# bin and hopper design lecture

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Bin and Hopper Design

Karl Jacob The Dow Chemical Company Solids Processing Lab [email protected]/17/00 KVJ 1

The Four Big Questionss s s s

What is the appropriate flow mode? What is the hopper angle? How large is the outlet for reliable flow? What type of discharger is required and what is the discharge rate?

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Hopper Flow Modess

s

s

Mass Flow - all the material in the hopper is in motion, but not necessarily at the same velocity Funnel Flow - centrally moving core, dead or non-moving annular region Expanded Flow - mass flow cone with funnel flow above itKVJ 3

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Mass Flow

D

Does not imply plug flow with equal velocity

Typically need 0.75 D to 1D to enforce mass flow

Material in motion along the walls

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Funnel Flow

Active Flow Channel

Dead or nonflowing region

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Expanded Flow

Funnel Flow upper section

Mass Flow bottom section

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Problems with Hopperss

Ratholing/Piping

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Ratholing/Piping

Stable Annular Region

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Void

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Problems with Hopperss s

Ratholing/Piping Funnel Flow

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Funnel Flow-Segregation -Inadequate Emptying -Structural Issues

Coarse

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Fine

Coarse

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Problems with Hopperss s s

Ratholing/Piping Funnel Flow Arching/Doming

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Arching/Doming

Cohesive Arch preventing material from exiting hopper

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Problems with Hopperss s s s

Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow

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Insufficient Flow- Outlet size too small - Material not sufficiently permeable to permit dilation in conical section -> plop-plop flow

Material under compression in the cylinder section

Material needs to dilate here

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Problems with Hopperss s s s s

Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing

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Flushings

Uncontrolled flow from a hopper due to powder being in an aerated state - occurs only in fine powders (rough rule of thumb - Geldart group A and smaller) - causes --> improper use of aeration devices, collapse of a rathole

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Problems with Hopperss s s s s s

Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate EmptyingKVJ 17

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Inadequate emptyingUsually occurs in funnel flow silos where the cone angle is insufficient to allow self draining of the bulk solid.

Remaining bulk solid

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Problems with Hopperss s s s s s s

Ratholing/Piping Funnel Flow Arching/Doming Insufficient Flow Flushing Inadequate Emptying Mechanical ArchingKVJ 19

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Mechanical Archings

s

Akin to a traffic jam at the outlet of bin - too many large particle competing for the small outlet 6 x dp,large is the minimum outlet size to prevent mechanical arching, 8-12 x is preferred

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Problems with HoppersRatholing/Piping s Funnel Flow s Arching/Doming s Insufficient Flow s Flushing s Inadequate Emptying s Mechanical Arching KVJ 3/17/00 s Time Consolidation - Cakings

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Time Consolidation - Cakings

s

Many powders will tend to cake as a function of time, humidity, pressure, temperature Particularly a problem for funnel flow silos which are infrequently emptied completely

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Segregations

Mechanisms - Momentum or velocity - Fluidization - Trajectory - Air current - FinesKVJ 23

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What the chances for mass flow?Cone Angle Cumulative % of from horizontal hoppers with mass flow 45 0 60 25 70 50 75 70 *data from Ter Borg at Bayer3/17/00 KVJ 24

Mass Flow (+/-)+ flow is more consistent+ reduces effects of radial segregation + stress field is more predictable + full bin capacity is utilized + first in/first out - wall wear is higher (esp. for abrasives) - higher stresses on walls - more height is required3/17/00 KVJ 25

Funnel flow (+/-)+ less height required - ratholing - a problem for segregating solids - first in/last out - time consolidation effects can be severe - silo collapse - flooding - reduction of effective storage capacity3/17/00 KVJ 26

How is a hopper designed?s

s

Measure - powder cohesion/interparticle friction - wall friction - compressibility/permeability Calculate - outlet size - hopper angle for mass flow - discharge ratesKVJ 27

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What about angle of repose?Pile of bulk solids

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Angle of Reposes

Angle of repose is not an adequate indicator of bin design parameters

In fact, it (the angle of repose) is only useful in the determination of the contour of a pile, and its popularity among engineers and investigators is due not to its usefulness but to the ease with which it is measured. - Andrew W. Jenikes

Do not use angle of repose to design the angle on a hopper!KVJ 29

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Bulk Solids Testings s

s s

Wall Friction Testing Powder Shear Testing - measures both powder internal friction and cohesion Compressibility Permeability

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Sources of Cohesion (Binding Mechanisms)s

s

Solids Bridges -Mineral bridges -Chemical reaction -Partial melting -Binder hardening -Crystallization -Sublimation Interlocking forcesKVJ

s

s

Attraction Forces -van der Waals -Electrostatics -Magnetic Interfacial forces -Liquid bridges -Capillary forces31

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Testing Considerationss

Must consider the following variables - time - temperature - humidity - other process conditions

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Wall Friction TestingWall friction test is simply Physics 101 - difference for bulk solids is that the friction coefficient, , is not constant.

P 101N

F = N

F

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Wall Friction TestingJenike Shear TesterBracket WxA Cover Ring SxA Bulk Solid

Wall Test Sample3/17/00 KVJ 34

Wall Friction Testing ResultsWall shear stress, Wall Yield Locus (WYL), variable wall friction Wall Yield Locus, constant wall friction Normal stress,

Powder Technologists usually express as the angle of wall friction,

= arctan 3/17/00 KVJ 35

Jenike Shear TesterWxA

Bracket

Cover Ring

SxA

Bulk Solid Bulk Solid

Shear plane3/17/00 KVJ 36

Other Shear Testerss s s s

Peschl shear tester Biaxial shear tester Uniaxial compaction cell Annular (ring) shear testers

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Ring Shear TestersArm connected to load cells, S x A

Bulk solid

WxA3/17/00 KVJ

Bottom cell rotates slowly38

Shear test data analysis

C

fc

1

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Stresses in Hoppers/Siloss s

Cylindrical section - Janssen equation Conical section - radial stress field Stresses = Pressures

s

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Stresses in a cylinderConsider the equilibrium of forces on a differential element, dh, in a straightsided siloPv A D dh dh (Pv + dPv) A A g dh D h

Pv A = vertical pressure acting from above A g dh = weight of material in element (Pv + dPv) A = support of material from below D dh = support from solid friction on the wall

(Pv + dPv) A + D dh = Pv A + A g dh3/17/00 KVJ 41

Stresses in a cylinder (contd)Two key substitutions = Pw (friction equation)

Janssens key assumption: Pw = K Pv This is not strictly true but is good enough from an engineering view. Substituting and rearranging, A dPv = A g dh - K Pv D dh Substituting A = (/4) D2 and integrating between h=0, Pv = 0 and h=H and Pv = Pv Pv = ( g D/ 4 K) (1 - exp(-4H K/D)) This 3/17/00 is the Janssen equation.KVJ 42

Stresses in a cylinder (contd)

hydrostatic

Bulk solids Notice that the asymptotic pressure depends only on D, not on H, hence this is why silos are tall and skinny, rather than short and squat.3/17/00 KVJ 43

Stresses - Converging SectionOver 40 years ago, the pioneer in bulk solids flow, Andrew W. Jenike, postulated that the magnitude of the stress in the converging section of a hopper was proportional to the distance of the element from the hopper apex.

r

= ( r, )This is the radial stress field assumption.

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Silo Stresses - Overall

hydrostatic

Bulk solid3/17/00

Notice that there is essentially no stress at the outlet. This is good for discharge devices! KVJ

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Janssen Equation - ExampleA large welded steel silo 12 ft in diameter and 60 feet high is to be built. The silo has a central discharge on a flat bottom. Estimate the pressure of the wall at the bottom of the silo if the silo is filled with a) plastic pellets, and b) water. The plastic pellets have the following characteristics: = 35 lb/cu ft = 20

The Janssen equation is Pv = ( g D/ 4 K) (1 - exp(-4H K/D)) In this case: D = 12 ft H = 60 ft = 35 lb/cu ft3/17/00 KVJ 46

= tan = tan 20 = 0.364 g = 32.2 ft/sec2

Janssen Equation - ExampleK, the Janssen coefficient, is assumed to be 0.4. It can vary according to the material but it is not often measured. Substituting we get Pv = 21,958 lbm/ft - sec2. If we divide by gc, we get Pv = 681.9 lbf/ft2 or 681.9 psf

Remember that Pw = K Pv,, so Pw = 272.8 psf. For water, P = g H and this results in P = 3744 psf, a factor of 14 greater!

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Types of BinsConicalPyramidal

Watch for inflowing valleys in these bins!3/17/00 KVJ 48

Types of BinsWedge/Plane Flow

Chisel

LB3/17/00

L>3BKVJ 49

A thought experiment1 c

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The Flow Functionc Time flow function

Flow function 13/17/00 KVJ 51

Determination of Outlet Sizec Time flow function

c,t c,i Flow factor3/17/00 KVJ

Flow function 152

Determination of Outlet Size B = c,i H()/H() is a constant which is a function of hopper angle

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H() Function3

H()

Circular2

Square

(L > 3B) ular outlets Rectang

1 10 20 30 40 50 60

Cone angle from vertical3/17/00 KVJ 54

Example: Calculation of a Hopper Geometry for Mass FlowAn organic solid powder has a bulk density of 22 lb/cu ft. Jenike shear testing has determined the following characteristics given below. The hopper to be designed is conical. Wall friction angle (against SS plate) = = 25 Bulk density = = 22 lb/cu ft Angle of internal friction = = 50 Flow function c = 0.3 1 + 4.3 Using the design chart for conical hoppers, at = 25 c = 17 with 3 safety factor & ff = 1.273/17/00 KVJ 55

Example: Calculation of a Hopper Geometry for Mass Flowff = /a or a = (1/ff) a > c

Condition for no arching =>

(1/ff) = 0.3 1 + 4.3

(1/1.27) = 0.3 1 + 4.3

1 = 8.82 c = 8.82/1.27 = 6.95

B = 2.2 x 6.95/22 = 0.69 ft = 8.33 in3/17/00 KVJ 56

Material considerations for hopper design

s s

s s s s

Amount of moisture in product? Is the material typical of what is expected? Is it sticky or tacky? Is there chemical reaction? Does the material sublime? Does heat affect the material?KVJ 57

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Material considerations for hopper design

s s s s

Is it a fine powder (< 200 microns)? Is the material abrasive? Is the material elastic? Does the material deform under pressure?

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Process Questionss s s s s s

How much is to be stored? For how long? Materials of construction Is batch integrity important? Is segregation important? What type of discharger will be used? How much room is there for the hopper?

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Discharge Ratess

s

s

Numerous methods to predict discharge rates from silos or hopper For coarse particles (>500 microns) Beverloo equation - funnel flow Johanson equation - mass flow For fine particles - one must consider influence of air upon discharge rateKVJ 60

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Beverloo equations

W = 0.58 b g0.5 (B - kdp)2.5

where W is the discharge rate (kg/sec) b is the bulk density (kg/m3) g is the gravitational constant B is the outlet size (m) k is a constant (typically 1.4) dp is the particle size (m) Note: Units must be SI3/17/00 KVJ 61

Johanson Equations

s

Equation is derived from fundamental principles - not empirical W = b (/4) B2 (gB/4 tan c)0.5

where c is the angle of hopper from vertical This equation applies to circular outlets Units can be any dimensionally consistent set Note that both Beverloo and Johanson show that W B2.5!3/17/00 KVJ 62

Discharge Rate - ExampleAn engineer wants to know how fast a compartment on a railcar will fill with polyethylene pellets if the hopper is designed with a 6 Sch. 10 outlet. The car has 4 compartments and can carry 180000 lbs. The bulk solid is being discharged from mass flow silo and has a 65 angle from horizontal. Polyethylene has a bulk density of 35 lb/cu ft.

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Discharge Rate ExampleOne compartment = 180000/4 = 45000 lbs. Since silo is mass flow, use Johanson equation. 6 Sch. 10 pipe is 6.36 in diameter = B W = (35 lb/ft3)(/4)(6.36/12)2 (32.2x(6.36/12)/4 tan 25)0.5 W= 23.35 lb/sec Time required is 45000/23.35 = 1926 secs or ~32 min. In practice, this is too long - 8 or 10 would be a better choice.3/17/00 KVJ 64

The Case of Limiting Flow Ratess

When bulk solids (even those with little cohesion) are discharged from a hopper, the solids must dilate in the conical section of the hopper. This dilation forces air to flow from the outlet against the flow of bulk solids and in the case of fine materials either slows the flow or impedes it altogether.KVJ 65

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Limiting Flow RatesInterstitial gas pressureBulk density

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Note that gas pressure is less than ambient pressure KVJ

Vertical stress66

Limiting Flow Ratess

The rigorous calculation of limiting flow rates requires simultaneous solution of gas pressure and solids stresses subject to changing bulk density and permeability. Fortunately, in many cases the rate will be limited by some type of discharge device such as a rotary valve or screw feeder.KVJ 67

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Limiting Flow Rates - Carleton Equation

4v sin 15 + B sd2 0 1/ 3 f3/17/00 KVJ

2/3 4/3 f 0 5/3 p

v

=g

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Carleton Equation (contd)where v0 is the velocity of the bulk solid is the hopper half angle s is the absolute particle density f is the density of the gas f is the viscosity of the gas3/17/00 KVJ 69

Silo Discharging Devicess s s s s

Slide valve/Slide gate Rotary valve Vibrating Bin Bottoms Vibrating Grates others

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Rotary ValvesQuite commonly used to discharge materials from bins.

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Screw FeedersDead Region

Better Solution

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Discharge AidsAir cannons s Pneumatic Hammers s Vibrators These devices should not be used in place of a properly designed hopper!s

They can be used to break up the effects of time consolidation.3/17/00 KVJ 73