CHAPTER 6: Simulation of the Structural Response of a Composite SRM
6.2 Analysis Parameters
6.2.1 Nozzle and Propellant Material Thermal Properties
To accommodate the thermoelasticity associated with the current problem, the collection of material properties employed in the previous simulation was extended to include the thermal properties reported in Yoo et al (2003) and used in the SRN1 simulation. For the sake of convenience, the relevant properties are shown again in Table 6.1 with respect to a cylindrical coordinate system, where kθ, kz, kr, αθ, αz and αr are the thermal conductivities and coefficients of thermal expansion in their associated directions, respectively, whilst Cp and ρ are the materials’
specific heat capacity and density, respectively.
Property 3D C-C 2D C-P Steel
kθ = kz, W/mK 13.96 2.38 40.6
kr, W/mK 13.96 0.38 40.6
αθ =αz, x10-6 /˚C 4.76 -1.5 14.6
αr, x10-6 /˚C 4.76 27 14.6
Cp, J/kgK 1153 1206 595
ρ, kg/m3 1514 1329 7800
Table 6.1 Thermal properties of SRN2’s constituent materials.
Owing to solution difficulties encountered when using the adiabatic wall condition to describe the propellant grain boundary in certain flow simulations, thermal properties were also assigned to represent the propellant. This designation was made on the approximate assumption that for the period of interest, the propellant grain would absorb heat from the exhaust gases and not actively combust. As heat transfer to such an inert propellant grain would be comparatively low during this phase, the thermal properties of the propellant would have a negligible effect on the adjacent flow stream and accurate definition of such properties is therefore not crucial.
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Nonetheless, approximate thermal properties were derived for a hypothetical ammonium perchlorate (AP) / hydroxyl-terminated polybutadiene (HTPB) propellant for the purposes of the simulation. This oxidiser/fuel combination is commonly employed as a non-aluminised propellant. The effective thermal properties of the propellant (assumed to be homogeneous) were calculated on the basis of 75% AP to 25% HTPB mass ratio using general constituent thermal properties and the rule of mixtures. The resulting values for thermal conductivity, specific heat capacity and density are displayed in Table 6.2.
Property AP/HTPB Propellant
k, W/mK 0.16
Cp, J/kgK 1500
ρ, kg/m3 1730
Table 6.2 Thermal properties of the AP/HTPB propellant.
6.2.3 Scaled Ignition Transients
To assess the sensitivity of SRN2’s structural response to the rate of SRM ignition, two additional ignition transients defining the the variation of pressure at the flow domain inlet, were considered. The additional transients are shown in relation to the original 0.6 s transient from which they were derived by temporal scaling in Figure 6.1.
Figure 6.1 Scaled pressure transients.
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The duration of the first scaled transient was reduced by 25%, whilst the duration of the second was increased by 25%, yielding transients 0.45 s and 0.75 s in length, respectively.
Correspondingly, additional transients defining the variation of temperature at the flow domain inlet were generated in an identical manner. Figure 6.2 shows the additional temperature transients in relation to the temperature transient considered previously.
Figure 6.2 Scaled temperature transients.
6.2.4 Ignition Period Modelling Approach
The ADINA fluid-structure interaction facility could not be employed to relay a transient temperature boundary condition primarily as a result of the fact that when compressible flow is being considered, interaction can only be simulated with respect to force and not heat flux. To counter this significant limitation, an indirect ignition period modeling approach was developed to allow the combined effects of thermal and pressure loading to be accounted for. As illustrated in Figure 6.3, this indirect approach utilised two simulation paths, designated T (thermal) and P (pressure), to compute the response of SRN2 to thermal and pressure loading in isolation. Each path comprised a flow model, to generate the associated loading condition, and a structural model, to which the loading condition was then applied to derive the required response.
To generate the thermal stress response, Flow Model T was solved as a conjugate heat transfer (CHT) problem to establish the transient temperature distribution in the nozzle, which was in turn mapped to Structural Model T where the thermostructural problem could be solved.
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Structural Model T was solved in respect of both the static and dynamic equations of motion, in order for the inertial nature of the thermal loading problem to be assessed.
To generate the pressure stress response, Flow Model P was solved to determine the pressure distribution along the nozzle’s wetted surface, 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. As it had already been established that the pressure stress response associated with this problem displayed negligible vibratory characteristics, the solution of Structural Model P was derived using a quasi-static simplification.
Figure 6.3 Ignition period modelling approach.
Boundary Conditions / Initial Conditions
FLOW MODEL T FLOW MODEL P
CHT Temperature Distribution
FSI Pressure Boundary Condition
STRUCTURAL MODEL T STRUCTURAL MODEL P
Thermal Response
SUPERPOSITION
Pressure Response
Effective Structural Response
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Finally, to calculate the combined effective response, results generated by either structural model were superimposed at each increment in time. It should be noted, of course, that the application of such a straightforward augmentation approach prevents the SRN2 structure from influencing the overall flow through the nozzle in response to thermal loading. That is, Flow Model T and Structural Model T are uncoupled.
6.2.5 Burn Period Modelling Approach
To simulate the response of SRN2 to pressure and thermal loading during the burn period, the modelling approach employed was similar to that used in the simulation described in Chapter 4.
To derive the transient temperature distribution in SRN2 during a 60 s burn period, a thermal model was constructed and subjected to a steady temperature boundary condition along the nozzle’s wetted surface. This temperature distribution was then mapped to an associated structural model, which in turn was subjected to steady pressure loading. By simultaneously accounting for thermal and pressure loading in this manner, the structural model was able to calculate the effective burn period structural response of the nozzle.
Figure 6.4 Burn period modelling approach.
Boundary Conditions / Initial Conditions
FLOW MODEL T
Temperature Loading Condition
THERMAL MODEL
Temperature Distribution STRUCTURAL MODEL
Effective Structural Response Pressure Loading Condition
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In the current case however, the required nozzle wall temperature and pressure distributions were calculated using Flow Model T. 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.
The overall modelling approach is outlined in Figure 6.4.