Resistance to airflow 2019-02-16¢  Airflow for drying Resistance to airflow Resistance of grain to airflow

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  • Airflow for drying Resistance to airflow

    Resistance of grain to airflow Pressure drop due to: Energy loss due to friction & turbulence To overcome this: 1. High pressure at inlet plenum chamber 2. Create a vacuum at the exit

  • Perdition by two math models

  • Pressure drop depends on

    • Rate of airflow

    • Surface and shape characteristics of the product

    • The number, configuration and size of voids

    • The variability of the product size

    • Depth of the product bed

  • Semi-log plots Airflow Vs. Pressure drop per unit depth

  • Mathematical modeling

    ∆𝑝′ = 𝑎𝑄𝑎

    2

    𝑙𝑛(1+𝑏𝑄𝑎) 1

    𝑄𝑎 =exp[A+B*ln∆𝑝′ +C (ln∆𝑝′ ) 2 -------2

    𝑄𝑎= air flow rate m3/s.m2 ∆𝑝 ′

    = pressure drop

    per unit depth Pa/m Hukill & Shredd - 1955

  • Constants

  • Pressure drop calculation for Rice (Calderwood, 1973)

    • SCM- Shredd Curve Multiplier

    • Eq-1 – “a” multiply by SCM

    • Eq-2 – replace Δp‘ by Δp‘/SCM

    • See next slide for SCM values

  • Static pressure drop is also affected by the moisture content of the grain and available fines

    • Corn 12% MC, fines (FM) 0-20% (passing through 4.76 mm sieve)

    • Airflow rate 0.076-0.38 m3/m2.s

    • ∆𝑝′ = 𝐶1𝑄𝑎 + 𝐶2𝑄 2 𝑎 + 𝐶3𝑄𝑎(𝐹𝑀)

    • C1= 436.67

    • C2 = 7363.04

    • C3 = 225.26 (Haque et al 1978)

  • Effect of moisture on Δp’

    • Δp’=AQa+B(Qa) 2+-CMQa

    • M- Moisture content w.b. as a percentage • Insert table 6.6

  • SI

  • Resistance of perforated metal to airflow

    • Δp=10-6/9 [Qa/εQf] 2

    • ε –Void space in grain% (decimal) • Qf

    – opening in floor % (decimal)

  • Pressure losses in ducts

    • Pressure loss is due to :

    • 1. Friction

    • 2.restriction to air (Fittings)

    • 3.Change in direction

    • 4. Enlargement or contraction of cros sectional area

    • Total pressure at any point of a duct = static pressure + Velocity pressure

  • • Static pressure – force perpendicular to the duct wall – independent of air velocity

    • Velocity pressure (head) – depends of movement and density of air (m of air)

    • V2/2g (V–m/s, g – acceleration of gravity-ms- 2)

    • In Pa = V2/2g (1.20)(9.81) = [v/1.29]2

    • 1.20 – air density kg/m3

  • Fans fitted directly to the plenum

    • Vey low air flow velocity- velocity pressure is assumed as 0

    • Total pressure = static pressure

    • Fans connected to the plenum with a duct:

    • Pressure loss in the duct is due to friction loss (dynamic losses)- due to surface friction

    • Dynamic losses are due to cross section changes or direction of flow changes

  • • Total pressure at the fan= total pressure at the plenum + pressure loss at the duct

    • Static pressure at the fan = total pressure – velocity pressure

    • Grain drying systems are designed based on the static pressure

  • Pressure loss – straight ducts

    • Eg. Temperature range 9-31 oC

    • Insert 6-6A friction loss chart

    • Different diameters & flow rates

  • Temp & elevation correction chart

    Use temperature KTand Height multiplier KEto extrapolate the values of the above chart

  • Pressure losses in Elbows

    • Pressure loss in Elbow

    • ΔpT= C(V/1.29) 2

    • C- pressure loss coefficient

    • Or use table values by the supplier

    • Insert table 6-8

  • Changers in cross sectional area

    • Change may be abrupt or gradual (empirical equations)

    • Expansion of Area

    • ΔpT= C1(V1/1.29) 2

    • Area reduction

    • ΔpT= C2(V2/1.29) 2

    • Insert fig 6-8

  • Fans

  • Air movement by an axial fan

  • Velocity of an air duct can be calculated as follows using the measured velocity pressure data

  • Fan performance measurements

  • Distance to get a uniform air flow velocity

  • Example

  • Fan laws

    fa2/ fa1 = (DPT2/ DPT1) 1/2 = (Wfi2/Wfi2)

    1/3

  • Combined flow and power equation

  • Typical fan performance Characteristics curve

  • At 50% free delivery air flow

  • End