Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer

Abstract

The statistical scaling properties of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) are presented. The intended flow is generated using the direct numerical simulation (DNS) TBL code of Simens et al. (2009) and Borrell et al. (2013), with a modified farfield boundary condition (BC). The conditions for self-similarity and appropriate scaling are derived, with mean and Reynolds stress profiles presented using this scaling. The APG and ZPG DNS are also compared under the classical viscous scaling.

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

“…Also note that the value of U + is not constant for in the APG TBL, contrary to what is observed in ZPG TBLs. This has been documented among others by Kitsios et al [37], and leads to problems in the determination of the boundary-layer thickness as discussed by Vinuesa et al [54]. On the other hand, note that the mean velocity profile at x s s / c = 0.4 was also reported by Hosseini et al [1], as part of a comparison between suction and pressure sides at matched R e τ values.…”

Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers

“…Note that the logarithmic skin-friction relation and its low- R e correction have found widespread preference compared to other empirical relations since the early work by Rotta [41]. The values of the various coefficients in the correlations (1) and (2) used in the present work for the ZPG, and the APG cases with constant β = 1 (including Kitsios et al [25]) and 2, are given in Table 3. In order to obtain the various coefficients, the data with R e 𝜃 > 2000 was first fit to Eq.…”

“…Figure 1 (bottom) includes, for reference, the Reynolds-number evolution of the Clauser pressure-gradient parameter of the five databases from the literature listed in Table 2. Note that in the two databases containing regions of constant β , namely the ones by Kitsios et al [25] and Lee [26], only the β values from the profiles analyzed here are shown.

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“…It is also interesting to note that the b 1 and b 2 cases, with constant value of β , are subjected to the same well-defined pressure-gradient magnitude throughout a considerable streamwise extent. In the present section we will focus on the b 1 and b 2 cases, together with the APG TBL with constant value of β = 1 by Kitsios et al [25], and report empirical curves that can be used to assess whether a particular APG TBL, with constant β = 1 or 2, can be considered to be well-behaved. Note that given the relatively low Reynolds number available for the present databases, we will focus on the skin-friction coefficient and shape factor, and therefore we will not provide an empirical curve for the wake parameter, which would require higher Reynolds numbers in order to not be affected by low- R e effects.…”

“…In particular, we will consider the numerical work by Kitsios et al [25], Lee [26] and Spalart and Watmuff [16], together with the experimental databases by Monty et al [27] and Nagib et al [28]. The various conditions present in the different databases lead to a variety of pressure-gradient evolutions, ranging from moderate-pressure-gradient cases to the strongly decelerated TBL on the suction side of a wing.…”