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Table 7: Natural frequencies (Q,) for linearly restrained ends (Third Mode) Fortran programme results

Table 7 Natural frequencies (Q,) for linearly restrained ends (Third Mode) Fortran programme results

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Fig. 1: Elastically Restrained Pipe with Spring Supported Ends. Consider a straight uniform single span pipe conveying fluid of length L where K, and K, are translational and kt, and kt, are rotational stiffness parameters as shown in fig. 1. The displacement of the pipe is assumed to be restrained in the z-x plane.
Fig. 1: Elastically Restrained Pipe with Spring Supported Ends. Consider a straight uniform single span pipe conveying fluid of length L where K, and K, are translational and kt, and kt, are rotational stiffness parameters as shown in fig. 1. The displacement of the pipe is assumed to be restrained in the z-x plane.
By non-dimensionalising equation (2), we assume the terms a: follows
By non-dimensionalising equation (2), we assume the terms a: follows
The present study aims in analyzing and validation of linearly restrained end conditions by simulation and experiment. In order to obtain the frequencies of linearly restrained ends with fluid flow effects on supports the following BC are applied Equation (15) is the general frequency equation of elastically restrained pipe conveying fluid.
The present study aims in analyzing and validation of linearly restrained end conditions by simulation and experiment. In order to obtain the frequencies of linearly restrained ends with fluid flow effects on supports the following BC are applied Equation (15) is the general frequency equation of elastically restrained pipe conveying fluid.
Fig. 3: Structure mesh for linearly restrained pipe structural analysis was done by considering 6764 nodes and 6640 elements. The shape of the element is quadrilateral, linear and shell type (S4). The CFD analysis was carried out for fluid flow in a pipe by meshing the model using hexahedral fluid elements (3200 elements and 4347 nodes); Element order is linear type used for fluid mesh is FC3D8. A convergent solution is obtained by bridging structural and fluid elements. The average aspect ratio at the holes, corners and fillet is good and is found to have less than 5% of meshing error.
Fig. 3: Structure mesh for linearly restrained pipe structural analysis was done by considering 6764 nodes and 6640 elements. The shape of the element is quadrilateral, linear and shell type (S4). The CFD analysis was carried out for fluid flow in a pipe by meshing the model using hexahedral fluid elements (3200 elements and 4347 nodes); Element order is linear type used for fluid mesh is FC3D8. A convergent solution is obtained by bridging structural and fluid elements. The average aspect ratio at the holes, corners and fillet is good and is found to have less than 5% of meshing error.
Table 5: Vibration analysis of linearly restrained pipe with fluid filled
Table 5: Vibration analysis of linearly restrained pipe with fluid filled
Table 6: Vibration analysis of linearly restrained pipe with fluid flow The results of simulation shows as flow velocity increases, the natural frequency decreases, and reaches critical velocity. At this point the pipe starts fluttering and experience maximum displacement with high stresses as shown in figure 9. The critical velocity where pipe flutters is found to be 15.195m/s and is shown in fig. 10.
Table 6: Vibration analysis of linearly restrained pipe with fluid flow The results of simulation shows as flow velocity increases, the natural frequency decreases, and reaches critical velocity. At this point the pipe starts fluttering and experience maximum displacement with high stresses as shown in figure 9. The critical velocity where pipe flutters is found to be 15.195m/s and is shown in fig. 10.
Fig.4: Test facility for measuring fluid induced vibrations in pipe
Fig.4: Test facility for measuring fluid induced vibrations in pipe
Fig. 5: Schematic diagram of linearly restrained pipe conveying fluid
Fig. 5: Schematic diagram of linearly restrained pipe conveying fluid
Fig. 7: Harmonic Analysis (sine sweep) for linearly restrained pipe.
Fig. 7: Harmonic Analysis (sine sweep) for linearly restrained pipe.
Fig. 10: Vibration of linearly restrained pipe with critical flow velocity of 15.190m/sec. Fig. 9: Vibration of linearly restrained pipe with Von Mises Stresses.
Fig. 10: Vibration of linearly restrained pipe with critical flow velocity of 15.190m/sec. Fig. 9: Vibration of linearly restrained pipe with Von Mises Stresses.
‘ig. 11: Non-dimensional natural frequency Vs. velocity and point of flutter for linearly restrained ends
‘ig. 11: Non-dimensional natural frequency Vs. velocity and point of flutter for linearly restrained ends
Related topics:
Piping Flexibility and Stress Analysis
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