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#1 |
New Member
Thien Xuan Dinh
Join Date: Jul 2014
Location: Japan
Posts: 8
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Dear Foamer,
Taking a look to ErgunWenYu drag model for the lagrangian tracking, OF 2.3.0 with alphac > 0.8, I think something wrong there, where the factor (1 - alphac) disappears. Furthermore, can someone explain why alphac appears in the denominator? Best, |
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#2 |
New Member
César Augusto Corrêa Miguéis
Join Date: Nov 2013
Location: Rio de Janeiro, Brasil
Posts: 26
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dinh, I'm stucked in the very same question, did you have sucess about this thread? The Ergun part seems correct, but I agree with you that something looks bad in the Wen and Yu part.
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César Miguéis Mechanical Engineer MSc. Student at COPPE/UFRJ |
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#3 | |
New Member
Li Linmin
Join Date: Nov 2015
Location: China
Posts: 27
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Quote:
(mass/p.rho())*(150.0*(1.0 - alphac)+1.75*Re)*muc/(alphac*sqr(p.d())) because alphac is divided with (alphac*sqr(p.d())). does anyone find the same question? |
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#4 |
New Member
QuocThien
Join Date: Apr 2013
Posts: 16
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I believe that the formula should be:
(mass/p.rho())*(150.0*(1.0 - alphac)/alphac+1.75*Re)*muc/(sqr(p.d())) Because Sp = V*beta/(1.0 - alphac) where beta = F*18*(1.0 - alphac)*alphac*muc/sqr(q.d()) Then there is no /alphac in the end in Ergun approximation. When I run Single particle sedimentation in openfoam, the velocity of particle is smaller than the result by numerical analysis. |
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#5 | |
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Shah Akib Sarwar
Join Date: Mar 2021
Posts: 41
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Quote:
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#6 |
Senior Member
Josh Williams
Join Date: Feb 2021
Location: Scotland
Posts: 114
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1-\alpha_c should not appear in the Lagrangian formulation of the model (only the two-fluid model version of the drag law).
If 1-\alpha_c is there, then the drag force will decay to 0 as the solid volume fraction approaches zero (e.g. a single small isolated sphere). However, it should not happen. The drag force should decay to stokes drag. I attached this figure showing drag force with varying \alpha_p and Re_p. Script to reproduce is below Code:
import numpy as np from numpy import pi import matplotlib.pyplot as plt def coeff_drag(Re): # if Re > 1000.0: # return 0.44*Re # else: return24.0*(1.0+0.15*Re**0.687) def dragmodel_current(alpha_p, Re, d_p=10e-6, rho_p=1207, muc=1.5e-5): alpha_c =1-alpha_p vol_p =4./3. * pi * (d_p/2)**3 return vol_p *0.75* coeff_drag(alpha_c*Re)*muc*pow(alpha_c, -2.65) / (alpha_c * np.square(d_p)) def dragmodel_literature(alpha_p, Re, d_p=10e-6, rho_p=1207, muc=1.5e-5): alpha_c =1-alpha_p vol_p =4./3. * pi * (d_p/2)**3 return vol_p *0.75* alpha_p * coeff_drag(alpha_c*Re)*muc*pow(alpha_c, -2.65) / (alpha_c * np.square(d_p)) def dragmodel_oneway(alpha_p, Re, d_p=10e-6, rho_p=1207, muc=1.5e-5): # alpha_p is unused num_vals = alpha_p.size alpha_p =None vol_p =4./3. * pi * (d_p/2)**3 return vol_p *0.75* coeff_drag(Re)*muc / np.square(d_p) * np.ones(num_vals) def stokes_drag(alpha_p, Re, d_p=10e-6, rho_p=1207, muc=1.5e-5): # alpha_p is unused num_vals = alpha_p.size alpha_p =None Re =None vol_p =4./3. * pi * (d_p/2)**3 # return vol_p * 0.75 * coeff_drag(Re)*muc / np.square(d_p) * np.ones(alpha_p.size) Cd =24 return vol_p *0.75* Cd * muc / np.square(d_p) * np.ones(num_vals) alpha_p = np.array([0] + (10**np.linspace(-4, -1, 6)).tolist() + np.linspace(0.1, 0.6, 10).tolist()) Re =10 # print(dragmodel_current(0.1, Re=10), dragmodel_literature(0.1, Re=10)) ls_list = ["-", "--", "dotted", "-."] fig, ax = plt.subplots() ax.scatter(alpha_p, stokes_drag(alpha_p, Re), label=f"Stokes drag", c="black") # plot drag force models at varying Reynolds numbers for i, Re inenumerate([0, 0.1, 100]): ax.plot(alpha_p, dragmodel_current(alpha_p, Re), label=f"Wen-Yu (OF), Re = {Re}", ls=ls_list[i], c="orange", lw=2) for i, Re inenumerate([0, 0.1, 100]): ax.plot(alpha_p, dragmodel_literature(alpha_p, Re), label=fr"Wen-Yu (with 1-$\alpha_f$), Re = {Re}", ls=ls_list[i], c="blue", lw=2) for i, Re inenumerate([0, 0.1, 100]): ax.plot(alpha_p, dragmodel_oneway(alpha_p, Re), label=f"Schiller-Nauman, Re = {Re}", ls=ls_list[i], c="green", lw=2) ax.set_yscale("log") ax.set_xscale("log") ax.set_ylabel(r"$\mathbf{f}_d$ [kg m / $s^2$]") ax.set_xlabel(r"$\alpha_p$ [-]") ax.set_title(r"Drag models at $d_p = 10^{-6} m$, $\rho_p = 1000$") # format plot for legend outside of plot box = ax.get_position() ax.set_position([box.x0, box.y0, box.width *0.6, box.height]) # tidy up for spine_i in ["top", "right"]: ax.spines[spine_i].set_visible(False) ax.legend(frameon=False,loc="center left", bbox_to_anchor=(1.,0.5)) plt.savefig("drag_forces.png", dpi=300) plt.show() |
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#7 |
Senior Member
Albrecht vBoetticher
Join Date: Aug 2010
Location: Zürich, Swizerland
Posts: 241
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...so, can I use the cuurent code formulation (I looked into OpenFOAM 7 or 10) with the DPMFoam solver for gravel bed erosion?
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#8 | |
Senior Member
Josh Williams
Join Date: Feb 2021
Location: Scotland
Posts: 114
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Quote:
Yes the code for WenYu model for lagrangian is fine (I checked OpenFOAM 10, also OpenFOAM 2.3 as in the original post). Both fine. The point I was making is that there should not be (1-alpha_c) in the Lagrangian form of the WenYu drag. I think OP maybe was comparing to the Eulerian drag formulation (two-fluid model), where 1-\alpha_c should appear. |
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