Unsteady Behavior of a Pressure-Induced Turbulent Separation Bubble

Abstract

Wall static-pressure and longitudinal-velocity fluctuations are measured in a pressure-induced turbulent separation bubble generated on a flat test surface by a combination of adverse and favorable pressure gradients. The Reynolds number, based on momentum thickness upstream of separation, is Re θ ≃ 5000 at a free-stream velocity of U ref 25 m∕s. The results indicate that the flow is characterized by two separate time-dependent phenomena: a lowfrequency mode, with a Strouhal number St 1 ≃ 0.01, which is related to a global "breathing" motion (i.e., contraction/ expansion) of the separation bubble, and a higher-frequency mode, with a Strouhal number St 2 ≃ 0.35, which is linked to the roll-up of vortical structures in the shear layer above the recirculating region and their shedding downstream of the bubble. These two phenomena are reminiscent of the "flapping" and "shedding" modes observed in fixed-separation experiments, though their normalized frequencies are different. The breathing mode is also shown to be strikingly similar to the low-frequency unsteadiness observed in shock-induced separated flows at supersonic speeds. Nomenclaturepower spectrum of movable sensor G xx = measured power spectrum of reference (fixed) sensor G yy = measured power spectrum of movable sensor h = maximum height of dividing streamline L = length scale in shock-induced separated flows L b = length of separation bubble, which is equal to 0.42 m p = static pressure p 0 = fluctuating static pressure Re θ = Reynolds number based on momentum thickness St, St 1;2 = Strouhal number, which is equal to fL b ∕U ref St f , St s = Strouhal number of flapping and shedding modes, which is equal to fx R ∕U ∞ St L = Strouhal number in shock-induced separated flows, which is equal to fL∕U ∞ St δ ω = Strouhal number of free shear layers, which is equal to fδ ω ∕ U T C = time constant of constant-voltage anemometer circuit Tu = turbulence level U = longitudinal velocity U = average velocity in the shear layer, which is equal to U max ∕2 U c = convective velocity U s = mean longitudinal velocity of inviscid flow at separation V w = voltage across hot-wire probe x = longitudinal position in test section x R = length scale in fixed-separation flows x det = longitudinal position of transitory detachment on test-section centerline, which is equal to 1.75 m x = nondimensional longitudinal position in test section, which is equal to x − x det ∕L b x D = short-time average of nondimensional instantaneous detachment position x R = short-time average of nondimensional instantaneous reattachment position y = vertical position under test surface, positive going down z = spanwise position in test section δ = 99% boundary-layer thickness δ ω = shear-layer vorticity thickness, which is equal to U max − U min ∕∂U∕∂y max γ = forward-flow fraction γ 0 = short-time average of forward-flow fraction ν = kinematic viscosity θ = momentum thickness ρ = air density Subscripts ref = measurement at wind-tunnel reference location (center of contraction exit area) rms = root mean...

Measurements of pressure and velocity fluctuations in a family of turbulent separation bubbles

“…This shows that the first maximum of is in fact the result of two separate phenomena: on the one hand, the signature of the low-frequency breathing motion, mostly apparent at the position of maximum adverse pressure gradient, and on the other hand the increase in high-frequency pressure fluctuations caused by the turbulent structures submitted to an APG and their subsequent lift-off from the wall. This reconciles the DNS results of Na & Moin (1998 b ) and Abe (2017) with the conclusions of Weiss et al (2015) and Mohammed-Taifour & Weiss (2016) obtained from observations of the Large TSB only.…”

“…At low frequency (, where is the Strouhal number, is the frequency and the size of the bubble defined as the distance between transitory detachment and transitory reattachment (Simpson 1989)), the TSB appears to expand and contract in a quasi-periodic breathing motion. This motion was educed using a pair of classical thermal-tuft probes in Weiss et al (2015) and later confirmed by high-speed particle image velocimetry (PIV) measurements in Mohammed-Taifour & Weiss (2016). At a medium normalized frequency of , the unsteady behaviour of the flow is characterized by roller-like structures similar to those observed in the DNSs of Na & Moin (1998 b ) and Abe (2017), and with a very close convection velocity of .…”

Spatio-temporal dynamics of turbulent separation bubbles

“…The thin solid vertical line marks the high-frequency f h = 0.0025 Uo/θo, the blue dashed vertical line represents the low-frequency f l = 0.001 Uo/θo, the dotted-dash vertical line marks fm = 0.002 Uo/θo. than some previous studies, because this motion agrees phenomenologically with the "breathing" phenomenon associated with the low-frequency motion in earlier studies of incompressible SBs (Pauley et al 1990;Spalart & Strelets 2000;Weiss et al 2015;Mohammed-Taifour & Weiss 2016).…”

“…The vast majority of computational studies and many experimental studies of APG induced separation have employed a suction-and-blowing configuration (Perry & Fairlie 1975;Patrick 1987;Na & Moin 1998a;Weiss et al 2015;Abe 2017;Wu & Piomelli 2018;). An advantage of this configuration is that the total mass flux at the inflow and outflow planes remains the same and this might simplify the the experiments as well as the analysis.…”

Large-eddy simulation study of unsteady wake dynamics and geometric sensitivity on a skewed bump

“…Both separation bubbles oscillate significantly in size at low frequencies, and the upstream separation bubble undergoes 'massive recirculation' events in which it meanders upwards and joins with the downstream separation bubble (Graziani et al 2018). The separation bubble induced by an adverse pressure gradient shows unsteady motion at very low frequency (Na & Moin 1998b;Weiss, Mohammed-Taifour & Schwaab 2015). Similar to the backward-facing step, the separation bubble grows downstream slowly, then contracts suddenly (Na & Moin 1998a).…”