SPH Modeling and Investigation of the Shear and Blender Mixers for Mixing Cement Paste

Document Type : Research Article


1 Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, I.R. IRAN

2 epartment of Chemical Engineering, Sirjan University of Technology, Sirjan, I.R. IRAN


Mixing and homogenization of cement paste are some of the most used phenomena in the construction and building industries. In most cases, a homogeneous mixture of cement paste is required and this is supplied by rotary mixers. In the present study, the rotary cement paste mixers in two-dimensional (2D) conditions are investigated by an Incompressible Smoothed Particle Hydrodynamics (ISPH) method. The method is validated and then used to model the cement paste mixer. The cement paste is considered a Bingham fluid. Two types of mixers are examined; shear mixer and blender. An appropriate mixing index that was previously applied to the discrete element method was successfully implemented for the ISPH method, and the performance of these two types of mixers is analyzed with this mixing index. The results show that the Reynolds number has a key role in the mixing in the shear mixers. In the low Reynolds numbers, an unmixed region is formed, which decreases with increasing Reynolds numbers. In blender mixers, the mixing rate is expected to increase with the multiplicity of vortices formed. But the coordinated motion of the vortices with the blades causes a fluid mass to move. Also, the resistance of the fluid to the moving components of the mixer is calculated and the difference in the performance of the two mixers in terms of energy consumption and mixing speed is compared and discussed.


Main Subjects

[1] Zhang X., Ahmadi G., Eulerian–Lagrangian Simulations of Liquid–Gas–Solid Flows in Three-Phase Slurry Reactors, Chem. Eng. Sci., 60: 5089-5104 (2005).
[2] Gingold R.A., Monaghan J.J., Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars, Mon. Not. R. Astron. Soc., 181: 375-389 (1977).
[3] Lucy L.B., A Numerical Approach to the Testing of Fusion Process, Astron. J., 88: 1013-1024 (1977).
[4] Rafiee A., Manzari M.T., Hosseini M., An Incompressible SPH Method For Simulation of Unsteady Viscoelastic Free-Surface Flows, Int. J.  Nonlin. Mech., 42: 1210–1223 (2007).
 [5] Kiara A., Hendrickson K., Yue D.K.P., SPH for Incompressible Free-Surface Flows. Part I: Error Analysis of the Basic Assumptions, Comput. Fluids, 86: 611-624 (2013).
[6] Kiara A., Hendrickson K., Yue D.K.P., SPH for Incompressible Free-Surface Flows. Part II: Performance of a Modified SPH Method, Comput. Fluids, 86: 510-536 (2013).
[7] Jiang T., Ouyang J., Li Q., Ren J., Yang B., A Corrected Smoothed Particle Hydrodynamics Method for Solving Transient Viscoelastic Fluid Flows, Appl. Math. Model., 35: 3833-3853 (2011).
[8] Cleary P.W., Modeling Confined Multi-Material Heat and Mass Flows Using SPH, Appl. Math. Model., 22: 981–993 (1998).
[9] Shadloo M.S., Zainali A.,   M., Simulation of Single Mode Rayleigh–Taylor Instability by SPH Method, Comput. Mech., 51(5): 699-715 (2013).
[10] Liu X., Xu H., Shao S., Lin P., An Improved Incompressible SPH Model for Simulation of Wave–Structure Interaction, Comput. Fluids, 71: 113-123 (2013).
[11] Rafiee A., Thiagarajan K.P., An SPH Projection Method for Simulating Fluid-Hypoelastic Structure Interaction, Comput. Methods Appl. Mech.  Eng., 198: 2785–2795 (2009).
[12] Hashemi M.R., Fatehi R., Manzari M.T., A Modified SPH Method for Simulating Motion of Rigid Bodies in Newtonian Fluid Flows, Int. J. Nonlin. Mech., 47: 626-638 (2012).
[13] Hashemi, M.R., Fatehi, R., Manzari,  M.T., SPH Simulation of Interacting Solid Bodies Suspended in a Shear Flow of an Oldroyd-B fluid, J. Non-Newton. Fluid., 166:1239-1252 (2011).
[14] Lai, J., Wang, H., Yang, H., Zheng, X., Wang, Q., Dynamic Properties and SPH Simulation of Functionally Graded Cementitious Composite Subjected to Repeated Penetration, Constr. Build Mater., 146: 54-65 (2017).
[16] Lenaerts T., Dutré P., Mixing Fluids and Granular Materials, Comput.  Graph. Forum., 28: 213-218 (2009).
[17] Robinson M., ClearyP., Monaghan J., Analysis of Mixing in a Twin Cam Mixer Using Smoothed Particle Hydrodynamics, AIChE Journal, 54: 1987-1998 (2008).
[18] Orthmann J., Kolb A., Temporal Blending for Adaptive SPH, Comput. Graph. Forum, 31: 1-12 (2012).
[19] Shamsoddini R., Sefid M., Fatehi R., ISPH Modelling and Analysis of Fluid Mixing in a Microchannel with an Oscillating or a Rotating Stirrer, Eng. Appl. Comp. Fluid., 8(2): 289-298 (2014).  
[20] Shamsoddini R., Sefid M., Fatehi R., Lagrangian Simulation and Analysis of the Micromixing Phenomena in a Cylindrical Paddle Mixer Using
a Modified Weakly Compressible
, Asia Pac. J. Chem. Eng., 15(1): 1-10 (2015).  
 [24] Shamsoddini R., Incompressible SPH Modeling of Rotary Micropump Mixers, Int. J. Comp. Meth. 15(4): 1850019 (2018).
[25] Abdolahzadeh M., Tayebi A., Omidvar P., Mixing Process of Two-Phase Non-Newtonian Fluids in 2D Using Smoothed Particle Hydrodynamics, Comput. Math. Appl., 78(1): 110-122 (2019).
[26] Bentaieb N., Benarima Z., Belaadi S., Calorimetric and Thermal Analysis Studies on the Influence of Coal on Cement Paste Hydration, Iran. J. Chem. Chem. Eng. (IJCCE), 39(6): 237-244 (2020)
[27] Abolpour B., Afsahi M.M., Hosseini S.G., Statistical Analysis of the Effective Factors on the 28 Days Compressive Strength and Setting Time of the Concrete, J. Adv. Res., 6(5): 699-709 (2015).
[29] Li D., Wang D., Ren C., Rui Y. Investigation of Rheological Properties of Fresh Cement Paste Containing Ultrafine Circulating Fluidized Bed Fly Ash, Constr Build Mater., 188(10): 1007-1013 (2018).
[30] Shuiping L., Xiaotian L., Lugang S. Simulation of the Flow Field of Cement Mixer Based on Numerical Methods, Adv. Syst. Sci. Appl., 11(3-4): 315-321 (2011).
[31] Beccati N., Ferrari C., Bonanno A., Balestra M., Calibration of a CFD Discharge Process Model of an Off-Road Self-Loading Concrete Mixer, J Braz. Soc. Mech. Sci. Eng., 41: 76 (2019).
[32] Asmar B., Langston P., Matchett A., A Generalised Mixing Index in Distinct Element Method Simulation of Vibrated Particulate Beds, Granul. Matter, 4: 129–138 (2002).
[33] Capone T., Panizzo A., Cecioni C., Dalrymple R.A., Accuracy and stability of Numerical Schemes in SPH, Proceedings of the Workshop "SPHERIC - Smoothed Particle Hydrodynamics European Research Interest Community, 156 (2007).
[34] Bonet J., Lok T.S., Variational and Momentum Preservation Aspects of Smooth Particle Hydrodynamic Formulation, Comput. Methods Appl. Mech. Eng., 180: 97-115 (1999).
[35] Jayasree C., Murali Krishnan J., Gettu R., Influence of Superplasticizer on the Non-Newtonian Characteristics of Cement Paste, Mater. Struct., 44: 929–942 (2011).
[36] Papanastasiou T.C., Flows of Materials with Yield., J. Rheol., 31: 385–404 (1987).
[37] Shadloo M.S., Zainali A., Sadek S.H., Yildiz M., Improved Incompressible Smoothed Particle Hydrodynamics Method for Simulating Flow Around Bluff Bodies, Comput. Methods Appl.  Mech. Eng., 200: 1008–1020 (2011).
[38] Sefid M., Fatehi R., Shamsoddini R., A Modified Smoothed Particle Hydrodynamics Scheme to Model the Stationary and Moving Boundary Problems for Newtonian Fluid Flows, ASME J. Fluids Eng., 137(3): 03120/1-9 (2015).
[39] Neofytou P., A 3rd order upwind finite volume method for generalised Newtonian fluid flows, Adv. Eng. Soft, 36 (10): 664-680 (2005).
[40] Rajamanickam A., Krishnaswamy B., Design and Development of Mathematical Model for Static Mixer, Iran. J. Chem. Chem. Eng. (IJCCE), 35(1): 109-116 (2016).