Amplification Of Kinetic Energy Research Articles

Numerical study of turbulent kinetic energy amplification during shock-wave diffraction

Numerical study of turbulent kinetic energy amplification during shock-wave diffraction

On nonmodal stability of elliptic pipe flow

The temporal nonmodal stability of the Poiseuille flow in a pipe of axially uniform elliptic cross section is numerically studied. In particular, it is shown that the maximum amplification of kinetic energy of disturbances depends significantly on the pipe aspect ratio, and this dependence is non-monotonic. It agrees with the corresponding dependence of the energy critical Reynolds number, which is the lower limit of the Reynolds numbers enabling the growth of disturbance kinetic energy. In other words, changing the aspect ratio similarly affects both nonmodal and monotonic stability of the flow. The optimal disturbances displaying the maximum amplification are streamwise counter-rotating vortices. These disturbances are streamwise uniform at sufficiently large Reynolds numbers and may become streamwise harmonic as the Reynolds number decreases. In addition, their symmetry with respect to the cross section axes varies with the aspect ratio. Thus, the obtained results suggest that changing the aspect ratio may be a perspective tool for the passive control of the subcritical laminar-turbulent transition in pipe flows. In other words, this factor is worth considering when designing various devices (e.g., heat exchangers or ventilation systems) containing pipes to enhance their efficiency.

Characteristic Scales in Shock–Turbulence Interaction

A semi-empirical estimate of the time-averaged thickness of a planar shock embedded in a turbulent mean flow is presented in an effort to quantify the characteristic time and length scales for turbulence modeling. Simplified Favre-averaged Navier–Stokes equations are reformulated and combined with the Rankine–Hugoniot relations to obtain an equation that relates the shock structure and its characteristic thickness to the upstream turbulent and mean flow quantities. The only mean flow and turbulence quantities needed to compute the shock thickness or velocity profile through the shock are upstream Mach number , turbulent Mach number , and the Taylor-based Reynolds number . The accuracy of method for the shock structure is validated against direct numerical simulations of shock–turbulence interaction and shows a very good agreement over a wide range of Mach, Reynolds, and turbulent Mach numbers. Finally, the obtained ratio of characteristic shock time scale to the upstream turbulence time scale is shown to be proportional to the turbulent kinetic energy amplification through the shock and supported through direct numerical simulations.

Highly Resolved Large Eddy Simulation Study of Gap Size Effect on Low-Pressure Turbine Stage

Blade-to-blade interactions in a low-pressure turbine (LPT) were investigated using highly resolved compressible large eddy simulations (LESs). For a realistic setup, a stator and rotor configuration with profiles typical of LPTs was used. Simulations were conducted with an in-house solver varying the gap size between stator and rotor from 21.5% to 43% rotor chord. To investigate the effect of the gap size on the prevailing loss mechanisms, a loss breakdown was conducted. It was found that in the large gap (LG) size case, the turbulence kinetic energy (TKE) levels of the stator wake close to the rotor leading edge were only one third of those in the small gap (SG) case, due to the longer distance of constant area mixing. The small time-averaged suction side separation on the blade, found in the LG case, disappeared in the SG calculations, confirming how stronger wakes can keep the boundary layer attached. The higher intensity wake impinging on the blade, however, did not affect the time-averaged losses calculated using the control volume approach of Denton. On the other hand, losses computed by taking cross sections upstream and downstream of the blade revealed a greater distortion loss generated by the stator wakes in the SG case. Despite the suction side separation suppression, the SG case gave higher losses overall due to the incoming wake turbulent kinetic energy amplification along the blade passage.

Local simulations of instabilities in relativistic jets - I. Morphology and energetics of the current-driven instability

We present the results of a numerical investigation of current-driven instability in magnetized jets. Utilizing the well-tested, relativistic magnetohydrodynamic code Athena, we construct an ensemble of local, co-moving plasma columns in which initial radial force balance is achieved through various combinations of magnetic, pressure, and rotational forces. We then examine the resulting flow morphologies and energetics to determine the degree to which these systems become disrupted, the amount of kinetic energy amplification attained, and the non-linear saturation behaviors. Our most significant finding is that the details of initial force balance have a pronounced effect on the resulting flow morphology. Models in which the initial magnetic field is force-free deform, but do not become disrupted. Systems that achieve initial equilibrium by balancing pressure gradients and/or rotation against magnetic forces, however, tend to shred, mix, and develop turbulence. In all cases, the linear growth of current-driven instabilities is well-represented by analytic models. CDI-driven kinetic energy amplification is slower and saturates at a lower value in force-free models than in those that feature pressure gradients and/or rotation. In rotating columns, we find that magnetized regions undergoing rotational shear are driven toward equipartition between kinetic and magnetic energies. We show that these results are applicable for a large variety of physical parameters, but we caution that algorithmic decisions (such as choice of Riemann solver) can affect the evolution of these systems more than physically motivated parameters.

A priori evaluation of the Pantano and Sarkar model in compressible homogeneous shear flows

In this study, a Reynolds stress closure, including the Pantano and Sarkar model of the mean part of the pressure–strain correlation is used for the computation of compressible homogeneous at high-speed shear flow. Several studies concerning the compressible homogeneous shear flow show that the changes of the turbulence structures are principally due to the structural compressibility effects which significantly affect the pressure field and then the pressure–strain correlation. Eventually, this term appears as the main term responsible for the changes in the magnitude of the Reynolds stress anisotropies. The structure of the gradient Mach number is similar to that of turbulence, therefore this parameter may be appropriate to study the changes in turbulence structures that arise from structural compressibility effects. Thus, the incompressible model of the pressure strain correlation and its corrected form by using the turbulent Mach turbulent only, fail to correctly evaluate the compressibility effects at high shear flow. An extension of the widely used incompressible Launder, Reece and Rodi model on compressible homogeneous shear flow is the major aim of the present work. From this extension, the standard coefficients C i become a function of the extra compressibility parameters (the turbulent Mach number M t and the gradient Mach number M g ) through the Pantano and Sarkar model. Application of the model on compressible homogeneous shear flow by considering various initial conditions shows reasonable agreement with the DNS results of Simone et al. and Sarkar. The observed trend of the dramatic increase in the normal Reynolds stress anisotropies, the significant decrease in the Reynolds shear stress anisotropy and the increase of the turbulent kinetic energy amplification rate with increasing the gradient Mach number are well predicted by the model. The ability of the model to predict the equilibrium states for the flow in cases A 1 to A 4 from DNS results of Sarkar is examined, the results appear to be very encouraging. Thus, both parameters M t and M g should be used to model significant structural compressibility effects at high-speed shear flow.

Modeling the Effect of Shock Unsteadiness in Shock/ Turbulent Boundary-Layer Interactions

Reynolds-averaged Navier-Stokes (RANS) methods often cannot predict shock/turbulence interaction correctly. This may be because RANS models do not account for the unsteady motion of the shock wave that is inherent in these interactions. Previous work proposed a shock-unsteadiness correction that significantly improves prediction of turbulent kinetic energy amplification across a normal shock in homogeneous isotropic turbulence. We generalize the modification to shock-wave/turbulent boundary-layer interactions and implement it in the κ-e, κ-ω, and Spalart-Allmaras models. In compression-comer flows, the correction decreases the turbulent kinetic energy amplification across the shock compared to the standard κ-e and κ-w models. This results in improved prediction of the separation shock location, delayed reattachment, and slower recovery of the boundary layer on the ramp. For the Spalart-Allmaras model, the modification amplifies eddy viscosity across the shock, moving the separation location closer to the experiment.

Transient energy growth for the Lamb–Oseen vortex

The transient evolution of infinitesimal flow disturbances which optimally induce algebraic growth in the Lamb–Oseen (Gaussian) vortex is studied using a direct-adjoint technique. This optimal perturbation analysis reveals that the Lamb–Oseen vortex allows for intense amplification of kinetic energy for two-dimensional and three-dimensional perturbations of azimuthal wavenumber m=1. In both cases, the disturbances experiencing the most growth initially take the form of concentrated spirals at the outer periphery of the vortex which rapidly excite bending waves within the vortex core. In the limit of large wavelengths, the optimal perturbation leads to arbitrarily large growths via an original scenario combining the Orr mechanism with vortex induction.

Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence

Direct Numerical Simulation (DNS) is used to study the interaction between normal shock waves of moderate strength (M 1= 1.2 and M 1 = 1.5) and isotropic turbulence. A complete description of the turbulence behaviour across the shock is provided and the influence of the nature of the incoming turbulence on the interaction is investigated. The presence of upstream entropy fluctuations satisfying the Strong Reynolds Analogy enhances the amplification of the turbulent kinetic energy and transverse vorticity variances across the shock compared to the solenoidal (pure vorticity) case. Budgets for the fluctuating-vorticity variances are computed, showing that the baroclinic torque is responsible for this additional production of transverse vorticity. More reduction of the transverse Taylor microscale and integral scale is also observed in the vorticity-entropy case while no influence can beseen on the longitudinal Taylor microscale. When the upstream turbulence is dominated by acoustic and vortical fluctuations, less amplification of the kinetic energy (for Mach numbers between 1.25 and 1.8), less reduction of the transverse microscale and more amplification of the transverse vorticity variance are observed through the shock compared to the solenoidal case. In all cases, the classic estimation of Batchelor relating the dissipation rate and the integral scale of the flow proves to be invalid. These results are obtained with the same numerical tool and similar flow parameters, and they are in good agreement with Linear Interaction Analysis (LIA).

Experiments of Kinetic Energy Amplification of Charged Particles

Experiments of Kinetic Energy Amplification of Charged Particles

Kinetic Energy Amplification of Charged Particles

Kinetic Energy Amplification of Charged Particles