Semi-Confined Flows

Underlying Flow Regime 3-34

Test Case

Brief Description of the Study Test Case

A 3D sketch of the experimental setup is shown in Fig. 1. The configuration presents a GlauertGoldschmied type body consisting of a relatively long fore body and a relatively short concave ramp comprising the aft part of the model mounted between two glass endplate frames with both leading edge and trailing edges faired smoothly with a wind tunnel splitter plate.

Figure 1: 3D sketch of experimental setup [‌1], [‌2]

Major geometric and flow parameters of the TC are presented in Fig.2 and summarized in Table 1 (note that in the “baseline” experiment considered here the slot shown in Fig.2 was closed).

Figure 2: Schematic of TC geometry of the flow parameters

Table 1: Major geometrical and flow parameters Parameter

Notation

Value

Free stream velocity

U

34.6 m/s

Hump chord

c

0.42 m

Crest height

h

0.0537 m

Reynolds number

Re=Uc/ν

936, 000

Mach number

M

0.1

The experimental data are available at http://cfdval2004.larc.nasa.gov/case3expdata.html (Case 3), at https://turbmodels.larc.nasa.gov/nasahump_val.html, and also enter the ERCOFTAC

�Classic Collection http://cfd.mace.manchester.ac.uk/ercoftac under number C.83. The data set includes: streamwise distributions of the surface pressure and skin-friction coefficients, C P and C f , and mean velocity and Reynolds stresses fields in the tunnel center-plane, roughly covering the region 0.63 < x/c < 1.39.

Test Case Experiments

A photo of the experimental rig is presented in Fig.3.

Figure 3: Photo of the experimental rig

The experiments were performed in the NASA Langley 20′′×28′′ shear flow tunnel. The flow was nominally 2D, although with side-wall effects (3D flow) expected near the endplates. The reference “chord” length of the model, c, is defined as the length of the hump on the wall and is equal to 420mm. The maximum thickness of the hump, h, is equal to 53.7mm. The model was equipped with 153 centre-span static pressure ports and 20 dynamic pressure ports in the vicinity of the separated flow region. Sixteen spanwise pressure ports were located on the fore body (x/c = 0.19) and on the ramp at (x/c = 0.86). Two-dimensional PIV data were acquired in a plane, along the model centreline and normal to the surface, starting from right upstream of the slot and ending well beyond the reattachment location at x/c ≈ 1.4. Stereoscopic PIV (3D) data were acquired in planes perpendicular to the flow direction, arranged to intersect the 2D plane from x/c = 0.7 to 1.3 in steps of approximately 0.1. Oil-film interferometry was used to quantify the skin friction over the entire model, from the region upstream of the hump to beyond the reattachment location. Two-dimensionality of the flow in the separated and reattachment region was thoroughly assessed via three methods: by considering the spanwise pressures on the ramp in the separated region, performing 3D PIV measurements in planes perpendicular to the flow direction, and by means of the surface oil-film flow visualization. Spanwise distribution of the surface pressure was also measured on the fore body of the model. It was shown that the spanwise variations of the flow parameters are small (e.g., at the test condition, the pressure variation over the central half of the model (–0.25 ≤ z/c ≤ 0.25) is ∆CP = ±0.005) and that departures from twodimensionality are observed mainly near the wall. At the inflow location (x/c = –2.14), pitot-probe and hot-wire anemometer data were compared with 2D and 3D PIV. Inflow skin friction was also documented using oil-film interferometry. Resulting inflow velocity profile which was used in the numerical studies as a benchmark for imposing boundary conditions at the inflow of the computational domain (see the next section) is shown in Fig.4.

Figure 4: Experimental profile of streamwise velocity at x/c = -2.14 (momentum thickness Re_θ=7200)

Experimental uncertainties reported in the original experimental papers are summarized in Table 2. Note that there is also an operational uncertainty associated with the endplates blockage effect, which should be compensated in the quasi-2D simulations (see next sub-section).