Swirling Boundary Layer in Conical Diffuser

Experiments by Clausen et al.

Description

Swirling boundary layer developing in a conical diffuser. The conical diffuser is placed 100 mm downstream of a rotating swirl generator of diameter D=260 mm and discharges into the atmosphere at X=510 mm. It has a 20^o included angle and an area ratio of 2.84.

Flow Characteristics

The swirling flow is created by a rotating cylinder including a honeycomb screen at its inlet. At its outlet, the inlet swirl is close to solid-body rotation. Along the diffuser, the swirl is of sufficient magnitude to prevent boundary layer separation but just insufficient to cause recirculation in the core flow. The axial pressure gradient and the curvature of the streamlines have been found to be the dominant perturbations imposed to the swirling boundary layer as it exits the cylindrical part and enters the conical diffuser. The swirl is responsible for severe radial gradients near the wall for most of the turbulence quantities.

Flow Parameters

• Air with a kinematic viscosity: = 1.5 × 10^-5 m²/s.
• Average axial velocity at inlet (x = -25 mm): U_o = 11.6 m/s.
• Reynolds number: U_oD/ = 202,000.
• Atmospheric pressure at outlet.

Inflow Conditions

The following measurements are provided at station -25, located at x = -25 mm, 75 mm downstream of the swirl generator and 25 mm upstream of the diffuser entrance. The swirl is close to solid-body rotation with a nearly uniform axial velocity in the core region outside the boundary layers. The swirl number is W_max/U_o = 0.59 where W_max is the maximal circumferential velocity. The wall shear stress is /U_o² = 0.00282 in the x direction and /U_o² = 0.00190 in the z direction. The wall streamline angle is = tan^-1(W/U)_y=0 = 34^o.

Profiles of

• First order moments from wall to centreline (files u-25.dat and w-25.dat) U/U_o, W/U_o
• Second order moments for y ranging from 4 to 20 mm (files usq-25.dat, vsq-25.dat, wsq-25.dat, uv-25.dat, uw-25.dat and vw-25.dat)
  • Reynolds stresses: /U_o², /U_o², /U_o², /U_o², /U_o², , /U_o²
  • Turbulent kinetic energy: k/U_o² (deduced)

Experimental Details

Available Measurements

The following measurements are available at 7 stations along the diffuser: x = 025, 060, 100, 175, 250, 330, 405 mm ($$$ in the file names)

• Velocity measurements: Profiles perpendicularly to diffuser wall of:
  • First order moments from wall to centreline (files u$$$.dat and w$$$.dat) U/U_o, W/U_o
  • Second order moments for y ranging from 4 to 20 mm (files usq$.dat, vsq.dat, wsq.dat, uv$.dat, uw$.dat and vw$.dat)
    • Reynolds stresses: /U_o², /U_o², /U_o², /U_o², /U_o², /U_o²
    • Turbulent kinetic energy: k/U_o² (deduced)
• Distribution along the diffuser of: (files Mm$$$.dat)
• Distribution of the wall shear stress: /U_o², /U_o² (files Mm$$$.dat)
• Pressure measurements (file cp.dat): The following measurements are available along the diffuser:
  • Distribution of the static pressure coefficient: C_p

Instructions for calculations

Computational domain:

The calculations should be performed for the whole diffuser (not only for the boundary layer).

Inlet conditions:

The calculation of the duct flow should be started at station x=-25 mm using the experimental values provided as inlet conditions.

Outlet conditions:

The diffuser discharges to the atmosphere at X=510 mm. Zero gradients may be assumed for the flow variables.

Presentation of results:

The following results should be plotted and compared with the data.

At x= 025, 060, 100, 175, 250, 330, 405 mm:

• normalized mean velocity, Reynolds stress and k profiles against y (perpendicular to diffuser wall)

Along the diffuser wall:

• C_pdistribution
• /U_o² and /U_o² distributions.

Previous Numerical Studies

Armfield et al. (ref. 2.) have used a k- and an algebraic Reynolds stress turbulence model with a two-layer wall function to calculate this case. The use of a two-layer, rather than a single-layer, wall function has been found to be necessary to accurately predict the level, location and the axial variation of the near-wall peak in turbulence quantities.

Main references