Skip to main content
SpringerLink
Log in

Conservation of Momentum

  • Chapter
Multiphase Flow Dynamics 1

  • 2696 Accesses

Introduction

As in Chapter 1, from the large number of formulations of the conservation equations for multiphase flows, local volume averaging as founded by Anderson and Jackson, Slattery, and Whitaker was selected to derive rigorously the momentum equations for multiphase flows conditionally and divided into three velocity fields. The heterogeneous porous-media formulation introduced by Gentry et al., commented on by Hirt, and used by Sha, Chao, and Soo, is then implanted into the formalism as a geometrical skeleton. Beyond these concepts, I perform subsequent time averaging. This yields a working form that is applicable to a large variety of problems. All interfacial integrals are suitably transformed in order to enable practical application. Some minor simplifications are introduced in the finally obtained general equation and working equations for each of the three velocity fields are recommended for general use in multiphase fluid dynamic analysis.

This chapter is an improved and extended version of the work published in Kolev (1994b). The strategy followed is: We first apply the momentum equations for each of the velocity fields, excluding the interfaces by replacing their actions by forces. Then, we write a force balance at the interfaces, considering them as immaterial and therefore inertialess. This interfacial force balance links the momentum equations that are valid for the both sides of the interface.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Albring, W.: Angewandte Strömungslehre. Theodor Steinkopff, Dresden (1970)

    Google Scholar 

  • Anderson, T.B., Jackson, R.: A fluid mechanical description of fluidized beds. Ind. Eng. Fundam. 6, 527 (1967)

    Article  Google Scholar 

  • Antal, S.P., Lahey Jr., R.T., Flaherty, J.E.: Analysis of phase distribution in a fully developed laminar bubbly two-phase flow. Int. J. Multiphase Flow 17(5), 635–652 (1991)

    Article  MATH  Google Scholar 

  • Auton, R.T.: The lift force on a spherical body in rotating flow. J. Fluid Mechanics 183, 199–218 (1987)

    Article  MATH  Google Scholar 

  • Barnea, D., Taitel, Y.: Interfacial and structural stability. Int. J. Multiphase Flow 20(suppl.), 387–414 (1994)

    Article  MATH  Google Scholar 

  • Bataille, J., Lance, M., Marie, J.L.: Bubble turbulent shear flows. In: ASME Winter Annular Meeting, Dallas (1990)

    Google Scholar 

  • Bernemann, K., Steiff, A., Weinspach, P.M.: Zum Einfluss von längsangeströmten Rohrbündeln auf die großräumige Flüssigkeitsströmung in Blasensäulen. Chem. Ing. Tech. 63(1), 76–77 (1991)

    Article  Google Scholar 

  • Biberg, D.: An explicit approximation for the wetted angle in two-phase stratified pipe flow. The Canadian Journal of Chemical Engineering 77, 1221–1224 (1999)

    Article  Google Scholar 

  • Biesheuvel, A., van Wijngaarden, L.: Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mechanics 168, 301–318 (1984)

    Article  Google Scholar 

  • Biesheuvel, A., Spoelstra, S.: The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Int. J. Multiphase Flow 15, 911–924 (1989)

    Article  MATH  Google Scholar 

  • Bournaski, E.: Numerical simulation of unsteady multiphase pipeline flow with virtual mass effect. Int. J. Numer. Meth. Eng. 34, 727–740 (1992)

    Article  MATH  Google Scholar 

  • Boussinesq, J.: Essai sur la théorie des eaux courantes. Mem. Pŕs. Acad. Sci., Paris 23, 46 (1877)

    Google Scholar 

  • Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Brauner, N., Maron, D.M.: Stability analysis of stratified liquid–liquid flow. Int. J. Multiphase Flow 18(1), 103–121 (1992)

    Article  MATH  Google Scholar 

  • Crowe, C.T., Pratt, D.T.: Analysis of the flow field in cyclone separators. Comp. Fluids 2, 249–260 (1974)

    Article  MATH  Google Scholar 

  • Cook, T.L., Harlow, F.H.: VORT: A computer code for bubble two-phase flow. Los Alamos National Laboratory documents LA-10021-MS (1983)

    Google Scholar 

  • Cook, T.L., Harlow, F.H.: Virtual mass in multi-phase flow. Int. J. Multiphase Flow 10(6), 691–696 (1984)

    Article  MATH  Google Scholar 

  • de Crecy, F.: Modeling of stratified two-phase flow in pipes, pumps and other devices. Int. J. Multiphase Flow 12(3), 307–323 (1986)

    Article  MATH  Google Scholar 

  • Deich, M.E., Philipoff, G.A.: Gas dynamics of two phase flows, Energoisdat, Moskva (1981)

    Google Scholar 

  • Delhaye, J.M.: Basic equations for two-phase flow. In: Bergles, A.E., et al. (eds.) Two-Phase Flow and Heat Transfer in Power and Process Industries. Hemisphere Publishing Corporation, McGraw-Hill Book Company, New York (1981)

    Google Scholar 

  • Delhaye, J.M., Giot, M., Riethmuller, M.L.: Thermohydraulics of two-phase systems for industrial design and nuclear engineering. Hemisphere Publishing Corporation, McGraw Hill Book Company, New York (1981)

    Google Scholar 

  • Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge Univ. Press, Cambridge (1981)

    MATH  Google Scholar 

  • Drew, D.A., Lahey Jr., R.T.: The virtual mass and lift force on a sphere in rotating and straining flow. Int. J. Multiphase Flow 13(1), 113–121 (1987)

    Article  MATH  Google Scholar 

  • Erichhorn, R., Small, S.: Experiments on the lift and drag of spheres suspended in a Poiseuille flow. J. Fluid Mech. 20(3), 513 (1969)

    Article  Google Scholar 

  • Gray, W.G., Lee, P.C.Y.: On the theorems for local volume averaging of multi-phase system. Int. J. Multi-Phase Flow 3, 222–340 (1977)

    Google Scholar 

  • Helmholtz, H.: Über diskuntinuirliche Flüssigkeitsbewegungen, Monatsberichte der Königlichen Akademie der Wissenschaften zu Berlin, pp. 215–228 (1868)

    Google Scholar 

  • Hetstrony, G.: Handbook of multi-phase systems. Hemisphere Publ. Corp., McGraw-Hill Book Company, Washington, New York (1982)

    Google Scholar 

  • Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for dynamics of free boundaries. J. of Comp. Physics 39, 201–225 (1981)

    Article  MATH  Google Scholar 

  • Ho, B.P., Leal, L.G.: Internal migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 78(2), 385 (1976)

    Article  Google Scholar 

  • Hwang, G.J., Schen, H.H.: Tensorial solid phase pressure from hydrodynamic interaction in fluid-solid flows. In: Proc. of the Fifth International Topical Meeting on Reactor Thermal Hydraulics, NURETH-5, Salt Lake City, UT, USA, September 21-24, vol. IV, pp. 966–971 (1992)

    Google Scholar 

  • Ishii, M.: Thermo-fluid dynamic theory of two-phase flow. Eyrolles, Paris (1975)

    MATH  Google Scholar 

  • Ishii, M., Michima, K.: Two-fluid model and hydrodynamic constitutive relations. NSE 82, 107–126 (1984)

    Google Scholar 

  • Jeffrey, D.: Condition to a random suspension of spheres. Proc. R. Soc. London A335, 355–367 (1973)

    Google Scholar 

  • Kendoush, A.A.: Modification of the classical theory of the virtual mass of an accelerated spherical particle. In: Proc. of the FEDSM 2006, 2006 ASME Joint US-European Fluids Engineering Summer Meeting, Miami, FL, July 17-20 (2006)

    Google Scholar 

  • Klausner, J.F., Mei, R., Bernhard, D., Zeng, L.Z.: Vapor bubble departure in forced convection boiling. Int. J. Heat Mass Transfer 36, 651–662 (1993)

    Article  Google Scholar 

  • Kolev, N.I.: Two-phase two-component flow (air-water steam-water) among the safety compartments of the nuclear power plants with water cooled nuclear reactors during lose of coolant accidents, PhD Thesis, Technical University Dresden (1977)

    Google Scholar 

  • Kolev, N.I.: Transiente Dreiphasen-Dreikomponenten Strömung, Teil 1: Formulierung des Differentialgleichungssystems, KfK 3910 (March 1985)

    Google Scholar 

  • Kolev, N.I.: Transiente Dreiphasen-Dreikomponenten Strömung, Teil 3: 3D-Dreifluid-Diffusionsmodell, KfK 4080 (1986a)

    Google Scholar 

  • Kolev, N.I.: Transient three-dimensional three-phase three-component non equilibrium flow in porous bodies described by three-velocity fields. Kernenergie 29(10), 383–392 (1986b)

    Google Scholar 

  • Kolev, N.I.: A three field-diffusion model of three-phase, three-component Flow for the transient 3D-computer code IVA2/001. Nuclear Technology 78, 95–131 (1987)

    Google Scholar 

  • Kolev, N.I.: IVA3: A transient 3D three-phase, three-component flow analyzer. In: Proc. of the Int. Top. Meeting on Safety of Thermal Reactors, Portland, Oregon, July 21-25, pp. 171–180 (1991a); Also presented at the 7th Meeting of the IAHR Working Group on Advanced Nuclear Reactor Thermal-Hydraulics, Kernforschungszentrum Karlsruhe, August 27-29 (1991)

    Google Scholar 

  • Kolev, N.I.: A three-field model of transient 3D multi-phase, three-component flow for the computer code IVA3, Part 1: Theoretical basics: conservation and state equations, Numerics. KfK 4948, Kernforschungszentrum Karlsruhe (September 1991b)

    Google Scholar 

  • Kolev, N.I., Tomiyama, A., Sakaguchi, T.: Modeling of the mechanical interaction between the velocity fields in three-phase flow. Experimental Thermal and Fluid Science 4(5), 525–545 (1991)

    Article  Google Scholar 

  • Kolev, N.I.: The code IVA3 for modeling of transient three-phase flows in complicated 3D geometry. Kerntechnik 58(3), 147–156 (1993)

    Google Scholar 

  • Kolev, N.I.: IVA3 NW: Computer code for modeling of transient three-phase flow in complicated 3D geometry connected with industrial networks. In: Proc. of the Sixth Int. Top. Meeting on Nuclear Reactor Thermal Hydraulics, Grenoble, France, October 5-8 (1993)

    Google Scholar 

  • Kolev, N.I.: Berechnung der Fluiddynamischen Vorgänge bei einem Sperrwasser-Kühlerrohrbruch, Projekt KKW Emsland, Siemens KWU Report R232/93/0002 (1993)

    Google Scholar 

  • Kolev, N.I.: IVA3-NW A three phase flow network analyzer. Input description, Siemens KWU Report R232/93/E0041 (1993)

    Google Scholar 

  • Kolev, N.I.: IVA3-NW components: relief valves, pumps, heat structures, Siemens KWU Report R232/93/E0050 (1993)

    Google Scholar 

  • Kolev, N.I.: IVA4: Modeling of mass conservation in multi-phase multi-component flows in heterogeneous porous media. Kerntechnik 59(4-5), 226–237 (1994a)

    Google Scholar 

  • Kolev, N.I.: The code IVA4: Modelling of momentum conservation in multi-phase multi-component flows in heterogeneous porous media. Kerntechnik 59(6), 249–258 (1994b)

    MathSciNet  Google Scholar 

  • Kolev, N.I.: The code IVA4: Second law of thermodynamics for multi phase flows in heterogeneous porous media. Kerntechnik 60(1), 1–39 (1995)

    Google Scholar 

  • Kolev, N.I.: Three Fluid Modeling with Dynamic Fragmentation and Coalescence Fiction or Daily practice? In: 7th FARO Experts Group Meeting Ispra, October 15-16 (1996); Proceedings of OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, MD, November 5–8 (1996); 4th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, ExHFT 4, Brussels, June 2-6 (1997); ASME Fluids Engineering Conference & Exhibition, The Hyatt Regency Vancouver, British Columbia, June 22-26 (1997); Invited Paper; Proceedings of 1997 International Seminar on Vapor Explosions and Explosive Eruptions (AMIGO-IMI), Aoba Kinen Kaikan of Tohoku University, Sendai-City, Japan, May 22-24 (1997)

    Google Scholar 

  • Kolev, N.I.: Comments on the entropy concept. Kerntechnik 62(1), 67–70 (1997)

    Google Scholar 

  • Kolev, N.I.: Verification of IVA5 computer code for melt-water interaction analysis, Part 1: Single phase flow, Part 2: Two-phase flow, three-phase flow with cold and hot solid spheres, Part 3: Three-phase flow with dynamic fragmentation and coalescence, Part 4: Three-phase flow with dynamic fragmentation and coalescence – alumna experiments. In: CD Proceedings of the Ninth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, CA, October 3-8 (1999); Log. Nr. 315

    Google Scholar 

  • Kreith, F., Sonju, O.K.: The decay of turbulent swirl in pipe. J. Fluid Mech. 2, part 2, 257–271 (1965)

    Article  Google Scholar 

  • Krepper, E., Lucas, D., Prasser, H.-M.: On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611 (2005)

    Article  Google Scholar 

  • Krepper, E., Egorov, Y.: CFD-Modeling of subcooled boiling and application to simulate a hot channel of fuel assembly. In: 13th Int. Conference on Nuclear Engineering, Beijing, China, May 16-20 (2005)

    Google Scholar 

  • Lahey Jr., R.T.: Void wave propagation phenomena in two-phase flow. AIChE Journal 31(1), 123–135 (1991)

    Article  Google Scholar 

  • Lahey Jr., R.T.: The analysis of phase separation and phase distribution phenomena using two-fluid models. NED 122, 17–40 (1990)

    Google Scholar 

  • Lahey Jr., R.T., Lopez de Bertodano, M., Jones Jr., O.C.: Phase distribution in complex geometry conditions. Nucl. Eng. Des. 141, 177–201 (1993)

    Article  Google Scholar 

  • Lance, M., Bataille, J.: Turbulence in the liquid phase of a uniform bubbly air-water flow. J. Fluid Mech. 22, 95–118 (1991)

    Article  Google Scholar 

  • Lamb, M.A.: Hydrodynamics. Cambridge University Press, Cambridge (1945)

    Google Scholar 

  • Lamb, H.: Hydrodynamics. Dover, New York (1945)

    Google Scholar 

  • Laurien, E., Niemann, J.: Determination of the virtual mass coefficient for dense bubbly flows by direct numerical simulation. In: 5th Int. Conf. on Multiphase Flow, Yokohama, Japan, paper no 388 (2004)

    Google Scholar 

  • Lopez de Bertodano, M.: Turbulent bubbly two-phase flow in triangular duct, PhD Thesis, Renssaelaer Polytechnic Institute, Troy, NY (1992)

    Google Scholar 

  • Mamaev, W.A., Odicharia, G.S., Semeonov, N.I., Tociging, A.A.: Gidrodinamika gasogidkostnych smesey w trubach, Moskva (1969)

    Google Scholar 

  • Mei, R.: An approximate expression for the shear lift force on spherical particle at finite Reynolds number. Int. J. Multiphase Flow 18(1), 145–147 (1992)

    Article  MATH  Google Scholar 

  • Mei, R., Klausner, J.F.: Shear lift force on spherical bubbles. Int. J. Heat Fluid Flow 15, 62–65 (1995)

    Article  Google Scholar 

  • Milne-Thomson, L.M.: Theoretical Hydrodynamics. MacMillan & Co. Ltd., London (1968)

    MATH  Google Scholar 

  • Mokeyev, G.Y.: Effect of particle concentration on their drag induced mass. Fluid. Mech. Sov. Res. 6, 161 (1977)

    Google Scholar 

  • Naciri, A.: Contribution à l’étude des forces exercées par un liquide sur une bulle de gaz: portance, masse ajoutée et interactions hydrodynamiques, Doctoral Dissertation, École Central de Lyon, France (1992)

    Google Scholar 

  • Nigmatulin, R.I.: Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. Multiphase Flow 4, 353–385 (1979)

    Article  Google Scholar 

  • Nigmatulin, R.T.: Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. of Multiphase Flow 5, 353–389 (1979)

    Article  MATH  Google Scholar 

  • No, H.C., Kazimi, M.S.: Effects of virtual mass of the mathematical characteristics and numerical stability of the two-fluid model. In: NSE, vol. 89, pp. 197–206 (1985)

    Google Scholar 

  • Pougatch, K., Salcudean, M., Chan, E., Knapper, B.: Modeling of compressible gas–liquid flow in convergent-divergent nozzle. Chemical Engineering Science 63, 4176–4188 (2008)

    Article  Google Scholar 

  • Prandtl, L.: Essentials of Fluid Dynamics, p. 342. Blackie & Son, Glasgow (1952)

    MATH  Google Scholar 

  • Ransom, V.H., et al.: RELAP5/MOD2 Code manual, vol 1: Code structure, system models, and solution methods, NUREG/CR-4312, EGG-2396. rev. 1 (March 1987)

    Google Scholar 

  • Ruggles, A.E., et al.: An investigation of the propagation of pressure perturbation in bubbly air/water flows. Trans. ASME J. Heat Transfer 110, 494–499 (1988)

    Article  Google Scholar 

  • Schlichting, H.: Boundary layer theory. McGraw-Hill, New York (1959)

    Google Scholar 

  • Sha, T., Chao, B.T., Soo, S.L.: Porous-media formulation for multi-phase flow with heat transfer. Nuclear Engineering and Design 82, 93–106 (1984)

    Article  Google Scholar 

  • Shi, J.-M., Burns, A.D., Prasser, H.-M.: Turbulent dispersion in poly-dispersed gas–liquid flows in a vertical pipe. In: 13th Int. Conf. on Nuclear Engineering, ICONE, Beijing, China, May 16-20, vol. 13 (2005)

    Google Scholar 

  • Slattery, J.C.: Flow of visco-elastic fluids through porous media. AIChE J. 13, 1066 (1967)

    Article  Google Scholar 

  • Slattery, J.C.: Interfacial transport phenomena. Springer, Heidelberg (1990)

    Google Scholar 

  • Slattery, J.C.: Advanced transport phenomena. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  • Staffman, P.G.: The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, Part 2, 385–400 (1965)

    Article  Google Scholar 

  • Staffman, P.G.: Corrigendum to “The lift on a small sphere in a slow shear flow”. J. Fluid Mech. 31, 624 (1968)

    Google Scholar 

  • Steenberger, W.: Turbulent flow in a pipe with swirl, PhD thesis Eindhoven University of Technology (1995)

    Google Scholar 

  • Stokes, G.G.: On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8, 287–305 (1845)

    Google Scholar 

  • Stuhmiller, J.H.: The influence of the interfacial pressure forces on the character of the two-phase flow model. In: Proc. of the 1977 ASME Symp. on Computational Techniques for Non-Equilibrium Two-Phase Phenomena, pp. 118–124 (1977)

    Google Scholar 

  • Thomas Jr., G.B., Finney, R.L., Weir, M.D.: Calculus and analytic geometry, 9th edn. Addison-Wesley Publishing Company, Reading (1998)

    Google Scholar 

  • Tomiyama, A.: Struggle with computational bubble dynamics. In: Proc. of the 3rd Int. Conf. on Multiphase Flow ICMF-1998, France (1998)

    Google Scholar 

  • Tomiyama, A., et al.: Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci. 57, 1849–1858 (2002)

    Article  Google Scholar 

  • Trent, D.S., Eyler, L.L.: Application of the TEMPTEST computer code for simulating hydrogen distribution in model containment structures, PNL-SA-10781, DE 83 002725 (1983)

    Google Scholar 

  • Truesdell, C.: Essays in the history of mechanics. Springer, New York (1968)

    MATH  Google Scholar 

  • van Wijngaarden, L.: Hydrodynamic interaction between the gas bubbles in liquid. J. Fluid Mechanics 77, 27–44 (1976)

    Article  MATH  Google Scholar 

  • van Wijngaarden, L.: On pseudo turbulence. Theor. Comp. Fluid Dyn. 10, 449–458 (1998)

    Article  MATH  Google Scholar 

  • Vasseur, P., Cox, R.G.: The lateral migration of spherical particles in two-dimensional shear flows. J. Fluid Mech. 78, Part 2, 385–413 (1976)

    Article  MATH  Google Scholar 

  • Wang, S.K., Lee, S.J., Jones, O.C., Lahey Jr., R.T.: 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13(3), 327–343 (1987)

    Article  Google Scholar 

  • Wellek, R.M., Agrawal, A.K., Skelland, A.H.P.: Shapes of liquid drops moving in liquid media. AIChE J. 12, 854 (1966)

    Article  Google Scholar 

  • Whitaker, S.: Diffusion and dispersion in porous media. AIChE Journal 13, 420 (1967)

    Article  Google Scholar 

  • Whitaker, S.: Advances in theory of fluid motion in porous media. Ind. Engrg. Chem. 61(12), 14–28 (1969)

    Article  Google Scholar 

  • Whitaker, S.: A Simple geometrical derivation of the spatial averaging theorem. Chem. Eng. Edu., 18–21, 50-52 (1985)

    Google Scholar 

  • Winatabe, T., Hirano, M., Tanabe, F., Kamo, H.: The effect of the virtual mass force term on the numerical stability and efficiency of the system calculations. Nucl. Eng. Des. 120, 181–192 (1990)

    Article  Google Scholar 

  • Wallis, G.B.: One-dimensional two-phase flow. McGraw-Hill, New York (1969)

    Google Scholar 

  • Yamamotto, Y., Potthoff, M., Tanaka, T., Kajishima, Tsui, Y.: Large-eddy simulation of turbulent gas-particcle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303–334 (2001)

    Article  Google Scholar 

  • Zuber, N.: On the dispersed two-phase flow in the laminar flow regime. Chem. Eng. Science 49, 897–917 (1964)

    Article  Google Scholar 

  • Zun, I.: The transferees migration of bubbles influenced by walls in vertical bubbly flow. Int. J. Multiphase Flow 6, 583–588 (1980)

    Article  Google Scholar 

Download references

Authors
  1. Nikolay Ivanov Kolev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kolev, N.I. (2011). Conservation of Momentum. In: Multiphase Flow Dynamics 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20605-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20605-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20604-7

  • Online ISBN: 978-3-642-20605-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation