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Research Papers: Flows in Complex Systems

Developing Swirl Boundary Layer and Flow Separation at the Inlet of a Coaxial Rotating Diffuser or Nozzle

[+] Author and Article Information
Ferdinand-J. Cloos

Department of Mechanical Engineering,
Technische Universität Darmstadt,
Darmstadt 64287, Hesse, Germany
e-mail: ferdinand.cloos@fst.tu-darmstadt.de

Peter F. Pelz

Professor
Department of Mechanical Engineering,
Technische Universität Darmstadt,
Otto-Berndt-Str. 2,
Darmstadt 64287, Hesse, Germany
e-mail: peter.pelz@fst.tu-darmstadt.de

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 6, 2018; final manuscript received November 14, 2018; published online January 7, 2019. Assoc. Editor: Philipp Epple.

J. Fluids Eng 141(7), 071102 (Jan 07, 2019) (13 pages) Paper No: FE-18-1085; doi: 10.1115/1.4042035 History: Received February 06, 2018; Revised November 14, 2018

When an axial flow enters a rotating diffuser or nozzle, a swirl boundary layer appears at the wall and interacts with the axial boundary layer. Below a critical flow number φc, there is a flow separation, known in the turbomachinery context as part load recirculation. This paper extends the previous work for a cylindrical coaxial rotating pipe still considering the influence of the centrifugal force by varying the pipe's radius, yielding a coaxial rotating circular diffuser or nozzle. The integral method of boundary layer theory is used to describe the flow at the inlet of a rotating circular diffuser or nozzle, obtaining a generalized von Kármán momentum equation. This work conducts experiments to validate the analytical results and shows the influence of Reynolds number, flow number, apex angle, and surface roughness on the boundary layers evolution. By doing so, a critical flow number for incipient flow separation is analytically derived, resulting in a stability map for part load recirculation depending on Reynolds number and apex angle. Hereby, positive apex angles (diffuser) and negative apex angles (nozzle) are considered.

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Figures

Grahic Jump Location
Fig. 1

Flow at the inlet of a rotating diffuser with apex angle α

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Fig. 2

Configuration test rig

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Fig. 3

Swirl boundary layer thickness versus axial coordinate depending on Reynolds number for (a) a nozzle with α = −1.08 deg and (b) a diffuser with α = 1.03 deg and Rz = 0.04% at φ = 0.25. Experiments and solution of the boundary layer theory.

Grahic Jump Location
Fig. 4

Swirl boundary layer thickness versus Reynolds number depending on flow number for (a) a nozzle with α = −1.08 deg and (b) a diffuser with α = 1.03 deg and Rz = 0.04% at z =2. Experiments and solution of the boundary layer theory.

Grahic Jump Location
Fig. 5

Swirl boundary layer thickness versus flow number depending on Reynolds number for (a) a nozzle with α = −1.08 deg and (b) a diffuser with α = 1.03 deg and Rz = 0.04% at z =2. Experiments and solution of the boundary layer theory.

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Fig. 6

Axial boundary layer thickness versus axial coordinate depending on the apex angle. Solution of the boundary layer theory for rotating diffuser and nozzle A0, A, G 0.

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Fig. 7

Axial boundary layer thickness versus axial coordinate depending on Reynolds number for (a) a nozzle with α = −1.08 deg and (b) a diffuser with α = 1.03 deg. Solution of the boundary layer theory for rotating A, G 0 and nonrotating A, G =0 diffuser or nozzle.

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Fig. 8

Axial boundary layer thickness versus flow number depending on Reynolds number for (a) α = −1.08 deg and (b) α = 1.03 deg at z =2. Solution of the boundary layer theory for rotating A, G 0 and nonrotating A, G =0 diffuser or nozzle.

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Fig. 9

Measured self-similar swirl velocity profile versus (a) axial coordinate, (b) Reynolds number, (c) flow number, and (d) apex angle for attached, turbulent, hydraulically smooth flow for Rz = 0.04%

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Fig. 10

Influence of surface roughness on swirl boundary layer thickness versus Reynolds number for α = −1.08 deg (black marker) and α = 1.03 deg (gray marker) at z =2 and φ = 0.35. Data for α = 0.00 deg (white marker) from Ref. [8].

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Fig. 11

Measured self-similar swirl velocity profile versus (a) axial coordinate, (b) Reynolds number, (c) flow number, and (d) apex angle and surface roughness for attached flow

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Fig. 12

Isolines of the axial wall pressure gradient versus flow number and axial coordinate depending on Reynolds number for (a) α = −1.08 deg and (b) α = 1.03 deg. Solution of the boundary layer theory for rotating diffuser or nozzle A, G 0.

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Fig. 13

Measured swirl velocity profile depending on axial coordinate and flow number to indicate incipient flow separation for (a) α = −1.08 deg and (b) α = 1.03 deg at log(Re) = 4.70 and Rz = 0.04%

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Fig. 14

Zero wall shear stress at φc,in and measured incipient separation depending on apex angle for hydraulically smooth flow at log(Re) = 4.70 and Rz = 0.04%. Data for α = 0 from Ref.[8].

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Fig. 15

Experimentally measured φc for fully separated flow depending on Reynolds number and apex angle at the inlet of a rotating diffuser, nozzle, and cylindrical pipe for the hydraulically smooth flow Rz = 0.04%

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Fig. 16

Swirl boundary layer thickness versus (a) axial coordinate, (b) Reynolds number, and (c) flow number for a nozzle with α = −1.83 deg with Rz = 0.04%. Experiments and solution of the boundary layer theory.

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Fig. 17

Swirl boundary layer thickness versus (a) axial coordinate, (b) Reynolds number, and (c) flow number for a nozzle with α = −0.61 deg with Rz = 0.04%. Experiments and solution of the boundary layer theory.

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Fig. 18

Swirl boundary layer thickness versus (a) axial coordinate, (b) Reynolds number, and (c) flow number for a diffuser with α = 0.47 deg with Rz = 0.04%. Experiments and solution of the boundary layer theory.

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Fig. 19

Swirl boundary layer thickness versus (a) axial coordinate, (b) Reynolds number, and (c) flow number for a diffuser with α = 1.55 deg with Rz = 0.04%. Experiments and solution of the boundary layer theory.

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