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INFLUENCE OF GOERTLER VORTICES SPANWISE WAVELENGTH ON HEAT TRANSFER RATES

Volume 5, Issue 5, 2013, pp. 389-400
DOI: 10.1615/ComputThermalScien.2013006557
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ABSTRACT

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction−the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise−average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented.

CITED BY
  1. Malatesta Vinicius, Souza Leandro F., Liu Joseph T.C., Kloker Markus J., Heat Transfer Analysis in a Flow Over Concave Wall With Primary and Secondary Instabilities, Procedia IUTAM, 14, 2015. Crossref

  2. Rogenski J. K., de Souza L. F., Floryan J. M., Influence of Pressure Gradients on the Evolution of the Görtler Instability, AIAA Journal, 54, 9, 2016. Crossref

  3. Rogenski J. K., de Souza L. F., Floryan J. M., Non-linear aspects of Görtler instability in boundary layers with pressure gradient, Physics of Fluids, 28, 12, 2016. Crossref

  4. Souza Leandro F., On the odd and even secondary instabilities of Görtler vortices, Theoretical and Computational Fluid Dynamics, 31, 4, 2017. Crossref

  5. Malatesta Vinicius, Rogenski Josuel Kruppa, Souza Leandro Franco de, Heat transfer enhancement via Görtler flow with spatial numerical simulation, International Journal of Numerical Methods for Heat & Fluid Flow, 27, 1, 2017. Crossref

  6. Lee Kiseok, Liu Joseph T. C., Modification of mean wake flow behind a very slender axisymmetric body of revolution by imposed nonlinear unstable helical modes, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470, 2165, 2014. Crossref

  7. Marques Larissa Ferreira, Rogenski Josuel Kruppa, de Souza Leandro Franco, Effects of streamwise wall curvature variation on the nonlinear evolution of different Görtler vortices wavelengths, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42, 7, 2020. Crossref

  8. Méndez M., Shadloo M. S., Hadjadj A., Heat-transfer analysis of a transitional boundary layer over a concave surface with Görtler vortices by means of direct numerical simulations, Physics of Fluids, 32, 7, 2020. Crossref

  9. Dagaut J., Negretti M. E., Balarac G., Brun C., Linear to turbulent Görtler instability transition, Physics of Fluids, 33, 1, 2021. Crossref

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