Advertisement

Brian Spalding: Some Contributions to Computational Fluid Dynamics During the Period 1993 to 2004

  • Michael R. MalinEmail author
Chapter
  • 127 Downloads

Abstract

This paper describes some contributions to Computational Fluid Dynamics (CFD) made by Professor Brian Spalding whilst working at Concentration Heat and Momentum Limited (CHAM) during the period 1993–2004. The discussions focus principally on those areas with which the author had been directly involved with Brian and colleagues at CHAM. Some of the material is now well known in the field, and some not, but familiar material is not submitted as a new or original contribution, but rather to provide examples of Brian’s unique approach to solving practical CFD problems and to explain their origin. The following areas of work are described together with their influence in the field, where this is appropriate: the differential-equation wall-distance calculator; the LVEL model of turbulence; the IMMERSOL model of thermal radiation; virtual mass modelling in Eulerian–Eulerian descriptions of two-phase flow; a space-marching method for hyperbolic and transonic flow; and an automatic convergence-promoting algorithm for SIMPLE-based CFD codes.

Keywords

Computational fluid dynamics Convergence Parabolic/hyperbolic solver Thermal radiation Transonic flow Turbulence modelling Two-phase flow Virtual mass forces Wall distance 

References

  1. 1.
    Spalding, D. B. (1981). A general-purpose computer program for multi-dimensional one- and two-phase flow. Mathematics and Computers in Simulation, 23, 267–276.CrossRefGoogle Scholar
  2. 2.
    Patankar, S. V., Pollard, A., Singhal, A. K., & Vanka, S. P. (1983). Numerical prediction of flow, heat transfer, turbulence and combustion: selected works of Professor D. Brian Spalding. Oxford: Pergamon Press.Google Scholar
  3. 3.
    Artemov, V., Escudier, M. P., Fueyo, N., Launder, B. E., Leonardi, E., Malin, M. R., et al. (2009). A tribute to D.B. Spalding and his contributions in science and engineering. International Journal of Heat and Mass Transfer, 52, 3884–3905.zbMATHGoogle Scholar
  4. 4.
    Runchal, A. K. (2009). Brian Spalding: CFD and reality—A personal recollection. International Journal of Heat and Mass Transfer, 52, 4063–4073.zbMATHCrossRefGoogle Scholar
  5. 5.
    Runchal, A. K. (2013). Emergence of computational fluid dynamics at Imperial College (1965–1975): A personal recollection. ASME Journal of Heat Transfer, 135(1), 011009-1.Google Scholar
  6. 6.
    Runchal, A. K.(2017). Origins and development of the finite volume CFD method at Imperial College. In CHT-17, 29 May–2 June, Naples, Italy.Google Scholar
  7. 7.
    Launder, B. E., Patankar, S. V., & Pollard, A. (2019). Dudley Brian Spalding. 9 January 1923–27 November 2016. Biographical Memoirs of Fellows of the Royal Society, 66, Article ID: 20180024.Google Scholar
  8. 8.
    Spalding, D. B. (1993). A turbulence length-scale formulation. CHAM Technical Note 4/9/93, CHAM, Wimbledon, London.Google Scholar
  9. 9.
    Spalding, D. B. (1994). Calculation of turbulent heat transfer in cluttered spaces. Presented at the 10th International Heat Transfer Conference, Brighton, UK.Google Scholar
  10. 10.
    Tucker, P. G. (1998). Assessment of geometric multilevel convergence robustness and a wall distance method for flows with multiple internal boundaries. Applied Mathematical Modelling, 22, 293–311.zbMATHCrossRefGoogle Scholar
  11. 11.
    Fares, E., & Schroder, W. A. (2002). Differential equation to determine the wall distance. International Journal for Numerical Methods in Fluids, 39, 743–762.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Tucker, P. G. (2003). Differential equation-based wall distance computation for DES and RANS. Journal of Computational Physics, 190(1), 229–248.zbMATHCrossRefGoogle Scholar
  13. 13.
    Tucker P. G, Rumsey, C. L, Bartels R. E., & Biedron R. T. (2003). Transport equation-based wall distance computations aimed at flows with time-dependent geometry. NASA TM-2003-212680, December.Google Scholar
  14. 14.
    Tucker, P. G., Rumsey, C. L., Spalart, P. R., Bartels, R. E., & Biedron, R. T. (2005). Computations of wall distances based on differential equations. AIAA Journal, 43(3), 539–549.CrossRefGoogle Scholar
  15. 15.
    Tucker, P. G. (2011). Hybrid Hamilton–Jacobi–Poisson wall distance function model. Computers & Fluids, 44, 130–142.zbMATHCrossRefGoogle Scholar
  16. 16.
    Xu, J., Yan, C., & Fan, J. (2011). Computations of wall distances by solving a transport equation. Applied Mathematics and Mechanics, 32(2), 141–150.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Belyaev, A. G., & Fayolle, P. A. (2015). On variational and PDE-based distance function approximations. Computer Graphics Forum, 34(8), 104–118.CrossRefGoogle Scholar
  18. 18.
    Wukie, N. A., & Orkwis, P. D. (2017). A p-Poisson wall distance approach for turbulence modelling. In AIAA 2017-3945, 23rd AIAA CFD Conference, 5–9 June, Denver, Colorado, USA.Google Scholar
  19. 19.
    Jefferson-Loveday, R. J. (2017). Differential-equation based specification of turbulence integral length scales for cavity flows. Journal of Engineering for Gas Turbines and Power, 139(6).Google Scholar
  20. 20.
    Watson, R. A., Trojak, W., & Tucker, P. G. (2018). A simple flux reconstruction approach to solving a Poisson equation to find wall distances for turbulence modelling. In 2018 Fluid Dynamics Conference, AIAA Aviation Forum (AIAA 2018-4261), Atlanta, Georgia.Google Scholar
  21. 21.
    Boger, D. A. (2001). Efficient method for calculating wall proximity. AIAA Journal, 39(12), 2404–2406.CrossRefGoogle Scholar
  22. 22.
    Van der Weide, E., Kalitzin, G., Schluter, J., & Alonso, J. J. (2006). Unsteady turbomachinery computations using massively parallel platforms. In 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-0421, Reno, NV.Google Scholar
  23. 23.
    Roget, B., & Sitataman, J. (2012). Wall distance search algorithm using voxelised marching spheres. In 7th International Conference on CFD (ICCFD7), Big Island, Hawaii, July 9–13.Google Scholar
  24. 24.
    Lohner, R., Sharov, D., Luo, H., & Ramamurthi, R. (2001). Overlapping unstructured grids. In AIAA 2001-0439, Reno, NV.Google Scholar
  25. 25.
    Tucker, P. G. (2016). Section 7.6.3 Nearest wall distance. In Advanced computational fluid and aerodynamics. Cambridge: Cambridge University Press.Google Scholar
  26. 26.
    Agonafer, D., Gan-Li, L., & Spalding, D. B. (1996). The LVEL turbulence model for conjugate heat transfer at low Reynolds numbers. In Proceedings of the EEP Application of CAE/CAD to Electronic Systems, ASME International Mechanical Engineering Congress and Exposition, Atlanta, GA.Google Scholar
  27. 27.
    Spalding, D. B. (1961). A single formula for the law of the wall. ASME Journal of Applied Mechanics, 28(3), 455–458.zbMATHCrossRefGoogle Scholar
  28. 28.
    Dhinsa, K. K., Bailey, C. J., & Pericleous, K. A. (2004). Turbulence modelling and its impact on CFD predictions for cooling of electronic components. In Proceedings of 9th Intersociety Conference Thermal and Thermomechanical Phenomena in Electronic Systems.Google Scholar
  29. 29.
    Dhinsa, K. K. (2006). Development and application of low Reynolds number turbulence models for air-cooled electronics. Ph.D. thesis, University of Greenwich, London, UK.Google Scholar
  30. 30.
    Rodgers, P., Lohan, J., Eveloy, V., Fager, C. M., & Rantala, J. (1999). Validating numerical predictions of component thermal interaction on electronic printed circuit boards in forced convection air flows by experimental analysis. Advanced Electronic Packaging, 1, 999–1008.Google Scholar
  31. 31.
    Eveloy, V. C. (2003). An experimental assessment of CFD predictive accuracy for electronic component operational temperatures. Ph.D. thesis, Dublin City University, Ireland.Google Scholar
  32. 32.
    Eveloy, V., Rodgers, P., & Hashmi, M. S. J. (2003). An experimental assessment of computational fluid dynamics predictive accuracy for electronic component operational temperature. In Proceedings of the ASME Heat Transfer Conference, Las Vegas, Nevada, USA, Paper Number HT2003-47282.Google Scholar
  33. 33.
    Rodgers, P., Eveloy, V., & Davies, M. (2003). An experimental assessment of numerical predictive accuracy for electronic component heat transfer in forced convection: Parts I and II. Transactions of the ASME, Journal of Electronic Packaging, 125(l), 67–83.Google Scholar
  34. 34.
    Choi, J., Kim, Y., Sivasubramaniam, A., Srebic, J., Wang, Q., & Lee, J. (2008). A CFD-based tool for studying temperatures in rack-mounted servers. IEEE Transactions on Computers, 57(8) 1129–1142.Google Scholar
  35. 35.
    De Marchi Neto, I., & Altemani, C. A. C. (2017). A matrix to evaluate the conjugate cooling of a heaters’ array. International Journal of Thermal Sciences, 118, 278–291.Google Scholar
  36. 36.
    Dhoot, P., Healey, C. M., Pardey, Z., & van Gilder, J. W. (2017). Zero-equation turbulence models for large electrical and electronics enclosure applications. LV-17-C078. In ASHRAE Winter Conference, Las Vegas, NV, USA.Google Scholar
  37. 37.
    Wang, S., & Zu, D. (2003). Application of CFD in retrofitting air-conditioning systems in industrial buildings. Energy and Buildings, 35, 893–902.CrossRefGoogle Scholar
  38. 38.
    Favarolo, P. A., & Manz, H. (2005). Temperature-driven single-sided ventilation through a large rectangular opening. Building and Environment, 40, 689–699.CrossRefGoogle Scholar
  39. 39.
    Pfeiffer, A., Dorer, V., & Weber, A. (2008). Modelling of cowl performance in building simulation tools using experimental data and computational fluid dynamics. Building and Environment, 43, 1361–1372.CrossRefGoogle Scholar
  40. 40.
    Myhren, J. A., & Holmberg, S. (2008). Flow patterns and thermal comfort in a room with panel, floor and wall heating. Energy and Buildings, 40, 524–536.CrossRefGoogle Scholar
  41. 41.
    Myhren, J. A., & Holmberg, S. (2009). Design considerations with ventilation-radiators: Comparisons to traditional two-panel radiators. Energy and Buildings, 41, 92–100.CrossRefGoogle Scholar
  42. 42.
    Yoo, S.-H., & Manz, H. (2011). Available remodelling simulation for a BIPV as a shading device. Solar Energy Materials and Solar Cells, 95, 394–397.CrossRefGoogle Scholar
  43. 43.
    Wang, F., Manzanares-Bennett, A., Tucker, J., Roaf, S., & Heath, N. (2012). Feasibility study on solar-wall systems for domestic heating—An affordable solution for fuel poverty. Solar Energy, 86, 2405–2415.CrossRefGoogle Scholar
  44. 44.
    Jurelionis, A., Gagytea, L., Seduikytea, L., Prasauskas, T., Ciuzas, D., & Martuzevicius, D. (2016). Combined air heating and ventilation increases risk of personal exposure to airborne pollutants released at the floor level. Energy and Buildings, 116, 263–273.CrossRefGoogle Scholar
  45. 45.
    Mathioulakis, E., Karathanos, V. T., & Belessiotis, V. G. (1998). Simulation of air movement in a dryer by computational fluid dynamics: Application for the drying of fruits. Journal of Food Engineering, 36, 183–200.CrossRefGoogle Scholar
  46. 46.
    Tchouveleva, A. V., Cheng, Z., Agranat, V. M., & Zhubrin, S. V. (2007). Effectiveness of small barriers as means to reduce clearance distances. International Journal of Hydrogen Energy, 32, 1409–1415.CrossRefGoogle Scholar
  47. 47.
    Hourri, A., Angers, B., Benard, P., Tchouvelev, A., & Agranat, V. (2011). Numerical investigation of the flammable extent of semi-confined hydrogen and methane jets. International Journal of Hydrogen Energy, 36, 2567–2570.CrossRefGoogle Scholar
  48. 48.
    Wang, H., Djambazov, G., Pericleous, K. A., Harding, R. A., & Wickins, M. (2011). Modelling the dynamics of the tilt-casting process and the effect of the mould design on the casting quality. Computers & Fluids, 42, 92–101.zbMATHCrossRefGoogle Scholar
  49. 49.
    Wang, H., Wang, S., Wang, X., & Li, E. (2015). Numerical modelling of heat transfer through casting–mould with 3D/1D patched transient heat transfer model. International Journal of Heat and Mass Transfer, 81, 81–89.CrossRefGoogle Scholar
  50. 50.
    Chen, C., Jonsson, L. T. I., Tilliander, A., Cheng, G., & Jönsson, P. G. (2015). A mathematical modelling study of the influence of small amounts of KCl solution tracer son mixing in water and residence time distribution of tracers in a continuous flow reactor-metallurgical tundish. Chemical Engineering Science, 137, 914–937.CrossRefGoogle Scholar
  51. 51.
    Solhed, H., Jonsson, L., & Jönsson, P. (2002). A theoretical and experimental study of continuous-casting tundishes focusing on slag-steel interaction. Metallurgical and Materials Transactions, B33B(2), 173–185.CrossRefGoogle Scholar
  52. 52.
    Solhed, H., Jonsson, L., & Jönsson, P. (2008). Modelling of the steel/slag interface in a continuous casting tundish. Steel Research International, 79(5), 348–357.CrossRefGoogle Scholar
  53. 53.
    Artemov, V. I., Minko, K. B., & Yankov, G. G. (2015). Numerical simulation of fluid flow in an annular channel with outer transversally corrugated wall. International Journal of Heat and Mass Transfer, 90, 743–751.CrossRefGoogle Scholar
  54. 54.
    Tucker, P. G., & Liu, Y. (2007). Turbulence modelling for flows around convex features giving rapid eddy distortion. International Journal of Heat and Fluid Flow, 28, 1073–1091.CrossRefGoogle Scholar
  55. 55.
    Spalding, D. B. (1994). Proposal for a diffusional radiation model for attachment to PHOENICS. CHAM Technical Note 18/10/94, CHAM, Wimbledon, London, UK.Google Scholar
  56. 56.
    Spalding, D. B. (1996). Radiation in PHOENICS HOTBOX, FLAIR, etc. CHAM Technical Note 4/9/96, CHAM, Wimbledon, London, UK.Google Scholar
  57. 57.
    Spalding, D. B. (1996). Immersed-solid heat transfer. CHAM Technical Note 11/9/96, CHAM, Wimbledon, London, UK.Google Scholar
  58. 58.
    Lockwood, F. C., & Shah, N. G. (1981). A new radiation method for incorporation in general combustion prediction procedures. In Proceedings of the 18th International Symposium on Combustion (pp. 1405–1414). London: The Combustion Institute.Google Scholar
  59. 59.
    Rosseland, S. (1936). Theoretical astrophysics: Atomic theory and the analysis of stellar atmospheres and envelopes. Clarendon Press.Google Scholar
  60. 60.
    Hamakar, H. C. (1947). Radiation and heat conduction in a light-scattering material. Philips Research Reports, 2, 55–67.Google Scholar
  61. 61.
    Schuster, A. (1905). Radiation through a foggy atmosphere. Astrophysical Journal, 21, 1–22.CrossRefGoogle Scholar
  62. 62.
    Spalding, D. B (1980). Lecture 9, Idealisations of radiation. In Mathematical modelling of fluid-mechanics, heat-transfer and chemical-reaction processes: A lecture course. HTS/80/1, Mech. Eng. Dept., Imperial College, University of London.Google Scholar
  63. 63.
    Siegel, R., & Howell, J. R. (1992). Thermal radiation heat transfer (3rd ed.). Washington DC, USA: Hemisphere Publishing Corporation.Google Scholar
  64. 64.
    Eddington, A. (1916). On the radiative equilibrium of the stars. Monthly Notices of the Royal Astronomical Society, 77, 16–35.zbMATHCrossRefGoogle Scholar
  65. 65.
    Marshak, R. E. (1947). Note on the spherical harmonics methods as applied to the Milne problem for a sphere. Physical Review, 71, 443–446.MathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Deissler, R. G. (1964). Diffusion approximation for thermal radiation in gases with jump boundary condition. ASME Journal Heat Transfer, 240–246.CrossRefGoogle Scholar
  67. 67.
    Liu, F. M., & Swithenbank, J. (1990). Modelling radiative heat transfer in pulverised coal-fired furnaces. In M. G. Carvalho, F. Lockwood, & J. Taine (Eds.), Heat transfer in radiating and combusting systems. Proceedings of the EUROTHERM (Vol. 17, pp. 358–373). Cascais, Portugal: Springer.Google Scholar
  68. 68.
    Spalding, D. B. (1995). Modelling convective, conductive and radiative heat transfer. Lecture LE3-1 in Industrial Computational Fluid Dynamics. Lecture Series 1995-03, Von Karman Institute for Fluid Dynamics, Belgium, April 3–7.Google Scholar
  69. 69.
    Spalding, D. B. (2013). Chapter 1, trends, tricks, and try ons in CFD/CHT, Section 3.1. The IMMERSOL radiation model. In E. M. Sparrow, Y. I. Cho, J. P. Abraham, & J. M. Gorman (Eds.), Advances in heat transfer (Vol. 45, pp. 1–78). Burlington: Academic Press.Google Scholar
  70. 70.
    Spalding, D. B. (1980). Numerical computation of multi-phase flow and heat transfer. In C. Taylor & K. Morgan (Eds.), Recent advances in numerical methods in fluids (pp. 139–167). Swansea: Pineridge Press.Google Scholar
  71. 71.
    Spalding, D. B. (2002). PEA for IMMERSOL. CHAM Technical Notes 23/7/02 & 24/07/02, CHAM, Wimbledon, London, UK.Google Scholar
  72. 72.
    Rasmussen, N. B. K. (2002). The composite radiosity and gap (CRG) model of thermal radiation. In: Proceedings of the 6th European Conference on Industrial Furnaces and Boilers (INFUB-6) 2002 Conference, Estoril, Lisbon, Portugal, 2002. (Also published as Danish Gas Technology Centre Report No. CO201, Hørsholm, Denmark.)Google Scholar
  73. 73.
    Osenbroch, J. (2006). CFD study of gas dispersion and jet fires in complex geometries. Ph.D. Thesis, The Faculty of Engineering and Science, Aalborg University, Denmark.Google Scholar
  74. 74.
    Yang, Y., de Jong, R. A., & Reuter, M. (2005). Use of CFD to predict the performance of a heat treatment furnace, In Proceedings of the 4th International Conference on CFD in the Oil and Gas, Metallurgical and Process Industries, Trondheim, Norway (pp. 1–9).Google Scholar
  75. 75.
    Yang, Y., de Jong, R. A., & Reuter, M. (2007). CFD prediction for the performance of a heat treatment furnace. Progress in Computational Fluid Dynamics, An International Journal, 7(2–4), 209–218.zbMATHCrossRefGoogle Scholar
  76. 76.
    Zhubrin, S. V. (2009). Discrete reaction model for composition of sooting flames. International Journal of Heat and Mass Transfer, 52, 4125–4133.zbMATHCrossRefGoogle Scholar
  77. 77.
    Aloqaily, A. M., & Chakrabarty, A. (2010). Jet flame length and thermal radiation: Evaluation with CFD simulations. In Global Congress on Process Safety. San Antonio, TX: AIChE.Google Scholar
  78. 78.
    Chakrabarty, A., & Aloqaily, A. (2011). Using CFD to assist facilities comply with thermal hazard regulations such as new API RP-752 recommendations. Hazards XXII, AICheE. Symp. Series No. 156.Google Scholar
  79. 79.
    Chakrabarty, A., Edel, M., Raibagkar, A., & Aloqaily, A. (2011). Thermal hazard evaluation for process buildings using CFD analysis techniques. In AIChE Annual Meeting, Conference Proceedings (Vol. 29).Google Scholar
  80. 80.
    Agranat, V., & Perminov, V. (2016). Multiphase CFD model of wildland fire initiation and spread. In Proceedings of the 5th International Fire Behavior and Fuels Conference, April 11–15, Portland, Oregon, USA.Google Scholar
  81. 81.
    Corbin, C. D., & Zhai, Z. J. (2010). Experimental and numerical investigation on thermal and electrical performance of a building integrated photovoltaic–thermal collector system. Energy and Buildings, 42, 76–82.CrossRefGoogle Scholar
  82. 82.
    Chiang, W. H., Wang, C. Y., & Huang, J. S. (2012). Evaluation of cooling ceiling and mechanical ventilation systems on thermal comfort using CFD study in an office for subtropical region. Building and Environment, 48, 113–127.CrossRefGoogle Scholar
  83. 83.
    Radhi, H., Fikiry, F., & Sharples, S. (2013). Impacts of urbanisation on the thermal behaviour of new built up environments: A scoping study of the urban heat island in Bahrain. Landscape and Urban Planning, 113, 47–61.CrossRefGoogle Scholar
  84. 84.
    Maragkogiannis, K., Kolokotsa, D., Maravelakis, E., & Konstantara, A. (2014). Combining terrestrial laser scanning and computational fluid dynamics for the study of the urban thermal environment. Sustainable Cities and Society, 13, 207–216.CrossRefGoogle Scholar
  85. 85.
    Radhi, H., Sharples, S., & Assem, E. (2015). Impact of urban heat islands on the thermal comfort and cooling energy demand of artificial islands—A case study of AMWAJ Islands in Bahrain. Sustainable Cities and Society, 19, 310–318.CrossRefGoogle Scholar
  86. 86.
    Zhang, L., Zhang, L., Jin, M., & Liu, J. (2017). Numerical study of outdoor thermal environment in a university campus in summer. Procedia Engineering, 205, 4052–4059.CrossRefGoogle Scholar
  87. 87.
    Radhi, H., Sharples, S., & Fikiry, F. (2013). Will multi-facade systems reduce cooling energy in fully glazed buildings? A scoping study of UAE buildings. Energy and Buildings, 56, 179–188.CrossRefGoogle Scholar
  88. 88.
    Zhang, L., Jin, M., Liu, J., & Zhang, L. (2017). Simulated study on the potential of building energy saving using the green roof. Procedia Engineering, 205, 1469–1476.CrossRefGoogle Scholar
  89. 89.
    Hien, H. N., & Istiadji, A.D. (2003). Effects of external shading devices on daylighting and natural ventilation. In Proceedings of the 8th International IBPSA Conference, Eindhoven, The Netherlands (pp. 475–482).Google Scholar
  90. 90.
    Vaidya, A. M., Maheshwari, N. K., & Vijayan, P. K. (2010). Estimation of fuel and clad temperature of a research reactor during dry period of de-fueling operation. Nuclear Engineering and Design, 240, 842–849.CrossRefGoogle Scholar
  91. 91.
    Kuriyama, S., Takeda, T., & Funatani, S. (2015). Study on heat transfer characteristics of the one side-heated vertical channel with inserted porous materials applied as a vessel cooling system. Nuclear Engineering and Technology, l47, 534–545.Google Scholar
  92. 92.
    Zamora, B., & Kaiser, A. S. (2012). Influence of the variable thermophysical properties on the turbulent buoyancy-driven airflow inside open square cavities. Heat and Mass Transfer, 48, 35–53.Google Scholar
  93. 93.
    Zamora, B., & Kaiser, A. S. (2016). Radiative effects on turbulent buoyancy-driven airflow in open square cavities. International Journal of Thermal Sciences, 100, 267–283.CrossRefGoogle Scholar
  94. 94.
    Zamora, B., & Kaiser, A. S. (2017). Radiative and variable thermophysical properties effects on turbulent convective flows in cavities with thermal passive configuration. International Journal of Heat and Mass Transfer, 109, 981–996.Google Scholar
  95. 95.
    Zamora, B. (2018). Heating intensity and radiative effects on turbulent buoyancy-driven airflow in open square cavities with a heated immersed body. International Journal of Thermal Sciences, 126, 218–237.CrossRefGoogle Scholar
  96. 96.
    Budiyanto, M. A., Shinoda, T., & Nasruddin, N. (2017). Study on the CFD simulation of refrigerated container. IOP Conference Series: Materials Science and Engineering, 257(1), 012042.CrossRefGoogle Scholar
  97. 97.
    Baltas, N., & Malin, M. R. (1997). The sudden release of gas from undersea pipelines. CHAM 2938/3, CHAM, Wimbledon, London.Google Scholar
  98. 98.
    Spalding, D. B. (1997). The virtual mass force in two-phase flow. CHAM Technical File Note: IPSA.Google Scholar
  99. 99.
    Malin, M. R., & Spalding, D. B. (1998). Extensions to the PHOENICS parabolic solver for under-expanded jets. CHAM C/4366/1 & C/4366/2, CHAM, London.Google Scholar
  100. 100.
    Patankar, S. V., & Spalding, D. B. (1966). 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. 2, pp. 50–63).Google Scholar
  101. 101.
    Patankar, S. V., & Spalding, D. B. (1967). A finite-difference procedure for solving the equations of the two-dimensional boundary layer. International Journal of Heat and Mass Transfer, 10, 1339.Google Scholar
  102. 102.
    Patankar, S. V., & Spalding, D. B. (1970). Heat and mass transfer in boundary layers (2nd ed.). London: Intertext Books.Google Scholar
  103. 103.
    Spalding, D. B. (1977). GENMIX: A general computer program for two-dimensional parabolic phenomena (1st ed.). Oxford: Pergamon Press.Google Scholar
  104. 104.
    Patankar, S. V., & Spalding, D. B. (1972). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15, 787.Google Scholar
  105. 105.
    Spalding, D. B., & Tatchell, D. G. (1973). A prediction procedure for flow, combustion and heat transfer close to the base of a rocket. HTS/73/42, Imperial College, London, UK.Google Scholar
  106. 106.
    Issa, R. I., Spalding, D. B., & Tatchell, D. G. (1974). Guide to the computer program REP3. CHAM Report 631/2, CHAM, London, UK.Google Scholar
  107. 107.
    Elgobashi, S., & Spalding, D. B. (1977). Equilibrium chemical reaction of supersonic hydrogen-air jets (The ALMA computer program). NASA CR-2725.Google Scholar
  108. 108.
    Markatos, N. C., Spalding, D. B., & Tatchell, D. G. (1977). Combustion of hydrogen injected into a supersonic air stream. NASA-CR 2802.Google Scholar
  109. 109.
    Spalding, D. B. (1977). The PAM2 code: An introduction. CHAM/TR/40, CHAM, Wimbledon, London, UK.Google Scholar
  110. 110.
    Jennions, I. K., Ma, A. S. C., & Spalding, D. B. (1977). A prediction procedure for 2-dimensional steady, supersonic flows (The GENMIX-H computer program). HTS/77/24, Imperial College, London.Google Scholar
  111. 111.
    Drummond, J. P. (2014). Methods for prediction of high-speed reacting flows in aerospace propulsion. AIAA Journal, 52(3), 465–485.MathSciNetCrossRefGoogle Scholar
  112. 112.
    Cousins, J. M. (1981). Calculation of conditions in an axisymmetric rocket exhaust plume: The REP3 computer program. PERME Technical Report No.218, Westcott, UK.Google Scholar
  113. 113.
    Pratap, V. S., & Spalding, D. B. (1975). Numerical computations of flow in curved ducts. Aeronautical Quarterly, 26, 219–228.Google Scholar
  114. 114.
    Singhal, A. K., & Spalding, D. B. (1978). A 2d partially-parabolic procedure for turbomachinery cascades. ARC R & M No. 3807, London, UK.Google Scholar
  115. 115.
    Jennions, I. K. (1980). The impingement of axisymmetric supersonic jets on cones. Ph.D. thesis, Imperial College, University of London, UK.Google Scholar
  116. 116.
    Spalding, D. B. (1978). Computer codes for rocket-plume analysis. CHAM TR/38, CHAM, Wimbledon, London.Google Scholar
  117. 117.
    Spalding, D. B., & Tatchell, D. G. (1973). The rocket base-flow computer program—BAFL, CHAM/640/1. CHAM, Wimbledon, London.Google Scholar
  118. 118.
    Jensen, D. E., Spalding, D. B., Tatchell, D. G., & Wilson, A. S. (1979). Computations of structures of flames with recirculating flow and radial pressure gradients. 34, 309–26.Google Scholar
  119. 119.
    Markatos, N. C., Spalding, D. B., Tatchell, D. G., & Mace, A. C. H. (1982). Flow and combustion in the base-wall region of rocket exhaust plumes. Combustion Science and Technology, 28, 15–29.CrossRefGoogle Scholar
  120. 120.
    Markatos, N. C., Mace, A. C. H., & Tatchell, D. G. (1982). Analysis of combustion in recirculating flow for rocket exhausts in supersonic streams. Journal of Spacecraft and Rockets, 19(6), 557–563.CrossRefGoogle Scholar
  121. 121.
    Spalding, D. B. (1980). Lecture 25, Improved procedures for hydrodynamic problems. In Mathematical modelling of fluid-mechanics, heat-transfer and chemical-reaction processes: A lecture course. HTS/80/1, Imperial College, University of London.Google Scholar
  122. 122.
    Spalding, D. B. (1982). Lecture 2, 4.2 SIMPLEST. In Four lectures on the PHOENICS computer code. CFD/82/5, Imperial College, University of London.Google Scholar
  123. 123.
    Palacio, A., Malin, M. R., Proumen, N., & Sanchez, L. (1990). Numerical computations of steady transonic and supersonic flow fields. International Journal of Heat and Mass Transfer, 33(6), 1193–1204.CrossRefGoogle Scholar
  124. 124.
    Malin, M. R., & Sanchez, L. (1988). One-dimensional steady transonic shocked flow in a nozzle. PHOENICS Journal, 1(2), 214–246 (CHAM, Wimbledon, London, UK).Google Scholar
  125. 125.
    Smith, A. G., & Taylor, K. (2000). Modelling of two-phase rocket exhaust plumes and other plume prediction development. PHOENICS Journal, 13(1) (CHAM, Wimbledon, London).Google Scholar
  126. 126.
    Spalding, D. B. (2004). The ‘convergence-promoting wizard’ for PHOENICS. In PHOENICS User Conference, Melbourne, Australia. http://www.cham.co.uk/phoenics/d_polis/d_lecs/d_conwiz/conwiz.htm.
  127. 127.
    Spalding, D. B. (1992). The expert-system CFD code; problems and partial solutions. In Conference Proceedings. Basel World User Days CFD 1992, May 24–28.Google Scholar
  128. 128.
    Spalding, D. B. (2013). Chapter 1 trends, tricks, and try ons in CFD/CHT, Section 2.2.2 General remarks about linear-equation solvers. In E. M. Sparrow, Y. I. Cho, J. P. Abraham, & J. M. Gorman (Eds.), Advances in heat transfer (Vol. 45, pp. 1–78). Burlington: Academic Press.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Concentration Heat and Momentum Limited (CHAM)Wimbledon, LondonUK

Personalised recommendations