Brian Spalding’s Legacy: A Tribute to the Pioneer of Computational Fluid Dynamics

Brian Spalding


Brian Spalding: A Pioneer in Computational Fluid Dynamics


Dr Rodney Eastwood, Emeritus Professor Brian Spalding and Mr Rajive Kaul (left to right) in 2014
Dr Rodney Eastwood, Emeritus Professor Brian Spalding and Mr Rajive Kaul (left to right) in 2014


Brian Spalding (9 January 1923 – 27 November 2016) was a renowned pioneer in computational fluid dynamics (CFD) and engineering simulation. His groundbreaking contributions include the development of the SIMPLE algorithm, revolutionizing fluid flow problem-solving. Founding Concentration, Heat & Momentum Limited (CHAM), he promoted practical CFD applications and the widely used PHOENICS software. Spalding’s extensive publications, prestigious awards, and active engagement in conferences cemented his influential legacy.


His work continues to shape the field, with his methods being widely employed. Brian Spalding’s remarkable career and dedication to advancing engineering simulation have left an indelible mark, influencing the resolution of fluid flow and heat transfer challenges to this day.


In recent years, Brian Spalding’s contributions to the field of computational fluid dynamics have been commemorated in various ways, including the publication of the newsletter “Brian Spalding at 100” by the PHOENICS Newsletter. This special edition newsletter serves as a tribute to Spalding’s remarkable career and celebrates his enduring impact on the field. Here is the link to the newsletter:


The “Brian Spalding at 100” newsletter features insightful articles and reflections from esteemed writers and experts in the field of CFD. Some of the notable contributors include:


  • • Dr. Suhas Patankar: A pioneer in the field of computational fluid dynamics (CFD) and Finite volume method. Spalding’s esteemed colleague and co-developer of the SIMPLE algorithm. He is currently a Professor Emeritus at the University of Minnesota.
  • • Dr. Brian Launder: Professor of Mechanical Engineering at the University of Manchester, United Kingdom. He is known for his work in the field of turbulent flows in general and turbulence modeling in particular. In 1994, he became a Fellow of the Royal Society.
  • • Dr. Wolfgang Rodi: Renowned expert in computational fluid dynamics (CFD) and turbulent flows. With a background in aeronautical engineering, he earned his Ph.D. at Imperial College London and held research positions there. Prof. Rodi’s career includes project management at the University of Karlsruhe and serving as a professor and head of the Turbulent Flows department.


In addition to the esteemed contributors mentioned earlier, the “Brian Spalding at 100” newsletter also features a remarkable text titled “A Contribution” by Guilherme A. Lima da Silva, CEO and Founder of ATS Aerothermal Solutions, Ph.D. at University of São Paulo and specialist in CFD; heat and mass transfer simulation; Aircraft Systems Engineering: Environmental Control, Ice Protection.


A Contribution: Guilherme A. Lima da Silva


D B Spalding’s early works were crucial to the development of my PhD thesis “Heat and Mass Transfer in Two-Phase Flow Around Airfoils Equipped with Aeronautical Anti-Icing Systems.” Although not directly related to combustion or computational fluid dynamics, his work on heat and mass transfer proved invaluable. My introduction to PHOENICS and D B Spalding’s work came from Prof Clemente Greco at the University of Sao Paulo in Brazil, where we discussed droplet evaporation and combustion. Prof Euryale Zerbini and Marcos Pimenta also introduced me to Spalding’s works on heat and mass transfer.


During my MSc and PhD, I relied heavily on “Convective Heat Transfer” by Kays and Crawford, which also builds upon Spalding’s theories. What caught my attention was Spalding’s rigorous and accurate approach to mass transfer, particularly the interaction between mass and heat transfer coupling. For anti-ice systems, evaporation plays a significant role in determining surface temperature, with dry areas experiencing normal convection and wet areas subjected to evaporative cooling effects. The influence of evaporation on thermal boundary layer thickness and heat transfer coefficient is also noteworthy. Prof Zerbini pointed out the incredible and ingenious calculation of the coupled effect, which worked wonders for my research.


Spalding’s “Convective Mass Transfer: An Introduction” from 1963 is still considered the bible for understanding underlying physical phenomena, with the double film approach being exceptionally well explained and implemented. Even current computational fluid dynamics codes are not as accurate as Spalding’s work. Spalding & Smith’s 1958 work, “Heat Transfer in a Laminar Boundary Layer with Constant Fluid Properties and Constant Wall Temperature,” remains a reference for calculating the heat transfer coefficient over an airfoil with ice formation. It is a part of several classic icing codes, including ONERA 2D by D Guffond, ONERA, France.


I relied on the TEXTAN code during my research, which was developed from STAN5, a code that traces its origins back to the first code developed by Patankar and Spalding, GEMNIX. I also utilized Tuncer Cebeci’s BLP2C code, which, despite being more modern and compressible, still employs the finite difference implementation from Spalding’s early codes. The mixture length turbulence model used is also similar to the one Spalding used in his early models.


Despite the references not being modern or directly related to computational fluid dynamics, Spalding’s classical works were fundamental in creating a realistic and accurate heat and mass transfer model over an airfoil with thermal anti-ice systems operating under atmospheric icing conditions. I also used superposition methods, a topic Spalding explored in his early works when computing power was not as robust as it is today. He considered the boundary layer history effect caused by the streamwise temperature gradient on the surface, as described in his work from 1958, “Heat Transfer from Surfaces of Non-Uniform Temperature”. The following are the works cited in this contribution:


Smith AG, Spalding DB Heat Transfer in a Laminar Boundary Layer with Constant Fluid Properties &and Constant Wall Temperature. J Royal Aeronautical Society, Vol. 62, pp 60-64, 1958.
Spalding, DB Heat Transfer from Surfaces of Non-Uniform Temperature. J of Fluid Mechanics, No. 4, pp 22-32, 1958.
Spalding, DB Convective Mass Transfer: An Introduction. New York: McGraw-Hill, 1963.
The Ph.D. thesis can be accessed here: 082825/en.php;
My Google Scholar: citations?user=WcDwizIAAAAJ&hl=en


Guilherme A. Lima da Silva, PhD, CEO
Aerothermal Solutions and Software Distributor LLC
201 S. Biscayne Blvd, Suite 1200 Miami, FL 33131 USA

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