Skip to main content Accessibility help

Unified approach for conjugate heat-transfer analysis of high speed air flow through a water-cooled nozzle

  • F. I. Barbosa (a1), E. L. Zaparoli (a1) and C. R. Andrade (a1)


This article presents a unified approach to solve steady-state conjugate heat-transfer problem including simultaneously gas, liquid and solid regions in just one 3D domain, distinguished by their particular properties. This approach reduces approximation errors and the time to solve the problem, which characterise iterative methods based on separated domains. The formulation employs RANS equations, realisable k-ε turbulence model and near-wall treatment model. A commercial CFD code solves the pressure-based segregated algorithm combined with spatial discretisation of second order upwind. The problem consists of a convergent-divergent metallic nozzle that contains cooling channels divided in two segments along the wall. The nozzle wall insulates the high-speed hot air flow, dealt as perfect gas, from the two low-speed cold water flows, dealt as compressed liquid, both influenced by transport properties dependent of the local temperature. The verification process uses three meshes with increasing resolutions to demonstrate the independence of the results. The validation process compares the simulation results with experimental data obtained in high-enthalpy wind tunnel, demonstrating good compliance between them. Results for the bulk temperature rise of the water in the second cooling segment of the nozzle showed good agreement with available experimental data. Numerical simulations also provided wall temperature and heat flux for the gas and liquid sides. Besides, distribution of temperature, pressure, density and Mach number were plotted along the nozzle centerline showing a little disturbance downstream the throat. This phenomenon has been better visualised by means of 2D maps of those variables. The analysis of results indicates that the unified approach herein presented can make easier the task of simulating the conjugate convection-conduction heat-transfer in a class of problems related to regeneratively cooled thrust chambers.


Corresponding author


Hide All
1.Marchi, C.H., Laroca, F., Silva, A.F. and Hinckel, J.N.Numerical solutions of flows in rocket engines with regenerative cooling, Numer Heat Transfer, Part A, 2004, 45, (7), pp 699717.
2.Naraghi, M.H., Dunn, S. and Coats, D. A model for design and analysis of regeneratively cooled rocket engines. Proceedings 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2004, Ft Lauderdale, FL, US.
3.Knab, O., Frey, M., Görgen, J., Maeding, C., Quering, K. and Wiedmann, D. Progress in combustion and heat transfer modelling in rocket thrust chamber applied engineering. Proceedings 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference 2009, Denver, CO, US.
4.Kirchberger, C., Hupferand, A., Kau, H.P., Soller, S., Martin, P., Bouchez, M. and Dufour, E. Improved prediction of heat transfer in a rocket combustor for GOX/kerosene. Proceedings 47th AIAA Aerospace Sciences Meeting, 2009, Orlando, FL, US.
5.Negishi, H., Kumakawa, A., Yamanishi, N. and Kurosu, A. Heat transfer simulations in liquid rocket engine subscale thrust chambers. Proceedings 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 2008, Hartford, CT, US.
6.Shope, F.L.Conjugate conduction-convection heat transfer with a high-speed boundary layer, J Thermophysics and Heat Transfer, 1994, 8, (2), pp 275281.
7.Engblom, W., Fletcher, B. and Georgiadis, N. Validation of conjugate heat-transfer capability for water-cooled high-speed flows. Proceedings 39th AIAA Thermophysics Conference, AIAA, 2007, Miami, FL, US.
8.Engblom, W., Fletcher, B. and Georgiadis, N. Conjugate conduction-convection heat transfer for water-cooled high-speed flows. Proceedings 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA, 2008, Hartford, CT, US.
9.Kang, Y.D. and Sun, B.Numerical simulation of liquid rocket engine thrust chamber regenerative cooling. J Thermophysics and Heat Transfer, 2011, 25, (1), pp 155164.
10.ANSYS, INC. ANSYS Fluent Theory Guide, Release 13.0, software documentation, June 2011.
11.Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J.A new k-ε eddy-viscosity model for high Reynolds number turbulent flows: model development and validation, Comput Fluids, 1995, 24, (3), pp 227238.
12.Gordon, S. and Mcbride, B.J. Chemical Equilibrium with Applications (CEA). NASA Lewis Research Center (now NASA Glenn Research Center), USA. In: online program CEARUN
13.Lemmon, E.W., Mclinden, M.O. and Friend, D.G. Thermophysical Properties of Fluid Systems, Standard Reference Database Number 69, NIST, Gaithersburg, MD. In: NIST Chemistry Web Book
14.ANSYS, Inc. ANSYS Meshing User's Guide, Release 13.0, software documentation, November 2010.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed