# Mixing (fluids.mixing)¶

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].

\begin{align}\begin{aligned}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}\end{aligned}\end{align}
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, [] 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

 [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.

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

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: 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] Kp : float Product of Power number and Reynolds number for laminar regime []

Notes

Example is from example 9-6 in [1]. Confirmed.

References

 [1] (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.
 [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

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: Kp : float Product of power number and Reynolds number for laminar regime [] N : float Speed of impeller, [revolutions/s] t : float Time for homogeneity [s]

Notes

Degree of homogeneity is not specified. Example is from example 9-6 in [1]. Confirmed.

References

 [1] (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.
 [2] (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

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: 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 [] 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 [1]. Low precision used in example.

References

 [1] (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.
 [2] (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

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: 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 [] CoV : float Standard deviation of dimensionless concentration [-]

Notes

Example 7-8.3.2 in [1], solved backwards.

References

 [1] (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.
 [2] (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

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: 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 [-] K : float Loss coefficient of mixer [-]

Notes

Related to example 7-8.3.2 in [1].

References

 [1] (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.
 [2] (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