When performing numerical modeling of fluid flows where a clear medium is adjacent to a porous medium, a degree of difficulty related to the condition at the interface between the two media, where slip velocity exists, is encountered. A similar situation can be found when a jet flow interacts with a perforated plate. The numerical modeling of a perforated plate by meshing in detail each hole is most often impossible in a practical case (many holes with different shapes). Therefore, perforated plates are often modeled as porous zones with a simplified hypothesis based on pressure losses related to the normal flow through the plate. Nevertheless, previous investigations of flow over permeable walls highlight the impossibility of deducing a universal analytical law governing the slip velocity coefficient since the latter depends on many parameters such as the Reynolds number, porosity, interface structure, design of perforations, and flow direction. This makes the modeling of such a configuration difficult. The present study proposes an original numerical interface law for a perforated plate. It is used to model the turbulent jet flow interacting with a perforated plate considered as a fictitious porous medium without a detailed description of the perforations. It considers the normal and tangential effects of the flow over the plate. Validation of the model is realized through comparison with experimental data.
References
[1]
Bjerg, B., Zhang, B. and Kai, P. (2008) Porous Media as Boundary Condition for Air Inlet, Slatted Floor and Animal Occupied Zone in Numerical Simulation of Airflow in a Pig Unit. AgEbg2008 International Conference on Agricultural Engineering Hersonissos, Hersonissos, 23 June 2008, 45.
[2]
Wu, W., Zong, C. and Zhang, G. (2013) Comparisons of Two Numerical Approaches to Simulate Slatted Floor of a Slurry Pit Model—Large Eddy Simulations. Computers and Electronics in Agriculture, 93, 78-89. https://doi.org/10.1016/j.compag.2013.02.002
[3]
Zong, C. and Zhang, G.Q. (2014) Numerical Modelling of Airflow and Gas Dispersion in the Pit Headspace via Slatted Floor: Comparison of Two Modelling Approaches. Computers and Electronics in Agriculture, 109, 200-211. https://doi.org/10.1016/j.compag.2014.10.015
[4]
Moureh, J., Tapsoba, M. and Flick, D. (2009) Airflow in a Slot-Ventilated Enclosure Partially Filled with Prous Boxes: Part II—Measurements and Simulations within Porous Boxes. Computer & Fluids, 38, 206-220. https://doi.org/10.1016/j.compfluid.2008.02.007
[5]
Sun, H.W., et al. (2004) Development and Validation of 3-D Models to Simulate Airflow and Ammonia Distribution in a High-Rise Hog Building during Summer and Winter Conditions. Agricultural Engineering International: The CIGR Journal of Scientific Research and Development, 6, 1-24.
[6]
Bjerg, B., Zhang, B. and Kai, P. (2008) CFD Investigations of a Partly Pit Ventilation System as Method to Reduce Ammonia Emission from Pig Production Units. The 8th ASABE International Livestock Environment Symposium.
[7]
Beavers, G.S. and Joseph, D.D. (1967) Boundary Conditions at a Naturally Permeable Wall. Journal of Fluid Mechanics, 30, 197-207. https://doi.org/10.1017/S0022112067001375
[8]
Brinkman, H.C. (1948) A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense of Particles. Journal of Applied Sciences Research, A1, 27-34. https://doi.org/10.1007/BF02120313
[9]
Ochoa-Tapia, J.A. and Whitaker, S. (1995) Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid—I. Theoretical Development. International Journal of Heat and Mass Transfer, 38, 2635-2646. https://doi.org/10.1016/0017-9310(94)00346-W
[10]
Kuznetsov, A.V. (1997) Influence of the Stress Jump Condition at the Porous-Medium/Clear-Fluid Interface on a Flow at a Porous Wall. International Communications in Heat and Mass Transfer, 24, 401-410. https://doi.org/10.1016/S0735-1933(97)00025-0
[11]
Saffman, P.G. (1971) On the Boundary Condition at the Surface of a Porous Medium. Studies in Applied Mathematics, 50, 93-101. https://doi.org/10.1002/sapm197150293
[12]
Larson, R.E. and Higdon, J.J.L. (1986) Microscopic Flow near the Surface of Two-Dimensional Porous Media. Part 1. Axial Flow. Journal of Fluid Mechanics, 166, 449-472. https://doi.org/10.1017/S0022112086000228
[13]
Larson, R.E. and Higdon, J.J.L. (1987) Microscopic Flow near the Surface of Two-Dimensional Porous Media. Part 2. Transverse Flow. Journal of Fluid Mechanics, 178, 119-136. https://doi.org/10.1017/S0022112087001149
[14]
Richardson, S.A. (1971) A Model for the Boundary Condition of a Porous Material. Part 2. Journal of Fluid Mechanics, 49, 327-336. https://doi.org/10.1017/S002211207100209X
[15]
Sahraoui, M. and Kaviany, M. (1992) Slip and No-Slip Velocity Boundary-Conditions at Interface of Porous, Plain Media. International Journal of Heat and Mass Transfer, 35, 927-943. https://doi.org/10.1016/0017-9310(92)90258-T
[16]
Neale, G. and Nader, W. (1974) Practical Significance of Brinkman’s Extension of Darcy’s Law: Coupled Parallel Flows within a Channel and a Bounding Porous Medium. Journal of Chemical Engineering, 52, 475-478. https://doi.org/10.1002/cjce.5450520407
[17]
Nield, D.A. and Bejan, A. (1992) Convection in Porous Media. https://doi.org/10.1007/978-1-4757-2175-1
[18]
Givler, R. and Altobelli, S. (1994) A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model. Journal of Fluid Mechanics, 258, 355-370. https://doi.org/10.1017/S0022112094003368
[19]
Lundgren, T.S. (1972) Slow Flow through Stationary Random Beds and Suspensions of Spheres. Journal of Fluid Mechanics, 51, 273-299. https://doi.org/10.1017/S002211207200120X
[20]
Durlofsky, L. and Brady, J.F. (1987) Analysis of the Brinkman Equation as a Model for Flow in Porous Media. Physics of Fluids, 30, 3329-3341. https://doi.org/10.1063/1.866465
[21]
Laplace, P. and Arquis, E. (1998) Boundary Layer over a Slotted Plate. The European Journal of Mechanics B/Fluid, 17, 331-355. https://doi.org/10.1016/S0997-7546(98)80262-8
[22]
Pozrikidis, C. (2004) Boundary Conditions for Shear Flow past a Permeable Interface Modeled as an Array of Cylinders. Computers & Fluids, 33, 1-17. https://doi.org/10.1016/S0045-7930(03)00030-6
[23]
Pozrikidis, C. (2005) Effect of Membrane Thickness on the Slip and Drift Velocity in Parallel Shear Flow. Journal of Fluids and Structures, 20, 177-187. https://doi.org/10.1016/j.jfluidstructs.2004.10.013
[24]
Pozrikidis, C. (2010) Slip Velocity over a Perforated or Patchy Surface. Journal of Fluid Mechanics, 643, 471-477. https://doi.org/10.1017/S0022112009992667
[25]
Karniadakis, G., Beskok, A. and Aluru, N. (2002) Microflows: Fundamentals and Simulation. https://doi.org/10.1115/1.1483361
[26]
Zheng, Q.S., Yu, Y. and Zhao, Z.H. (2005) Effects of Hydraulic Pressure on the Stability and Transition of Wetting Modes of Superhydrophobic Surfaces. Langmuir, 21, 12207-12212. https://doi.org/10.1021/la052054y
[27]
Boutier, A. (2012) Vélocimétrie laser pour la mécanique des fluides.
[28]
Diop, M., Piponniau, S. and Dupont, P. (2019) High Resolution LDA Measurements in Transitional Oblique Shock Wave Boundary Layer Interaction. Experiments in Fluids, 60, 57. https://doi.org/10.1007/s00348-019-2701-x
Dantec-Dynamics-SAS (2016) Système de Vélocimétrie Laser Doppler.
[31]
Malavasi, S., Macchi, S. and Merighetti, E. (2008) Cavitation and Dissipation Efficiency of Multihole Orifices. In: Prague, C.Z., Zolotarev, I. and Horacek, J., Eds., Flow-Induced Vibration, Institute of Thermomechanics, Prague, 581-586.
[32]
Malavasi, S., et al. (2012) On the Pressure Losses through Perforated Plates. Flow Measurement and Instrumentation, 28, 57-66. https://doi.org/10.1016/j.flowmeasinst.2012.07.006
[33]
Macchi, S. (2009) Analysis of Multi-Hole Orifices and Their Use in a Control Device [Dissertation].
[34]
Idel’chik, I.E. (1966) Coefficients of Local Resistance and of Friction. U.S. Atomic Energy Commission and the National Science Foundation, Washington DC.
[35]
Tullis, J.P. (1989) Hydraulics of Pipelines—Pumps, Valves, Cavitation, Transients. https://doi.org/10.1002/9780470172803
[36]
Kim, J.M., et al. (1986) Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number. Journal of Fluid Mechanics, 177, 133-166. https://doi.org/10.1017/S0022112087000892
[37]
Cannon, J.N., et al. (1979) A Study of Transpiration from Porous Flat Plates Simulating Plant Leaves. International Journal of Heat and Mass Transfer, 22, 469-483. https://doi.org/10.1016/0017-9310(79)90013-9
[38]
Naot, D. and Kreith, F. (1979) On the Penetration of Turbulence through Perforated Flat Plates. International Journal of Heat and Mass Transfer, 23, 566-568. https://doi.org/10.1016/0017-9310(80)90099-X
[39]
Breugem, W., Boersma, B.J. and Uittenbogaard, R.E. (2005) The Laminar Boundary Layer over a permeable Wall. Transport in Porous Media, 59, 267-300. https://doi.org/10.1007/s11242-004-2557-1
[40]
Kuwata, Y. and Suga, K. (2019) Extensive Investigation of the Influence of Wall Permeability on Turbulence. International Journal of Heat and Fluid Flow, 80, Article ID: 108465. https://doi.org/10.1016/j.ijheatfluidflow.2019.108465
[41]
Spalding, D.B. (1961) A Single Formula for the Law of the Wall. Journal of Applied Mechanics, 83, 455. https://doi.org/10.1115/1.3641728
[42]
Singh, D., Premachandran, B. and Kohli, S. (2013) Numerical Simulation of the Jet Impingement Cooling of a Circular Cylinder. Numerical Heat Transfer, Part A: Applications, 64, 153-185. https://doi.org/10.1080/10407782.2013.772869
[43]
Issac, J., Singh, D. and Kango, S. (2020) Experimental and Numerical Investigation of Heat Transfer Characteristics of Jet Impingement on a Flat Plate. Heat and Mass Transfer, 56, 531-546. https://doi.org/10.1007/s00231-019-02724-9
[44]
Bahmani, S. and Nazif, H.R. (2021) Anisotropic Turbulent Flow Model Effect on the Prediction of the Erosion Rate of the Micro Particulate Flow in the Elbow. Particulate Science and Technology, 39, 1000-1019. https://doi.org/10.1080/02726351.2021.1879980
[45]
Launder, B.E., Reece, G.J. and Rodi, W. (1975) Progress in the Development of a Reynolds Stress Turbulence Closure. Journal of Fluid Mechanics, 68, 537-566. https://doi.org/10.1017/S0022112075001814
[46]
Fluent, I. (2018) Fluent 18.1 User’s Guide.
[47]
Patankar, S.V. (1990) Numerical Heat Transfer and Fluid Flow. 126-129.
[48]
Salim, S.M. and Cheah, S.C. (2009) Wall y + Strategy for Dealing with Wall-Bounded Turbulent Flows. Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong, 18-20 March 2009.
[49]
Moureh, J. and Flick, D. (2005) Airflow Characteristics within a Slot-Ventilated Enclosure. International Journal of Heat and Fluid Flow, 26, 12-24. https://doi.org/10.1016/j.ijheatfluidflow.2004.05.018
[50]
Lam, C.K.G. and Bremhorst, K. (1981) A Modified Form of the k-ε Model for Predicting Wall Turbulence. ASME Journal of Fluids Engineering, 103, 456-460. https://doi.org/10.1115/1.3240815
[51]
Diop, M., Flick, D., Alvarez, G.L. and Moureh, J. (2022) Experimental Study of the Diffusion of a Confined Wall Jet through a Perforated Plate: Influence of the Porosity and the Geometry. Open Journal of Fluid Dynamics, 12, 96-126. https://doi.org/10.4236/ojfd.2022.121006
[52]
Leschziner, M.A. (2000) Turbulence Modelling for Separated Flows with Anisotropy-Resolving Closures. Philosophical Transactions of the Royal Society A, 358, 3247-3277. https://doi.org/10.1098/rsta.2000.0707
[53]
Wilcox, D.C. (1994) Turbulence Modeling for CFD. DCW Industries, Inc., La Canada.
[54]
Menter, F.R. (1997) Eddy Viscosity Transport Equations and Their Relation to the k-ε Model. ASME Journal of Fluids Engineering, 119, 876-884. https://doi.org/10.1115/1.2819511
[55]
Launder, B.E. (1989) Second-Moment Closure and Its Use in Modelling Turbulent Industrial Flows. International Journal for Numerical Methods in Fluids, 9, 963-985. https://doi.org/10.1002/fld.1650090806
[56]
Verhoff, A. (1963) The Two-Dimensional Turbulent Wall Jet with and without an External Stream. Rep. 626, Princeton University, Princeton.
