lib.neumatic module

Module with neumatic conveying equipment library

lib.neumatic.saltation_Rizk(M, dp, rhog, D)

Calculates saltation velocity of gas for pneumatic conveying, using

the correlation of Rizk (1973) as described in [1]

\[\begin{split}\begin{array}[t]{c} \frac{M}{\rho_g V_{salt} A} = \frac{1}{10^{\delta}} \left(\frac{V_{salt}}{\sqrt{gD}}\right)^{\chi}\\ \delta = 1440d_p + 1.96\\ \chi = 1100d_p + 2.5\\ A = \frac{pi}{4} D^2\\ \end{array}\end{split}\]

Rearanged saltation velocity

\[V{salt} = \left(\frac{M 10^\delta (g D)^{0.5 \chi}}{\rho_g A}\right)^ {\frac{1}{\chi+1}}\]

Parameters:

Mfloat

Solid mass flow rate, [kg/s]

dpfloat

Particle diameter, [m]

rhogfloat

Gas density, [kg/m³]

Dfloat

Diameter of pipe, [m]

Returns:

Vsfloat

Saltation velocity of gas, [m/s]

References

[1] Rhodes, M.; Introduction to Particle Technology 2Ed. (John Wiley & Sons) 2008

[2] Rizk, F.; Pneumatic conveying at optimal operation conditions and a solution of Bath’s equation. Proceedings of Pneumotransport 3, paper D4. BHRA Fluid Engineering, Cranfield, England (1973)

Examples

Example 8.1 from [1], pag. 238

>>> "%0.2f" % (saltation_Rizk(M=0.25, dp=1e-4, rhog=1.2, D=0.078))
'9.88'

lib.neumatic.saltation_Matsumoto(M, rhop, dp, rhog, D, Vt, method='1977')

Calculates saltation velocity of the gas for pneumatic conveying,

according to any of method defined in Matsumoto papers.

• 1974 method, [3].

\[\begin{split}\begin{array}[t]{c} \frac{M}{\rho_g V_{salt} A} = 0.488 \left(\frac{\rho_p}{\rho_f}\right) ^{0.5} \left(\frac{Fr_t}{10}\right)^{-1.75} \left(\frac{Fr_s}{10}\right)^{3}\\ Fr_s = \frac{V_{salt}}{\sqrt{g D}}\\ Fr_t = \frac{V_{t}}{\sqrt{g d_p}}\\ A = \frac{pi}{4} D^2\\ \end{array}\end{split}\]

• 1975 method changing only the parameters of equation, [4].

\[\frac{M}{\rho_g V_{salt} A} = 1.11 \left(\frac{\rho_p}{\rho_f}\right) ^{0.55} \left(\frac{Fr_t}{10}\right)^{-2.3} \left(\frac{Fr_s}{10}\right)^{3}\]

• 1977, [5]. In this case the correlations have two step formulation

definning a critical particle diameter

\[\frac{d_c}{D} = 1.39\left(\frac{\rho_p}{\rho_g}\right)^{0.74}\]

For \(d_p < d_c\):

\[\frac{M}{\rho_g V_{salt} A} = 5560 \left(\frac{d_p}{D}\right)^{1.43} \left(\frac{Fr_s}{10}\right)^{4}\]

For \(d_p > d_c\):

\[\frac{M}{\rho_g V_{salt} A} = 0.373 \left(\frac{\rho_p}{\rho_f}\right) ^{1.06} \left(\frac{Fr_t}{10}\right)^{-3.7} \left(\frac{Fr_s}{10}\right)^{3.61}\]

Parameters:

Mfloat

Solid mass flow rate, [kg/s]

rhopfloat

Particle density, [kg/m^3]

dpfloat

Particle diameter, [m]

rhogfloat

Gas density, [kg/m^3]

Dfloat

Diameter of pipe, [m]

Vtfloat

Terminal velocity of particle settling in gas, [m/s]

methodstr

Specified the method from the year of paper, 1974|1975|1977

Returns:

Vsfloat

Saltation velocity of gas, [m/s]

References

[3] Matsumoto, S., Hara, M., Saito, S., Maeda, S.; Minimum Transport Velocity for Horizontal Pneumatic Conveying. J. Chem. Eng. Japan 7(6) (1974) 425-430

[4] Matsumoto, S., Harada, S., Saito, S., Maeda, S.; Saltation Velocity for Horizontal Pneumatic Conveying. J. Chem. Eng. Japan 8(4) (1975) 331-333

[5] Matsumoto, S., Kikuta, M., Maeda, S.; Effect of Particle Size on the Minimum Transport Velocity for Horizontal Pneumatic Conveying of Solids. J. Chem. Eng. Japan 10(4) (1977) 273-279

Examples

>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16, method="1974"))
'18.03'
>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16, method="1975"))
'16.49'
>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16))
'10.51'

lib.neumatic.saltation_Ochi(M, dp, rhog, D, Vt, fp=0.4)

Calculates saltation velocity of the gas for pneumatic conveying,

according to Ochi correlation, [6].

\[\begin{split}\begin{array}[t]{c} Fr_s = 1.05 f_d^{0.47}Fr_t^{0.82} \mu_s^{0.25}\\ Fr_t = \frac{V_{t}}{\sqrt{g d_p}}\\ \mu_s = \frac{M}{\rho_g V_{salt} A}\\ A = \frac{pi}{4} D^2\\ \end{array}\end{split}\]

Rearanged saltation velocity

\[V_{salt} = \left(\frac{1.05 M^{0.25} f^{0.47} Fr_t^{0.82} \sqrt{g d_p}} {\left(\rho_g A\right)^{0.25}}\right)^{0.8}\]

Parameters:

Mfloat

Solid mass flow rate, [kg/s]

dpfloat

Particle diameter, [m]

rhogfloat

Gas density, [kg/m^3]

Dfloat

Diameter of pipe, [m]

Vtfloat

Terminal velocity of particle settling in gas, [m/s]

fpfloat

Coefficient of friction between particles and surface, [-]

Returns:

Vsfloat

Saltation velocity of gas, [m/s]

References

[6] Ochi, M.; Saltation Velocity of the Gas-Solid Two-Phase Flow in a Horizontal Pipe. Trans. JSME B. 59(564) (1993) 2416-2421

Examples

>>> "%0.2f" % (saltation_Ochi(M=0.25, dp=4.7e-4, rhog=1.2, D=0.0026, Vt=3.16))
'8.82'

lib.neumatic.V_saltation(method=0, *args)

List with all saltation velocity correlations availables

• 0 - Rizk (1973)

• 1 - Matsumoto (1977)

• 2 - Matsumoto (1975)

• 3 - Matsumoto (1974)

• 4 - Ochi (1991)

lib.neumatic.fs_Stemerding()

Calculate solid friction factor as define in [7].

This method give a constant value withoud dependent variables based in experiment in vertical neumatic conveying

Returns:

fsfloat

Solid friction factor, [-]

References

[7] Stemerding, S.; The pneumatic transport of cracking catalyst in vertical risers. Chem. Eng. Sci. 17(8) (1962) 599-608

lib.neumatic.fs_Reddy(Vs)

Calculate solid friction factor as define in [8].

Parameters:

Vsfloat

Solid velocity of particle, [m/s]

Returns:

fsfloat

Solid friction factor, [-]

References

[8] Reddy, K.V.S., Pei, D.C.T.; Particle Dynamics in Solids-Gas Flow in a Vertical Pipe. Ind. Eng. Chem. Fundamen. 8(3) (1969) 490-497

lib.neumatic.fs_Swaaij(Vs)

Calculate solid friction factor as define in [9].

Parameters:

Vsfloat

Solid velocity of particle, [m/s]

Returns:

fsfloat

Solid friction factor, [-]

References

[9] van Swaaij, W.P.M., Buurman, C., van Breugel, J.W.; Shear Stresses on the Wall of a Dense Gas-Solids Riser. Chem. Eng. Sci. 25(11) (1970) 1818-1820

lib.neumatic.fs_Capes(Vs)

Calculate solid friction factor as define in [10].

Parameters:

Vsfloat

Solid velocity of particle, [m/s]

Returns:

fsfloat

Solid friction factor, [-]

References

[10] Capes, C.E., Nakamura, K.; Vertical Pneumatic Conveying: An Experimental Study with Particles in the Intermediate and Turbulent Flow Regimes. Can. J. Chem. Eng. 51(1) (1973) 31-38

lib.neumatic.fs_Konno(Vs, D)

Calculate solid friction factor as define in [11].

Parameters:

Vsfloat

Solid velocity of particle, [m/s]

Dfloat

Diameter of pipe, [m]

Returns:

fsfloat

Solid friction factor, [-]

References

[11] Konno, H., Saito, S.; Pneumatic Conveying of Solids Through Straight Pipes. J. Chem. Eng. Japan 2(2) (1969) 211-217

lib.neumatic.fs_Yang(Vs, eps, Vt, V)

Calculate solid friction factor as define in [12].

Parameters:

Vsfloat

Solid velocity of particle, [m/s]

epsfloat

Voidage in transporting line, [-]

Vtfloat

Terminal velocity of faling particle, [m/s]

V: float

Fluid velocity, [m/s]

Returns:

fsfloat

Solid friction factor, [-]

References

[12] Yang, W.-C.; A Correlation for Solid Friction Factor in Vertical Pneumatic Conveying Lines. AIChE J. 24(3) (1978) 548-552

lib.neumatic.f_solid(method=0, *args)

List with all solid friction factor correlations availables for vertical conveying

• 0 - Stemerding (1962)

• 1 - Reddy-Pei (1969)

• 2 - Swaaij-Buurman-Breugel (1970)

• 3 - Capes-Nakamura (1973)

• 4 - Konno-Saito (1969)

• 5 - Yang (1978)

lib.neumatic.fs_Yang_Horizontal(eps, V, D)

Calculate solid friction factor as define in [13].

Parameters:

epsfloat

Voidage in transporting line, [-]

V: float

Fluid velocity, [m/s]

Dfloat

Diameter of pipe, [m]

Returns:

fsfloat

Solid friction factor, [-]

References

[13] Yang, W.-C.; Correlations for Solid Friction Factors in Vertical and Horizontal Pneumatic Conveying. AIChE J. 20(3) (1974) 605-607

References

[1] (1,2,3)

Rhodes, M.; Introduction to Particle Technology 2Ed. (John Wiley & Sons) 2008

[2]

Rizk, F.; Pneumatic conveying at optimal operation conditions and a solution of Bath’s equation. Proceedings of Pneumotransport 3, paper D4. BHRA Fluid Engineering, Cranfield, England (1973)

[3] (1,2)

Matsumoto, S., Hara, M., Saito, S., Maeda, S.; Minimum Transport Velocity for Horizontal Pneumatic Conveying. J. Chem. Eng. Japan 7(6) (1974) 425-430

[4] (1,2)

Matsumoto, S., Harada, S., Saito, S., Maeda, S.; Saltation Velocity for Horizontal Pneumatic Conveying. J. Chem. Eng. Japan 8(4) (1975) 331-333

[5] (1,2)

Matsumoto, S., Kikuta, M., Maeda, S.; Effect of Particle Size on the Minimum Transport Velocity for Horizontal Pneumatic Conveying of Solids. J. Chem. Eng. Japan 10(4) (1977) 273-279

[6] (1,2)

Ochi, M.; Saltation Velocity of the Gas-Solid Two-Phase Flow in a Horizontal Pipe. Trans. JSME B. 59(564) (1993) 2416-2421

[7] (1,2)

Stemerding, S.; The pneumatic transport of cracking catalyst in vertical risers. Chem. Eng. Sci. 17(8) (1962) 599-608

[8] (1,2)

Reddy, K.V.S., Pei, D.C.T.; Particle Dynamics in Solids-Gas Flow in a Vertical Pipe. Ind. Eng. Chem. Fundamen. 8(3) (1969) 490-497

[9] (1,2)

van Swaaij, W.P.M., Buurman, C., van Breugel, J.W.; Shear Stresses on the Wall of a Dense Gas-Solids Riser. Chem. Eng. Sci. 25(11) (1970) 1818-1820

[10] (1,2)

Capes, C.E., Nakamura, K.; Vertical Pneumatic Conveying: An Experimental Study with Particles in the Intermediate and Turbulent Flow Regimes. Can. J. Chem. Eng. 51(1) (1973) 31-38

[11] (1,2)

Konno, H., Saito, S.; Pneumatic Conveying of Solids Through Straight Pipes. J. Chem. Eng. Japan 2(2) (1969) 211-217

[12] (1,2)

Yang, W.-C.; A Correlation for Solid Friction Factor in Vertical Pneumatic Conveying Lines. AIChE J. 24(3) (1978) 548-552

[13] (1,2)

Yang, W.-C.; Correlations for Solid Friction Factors in Vertical and Horizontal Pneumatic Conveying. AIChE J. 20(3) (1974) 605-607

[14]

; .