Schematics of the sharp cone model. 

Contexts in source publication

Context 1

... cross-spectrum depends heavily on the simultaneous behaviour of the signals at two frequencies f 1 = 1 /a 1 and f 2 = 1 /a 2 . In particular, when the goal is to study non-stationary signal with multi-scale local disturbance, wavelet cross-spectrum can point out the interaction level of different frequency components included in local disturbance. Experiments were carried out in the hypersonic blow-down wind tunnel. This tunnel was designed for the Mach numbers M ∞ = 5 − 15 and the unit Reynolds number Re 1 at 5 × 10 5 − 7 × 10 7 m − 1 , with a set of changeable profile and conic axis-symmetric nozzles. An Ohmic heater was used for maintaining air temperature in the settling chamber up to 700–1300 K. The open-jet test section has the length of 1600 mm with the nozzle end diameter of 480 mm. The stagnation pressure P 0 and stagnation temperature T 0 were measured and kept to be constant. Here the stagnation pressure is 2.69 MPa, and the stagnation temperature T 0 is 702 K. The unit Reynolds number Re 1 is 1 . 3 × 10 7 m − 1 . The model is a cone sharp with half-angle of 5 ◦ and length 600 mm, as shown in Fig. 1. The model consists of a sharp cone nose of 1 mm in bluntness ra- dius and the base part equipped with 28 Pt-thin-film thermocouple sensors to measure the wall temperature. The thermocouple sensors are located along the bottom generatrix. The first thermocouple sensor is located at 90 mm from the cone apex; and the other ones are placed in uniform separation from each other. The output signals were digitized by 12-bit analog- to-digital converter data acquisition cards with ± 5 V range and 1 MHz sampling rate. At each location of measurement, 524288 samples are recorded. Figure 2 shows the wavelet coefficients magnitude contour of the temperature signals at different stations along one generatrix. The corresponding temperature signals are also presented under the contours to compare the disturbance occurrence locations. For the purpose of clarity, only a section of 7 ms of the signals is presented in the figure. From the plane rep- resentation of the wavelet coefficients, it can be seen that some local high magnitudes of the wavelet coefficients exist at different time in the scale range of 200 kHz to 300 kHz corresponding to the second-mode disturbance. The second mode disturbance is dominant in a hypersonic laminar boundary layer. More and more large amplitude disturbances are triggered downstream with the development of the disturbance. At the last station X = 480 mm, the disturbance is fully developed and the transition reaches its peak. Figure 3 shows the multi-scale wavelet cross- spectrum calculated by Eq. (3) providing the development details of the frequency interaction of disturbance in hypersonic boundary layer. At the initial stage of transition, the frequency band of the disturbance is narrow, the border between the first mode and the second mode is confused. No significant frequency peak is observed in the plot of wavelet cross spectrum. However, the disturbance at different frequencies within this narrow band is important. They couple each other with nonlinearity and give rise to their enhancement. The nonlinear interaction leads to new disturbance modulation arising and the band range of disturbance frequencies becomes broader with the boundary layer developing downstream. These are qualitative indicators of nonlinear interaction growth among different frequency components in the disturbance frequency band. The disturbance develops across a broader frequency range and two significant frequency peaks appear gradually rep- resenting the first mode and the second mode respec- tively. There is a very clear dominant frequency band including the first mode and the second mode in the hypersonic laminar boundary layer. At X = 480 mm the first mode and the second mode can be identified clearly. This also indicates that the transition reaches its peak while the second mode is centred at f 2 = 226 kHz and the first mode is centred at f 1 = 68 kHz. In summary, a new analysis method based on wavelet transform, termed as the wavelet cross spec- tra, is presented to investigate the evolution mech- anism of unstable disturbance during hypersonic boundary layer transition. The measurement results show that the initial unstable disturbances cause nonlinear interactions between different frequencies. The nonlinear interactions among different frequencies broaden the band frequency range of unstable disturbances in return. Both the low-frequency and the second mode disturbance are important for interactions among different unstable frequencies in the initial stage of transition. This interaction precedes the final breakdown of the hypersonic laminar boundary layer and transition to turbulence. The authors would like to gratefully acknowledge the support from the China Aerodynamics Technique Research Academy for collecting the experimental ...

Context 2

... [9,10] f 1 = 1/a 1 and f 2 = 1/a 2 . In particular, when the goal is to study non-stationary signal with multi-scale lo- cal disturbance, wavelet cross-spectrum can point out the interaction level of different frequency components included in local disturbance. The model is a cone sharp with half-angle of 5 • and length 600 mm, as shown in Fig. 1. The model consists of a sharp cone nose of 1 mm in bluntness ra- dius and the base part equipped with 28 Pt-thin-film thermocouple sensors to measure the wall tempera- ture. The thermocouple sensors are located along the bottom generatrix. The first thermocouple sensor is located at 90 mm from the cone apex; and the other ones are ...