Tài liệu Compressible flow friction docx

Coefficient λ•In pipelines of gasses flow functional reliance λ = f∆e,Re is valid.It means ,that friction depend from the equivalent roughness and flow regime.. •For copper or plastic ga

COMPRESSIBLE FLOW

FRICTION

Friction in gas pipelines

Coefficient λ

•In pipelines of gasses flow functional reliance λ = f(∆e,Re) is

valid.It means ,that friction depend from the equivalent roughness and flow regime

•For steel material of gas pipes equivalent roughness ∆e = 0,1 mm

•For copper or plastic gas pipes ∆e = 0,0015–0,003 mm only.(see Table)

•According the Moody chart,5 zones of friction factor λ is valid: 1) Laminar flow.For laminar flow friction factor is independent

of relative roughness,and can be estimated by formula:

Re

64

=

λ (1) Where : Re < 2000 –Reinold’s number;

•For the transition II zone,(2000 < Re < 4000),the flow can be

laminar or turbulent(or an unsteady mix of both) depending on the specific circumstances involved.Coefficient λ can be find according empirical formula Zaichenko:

3

0025

=

λ (2)

•For the turbulent flow in hydraulically smooth pipe III zone(Re >

4000 ,and Re < 105,and Re ∆e/d<10) the Blazius formula is fit:

, Re

,

,25

0

3164

0

=

λ (3)

•In the same III zone when pressure is medium or high and plastic pipes is used,the friction loss coefficient λ can be found:

70000 < Re < 700000

, Re

,

,194

0

171

0

=

•For flows with moderate values of Re in the turbulent IV zone(Re

>4000, and 10 < Re ∆e/d <500 ) coefficient λ depend on both - the Re number and relative roughness (λ = f ( Re, ∆e/d )).For this case the

formula of Altshull- Kunigelis can be used:

Re

d d

,

, e

e

25 0

68 11









 ∆ +











 + ∆

=

•For the flows in the rough turbulent V zone(Re >4000, and

Re ∆e/d >500) surface roughness completely dominates the

character of the flow near the wall.(λ = f (∆e/d))From the (5) formula

we can find in that case:

d

,

, e

25

0

11









 ∆

=

λ (6)

Equivalent Roughness ∆efor New Pipes

Commercial steel or wrought

Plastic, glass 0.0 (hydraulically smooth)

•NOTE: Even for hydraulically smooth pipes the friction factor is not zero.That is,there is a head loss in any pipe,no matter how smooth the surface is made.This is a result of the no-slip boundary conditions

that requires any fluid to stick to any solid surface it flows over.There

is always some microscopic surface roughness that produces the no-slip behavior on the molecular level, even when the roughness is

considerably less then the viscous sub layer thickness

•According the practice and investigations of gas flow in pipelines it can be conclude that we can found all 5 flow resistance zones in steel

gas pipe network Table Flow regimes in gas networks, in %

Flow regime zones

Minor pressure network

Medium pressure network

High pressure network

I zone

II zone III zone

IV zone

V zone

8 13 59 20 –

– – 1 86 13

– – – 24 76

•Turbulent flow regime in I.F.Moody diagram is characterized by a family of curves.The lowest curve of the family expresses λ - Re

relationship for ∆e/d = 0.It is a smooth pipe case – pipe wall

roughness elements are hidden in a laminar film and the roughness makes no influence on the friction factor λ

•Each of the rest curves of the family represents definite relative

roughness ∆e/d.Thus, a friction factor here depends from both Re and

∆e/d

•At the right side of the diagram the curves expressing λ = f(Re,∆e/d relationship are parallel to Re axis.It means that Re has no influence

on λ, it depends on relative roughness ∆e/d only.It is a rough pipe

case

•Reynolds number Re and relative roughness ∆e/d are to be known to

read friction factor on the Moody diagram When flow rate Q is

computed and there is no possibility to compute Re ,λ is read from a rough pipe zone of the chart.Then the actual meanings of Re is

computed and friction factor is corrected

Formulae of practical gas pipe

network calculation

•They are derived from the last ones when normal conditions of the gas flowing in the pipe linesis estimated:

ρn = 0,73 kg/m3; νn = 14,3⋅10–6 m2/s; p n = 101,3 kPa

Re =

n

n

d

Q

ν

2827 (7)

Where :

Q n – gas flow rate in normal conditions,in m3/h

•When estimate that

,

l d

Q ,

2

81

0 λρ

=

∆

, Re

,

,25

0

3164

0

= λ

and in the gas pipe line networks of minor pressure we can find:

,

1,75 75

4

75

1 9

-10

6,473 l s l Q

d

Q

,

Here s = 6,473·10–9 d –4,75 – an comparative pressure losses;

Q – flow rate,in m3/h

•When we are calculated pressure losses of plastic pipelines in the medium or high pressure gas networks then:

.l d

Q p

, p

p

n

n 5

2 2

2

2 1

2

62

1 λρ

=

−

=

∆

, Re

,

,194

0

171

0

= λ

l d

Q ,

p p

, ,

n

n 4 806

806

1 194

0

2 2

2 1

•After estimation that for natural gasses ρn = 0,73 kg/m3, νn =

14,3·10–6 m2/s one can found:

= 8,50∆ p2 ⋅10–4 4,806 1,806,

806 ,

1

n

n l S l Q d

Q

S = 8,50 ⋅ 10–4 d–4,806 (11)

Where: Q n – gas flow rate,in m3/h;

∆p2 - pressure loss,in Pa2

The coefficients of minor loss in gas pipelines

•These coefficients are found experimentally

•The meaning of minor coefficient depend on obstacle geometry and measurement as well as flow regimes.( influence of regimes is when Re < 105 and more significant - when laminar flow exist)

•When the distance between neighboring elements of obstacles is small the impact on flow resistance can be That must be estimated

in the case by modification of minor coefficient ζ

•The impact distance can be found by A.D.Altshul formula:

lkl = 0,5 d

λ

ζ

(12)

Where: l kl – impact distance

•When coefficient of minor loss ζ is calculate the velocity is

measured after obstacle in the cross-section

d

Q ,

2

81

0 ρ Σ ζ

=

4 2

2 2 2 2

4 1

2 1 1

1 0 81 81

0

d

Q ,

d

Q ,

pv = ρ ζ = ρ ζ

∆

When: < 0,05 p∆ pv 1 ρ1 = ρ2 and Q 1 = Q 2

4 2

1 2

1 = ζ    

ζ

d

d

(13)

•The triplex tap is assign to section with less flow rate when

calculating

•For gas network of town ∆p v = (5 – 10)% of ∆p L

•For short and complicate inner gas pipelines all ζ must be estimated

SYMBOL MINOR LOSS COEFFICIENT ζ

Sudden contraction

Triplex in the junction

Triplex in the bend

Triplex between the bend

Quadrilateral junction

Quadrilateral bend

Rounded bend 90 0

Cork tap d s = 15 ≥ 20

Valve d = 15

20

25, 32, 40 ≥ 50

Valve d = 50–100 mm

d = 175–200 mm

d ≥ 300 mm

0,35

1

1,5

3,0

2

3

0,3

4 2 11 7 6 5 0,5 0,25 0,15