thermal and fluids in architectural engineering 10...
TRANSCRIPT
1
Thermal and Fluids
in Architectural Engineering
10. External flows
Jun-Seok Park, Dr. Eng., Prof.
Dept. of Architectural Engineering
Hanyang Univ.
Where do we learn in this chaper
1. Introduction
2.The first law
3.Thermal resistances
4. Fundamentals of fluid mechanics
5. Thermodynamics
6. Application
7.Second law
8. Refrigeration,
heat pump, and
power cycle
9. Internal flow
10. External flow
11. Conduction
12. Convection
14. Radiation
13. Heat Exchangers15. Ideal Gas Mixtures
and Combustion
10.1 Introduction
10.2 Boundary Layer Concepts
10.3 Differential Equations of fluid flows
10.4 Drag and Lift concepts
10.5 Drag force
10.6 Lift force
10. External flows
10.1 Introduction
□ External flow- flows around a body
- flows far away a body
□ Drag force- The force that acts parallel to the direction of the fluid flow
- Pressure + Viscous forces
□ Lift force- The force that acts perpendicular to the direction of the
fluid flow
- Pressure + Viscous forces
10.2 Boundary Layer Concepts
Source: Introduction to Thermal and Fluid engineering,Wiely, pp448
10.2 Boundary Layer Concepts
□ inviscid flow (free stream)- a outside of viscous influenced region
- no viscous stresses
□ viscous flow (boundary layer)- a inside of viscous influenced region
- viscous stresses act
□ Boundary layer thickness- boundary layer velocity reaches 99% of the free stream
velocity
- laminar region, transition region, turbulent region
M W - Q ΔE
□ Differential Equations of fluid flows
) (c.s) (c.v
..
유출입량통한를질량변화에서의
SCVC
dAVdVt
)() () (
)()()(...
내부운동량변화유출입량운동량힘주어지는외부에서
VCSCVC
tp dVVt
dAVVdVbFF
) () ( ) (
)(..
변화량내부에너지유출입물질의일에너지와
VCSC
dVet
dAVedWdQ
질량보존방정식(연속방정식)
운동량보존방정식(Euler/Bernoulli/
N-S)
에너지보존방정식
10.3 Differential Equations of fluid flows
10.3 Differential Equations of fluid flows
M W - Q ΔE
□Mass conservation equation
c.s)on flows (mass)c.vin changes (mass
..
SCVC
dAVdVt
c.v
c.s
M W - Q ΔE
))()()(
(
))((
) theory Gauss(
)(
(
..
..
z
w
y
v
x
u
t
Vt
dAVdVV
dVVdVt
dAVdVt
SV
VCVC
SCVC
10.3 Differential Equations of fluid flows
□Mass conservation equation
M W - Q ΔE
□Momentum conservation equation
• 응력(Stress) : 유체의 임의의 체적 요소에 작용하는 힘
-Body force : 체적요소의 표면에 작용하지 않고체적 전체의 질량에 분포되는 힘 (중력, 자력 등), Fb
-Surface force : 체적요소의 표면이 주위와 접촉하여 발생하는 힘, Fs
체적요소 표면에서의 유체 정압(P), Fp>표면에 수직으로 작용하는 힘
점성(Viscous)에 따른 전단응력(τ), Ft> 표면의 접선방향으로 작용하는 힘
Fp
FtFs
10.3 Differential Equations of fluid flows
M W - Q ΔE
VCSCVCtp
VCSCbs
dVVt
dAVVdVbFF
dVVt
dAVVFF
...
..
)()()(
)(
Surface force
Body force Momentum flows
on c.s
Momentum
changes in c.v.
VCVCVCtp dVV
tdVVVdVbFF
...)()()(
10.3 Differential Equations of fluid flows
□Momentum conservation equation
M W - Q ΔE
Surface force (Ft and Fp)
10.3 Differential Equations of fluid flows
□Momentum conservation equation
M W - Q ΔE
- Surface force in each direction
)(3
2)(2
)(3
2)(2
)(3
2)(2
)( ),( ),(
z
w
y
v
x
u
y
w
z
w
y
v
x
u
y
v
z
w
y
v
x
u
x
u
x
w
z
u
z
v
y
w
y
u
x
v
zz
yy
xx
xzzxzyyzyxxy
10.3 Differential Equations of fluid flows
□Momentum conservation equation
M W - Q ΔE
VCSCtp dVV
tdAVVFF
..)()(
Surface force
)(z
ww
y
vv
x
uu
t
wvu
),,(
Momentum flows
on c.s
Momentum
changes in c.v.
10.3 Differential Equations of fluid flows
□Momentum conservation equation
M W - Q ΔE
t
w
z
ww
y
vv
x
uu
Yz
w
y
v
x
u
y
w
zz
v
y
w
yx
w
z
u
xz
pz
t
v
z
ww
y
vv
x
uu
Yz
v
y
w
zz
w
y
v
x
u
y
v
yy
u
x
v
xy
py
t
u
z
ww
y
vv
x
uu
Xz
v
y
w
zy
u
x
v
yz
w
y
v
x
u
x
u
xx
px
)(
)(3
2)(2)()(- :
)(
)()(3
2)(2)(- :
)(
)()()(3
2)(2(- :
Navier-Stokes Equation
10.3 Differential Equations of fluid flows
□Momentum conservation equation
M W - Q ΔE
□ Energy conservation equation
(1) kinetic Energy: V2/2
(2) Potential Energy: b, body force
(3) Internal Energy:e
10.3 Differential Equations of fluid flows
M W - Q ΔE
) (
)2
()2
()2
())(
n)(Conductioflow) mass fromenergy and convextion())((
)(
222
.
.
..
z
Tk
zy
Tk
yx
Tk
x
Vew
z
Vev
y
Veu
xdAVedQ
dAVedQ
dVet
dAVedWdQ
SC
SC
VCSC
열전달전도
10.3 Differential Equations of fluid flows
□ Energy conservation equation
M W - Q ΔE
t
edVe
t
wvuz
wvuy
wvu
z
pw
y
pv
x
puZwYuXudW
dVet
dAVedWdQ
VC
zzzyzxyzyyyxxzxyxx
VCSC
)(
)()()(x
)()()()(
)(
.
..
10.3 Differential Equations of fluid flows
□ Energy conservation equation
M W - Q ΔE
t
e
wvuz
wvuy
wvu
z
pw
y
pv
x
puZwYuXu
z
Tk
zy
Tk
yx
Tk
x
Vew
z
Vev
y
Veu
x
zzzyzxyzyyyxxzxyxx
)(
)()()(x
)()()()(
)2
()2
()2
(222
-Energy including Kinetic energy
10.3 Differential Equations of fluid flows
□ Energy conservation equation
M W - Q ΔE
t
e
z
w
y
v
x
up
z
Tk
zy
Tk
yx
Tk
xz
ew
y
ev
x
eu
)(
-Energy exclude Kinetic energy
10.3 Differential Equations of fluid flows
□ Energy conservation equation
10.4 Drag and Lift Force
• Fluid dynamic forces are
due to pressure and
viscous forces
acting on the body surface.
• Drag: component parallel
to flow direction.
• Lift: component normal to
flow direction.
Source: Fundamentals of Thermal-Fluid
Sciences, McGraw-hill, pp592
10.4 Drag and Lift Concept
□ Lift and drag forces can be found by integrating
pressure and wall-shear stress.
Source: Fundamentals of Thermal-Fluid
Sciences, McGraw-hill, pp592
10.4 Drag and Lift Concept
□ Lift FL and drag FD forces are a function of
density and velocity V.
□ Dimensional analysis gives 2 dimensionless
parameters: lift and drag coefficients.
□Area A can be frontal area (drag applications),
planform area (wing aerodynamics), or wetted-
surface area (ship hydrodynamics).
10.4 Drag and Lift Concept
□ Example : lift and drag coefficients.
Scion XB Porsche 911
CD = 1.0, A = 25 ft2, CDA = 25ft2 CD = 0.28, A = 10 ft2, CDA = 2.8ft2
• Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB
• Source is large CD and large projected area
• Power consumption P = FDV =1/2V3(CDA) for both scales with V3!
10.4 Drag and Lift Concept
□ For applications such as tapered wings, CL and
CD may be a function of span location.
□ For these applications, a local CL,x and CD,x are
introduced and the total lift and drag is determined
by integration over the span L
10.5 Drag force
□Analytic solutions are not possible for external flows- Experiments, numerical analysis, CFD
□ Drag force- drag force on a body is the sum of the pressure and
shear forces acting parallel to the flow velocity
□ In a flat plate- drag force is caused only by shear stress (P=0)
10.5 Drag force
• Fluid dynamic forces are comprised of pressure and friction effects.
• Often useful to decompose,
– FD = FD,friction + FD,pressure
– CD = CD,friction + CD,pressure
• This forms the basis of ship model testing where it is assumed that
– CD,pressure = f(Fr)
– CD,friction = f(Re)
Friction drag
Pressure drag
Friction & pressure dragSource: Fundamentals of Thermal-Fluid
Sciences, McGraw-hill, pp594
10.5 Drag force
• Streamlining reduces drag
by reducing FD,pressure, at the
cost of increasing wetted
surface area and FD,friction.
• Goal is to eliminate flow
separation and minimize
total drag FD
• Also improves structural
acoustics since separation
and vortex shedding can
excite structural modes.
10.5 Drag force
□ Example
10.5 Drag force
• For many geometries, total drag
CD is constant for Re > 104
• CD can be very dependent upon
orientation of body.
• As a crude approximation,
superposition can be used to add
CD from various components of a
system to obtain overall drag.
However, there is no
mathematical reason (e.g., linear
PDE's) for the success of doing
this. Source: Fundamentals of Thermal-Fluid
Sciences, McGraw-hill, pp598
10.5 Drag force
Source: Fundamentals of Thermal-Fluid Sciences, McGraw-hill, pp600
10.5 Drag force
□ Drag on flat plate is solely due to friction created by laminar, transitional, and turbulent boundary layers.
Source: Fundamentals of Thermal-Fluid Sciences, McGraw-hill, pp605
10.5 Drag force
• Local friction coefficient
– Laminar:
– Turbulent:
• Average friction coefficient
– Laminar:
– Turbulent:
For some cases, plate is long enough for turbulent flow,
but not long enough to neglect laminar portion
Source: Fundamentals of Thermal-Fluid
Sciences, McGraw-hill, pp607
10.6 Lift force
• Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction.
• Lift coefficient
• A=bc is the planform area
Source: Fundamentals of Thermal-Fluid Sciences,
McGraw-hill, pp614
10.6 Lift force
• Thin-foil theory shows that CL≈2 for < stall
• Therefore, lift increases linearly with
• Objective for most applications is to achieve maximum CL/CD
ratio.
• CD determined from wind-tunnel or CFD (BLE or NSE).
• CL/CD increases (up to order 100) until stall.
Source: Fundamentals of Thermal-
Fluid Sciences, McGraw-hill, pp616