A weakly nonlinear framework to study shock–vorticity interaction

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

KINERJA POMPA JET EJECTOR DENGAN MODIFIKASI HELMHOLTZ RESONATOR PADA PIPA NORMAL SHOCK

Setiap fluida yang mengalir selalu memiliki bunyi dengan intensitas dan frekwensi tertentu di dalam atau diluar ambang batas audio. Sifat akustik dari aliran fluida ini menjadi ide untuk memodifikasi normal shock diffuser dari suatu sistem fluida dengan menerapkan helmholtz resonator sebagai pengganti normal shock diffuser dengan menggabungkan dua pompa yang di aliri fluida, yaitu pompa sentrifugal tekanan rendah berkapasitas tinggi dan pompa injeksi tekanan tinggi berkapasitas rendah. Penelitian ini bertujuan untuk menentukan berapa besar pengaruh variasi jumlah pipa kapiler helmholtz resonator terhadap kinerja aliran fluida hidrolik booster-jet ejector pump. Penelitian ini bersifat eksperimental, dengan menerapkan sensor magneto flow meter arduino mega untuk mengukur kapasitas aliran fluida. Hasil penelitian ini menunjukan daya terbesar berada pada helmholtz resonator dengan jumlah 4 pipa kapiler yaitu sebesar 170,914353 Watt. Disimpulkan bahwa kinerja pompa jet-ejector mengalami peningkatan sebesar 36% dari daya sebesar 125 Watt sebelum modifikasi. Kata Kunci : Booster Jet Ejector, Resonator Helmholtz, Normal Shock Every fluid that flows always has a sound with a certain intensity and frequency, within or outside the audio threshold. The acoustic properties of this fluid flow became the idea to modify the normal shock diffuser of a fluid system by applying a Helmholtz resonator as a substitute for the normal shock diffuser by combining two pumps that are fed with fluid entering through a high-capacity low-pressure centrifugal pump and the other pump namely high pressure -low capacity injection pump. This study aims to determine how much the variation in the number of Helmholtz resonator capillaries towards performance of the hydraulic fluid flow of the booster-jet ejector pump. This research is experimental, by applying the arduino mega magneto flow meter sensor to measure the fluid flow capacity. The results of this study show that the greatest power is in the helmholtz resonator with a total of 4 capillary pipes, which is 170.914353 Watt. It is concluded that the performance of the jet-ejector pump has increased by 36% from the power of 125 Watt before modification. Keywords: Booster Jet Ejector, Helmholtz Resonator, Normal Shock

Experimental Study on Interaction between Nanosecond Pulsed Laser and Normal Shock Wave

Nanosecond pulsed lasers possess two remarkable advantages: a high peak power density and the ability to break down air to form plasma readily. Therefore, they have significant practical value in the drag reduction of a supersonic body. An experimental investigation is conducted on the fundamental physical phenomenon of the interaction of the pulsed laser plasma with a normal shock wave to reveal the mechanism of drag reduction. Moreover, a high-precision schlieren system is developed to measure complex wave structures with a time resolution of up to 30 ns and a spatial resolution up to 1 mm. A high-speed particle image velocimetry system is set up to measure the velocity and vorticity of the flow field quantitatively; the system has a time resolution of up to 500 ns. The characteristics of the spherical shock wave and the high-temperature and low-density region induced by the laser plasma are presented. The flow characteristics and evolution process of the laser plasma under a normal shock wave are substantially revealed. The cause of the supersonic drag reduction by the pulsed laser plasma is illustrated with numerical simulation results. The following results are obtained in this study: the initial Mach number of the shock wave induced by the laser plasma increases with the laser energy, and the shape of the wave gradually evolves from a droplet shape to a spherical shape. The propagation velocity decreases with time and is close to the sound velocity after 50 μs. The shape of the initial high-temperature and low-density region is approximately spherical; it subsequently destabilizes to form a sharp spike structure in the laser’s incident direction. Ultimately, the region evolves into a double-vortex ring structure with upper and lower symmetry; the size of this region increases with the laser energy.

Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

The upgraded elastic surface algorithm (UESA) is a physical inverse design method that was recently developed for a compressor cascade with double-circular-arc blades. In this method, the blade walls are modeled as elastic Timoshenko beams that smoothly deform because of the difference between the target and current pressure distributions. Nevertheless, the UESA is completely unstable for a compressor cascade with an intense normal shock, which causes a divergence due to the high pressure difference near the shock and the displacement of shock during the geometry corrections. In this study, the UESA was stabilized for the inverse design of a compressor cascade with normal shock, with no geometrical filtration. In the new version of this method, a distribution for the elastic modulus along the Timoshenko beam was chosen to increase its stiffness near the normal shock and to control the high deformations and oscillations in this region. Furthermore, to prevent surface oscillations, nodes need to be constrained to move perpendicularly to the chord line. With these modifications, the instability and oscillation were removed through the shape modification process. Two design cases were examined to evaluate the method for a transonic cascade with normal shock. The method was also capable of finding a physical pressure distribution that was nearest to the target one.