Linear interaction of two-dimensional free-stream disturbances with an oblique shock wave

2019 ◽  
Vol 873 ◽  
pp. 1179-1205 ◽  
Author(s):  
Zhangfeng Huang ◽  
Huilin Wang
Keyword(s):  
Shock Wave ◽  
Plane Wave ◽  
Transmission Coefficient ◽  
Acoustic Waves ◽  
Interaction Analysis ◽  
Oblique Shock Wave ◽  
Theoretical Problem ◽  
Linear Interaction ◽  
Incident Plane ◽  
Excited Wave

The problem of interaction between disturbances and shock waves was solved by a theoretical approach called linear interaction analysis in the mid-twentieth century. More recently, great progress has been made in analysing shock–turbulence interactions by direct numerical simulation. However, an unsolved theoretical problem remains: What happens when no acoustic waves are stimulated behind the shock wave? The concept of a damped wave is introduced, which is a type of excited plane wave. Based on this, the dispersion and amplitude relationships between any incident plane wave and resulting stimulated waves are constructed analytically, systematically and comprehensively. The physical essence of damped waves and the existence of critical angles are clarified. It is demonstrated that a damped wave is a complex number space solution to the acoustic dispersion relationship under certain conditions. It acts as a bridge connecting fast and slow acoustic waves at the position where the $x$ component of the group velocity is zero. There are two critical angles that can excite fast and slow acoustic waves, which determine the conditions that stimulate a damped wave. Our results show good agreement with theoretical and simulation results. The contribution of each excited wave to the transmission coefficient is evaluated, the distribution of the transmission coefficient is analysed and application to an engineering wedge model is performed.

A weakly nonlinear framework to study shock–vorticity interaction

2022 ◽  
Vol 933 ◽  
Author(s):  
Pranav Thakare ◽  
Vineeth Nair ◽  
Krishnendu Sinha
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Significant Contribution ◽  
Interaction Analysis ◽  
Nonlinear Effects ◽  
Normal Shock ◽  
Linear Interaction ◽  
Weakly Nonlinear ◽  
High Incidence ◽  
Vorticity Generation

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.

Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

2014 ◽  
Vol 756 ◽  
Author(s):  
Jaiyoung Ryu ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Longitudinal Velocity ◽  
Wave Structure ◽  
Turbulence Structure ◽  
Turbulent Structures ◽  
Linear Interaction ◽  
Third Invariant

AbstractThe interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

Evolution of enstrophy in shock/homogeneous turbulence interaction

2012 ◽  
Vol 707 ◽  
pp. 74-110 ◽  
Author(s):  
Krishnendu Sinha
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Interaction Analysis ◽  
Direct Numerical Simulations ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Flow ◽  
Linear Interaction

AbstractInteraction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier–Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of$k$–$\epsilon $equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock–boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

Turbulent energy flux generated by shock/homogeneous-turbulence interaction

2016 ◽  
Vol 796 ◽  
pp. 113-157 ◽  
Author(s):  
Russell Quadros ◽  
Krishnendu Sinha ◽  
Johan Larsson
Keyword(s):  
Shock Wave ◽  
Turbulent Flows ◽  
Energy Flux ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Turbulent Energy ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Linear Interaction

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.

Experimental Research of Gasdynamic Liquid Drops Breakup in the Supersonic Flow with an Oblique Shock Wave

2020 ◽  
Author(s):  
K. Yu. Arefyev ◽  
O. V. Guskov ◽  
A. N. Prokhorov ◽  
A. S. Saveliev ◽  
E. E. Son ◽  
...  
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Experimental Research ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Liquid Drops

scholarly journals Core-Shell Nano-Antenna Configurations for Array Formation with More Stability Having Conventional and Non-Conventional Directivity and Propagation Behavior

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 99
Author(s):  
Qaisar Hayat ◽  
Junping Geng ◽  
Xianling Liang ◽  
Ronghong Jin ◽  
Sami Ur Rehman ◽  
...  
Keyword(s):  
Plane Wave ◽  
Propagation Direction ◽  
Core Shell ◽  
Incident Plane Wave ◽  
Polarization Direction ◽  
Shell Nanoparticles ◽  
Incident Plane ◽  
Core Shell Nanoparticles ◽  
Coated Nanoparticle ◽  
2D Array

The enhancement of optical characteristics at optical frequencies deviates with the choice of the arrangement of core-shell nanoparticles and their environment. Likewise, the arrangements of core-shell nanoparticles in the air over a substrate or in liquid solution makes them unstable in the atmosphere. This article suggests designing a configuration of an active spherical coated nanoparticle antenna and its extended array in the presence of a passive dielectric, which is proposed to be extendable to construct larger arrays. The issue of instability in the core-shell nanoantenna array models is solved here by inserting the passive dielectric. In addition to this, the inclusion of a dielectric in the array model reports a different directivity behaviour than the conventional array models. We found at first that the combination model of the active coated nanoparticle and passive sphere at the resonant frequency can excite a stronger field with a rotated polarization direction and a propagation direction different from the incident plane-wave. Furthermore, the extended 2D array also rotates the polarization direction and propagation direction for the vertical incident plane-wave. The radiation beam operates strong multipoles in the 2D array plane at resonant frequency (behaving non-conventionally). Nevertheless, it forms a clear main beam in the incident direction when it deviates from the resonance frequency (behaving conventionally). The proposed array model may have possible applications in nano-amplifiers, nano-sensors and other integrated optics.

scholarly journals Analysis of transonic buffet using dynamic mode decomposition

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Antje Feldhusen-Hoffmann ◽  
Christian Lagemann ◽  
Simon Loosen ◽  
Pascal Meysonnat ◽  
Michael Klaas ◽  
...  
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Measurement Data ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Transonic Buffet

AbstractThe buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by a feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. High-speed particle-image velocimetry measurements are performed to investigate this feedback loop in transonic buffet flow over a supercritical DRA 2303 airfoil. The freestream Mach number is $$M_{\infty } = 0.73$$ M ∞ = 0.73 , the angle of attack is $$\alpha = 3.5^{\circ }$$ α = 3 . 5 ∘ , and the chord-based Reynolds number is $${\mathrm{Re}}_{c} = 1.9\times 10^6$$ Re c = 1.9 × 10 6 . The obtained velocity fields are processed by sparsity-promoting dynamic mode decomposition to identify the dominant dynamic features contributing strongest to the buffet flow field. Two pronounced dynamic modes are found which confirm the presence of two main features of the proposed feedback loop. One mode is related to the shock wave oscillation frequency and its shape includes the movement of the shock wave and the coupled pulsation of the recirculation region downstream of the shock wave. The other pronounced mode represents the disturbances which form the downstream propagating part of the proposed feedback loop. The frequency of this mode corresponds to the frequency of the acoustic waves which are generated by these downstream traveling disturbances and which form the upstream propagating part of the proposed feedback loop. In this study, the post-processing, i.e., the DMD, is highlighted to substantiate the existence of this vortex mode. It is this vortex mode that via the Lamb vector excites the shock oscillations. The measurement data based DMD results confirm numerical findings, i.e., the dominant buffet and vortex modes are in good agreement with the feedback loop suggested by Lee. Graphic abstract

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