Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

The accurate prediction of bending stiffness is important to analyze the buckling and vibration behavior of reinforced thermoplastic pipes(RTPs)in practical ocean engineering.In this study,a theoretical method in which the constitutive relationships between orthotropic and isotropic materials are unified under the global cylindrical coordinate system is proposed to predict the bending stiffness of RTPs.Then,the homogenization assumption is used to replace the multilayered cross-sections of RTPs with homogenized ones.Different from present studies,the pure bending case of homogenized RTPs is analyzed,considering homogenized RTPs as hollow cylindrical beams instead of using the stress functions proposed by Lekhnitskii.Therefore,the bending stiffness of RTPs can be determined by solving the homogenized axial elastic moduli and moment of inertia of cross sections.Compared with the existing theoretical method,the homogenization method is more practical,universal,and computationally stable.Meanwhile,the pure bending case of RTPs was simulated to verify the homogenization method via conducting ABAQUS Explicit quasi-static analyses.Compared with the numerical and existing theoretical methods,the homogenization method more accurately predicts the bending stiffness and stress field.The stress field of RTPs and the effect of winding angles are also discussed.

Stability management of high speed axial flow compressor stage through axial extensions of bend skewed casing treatment

This paper presents the experimental results to understand the performance of moderately loaded high speed single stage transonic axial flow compressor subjected to various configurations of axial extensions of bend skewed casing treatment with moderate porosity.The bend skewed casing treatment of 33%porosity was coupled with rectangular plenum chamber of depth equal to the slots depth.The five axial extensions of 20%,40%,60%,80%and 100%were used for the experimental evaluations of compressor performance.The main objective was to identify the optimum extension of the casing treatment with reference to rotor leading edge which results in maximum stall margin improvements with minimum loss in the stage efficiency.At each axial extension the compressor performance is distinctive.The improvement in the stall margin was very significant at some axial extensions with 4%–5%penalty in the stage efficiency.The compressors stage shows recovery in terms of efficiency at lower axial extensions of 20%and 40%with increase in the peak stage efficiency.Measurements of flow parameters showed the typical behaviors at near stall flow conditions.Hot wire sensor was placed at the rotor upstream in the tip region to capture the oscillations in the inlet axial and tangential velocities at stall conditions.In the absence of casing treatment the compressor exhibit abrupt stall with very high oscillations in the inlet axial and tangential velocity of the flow.The extents of oscillations reduce with bend skewed casing treatment.Few measurements were also performed in the plenum chamber and salient results are presented in this paper.