Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels.
Rayleigh streaming is a steady flow generated by the interaction between an acoustic wave and a solid wall, generally assumed to be second order in a Mach number expansion. Acoustic streaming is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at antinode. For higher acoustic levels, additional streaming cells have been observed. Results of laser Doppler velocimetry measurements are here compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming velocities is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency on acoustics going from quadratic to linear. The evolution of streaming flow is different for outer cells and for inner cells. Also, the hypothesis of radial streaming velocity being of second order in a Mach number expansion, is not valid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.
An unexpected balance between outer Rayleigh streaming sources
Acoustic streaming generated by a plane standing wave between two infinite plates or inside a cylindrical tube is considered, under the isentropic flow assumption. A two-dimensional analysis is performed in the linear case of slow streaming motion, based on analytical formal solutions of separate problems, each associated with a specific source term (Reynolds stress term). In order to obtain these analytical solutions, a necessary geometrical hypothesis is that $(R/L)^{2}\ll 1$ , where $R$ and $L$ are the guide half-width (or radius) and length. The effect of the two source terms classically taken into account is quantified in order to derive the dependence of the maximum axial streaming velocity on the axis as a function of the ratio $R/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ , where $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ is the acoustic boundary layer thickness. The effect of two other source terms that are usually neglected, is then analysed. It is found that one of these terms can generate a counter-rotating streaming flow. While negligible for very narrow guides, this term can become important for some values of the aspect ratio $L/R$ .
THE PERFORMANCE OF STEADY DETONATION ENGINES
Propulsion systems driven by steady normal detonations are studied. The practical di‐culties associated with stabilizing a detonation wave are highlighted. The requirement on the freestream total enthalpy is considered in parallel with efiects such as condensation or auto-ignition of the fuel-air mixture and limitations associated with fuel sensitivity to detonation. A criterion for detonation stabilization is formulated and applied to an analytical treatment of a detonation ramjet and a detonation turbojet, which are the respective analogs of the ramjet and the turbojet using detonative combustion. The performance of these engines is evaluated and compared to the ideal ramjet and turbojet models for hydrogen and JP10. A limitation is placed on the maximum total temperature allowed in the combustor, based on material considerations. The results show that steady detonation engines have a small thrust-producing range, due to the requirements for detonation stabilization. Their performance is always lower than that of the conventional ramjet and turbojet because of the total pressure loss across the detonation.