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Professor Dr. Noor Afzal
Ex-Officiate Vice Chancellor Aligarh Muslim University (1998-2004) Amongst the World's Top 2 percent of Scientists in World. Listed during 2020 on the website of Stanford University, California USA. Rank worldwide Top % = 1.2695, Rank worldwide (by Subject area) 1171, C-Store = 3.2477, Number of papers published = 96, Duration = 1971 to 2018Area of Expertise: Aerospace and Mechanical Engineering
- Turbulent shear flows (boundary layers, channel, pipe, wall jets),
- Flow Controls,
- Aero-space Aerodynamics, Missile Aerodynamics,
- Meteorology: Turbulent Ekman layer over the transitional rough surface
- Turbulent Hydraulic jump over smooth and rough bed channel and shock wave analogy
- Primary focus on multiscale turbulence using asymptotic methods.
- Computational Fluid Dynamics (DNS data).
- Friction factor Moody diagram extension for inflectional /sand grain/wall roughness
- Experimental Fluid Dynamics (HW & LDA).
- Thermo-fluid dynamics. Higher-order laminar boundary layer
- Flow over moving /stretching industrial surfaces.
Turbulence:
1. Noble Laureate 1932 Werner Heisenberg (1901-1976) German theoretical quantum physicist was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."
2. Horace Lamb FRS (1849-1934) In 1932 Lamb in an address to the British Association for the Advancement of Science, wittily expressed on the difficulty of explaining and studying turbulence in fluids. He reportedly said, "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former, I am rather optimistic."
3. Noble Laureate 1965 Richard Feynman (1918-1988) described “Turbulence as the most important unsolved problem of classical physics”.
4. Noble Laureate 1983 Subrahmanyan Chandasekhar (1910-1995) after 50 years of 1930's research work in Astro-physics (Chandasekhar limit determines whether a star ends its life, can collapse under their own gravity. as a smoldering white dwarf, or explodes in a supernova to become a neutron star or black hole. The Chandrasekhar limit value for a white dwarf star is generally considered to be 1.4 solar masses. “Chandra made a couple of visits to India at that one time, RN (Roddam Narasimha) asked him during his 1960 visit, whether he is continuing his work on turbulence. The answer was no. It is too controversial for me”. Reference:
Symposium on "Turbulence - the Historical Perspective", 16-17 September 2011, Faculty of Physics, University of Warsaw, Poland
https://www.youtube.com/watch?v=wc3dOJEXYFE
Nobels neglect fluid dynamics, Physics Today 74, 1, 10 (2021)
Sir Geoffery Ingram Taylor OM FRS in 1935 privately complained about the Nobel Committee’s preference for “atomic physics,” owing to nominations being made by previous recipients. Believing that Prandtl should have been awarded a Nobel, Taylor wrote that the prize needed to be opened up to “non-atomic physicists.”. Von Karman expressed similar thoughts regarding Prandtl’s deservedness. The Nobel Committee’s dismissive attitude toward fluid mechanics continues to this day.
Turbulence : Distinguished outstanding research contributions:
Formulation of the Izakson- Millikan - Kolmogorov hypothesis (Afzal, N. & Narasimha, R. 1976 Journal of. Fluid Mechanics, and Afzal, N. 1976 Physics of Fluids) about the matching of the two asymptotic expansions in MMX while dealing with open equations of turbulent motion of a fluid, without any closure model; like eddy viscosity. mixing length etc.
Founder of mesolayer (intermediate layer) in a turbulent shear flow (1982-1985) around peak of Reynolds shear stress domain being the geometric mean of 1930's inner wall layer and outer shallow wake layer of turbulent shear flow -- classical discovery by Ludwig Prandtl and Theodore Von Karman. The mesolayer length scale is the order of the Taylor micro length scale. The mesolayer time scale of the order of the Taylor micro time scale; has been turbulent energy bursting time process.
Founder of the power law turbulent velocity profile theory (1997-2009), being equivalent to log law theory for large Reynolds numbers
Hydraulic jump over smooth and rough bed channel (2002-2011).
Extension of fictional roughness Moody diagram for an inflectional rough surface. (2007)
Invention of the Roughness Reynolds number (2006).
Invention of the Roughness friction Reynolds number (2006).
Invention of the Roughness Froude Number (2011).
Turbulent closure model (2022): A new formulation between Reynolds shear stress - \rho<u'v'> with mean velocity ratio u/U_c in the turbulent boundary layer, channel and pipe flows,
LANDMARKS Scientific Research Contributions:
1. Egolf, P.W. and Hutter, K. 2020 Nonlinear, Nonlocal and Fractional Turbulence: Alternative recipes for the modeling of turbulence. pp 65-67, Cham - Springer:
Table 5.3 The preference for a logarithmic and a power law was alternating over the last hundred years - page 65:
1938 Millikan (1938) Similarity hypothesis favors the logarithmic law
2001 Afzal (2001) Shows that similarity consideration of Millikan can also be applied to confirm a power law
6.1 In a publication of Cipra (1996) in “Science” Chorin is cited: "The 'law of the wall' was viewed as one of the few certainties in the difficult field of turbulence, and now it has been dethroned". He further continues by writing “Generations of engineers, who learned the law, will have to abandon it.”
Cipra, B. 1996 A new theory of turbulence causes a stir among experts. Science. 272 (5264), page 951. https://science.sciencemag.org/content/272/5264/951.full
6.2 Then at the very beginning of the new millennium Afzal (2001) demonstrated that the Millikan/Izakson/Clauser idea can also be applied to prove consistency with a power law as averaged velocity profile of the overlap region. This work then immediately removed a believed theoretical obstacle for acceptance of a power law.
References:Noor Afzal 2001a Power and log laws velocity profiles in turbulent boundary layer flows: equivalent relations at large Reynolds numbers. Acta Mechanica, Vol 151, pp.195-216.Noor Afzal 2001b Power and log laws velocity profiles in fully developed turbulent pipe flow: equivalent relations at large Reynolds numbers. Acta Mechanica, Vol 151, pp.171-183.Noor Afzal 1997 Power laws in the wall and wake layers of a turbulent boundary layer. pp 805 - 808 in Proc 7 Asian Congress of Fluid Mechanics at Chennai. Allied Publisher New Delhi. arXiv:2006.02697v2 [physics.flu-dyn] 9 Jun 2020
2. When Prandtl was asked by a colleague about the theoretical derivation of Blasius 1/4 power law , Prandtl answered:
Whoever finds it will become a famous man
Reference: (Prandtl, L, 1923 Sie fragen nach der theoretischen Ableitung des Blasiusschen Widerstandsgesetzes fr Rohre. Wer der wird dadurch ein berhmter Mann! Prandtl to Birnbaum, 7 June 1923, MPGA, Abt. III, Rep. 61, Nr. 137), Page 271 footnore 37 in Micheal Eckert, Pipe flow: A gateway to turbulence. Archive for History of Exact Sciences 75,(3) pp. 249-282, Year 2021. ---
Afzal (2001a.b) has rationally derived the power law velocity and friction factor for all vales of "n" the power law index for turbulent boundary layer and pipe flow. Further, the power law velocity and power law friction factor have envelopes and a tangent at any point on envepoes lead to log law velocity and log law friction factor for a general values of power law index "n" for all values of Reynolds numbers in the turbulent flow domain.
2i) Prandtl (1935, page 135) proposed log law u_+ = \ka^{-1} \ln y_+ + B for large Reynolds numbers, and likewise power law of form u_+ = C y_+^\al + C* a very useful formula for smaller Reynolds numbers. [Prandtl, L. 1935 The Mechanics of Viscous Fluids. In: W.F, D. (ed.) Aerodynamic Theory III. Berlin: Springer. Refer page. 135 eqns (21.18) and (21.19)]. Afzal (2001) has shown that the power law velocity and power law friction factor have envelopes and a tangent at any point leads to log law velocity and log law friction factor for all values of power law index ,'n' and all Reynolds numbers in turbulent flow domain'
3. P. S. Granville [1987, J. Ship Research 31(3), 207] has termed the research work by N.Afzal and R. Narasimha (1976 Journal Fluid Mechanics 74, 113-25) as ”LANDMARK PAPER”, dealing with turbulent flow on axially symmetric cylindrical missile like objects with experimental confirmation of this approach provided by N. Afzal & K.P. Singh (1976, Royal Aeronautical Society, London: Aero. Quart. Vol 27, pp. 217-228). And others have noted it as a widely accepted rational theory: NASA Ames: J.C.Neves, P. Moin & R.D. Moser (1994 Journal Fluid Mechanics 272, 349-381) and R.M. Lueptow (1988 Report NUSC TR 8389, Naval Underwater System Center, New Port R.I., USA).
4. The measurements of N. Afzal and K . P. Singh (1976, Aeronautical Quarterly: Royal Aeronautical Society London Vol 27, pp 217-228) have for long been.
”the only measurements of turbulent quantities”
in the flow (Denli & Landweber 1979 J. Hydronautics 13, 93) and have been extensively reviewed by Lueptow (1988 Report NUSC Technical Report 8389 Naval Underwater System Center, New Port R.I., USA).
5. Recognizing the nature of an argument in the abstract is often a very big advance, because it illuminates a wide variety of situations earlier thought to be diverse. This of course was the kind of contribution S. Kaplun, P.A. Lagrestrom and Coworker in California Institute of Technology Pasadena California during 1957 made when they invented (or 'abstracted' ) from Prandtl1s 1904 work on laminar boundary layer) the principles of matched asymptotic expansions, for a closed equations, say; laminar motion. In a turbulent flow we deal with open equations of turbulent motion and contribution made by N. Afzal and R. Narasimha (1976, Journal of Fluid Mechanics) and N. Afzal (1976, Physics of Fluids) when they invented Izakson-Millikan-Kolmogorov hypothesis (or 'abstracted' from Izakson 1937, Millikan 1939 & Kolmogorov 1941 work on the turbulent motion) as the principles of matching in the method of matched asymptotic expansions for instantaneous Navier-Stokes equations for turbulent flow, or the open Reynolds equations of mean turbulent flow and instantaneous turbulent fluctuations.
Reference: DIALOGUE CONCERNING THE USE OF MATCHED ASYMPTOTIC EXPANSIONS IN TURBULENT FLOWS between Roddam Narasimha and Donald Coles held at California Institue of Technology, Pasadena, California . Report 77 FM 15, December 1977 , Bangalore 560012, India.
Founder of mesolayer (intermediate layer) in a turbulent shear flow (Afzal 1982-1985) is around the peak of Reynolds shear stress domain, being the geometric mean of inner wall layer and outer wake layer of a turbulent shear flow -- after 1930's classical discovery of inner and outer layers by Ludwig Prandtl and Theodore Von Karman. The mesola2yer length scale is the order of the Taylor micro length scale. The mesolayer time scale is of the order of the Taylor micro time scale; having turbulent energy bursting time process phenomena.
Noor Afzal's Invention of an Intermediate layer (mesolayer) in a turbulent shear flow in space and time variables (Afzal 1982 Ingenieur-Archiv Vol 52, pp. 355-377 Springer Verlag, Berlin) being geometric mean of inner layer and outer layer scales for space and time scales in turbulent pipe, channel and boundary layer flows; after 1930's wall layer and outer layer from Prandtl and Karman : Review of four decades research, Technical Report No 5 of 14 July 2022 AMU Aligarh India. Perspectives of world wide plagiarism by the researchers in advance Counties, Submitted to Journal of Fluid Mechanics with a letter to Colm-cille P. Caulfield Editor, Journal of Fluid Mechanics.
7. Part of work in Afzal (1983 Int. J. Engineering Sciences Vol 21, pp. 563-576) was presented by Noor Afzal (1980) and published in the Proceedings of the First Asian Congress of Fluid Mechanics (ACFM) Bangalore. The ACFM Bangalore Organizer, Professor Roddam Narasimha, sent the manuscript or review to Professor Akiva Moiseevich Yaglom, Moscow and his comments. Yaglom in a letter dated 6 December 1979 addressed to the Chairman ACFM wrote, a part of which is quoted below:
(Quote begins) " The most exciting statement of Afzal's paper from my point of view is the proof of the half-power law with the non-constant coefficients A(L) and C(LRp). Unfortunately, I must confess that I do not understand this proof. In fact, we tried hard to obtain theoretically, the half-power law with A(L) when working at the power with Kader*. At least twice we had the feeling that we have found the proof, but after that, we found deficiencies in our arguments. Now my feeling is that this law can not be proved logically but I 'II be happy if I am not right and you are right ---- I think that the topic is very exciting and I hope you will continue the work --"(Quote ends).
*Kader B. A. Yaglom, A.M. 1978 Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients, Journal of Fluid Mechanics 89(02):305 - 342
8. M. H. Buschmann, and M. Gad-el-Hak 2007 Recent developments in scaling of wall-bounded flows, Progress in Aerospace Sciences, Vol. 42 , pp. 419-467. 50 citations of Afzal's recent work-See Section 6. Power laws by N. Afzal and W. Nunner page 446 - 4526.1 The open functional equation by N.Afzal page 446 6.2 The power law by W. Nunner page 4486.3 Experimental evidence of Afzal’s and Nunner’s power laws page 450
9. Discovery 2006: Two non-dimensional numbers for transitional rough wall.
10. Discovery 2007: Friction factor for inflectional /sand grain/ machine honed roughness :
This is a variant of Figure 1 in McGovern (2011) that includes inflectional roughness curves in accordance with Equation 20, where j has a value of 11. Jim McGovern 2011 Friction Factor Diagrams for Pipe Flow. Dublin Institute of Technology, Dublin Ireland. http://arrow.dit.ie/cgi/viewcontent.cgi?article=1030\&context=engschmecart
Significant examples: The friction factor diagram lambda vs Re for any rough pipe for specific roughness function phi = exp (k grad U+) (say, for Colebrook, sand grain roughness etc) is reduced to universal friction factor line lambda vs Re/phi for all types of transitional roughness. Blasius (1908) 1/4 power law friction factor lambda = 0.3164 Re^{-1/4} for fully smooth pipe is extended to transitional rough pipes friction factor law lambda = 0.3164 (Re/phi)^{-1/4} for all types of transitional roughness. Dean (1958) power law friction factor lambda = 0.294 Re^{-1/4} for fully smooth channel is extended to transitional rough channel friction factor law lambda = 0.294 (Re/phi)^{-1/4} for all types of transitional rough channels.
Friction factor for inflectional /sand grain/ machine honed roughness :
Afzal (2007, 2011) have provided an extension of the Colebrook White equation (1939) that is capable of representing Nikuradse’s (1933) data and data from modern pipes that have inflectional friction factor curves with good accuracy, Equation 20. This is identical to the Colebrook White equation when the dimensionless roughness parameter j has a value of zero. Afzal found that a value of j = 11 provided a good fit to the data of Sletfjerding and Gudmundsson (2003), Shockling (2005; 2007) , and Nikuradse (1933). The version of Equation 20 given by Afzal (2007, 2011) appears to omit a factor of two in the exponential term. The experimental data with j=11 confirm good agreement with friction factor (Afzal 2007)
11. Discovery 2011: Roughness Froude number Fs = F [(1- l)(1+b) - G ]^{1/2}
Afzal, N., Bushra, A. and Seena, A. 2011 Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel: Universal Relations, Journal of Engineering Mechanics, Proc ASCE 137 (12) , 835-845.
Here i is the channel bed drag coefficient, b is kinetic energy correction factor and G is the effective Reynolds normal stress coefficient in hydraulic jump and F is the conventional Froude number in a fully smooth bed channel. The turbulent jump over a smooth bed channel predictions are extended to turbulent hydraulic jump over a transitional rough bed channel. Thus Fs be termed as Afzal channel number.
Significant example: The hydraulic jump depth ratio (the Belanger 1840 type relation) h2/h1, product of mean velocity across jump U1 U2 (analogous Prandtl relation of product of mean velocity across shock wave) etc for fully smooth bed channel pipe are extended to transitional rough bed channels provided conventional Froude number F is replaced by effective Froude number Fs.
12. M.H. Buschmann and M. Gad-el-Haq (2003 AIAA J. 41(1),page 40) have termed that ”Afzal (2001 Acta Mechanica, v 151, pp171-183 and pp195-216) rigorously demonstrated the equivalence of the log and power laws at very large Reynolds numbers”, and on page 47 have termed that ”the second order theory was originally derived by Afzal (1976, Physics of Fluids 19, 600-602) and third order theory developed by Afzal & Bush (1985,Proc Ind. Acad Sci A: 94, 135-48)”.
13. M. H. Buschmann and M. Gad-el-Haq (2002 IUTAM Symposium Princeton Uni) on first page stated that ”Alternative Reynolds number dependent power laws (George & Castillo 1997, Barenblatt etal 2000, Afzal 2001) have been advanced”.
14. The summary report by Eaton, J. K. & Nagib, H. M. (2004) on the ’Second International Workshop on wall bounded turbulent flows’ by M.H. Nagib and A. J. Smits held on 2-5 Nov 2004 at the Abdus Salam International Center of Theoretical Physics, Trieste on page 3 stated that ” Noor Afzal highlighted a number of limitations in the asymptotic analysis leading to the power law for the boundary layer theory by George et al (1996-2003). (see also Paper No AIAA-2005-0109 by Afzal).
15. N. Afzal & A. Bushra (2011, 2006, 2002) J. Hydraulic Research provided the rational theory to the outstanding flow problem in the Structure of turbulent hydraulic jump for rough and smooth bed open channels, after 175 years of Belanger (1928) hydraulic jump conditions (see review by W.H. Hager 1990 Schweizer Ingenieur & Architect No 25 pp728-735).
16. Noor Afzal, 2012 Erratum/IIPR "Accounting for uncertainty in the analysis of overlap layer mean velocity models T. A. Oliver and R.D. Moser [Phys. Fluids 24, 075108 (2012)]", Technical Report No 2/2012 ASCD-ME,Aero-Space Consultancy Division, Golden Apartment, Sahab Bagh, Aligarh 202002 India.
18 Noor Afzal 2023 INDUSTRIAL THERMO-FLUID-DYNAMICS: A CONTINUOUS SURFACE MOVING THROUGH A FLUID Department of Mechanical Engineering, Aligarh Muslim University Aligarh 202002, India
ALIGARH MUSLIM UNIVERSITY, ALIGARH 202002, UP, INDIA
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