Supersonic turbulent boundary layer drag control using spanwise wall oscillation

Abstract

Spanwise wall oscillation has been extensively studied to explore possible drag control methods, mechanisms and efficacy – particularly for incompressible flows. We performed direct numerical simulation for fully developed turbulent channel flow to establish how effective spanwise wall oscillation is when the flow is compressible and also to document its drag reduction (${\mathcal{D}}{\mathcal{R}}$) trend with Mach number. Drag reduction ${\mathcal{D}}{\mathcal{R}}$ is first investigated for three different bulk Mach numbers $M_{b}=0.3$, $0.8$ and $1.5$ at a fixed bulk Reynolds number $Re_{b}=3000$. At a given velocity amplitude $A^{+}$ ($=12$), ${\mathcal{D}}{\mathcal{R}}$ at $M_{b}=0.3$ agrees with the strictly incompressible case; at $M_{b}=0.8$, ${\mathcal{D}}{\mathcal{R}}$ exhibits a similar trend to that at $M_{b}=0.3$: ${\mathcal{D}}{\mathcal{R}}$ increases with the oscillation period $T^{+}$ to a maximum and then decreases gradually. However, at $M_{b}=1.5$, ${\mathcal{D}}{\mathcal{R}}$ monotonically increases with $T^{+}$. In addition, the maximum ${\mathcal{D}}{\mathcal{R}}$ is found to increase with $M_{b}$. For $M_{b}=1.5$, similar to the incompressible case, ${\mathcal{D}}{\mathcal{R}}$ increases with $A^{+}$, but the rate of increase decreases at larger $A^{+}$. Unlike the flow behaviour when incompressible, the flow surprisingly relaminarizes when it is supersonic (at $A^{+}=18$ and $T^{+}=300$) – this enigmatic behaviour requires further detailed studies for different domain sizes, $Re_{b}$ and $M_{b}$. The Reynolds number effect on ${\mathcal{D}}{\mathcal{R}}$ is also investigated. Although ${\mathcal{D}}{\mathcal{R}}$ generally decreases with $Re_{b}$, it is less affected at small $T^{+}$, but drops rapidly at large $T^{+}$. We introduce a simple scaling for the oscillation period as $T^{\ast }=T_{C}^{+}l_{I}^{+}/l_{C}^{+}$, with $l_{I}^{+}$ and $l_{C}^{+}$ denoting the mean streak spacing for incompressible and compressible cases, respectively. At the same semi-local Reynolds number $Re_{\unicode[STIX]{x1D70F}c}^{\ast }\equiv Re_{\unicode[STIX]{x1D70F}}\sqrt{\overline{\unicode[STIX]{x1D70C}}_{c}/\overline{\unicode[STIX]{x1D70C}}_{w}}/(\overline{\unicode[STIX]{x1D707}}_{c}/\overline{\unicode[STIX]{x1D707}}_{w})$ (subscripts $c$ and $w$ denote quantities at the channel centre and wall, respectively), ${\mathcal{D}}{\mathcal{R}}$ as a function of $T^{\ast }$ exhibits good agreement between the supersonic and strictly incompressible cases, with the optimal oscillation period becoming $M_{b}$-invariant as $T_{opt}^{\ast }\approx 100$.

On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows

“…2019) and active/passive control approaches (Gose et al. 2018; Yao, Chen & Hussain 2018; Li & Liu 2019; Yao & Hussain 2019), to date, very few works have investigated the features of wall-shear stress fluctuations and their associated dynamics. Despite this lack of analysis, wall-shear stress fluctuations are of importance for noise radiation, structural vibration, drag generation and wall heat transfer, among others (Choudhari & Khorrami 2007; Diaz-Daniel, Laizet & Vassilicos 2017; Zhang et al.…”

“…τ w = τ w + τ w . Although many studies have focused on the properties of the mean wall-shear stress, such as its Reynolds number dependence (Nagib, Chauhan & Monkewitz 2007;Chauhan, Monkewitz & Nagib 2009;Schlatter & Örlü 2010), its physical-informed decomposition and connection with the statistical quantities across the wall layer (Fukagata, Iwamoto & Kasagi 2002;Renard & Deck 2016;Yoon et al 2016;Modesti et al 2018;Fan, Cheng & Li 2019a;Fan, Li & Pirozzoli 2019b; and active/passive control approaches (Gose et al 2018;Yao, Chen & Hussain 2018;Yao & Hussain 2019), to date, very few works have investigated the features of wall-shear stress fluctuations and their associated dynamics. Despite this lack of analysis, wall-shear stress fluctuations are of importance for noise radiation, structural vibration, drag generation and wall heat transfer, among others (Choudhari & Khorrami 2007;Diaz-Daniel, Laizet & Vassilicos 2017;Zhang et al 2017;Bae et al 2018).…”

Active control of compressible channel flow up to Mab=3 using direct numerical simulations with spanwise velocity modulation at the walls

“…So far, the method by Viotti et al [48] was only applied to incompressible channel flow. Additionally, similar methods investigated mostly moderate Mach numbers [51]. The present publication extends their work in simulating flows at different Reynolds and Mach numbers as well as control wavelengths, to find out, how variable property compressibility effects [8] are influenced by wall oscillations.…”

“…DNSs are thus conducted for three different Mach numbers , 1.5, and 3.0 each for two different semi‐local Reynolds numbers and 400 to study the influence of these two non‐dimensional parameters (an idea of the variation of , increasing strongly toward the wall, can be seen in Figure 5, to be discussed later). Additional strictly incompressible cases were not pursued as Yao and Hussain [51] virtually found no differences to the nearly incompressible flow with Mach number , except for marginal deviations of the phase averaged spanwise velocity profile from the laminar Stokes layer, that is often used for comparison of incompressible cases. Each Reynolds/Mach number combination is done for two domain sizes with different streamwise dimensions in order to fit integer multiples of various wavelengths of the control method into it.…”

“…Only few investigations were performed in this regard. Yao and Hussain [51] studied spanwise wall oscillations in turbulent channel flow at rather moderate Mach numbers. They reported performance benefits at the highest of their investigated Mach numbers, , accompanied by a monotonic increase of drag reduction with the oscillation period, that partly vanished at a higher Reynolds number.…”