Mixing (fluids.mixing)¶
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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 [R515].
\[N_p = \frac{Pg}{\rho N^3 D^5}\]\[Re_{imp} = \frac{\rho D^2 N}{\mu}\]\[\text{constant} = N_p^{1/3} Re_{imp}\]\[Fo = 5.2/\text{constant} \text{for turbulent regime}\]\[Fo = (183/\text{constant})^2 \text{for transition regime}\]- Parameters
N : float:
Speed of impeller, [revolutions/s]
P : float
Actual power required to mix, ignoring mechanical inefficiencies [W]
T : float
Tank diameter, [m]
H : float
Tank height, [m]
mu : float
Mixture viscosity, [Pa*s]
rho : float
Mixture density, [kg/m^3]
D : float, optional
Impeller diameter [m]
homogeneity : float, optional
Fraction completion of mixing, []
- Returns
t : float
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
- R515(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.
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.
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 [R516], 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
D : float
Impeller diameter [m]
h : float
Ribbon mixer height, [m]
nb : float:
Number of blades, [-]
pitch : float
Height of one turn around a helix [m]
width : float
Width of one blade [m]
T : float
Tank diameter, [m]
- Returns
Kp : float
Product of Power number and Reynolds number for laminar regime []
Notes
Example is from example 9-6 in [R516]. Confirmed.
References
- R516(1,2,3)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- R517
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.
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 [R519] method recommended in [R518].
\[t = 896\times10^3K_p^{-1.69}/N\]- Parameters
Kp : float
Product of power number and Reynolds number for laminar regime []
N : float
Speed of impeller, [revolutions/s]
- Returns
t : float
Time for homogeneity [s]
Notes
Degree of homogeneity is not specified. Example is from example 9-6 in [R518]. Confirmed.
References
- R518(1,2,3)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- R519(1,2)
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
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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 [R520]. Assumes turbulent flow. The smaller stream in injected into the main pipe, which continues straight. COV calculation is according to [R521].
\[TODO\]- Parameters
Q1 : float
Volumetric flow rate of larger stream [m^3/s]
Q2 : float
Volumetric flow rate of smaller stream [m^3/s]
D : float
Diameter of pipe after tee [m]
D2 : float
Diameter of mixing inlet, optional (optimally calculated if not specified) [m]
n : float
Number of jets, 1 to 4 []
pipe_diameters : float
Number of diameters along tail pipe for CoV calculation, 0 to 5 []
- Returns
CoV : float
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 [R520]. Low precision used in example.
References
- R520(1,2,3)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- R521(1,2)
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.
COV_motionless_mixer
(Ki, Q1, Q2, pipe_diameters)[source]¶ Calculates CoV of a motionless mixer with a regression parameter in [R522] and originally in [R523].
\[\frac{CoV}{CoV_0} = K_i^{L/D}\]- Parameters
Ki : float
Correlation parameter specific to a mixer’s design, [-]
Q1 : float
Volumetric flow rate of larger stream [m^3/s]
Q2 : float
Volumetric flow rate of smaller stream [m^3/s]
pipe_diameters : float
Number of diameters along tail pipe for CoV calculation, 0 to 5 []
- Returns
CoV : float
Standard deviation of dimensionless concentration [-]
Notes
Example 7-8.3.2 in [R522], solved backwards.
References
- R522(1,2,3)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- R523(1,2)
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 [R524] and originally in [R525].
\[K = K_{L/T}f\frac{L}{D}\]- Parameters
K : float
Correlation parameter specific to a mixer’s design, [-] Also specific to laminar or turbulent regime.
L : float
Length of the motionless mixer [m]
D : float
Diameter of pipe [m]
fd : float
Darcy friction factor [-]
- Returns
K : float
Loss coefficient of mixer [-]
Notes
Related to example 7-8.3.2 in [R524].
References
- R524(1,2,3)
Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.
- R525(1,2)
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