ENGINEERING AND CFD

The flow layer near the surface of a body - the boundary layer - can have a smooth, steady, low-momentum laminar state, but also an unsteady, turbulent, layer-stirring state with increased friction drag and wall heat flux. Wall heating is especially severe with supersonic hot gas flows like, e.g., in a rocket (Laval-) nozzle extension. To protect the walls from thermal failure a cooling gas is injected building a cooling film. Its persistence depends strongly on the layer state of the hot-gas flow, the type of cooling gas, and the form and strength of injection. Fundamental studies are performed using direct numerical simulations, providing also valuable benchmark data for less intricate computational-fluid-dynamics methods using turbulence models.

The present project explores the laminar-to-turbulent transition, turbulence, and flow control in boundary layers at flow speeds from subsonic to hypersonic regimes. Supercomputer re-sources are needed to resolve the multi-scale unsteady fluctuations using Direct Numerical Simulation (DNS) without turbulence modelling, based on discretizing the full underlying (Na-vier-Stokes) equations by spectral and compact finite-difference schemes. The physical problems under investigation are related to instabilities of the smooth, steady laminar flow leading to the inherently unsteady, self-sustaining turbulent state in the friction-forces domi-nated flow layer near walls. The turbulent flow state causes strongly increased mixing of the outer and near-wall flow, higher friction drag, and heat transfer. In supersonic flow the in-creased wall heating poses a severe challenge for the solid surfaces where the high kinetic energy is transformed to heat due to friction.

The heating not only occurs at the skin of aircraft flying at supersonic speeds but also in in-ternal flows. In a rocket (Laval-) nozzle extension the hot combustion-gas core flow is accel-erated to supersonic speeds, and to protect the walls from thermal failure a cooling gas has to be injected either tangentially, or normally from the wall, building a cooling film. The persis-tence of the cooling film depends strongly on the state of the hot-gas flow – laminar or turbu-lent. With main-flow turbulence strong mixing occurs, and the protecting film may dissolve rapidly. Strong tangential blowing through a backward facing step slit seems at first superior to wall-normal blowing, but the latter can be more easily applied in a repeated fashion by successive blowing holes or slits at the wall, or a porous surface like ceramics.

To understand the fundamental cooling characteristics the film behavior in a supersonic air main flow at a Mach number of 2.7 over an insulated flat plate is investigated. Air and helium are employed as cooling gases and are injected with a low rate in the wall-normal direction through a single infinite spanwise slit into the laminar or turbulent boundary-layer flow. The blowing is realized by prescribing a fixed distribution of the cooling-gas mass flux, mass frac-tion, and temperature at either simply the orifice location without the cooling-gas channel (modeled blowing) or at the lower end of the included blowing channel (simulated/interacting blowing), thus allowing for an interaction of the main and cooling-gas flows. The results of this fundamental DNS study provide valuable benchmark data for the validation of less ex-pensive and more flexible conventional computational fluid dynamics (CFD) methods using turbulence models (RANS/LES computations).

It was found that turbulence gives rise to a much stronger wall-normal heat conduction com-pared to the laminar case, resulting in a more rapid heating of the cooling film. A similar cool-ing effect is reduced to about 30% of the laminar streamwise stretch. Moreover, the pressure increase by the blockage effect of the blowing is stronger due to the larger hot-gas velocity close to the wall with turbulence, and a larger driving pressure is necessary for the same blowing rate. The simulated and simply modeled blowings largely give the same results in the case of the laminar boundary layer, despite the heat conduction into the channel flow in the simulations including the channel. For the turbulent boundary layer, however, turbulent fluctuations travel into the channel, leading to a premixing process, and thus a cooling effec-tiveness loss of about 10% (helium) to 15% (air). For a more accurate blowing modeling, the prescribed cooling-gas mass fraction, temperature, and turbulence distribution along the slit especially need to be more adapted to the actual profiles computed in this work. This is es-pecially important for conventional CFD methods.

Helium blowing leads to a higher cooling effectiveness, mainly due to its high heat capacity: After 20 slit widths, the effectiveness value is still 0.7 compared to 0.25 for air, and argon yields only 0.14 in laminar flow; note that a value of 1 means that the wall attains the temper-ature of the injected unmixed cooling gas, and zero means the original temperature without cooling. At an equal blowing rate (density times blowing velocity), a light cooling-gas jet has higher momentum. This leads to a higher boundary-layer penetration but, due to the lower density, also stronger deflection, and a thicker cooling film results. The decline of the cooling effectiveness with turbulence is slightly less for helium, despite the main-flow turbulent kinetic energy penetrating deeper into the channel, and the temperature fluctuations are distinctly higher downstream, starting palpably in front of the slit. But, the turbulent kinetic energy is lower in the downstream cooling range of the slit with helium. A small Reynolds-number-lowering effect in the case of helium blowing is present, but it is far too small to cause a re-laminarization of the boundary layer. Such a beneficial effect may occur with successive slits.