CHAPTER 6: Simulation of the Structural Response of a Composite SRM
6.7 Results and Discussion
6.7.2 Stress Field Development during Burn Period
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Figure 6.35 Axial temperature distributions at t = 0.1 s.
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and extreme thermal gradient at this location. The heated material zone can be seen inducing a zone of tensile hoop and axial stresses in the unheated central region of the ITE in response to significant thermal expansion. Along the entrance section and in the vicinity of the leading edge of the ITE, quite significant compressive radial stresses can be seen developing in response to the expansion resistance imposed by unheated 3D C-C material. The insulator, subjected to maximum chamber pressure loading was observed to flex inwards in response to the distortion of the attach structure, resulting in high tensile hoop stresses in this component, particularly in the area adjacent to the ITE. The negative coefficient of thermal expansion in the hoop direction of the constituent 2D C-P material contributed to this stress. The highly localised zone of intense tensile radial stress, found in the insulator towards the nozzle’s motor attachment point appears to have arisen spuriously. The error, which also manifests at the subsequent solution times, is believed to be as a consequence of the application of a very low mesh density in the vicinity of the intersection between a heated and adiabatic boundary. High tensile hoop stresses were also observed at the head of the exit cone, again in response to the pressure induced distortion of the attach structure and concentrated by the geometric discontinuity created by the corner along its external surface.
By the 30 s midway point of motor operation, the increase in thermal penetration displayed by Figure 6.37, has increased the presence of compressive stresses in the nozzle, and has relieved to some extent the submerged tensile hoop stresses in the ITE. The zone of tensile axial stresses in the substructure however, has become more prolific. Significantly, the severe compressive stresses encountered in the throat region have not subsided, and the zone of compression has deepened appreciably. It is believed that this phenomenon can be attributed to the notably stiffer and insulated steel attach structure retarding the radial expansion of the ITE. An area of high tensile hoop stress can once again be seen in the insulator at its heated junction with the ITE, the magnitude of which has increased significantly. Tensile axial stresses have also been shown to increase at the corner feature at the head of the exit cone.
By the end of the burn period, at 60 s, hoop stress in the ITE and exit cone are predicted as being almost entirely compressive. The severe compressive stress zone at the nozzle’s throat has deepened further and progressed in the upstream and downstream directions, although the magnitude of the highest recorded stress has decreased slightly. Tensile hoop stresses have spread across the heated surface of the insulator as a consequence of further thermally-induced
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material contraction. The submerged region of tensile axial stress in the ITE has increased in size, whilst tensile axial stresses in the adjacent insulator have risen to a notable magnitude. In addition, a small zone of compressive radial stress can also be seen developing at the head of the insulator as a result of the significant differential expansion in the radial direction.
When considering the stresses arising from the unequal expansion of separate substructures such as the ITE and insulator, it is important to bear in mind that in reality, expansions gaps and slip surfaces are designed into the nozzle structure for the specific purpose of alleviating these stresses. Even in the case that substructures are bonded together with adhesives, a significant amount of expansion stress can be dissipated by the characteristically low modulli of elasticity associated with these adhesives. As these features were not included in the SRN2 design or structural models, and in consideration of the novelty of the design itself, it is clear that to a degree, simulated stress magnitudes in certain zones of the Burn Period Structural Model were unavoidably overestimated. Having said this however, it is believed that the fidelity of the ignition period structural response was substantially less affected by these technical simplifications as an elementary consequence of the highly localised nature of heat penetration.
To gain a more precise understanding of the stress magnitudes encountered during the burn period, hoop, radial and axial stress histories were recorded at the five sample points A, B, C, D and E, and are exhibited in Figures 6.38-6.43, respectively. The establishment of histories at these points was important as it would allow ignition period and burn period responses to be compared at identical locations.
The most marked observation made in relation to these results is that at each point, with the exception of the axial stress history, the highest stress magnitudes recorded were shown to be reached by the first time step of the simulation. Furthermore, the magnitude of the predominant hoop and axial stresses at the nozzle’s surface declined considerably from this peak over the remaining duration of the simulation, as the depth of thermal penetration increased and relieved the constricting effect imposed by unheated regions. This decline wasn’t as significant in the hoop stress history recorded at point B, however. It is suggested that the trend was not followed at this point as a result of the radial expansion constriction imposed by the attach structure.
Nonetheless, this observation was notable as it indicated the significance of the ignition period in generating nozzle surface stresses and the role played by thermoelasticity in this regard.
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Figure 6.36 Temperature distribution and (a) hoop, (b) radial and (c) axial stress fields at t = 10 s.
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Figure 6.37 Temperature distribution and (a) hoop, (b) radial and (c) axial stress fields at t = 30 s.
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Figure 6.38 Temperature distribution and (a) hoop, (b) radial and (c) axial stress fields at t = 60 s.
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Figure 6.39 Burn duration hoop, radial and axial stress histories at point A.
Figure 6.40 Burn duration hoop, radial and axial stress histories at point B.
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Figure 6.41 Burn duration hoop, radial and axial stress histories at point C.
Figure 6.42 Burn duration hoop, radial and axial stress histories at point D.
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Figure 6.43 Burn duration hoop, radial and axial stress histories at point E.
Also noted was the apparent directional hierarchy amongst the hoop, radial and axial responses.
In general, surface stresses in the hoop direction were shown to be most severe, followed by axial stresses, whilst radial stresses appeared to remain insignificant for the duration of the simulation. As a result of point A’s perpendicular orientation relative to the other points, a slightly different hierarchy was observed in which the axial stress response as opposed to the radial stress response was shown to be comparatively negligible. As far as stress direction is concerned, almost every response remained compressive throughout the simulation, although interestingly, the hoop stress histories at points C and D were observed to become slightly tensile in the second half of the time interval.
6.7.3 Nozzle Displacements Attributable to Ignition Period Pressure and Thermal Loading