Mixing (fluids.mixing)¶
This module contains some basic functions for fluid mechanics mixing calculations.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.
Misc Functions¶
- 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].
- 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
- 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
- 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
- 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
- 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
- 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