Near-wall modelling in Eulerian-Eulerian simulations. (English) Zbl 1496.76012
Summary: The near-wall region in turbulent Eulerian-Eulerian (E-E) simulations has hitherto received little to no attention. A standard approach to modelling this region is through the employment of single-phase wall-functions in the fluid-phase, and it is unclear whether such an approach is capable of capturing the turbulent fluid-particle interaction in the near-wall region. In order to both investigate and alleviate E-E models reliance on single-phase wall-functions we propose an E-E elliptic relaxation model to account for the near-wall non-homogeneity which arises in wall-bounded flows. The proposed model is derived within an E-E framework and enables the full resolution of the boundary layer and arbitrary wall sensitivity. The model is then compared against the conventional \(k_f - \varepsilon_f\) turbulence model with standard single-phase wall-functions. Additionally, the modelling is compared against a low-Re number turbulence model. The elliptic relaxation model is implemented within the open-source CFD toolbox OpenFOAM, applied to a vertical downward-facing channel and validated against the benchmark experimental data of J. D. Kulick et al. [“Particle response and turbulence modification in fully developed channel flow”, J. Fluid Mech. 277, 109–134 (1994; doi:10.1017/s0022112094002703)]. Model results show marked improvements over the conventional turbulence model across mean flow and turbulence statistics predictions. The use of conventional single-phase wall functions were shown to negatively impede on the prediction of the velocity covariance coupling term and as a result the particle fluctuation energy. Moreover, this also lead to an underestimation of the near-wall volume fraction accumulation. Finally, the elliptic relaxation model, E-E model and accompanying validation cases are made open-source.
MSC:
| 76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |
Software:
OpenFOAMReferences:
| [1] | Kulick, J.; Fessler, J. R.; Eaton, J. R., Particle response and turbulence modification in fully developed channel flow, J Fluid Mech, 277, 109-134 (1994) |
| [2] | Caraman, N.; Borée, J.; Simonin, O., Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: experimental and theoretical analysis, Phys Fluids, 15, 12, 3602-3612 (2003) · Zbl 1186.76091 |
| [3] | Fessler, J. R.; Eaton, J. K., Turbulence modification by particles in a backward-facing step flow, J Fluid Mech, 394, 1999, 97-117 (1999) · Zbl 0944.76520 |
| [4] | Gore, R.; Crowe, C., Effect of particle size on modulating turbulent intensity, Int J Multiphase Flow, 15, 2, 279-285 (1989) |
| [5] | Lee, S.; Durst, F., On the motion of particles in turbulent duct flows, Int J Multiphase Flow, 8, 2, 125-146 (1982) |
| [6] | Tsuji, Y.; Morikawa, Y., LDV measurements of an air-solid two-phase flow in a vertical pipe, J Fluid Mech, 120, 385-409 (1984) |
| [7] | Kubik, A.; Kleiser, L., Influence of mass loading on particle-laden turbulent channel flow, PAMM, 6, 1, 531-532 (2006) |
| [8] | Li, Y.; McLaughlin, J. B.; Kontomaris, K.; Portela, L., Numerical simulation of particle-laden turbulent channel flow, Phys Fluids, 13, 10, 2957-2967 (2001) · Zbl 1184.76325 |
| [9] | Rouson, D. W.I.; Eaton, J. K., On the preferential concentration of solid particles in turbulent channel flow, J Fluid Mech, 428, 149-169 (2001) · Zbl 0967.76039 |
| [10] | Strömgren, T.; Brethouwer, G.; Amberg, G.; Johansson, A. V., Modelling of turbulent gas-particle flows with focus on two-way coupling effects on turbophoresis, Powder Technol, 224, 36-45 (2012) |
| [11] | Vreman, A. W., Turbulence attenuation in particle-laden flow in smooth and rough channels, J Fluid Mech, 773, 103-136 (2015) |
| [12] | Wang, Q.; Squires, K. D., Large eddy simulation of particle-laden turbulent channel flow, Phys Fluids, 8, 5, 1207-1223 (1996) · Zbl 1086.76032 |
| [13] | Yamamoto, Y.; Potthoff, M.; Tanaka, T.; Kajishima, T.; Tsuji, Y., Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions, J Fluid Mech, 442, 303-334 (2001) · Zbl 1004.76513 |
| [14] | Marchioli, C.; Soldati, A., Mechanisms for particle transfer and segregation in a turbulent boundary layer, J Fluid Mech, 468, 283-315 (2002) · Zbl 1152.76401 |
| [15] | Reeks, M., The transport of discrete particles in inhomogeneous turbulence, J Aerosol Sci, 14, 6, 729-739 (1983) |
| [16] | Pedinotti, S.; Mariotti, G., Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels, 18, 6, 927-941 (1992) · Zbl 1144.76440 |
| [17] | Rashidi, M.; Hetsroni, G.; Banerjee, S., Particle-turbulence interaction in a boundary layer, Int J Multiphase Flow, 16, 6, 935-949 (1990) · Zbl 1134.76648 |
| [18] | Li, T., Revisiting the johnson and jackson boundary conditions for granular flows, IFAC Proceedings Volumes (2009) |
| [19] | Mito, Y.; Hanratty, T. J., Effect of feedback and inter-particle collisions in an idealized gas-liquid annular flow, Int J Multiphase Flow, 32, 6, 692-716 (2006) · Zbl 1136.76577 |
| [20] | Pan, Y.; Banerjee, S., Numerical simulation of particle interactions with wall turbulence, Phys Fluids, 8, 10, 2733-2755 (1996) |
| [21] | Young, J.; Leeming, A., A theory of particle deposition in turbulent pipe flow, J Fluid Mech, 340, 129-159 (1997) · Zbl 0890.76085 |
| [22] | Gidaspow, D., Multiphase flow and fluidization (1994) · Zbl 0789.76001 |
| [23] | Schlichting, H.; Gersten, K.; Krause, E.; Oertel, H.; Mayes, K., Boundary-layer theory (1955), Springer · Zbl 0065.18901 |
| [24] | Hanjalic, K.; Launder, B., Sensitizing the dissipation equation to irrotational strains, J Fluids Eng, 102, 1, 34-40 (1980) |
| [25] | Rizk, M. A.; Elghobashi, S. E., A two-equation turbulence model for dispersed dilute confined two-phase flows, Int J Multiphase Flow, 15, 1, 119-133 (1989) |
| [26] | Saber, A.; Lundström, T.; Hellström, J., Influence of inertial particles on turbulence characteristics in outer and near wall flow as revealed with high resolution particle image velocimetry, J Fluids Eng Trans ASME, 138, 9, 1-12 (2016) |
| [27] | Benyahia, S.; Syamlal, M.; O’Brien, T. J., Evaluation of boundary conditions used to model dilute, turbulent gas/solids flows in a pipe, Powder Technol, 156, 2, 62-72 (2005) |
| [28] | Bolio, E. J.; Yasuna, J. A.; Sinclair, J. L., Dilute turbulent gas-solid flow in risers with particle-particle interactions, AIChE J, 41, 6, 1375-1388 (1995) |
| [29] | Dasgupta, S.; Jackson, R.; Sundaresan, S., Gas-particle flow in vertical pipes with high mass loading of particles, Powder Technol, 96, 1, 6-23 (1998) |
| [30] | Zheng, Y.; Wan, X.; Qian, Z.; Wei, F.; Jin, Y., Numerical simulation of the gas-particle turbulent flow in riser reactor based on k-ϵ-kp-ϵp-\(θ\) two-fluid model, Chem Eng Sci, 56, 24, 6813-6822 (2001) |
| [31] | Patel, V. C.; Rodi, W.; Scheuerer, G., Turbulence models for near-wall and low Reynolds number flows - a review, AIAA J, 23, 9, 1308-1319 (1985) |
| [32] | Chien, K.-Y., Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model, AIAA J, 20, 1, 33-38 (1982) · Zbl 0484.76064 |
| [33] | Launder, B.; Sharma, B., Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Lett Heat Mass Transfer, 1, 2, 131-137 (1974) |
| [34] | Rodi, W.; Mansour, N. N., Low reynolds number k-epsilon modelling with the aid of direct simulation data, J Fluid Mech, 250, 509-529 (1993) · Zbl 0775.76067 |
| [35] | Shih, T. H.; Hsu, A. T., An improved k-epsilon model for near wall turbulence, Research Briefs: 1990 (1991), Center for Modeling of Turbulence and Transition (CMOTT) |
| [36] | Durbin, P. A., Near-wall turbulence closure modeling without “damping functions”, Theor Comput Fluid Dyn, 3, 1, 1-13 (1991) · Zbl 0728.76053 |
| [37] | Behnia, M.; Parneix, S.; Durbin, P., Prediction of heat transfer in an axisymmetric turbulent jet impinging on a flat plate, Int J Heat Mass Transfer, 41, 12, 1845-1855 (1998) |
| [38] | Davidson, L.; Nielsen, P. V.; Sveningsson, A., Modifications of the v2-f model for computing the flow in a 3d wall jet, Turbulence, heat and mass transfer, 577-584 (2003) |
| [39] | Lien, F.-S.; Kalitzin, G., Computations of transonic flow with the v2-f turbulence model, Int J Heat Fluid Flow, 22, 1, 53-61 (2001) |
| [40] | Ooi, A.; Iaccarino, G.; Durbin, P.; Behnia, M., Reynolds averaged simulation of flow and heat transfer in ribbed ducts, Int J Heat Fluid Flow, 23, 6, 750-757 (2002) |
| [41] | Sveningsson, A., Analysis of the Performance of Different v2f Turbulence Models in a Stator Vane Passage Flow (2003), PhD Thesis |
| [42] | Fox, R. O., On multiphase turbulence models for collisional fluid-particle flows, J Fluid Mech, 742, 368-424 (2014) · Zbl 1328.76072 |
| [43] | Février, P.; Simonin, O.; Squires, K. D., Partitioning of particle velocities in gas – solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J Fluid Mech, 533, 1-46 (2005) · Zbl 1101.76025 |
| [44] | Riella, M.; Kahraman, R.; Tabor, G., Reynolds-averaged two-fluid model prediction of moderately dilute fluid-particle flow over a backward-facing step, Int J Multiphase Flow, 106, 95-108 (2018) |
| [45] | Riella, M.; Kahraman, R.; Tabor, G., Inhomogeneity and anisotropy in eulerian-eulerian near-wall modelling, Int J Multiphase Flow, 114, 9-18 (2019) · Zbl 1496.76012 |
| [46] | Rumsey, C. L., Compressibility considerations for kw turbulence models in hypersonic boundary-layer applications, J Spacecraft Rockets, 47, 1, 11-20 (2010) |
| [47] | Pope, S. B., Turbulent flows (2011), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 1308.76134 |
| [48] | Launder, B. E.; Reece, G. J.; Rodi, W., Progress in the development of a reynolds-stress turbulence closure, J Fluid Mech, 68, 3, 537-566 (1975) · Zbl 0301.76030 |
| [49] | Weller, H. G.; Tabor, G.; Jasak, H.; Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput Phys, 12, 6, 620-631 (1998) |
| [50] | Riella M.. ratfmfoam for openfoam-2.2.2.2019a; 10.5281/zenodo.2620412; Riella M.. ratfmfoam for openfoam-2.2.2.2019a; 10.5281/zenodo.2620412 |
| [51] | Riella, M., Turbulence modelling of fluid-particle interaction (2019), University of Exeter |
| [52] | Ferziger, J. H.; Peric, M., Computational Methods for Fluid Dynamics (2002) · Zbl 0998.76001 |
| [53] | Issa, R. I., Solution of the implicitly discretised fluid flow equations by operator-splitting, J Comput Phys, 62, 1, 40-65 (1986) · Zbl 0619.76024 |
| [54] | Zalesak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids, J Comput Phys, 31, 3, 335-362 (1979) · Zbl 0416.76002 |
| [55] | Durbin, P. A.; Reif, B. A.P., Statistical theory and modeling of turbulence flow, 109-154 (2010), John Wiley & Sons, Ltd |
| [56] | Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J., Comparison between lagrangian and mesoscopic eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence, J Comput Phys, 227, 13, 6448-6472 (2008) · Zbl 1338.76035 |
| [57] | Vance, M. W.; Squires, K. D.; Simonin, O., Properties of the particle velocity field in gas-solid turbulent channel flow, Phys Fluids, 18, 6, 063302 (2006) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
