The eﬀect of wall thermal conductivity on shock wave reﬂection - Berry, Richard (My University, 2017)
In traditional two-dimensional shock wave theory the reﬂection of a shock wave oﬀ a surface is treated as an adiabatic process and that the reﬂection surface is perfectly rigid and smooth with an inviscid ﬂow of the ﬂuid. In reality it has been found that these assumptions are not entirely accurate, and that although they are a good indication in the regular and irregular reﬂection domains of shock waves over the surface, viscous and thermal eﬀects are present within the ﬂow ﬁeld. It has been experimentally shown that the transition of regular reﬂection to irregular reﬂection exceeds the theoretical limit, which is known as the von Neumann paradox. This paradox has largely been accounted for in the formation of a viscous boundary layer behind the reﬂected shock wave, based on numerous experimental and computational studies. However, the thermal eﬀects in the reﬂection process have largely been neglected as the assumption of heat transfer between the post-shock wave gas and the reﬂection surfaces is assumed to be invalid. These thermal eﬀects were investigated by testing materials with a varying range of thermal conductivities (1.13 to 401 W/mK) and similar surface roughness’s below the suggested limit for hydraulic smoothness. Each experiment placed two test pieces at the same incidence angle, symmetrically in the shock tube. This allowed ﬂow properties to be exactly the same for the two materials being tested with a single plane shock wave. Test Mach numbers ranged from 1.2790 to 1.3986, with tests conducted at shock wave incidence angles of 36◦, 40◦, 60◦ and 70◦. This allowed both the regular and irregular reﬂection domains to be tested. Shadowgraph images were created using a z-conﬁguration optical set up. These shadowgraph images were analysed quantitatively based on the angles measured as well as qualitatively based on ﬂow features and symmetry. Both the quantitative and qualitative tests indicated that there was a diﬀerence in the angles between the reﬂected shock waves and surfaces based on the material thermal conductivity. In the quantitative tests the value of this angle was larger for materials with a lower thermal conductivity, and smaller for ones with a higher thermal conductivity for the regular reﬂection cases. In the irregular reﬂection cases the angle between the reﬂected and incident shock waves was larger for materials with a higher thermal conductivity. The materials with midrange thermal conductivities had reﬂection angles that lay within the bounds of the glass and copper angle values. The qualitative images supported these ﬁndings showing asymmetry in materials with diﬀerent thermal conductivities with the intersection of reﬂected shock waves lying closer to the material with a higher thermal conductivity. Control experiments using test pieces made from an identical material showed no bias due to the location of the test piece in the shock tube
A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulﬁlment of the requirements for the degree of Master of Science in Engineering, 2017.
Keywords: Shock waves; Thermal conductivity