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Validation of the k–ω turbulence model for the thermal boundary layer profile of effusive cooled walls

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Abstract

The choice of materials for rocket chamber walls is limited by its thermal resistance. The thermal loads can be reduced substantially by the blowing out of gases through a porous surface. The k–ω-based turbulence models for computational fluid dynamic simulations are designed for smooth, non-permeable walls and have to be adjusted to account for the influence of injected fluids. Wilcox proposed therefore an extension for the k–ω turbulence model for the correct prediction of turbulent boundary layer velocity profiles. In this study, this extension is validated against experimental thermal boundary layer data from the Thermosciences Division of the Department of Mechanical Engineering from the Stanford University. All simulations are performed with a finite volume-based in-house code of the German Aerospace Center. Several simulations with different blowing settings were conducted and discussed in comparison to the results of the original model and in comparison to an additional roughness implementation. This study has permitted to understand that velocity profile corrections are necessary in contrast to additional roughness corrections to predict the correct thermal boundary layer profile of effusive cooled walls. Finally, this approach is applied to a two-dimensional simulation of an effusive cooled rocket chamber wall.

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Abbreviations

AS:

Institut für Aerodynamik und Strömungstechnik (engl. Institute of Aerodynamics and Flow Technology)

CEA:

Chemical equilibrium with applications

CFD:

Computational fluid dynamic

CMC:

Ceramic matrix composite

DLR:

German aerospace center

KSK:

Keramische Schub-Kammer (engl. ceramic thrust chamber)

NASA:

National Aeronautics and Space Administration

TAU:

In-house CFD code of the DLR

A :

Thermal diffusivity (m2/s)

c p :

Constant heat capacity at constant pressure

F :

Blowing ratio (–)

k :

Turbulent kinetic energy (kg/m)

\(k_{r}^{ + }\) :

Nondimensional roughness (–)

O/F:

Oxidant-to-fuel mixture ratio (–)

Pr:

Prandtl number

Pr t :

Turbulent Prandtl number

\(\dot{q}_{w}\) :

Surface heat flux (W/m2)

Re :

Reynolds number (–)

Re:

Roughness Reynolds number (–)

S B :

Blowing parameter (–)

St:

Stanton number (–)

St r :

Roughness Stanton number (–)

T :

Temperature (K)

t + :

Nondimensional temperature (K)

t w :

Surface temperature (K)

u :

Velocity (m/s)

\(u^{ + }\) :

Nondimensional velocity (–)

\(u_{\tau }\) :

Friction velocity at the wall (m/s)

v w :

Average normal flow velocity (m/s)

\(v_{w}^{ + }\) :

Nondimensional average normal flow velocity (–)

y :

Wall distance (m)

\(y^{ + }\) :

Nondimensional wall distance (–)

κ :

Von Kármán constant (–)

\(\lambda\) :

Thermal conductivity (W/m K)

\(\mu\) :

Dynamic viscosity (kg/m s)

\(\mu_{t}\) :

Turbulent dynamic viscosity (kg/m s)

v :

Kinematic viscosity (m/s)

\(\rho\) :

Density (kg/m3)

\(\tau\) :

Shear stress (N/m2)

\(\omega\) :

Specific dissipation rate (1/s)

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  1. German Aerospace Center, Lilienthalplatz 7, 38108, Brunswick, Germany

    R. Hink

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Correspondence to R. Hink.

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This paper is based on a presentation at the German Aerospace Congress, September 16–18, 2014, Augsburg, Germany.

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Hink, R. Validation of the k–ω turbulence model for the thermal boundary layer profile of effusive cooled walls. CEAS Space J 7, 389–398 (2015). https://doi.org/10.1007/s12567-015-0089-x

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