# Chapter 6 Pneumatic Transport

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1 Chapter 6 Pneumatic Transport 6.1 Pneumatic Transport Use of a gas to transport a particulate solid through pipeline Powder Rotary valve Blower Three major variables for pneumatic conveying - solid mass flow rate - gas mass flow rate - pressure gradient(pressure drop per unit length) 1) Dilute-Phase and Dense-Phase Transport Dilute-Phase High gas velocity (> 20 m/s) Low solids concentration (< 1 % by volume) Low pressure drop (<5 mbar/m) Short-route, continuous transport(< 10 ton/h) Capable under negative pressure Particles ; Behaves as individuals Fully suspended in gas Fluid-particle : dominates Dense-Phase Low-gas velocity (1-5 m/s) High solids concentration (> 30 % by volume) High pressure drop (> 20 mbar/m) Batch or semibatch transport Not-fully suspended in gas Much interaction between particles and between particle and wall

2 2) The Choking Velocity in Vertical Transport Figure Δp/ΔL vs. U (gas superficial velocity) at various solids flow flux G - static head of solids vs. friction resistance Choking velocity, U CH The lowest velocity at which the dilute-phase transport can operate at G given U CH ε CH -U T = G ρ p (1-ε CH ) ρ 0.77 f = 2250D( ε CH -1) [ U CH ε -U T CH ] 2 3) Saltation Velocity in Horizontal Transport Figure Δp/ΔL vs. U (gas superficial velocity) at various solids flow flux G Saltation velocity, U SALT The gas velocity at which the solids to begin to settle out M p ρ f U SALT A = { solid loading 1 10 ( 1440x +1.96) }{ U SALT gd } ( 1100x +2.5) Froude number at saltation where M p : particle mass velocity D : pipe diameter 4) Fundamentals

3 Gas and particle velocity Superficial velocity Actual velocity U fs = Q f A and U fp = Q p A U f = Q f Aε = U fs ε and U p = Q p A(1-ε) = U ps 1-ε * Slip velocity U slip U rel = U f - U p U slip U T for vertical dilute phase flow for U T < 7.6 m/s Continuity Gas mass flow rate Particle mass flow rate M f = AU f ερ f Solid loading M p = AU p (1-ε)ρ p M p M f = U p(1-ε)ρ p U f ερ f Pressure drop From Newton's 2nd law of motion Figure 6.3 Rate of momentum for flowing gas-solid mixture = Net force exerting on the mixture p 1 - p 2 = 1 2 ρ ε f U 2 f ρ p(1-ε) U 2 p + F fw L + F pw L gas solids gas-wall solids-wall acceleration acceleration friction friction +ρ f Lεgsinθ+ρ p L(1-ε)gsinθ gas gravity solids gravity - 3 -

4 * Economy - Specific energy consumption(sec) : energy consumed per unit mass of solids transported per unit distance travelled 5) Design for Dilute Phase Transport To see the dense-phase transport Gas velocity U f ~ 1.5U SALT since U SALT >U CH for systems comprising both vertical and horizontal lines U f ~ 1.5U CH for vertical line only Table. Approximate air velocity for powder transport Powder Wheat, rice, plastic pellets Grains, limestone powder Soda ash, sugar PVC powder Carbon powder Cement Alumina powder Sand U, m/s Pipeline pressure drop F pw L = 0.057GL g D for vertical transport F pw L= 2f p(1-ε)ρ p U 2 pl D = 2f pgu p L D where U p = U f ( d 0.3 f p = 3 8 ρ 0.5 p p for horizontal transport ) and ρ f ρ p C D D d p ( U f- U p U p ) - 4 -

5 C D : drag coefficient (fn of Re p ) Bend ~ 7.5 m of vertical section pressure drop * Downflow through vertical-to-horizontal bend : - greater tendency for saltation - avoided if possible. * Blinded tee bend : Figure prolonging service life due to cushioning effect - with the same pressure drop and solid attrition rate Worked Example 6.1 Equipment Figure 6.5 Positive pressure system Figure 6.6 Negative Pressure system * Centrifugal blowers(fan) vs. Positive displacement blower low pressure high pressure small amount of dust allowed no dust is allowed Some Problems in pneumatic transport - Blocking: possible at high concentration region(around solid feeder and bend) Avoided by feeding at dispersed state sufficient acceleration length adequate bend curvature - Adhesion: possible with moisty, low-melting or electrically charged powder - 5 -

6 Avoided by adequate range of gas velocity - Attrition : possible at bend Avoided by low gas velocity higher solid load changing collision angle and bend material. 6) Dense Phase Transport Flow Patterns Horizontal - Figure 6.7 Saltating flow - unstable, bad flow pattern Discontinuous dense phase flow* Dune Flow / Discrete Plug Flow / Plug Flow* Continuous Dense Phase Flow - requires high pressure adequate for short-pipe transport Equipment Blow tanks : with fluidizing element (Figure 6.13) without fluidizing element (Figure 6.14) Plug formation : air knife (Figure 6.10) air valve (Figure 6.11) diaphragm (Figure 6.12) Plug break-up : bypass (Figure 6.8) pressure actuated valves (Figure 6.9) Design and Operation - Use of test facilities + past experience - Group A, D better than Group B, C for dense phase conveying - Higher permeability: more suitable for plug flow type conveying - Higher air retention: more suitable for dune mode flow - 6 -

7 5.4 Flow of Liquid-Solid Suspension (Slurries) Slurry tank Pump Characteristics of hydraulic transport Log(Δp/L) Slurry Liquid only Saltation Heterogeneous Homogeneous U SALT U tr Log(U f ) Transition velocity Durand(1953) U tr =11.9(U T D) 1/2 d 1/4 p where D : pipe diameter Critical(saltation) velocity Durand(1953) - 7 -

8 Hanks (1980) U c = F L [2gD(ρ p /ρ f -1)] 1/2 where F L : function of d p and ε U c = 3.12(1- ε) ( d p D ) 1/6 [2gD(ρ p /ρ f -1)] 1/2 1) Homogeneous Suspensions Types of Rheological Behavior Type Newtonian Pseudoplastic Dilatant Plastic Examples Slurries at very low solid concentration Slurries at large concentration at very low and very large shear rate Most slurries, muds, polymer solutions, blood, slutions of natural gums, motor oil Suspension of starch, potassium silicate Bread dough, toothpaste, jellies Time-independent Rheological Behavior Plastic Pseudoplastic Shear stress, τ Newtonian Dilatent Time-dependent Rheological Behavior Instantaneous Shear rate, γ (s -1 ) Shear stress, τ Thixotropy Shear stress, τ Antithixotropy Instantaneous Shear rate, γ (s -1 ) Shear rate, γ (s -1 ) e.g., paints, inks, chocolate - 8 -

9 Viscoelastic Behavior - elastic deformation - exerting both normal and shear force to resist flow e.g. rubbery polymer suspension Pressure Drop L P 2 P 1 θ p 1 - p 2 = 1 2 ρ mu 2 f + F mw L +ρ m Lgsinθ (*) where F mw = 4 τ mw L D τ mw : from various models above τ 에대한모델이다를뿐모든수송의계산은액체의경우와같다. 2) Hetrogeneous Suspension Horizontal Flow Friction gradient - civil and mining engineering i f - ( Δp ΔL ) f 1 ρ f g i m - ( Δp ΔL ) m 1 ρ f g j m - ( Δp ΔL ) m 1 ρ m g By experiment Slurry 의농도변화가심한경우는 effective fluid 가생기는 유속에서운전하면안정하다

10 j m Effective fluid C 3 C 2 C 1 Pure fluid(vehicle) U m Typical j m vs. U m with respect to solid volume concentration C Models for solids transport - Suspended load : Particles which are carried by turbulent suspension Solid-wall friction neglected. i m or j m from (*) - Contact load : Particles transported by sliding bed or saltation i m = i f +(S m -1)fn ( V m V 50 ) 0.22 ( V m V 50 ) 1.7 where V 50 : the mixture velocity at which 50% of the solids are conveyed as contact load Vertical Flow - Δ P ΔL = ρ m 'g+f fw +F pw where ρ m ' : In-situ slurry density different with respect to the direction of flow F pw : Given empirically

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