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
- 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 []
- Q1
- Returns
- CoV
float
Standard deviation of dimensionless concentration [-]
- CoV
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].
- Parameters
- Returns
- CoV
float
Standard deviation of dimensionless concentration [-]
- CoV
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].
- Parameters
- Returns
- K
float
Loss coefficient of mixer [-]
- K
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].
- Parameters
- Nfloat:
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]
- t
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.
- Parameters
- Returns
- Kp
float
Product of Power number and Reynolds number for laminar regime []
- Kp
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].
- Parameters
- Returns
- t
float
Time for homogeneity [s]
- t
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