Wind Tunnel Modeling for Civil Engineering Applications!

Dorothy Reed!Civil & Environmental Engineering!

Civil Engineering Modeling!

•  Boundary Layer Modeling essential for most civil engineering applications: ASCE7-10 requirements must be met!

•  Aeronautical (short) tunnel OK for bridge decks and whenever the modeling of the atmospheric boundary layer not critical!

Questions of scale!

•  Dimensionless Numbers!•  Similarity Criteria!

Basic Similarity Requirements!

•  Conservation equations for mass, momentum and energy!

•  Equations of state of the fluid!

F =d!"U #D$n% µ&g'

F is a force

=d

"dimensionally equal to"! is densityU is the wind velocityD is the relevant dimensionn is a frequencyµ is a viscosityg is gravitational acceleration

Dimensional!Analysis!

Dimensionally, all quantities are limited to a combination of mass

M, length L and time T. "Rewrite the force equation in

terms of these three…!

MLT 2

! " #

$ % & =d ML3

! " #

$ % & ' LT! " #

$ % & (

L' 1T! " #

$ % & ) MLT

! " #

$ % & * LT 2! " #

$ % & +

M ,1= ' + *L,1= -3' + ( + . -* + +T,-2 = -( -) -* - 2+/' =1-*( = 2 -* -) - 2+. = 2 -* + ) + +

F =d!1"#U 2"#"$ "2%D2"# +$ +% n$ µ#g%

=d!U 2D2 Dn

U& ' (

) * + $ µ!UD

&

' (

)

* + #DgU 2

& ' (

) * + %

, F!U 2D2 =

d DnU

& ' (

) * + $ µ!UD

&

' (

)

* + #DgU 2

& ' (

) * + %

DnsU

= S !Strouhal Number

where ns ! shedding frequencyDnmU

! reduced frequency

where nm ! mechanical frequency of vibrationUnmD

! reduced velocity

nzU

! Monin or similarity coordinate

UDfc

= Ro Rossby Number where n = fc = Coriolis Parameter

Interpretations of Ratio Number One !

µ!UD

is the reciprocal of the Reynold's Number, i.e.

Re = !UDµ

= UD"

where " = µ!# kinematic molecular viscosity

" turb $ u*z0

Ratio Number 2!

DgU 2 = Fr ! Froude Number

If thermal effects are important :

Pr =µCp

K! Prandtl Number

or

Ri = "##

DgU 2

$ % &

' ( ) ! Richardson Number

K = thermal conductivity# = temperature

Ratio Number 3!

!s

! f

"

# $ $

%

& ' ' m

= !s

! f

"

# $ $

%

& ' ' p

!s = density of the structure! f = density of the fluidModel density scaling = Prototype density scaling

Basic Scaling Considerations!

!L = Dm

Dp

Length Scale

!v = Um

U p

Velocity Scale

!p = "m

"p

Density Scale. Usually =1.

From dimensional analysisDnU

! " #

$ % & m

= DnU

! " #

$ % & p

Frequency Scale

'n = 'v'L

= 1'T

Consider Froude Number similitude

U 2

Dg!

" #

$

% & m

= U 2

Dg!

" #

$

% & p

In scaling terms :'v

2

'L'g= 1

Note that 'g =1 because we can't change this easily.

('v = 'L

or 'n = 1'L

Consider Reynolds Number similitude

!UDµ

"

# $

%

& ' m

= !UDµ

"

# $

%

& ' p

This requires (v(L =1or

(v = 1(L

!The two requirements are

"v = "Land

"v = 1"L

.

This only holds if"L = 1.That is, if full - scale = model scale.Therefore, we have a REYNOLDS NUMBER VIOLATION.

What does this mean?!

•  Tunnel modeling for Reynolds Number sensitive dynamic effects is difficult if not impossible.!

•  Usually if the Reynolds Number is at least 104, then the violation isn’t too significant.!

•  Reynolds Numbers for full-scale applications are usually about 108 !

ASCE7-10 Chapter 31, p. 357!

•  Seven Test Conditions!–  1. The natural atmospheric boundary layer has

been modeled to account for variation of wind speed with respect to height.!

–  2. The relevant macro (integral) length and micro length scales of the longitudinal component of atmospheric turbulence are modeled to approximately the same scale as that used to model the building or structure!

ASCE7 continued!

–  3. …modeled building..and surrounding structures and topography are geometrically similar…!

–  4. The projected area of the modeled building ot other structure and surroundings is less than 8% of the test cross-sectional area unless correction is made for blockage.!

–  5. The longitudinal pressure gradient in the wind tunnel test section is accounted for;!

ASCE7 continued!

–  6. Reynolds number effects on pressures and forces are minimized;!

–  7. Response characteristics of the wind-tunnel instrumentation are consistent with the required measurements.!

Section 31.3!

•  Dynamic Response!•  Tests for the purpose of determining the

dynamic response of a building or other structure shall be in accordance with section 31.2 [previous section]. The structural model and associated analysis shall account for mass distribution, stiffness and damping.!

Boundary Layer Modeling!

•  Pressure loadings for urban settings!•  Pedestrian comfort criteria!•  Agricultural considerations!•  Air pollution studies!

BRE wind tunnel, Tsukuba, Japan! Sample pressure data listing, Peterka & Associates!

Other types of testing!

•  Short sections!•  Can be open or return!•  Bridge decks are the primary application;

especially for long spans!•  Full scale testing of low-rise buildings for

hurricane-type winds under discussion!

Akayama (Honshu-Shikoku Bridge Authority), Reed & !Sato (PWRI) in front of Tatara Bridge (1999)!

PWRI tunnel facility at Tsukuba 1999! Akashi Model in tunnel at Tsukuba!