The unsteady behaviour of a massively separated, pressure-induced turbulent separation bubble (TSB) is investigated experimentally using high-speed particle image velocimetry (PIV) and piezo-resistive pressure sensors. The TSB is generated on a flat test surface by a combination of adverse and favourable pressure gradients. The Reynolds number based on the momentum thickness of the incoming boundary layer is 5000 and the free stream velocity is$25~\text{m}~\text{s}^{-1}$. The proper orthogonal decomposition (POD) is used to separate the different unsteady modes in the flow. The first POD mode contains approximately 30 % of the total kinetic energy and is shown to describe a low-frequency contraction and expansion, called ‘breathing’, of the TSB. This breathing is responsible for a variation in TSB size of approximately 90 % of its average length. It also generates low-frequency wall-pressure fluctuations that are mainly felt upstream of the mean detachment and downstream of the mean reattachment. A medium-frequency unsteadiness, which is linked to the convection of large-scale vortices in the shear layer bounding the recirculation zone and their shedding downstream of the TSB, is also observed. When scaled with the vorticity thickness of the shear layer and the convection velocity of the structures, this medium frequency is very close to the characteristic frequency of vortices convected in turbulent mixing layers. The streamwise position of maximum vertical turbulence intensity generated by the convected structures is located downstream of the mean reattachment line and corresponds to the position of maximum wall-pressure fluctuations.
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...
This tutorial introduces the Proper Orthogonal Decomposition (POD) to engineering students and researchers interested in its use in uid dynamics and aerodynamics. The objectives are rstly to give an intuitive feel for the method and secondly to provide example MATLAB codes of common POD algorithms. The discussion is limited to the nite-dimensional case and only requires knowledge of basic statistics and matrix algebra. The POD is rst introduced with a two-dimensional example in order to illustrate the dierent projections that take place in the decomposition. The n-dimensional case is then developed using experimental data obtained in a turbulent separation-bubble ow and numerical results from simulations of a cylinder wake ow. I.
The design, construction, and validation of a new academic wind tunnel is described in detail. The wind tunnel is of a classical, blow-down type and generates a pressure-induced, turbulent separation bubble on a flat test surface by a combination of adverse and favorable pressure gradients. The Reynolds number, based on momentum thickness just upstream of separation, is Re θ 5,000 at a free-stream velocity of U ref = 25ms -1 . The length of the separation bubble is estimated at 0·42 ± 0·02m by three different methods. Results of a numerical simulation demonstrate the absence of flow separation in the wind-tunnel contraction. This results in a turbulence level of about 0·05% in the test section. Oil-film visualisation experiments show that the flow near the wall is strongly three-dimensional in the recirculating region and that the topology of the limiting streamlines is consistent with experiments performed on configurations with fixed separation. Finally, spatial variations of the forward-flow fraction have been documented using a thermal-tuft probe and are shown to compare well with the results of the oil-film visualisation.
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