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Ventilation10 Duct Design

Vladimír Zmrhal (room no. 814)

http://users.fs.cvut.cz/~zmrhavla/index.htmDpt. Of Environmental Engineering

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Laminar and turbulent flows

Reynolds number

laminar flow Re 2300

transitional flow 2300 < Re < 10000

fully turbulent flow Re > 10 000

air… kinematic viscosity [m2/s] = 14,5.10-6 [m2/s]

Rewd

2

3

Flow characteristics

n …exponent f(Re)

1/

max

1n

w yw r

2

1/

max2

1

11 2

s

sS

n

sS

V w S

w wdSr

yw w ydy

r r

max

0,817sww

Laminar and turbulent flows

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Bernoulli equation (energy)

Pressures in the duct

Pressure losses

2 21 1 1 2 2 22 2s sp h g w p h g w p

2

2s d

wp p p p

2 21 1 2 2 1 22 2s s t tp p w p w p p

3

5

friction

local pressure losses

2 2

.2 2

lf

t

pp

l w wp R l Z

d

22

2t

l wp kV

d

Pressure losses

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Laminar flow

Turbulent flow

Colebrook (1939)/d – relative roughness

Smolik (1959) for = 0,15

64Re

0,125 0,11

0,0812Re d

1 / 2,512log

3,71 Re

d

Friction losses

4

7

Turbulent flow

for smooth pipes and duct (plastic)

5000 < Re 80 0004

0,3164

Re

Friction losses

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Material (mm)

Galvanized steel 0,15

Concrete duct – smooth surface 0,5

Concrete duct – rough surface 1,0 – 3,0

Smooth brass, copper 0,015

Hose pipe 0,6 - 3

Plastic pipe 0,007

Roghness height of the conduit wall surfaces

Friction losses

5

9

Hydraulic diameter

Rectangular ducts

4 4 22( )h

A ab abd

O a b a b

dC

1,1 0,1b

Ca

Friction losses

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Moody‘s diagram

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Local pressure losses are caused by the fluid flow through the duct fittings: which change the direction of the flow (elbows, bands, etc.)

affect the flow in the straight duct with constant cross-section(valves, stopcocks, filters etc.).

… local loss coefficient (experiments - see Idelchik 1986)

Borda loss prediction

Local pressure losses

2

2l d

wp p

12

109876543210

Local pressure losses

7

13

109876543210

0,08

1,11ab

Local pressure losses

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Duct design

Methods

velocity method

equal-friction method

static regain method

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Velocity method

Duct design procedure:

1) Find the main line

Rule no. 1: the main line is the maximum pressure loss line

(longest line, most segment line (?))

2) Air flow rate V (m3/h) in duct sections is known

3) Selection of the air velocity in the duct w

Rule no. 2: Air velocity increase towards the fan

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Air velocity w (m/s)

Main section Side section

Ventilation and low-pressure air-conditioning

recomend. max. recomend. max.

- residential buildings 3,5 - 5 6 3 5

- public buildings 5 – 7 8 3 – 4,5 6,5

- industry 6 - 9 11 4 - 5 9

High-pressure air-conditioning 8 - 12 15 - 20 8 - 10 18

Velocity method

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4) duct area A (m2) diameter d or a x b

nominal diameter dN or aN x bN

Rule no. 3: Duct sizes: 80, 100, 125, 140, 160, 180, 200, 250, 315,355, 400, 450, 500, 560, 630, 710, 800, 900, 1000, 1120, 1250,1400, 1600, 1800, 2000

4Vd

w

Velocity method

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5) dN real velocity wreal

6) calculation of dynamic pressure pd

7) Reynolds number friction coefficient 8) local loss coefficients 9) pressure loss of the duct section pz,i

2

4real

N

Vw

d

2

,, 2

i iz i

s i

l wp

d

Velocity method

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Rule no. 4: Balancing

10) total pressure loss is the sum of the duct sections pressurelosses

,ext z ip p

, , , ,z F z E z G z Ip p p p

Velocity method

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, , , , ,z z A z B z D z G z Ip p p p p p

1 2 3 4 5cV V V V V V

Velocity method

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Example

Example 1: Dimension the air duct system. Use the velocity method. air velocity w = 6 - 10 m/s,air density = 1,2 kg/m3, kinematic viscosity = 14,5.10-6 m2/s.

V1 = 9 000 m3/h

V2 = 1 440 m3/h

V3 = 2 160 m3/h

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Example

Example 1:

2

0,125 0,11

2 2

,

4 4

0,0812Re

Re

2 2

( )

calc N realN

realt N

N

real realf l

t i f l el

V VD D w

w D

w D

D

w wlp p

D

p p p p

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Example

Line l V V wcalc Dcalc DN wreal pd Re l pf pl pel pt

- m m3/h m3/s m/s mm mm m/s Pa - - Pa - Pa Pa Pa

0,41 19

0,96 0

0,46 0

2,04 0

TOTAL XX

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Equal-Friction Method

Duct design procedure:

1) selection of pressure loss per unit length R = 0,8 – 4 Pa/m

2) local pressure losses friction in straight duct with equivalentlength

3) duct section pressure loss

212

wR

d

2 2

2 2e

e

l w wl d

d

z ep R l l

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Friction chart

Choice:

R = 1 Pa/m

Air flow rate:

1 000 m3/h

diameter D:

280 mm

Velocity :

w = 4,5 m/s

Equal-Friction Method

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Static Regain Method

for uniform air supply

constant static pressure before thebranch

Principles

cross section reduction afterbranches to change the dynamicpressure

decreasing of dynamic pressurebalances the pressure losses in theduct section

3 2 3 2z d dp p p

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Assumptions:

V = const.

b = const.

i = n, n - 1, …. 1

calculation of dimension a

1

1 11

11 i

i i ii

ia a l

d i

Static Regain Method

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Deduction:

kde 2 2 2

1 1 2 1

1 2 2 2l w w wd

2 1 2 1z d dp p p

1 21 2

1 2

,V V

w wa b a b

2 2 2

1 1 2 12 2 2 2 2 2

1 1 2 1

l V V Vd a b a b a b

Static Regain Method

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2 2 21 1 2 1

2 2 21 1 2 1

l V V Vd a a a

1 2, 2V V V V

2 22 2 2 2 2 2 21 1

2 2 2 2 2 21 1 1 2 1 1 1

1 11 1 2 i

i i i i

i il V V V l id a a a d a a a

22 2 21 11 1 1

1 1

11 1 1i i

i i i i ii i

l ia i a i a a l

d d i

Static Regain Method

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Duct systems

Shapes

rectangular

round

flexible duct

Materials

steel galvanized

aluminium

plastic PVC

textile

ALP

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Duct leakage rate

where Sv … duct surface [m2]

0,67vV m p S

Duct systems

Class Charakteristics of the leakage pathm [m3/s per m2]

A 0,027 . 10-3

B 0,009 . 10-3

C 0,003 . 10-3

D 0,001 . 10-3

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Purpose

condensation risk

heat losses/gains

Thickness of TI

indoor 45 – 60 mm

outdoor 80 – 100 mm (with sheet covering)

Thermal insulation

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Thank you for your attention