Laminar and turbulent flows

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Ventilation 0 Duct Design Vladimír Zmrhal (room no. 84) http://users.fs.cvut.cz/~zmrhavla/index.htm Dpt.

1 Ventilation 0 Duct Design Vladimír Zmrhal (room no. 84) Dpt. Of Environmental Engineering Laminar and turbulent flos Reynolds number d Re = ν laminar flo Re 300 transitional flo 300 < Re < 0000 fully turbulent flo Re > ν air kinematic viscosity [m /s] = 4,5.0-6 [m /s]

2 Laminar and turbulent flos Flo characteristics max y = r / n V = S s s = πr S ds / n y s = max π ydy πr S r n exponent f(re) s max = 0,87 3 Pressure losses Bernoulli equation (energy) ρ ρ p + h ρg + = p + h ρg + + p z, Pressures in the duct pc = p + pd = p + ρ ρ ρ p = p + p + = p p z, c c 4

3 Pressure losses friction local pressure losses l pz, = λ ρ + ζ ρ = R. l + Z d p t p l pz, = λ + ζ ρ = kv d m 5 Friction losses Laminar flo 64 λ = Re Turbulent flo ε / d,5 = log + λ 3,7 Re λ 0,08 λ = Re d 0,5 0, Colebrook (939) ε/d relative roughness Smolik (959) for ε = 0,5 6 3

4 Friction losses Turbulent flo 0,364 λ = 4 Re for smooth pipes and duct (plastic) 5000 < Re Friction losses Roghness height of the conduit all surfaces Material ε (mm) Galvanized steel 0,5 Concrete duct smooth surface 0,5 Concrete duct rough surface,0 3,0 Smooth brass, copper 0,05 Hose pipe 0,6-3 Plastic pipe 0,

5 Friction losses Hydraulic diameter d h 4A 4ab ab = = = O ( a + b) a + b Rectangular ducts λ = d Cλ C =, 0, b a 9 Moody diagram 0 5

Local pressure losses Local pressure losses are caused by the fluid flo through the duct fittings: hich change the direction of the flo (elbos, bands, etc.

6 Local pressure losses Local pressure losses are caused by the fluid flo through the duct fittings: hich change the direction of the flo (elbos, bands, etc.) affect the flo in the straight duct ith constant cross-section (valves, stopcocks, filters etc.). pm = ζ pd = ζ ρ ζ local loss coefficient (experiments - see Idelchik 986) Borda loss prediction Local pressure losses

Local pressure losses ζ, a = b 0,08 0 9 8 7 6 5 4 3 0 3 Duct design

7 Local pressure losses ζ, a = b 0, Duct design Methods velocity method equal-friction method static regain method 4 7

8 Velocity method Duct design procedure: ) Find the main line Rule no. : the main line is the maximum pressure loss line (longest line, most segment line (?)) ) Air flo rate V (m 3 /h) in duct sections is knon 3) Selection of the air velocity in the duct Rule no. : Air velocity increase toards the fan 5 Velocity method Ventilation and lo-pressure airconditioning Main section Air velocity (m/s) Side section recomend. max. recomend. max. - residential buildings 3, public buildings ,5 6,5 - industry High-pressure air-conditioning

9 Velocity method 4) duct area A (m ) diameter d or a x b d = 4V π nominal diameter d N or a N x b N Rule no. 3: Duct sizes: 80, 00, 5, 40, 60, 80, 00, 50, 35, 355, 400, 450, 500, 560, 630, 70, 800, 900, 000, 0, 50, 400, 600, 800, Velocity method 5) d N real velocity real real 4V = πd N 6) calculation of dynamic pressure p d 7) Reynolds number friction coefficient λ 8) local loss coefficients ζ 9) pressure loss of the duct section p z,i l i i pz, i = λ + ζ ρ ds, i 8 9

10 Velocity method Rule no. 4: Balancing p + p = p + p z, F z, E z, G z, I 0) total pressure loss is the sum of the duct sections pressure losses p = p ext z, i 9 Velocity method p = p + p + p + p + p z z, A z, B z, D z, G z, I V = V + V + V + V + V c

11 Example Example : Dimension the air duct system. Use the velocity method. air velocity = 6-0 m/s, V air density ρ =, kg/m 3 = m 3 /s, kinematic viscosity ν = 4,5.0-6 m /s. V = 440 m 3 /s V 3 = 60 m 3 /s Example Line l V V calc D calc D N real p d Re l R.l Σζ Z p el p z - m m 3 /h m 3 /s m/s mm mm m/s Pa - - Pa - Pa Pa Pa TOTAL 0,4 9 0,96 0 0,46 0,04 0 XX

12 Equal-Friction Method Duct design procedure: ) selection of pressure loss per unit length R = 0,8 4 Pa/m R = λ ρ d ) local pressure losses friction in straight duct ith equivalent length le λ ρ = ζ ρ le = d 3) duct section pressure loss z ( ) p = R l + l e ζ d λ 3 Equal-Friction Method Friction chart Choice: R = Pa/m Air flo rate: 000 m 3 /h diameter D: 80 mm Velocity : = 4,5 m/s 4

13 5 Static Regain Method for uniform air supply constant static pressure before the branch Principles cross section reduction after branches to change the dynamic pressure decreasing of dynamic pressure balances the pressure losses in the duct section p = p p z 3 d 3 d 6 3

14 Static Regain Method Assumptions: V = const. b = const. i = n, n -,. calculation of dimension a λi i = i + i di a a l i i 7 Static Regain Method Deduction: p = p p z d d l λ ρ = ρ ρ d kde V V =, = a b a b l V V V λ = d a b a b a b 8 4

Static Regain Method l V V V λ = d a a a V =

rectangular round flexible duct Materials

15 Static Regain Method l V V V λ = d a a a V = V, V = V ( i ) ( i ) l V V V li λ + = λ i + = d a a a di ai ai ai l i ( ) λi i ai + λ i = ai i ai ai = + li di di i 9 Duct systems Shapes rectangular round flexible duct Materials steel galvanized aluminium plastic PVC textile ALP 30 5

16 Duct systems Duct leakage rate 0,67 V = m p S v here S v duct surface [m ] Class Charakteristics of the leakage path m [m 3 /s per m ] A 0, B 0, C 0, D 0, Thermal insulation Purpose condensation risk heat losses/gains Thickness of TI indoor mm outdoor mm (ith sheet covering) 3 6

17 Thank you for your attention 33 7

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts. Flow in Pipes and Ducts. Flow in Pipes and Ducts (cont d)

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts. Flow in Pipes and Ducts. Flow in Pipes and Ducts (cont d) ME 305 Fluid Mechanics I Flow in Pipes and Ducts Flow in closed conduits (circular pipes and non-circular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared