F. Bataille

Uncertainty Propagation for a Turbulent, Compressible Nozzle Flow Using Stochastic Methods

A fully spectral, polynomial chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow is described. The method is applied to the flow in a quasi-one-dimensional nozzle. Results demonstrate the ability of the method to propagate accurately the uncertainty throughout the entire numerical field. Comparison and validation were made with the reference Monte Carlo method. An exact method and an approximate method for the computation of inner products are also discussed in terms of efficiency and number of operations required

Prediction of thermal protection of walls by blowing with different fluids

Abstract This work concerns the modelling of heat and mass transfer in the boundary layer and inside a plane porous plate which is below a hot fluid flow and submitted to cold fluid blowing. A preliminary study of the heat transfer rates in the boundary layer without blowing permits us to validate, comparing with experimental results, the RNG κ-ϵ model. The RNG κ-ϵ model, with kinematic and thermal laws for the wall, linked with a model of blowing, is then used to study the heat and mass transfer rates at the wall when the main flow and the injected fluids are the same species - air - but at different temperatures. The comparison between calculated friction factors, Stanton numbers and published results confirms the validity of our model. We also show the strong influence of the injection rate on the thermal convective coefficient of the wall. In the last part, results on cooling by blowing with water vapour in a main flow of air are given. Comparisons of the evolution of Stanton numbers and friction factors show that blowing with water vapour is more efficient than air injection in terms of momentum transfer and thermal protection of walls.

Blowing models for cooling surfaces

Abstract To study the cooling of surfaces exposed to high temperature stress and heat flux, the blowing, or transpiration, technique is numerically investigated in the case of a porous circular cylinder. Two models are developed to simulate the blowing impact on the outer flow and an experimental set-up available allows for direct comparison and validation of the numerical simulations. The heat exchange occuring within the porous wall itself between the coolant and the solid part of the wall is accounted. The results show an excellent effectiveness of the blowing in terms of surface temperature reduction, even for low blowing ratii. The incident heat flux exhibits a maximum for medium blowing rates due to a decreasing heat transfer coefficient and a growing temperature difference between the surface and the main flow with the injection rate. Finally, the blowing is demonstrated to be very effective in cooling heavily thermally stressed parts in terms of homogeneity and coolant rate required.

Near wake of a circular cylinder submitted to blowing. II: Impact on the dynamics

Abstract The near wake of a porous circular cylinder in cross-flow submitted to blowing through its whole surface is experimentally studied. The blowing impact on the Strouhal number exhibits a linear decrease of the vortex shedding frequency with the blowing ratio. A simple model representing this decrease as a function of the injection rate is developed, based on the wake static pressure profile evolution. The main flow temperature influence is also investigated in case of non-isothermal blowing and is shown to have no effect on the Strouhal number evolution. Finally, the interaction between the blowing and the shear layer is investigated through a spectral analysis of the velocity signal. A modification of the shear layer power spectrum is observed when injection occurs. The dynamics are slowed down and characteristic patterns, denoted sub-peaks, appear while the relationship between the von Karman and the shear layer frequencies without blowing remains valid.

Prediction of turbulent heat transfer with surface blowing using a non-linear algebraic heat flux model

Abstract The paper reports on the prediction of the effects of blowing on the evolution of the thermal and velocity fields in a flat-plate turbulent boundary layer developing over a porous surface. Closure of the time-averaged equations governing the transport of momentum and thermal energy is achieved using a complete Reynolds-stress transport model for the turbulent stresses and a non-linear, algebraic and explicit model for the turbulent heat fluxes. The latter model accounts explicitly for the dependence of the turbulent heat fluxes on the gradients of mean velocity. Results are reported for the case of a heated boundary layer which is first developed into equilibrium over a smooth impervious wall before encountering a porous section through which cooler fluid is continuously injected. Comparisons are made with LDA measurements for an injection rate of 1%. The reduction of the wall shear stress with increase in injection rate is obtained in the calculations, and the computed rates of heat transfer between the hot flow and the wall are found to agree well with the published data.

STUDIES OF THE TRANSPIRATION COOLING THROUGH A SINTERED STAINLESS STEEL PLATE

This study concerns the liquid transpiration cooling effect on thermal protection of a porous plate wall. The results indicate that the effectiveness reaches more than 95% for a very weak effusion rate, about 0.1%, that is to say 50 times weaker than that of gas effusion. The concentration profile in the boundary layer is calculated experimentally and the rate of liquid evaporated is then calculated numerically, using a model based on utilization of momentum equations in laminar flow for the boundary layer. The results of this numerical study confirm evaporation rates calculated by semi-empirical relations.

Comparison between two models of cooling surfaces using blowing.

Abstract: To protect surfaces against high temperatures, the blowing through a porous material is studied. The geometry is that of a circular cylinder in cross‐flow and the effectiveness of the blowing for the thermal protection is numerically investigated. Two models are developed for the blowing simulation and comparisons are made with experimental data obtained in a heated wind‐tunnel. It is shown that the blowing strongly affects the dynamical and thermal profiles over the surface, thickening the boundary layers and decreasing the external transfer coefficients. It results in a lower viscous drag and thermal stress. The wall temperature dramatically decreases with blowing and the heat flux is also affected.

Experimental Investigation of the Mixing Between Hot and Cold Gas in Two Cooling Processes

The mixing between a hot turbulent flow and a cold fluid, injected through a porous plate or using a discrete injection, is experimentally investigated. The blowing is shown to dramatically modify the dynamic and thermal fields, whereas the discrete injection has a weaker effect. The influence on the average quantities and fluctuating parts are found to be different. The effect of the main flow temperature is addressed and a discussion for the mixing in the blowing and discrete injection cases is proposed.

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.