300 Z.B. Riley and J.J. McNamara 0 0.2 0.4 0.6 0.8 1 0 50 100 150 x/L RMS Pressure (Pa) Overshoot No overshoot 0 0.2 0.4 0.6 0.8 1 −600 −300 0 300 600 x/L Fluctuating Pressure (Pa) Overshoot No overshoot a b Fig. 27.3 Transitional fluctuating pressure load model. (a) RMS of fluctuating pressure. (b) Fluctuating pressure snapshot envelope Table 27.1 Freestream conditions and panel geometry Mach number 4.0 Altitude 30km Unit Reynolds number 1.461e6 m 1 Turn angle 5.0ı Length 1.00m Thickness 2.50mm Material Aluminum 7075 An example of the transitional pressure load is provided in Fig. 27.3 in terms of the RMS pressure (Fig. 27.3a) and a snapshot of the fluctuating pressure envelope (Fig. 27.3b), for transition beginning at x=LD0:3and ending at x=LD0:5.As with the heat flux profiles in Fig. 27.2, results are presented for shifted and unshifted turbulent boundary layers to demonstrate the effect of accounting for or neglecting transitional overshoot. The RMS pressure in Fig. 27.3a demonstrates that the present formulation results in a smooth spatial variation in the RMS pressure throughout transition, with peak magnitudes occurring at the end of transition. The fluctuating pressure envelope in Fig. 27.3b represents the minimum and maximum bounds of the instantaneous pressure load acting on the panel. 27.2.3 Problem Description The freestream conditions and panel geometry considered in this study are listed in Table 27.1. It is assumed that the panel lies 1m downstream of the leading edge of a wedge with a5:0ı half angle. Therefore, the flow the panel experiences corresponds to the post oblique shock conditions (i.e. MD3:64). The material properties of the panel are listed in Table 27.2. Note that the modulus of elasticity, specific heat capacity, thermal conductivity, and thermal expansion coefficient are temperaturedependent properties where the listed values correspond to a temperature of 300K. The numerical parameters used in this study, listed in Table 27.3, were determined through a convergence study of the post-instability, limit cycle response of the panel. This configuration (geometry, material, freestream conditions) is selected for this study as it has been thoroughly examined in past works [23, 28, 29]. While this configuration does not represent an actual structure intended for use on a hypersonic vehicle, it provides the means to study a representative coupled response over a relatively short time record [28].
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