Buckling of the supersonic axisymmetric HT MLN structure

The aim of this work is to develop a numerical calculation program to determine the first critical buckling force of the axisymmetric supersonic MLN in the adaptation regime by the energetic method for the needs of the future aerospace construction. After designing the MLN by the HT MOC, the contour of the nozzle will be determined point by point meeting the requirements for eliminating thrust losses. The design essentially depends on the exit Mach number and the stagnation temperature of the combustion chamber. In this first step, the distribution of the wall pressure ratio at each internal point along the internal wall of the nozzle, as well as the thrust force are determined. Its resultant necessarily applied to the thrust center in relation to the throat of the nozzle, which must also be determined in order to assimilate the nozzle as being a beam of variable section embedded in the throat and free at the exit of the nozzle. The section of the beam is of the thin-walled circular shape having a constant thickness across the longitudinal axis and constructed of a same material. Using the energy method, one can numerically determine the value of the first critical buckling force of the nozzle corresponding to the data. The obtained integrals are calculated by the Simpson method. The cubic spine interpolation is used to interpolate the buckling deformation in eatch iteration. A new dimensionless coefficient of the critical force is introduced. We also consider a new other buckling coefficient λ as being the Logarithm of the ration between the critical buckling force under the thrust force, making it possible to directly indicate the existence or absence of buckling in the nozzle during the flow in the nozzle. Then if λ>0.0, the buckling phenomenon is absent in the flow, and it is present if λ≤0.00. Truncation of the nozzle is considered in order to see the possibility of increasing the critical buckling force. The application is made for Air. An example of the structural sizing of the nozzle to avoid the buckling phenomenon is considered in this study.