Weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher order higher resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling showsmore » that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.« less

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Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability

This paper discusses the performance enhancement of supersonic air intake model through the implementation of blunted leading edge to the cowl lip section of the model. A supersonic air intake model with sharp cowl leading edge is initially considered to numerically investigate its performance. Mach 3, supersonic intake flow through the base model has been simulated using commercial CFD package Ansys Fluent-15. Comparison of numerical predictions and experimental measurements is presented to demonstrate the correctness and accuracy of numerical frame work followed in the present study. Higher order spatial accuracy of the solver along with suitably refined mesh helped in accurate capturing of the flow field. Modification to the cowl lip is proposed as an effective method to improve the performance of the supersonic air intake. Two different blunted cowl leading edge geometries were investigated to identify the possible enhancement in performance parameters. Improvement in mass capture and combustion stability attained through the use of forward shifted blunt cowl leading edge is presented. It is also revealed through the present study that the blunt cowl leading edge can reduce the intensity of shock wave boundary layer interaction occurring at the isolator entry section. Deviation in total pressure recovery and flow distortion observed with different supersonic air intake models are also discussed with reasons for the same. This study demonstrates the scope of overall improvement in scramjet engine performance through the use of suitably positioned blunt cowl leading edge.

https://jafmonline.net/JournalArchive/download?file_ID=44250&issue_ID=246

Alterations of Cowl Lip for the Improvement of Supersonic-Intake Performance

Results are presented of direct numerical simulations (DNS) of a viscous, laminar ring. The effects of different generator configurations and velocity programs on the formation and post‐formation characteristics of the ring are studied. It is shown that during the formation phase of the ring, total circulation and impulse in the flowfield are approximately the same for the ‘‘nozzle’’ and ‘‘orifice’’ generators. It is also found that throughout this period the slug flow model under‐predicts the total circulation in the flow. During the formation phase, the simulation results for the time evolution of total circulation and location of the vortex spiral center are in agreement with the experimental findings of Didden [J. Appl. Mech. Phys. (ZAMP) 30, 101 (1979)]. The results of the flow visualization studies show that during the post‐formation phase a vortex bubble is formed. As the bubble propels itself forward a wake is formed in the rear of the bubble. The impulse and vorticity from the bubble are continuo...

Direct numerical simulation of a laminar vortex ring

Numerical and experimental study of pulse-jet cleaning in fabric filters

Counter-rotating vortex rings (CRVRs) are observed to form ahead of a primary compressible vortex ring that is generated at the open end of a shock tube at sufficiently high Mach numbers. In most of the earlier studies, the embedded shock strength has been asserted as the cause for the formation of CRVRs. In the present study, particle image velocimetry (PIV) measurements and high-order numerical simulations show that CRVRs do not form in the absence of a Mach disk in the sonic under-expanded jet behind the primary vortex ring. Kelvin–Helmholtz-type shear flow instability of the slipstream originating from the triple point of the Mach disk and subsequent eddy pairing, as observed by Rikanati et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174503) in shock-wave Mach reflection, is found to be responsible for CRVR formation. The growth rate of the slipstream in the present problem follows the model proposed by them. The parameters influencing the formation of CRVRs as well as their dynamics is investigated. It is found that the strength of the Mach disk and its duration of persistence results in an exit impulse that determines the number of CRVRs formed.

Role of slipstream instability in formation of counter-rotating vortex rings ahead of a compressible vortex ring

Formation and evolution of a compressible vortex ring generated at the open end of a short driver section shock tube has been simulated numerically for pressure ratios (PR) of 3 and 7 in the present study. Numerical study of compressible vortex rings is essential to understand the complicated flow structure and acoustic characteristics of many high Mach number impulsive jets where simultaneously velocity, density and pressure fields are needed. The flow development, incident shock formation, shock diffraction, vortex ring formation and its evolution are simulated using the AUSM+ scheme. The main focus of the present study is to evaluate the time resolved vorticity field of the vortex ring and the shock/expansion waves in the starting jet for short driver section shock tubes—a scenario where little data are available in existing literature. An embedded shock and a vortex induced shock are observed for PR =  7. However the vortex ring remains shock free, compact and unaffected by the trailing jet for PR =  3. Numerical shadowgraph shows the evolution of embedded shock and shock/expansion waves along with their interactions. The velocity and vorticity fields obtained from simulation are validated with the particle image velocimetry results and these data match closely. The translational velocity of the vortex ring, velocity across the vortex and the centre line velocity of the jet obtained from simulation also agree well with the experimental results.

Numerical simulation and PIV study of compressible vortex ring evolution

Vortices generated at the open end of a planar shock tube are numerically simulated using the AUSM+ scheme. This scheme is known to have low numerical dissipation and therefore is suitable for capturing unsteady vortex motion. However, this low numerical dissipation can also cause oscillations in the vorticity field. Numerical experiments presented here highlight the effect of numerical dissipation on the simulated vortex, as well as the role played by turbulence models. Two turbulence models-the shear-stress-transport (SST) and its modified version for unsteady flows (SST-SAS)-are employed to observe the effect of including turbulence models in such complex flows where the vortex has an embedded shock.

Numerical simulation of shock tube generated vortex: effect of numerics

Navier–Stokes simulation of shock-heavy bubble interaction: Comparison of upwind and WENO schemes

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number $$M = 1.36$$
 ) and shock-embedded $$(M = 1.57)$$
 compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for $$M = 1.36$$
 and it reaches up to 60 % for $$M = 1.57$$
 . The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.

Sudipta De

Papers

Numerical simulation and PIV study of compressible vortex ring evolution

Numerical simulation of shock tube generated vortex: effect of numerics

Navier–Stokes simulation of shock-heavy bubble interaction: Comparison of upwind and WENO schemes

Numerical simulation of a compressible vortex–wall interaction

High resolution numerical simulation of a shock-accelerated Refrigerant-22 bubble