Author(s): Purdue University Jet Propulsion Center
Laboratory: Air Force Aero Propulsion Laboratory
Date of Publication: 1970-10-28
Pages: 180
Contract: F33615-67-C-1068
DoD Project: None Given
Identifier: AD0878642
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.
Provenance: Lockheed Martin Missiles & Fire Control
Author(s): Snyder, Lynn E,, Thompson, H. Doyle
Corporate Author(s): Purdue University Jet Propulsion Center
Laboratory: Air Force Aero Propulsion Laboratory
Date of Publication: 1970-10-28
Pages: 180
Contract: F33615-67-C-1068
DoD Project: None Given
Identifier: AD0878642
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.
Provenance: Lockheed Martin Missiles & Fire Control