CEE 452/652 Week 11, Lecture 2 Forces acting on articles, Cyclones Dr. Dave DuBois Division of Atmosheric Sciences, Desert Research Institute
Today s toics Today s toic: Forces acting on articles control systems and cyclones Read chaters 3 and 4 Homework on ch. 3, due next Thurs. Select resentation toic by Nov. 15 Reminder: all lecture materials are on course website: htt://wolfweb.unr.edu/homeage/daved/cee_452-652.html 2
Photohoresis Secial case of thermohoresis where the absortion of light creates a temerature gradient in the article Gas immediately surrounding the article takes on the gradient and establishes a radiometric force No thermal gradient in the gas 3
Radiation Pressure Direct transfer of momentum by hoton deflection and absortion Causes a force that is directed away from the source of light Cause for comet s tails to be ushed away from sun Usually done with lasers, exerting iconewtons of force, affecting micron-size articles 4
Otical Levitation Here 10 to 20 micron drolets are levitated (traed) in the laser beam Laser oints u Laser oints u 5
The Drag Force A fluid exerts a drag force on the article, which acts to oose the relative velocity of the article F C A ρ v r D D P F F D density of 1 2 drag force, C N drag coefficient D rojected area of fluid, A kg/m relative velocity, m/s ρ F article, 3 v m 2 r 2 6
Drag Coefficient Usually determined exerimentally for a given Reynolds number Re d v r μ ρ F d article diameter, m μ fluid viscosity, kg/m s 7
Re < 1 Tyes of Flow 8
Drag coefficients for sheres, disks and cylinders Stokes Regime, Re < 1 9
Drag Force for Sheres Calculating drag coefficient as a function of Reynolds number, in Stokes region Re < 1 F 3πμd F D D 1 2 C D A v r ρ F v 2 r Re d v r μ ρ F Solve for C D C D 24 / Re The linear region on revious grah for Re < 1 10
Excetions for Very Small Particles Aly Cunningham correction factor C 1+ 2 d λ / [ ] 0.55 λ 1.257 + 0.4e Drag coefficient for small articles becomes (also called sli correction) C C D D / C d λ mean free ath, m Use correction for articles < 1 µm 11
Forces Acting on Particle Assume article is moving relative to the fluid, there is an External force, F e v r F D F e Newton s 2 nd Law of motion says: F F e D M dv dt r 12
For a Shere Assume Stokes region dv dt r 18μ + ρ d 2 v r F M e Using M Vρ and F 3πμd D Can define characteristic time, τ τ ρ 2 d 18 μ v r 13
For a Shere The general equation of motion for article in Stokes region dv dt With small article correction r v + r τ τ τ C F M e Net external force er unit mass This can be electrostatic field, centrifugal field, gravity, etc. 14
Gravitational Settling For a article settling in still air, the alied force is the gravitational force, F e mg F M e mg m ( ρ ρ air ) Vg ( ρ ρ air ) g ρ V ρ dv dt r vr + τ F M e ( ρ ρ ρ air ) g 15
Gravitational Settling The solution to the velocity equation becomes, v r ( t) v t (1 e t /τ ) Where v t is the terminal settling velocity. Now to derive the exression for v t. At the moment of terminal velocity, drag force is in balance with gravitational force. 16
F F D D 3πμvd Gravitational Settling F G 3πμvd ( ρ and ρ 6 solve for velocity, F air G v ) πd mg 3 ρ g d 2 18μ ( ρv ) g g Terminal Velocity for a shere This is valid for articles in the size range d > 1µm and Re < 1. 17
Gravitational Settling For other article sizes (e.g. other Re #) Or you can use a grah! 18
Terminal Settling Velocity For sheres in air at STP. Particle density given in g/cm 3 19
Aerodynamic Diameter Diameter of a unit density shere that has the same settling velocity as the article in question d a 18μvt Cρ g w d a aerodynamic diameter, m C Cunningham correction factor µ gas viscosity, kg m -1 s -1 v t settling velocity, m s -1 ρ w density of water, kg m -3 g gravitational acceleration, m s -2 20
Particle Collection Imaction article strikes the object Intercetion barely misses the object, but still touches Diffusion randomly hit the object Collection ossible if there are short-range forces to hold them on surface (e.g. van der Waals, electrostatic, chemical) 21
Stoing Distance Consider a shere in the Stokes region rojected with an initial velocity, v o into a motionless fluid. The velocity is given by v( t) v o e t / τ The total distance travelled before it comes to rest is x sto v o 0 v dt τ 22
Particle Penetration Efficiency Define the enetration of a device as the mass fraction that is NOT collected Pt 1 η Pt overall Pt i n i 1 Pt overall overall enetration Pt i enetration of device i 23
Control System Efficiency 24
Cyclone Most widely used article control devices Outer and inner vortex Inexensive No moving arts Can withstand harsh oerating conditions Centrifugal force and inertia cause articles to move outward, collide with outer wall and slide down to bottom of device Used as re-cleaners for more efficient devices such as a baghouse 25
Alications of Cyclones Wood dust Grain and feed Agricultural roducts Leather Rubber Pharmaceuticals Polymer and Plastics Sugar Textiles Brick Fly Ash Chemicals Minerals Ashalt Metal Grindings Pul and Paer 26
Advantages and Disadvantages Advantages Low caital cost Ability to oerate at high temeratures Low maintenance requirements-no moving arts Can have high efficiency for large articles Disadvantages Low efficiency for small articles High oerating costs due to ressure dros 27