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A tribute to D.B. Spalding and his contributions in science and engineering. (English) Zbl 1167.80300

Summary: This paper presents a summary of some of the scientific and engineering contributions of Prof. D.B. Spalding up to the present time. Starting from early work on combustion, and his unique work in mass transfer theory, Spalding’s unpublished “unified theory” is described briefly. Subsequent to this, developments in algorithms by the Imperial College group led to the birth of modern computational fluid dynamics, including the well-known SIMPLE algorithm. Developments in combustion, multi-phase flow and turbulence modelling are also described. Finally, a number of academic and industrial applications of computational fluid dynamics and heat transfer applications considered in subsequent years are mentioned.

MSC:

80-03 History of classical thermodynamics
01A61 History of mathematics in the 21st century
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
76-03 History of fluid mechanics

Software:

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References:

[1] D.B. Spalding, The Combustion of Liquid Fuels, Ph.D. thesis, Cambridge University, 1951.
[2] Von Kármán, T.: Über laminare und turbulente reibung, Z. agnew. Math. mech. 1921, No. 1, 233-252 (1921) · JFM 48.0968.01 · doi:10.1002/zamm.19210010401
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[8] Spalding, D. B.: Some fundamentals of combustion, (1955)
[9] Spalding, D. B.: Convective mass transfer; an introduction, (1963) · Zbl 0124.42702
[10] Spalding, D. B.: A standard formulation of the steady convective mass transfer problem, Int. J. Heat mass transfer 1, 192-207 (1960)
[11] Kays, W. M.; Crawford, M. E.; Weigand, B.: Convective heat and mass transfer, (2005)
[12] Mills, A. F.: Mass transfer, (2001)
[13] Spalding, D. B.: A single formula for the law of the wall, ASME J. Appl. math. 28, No. 3, 455-458 (1961) · Zbl 0098.17603 · doi:10.1115/1.3641728
[14] D.B. Spalding, Heat transfer to a turbulent stream from a surface with a step-wise discontinuity in wall temperature, in: Proceedings of the International Developments in Heat Transfer, Part II, 1961, pp. 439 – 446.
[15] Kestin, J.; Persen, L. N.: Application of Schmidt’s method to the calculation of spalding’s function and the skin-friction coefficient in turbulent flow, Int. J. Heat mass transfer 5, 143-152 (1962)
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[17] Smith, A. G.; Shah, V. L.: The calculation of wall and fluid temperatures for the incompressible turbulent boundary layer, with arbitrary distribution of wall heat flux, Int. J. Heat mass transfer 5, 1170-1189 (1962)
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[19] Jayatillake, C. L. V.: The influence of Prandtl number and surface roughness on the resistance of the laminar sub-layer to momentum and heat transfer, Prog. heat mass transfer 1, 193-329 (1969)
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[21] D.B. Spalding, A Unified Theory of Friction, Heat Transfer, and Mass Transfer in the Turbulent Boundary Layer and Wall Jet, ARC No. 25 925, Her Majesty’s Stationery Office, London, 1964.
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[26] D.B. Spalding, The Kinetic-Energy Deficit Equation of the Turbulent Boundary Layer, AGARDograph No. 97, Part 1, 1965, pp. 191 – 244.
[27] Escudier, M. P.; Nicoll, W. B.: The entrainment function in turbulent-boundary-layer and wall-jet calculations, J. fluid mech. 25, No. 2, 337-366 (1966)
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[32] S.V. Patankar, D.B. Spalding, A calculation procedure for heat transfer by forced convection through two-dimensional uniform-property turbulent boundary layers on smooth impermeable walls, in: Proceedings of the 3rd International Heat Transfer Conference, Chicago, vol. II, 1966, pp. 50 – 63.
[33] A. Thom, An Investigation of Fluid Flow in Two Dimensions, ARC R&M No. 1194, Her Majesty’s Stationery Office, 1928.
[34] Burggraf, O. R.: Analytical and numerical studies of steady separated flows, J. fluid mech. 24, 113-151 (1966)
[35] Courant, R.; Isaacson, E.; Rees, M.: On the solution of non-linear hyperbolic differential equations by finite-differences, Commun. pure appl. Math. 5, 243-255 (1952) · Zbl 0047.11704 · doi:10.1002/cpa.3160050303
[36] A.K. Runchal, Three finite difference methods for Navier – Stokes equations, in: Proceedings of the 2nd Applied Mechanics Conference, University of Strathclyde, Glasgow, 1967.
[37] A.K. Runchal, D.B. Spalding, M. Wolfshtein, The Numerical Solution of the Elliptic Equations for the Transport of Vorticity, Heat and Matter in Two Dimensional Flows, SF/TN/2, Imperial College, Mech. Eng. Dept., 1967. · Zbl 0211.29403
[38] A.K. Runchal, M. Wolfshtein, A Finite-Difference Procedure for the Integration of the Navier – Stokes Equations, SF/TN/1, Imperial College, Mech. Eng. Dept., 1966. · Zbl 0242.76012
[39] A.K. Runchal, M. Wolfshtein, A Fortran IV Computer Program for the Solution of Steady-State, Two-Dimensional Equations of Motion, Energy and Concentrations, SF/TN/10, Imperial College, Mech. Eng. Dept., 1967.
[40] Gosman, A. D.; Pun, W. M.; Runchal, A. K.; Spalding, D. B.; Wolfshtein, M.: Heat and mass transfer in recirculating flows, (1969) · Zbl 0239.76001
[41] Mallinson, G. D.; De Vahl Davis, G.: Three-dimensional natural convection in a box – A numerical study, J. fluid mech. 83, No. 1, 1-31 (1977)
[42] Patankar, S. V.; Spalding, D. B.: A finite-difference procedure for solving the equations of the two-dimensional boundary layer, Int. J. Heat mass transfer 10, 1389-1412 (1967) · Zbl 0157.57301 · doi:10.1016/0017-9310(67)90028-2
[43] Runchal, A. K.; Spalding, D. B.; Wolfshtein, M.: Numerical solution of the elliptic equations for transport of vorticity, heat, and matter in two-dimensional flow, Phys. fluids 12, 21-28 (1969) · Zbl 0211.29403 · doi:10.1063/1.1692439
[44] Patankar, S. V.; Spalding, D. B.: Heat and mass transfer in boundary layers, (1967) · Zbl 0157.57301
[45] Patankar, S. V.; Spalding, D. B.: Heat and mass transfer in boundary layers: A general calculation procedure, (1970) · Zbl 0246.76080
[46] F.C. Lockwood, D.B. Spalding, Prediction of Turbulent Reacting Duct Flow with Significant Radiation, Report No. CCK/TN/A/6, Mech. Eng. Dept., Imperial College, London, 1971.
[47] Spalding, D. B.: Convergence and accuracy of three finite difference schemes for a two dimensional conduction and convection problem, Int. J. Numer. methods eng. 4, 540-550 (1972)
[48] Runchal, A. K.: Convergence and accuracy of three finite difference schemes for a two dimensional conduction and convection problem, Int. J. Numer. methods eng. 4, No. 4, 541-550 (1972)
[49] Leonard, B. P.: A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. methods appl. Mech. eng. 19, No. 1, 59-98 (1979) · Zbl 0423.76070 · doi:10.1016/0045-7825(79)90034-3
[50] Spalding, D. B.: GENMIX: A general computer program for two-dimensional parabolic phenomena, (1977)
[51] Spalding, D. B.: PHOENICS a general-purpose computer program for multi-dimensional one- and two-phase flow, Math. comput. Simul. 23, 267-276 (1981)
[52] Caretto, L. S.; Curr, R. M.; Spalding, D. B.: Two numerical methods for three-dimensional boundary layers, Comput. methods appl. Mech. eng. 1, No. 1, 39-57 (1972) · Zbl 0261.76017 · doi:10.1016/0045-7825(72)90020-5
[53] Harlow, F. H.; Welch, J. E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. fluids 8, No. 12, 2182-2189 (1965) · Zbl 1180.76043 · doi:10.1063/1.1761178
[54] Chorin, A. J.: The numerical solution of the Navier – Stokes equations for an incompressible fluid, Bull. am. Math. soc. 73, 928-931 (1967) · Zbl 0168.46501 · doi:10.1090/S0002-9904-1967-11853-6
[55] Patankar, S. V.; Spalding, D. B.: A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat mass transfer 15, No. 10, 1787-1806 (1972) · Zbl 0246.76080 · doi:10.1016/0017-9310(72)90054-3
[56] Van Doormaal, J. P.; Raithby, J. P.: Enhancements of the SIMPLE method for predicting incompressible fluid flows, Numer. heat transfer B fundam. 7, No. 2, 147-163 (1984) · Zbl 0553.76005 · doi:10.1080/01495728408961817
[57] Patankar, S. V.: A calculation for two-dimensional elliptic problems, Numer. heat transfer 4, 409-426 (1981)
[58] D.B. Spalding, Mathematical Modelling of Fluid-Mechanics, Heat-Transfer and Chemical-Reaction Processes: A Lecture Course, HTS/80/1, Computational Fluid Dynamics Unit, Imperial College, University of London, London, 1980.
[59] D.B. Spalding, IPSA 1981, New Developments and Computed Results, HTS/81/2, Imperial College, London, 1981.
[60] Spalding, D. B.: Numerical computation of multi-phase flow and heat transfer, Recent advances in numerical methods in fluids, 139-168 (1980) · Zbl 0467.76094
[61] D.B. Spalding, The calculation of free-convection phenomena in gas – liquid mixtures, in: D.B. Spalding, N. Afgan (Eds.), Heat Transfer & Turbulent Buoyant Convection, vol. 2, Hemisphere, Washington, DC, 1977.
[62] D.B. Spalding, A Method for Computing Steady and Unsteady Flows Possessing Discontinuities of Density, Report 910/2, CHAM Ltd., Wimbledon, London, 1974.
[63] Lahey, R. T.; De Bertodano, M. Lopez; Jones, O. C.: Phase distribution in complex geometry conduits, Nucl. eng. Des. 141, 177-201 (1993)
[64] Malin, M. R.; Spalding, D. B.: A two-fluid model of turbulence and its application to heated plane jets and wakes, Physicochem. hydrodyn. 5, No. 5-6, 339-361 (1984)
[65] Ilegbusi, O. J.; Spalding, D. B.: A two-fluid model of turbulence and its application to near-wall flows, Physicochem. hydrodyn. 9, No. 1-2, 127-160 (1987)
[66] Ilegbusi, O. J.; Spalding, D. B.: Application of a two-fluid model of turbulence to turbulent flow in conduits and free shear layers, Physicochem. hydrodyn. 9, No. 1 – 2, 161-181 (1987)
[67] Ilegbusi, O. J.; Spalding, D. B.: Prediction of fluid flow and heat transfer characteristics of turbulent shear flows with a two-fluid model of turbulence, Int. J. Heat mass transfer 32, No. 4, 767-774 (1989)
[68] D.B. Spalding, Towards a Two-Fluid Model of Turbulent Combustion in Gases with Special Reference to the Spark Ignition Engine, CFD/82/18, Computational Fluid Dynamics Unit, Imperial College, London, 1982.
[69] Spalding, D. B.: The two-fluid model of turbulence applied to combustion phenomena, Aiaa j. 24, No. 6, 876-884 (1986)
[70] Spalding, D. B.: A turbulence model for buoyant and combusting flows, Int. J. Numer. methods eng. 24, No. 1, 1-23 (1987) · Zbl 0612.76069 · doi:10.1002/nme.1620240102
[71] S.J. Kline, M.V. Morkovin, G. Sovran, D.J. Cockrell, Computation of turbulent boundary layers, in: AFOSR-IFP-Stanford Conference, 1968.
[72] Spalding, D. B.: Heat transfer from turbulent separated flows, J. fluid mech. 27, 97-109 (1967)
[73] Prandtl, L.: Uber ein neues formelsystem für die ausgebildete turbulenz, Nachr. akad. Wiss. göttingen, 6-19 (1945) · Zbl 0061.45401
[74] Launder, B. E.; Spalding, D. B.: The numerical computation of turbulent flows, Comput. methods appl. Mech. eng. 3, No. 2, 269-289 (1974) · Zbl 0277.76049 · doi:10.1016/0045-7825(74)90029-2
[75] Kolmogorov, A. N.: Equations of turbulent motion of an incompressible fluid, Izv. akad. Nauk. SSSR ser. Phys. V, No. 1 – 2, 56-58 (1942)
[76] J. Rotta, Statistische Theorie Nichthomogener Turbulenz I and II, Z. Phys. 129, 131 (1951) 547 – 572, 51 – 77 (Translated into English by W. Rodi as Imperial College, Mech. Eng. Dept. Technical Notes Nos. TWF/TN/38 and TWF/TN/39). · Zbl 0043.40202
[77] Spalding, D. B.: The calculation of the length scale of turbulence in some turbulent boundary layers remote from walls, Progress in heat & mass transfer, 255-266 (1967)
[78] Rodi, W.; Spalding, D. B.: A two-parameter model of turbulence, and its application to free jets, Wärme stoffübertrag. 3, No. 2, 85-95 (1970)
[79] Ng, K. H.; Spalding, D. B.: Some applications of turbulence models for boundary layers near walls, Phys. fluids 15, No. 1, 20-30 (1972) · Zbl 0232.76062
[80] D.B. Spalding, The Prediction of Two-Dimensional, Steady, Turbulent Elliptic Flows, Heat and Mass Transfer in Turbulent Flows with Separated Regions and Measurement Techniques, Paper Delivered at International Center for Heat and Mass Transfer Seminar, Herceg-Novi, Yugoslavia, Imperial College, Mech. Eng. Dept. Report No. EF/TN/A/16, London, 1969.
[81] Spalding, D. B.: Concentration fluctuations in a round turbulent free jet, Chem. eng. Sci. 26, No. 1, 95-107 (1971)
[82] D.B. Spalding, The kW Model of Turbulence, Technical Note No. TM/TN/A16, Mech. Eng. Dept., Imperial College, London, 1971. · Zbl 0228.76122
[83] Spalding, D. B.: A two-equation model of turbulence, commemorative lecture for prof. F. bosnajakovic, VDI forschungsheft 549, 5-16 (1972)
[84] Hanjalic, K.; Launder, B. E.: A Reynolds-stress model of turbulence and its application to asymmetric shear flows, J. fluid mech. 52, 609-638 (1972) · Zbl 0239.76069 · doi:10.1017/S002211207200268X
[85] Jones, W. P.; Launder, B. E.: The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat mass transfer 15, 301-314 (1972)
[86] Wilcox, D. C.: Reassessment of the scale-determining equation for advanced turbulence models, Aiaa j. 26, 1299-1310 (1988) · Zbl 0664.76057 · doi:10.2514/3.10041
[87] Menter, F. R.: Two-equation eddy-viscosity turbulence models for engineering applications, Aiaa j. 32, 1598-1605 (1994)
[88] B.E. Launder, A. Morse, W. Rodi, D.B. Spalding, The prediction of free shear flows – a comparison of the performance of six turbulence models, in: Proceedings of the NASA Conference on Free Shear Flows, Langley VA, 1972.
[89] Malin, M. R.; Spalding, D. B.: The prediction of turbulent jets and plumes by the use of the k-w model of turbulence, Physicochem. hydrodyn. 5, No. 2, 153-198 (1984)
[90] Ilegbusi, O. J.; Spalding, D. B.: An improved version of the k-w model of turbulence, ASME J. Heat transfer 107, No. 1, 63-69 (1985)
[91] D.B. Spalding, The Vorticity-Fluctuations (kW) Model of Turbulence; Early Papers, Report CFD/82/17, Computational Fluid Dynamics Unit, Imperial College, London, 1982.
[92] D.B. Spalding, The ESCIMO Theory of Turbulent Combustion, HTS/76/13, Department of Mechanical Engineering, Imperial College, London, 1976.
[93] D.B. Spalding, Mixing and chemical reaction in steady confined turbulent flames, in: Proceedings of the 13th Symposium (International) on Combustion, Pittsburgh, PA, 1971, pp. 649 – 657.
[94] D.B. Spalding, The spread of turbulent flames in confined ducts, in: Proceedings of the 11th Symposium (International) on Combustion, 1967, pp. 807 – 815.
[95] Khalil, E. E.; Spalding, D. B.; Whitelaw, J. H.: The calculation of local flow properties in two-dimensional furnaces, Int. J. Heat mass transfer 18, No. 6, 775-791 (1975)
[96] Spalding, D. B.: Mathematical-models of turbulent flames, Combust. sci. Technol. 13, No. 1 – 6, 3-25 (1976)
[97] Spalding, D. B.: Some general-comments on papers concerned with theory of reactive turbulence, Combust. sci. Technol. 13, No. 1 – 6, 245-255 (1976)
[98] D.B. Spalding, Development of the eddy-breakup model of turbulent combustion, in: Proceedings of the 16th Symposium (International) on Combustion, Pittsburgh, PA, 1977, pp. 1657 – 1663.
[99] D.B. Spalding, Computer Modelling Techniques for Laminar and Turbulent Combustion, HTS/77/12, Department of Mechanical Engineering, Imperial College, London, 1977.
[100] Spalding, D. B.: A general theory of turbulent combustion, J. energy 2, No. 1, 16-23 (1978)
[101] D.B. Spalding, The influences of laminar transport and chemical kinetics on the time-mean reaction rate in a turbulent flame, in: Proceedings of the 17th Symposium (International) on Combustion, 1979, pp. 431 – 440.
[102] Kerstein, A. R.: Linear-eddy modeling of turbulent transport. II: application to shear layer mixing, Combust. flame 75, 397-413 (1989)
[103] D.B. Spalding, Developments in the IPSA procedure for numerical computation of multiphase-flow phenomena with interphase slip, unequal temperatures, etc, in: T.M. Shih (Ed.), Proceedings of the 2nd International Conference on Numerical Properties and Methodologies in Heat Transfer, Maryland University, 1981, pp. 421 – 436. · Zbl 0514.76104
[104] B.F. Magnussen, On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow, in: 19th AIAA Aerospace Science Meeting, St. Louis, Missouri, 1981.
[105] D.B. Spalding, Multi-fluid models of turbulence progress and prospects, in: Proceedings of the CFD96 4th Annual Conference of the CFD Society of Canada, Ottawa, 1996, pp. 27 – 56.
[106] D.B. Spalding, Turbulent mixing and chemical reaction; the multi-fluid approach, in: International Symposium on the Physics of Heat Transfer in Boiling and Condensation, Moscow, 1997.
[107] D.B. Spalding. Connexions between the multi-fluid and flamelet models of turbulent combustion, A lecture delivered at the University of Leeds, England. <http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/flamelet.htm>, 1998 (Accessed 3 March 2008).
[108] Dopazo, C.: Probability density function approach for a turbulent axisymmetric heated jet centerline evolution, Phys. fluids 22, No. 1, 20-30 (1979) · Zbl 0401.76049
[109] Pope, S. B.: Monte-Carlo method for the PDF equations of turbulent reactive flow, Combust. sci. Technol. 25, 159-174 (1981)
[110] Spalding, D. B.; Stephenson, P. L.: Laminar flame propagation in hydrogen and bromine mixtures, Proc. R. Soc. lond. Ser. A math. Phys. sci. 324, No. 1558, 315-337 (1971)
[111] Spalding, D. B.: Predicting the performance of diesel engine combustion chambers, Proc. imeche 184, 241-251 (1969)
[112] S.V. Patankar, D.B. Spalding, Mathematical models of fluid flow and heat transfer in furnaces, in: Proceedings of the 4th Symposium of Flames & Industry; Predictive Methods for Industrial Flames, 1972, pp. 1 – 5.
[113] W.M. Pun, D.B. Spalding, A procedure for predicting the velocity and temperature distribution in a confined, steady, turbulent, gaseous diffusion flame, in: Proceedings of the International Astronautics Federation Meeting, Belgrade, 1967, pp. 3 – 21.
[114] D.B. Spalding, Turbulent, Physically-Controlled Combustion Processes, Report RF/TN/A/4, Mech. Eng. Dept. Imperial College, University of London, London, 1971.
[115] Lockwood, F. C.; Naguib, A. S.: The prediction of the fluctuations in the properties of free, round-jet, turbulent, diffusion flames, Combust. flame 24, 109-124 (1975)
[116] J.H. Kent, R.W. Bilger, The prediction of turbulent diffusion flame fields and nitric oxide formation, in: Proceedings of the 16th Symposium (International) on Combustion Pittsburgh, PA, 1976, pp. 1643 – 1656.
[117] S.V. Patankar, D.B. Spalding, A computer model for three-dimensional flow in furnaces, in: Proceedings of the 14th International Symposium on Combustion, 1972, pp. 605 – 614. · Zbl 0246.76080
[118] S.V. Patankar, D.B. Spalding, Simultaneous predictions of flow pattern and radiation for three-dimensional flames, in: N. Afgan, J. Beer (Eds.), Heat Transfer in Flames, Hemisphere, Washington, 1974, pp. 73 – 94.
[119] M.A. Serag-Eldin, The Numerical Prediction of the Flow and Combustion Processes in a Three-Dimensional Combustion Chamber, Ph.D. thesis, Imperial College, London, 1977.
[120] V.S. Pratap, Flow and Heat Transfer in Curved Ducts, Ph.D. thesis, Imperial College, University of London, London, 1975. · Zbl 0291.73007
[121] Dean, W. R.: Note on the motion of fluid in a curved pipe, Phil. mag. 14, 208-223 (1927) · JFM 54.0909.05
[122] Dean, W. R.: Stream-line motion of a fluid in a curved pipe, Phil. mag. 5, 673-695 (1928) · JFM 54.0909.05
[123] Patankar, S. V.; Pratap, V. S.; Spalding, D. B.: Prediction of laminar flow and heat transfer in helically coiled pipes, J. fluid mech. 62, 539-551 (1974) · Zbl 0279.76020 · doi:10.1017/S0022112074000796
[124] L.R. Austin, The Development of Viscous Flow within Helical Coils, Ph.D. thesis, University of Utah, 1971.
[125] Mori, Y.; Nakayama, W.: Study on forced convective heat transfer in curved pipes (1st report, laminar region), Int. J. Heat mass transfer 8, 67-82 (1965) · Zbl 0133.20703 · doi:10.1016/0017-9310(65)90098-0
[126] Dravid, A. N.; Smith, K. A.; Merrill, E. W.; Brian, P. L. T.: Effect of secondary fluid motion on laminar flows and heat transfer in helically coiled tubes, Aiche J. 17, 1017-1122 (1971)
[127] Patankar, S. V.; Pratap, V. S.; Spalding, D. B.: Prediction of turbulent flow in curved pipes, J. fluid mech. 67, 583-595 (1975) · Zbl 0307.76025 · doi:10.1017/S0022112075000481
[128] Pratap, V. S.; Spalding, D. B.: Fluid flow and heat transfer in three-dimensional duct flows, Int. J. Heat mass transfer 19, No. 10, 1183-1188 (1976) · Zbl 0342.76032 · doi:10.1016/0017-9310(76)90152-6
[129] Pratap, V. S.; Spalding, D. B.: Numerical computations of flow in curved ducts, Aeronaut. Q. 26, 219-228 (1975)
[130] Majumdar, A. K.; Pratap, V. S.; Spalding, D. B.: Numerical computation of flow in rotating ducts, ASME J. Fluids eng. 99, 148153 (1977) · Zbl 0361.76032
[131] A.K. Majumdar, D.B. Spalding, A numerical investigation of three-dimensional flows in a rotating duct by a partially-parabolic procedure, in: Proceedings of the ASME Paper No. 77-WA/FE-7, 1977. · Zbl 0361.76032
[132] Pollard, A.; Spalding, D. B.: The prediction of the three-dimensional turbulent flow field in a flow splitting tee-junction, Comput. math. Appl. mech. Eng. 13, 293-306 (1978) · Zbl 0378.76042 · doi:10.1016/0045-7825(78)90064-6
[133] Majumdar, A. K.; Morris, W. D.; Skiadaressis, D.; Spalding, D. B.: Heat transfer in rotating ducts, Mech. eng. Bull. (Durgapur) 8, No. 4, 87-95 (1978)
[134] Majumdar, A. K.; Spalding, D. B.: Numerical investigation of flow in rotating radial diffusers, Mech. eng. Bull. (Durgapur) 8, No. 1 – 2, 19-28 (1977)
[135] P. Bradshaw. Complex turbulent flows, in: W.T. Koiter (Eds.), Proceedings of the 14th Iutam Congress, Theoretical and Applied Mechanics, North Holland, Delft, 1976, pp. 103 – 113.
[136] Abdelmeguid, A. M.; Spalding, D. B.: Turbulent flow and heat transfer in pipes with buoyancy effects, J. fluid mech. 94, No. 2, 383-400 (1979)
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[189] D.B. Spalding, Notes on the PARMIX Program, Report BL/TN/A/35, Imperial College, Mech. Eng. Dept., London, 1970.
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[212] D. Radosavljevik, The Numerical Simulation of Direct-Contact Natural-Draught Cooling Tower Performance under the Influence of Cross-Wind, Ph.D. thesis, Imperial College, University of London, 1988.
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[215] S.B. Beale, Fluid Flow and Heat Transfer in Tube Banks, Ph.D. thesis, Imperial College, University of London, 1993.
[216] D.B. Spalding, Numerical Modelling of CVD Reactors, HTS/79/6, Mech. Eng. Dept., Imperial College, University of London, London, 1979.
[217] Heritage, J. R.: PHOENICS-CVD: a code for the design and development of chemical vapour deposition equipment and processes, PHOENICS J. Comput. fluid dyn. Appl. 7, No. 4, 165-180 (1994)
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