Free Interaction Theory Research Articles

Modeling Free Shock Separation Induced Side Loads in Overexpanded Rocket Nozzles

While operating in an overexpanded condition, rocket nozzles exhibit dynamic off-axis loads caused by asymmetric internal flow separation. It has been demonstrated that topologies, which only display free shock separation, produce side-load magnitudes lower than those that can transition to restricted shock separation. It is therefore suggested that geometries such as truncated ideal contour nozzles could be used on launchers with large-area-ratio designs providing improved vacuum performance. Part of the challenge of designing nozzles to operate in the overexpanded regime is characterizing and quantifying associated side loads. This paper presents the methodology and results of an analytical model that simulates side loads induced by free shock separation. The pressure distribution within a separated rocket nozzle is produced using free interaction theory, and a spring–damper analogy is used to model shock fluctuations in response to external pressure disturbances. Good agreement has been found between simulated side loads and experimentally measured forces on four conical and one truncated ideal contour nozzle.

Steady subsonic boundary layer in domains of local surface heating

The perturbed flow in a laminar boundary layer is investigated when there are heating elements on the body surface. The flow is assumed to be laminar and subsonic everywhere. It is shown that such flows can be described within the scope of free interaction theory. A solution of a plane steady-state problem is constructed in the linear approximation. The results of analytical and numerical analysis are presented.

Local temperature perturbations of the boundary layer in the regime of free viscous–inviscid interaction

AbstractWe analyse the disturbed flow in the subsonic laminar boundary layer, disturbances being generated by local heating elements, which are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal sources. We construct the numerical solution for the case of a flat subsonic stream in the viscous asymptotic layer, in which the flow is described by nonlinear equations for vorticity, temperature and an interaction condition which provides the influence of perturbations to the pressure in the main order. The obtained solutions are compared with those for corresponding linear problems with small perturbations. It is demonstrated that strong temperature perturbations in some situations allow us to obtain the flow close to the separated flow.

Considerations on shock wave/boundary layer interaction in undular hydraulic jumps in horizontal channels with a very high aspect ratio

It can be seen in the literature that the fundamental factors governing oblique shock wave development, typically in very large channels with straight sidewalls, have not yet been completely understood and remain at the level of indicating its presence and formation. In this study, in addition to an analysis of various properties of hydraulic jump behaviour in very large channels, some aspects of boundary layer development and its detachment from the channel lateral sidewall are also investigated. At the detachment point of the lateral shock waves, it was noted that the displacement thickness experiences a significant increase; this is accompanied by a significantly reduced gradient normal to the channel sidewalls of the flow velocity as well as the occurrence of a strong, sudden adverse pressure gradient. An analysis of the flow velocity distribution and the background turbulence intensity of both the streamwise and spanwise velocity components was also carried out. Furthermore, it is argued that the supersonic flow separation analogy with a supercritical free surface flow can be applied to this case study and that the behaviour of the supercritical flow during separation can be interpreted by the free interaction theory typically used in aerodynamics.

Two-dimensional numerical investigations of small-amplitude disturbances in a boundary layer at Ma=4.8: Compression corner versus impinging shock wave

Two-dimensional direct numerical simulations and linear stability theory investigations have been carried out for a compression ramp at Ma=4.8 and compared to earlier results of a laminar boundary layer with impinging shock wave. The inflow parameters in both flows were identical; the ramp angle of the compression corner was chosen to cause a separation bubble, which has exactly the same length compared to the case with impinging shock. It turned out, that the two cases are almost identical for the base flow properties. This is in accordance with similarity assumptions, e.g., free interaction theory, which for smaller Reynolds numbers states, that the boundary layer should be independent of the sort of shock-boundary layer interaction. However, linear stability theory results differ near the corner and the impinging shock, respectively. Direct numerical simulations of small-amplitude disturbances, which were introduced into the laminar boundary layer, also behave in a very similar way. Amplitude distributions exhibit the same characteristics. The according distributions of the ramp flow have slightly larger amplitudes than the case with impinging shock.

Formation of supersonic zones and local separation zones in transonic steady-state flow past surface roughness in the free interaction regime

Within the framework of free interaction theory numerical methods are used to investigate the occurrence of supersonic zones with shocks in the outer inviscid region for flow past roughness in the lower viscous sublayer, with and without the formation of local separation zones.

Experimental, analytical, and computational methods applied to hypersonic compression ramp flows

Experimental data fully laminar and transitional shock-wave/boundary-layer interactions in two-dimensional compression corners are provided and used for the validation of two full Navier-Stokes solvers, as well as for checking the capabilities and limitations of simple analytical prediction methods. Viscous pressure interaction, free interaction, and inviscid oblique shock theory are found to predict well the pressure levels the flat plate upstream of the interaction, within the separated region, and downstream of the interaction, respectively. The reference temperature theory is found to perform well in attached flow regimes both upstream and downstream of the interaction region and to provide the basis for a universal peak heating correlation law. Full Navier-Stokes computations are necessary, however, to predict the extent of the interaction region and the associated influence the pressure distribution (control effectiveness) as well as the detailed heat transfer distribution. To achieve this, very fine gridding coupled with the use of strict convergence criteria (based the evolution of the location of the separation point rather than standard density residuals) is shown to be necessary. It is finally shown that, although sophisticated turbulence models need to be further developed before the detailed characteristics of fully turbulent shock-wave/boundary-layer interactions may be predicted, transitional interactions (where transition typically occurs in the neighborhood of reattachment) may be adequately handled by algebraic turbulence models switched on just downstream of reattachment.

Nonlinear interaction of a large vortex with a boundary layer

The nonlinear problem of boundary layer instability under the influence of a plane vortex is investigated for high Reynolds numbers. The vortex occupies the entire thickness of the boundary layer and has a longitudinal dimension of the order of the Tollmien-Schlichting wavelength. The initial vortex is rapidly swept away by the flow, inducing a Stokes layer near the surface of the plate. Expanding, this layer reaches the dimensions of the viscous sublayer of free interaction theory, where wave packet generation takes place. In the case in question a feature of the nonlinear stage of development of the disturbances is the formation of a concentrated vortex, which arises in the Stokes layer and grows rapidly, whereas the wave packet propagated ahead of it remains linear. From the calculations there emerges a tendency for the new vortex to be formed above the wail, whereas the maximum vorticity of the vortex generated in the Stokes layer corresponds to the wall itself.

Viscous instability of hypersonic flow past a wedge

Let us consider the case of uniform hypersonic viscous gas flow past a thin wedge. The nose of the wedge is sharp, and the relation between the wedge angle and the Mach number of the oncoming flow is such that an attached shock originating at the nose of the wedge is formed. We require the shock wave to enter the outer part of the free interaction zone resulting from the presence of some local flow inhomogeneity (protuberance, blowing-suction, etc.) at a distance L* from the nose of the wedge. We introduce the Reynolds number R = p*~ U*=L*/g* calculated from parameters of the uniform flow behind the shock (U* is the velocity, V*~ is the density, and/x~is the dynamic viscosity) and use it to define the small parameter ~ = R -1/8. We also let the Math number M= of the flow behind the shock tend to infinity. In free interaction theory most information can be extracted from the viscous wall sublayer with the characteristic space coordinates and time _3/,