Fahrzeug- und
Windradaerodynamik
Geometrically simple bodies
Dr.-Ing. A. Henze, Prof. Dr.-Ing. W. Schröder
Institute of Aerodynamics, RWTH Aachen University
Circular cylinder
Experimental conditions
• large models for large Re-number (conflict with Mach number)
• large models large obstruction
• sensitive against disturbances like turbulence in the inflow, wall roughness
• Separation and turbulence are threedimensional Influence of span width
Frictionless solution
• agreement on front side
• disagreement on rear side
• Asymmety
Foto: S. Hucho
• alternating vortices
• oscillating lateral force
Circular cylinder
• pressure distribution on the surface of the cylinder
• comparison between ideal and real flow
• for low Re numbers: separation in front of the thickest point
large dead water region, large under pressur
large drag
• for higher Re numbers: separation behind the thickest point
turbulent boundary layer stronger pressure gradient
smaller wake smaller drag
Very simple sketch, „Textbook plot“
S. Hoerner, Fluid dynamic drag, Midland Park, New Jersey
Selbstverlag des Autors, 1965
Circular cylinder
Pressure distribution at the circular cylinder
Comparison between different authors
Real progress of drag coefficient
Circular cylinder
Re → 0
Creeping symmetric flow, extremely
high drag, z.B.: thin wires
Til A: 3-4 < Re < 30-40
Laminar boundary layer separates at Re= 40,
symmetric, steady
xR increases with increasing Re zu, cpB increases,
Drag decreases
A-B: 40 < Re < 140-200
At Re = 50 unsteady, asymmetric, alternating
vortices, Kármán vortex street, vortices are
Stable til 80 D, Base pressure decreases but the
width of the dead water region also decreases
→ drag decreases
B-C: 190 < Re < 260
First small longitudinal vortices, 3-D
Dependency of the attributes of the cylinder
on the Re number, a) Drag, b) Base pressure
c) Strouhal number
Circular cylinder
C-D: 260 < Re < 103
Pulsating longitudinal vortices, turbulent
Reynolds stresses decrease, dead water
Becomes shorter, but base pressure increases,
Drag decreases
D-E: 1000 < Re < 2* 105
laminar boundary layer, separation angle at 80°,
uniform formation of vortices, constant
Strouhal number, ‚aeolian harp‘ at Re ~ 1000
2-d vortices dissipate fast, dead water becomes
shorter, vortices approximate to the base,
Base pressure decreases, high drag
E-F-G: 2* 105 < Re < 4* 105
``critical``, laminare boundary layer separates,
Bubble, turbulent reattachment, turbulent separation at 140°, narrow dead water, drag
Decreases rapidly, frequency increases
Dependency of the attributes of the cylinder
on the Re number, a) Drag, b) Base pressure
c) Strouhal number
F: initially one sided bubble asymmetric,
Lift, slightly higher Re number: double sided
bubble
Circular cylinder
G-H: 4*105 < Re < 7 * 105
„supercritical“, symmetrical, laminar separation,
Transition, reattachment, high cross velocities,
boundary layer is more stable against pressure
increase, large base pressure, low drag
H-J: Re > 7 * 105
„transcritical“, turbulent transition moves upstream,
no bubble, separation moves upstream, large
dead water, constant drag cw = 0.7,
narrow band frequency spectrum, Sr = 0.28,
uniform structures
Dependency of the attributes of the cylinder
on the Re number, a) Drag, b) Base pressure
c) Strouhal number
Circular cylinder
Kármán vortex street, Re=105
Van Dyke, An album of fluid motion, 1997
Length of dead water
a) Very small Re
b) Small and larger Re
Circular cylinder
a)
Characteristics of the BL at the cylinder
a) Transition laminar/turbulent
b) Separation
b)
Transition laminar/turbulent at a
separation bubble
Different separation point
lateral force
Circular cylinder
Measurements in Göttingen high pressure tunnel
(HDG, DLR, 1985)
• Step A: one sided transition
• Step B: two sided transition
The lateral force is similar to the drag, only one third
Drag is dynamic, RMS is 5 times smaller than than
RMS of the lateral force
RMS = Root Mean Square
Circular cylinder
Different flow patterns
• Instabilities form in the wake and move
upwards
• Instabilities reach the dead water
• Shear layers become unstable
• boundary ayer becomes turbulent
M.V. Morkovin, Flow around circular cylinder- A kaleidoscopeof challenging
Fluid phenomena, A.G. Haswen, Symposium on fully separated flows,
Amer. Soc. Of Mech. Eng., 1964
Circular cylinder
Effect of roughness on drag and
Strouhal number
Drag as a function of turbulence degree
• critical Re number becomes smaller
• critical region becomes larger
• B.L. transition earlier
• later separation