^{1,a)}, Miguel R. Visbal

^{1}and Paul D. Orkwis

^{2}

### Abstract

A numerical study is conducted to examine the vortex structure and aerodynamic loading on a revolving wing in quiescent flow. A high-fidelity, implicit large eddy simulation technique is employed to simulate a revolving wing configuration consisting of a single, aspect-ratio-one rectangular plate extended out a distance of half a chord from the rotational axis at a fixed angle relative to the axis. Shortly after the onset of the motion, the rotating wing generates a coherent vortex system along the leading-edge. This vortex system remains attached throughout the motion for the range of Reynolds numbers explored, despite the unsteadiness and vortex breakdown observed at higher Reynolds numbers. The average and instantaneous wing loading also increases with Reynolds number. At a fixed Reynolds number, the attachment of the leading-edge vortex is also shown to be insensitive to the geometric angle of the wing. Additionally, the flow structure and forcing generated by a purely translating wing is investigated and compared with that of the revolving wing. Similar features are present at the inception of the motion, however, the two flows evolve very differently for the remainder of the maneuver. Comparisons of the revolving wing simulations with recent experimental particle image velocimetry (PIV) measurements using a new PIV-like data reduction technique applied to the computational solution show very favorable agreement. The success of the data reduction technique demonstrates the need to compare computations and experiments of differing resolutions using similar data-analysis techniques.

This work is supported in part by AFOSR under a task monitored by Dr. D. Smith and also by a grant of HPC time from the DoD HPC Shared Resource Centers at AFRL and ERDC. The authors would like to thank Dr. C. Ozen and Professor D. Rockwell of Lehigh University for providing their experimental results and details of the measurements.

I. INTRODUCTION

II. GOVERNING EQUATIONS

III. NUMERICAL PROCEDURE

IV. DETAILS OF THE COMPUTATIONS

A. Geometry and kinematic definitions

B. Computational mesh and boundary conditions

V. RESULTS

A. Effect of spatial resolution

B. Effect of Reynolds number

1. Three-dimensional flow structure

2. Aerodynamic loads

C. Separation of dynamic forces for the revolving wing

D. Rotation versus translation for a fixed Reynolds number

E. Effect of geometric orientation of the wing for a fixed Reynolds number

F. Experimental comparisons at Re = 3600

VI. CONCLUSIONS

### Key Topics

- Rotating flows
- 150.0
- Reynolds stress modeling
- 59.0
- Aerodynamics
- 22.0
- Kinematics
- 17.0
- Coriolis effects
- 16.0

## Figures

Definition of the (a) wing geometry and (b) revolving configuration.

Definition of the (a) wing geometry and (b) revolving configuration.

Rotational angle in time.

Rotational angle in time.

Near-field computational mesh.

Near-field computational mesh.

Effect of grid resolution on (a) the instantaneous flow structure and (b) the aerodynamic loads generated on the revolving wing for Re = 14 500 and θ = 30°.

Effect of grid resolution on (a) the instantaneous flow structure and (b) the aerodynamic loads generated on the revolving wing for Re = 14 500 and θ = 30°.

Instantaneous Q-criterion iso-surfaces (Q = 5) showing the three-dimensional flow structure at various angles during the wing's rotation for 500 ⩽ Re ⩽ 60 000 and θ = 30°. For Re ⩾ 2 000, the time-averaged solution between ϕ = 90° and 270° is provided.

Instantaneous Q-criterion iso-surfaces (Q = 5) showing the three-dimensional flow structure at various angles during the wing's rotation for 500 ⩽ Re ⩽ 60 000 and θ = 30°. For Re ⩾ 2 000, the time-averaged solution between ϕ = 90° and 270° is provided.

Expanded view of the shear-layer substructure present for Re = 14 500 and ϕ = 90°.

Expanded view of the shear-layer substructure present for Re = 14 500 and ϕ = 90°.

Instantaneous surface pressure (−C p ) contours on the suction side of the plate for 200 ⩽ Re ⩽ 60 000 and θ = 30°. For Re ⩾ 2000, the time-averaged solution between ϕ = 90° and 270° is provided.

Instantaneous surface pressure (−C p ) contours on the suction side of the plate for 200 ⩽ Re ⩽ 60 000 and θ = 30°. For Re ⩾ 2000, the time-averaged solution between ϕ = 90° and 270° is provided.

Iso-surfaces of relative total pressure (p t /p t, ref = 0.97 and 0.99) highlighting the vortex core after the unpinning and reconnection of the leading-edge and wing-tip vortices for each Reynolds number. Images correspond to a rotational angle of ϕ = 45°.

Iso-surfaces of relative total pressure (p t /p t, ref = 0.97 and 0.99) highlighting the vortex core after the unpinning and reconnection of the leading-edge and wing-tip vortices for each Reynolds number. Images correspond to a rotational angle of ϕ = 45°.

Contours of relative span-wise velocity at 25%, 50%, and 75% span locations. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Contours of relative span-wise velocity at 25%, 50%, and 75% span locations. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Span-wise locations of flow reversal within the leading-edge vortex core at a rotational angle of ϕ = 90°. Reversed flow was not encountered within the core for Re < 2000.

Span-wise locations of flow reversal within the leading-edge vortex core at a rotational angle of ϕ = 90°. Reversed flow was not encountered within the core for Re < 2000.

Iso-surfaces of total pressure (p t /p t, ref = 0.96 and 0.99) highlighting the sudden expansion of the leading-edge vortex core for Re ⩾ 2000 at a rotational angle of ϕ = 90°.

Iso-surfaces of total pressure (p t /p t, ref = 0.96 and 0.99) highlighting the sudden expansion of the leading-edge vortex core for Re ⩾ 2000 at a rotational angle of ϕ = 90°.

The instantaneous streamlines about the revolving wing for several rotational angles and Re = 500.

The instantaneous streamlines about the revolving wing for several rotational angles and Re = 500.

Effect of Reynolds number on the (a) instantaneous aerodynamic loads, (b) mean forces, and (c) mean force ratio generated on the wing during its revolution at a fixed angle of θ = 30°. Mean lift and drag are taken between ϕ = 45° and 315°.

Effect of Reynolds number on the (a) instantaneous aerodynamic loads, (b) mean forces, and (c) mean force ratio generated on the wing during its revolution at a fixed angle of θ = 30°. Mean lift and drag are taken between ϕ = 45° and 315°.

Span-wise components of the centrifugal, Coriolis, pressure gradient, and total dynamic forces at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Span-wise components of the centrifugal, Coriolis, pressure gradient, and total dynamic forces at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Surface-normal components of the centrifugal, Coriolis, pressure gradient, and total dynamic forces at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Surface-normal components of the centrifugal, Coriolis, pressure gradient, and total dynamic forces at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Contours of centrifugal, Coriolis, pressure gradient, and total dynamic force magnitudes at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Contours of centrifugal, Coriolis, pressure gradient, and total dynamic force magnitudes at 25%, 50%, and 75% span locations for Re = 2000 and ϕ = 90°. A single contour line of relative total pressure (p t /p t, ref = 0.99) is superimposed in each image to highlight the leading-edge vortex. View is directed root-to-tip at ϕ = 90°.

Net contribution of (a) the span-wise and (b) the surface-normal forces across the span. At each span-wise location, the forces are integrated across an area that extends from the wing surface to half a chord off the suction side and 0.1c off the leading- and trailing-edges.

Net contribution of (a) the span-wise and (b) the surface-normal forces across the span. At each span-wise location, the forces are integrated across an area that extends from the wing surface to half a chord off the suction side and 0.1c off the leading- and trailing-edges.

Instantaneous iso-surfaces of relative total pressure showing the vortex flow structure around the rotating and translating wings at . Corresponding images between the two cases match the stroke distance of the mid-span of the wing.

Instantaneous iso-surfaces of relative total pressure showing the vortex flow structure around the rotating and translating wings at . Corresponding images between the two cases match the stroke distance of the mid-span of the wing.

Instantaneous surface pressure distribution for the rotating and translating wings at . Corresponding images between the two cases match the stroke distance of the mid-span of the wing.

Instantaneous surface pressure distribution for the rotating and translating wings at . Corresponding images between the two cases match the stroke distance of the mid-span of the wing.

Instantaneous contours of relative span-wise velocity at 25%, 50%, and 75% span locations for the rotating and translating wings at at a mid-span stroke distance of r g ϕ = y = 1.6.

Instantaneous contours of relative span-wise velocity at 25%, 50%, and 75% span locations for the rotating and translating wings at at a mid-span stroke distance of r g ϕ = y = 1.6.

Aerodynamic loading for the rotating and translating wings at . Bottom image shows the corresponding mid-span stroke travel for both cases.

Aerodynamic loading for the rotating and translating wings at . Bottom image shows the corresponding mid-span stroke travel for both cases.

Effect of geometric angle, θ, on the (a) instantaneous Q-criterion iso-surfaces (Q = 5) and (b) surface pressure for Re = 500. Images correspond to a rotational angle of ϕ = 270°.

Effect of geometric angle, θ, on the (a) instantaneous Q-criterion iso-surfaces (Q = 5) and (b) surface pressure for Re = 500. Images correspond to a rotational angle of ϕ = 270°.

Examination of (a) the mean forces, (b) the lift and drag polar, and (c) the lift-to-drag ratio with varying geometric angle relative to the rotational axis for Re = 500. Force values correspond to the average loads computed for 45° ⩽ ϕ ⩽ 315°.

Examination of (a) the mean forces, (b) the lift and drag polar, and (c) the lift-to-drag ratio with varying geometric angle relative to the rotational axis for Re = 500. Force values correspond to the average loads computed for 45° ⩽ ϕ ⩽ 315°.

Mid-span, planar contours of instantaneous span-wise vorticity, ω z , from the (a) computational solution and (b) experimental measurement at a rotational angle of ϕ = 90° and Reynolds number of 3600.

Mid-span, planar contours of instantaneous span-wise vorticity, ω z , from the (a) computational solution and (b) experimental measurement at a rotational angle of ϕ = 90° and Reynolds number of 3600.

Depiction of (a) the PIV-like sampling of the computational solution and the application of (b) non-overlapping and (c) overlapping local averaging.

Depiction of (a) the PIV-like sampling of the computational solution and the application of (b) non-overlapping and (c) overlapping local averaging.

Mid-span, planar contours of span-wise vorticity for Re = 3600 and θ = 30°.

Mid-span, planar contours of span-wise vorticity for Re = 3600 and θ = 30°.

## Tables

Baseline mesh dimensions.

Baseline mesh dimensions.

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