Cylindrical converging shock waves interacting with an array of aerodynamic obstacles are investigated numerically for diverse shock strengths and for different obstacle configurations in air in standard conditions. The considered number of obstacles N is 4, 6, 8, 16, and 24. Obstacles are lenticular airfoils with thickness-to-chord ratios t/c of 0.07, 0.14, and 0.21. The distances of the airfoil leading edge from the shock focus point rLE/rref LE are 1, 2, and 2.5, where rref LE = 7 is the dimensionless reference distance from the origin. Considered impinging shock Mach numbers Ms are 2.2, 2.7, and 3.2 at the reference distance from the origin. The reference experimental configuration (N = 8,t/c = 0.14,rLE = 7,Ms = 2.7) was proposed by Kjellander et al. ["Thermal radiation from a converging shock implosion," Phys. Fluids 22, 046102 (2010)]. Numerical results compare fairly well to available one-dimensional models for shock propagation and to available experimental results in the reference configuration. Local reflection types are in good agreement with the classical criteria for planar shock waves. The main shock reshaping patterns are identified and their dependence on the shock strength and obstacle configuration is exposed. In particular, different shock patterns are observed after the leading edge reflection, which results in polygonal shock wave with N, 2N, 3N, and 4N sides. The largest temperature peak at the origin is obtained for the 8-and the 16-obstacle configurations and for the smallest thickness to length ratio, 0.07, located at distance from the origin of 2rref LE. In terms of compression efficiency at the origin, the 16-obstacle configuration is found to perform slightly better than the reference 8-obstacle configuration-with an efficiency increase of about 2%-3%, which is well within the model accuracy-thus confirming the goodness of the obstacle arrangement proposed by Kjellander and collaborators

A multi-domain finite-volume approach is presented to simulate the interaction of converging shock waves and aerodynamic obstacles for dilute gases. The so-called reshaping process, in which the cylindrical shock is reshaped into a polygonal shock due to the presence of obstacles along the shock path, is studied. To accurately capture the diverse spatial scales of the problem, the computational domain is divided into three sub-domains, namely, the far-field region, the obstacle region and the focus region. Shock propagation in the far-field region is simulated under the axisymmetric, namely, one-dimensional approximation. The obstacle region is described by a fully two-dimensional model, in which initial conditions are interpolated from the far-field. The solution in the obstacle region is then interpolated into the focus region surrounding the center of the imploding shock. These two regions partially overlap to allow for linear interpolation. Numerical results are presented for air in dilute conditions and for four, eight, sixteen and twenty four aerodynamic obstacles. The proposed multi-domain solution technique is found to be capable of describing the complex gas dynamics of the shock propagation and reshaping, while reducing the computational burden for a large number of obstacles of one order of magnitude with respect to fully two-dimensional simulations

The unsteady reflection of cylindrical converging shock waves over convex obstacles is investigated numerically. At the leading edge, numerical simulations show the occurrence of all types of regular and irregular reflections predicted by the pseudosteady theory for planar shock-wave reflections over planar surfaces, although for different combinations of wedge angles and incident shock Mach number. The domain of occurrence of each reflection type and its evolution in time due to shock acceleration and to the non-planar geometry is determined and it is compared to the results of the pseudo-steady theory. The dependence of the reflection pattern on the (local) values of the wedge angle is in good agreement with the pseudo-steady theory. Less complex reflection patterns are instead observed at larger values of the leading edge shock Mach number at which the pseudo-steady theory predicts the occurrence of more complex reflection patterns

An analytical model for the evolution of regular reflections of cylindrical converging shock waves over circular-arc obstacles is proposed. The model based on the new (local) parameter, the perceived wedge angle, which substitutes the (global) wedge angle of planar surfaces and accounts for the time-dependent curvature of both the shock and the obstacle at the reflection point, is introduced. The new model compares fairly well with numerical results. Results from numerical simulations of the regular to Mach transition-eventually occurring further downstream along the obstacle-point to the perceived wedge angle as the most significant parameter to identify regular to Mach transitions. Indeed, at the transition point, the value of the perceived wedge angle is between 39° and 42° for all investigated configurations, whereas, e.g., the absolute local wedge angle varies in between 10° and 45° in the same conditions

A non-intrusive measurement technique of the heat transfer coefficient field, based on IR-thermography, is applied on a 12-mm-height rectangular channel of 1:10 aspect ratio, whose lower surface is enhanced by chevron-shaped square-cross-section ribs. The channel is operated at imposed heat flux while forced-air flows for Reynolds numbers ranging from 700 to 8000. In particular, the technique uses local temperature measurements to retrieve the radiative heat flux with a three-wavelength-band model for partially transparent enclosures, and the conductive flux towards the backside with a FEM model, which allow an edge-to-edge estimation of the local convective heat transfer. The resulting local Nusselt number maps are presented and compared to data obtained operating both at fixed temperature and inside a channel with flat surfaces.