HIGH-AMPLITUDE WALL PRESSURE EVENTS AND THEIR RELATION TO TURBULENT STRUCTURE IN CHANNEL FLOW

Direct Numerical Data (DNS) set of fully developed turbulent channel flow is utilized to study the turbulent structures associated with positive and negative High Amplitude Pressure Peaks (HAPPKs) at different Reynolds number. Conditional average is conducted based on the wall pressure extrema that exceed a certain threshold value. The results indicate near-wall shear layer in the buffer zone, and the large-scale streamwise velocity upstream the detection point together contribute to average positive pressure. Upon splitting the total pressure to its slow and rapid parts, the contribution from the rapid part, that represents the effect of large-scale motion, is dominant throughout the channel except close to the wall which its comparable with slow part. Hence, positive HAPPKs result from both smalland largescale structures. Negative peaks are found to be associated with the core of the vortex structure. The conditional averaged Q-value introduced an organized vortex structure that scale with wall units with negative peak coincides with its core, and hence negative peaks are generated from the small-scale motion. The effect of Reynolds number appears only in the positive peaks. INTRODUCTION The generation of pressure fluctuations inside turbulent boundary layer is connected to the dynamics of the velocity fluctuations linearly, via the interaction between the velocity fluctuations and the mean shear, and nonlinearly via the interaction of velocity fluctuations with themselves. Among the pressure fluctuations, wall pressure fluctuations had been studied extensively due to the difficulty inherent in measuring the fluctuations of pressure inside the boundary layer. High Amplitude Pressure Peaks (HAPPKs) refer to both positive and negative pressure fluctuations that exceed a threshold value k larger than the root mean square (r.m.s) value rms p . These HAPPKs are the main responsible for the sound generation that often lead to undesirable structural vibrations. Starting with analysis of Kim (1981) with variable-interval space averaging (VISA) detection method, he found that bursting phenomeon is associated with a pressure signature characterized by a positive peak surrounded by small negative amplitude regions. Later, Johansson et al. (1987) concluded that buffer region shear layer structures are responsible for the generation of positive peaks. As the wall pressure fluctuations are generated from linear and nonlinear interactions, they suggested that positive HAPPKs are generated from the interaction with the mean shear which were supported by Johanson et al. (1991) in their study of shear layer structures. On the other hand, negative peaks were conjectured to be associated with sweep type events. Robinsson (1991) calimed that negative pressure troughs beneath the extended vortex leg, while positive pressure is located along the high-low speed interface of the near wall shear layers that seem to extended to the wall. This near wall shear layers are created when high-speed fluid impacts low-speed fluid lifted by quasistreamwise vortices. Moreover, Kim et al. (2002) suggested that positive peaks are associated with the inward motion because of the streamwise vortices above the wall, whereas high neagtive wall pressure occur beneath the outward motion in the vicinity of the wall. The analysis of Ghaemi and Scarano (2013) led them to the conclusion that positive HAPPK region is overlapping with the shear layer structure, in agreeament with Johansson et al. (1987), where interaction between upstream sweep events, initiated from the outer layer, and downstream ejection ones, formed by the hairpin category in the inner layer, forms the shear layer. In agreemant with Robinson (1991), they related the negative pressure to the core of the vortical structures which could be either spanwise or streamwise section of a hairpin vortex, or it may be associated with an isolated streamwise vortex. It is apparent from these and other studies that the various coupling mechanisms between flow structures in both the inner and the outer layers of the boundary layer, and wall pressure 10 International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 2 9B-5 fluctuations peaks are quite complex. In addition, the work of Ghaemi and Scarano (2013) was handled at relatively moderate Reynolds number, 770 Re = τ based on friction velocity τ u and kinematic viscosity ν . Consequently, it is not clear if theses structures depend on Reynolds number or not. DNS data set of fully deveoped turbulent channel flow covers a wide range of Reynolds number, from 180 Re = τ to 4000 , ν τ τ / Re h u = , where h is channel half width, are used for firstly, studying the turblence structures concerned with both positive and negative HAPPKs, and secondly, to check their universality with Reynolds number. The abstract is organized as follows. In section II, an overview of the utilized DNS data set is introduced. Section III will be concerned with discussion of the results the conditiona average analysis of positive and negative HAPPks. Finnally, the conclusion will be given in Section V. NUERICAL SIMULATION The simulations reported in this study are DNSs of incompressible turbulent flow between two parallel planes. The coordinate system is taken to be ) , , ( z y x that are representing the streamwise, wall-normal, and spanwise coordinates, respectively with 3 , 2 , 1 ), , , ( ) , , ( 3 2 1 = = = i w v u u u u ui are the three components of velocity in the same directions. For the pressure, p is used to denote the total pressure. In streamwise ) (x and spanwise ) (z directions, periodic boundary conditions are applied, and no-slip/no-penetration boundary conditions are applied at the wall. The mass flux through the channel remains constant by a uniform streamwise pressure gradient that drives the flow field. DNSs of the incompressible Navier–Stokes equation are conducted by a hybrid Fourier spectral ) , ( z x and the secondorder central difference method in ) (y direction, where aliasing error in the streamwise and spanwise directions is removed by the phase shift method. For time progress, third-order accuracy Runge-Kutta method is applied to the convection term, CrankNicolson method is applied to the viscosity term, and the Euler implicit method is applied to the pressure term. The present DNS conditions are shown in Table 1. The domain size is relatively large to detect the large-scale structures exist around the center of the channel. The time taken for a hypothesized turbulent eddy to perform one complete 3600 rotation and, known as eddy turn over time + T , is given also in Table 1. Table 1 illustrates the computational domain size in streamwise and spanwise directions ) , ( z x L L , in addition to the grid resolutions in the three directions ) , , ( + + + Δ Δ Δ z y x , where + Δ w y represents the grid resolution at the wall, and + Δ c y is at the center of the channel. Table 1 gives the number of grid points in y N the wall-normal direction. STATISTICAL ANALYSIS Statistical Features of Pressure Fluctuations The data to be presented will show that the probability distribution of the amplitudes has features obviously different from the Gaussian signal. In comparison to the Gaussian distribution, the wall pressure fluctuations have larger positive and negative amplitudes as illustrated in Figure 1. A comparison of the higher moments of the probability distribution between the present data and the Gaussian distribution illustrates this distinction. Table 2 gives the values of the skewness, as a measure of the asymmetry behavior of the probability distribution, and the kurtosis, as a measure of the intermittent character, of wall pressure in comparison with the previous study of Schew (1983) for turbulent boundary layer at 1400 Re = θ , based on the momentum thickness of the boundary layer. We compare the results of Schew (1983) with the smallest transducer + d comparable with the grid spacing in the streamwise direction + Δx . In addition, we compare our results for the higher Reynolds number with the successful experimental study of Tsuji et al. (2007). The flatness factor value shows the intermittent feature of the wall pressure as it takes a value of 5 . 5 ≈ irrespective of Reynolds number, but the results of Tsuji et al. (2007) shows a monotonic decreasing with the Reynolds number. On the other hand, the skewness factor shows slight increase with Reynolds number. In addition, it takes positive value for the higher Reynolds numbers of 2000 and 4000 in agreement with the results of Tsuji et al. (2007). Figure 2 shows the contribution of the HAPPKs to the total r.m. s of wall pressure fluctuations at different k values. The contributions were determined by computing the r.m. s values from all events that exceeded the current threshold. Obviously, the data show large amplitude events more than 3 threshold value contribute to nearly 40.7% of the total r.m. s of pressure fluctuations which coincides with the results of Schew (1983). Figure 1. Probability Density Distribution (pdf) of wall pressure fluctuations for Reynolds number range in Table 1 in (a) linear, and (b) logarithmic scale Table 1. Calculation conditions for DNS data set τ Re h Lx h Lz + Δx + Δz + Δ w y + Δ c y y N