# -*- coding: utf-8 -*- '''Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.''' from __future__ import division from fluids.constants import g from math import log, pi __all__ = ['agitator_time_homogeneous', 'Kp_helical_ribbon_Rieger', 'time_helical_ribbon_Grenville', 'size_tee', 'COV_motionless_mixer', 'K_motionless_mixer'] max_Fo_for_turbulent = 1/1225. min_regime_constant_for_turbulent = 6370. def adjust_homogeneity(fraction): '''Base: 95% homogeneity''' multiplier = log(1-fraction)/log(0.05) return multiplier def agitator_time_homogeneous(N, P, T, H, mu, rho, D=None, homogeneity=.95): r'''Calculates time for a fluid mizing in a tank with an impeller to reach a specified level of homogeneity, according to [1]_. .. math:: N_p = \frac{Pg}{\rho N^3 D^5} .. math:: Re_{imp} = \frac{\rho D^2 N}{\mu} .. math:: \text{constant} = N_p^{1/3} Re_{imp} .. math:: Fo = 5.2/\text{constant} \text{for turbulent regime} .. math:: 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. 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 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. ''' if not D: D = T*0.5 Np = P*g/rho/N**3/D**5 Re_imp = rho/mu*D**2*N regime_constant = Np**(1/3.)*Re_imp if regime_constant >= min_regime_constant_for_turbulent: Fo = (5.2/regime_constant) else: Fo = (183./regime_constant)**2 time = rho*T**1.5*H**0.5/mu*Fo multiplier = adjust_homogeneity(homogeneity) return time*multiplier def Kp_helical_ribbon_Rieger(D, h, nb, pitch, width, T): r'''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. .. math:: 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 [1]_. Confirmed. Examples -------- >>> Kp_helical_ribbon_Rieger(D=1.9, h=1.9, nb=2, pitch=1.9, width=.19, T=2) 357.39749163259256 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. .. [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. ''' c = 0.5*(T - D) return 82.8*h/D*(c/D)**-.38*(pitch/D)**-0.35*(width/D)**0.2*nb**0.78 def time_helical_ribbon_Grenville(Kp, N): r'''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]_. .. math:: 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 [1]_. Confirmed. Examples -------- >>> time_helical_ribbon_Grenville(357.4, 4/60.) 650.980654028894 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. .. [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. ''' return 896E3*Kp**-1.69/N ### Tee mixer def size_tee(Q1, Q2, D, D2, n=1, pipe_diameters=5): r'''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]_. .. math:: 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 [1]_. Low precision used in example. Examples -------- >>> size_tee(Q1=11.7, Q2=2.74, D=0.762, D2=None, n=1, pipe_diameters=5) 0.2940930233038544 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. .. [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. ''' V1 = Q1/(pi/4*D**2) Cv = Q2/(Q1 + Q2) COV0 = ((1-Cv)/Cv)**0.5 if not D2: D2 = (Q2/Q1)**(2/3.)*D V2 = Q2/(pi/4*D2**2) B = n**2*(D2/D)**2*(V2/V1)**2 if not n == 1 and not n == 2 and not n == 3 and not n ==4: raise Exception('Only 1 or 4 side streams investigated') if n == 1: if B < 0.7: E = 1.33 else: E = 1/33. + 0.95*log(B/0.7) elif n == 2: if B < 0.8: E = 1.44 else: E = 1.44 + 0.95*log(B/0.8)**1.5 elif n == 3: if B < 0.8: E = 1.75 else: E = 1.75 + 0.95*log(B/0.8)**1.8 else: if B < 2: E = 1.97 else: E = 1.97 + 0.95*log(B/2.)**2 COV = (0.32/B**0.86*(pipe_diameters)**-E )**0.5 return COV ### Commercial motionless mixers '''Data from: Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. Handbook of Industrial Mixing: Science and Practice. Hoboken, N.J.: Wiley-Interscience, 2004.''' StatixMixers = {} StatixMixers['KMS'] = {'Name': 'KMS', 'Vendor': 'Chemineer', 'Description': 'Twisted ribbon. Alternating left and right twists.', 'KL': 6.9, 'KiL': 0.87, 'KT': 150, 'KiT': 0.5} StatixMixers['SMX'] = {'Name': 'SMX', 'Vendor': 'Koch-Glitsch', 'Description': 'Guide vanes 45 degrees to pipe axis. Adjacent elements rotated 90 degrees.', 'KL': 37.5, 'KiL': 0.63, 'KT': 500, 'KiT': 0.46} StatixMixers['SMXL'] = {'Name': 'SMXL', 'Vendor': 'Koch-Glitsch', 'Description': 'Similar to SMX, but intersection bars at 30 degrees to pipe axis.', 'KL': 7.8, 'KiL': 0.85, 'KT': 100, 'KiT': 0.87} StatixMixers['SMF'] = {'Name': 'SMF', 'Vendor': 'Koch-Glitsch', 'Description': 'Three guide vanes projecting from the tube wall in a way as to not contact. Designed for applications subject to plugging.', 'KL': 5.6, 'KiL': 0.83, 'KT': 130, 'KiT': 0.4} def COV_motionless_mixer(Ki, Q1, Q2, pipe_diameters): r'''Calculates CoV of a motionless mixer with a regression parameter in [1]_ and originally in [2]_. .. math:: \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 [1]_, solved backwards. Examples -------- >>> COV_motionless_mixer(Ki=.33, Q1=11.7, Q2=2.74, pipe_diameters=4.74/.762) 0.0020900028665727685 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. .. [2] Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and application of motionless mixer technology, Proc. ISMIP3, Osaka, pp. 107-114. ''' Cv = Q2/(Q1 + Q2) COV0 = ((1-Cv)/Cv)**0.5 COVr = Ki**(pipe_diameters) COV = COV0*COVr return COV def K_motionless_mixer(K, L, D, fd): r'''Calculates loss coefficient of a motionless mixer with a regression parameter in [1]_ and originally in [2]_. .. math:: 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 [1]_. Examples -------- >>> K_motionless_mixer(K=150, L=.762*5, D=.762, fd=.01) 7.5 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. .. [2] Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and application of motionless mixer technology, Proc. ISMIP3, Osaka, pp. 107-114. ''' return L/D*fd*K