SAJJAD KHUDHUR ABBASCeo , Founder & Head of SHacademyChemical Engineering , Al-Muthanna University, IraqOil & Gas Safety and Health Professional – OSHACADEMYTrainer of Trainers (TOT) - Canadian Center of Human Development

Episode 39 : Hopper Design

Problem:1 -experiments with shear box jenike on a particulate catalyst to give the family yield locus as in 1. given that the bulk density is 1000 kg/m3 particulates and wall friction angle is 15 a-from design chart silo cone, do design a mass flow hopper for the material. b-if the average size is 100 um, calculate the discharge flow rate passing through the discharge opening 2 - For the above materials using stainless steel is required to store 1000 tons of particulate in it. Coefficient of friction at the wall is given as 0.45 for each value and the formula that you use the appropriate justify the design. a - draw the dimensions of the silo you and draw a vertical stress profile and the wall of the silo whole time say powerful particleb- specify the maximum vertical stress and the wall of the silo youc - if you use several different approaches in the design you provide appropriate recommendations to your employer for work before the end of the casting device fabrication started.d - if problems such as the formation of the entrance are available after a certain time interval suggest measures - flow improvement measures to be taken to your employer 

Procedures of design:

1- Calculation of Simi included angle( θ ) and flow factor (ff ):2- Calculation of CAS3- Calculation of min. outlet diameter (B)4- Calculation of discharge rate 5- Calculation of silo dimensions6- Determination of vertical stress and wall stress profile7- Calculation of max. vertical stress and max. wall stress8- Methods of blockage clearance

Calculation of Simi included angle( θ ) and flow factor ( ff ):

For the given data : -Effective angle of internal friction ( δ )= 40o -Angle of wall friction (δw) = 16o

By using the following chart we will find the value of θ and ff θ = 30o

ff=1.5

From the Fig. 1

θ = 30o

ff=1.5

Fig. 1: calculation of θ and ff

θ = 30o

30o

Simi Included Angle ( θ )

Fig. 2: Simi Included Angle θ

Calculation of Critical Applied Stress (CAS)

From the given relationship between compaction stress ( σ1 ) and yield stress (YS) :

According to this equation several point will be created to draw the flow function curve. The intersection of this curve with line through the origin having slop of 1/ff will give the value of Critical Applied Stress (CAS)

Data For MFF curve and 1/ff line MFF 1/ff

YS YS0 0 0 01 1 1 0.6672 1.366 2 1.3343 1.639 3 2.0014 1.866 4 2.668

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

3

MFF1/ff

Compaction Stress Yi

eld

Stre

ss

MFF

1/ff

CAS

From Fig.3 CAS = 1.39

Fig. 3: Calculation of Critical Applied Stress (CAS)

Calculation of minimum outlet diameter (B)

Calculation of discharge rate ( m.)For particle diameter less than 500 μm

 V0: Average velocity of solid discharge (m/s)A: Area of outlet opening B: Outlet diameter μ , ρ : Viscosity and density of air ρp: Particle density dp: Particle diameter ρb: Bulk density

ρ= 1.184 kg/m3 , μ= 1x10-5 Pa.s and ρp= 1200 kg/m3

Dimensions of Bin and Conical section

 

D

B

H

θ

θ

Assume H/D=5 Total volume = 1000 m3

 

Determination of vertical stress (σv) and wall stress (σw) with the silo height

Section 3 conical

Section 2

H>D

Section 1

H=DThe silo will be divided to three sections (from top to bottom) to calculate vertical and wall stress with height in each section:

Section 1 : h=DSection 2 : h˃ DSection 3 : conical section

Section 1 :

 

m

For the values of h=0 to h=D=6.22 m the following data obtained for and

h σv σ w0 0 01 8282.585 4969.5512 14136.76 8482.0563 18374.52 11024.714 21199.12 12719.475 24727.28 14836.376 27445.2 16467.12

6.22 28100.3 16860.18

Section 1 Data of σ v and σ w

Section 2:K=0.6μ=0.45 Kμ = 0.27 From Fig: 4 for several values of h/D and Kμ = 0.27 find the values of σv/γD .σv/γD=a γ=ρgσv = a γ D And σw= K σvThe results of σv and σw in the following table.

Fig. 4: calculation of σv/γD

h σv σ w7 30458.2 18274.9215 50018.2 30010.9220 60021.8 36013.0825 67823.6 40694.16

31.106 75425.5 45255.3

Section 2: Data of σ v and σ w

D

h0

Bh

hB

Section 3: Calculation of h0 and h

θ

Calculation of σv and σw

αθ σ α

σ w

σ v

 

For the values of h=0 to h=5.083 m the following data obtained for and

Section 3: Data of σ v and σ w

h σv σ w5 75425 113137.54 22270.08 33405.123 10054.63 15081.952 5013.691 7520.5361 2292.473 3438.710 0 0

Fig. 5 vertical and wall stress profile

Fig. 6: Kmax. For δ = 40

From Fig. 6 for α = 30 δ = 40and ϕw = 16 Kmax = 22

Calculation of Kmax.

Calculation of σv max and σw max

At H= 31.106 m σv = 75425.5 Pa σw= 45255.3σv max = Kmax * σv maxσv max = 22 x 75425.5

σv max = 1659.4 Kpaσw max = Kmax * σw σw max = 22 x 45255.3σw max = 995.61 Kpa

There are many methods for blockage clearance in silo when build-ups formed : 1- AIR-SLIDE Flow-Aid: it is the ultimate material flow problem solver.which is used to create and maintain material flow while also eliminating sticky and tacky build-up, arching, rat holes, and blockages. As shown in the pictures

Methods of Blockage Clearance

(1)

(3)

(2)

2- Vibrating Bin Dischargers

Vibrating Bin Dischargers are designed to ensure even flow of granular or powdered materials out of a holding silo or hopper

Bin vibrating discharge

References:

1- Teknologi Zarah , 2008 Siti Masrinda Tasrin 2- introduction to particle tecnologi , 2008 Martin Rhodes

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ABBAS