Thermal and structural models were developed to simulate the structural response of the exploratory nozzle design under instantaneous application of pressure and thermal load conditions derived from the literature. This arrangement allowed a more realistic representation of the interaction between the fluid, thermal and structural fields in question.
Introduction
Composite Rocket Nozzle Design and Analysis
Principles of Solid Rocket Motor Operation
Simulation of the structural response of an SRM composite nozzle to instantaneous thermal and pressure loading. Simulation of the structural response of an SRM composite nozzle to transient thermal and pressure loading.
Solid Rocket Motor Nozzle Design and Analysis
- Nozzle Design Configurations
- Materials of Construction
- Carbon-Carbon Composites
- General Design and Analysis Process
Numerical Simulation of Solid Rocket Motor Nozzles
- Numerical Simulation of SRM Nozzle Flows
- Numerical Simulation of SRM Structural Response Behaviour
- Numerical Simulation of SRM Nozzle Fluid-Structure Interaction
Multidisciplinary Numerical Simulation Methodology
Introduction
Flow Modelling
Thermal Modelling
Structural Modelling
Fluid-Structure Interaction Modelling
Validation of Numerical Simulation Methodologies
Conclusion
Simulation of the Structural Response of a Composite SRM
Introduction
Analysis Parameters
- Solid Rocket Nozzle 1
- Nozzle Material Properties
- Loading Conditions
- Modelling Approach
Structural and Thermal Modelling
- Geometry Definition
- Boundary Conditions
- Finite Element Meshing
- Simulation Time Parameters
- Results Sampling
Results and Discussion
- Motor Burn Period Assessment
- Ignition Period Dynamic Structural Response
Conclusion
Simulation of the Structural Response of a Composite SRM
Introduction
Analysis Parameters
- Solid Rocket Nozzle 2
- Nozzle and Flow Material Properties
- Flow domain definition
- Ignition Transient
- Modelling Approach
Flow Modelling
- Geometry Definition
- Initial Conditions
- Boundary Conditions
- Finite Element Meshing
- Simulation Time Parameters
Structural Modelling
- Geometry Definition
- Boundary Conditions
- Finite Element Meshing
- Results Sampling
Results and Discussion
- Assessment of Simulated Steady Flow Field
- Assessment of Simulated Transient Flow Field
- Characteristic Fluid-Structure Interaction Modes
- Coupled and Uncoupled Responses at Samples Points
Conclusion
Simulation of the Structural Response of a Composite SRM
Introduction
As an advancement of the work described in Chapter 5, the current chapter describes the modeling methodology developed to also include the effects of thermoelasticity in the simulated ignition period response of the rocket's solid nose 2. The details of the flow, thermal, and structural models used in the simulations are provided and a wide range of results are presented and discussed regarding the ignition and burn period response of the structure. As in the simulation described in Chapter 5, a set of flow and structural models were solved simultaneously to derive the structure's response to pressure loading.
The effective structural response of the nozzle at the time of ignition was obtained by superposition of the responses arising from each of these solution paths. The heat solution flow and structural models were then constructed according to these discretization requirements based on the flow and structural models described in the previous chapter. The ignition period simulation results highlighted several important features related to the response of the SRN2 structure.
Comparisons were also made between the ignition and burn period structural simulation results to determine the importance of stresses induced during ignition in the context of stresses generated during engine operation. Two additional ignition period structural simulations performed with reference to time-scaled versions of the benchmark ignition transient allowed the sensitivity of the nozzle structural response to engine ignition rate to be determined.
Analysis Parameters
- Nozzle and Propellant Material Thermal Properties
- Scaled Ignition Transients
- Ignition Period Modelling Approach
- Burn Period Modelling Approach
Nevertheless, for simulation purposes, approximate thermal properties of a hypothetical ammonium perchlorate (AP)/hydroxyl-terminated polybutadiene (HTPB) propellant were obtained. The effective thermal properties of the propellant (assumed to be homogeneous) were calculated based on a mass ratio of 75% AP to 25% HTPB using the general thermal properties of the ingredients and the rule of mixture. The duration of the first scaled transient was reduced by 25%, while the duration of the second was increased by 25%, yielding transients of length 0.45 s and 0.75 s, respectively.
The ADINA fluid-structure interaction facility could not be used to pass a transient temperature boundary condition primarily as a result of the fact that when compressible flow is considered, interaction can only be simulated in terms of force and not heat flux. Structural model T was solved in terms of both the static and dynamic equations of motion in order to assess the inertial nature of the thermal loading problem. To generate the pressure-strain response, Flow Model P was solved to determine the pressure distribution along the wetted surface of the nozzle, which was subsequently mapped to Structural Model P at each solution time step using the FSI facility in uncoupled mode to allow the structural response to be established.
By simultaneously considering thermal and compressive loads in this way, the structural model was able to calculate the effective structural response of the nozzle during the fire period. Temperatures and pressures were recorded at specific points in the Flow Model T results file, and spatial functions were then used to prescribe the variation of the two parameters along the wetted surfaces of the thermal and structural models.
Thermal Penetration Zone Element Sizing
However, in the current case, the required temperature and pressure distributions of the nozzle wall were calculated using the flow model T. Regarding this condition, Figure 6.5 shows the temperature histories at different points along the SRN2 wall, which were derived from the flow model considered in the previous section. The next parameters that had to be solved were the dimensions of the elements of the TPZ models in the directions normal and parallel to the heated surface.
The results of this evaluation are shown in Figure 6.13 and demonstrate the dramatic increase in computational time required for an increase in the resolution factor. A significant difference in thermal and structural resolution times can also be observed that manifests itself with an increase in the resolution factor. It is useful to consider the results shown in Figure 6.13 in the context of the relative resolution error that exists between the girth stress predictions using a resolution factor of 4 and those calculated for factors of 1, 2, and 3.
More significantly, however, the relative error in the maximum stresses predicted at the hot surface is small, even for a resolution factor of 1 and at the earliest resolution time. This involves the cost of using each mesh resolution factor relative to the accuracy of the resulting solution, the limitations that the TPZ element size placed on discretization in the flow models, and the capacity of the computational resources available for use.
Flow Modelling
- Flow Model T
- Flow Model P
After careful consideration of these issues, a resolution factor of 3 was selected to scale the discretization of the TPZ bands in Flow Model T and Structural Model T. With regard to the finite element mesh of Flow Model T, the mesh density in the solid domain represents the The thermal penetration zone was effectively determined by the results of the element size sensitivity study. This condition inevitably contributed to a high mesh density in the general flow domain, significantly higher than that of the previous flow model.
Four separate simulations were performed using Flow Model T; a simulation for each of the three transients and a quasi-steady simulation to generate thermal and compressive stress data for the thermal and structural models of the fire period. Furthermore, due to the extremely large memory requirements of the Flow Model T results file for the 0.3 s simulations, a solution longer than a few seconds would have become unmanageable and was ruled out. The details of the time step configuration used for each simulation are shown in Table 6.4.
Flow model P differed from the original flow model described in Chapter 5 only in terms of the finite element network shown in Figure 6.19, which for consistency contained a finite element scheme identical to that of Flow Model T. In light of the strong similarities between Flow Model T and Flow Model P, the same time step configurations were applied in each of the three Flow Model T ignition period simulations used for the corresponding Flow Model P simulations, as shown in Table 6.5.
Thermal Modelling
- Burn Period Thermal Model
The position of each start and end point of the spatial function is shown in Figure 6.20, with the temperatures determined for each point detailed in Table 6.6. The reason for this loading is to take care of the local heating effect that would occur due to combustion on the adjacent surfaces. To take into account the convective heat transfer from the nozzle to the external atmosphere, a convective load was applied to the outer surfaces of the model with respect to the ambient temperature of 298 K and a constant heat transfer coefficient of 0.15 m-1.
Regarding the material specification in the thermal model of the combustion period, three material models were created according to the data included in Table 6.1, to define the 3D C-C, 2D C-P and steel components. After that, three sets of conduction elements and one set of convection elements were created in preparation for meshing the geometry. The discretization was driven by the same geometric subdivision scheme used in the structural model described in Chapter 5.
Given the long duration of the simulation, the moderate mesh density prescribed by this scheme was considered acceptable. The finite element mesh architecture of the Burn Period Thermal Model is presented in Figure 6.21.
Structural Modelling
- Structural Model T
- Structural Model P
- Burn Period Structural Model
- Results Sampling
As a consequence of the satisfactory performance of the first SRN2 structural model described in Chapter 5, Structural Model P was a copy of this model in every respect. However, since it had been demonstrated that no inertial effects manifested in the response of this model to compressive loading alone, the fluid-structure interaction solution incorporating structural model P used a less expensive static solution regime. The fire period structural model contained the same materials, element groups, full fixity constraint and finite element mesh as structural model P.
However, to describe the pressure loading, the constant pressure distribution derived from the 1 s flow model T simulation was applied, instead of using the FSI boundary condition of Structural Model P. The pressure distribution was determined by referring to the same eleven geometric points used to determine the temperature distribution in the thermal model of the combustion period, shown in Figure 6.20, and was applied identically based on the ten spatial functions. The results of the element size sensitivity study of the thermal penetration zone gave a clear indication that thermally induced stresses much more severe than those attributable to pressure loading can be expected in the regions adjacent to the hot walls of SRN2.
Considering these indications, it was clear that the most suitable locations to record reaction histories would be at points along the wetted surface of the nozzle. Five points were therefore chosen for this purpose based on the insight they were believed to be able to provide into the response characteristics of the nozzle.
Results and Discussion
- Flow Model T Flow Field Assessment
- Stress Field Development during Burn Period
- Nozzle Displacements Attributable to Ignition Period Pressure
- Transient Stress Distributions Attributable to Pressure
- Evaluation of Effective Surface Stresses
- Sensitivity of Thermostructural Response to Inertial Effects
- Sensitivity of Effective Structural Response to Ignition Rate
The throat region of the ITE has been shown to experience very high compressive and axial stresses, mainly due to the strong thermal loading. It can be seen that the heated material zone induces a zone of tensile hoops and axial stresses in the unheated central region of the ITE in response to significant thermal expansion. The negative coefficient of thermal expansion in the annular direction of the constituent 2D CP material contributed to this stress.
It has also been shown that tensile axial stresses increase at the corner feature at the head of the exit cone. By the end of the burning period, at 60 s, hoop stress in the ITE and exit cone is predicted to be almost completely compressive. Tensile hoop stresses spread over the heated surface of the insulator due to further thermally induced.
In addition, a small zone of compressive radial stress can also be seen developing at the head of the insulator due to the significant differential expansion in the radial direction. In general, surface stresses in the hoop direction were shown to be the worst, followed by axial stresses, while radial stresses appeared to remain insignificant for the duration of the simulation.
Conclusion
CONCLUDING REMARKS
