Mixing (fluids.mixing)¶
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fluids.mixing.
COV_motionless_mixer
(Ki, Q1, Q2, pipe_diameters)[source]¶ Calculates CoV of a motionless mixer with a regression parameter in [1] and originally in [2].
\[\frac{CoV}{CoV_0} = K_i^{L/D}\]- Parameters
- Kifloat
Correlation parameter specific to a mixer’s design, [-]
- Q1float
Volumetric flow rate of larger stream [m^3/s]
- Q2float
Volumetric flow rate of smaller stream [m^3/s]
- pipe_diametersfloat
Number of diameters along tail pipe for CoV calculation, 0 to 5 []
- Returns
- CoVfloat
Standard deviation of dimensionless concentration [-]
Notes
Example 7-8.3.2 in [1], solved backwards.
References
- 1(1,2)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- 2
Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and application of motionless mixer technology, Proc. ISMIP3, Osaka, pp. 107-114.
Examples
>>> COV_motionless_mixer(Ki=.33, Q1=11.7, Q2=2.74, pipe_diameters=4.74/.762) 0.0020900028665727685
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fluids.mixing.
K_motionless_mixer
(K, L, D, fd)[source]¶ Calculates loss coefficient of a motionless mixer with a regression parameter in [1] and originally in [2].
\[K = K_{L/T}f\frac{L}{D}\]- Parameters
- Kfloat
Correlation parameter specific to a mixer’s design, [-] Also specific to laminar or turbulent regime.
- Lfloat
Length of the motionless mixer [m]
- Dfloat
Diameter of pipe [m]
- fdfloat
Darcy friction factor [-]
- Returns
- Kfloat
Loss coefficient of mixer [-]
Notes
Related to example 7-8.3.2 in [1].
References
- 1(1,2)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- 2
Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and application of motionless mixer technology, Proc. ISMIP3, Osaka, pp. 107-114.
Examples
>>> K_motionless_mixer(K=150, L=.762*5, D=.762, fd=.01) 7.5
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fluids.mixing.
Kp_helical_ribbon_Rieger
(D, h, nb, pitch, width, T)[source]¶ Calculates product of power number and Reynolds number for a specified geometry for a heilical ribbon mixer in the laminar regime. One of several correlations listed in [1], it used more data than other listed correlations and was recommended.
\[K_p = 82.8\frac{h}{D}\left(\frac{c}{D}\right)^{-0.38} \left(\frac{p}{D}\right)^{-0.35} \left(\frac{w}{D}\right)^{0.20} n_b^{0.78}\]- Parameters
- Dfloat
Impeller diameter [m]
- hfloat
Ribbon mixer height, [m]
- nbfloat:
Number of blades, [-]
- pitchfloat
Height of one turn around a helix [m]
- widthfloat
Width of one blade [m]
- Tfloat
Tank diameter, [m]
- Returns
- Kpfloat
Product of Power number and Reynolds number for laminar regime []
Notes
Example is from example 9-6 in [1]. Confirmed.
References
- 1(1,2)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- 2
Rieger, F., V. Novak, and D. Havelkov (1988). The influence of the geometrical shape on the power requirements of ribbon impellers, Int. Chem. Eng., 28, 376-383.
Examples
>>> Kp_helical_ribbon_Rieger(D=1.9, h=1.9, nb=2, pitch=1.9, width=.19, T=2) 357.39749163259256
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fluids.mixing.
agitator_time_homogeneous
(N, P, T, H, mu, rho, D=None, homogeneity=0.95)[source]¶ Calculates time for a fluid mizing in a tank with an impeller to reach a specified level of homogeneity, according to [1].
\[N_p = \frac{Pg}{\rho N^3 D^5}\]\[Re_{imp} = \frac{\rho D^2 N}{\mu}\]\[\text{constant} = N_p^{1/3} Re_{imp}\]\[Fo = 5.2/\text{constant} \text{for turbulent regime}\]\[Fo = (183/\text{constant})^2 \text{for transition regime}\]- Parameters
- Nfloat:
Speed of impeller, [revolutions/s]
- Pfloat
Actual power required to mix, ignoring mechanical inefficiencies [W]
- Tfloat
Tank diameter, [m]
- Hfloat
Tank height, [m]
- mufloat
Mixture viscosity, [Pa*s]
- rhofloat
Mixture density, [kg/m^3]
- Dfloat, optional
Impeller diameter [m]
- homogeneityfloat, optional
Fraction completion of mixing, []
- Returns
- tfloat
Time for specified degree of homogeneity [s]
Notes
If impeller diameter is not specified, assumed to be 0.5 tank diameters.
The first example is solved forward rather than backwards here. A rather different result is obtained, but is accurate.
No check to see if the mixture if laminar is currently implemented. This would under predict the required time.
References
- 1
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
Examples
>>> agitator_time_homogeneous(D=36*.0254, N=56/60., P=957., T=1.83, H=1.83, mu=0.018, rho=1020, homogeneity=.995) 15.143198226374668
>>> agitator_time_homogeneous(D=1, N=125/60., P=298., T=3, H=2.5, mu=.5, rho=980, homogeneity=.95) 67.7575069865228
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fluids.mixing.
size_tee
(Q1, Q2, D, D2, n=1, pipe_diameters=5)[source]¶ Calculates CoV of an optimal or specified tee for mixing at a tee according to [1]. Assumes turbulent flow. The smaller stream in injected into the main pipe, which continues straight. COV calculation is according to [2].
\[TODO\]- Parameters
- Q1float
Volumetric flow rate of larger stream [m^3/s]
- Q2float
Volumetric flow rate of smaller stream [m^3/s]
- Dfloat
Diameter of pipe after tee [m]
- D2float
Diameter of mixing inlet, optional (optimally calculated if not specified) [m]
- nfloat
Number of jets, 1 to 4 []
- pipe_diametersfloat
Number of diameters along tail pipe for CoV calculation, 0 to 5 []
- Returns
- CoVfloat
Standard deviation of dimensionless concentration [-]
Notes
Not specified if this works for liquid also, though probably not. Example is from example Example 9-6 in [1]. Low precision used in example.
References
- 1(1,2)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- 2
Giorges, Aklilu T. G., Larry J. Forney, and Xiaodong Wang. “Numerical Study of Multi-Jet Mixing.” Chemical Engineering Research and Design, Fluid Flow, 79, no. 5 (July 2001): 515-22. doi:10.1205/02638760152424280.
Examples
>>> size_tee(Q1=11.7, Q2=2.74, D=0.762, D2=None, n=1, pipe_diameters=5) 0.2940930233038544
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fluids.mixing.
time_helical_ribbon_Grenville
(Kp, N)[source]¶ Calculates product of time required for mixing in a helical ribbon coil in the laminar regime according to the Grenville [2] method recommended in [1].
\[t = 896\times10^3K_p^{-1.69}/N\]- Parameters
- Kpfloat
Product of power number and Reynolds number for laminar regime []
- Nfloat
Speed of impeller, [revolutions/s]
- Returns
- tfloat
Time for homogeneity [s]
Notes
Degree of homogeneity is not specified. Example is from example 9-6 in [1]. Confirmed.
References
- 1(1,2)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- 2
Grenville, R. K., T. M. Hutchinson, and R. W. Higbee (2001). Optimisation of helical ribbon geometry for blending in the laminar regime, presented at MIXING XVIII, NAMF.
Examples
>>> time_helical_ribbon_Grenville(357.4, 4/60.) 650.980654028894