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Welcome to my personal webpage

 

Education:

B.Sc. in Mechanical Engineering, Alexandria University, Egypt 1997

M.Sc. in Mechanical Engineering, Alexandria University, Egypt 2000

Ph.D. in Mechanical and Aeronautical Engineering, University of California, Davis, USA 2004

PhD Advisor: Prof/ Mohamed Hafez

PhD research topic: CFD

 

What is "CFD" ?

"CFD" stands for: Computational Fluid Dynamics. This branch of fluid mechanics deals with the application of advanced numerical methods to the equations of fluid motion (either in differential or integral form). The whole CFD process could be divided into three major parts:

  • Grid Generation: The physical space is divided into either nodes (for finite difference methods) or control volumes (for finite volume or finite element methods)
  • Discretization of the governing equations: Three major methods are used for discretization in CFD, namely, finite difference methods, finite volume methods and finite element methods. Finite difference methods use Taylor's expansion series to approximate the differential form of the governing equations. Finite volume methods use the integral form of the governing equations to balance mass, momentum and energy over the finite control volumes generated by the grid. Finite element methods use a piecewise polynomial approximation over each finite element and minimize the square of the resulting residual.
  • Solution of the resulting system of nonlinear algebraic equations: The resulting system of nonlinear algebraic equations is first linearized by either lagging part of the nonlinear term or by using Newton's method. The resulting linearized system is then solved using either direct methods (for example Gaussian Elimination) or iterative methods (for example relaxation methods). The convergence of the solution of the system of equations can be accelerated by using convergence acceleration techniques such as local time stepping, residual smoothing and multigrid methods.

    • Research Topic

    My research is concerned with the development of a novel hierarchical formulation for the equations of fluid motion based on a potential function augmented with entropy and vorticity corrections. This is achieved through a velocity decomposition method similar to Helmholtz decomposition where the velocity vector is split into the gradient of a potential function plus a rotational (vortical) component. The density and pressure are reformulated in terms of the speed and entropy. The present method holds several computational advantages over standard Euler and Navier-Stokes solvers in terms of domain decomposition, multigrid, upwinding and the incompressible flow limit. To quantitatively assess the merits of this new approach, a wide range of inviscid and viscous flow problems are simulated spanning the Mach number range from incompressible to supersonic flows with special emphasis on transonic flows. Some of the problems considered are:

  • The Trailing Edge Problem; Comparisons with Triple Deck Theory
  • Shock wave/Boundary Layer Interaction
  • Viscous/Inviscid Interaction
  • Inviscid Separation; Euler solutions involving separation
  • Inviscid and Viscous Flows over Airfoils
  • Inviscid and Viscous Flows over Elliptic Wings; Comparisons with Lifting Line Theory
  • Inviscid and Viscous Flows over Swept Wings; Comparison with standard Euler and Navier-Stokes solvers
  • Multigrid Methods; Exploiting the acoustic and convective modes for Navier-Stokes equations

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    Publications:

    1. Warda, H.A., Kandil, H.A., Elmiligui A.A. and Wahba, E.M.., "Modeling Pressure Transients in Viscoelastic Pipes", PVP-Vol 431, Emerging Technologies for Fluids, Sturctures and Fluid-Structure Interaction, pp 305-323, ASME 2001
    2. Warda, H.A., Kandil, H.A., Elmiligui A.A. and Wahba, E.M.., "Modeling unsteady friction in rapid transient pipe flows", Alexandria Engineering Journal, Vol 40 (2001), pp783-795
    3. Warda, H.A., Kandil, H.A., Elmiligui A.A. and Wahba, E.M.., "Modeling Pressure Transients in Viscoelastic Pipes", Alexandria Engineering Journal, Vol 40 (2001), pp797-809
    4. Wahba, E.M.., "The effect of unsteady friction and column separation on transient flow in viscoelastic pipes", M.Sc. thesis, Alexandria University, Egypt (2000)
    5. Warda, H.A., Kandil, H.A., Elmiligui A.A. and Wahba, E.M.., "Column Separation with the effect of Air Release in Viscoelastic Pipes", Alexandria Engineering Journal, Vol 41 (2002), pp189-203
    6. Hafez, M.M. and Wahba, E.M., "Numerical Simulations of Sonic Booms in Non-uniform Flows",  Proceedings of the Second International Conference on Computational Fluid Dynamics (ICCFD2), Australia 2002 
    7. Hafez, M.M. and Wahba, E.M.., "Hierarchical Formulations for Transonic Flow Simulations",  Proceedings for Symposium Transsonicum IV, Germany 2002, also appeared in Computational Fluid Dynamics Journal, vol.11 no.4, pp377–382, 2003 
    8. Hafez, M.M. and Wahba, E.M.., "Inviscid Flows over a Cylinder",  Computer Methods in Applied Mechanics and Engineering, vol.193, pp 1981-1995, 2004
    9. Hafez, M.M. and Wahba, E.M.., "Numerical Simulations of Transonic Aerodynamic Flows based on a Hierarchical Formulation",  AIAA Paper 03-3564, 2003, also to appear in International Journal for Numerical Methods in Fluids
    10. Hafez, M.M. and Wahba, E.M.., "Multigrid Acceleration of Transonic Aerodynamic Flow Simulations based on a Hierarchical Formulation",  Proceedings of the Third International Conference on Computational Fluid Dynamics (ICCFD3), Toronto, Canada, 2004, also to appear in International Journal for Numerical Methods in Fluids
    11. Hafez, M., Shatalov, A. and Wahba, E.., "Numerical Simulations of Incompressible Aerodynamic Flows using Viscous/Inviscid Interaction Procedures",  To appear in Computer Methods in Applied Mechanics and Engineering
    12. Hafez, M.M. and Wahba, E.M.., "Viscous/Inviscid Interaction Procedures for Compressible Aerodynamic Flow Simulations",  To appear in Computers and Fluids
    13. Hafez, M.M. and Wahba, E.M.., "Incompressible Viscous Steady Flows over Finite Flat Plate and Rotating Cylinder with Suction",  To appear in Computational Fluid Dynamics Journal

     

    Awards:

    1. Joseph L. Steger Award for outstanding graduate achievements in CFD. (University of California, Davis 2003)
    2. Essam A. Salem Award for best thesis in Fluid Mechanics. (Alexandria University, 2004)
    3. Dean of Engineering Award for ranking first over the Mechanical Engineering Department. (Alexandria University 1994,1995,1996,1997)

     

    Academic Experience:

    1. Teaching Assistant , Mechanical Engineering Department, Alexandria University, Egypt (1997 - 2000)
    2. Research Assistant , Mechanical and Aeronautical Engineering Department, University of California, Davis (2001 - present)
    3. Associate Lecturer , Mechanical Engineering Department, Alexandria University, Egypt (2000 - present)

    Historical development of Fluid Mechanics

  • Aristotle (384-322 BC): He introduced the concept of a continuum.
  • Archimedes (287-212 BC): The founder of fluid statics, he explained the origin of bouyancy forces exerted by fluids on immersed bodies, the well known Archimedes Principle.
  • Leonardo Da Vinci (1452-1519): First statement of the continuity equation (AV=constant).
  • Galileo Galilei (1564-1642): He introduced the basic elements for classical mechanics.
  • Isaac Newton (1642-1727): He laid down the firm mathematical foundation for classical mechanics based on his three famous laws. Newton's second law together with the conservation laws of mass and energy govern how fluids flow. He also introduced the concept of a Newtonian fluid, which in turn defines the relation between the stress and the rate of strain in a fluid.
  • Daniel Bernoulli (1700-1782): He introduced the most famous equation in fluid mechanics, namely Bernoulli's law.
  • Leonhard Euler (1707-1783): He developed the concept of the material derivative and in turn was able to derive the governing equations for inviscid fluid motion.
  • Jean le Rond D'Alembert (1717-1783): Well known for D'Alembert's paradox which states that there is no drag exerted on a body immersed in an inviscid free stream, this led to wide criticism of the invsicd theory and in turn led to the rise of experimental fluid mechanics.
  • Pierre-Simon Laplace (1749-1827): Accurate calculation of the speed of sound.
  • Louis Navier (1785-1836) and George Stokes (1819-1903): They derived independently the governing equations for viscous fluid flow.
  • Osborne Reynolds (1842-1912): the most famous experiment in fluid mechanics, he used a dye injected in a pipe flow to demonstrate the transition of the flow from laminar to turbulent. This gave rise to the most well known dimensionless number in fluid mechanics, the Reynolds number. He also derived the Reynolds averaged version of the Navier-Stokes equations which showed the Reynolds stresses arising from turbulence.
  • Ernest Mach (1838-1916): He pointed out the importance of the relative value of the flow velocity with respect to the speed of sound. The ratio of these two variables leads to the well known Mach Number and the consequent effects of compressibility. He also captured the first photograph of a shock wave in a lab.
  • William Rankine (1820-1872) and Pierre Henri Hugoniot (1851-1887): They developed the equations governing the jump conditions across a normal shock, well known as the Rankine-Hugoniot jump conditions.
  • Ludwig Prandtl (1875-1953): He published the most famous paper ever in fluid mechanics, in which he introduced the concept of the boundary layer. He also developed the oblique shock relations, the Prandtl-Meyer relations for expansion fans and the lifting line theory for wings. He introduced the concept of viscous-inviscid interaction. He also developed the mixing length model for turbulent flows. For all these achievements, he is well known, and rightfully so, as the father of modern fluid mechanics.

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    About Alexandria, Egypt

    In the first part of 331 BC, shortly after being crowned Pharaoh in Memphis, Alexander the Great sailed northwards down the Nile and there he began his most lasting contribution to civilization. On the natural harbor near Rhacotis he built a fortified port and named it Alexandria. Alexander then connected the island of Pharos, located in the center of the bay, to the mainland with a 1,300-meter causeway, the Heptastadion. Thus two great harbors were created for his city and towering over it all, the Pharos Lighthouse, one of the Seven Wonders of the Ancient World.

    Following Alexander's death, his generals divided the Empire, each setting up their own kingdoms. One of them, Ptolemy, took Egypt as his share and made Alexandria his capital, ruling as Ptolemy I Soter and thus established the last dynasty that would rule Egypt with the title of Pharaoh. He brought Alexander's body with him to be buried in the city, reuniting the famed conqueror with the city that bore his name. It was under the Ptolemaic Dynasty that Alexandria truly became the cultural and economic center of the ancient world. Egypt was ruled from Alexandria by Ptolemy's descendants until the death of Cleopatra VII in 30 BC.

    This was quite literally a golden age for the citizens of Alexandria, and for Egypt as a whole. Although Alexander never lived to see its glory, it nevertheless became the racial melting pot he is said to have wanted for his capital city. Ptolemy decided early on that Alexandria would be not just another port capital, but the home of a new age in science and art. It may seem surprising to find such an impulse in a military man, but Ptolemy was more than just another general. He was a great writer of histories, including detailed accounts of Alexander's campaigns, and this love for learning did not die with him. Ptolemy's son and heir Ptolemy II Philadelphus, for instance, had a passion for science, and Ptolemy III was a manic collector of books. Ptolemy invited scholars and artists from all over the known world to come to Alexandria to foster the learning culture of Alexandria. The arrival of many of these learned people, and later the successors they found amongst the citizens of their new home, resulted in one of the most famous images of historic Alexandria: the Library.

    The Library at Alexandria was conceived largely as an attempt to bring together in Alexandria the whole of the earlier Greek science, art, and literature. The models for this project may very well have been the research center created by Aristotle at the Lyceum, as well as Plato's Academy. However, the Library of Alexandria did not just archive information, it made it accessible to those who sought it, and in return, added to it. And add to it they did. At one point the Library held close to fifty thousand books, for the ancient world an astonishing number.

     

    The Contribution of Alexandria to Mathematics and Engineering

    1. Euclid of Alexandria: The father of geometry, Euclidean Geometry is named after him. He is author of "The Elements" a series of books in which he summarizes all the axioms and theories of geometry. Although this was done around 300 B.C., "The Elements" is still more or less the main source for Euclidean Geoemetry taught in schools nowadays.
    2. Diophantus of Alexandria: Considered by many as the father of algebra. He is author of "Arithmetica" a work on the solution of algebraic equations and the theory of numbers. He was the first to introduce algebraic symbolism.
    3. Hero of Alexandria: His book on pneumatics gave rise to the Alexandria-born science of Hydraulics. The book includes nearly 80 ingenious inventions (such as siphons, fountains, and engines) and it also describes many gadgets and magical tricks, including the first suggestion of a steam engine. He is also remembered for his formula for the area of a triangle and a method for approximating the square root of a number.
    4. Pappus of Alexandria: Another great mathematician. His most famous theorem (Pappus' Theorem) is considered the basis of modern projective geometry.

     

     

    Contact Details:

    Home Phone: 001-530-7581920

    email         : eswahba@ucdavis.edu