Forman A. Williams

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Forman A. Williams
Forman A. Williams.jpg
Born (1934-01-12) January 12, 1934 (age 89)
Alma materPrinceton University
California Institute of Technology
Known forG equation
Williams spray equation
Williams diagram
Emmons–Williams equation
Clavin–Williams equation
Peters-Williams chemistry
Activation energy asymptotics
Cool flame
Klimov-Williams criterion
San Diego Mechanism
Flame stretch
Combustion instabilities
Laminar flamelet model
Scientific career
FieldsFluid dynamics
Aerospace Engineering
InstitutionsHarvard University
University of California, San Diego
Princeton University
Yale University
ThesisTheoretical Studies In Heterogeneous Combustion (1958)
Doctoral advisorStanford S. Penner[1]
Doctoral studentsChung K. Law
Carlos Fernández-Pello

Forman Arthur Williams (born January 12, 1934) is an American academic in the field of combustion and aerospace engineering who is Emeritus Professor of Mechanical and Aerospace Engineering at the University of California San Diego.[2]


Williams received his bachelor's degree from Princeton University in 1955 and on Martin Summerfield's advice, he moved to California Institute of Technology to pursue his PhD, graduating it in 1958 under the supervision of Sol Penner, with Richard Feynman on the thesis committee.[3] He presented his PhD thesis to von Kármán at his home, who had influenced Williams greatly.[4]


After finishing his PhD, Williams worked in the Division of Engineering and Applied Physics at Harvard University until 1964, after which he joined the faculty at UCSD. He was the fourth faculty member to be appointed, when Sol Penner founded the Engineering department in University of California, San Diego. In January 1981, he accepted the Robert H. Goddard chair at Princeton, eventually returning to UCSD in 1988. Williams also served as an adjunct Professor at Yale University for one month of each year starting in 1997 and culminating after ten years. He was also the director of Center for Energy Research from 1990 to 2006 at UCSD. He served as a department chair at UCSD for four years.[5]


Williams' research interests includes combustion, propulsion applications, micro-gravity flames etc. He made seminal contributions to the combustion field for the past six decades and considered as one of the prominent scientist in combustion.[6] He wrote the Williams spray equation in 1958[7] when he was still a PhD student, as a statistical model for spray combustion analogous to Boltzmann equation. Though Activation Energy Asymptotics were known to Russian scientists forty years ago, it was Williams' call in 1971 in Annual Review of Fluid Mechanics[8] which made the western scientific community to start using the analysis.[9] He wrote down the G equation in 1985,[10] a model for premixed turbulent flame as a wrinkled flame. The classification of Combustion instabilities was first introduced by Williams and Barrère in 1969.[11]

He worked on number of projects with NASA, Air force and other organizations. He is the principal investigator of the following International Space Station experiments, MDCA (Multi-user Droplet Combustion Apparatus), FSDC (Fiber Supported Droplet Combustion), FSDC-2 (Fiber Supported Droplet Combustion - 2),[12] DCE (Droplet Combustion Experiment),[13] FLEX (Flame Extinguishment Experiment),[14] FLEX-2 (Flame Extinguishment Experiment - 2),[15] Cool Flames Investigation.[16] He conducted lot of experiments, some of his recent experiments include spiral flames in von Kármán swirling flow, ethanol flames, fire spread etc.


Williams Combustion Theory, second edition published in 1985, is still an authoritative book in the combustion field.


  • Stanford S. Penner, Forman A. Williams (Eds) (1962). Detonation and Two-Phase Flow. Academic Press. ISBN 978-0-12-395556-2.
  • Forman A. Williams, Marcel Barrère, N. C. Huang (1969). Fundamental aspects of solid propellant rockets. Technivision Services.{{cite book}}: CS1 maint: multiple names: authors list (link) "Fundamental aspects of solid propellant rockets" (PDF).[dead link]
  • Paul A. Libby, Forman A. Williams (Eds) (1980). Turbulent reacting flows. Springer. ISBN 978-3-662-31257-5.
  • Forman A. Williams (1985). Combustion Theory. Benjamin Cummings. ISBN 978-0201407778.
  • Paul C. Fife, Amable Liñán, Forman A. Williams (Eds) (1991). Dynamical Issues in Combustion Theory. Springer. ISBN 978-1461269571.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Amable Liñán, Forman A. Williams (1993). Fundamental Aspects of Combustion. Oxford University Press. ISBN 978-0195076264.
  • Forman A. Williams, A.K. Oppenheim, D.B. Olfe, M. Lapp (Eds) (1993). Modern Developments in Energy, Combustion and Spectroscopy. Pergamon Press. ISBN 978-0080420196.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Paul A. Libby, Forman A. Williams (Eds) (1994). Turbulent reacting flows. Academic Press. ISBN 978-0124479456.

Lecture Notes[edit]

  • Forman A. Williams (1972). Some Mathematical Methods useful in Applied Science.


Williams is an elected member of National Academy of Engineering (1988)[17] and also in American Academy of Arts and Sciences (2010).[18] He is a fellow of The Combustion Institute.[19] He is elected as a fellow of APS in 2002.[20] He is also a member of AIAA, SIAM etc. He holds an honorary doctorate degree from Technical University of Madrid. He has been in the editorial board of various journals, currently he is in the editorial board of Progress in Energy and Combustion Science,[21] Combustion Science and Technology.[22] He was a member of the National Construction Safety Team Advisory Committee in reporting the Collapse of the World Trade Center.[23][24] Some of his awards include:

A conference titled Symposium on Advancements in Combustion Theory was conducted at UCSD in 2004 in honor of Williams 70th birthday.[30] Combustion Science and Technology released a special issue in honor of Williams 80th birthday.[31]


  1. ^ "Stanford Penner - the Mathematics Genealogy Project".
  2. ^ "UCSD Jacobs School of Engineering".
  3. ^[bare URL PDF]
  4. ^ "History | Mechanical and Aerospace Engineering".
  5. ^ "UCSD Jacobs School of Engineering".
  6. ^ Law, Chung K.; Yang, Vigor (2015). "Preface to the Special Issue Celebrating Professor forman a. Williams'S 80th Birthday". Combustion Science and Technology. 187 (1–2): 1–2. doi:10.1080/00102202.2015.975005. S2CID 94126136.
  7. ^ Williams, F. A. "Spray combustion and atomization." The physics of fluids 1.6 (1958): 541-545.
  8. ^ Williams, F. A. "Theory of combustion in laminar flows." Annual Review of Fluid Mechanics 3.1 (1971): 171-188.
  9. ^ Buckmaster, John David, and Geoffrey Stuart Stephen Ludford. Theory of laminar flames. Cambridge University Press, 1982.
  10. ^ Williams, F. A. "Turbulent combustion." The mathematics of combustion 2 (1985): 267-294.
  11. ^ Barrere, M., & Williams, F. A. (1969, January). Comparison of combustion instabilities found in various types of combustion chambers. In Symposium (International) on Combustion (Vol. 12, No. 1, pp. 169-181). Elsevier.
  12. ^[bare URL PDF]
  13. ^[bare URL PDF]
  14. ^ "Experiment Details".
  15. ^ "Experiment Details".
  16. ^ "Experiment Details".
  17. ^ "Dr. Forman A. Williams".
  18. ^ "Forman A. Williams".
  19. ^ "Fellows of the Combustion Institute | the Combustion Institute". 20 June 2017.
  20. ^ "APS Fellow Archive".
  21. ^ "Editorial board - Progress in Energy and Combustion Science - ISSN 0360-1285".
  22. ^ "Combustion Science and Technology".
  23. ^ "PULSE - UCSD Jacobs School of Engineering Newsletter". Archived from the original on 2020-05-03. Retrieved 2020-06-06.
  24. ^ Quintiere, James G.; Williams, Forman A. (2014). "Comments on the National Institute of Standards and Technology Investigation of the 2001 World Trade Center Fires". Journal of Fire Sciences. 32 (3): 281–291. doi:10.1177/0734904114528457. S2CID 112642526.
  25. ^ "Bernard Lewis Gold Medal | the Combustion Institute". 24 June 2016.
  26. ^ "Home : The American Institute of Aeronautics and Astronautics".
  27. ^ "Awards".
  28. ^ "Home : The American Institute of Aeronautics and Astronautics". Archived from the original on 2017-04-14. Retrieved 2017-04-13.
  29. ^ "NASA's 2017 Distinguished Public Service Medal Honorees".
  30. ^ Law, Chung K.; Peters, Norbert (2005). "Preface". Combustion Science and Technology. 177 (5–6): 843–844. doi:10.1080/00102200590926879. S2CID 218574476.
  31. ^ Law, C. K., & Yang, V. (2015). Preface to the Special Issue Celebrating Professor forman a. Williams’ S 80th Birthday. Combustion Science and Technology, 187(1-2), 1-2.

External links[edit]