A preliminary study of the effect of the external stream structure on turbulent spots generation during by‐pass transition

Abstract

The investigation of turbulent spots production rate and average length at various FST turbulence length scales is worked on both the Narasimha's concept of the intermittency and the wavelet transform.The final phase of laminar boundary layer transition starts with the occurrence of first turbulent spots, e.g. [1]. Spots production controls the length of transition region. The effect of the free stream turbulence (FST) level T u on the location of transition onset is known long ago [2]. The authors clearly proved [3,4] that the length scale L e of the FST also influences and experimental data (symbols as in Fig. 1).the start of boundary layer by-pass transition. This effect was emphasized also in [4][5][6]. But a clear physical notion on the role of the FST length scale in transition process is not elaborated yet. The authors joined experiences (e.g.[8]) of the instantaneous wall-friction, τ w (t) measurement and that one (e.g.[9]) of the spot detection procedure to perform a preliminary study of the spots behaviour during transition at various FST scales with aim to contribute to the problem explanation.The experiment has been made in the close circuit wind tunnel IT Prague (0.5 x 0.9) m 2 on a smooth wooden plate (zero pressure gradient) 2.75 m in length. Boundary conditions correspond to the ERCOFTAC Test Case T3A+: free stream velocity U e = 5 m/s and the FST level T u = 0.03 with different length parameters L e = 3.8; 5.9 and 33.4 mm respectively in the leading edge plane (x = 0). Plane grids of different geometry (cylindrical rods and square holes) placed across the flow produce homogeneous nearly isotropic turbulence. Wellsophisticated hot wire calibration and the wall-proximity corrections of the CTA measuring method allow determine digital records (25 kHz, 750000 samples) of the instantaneous velocity U (t, x, y) and wall-friction τ w (t) rows and carry out relevant statistical analyses, e.g. [4]. The flow intermittency analysis is based on digital records of τ w (t). It is very similar to e.g. [9] i.e. the detector function, threshold and indicator function I(t) are evaluated. Finally the transitional intermittency factor γ(x) is calculated. The distributions γ versus Re x shown in Figure 1 confirm the effect of Le. Even though always T u = 0.03 at x = 0, the start of transition is moving upstream and the termination of transition region is moving downstream with increasing FST length scale Le. According to the Narasimha [1] concept, some information on the effect of the FST scale L e on the spot production rate n and Emmon's non-dimensional propagation parameter σ could be assessed from the γ-distributionwhere nσ/U e is assumed constant. Narasimha derived that formula ( Our measurements are compatible with Narasimha universal form as shown in the Figure 2. Following Narasimha, the dimensionless spot production rates n * σ = nυ 2 σ/U e 3 for different Le related to ΔRe tr were evaluated. They are shown in *