Three-dimensional instabilities in compressible flow over open cavities

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows

Reduced-Order Modeling of Diffusive Effects on the Dynamics of Bubbles

The Rayleigh-Plesset equation and its extensions have been used extensively to model spherical bubble dynamics, yet radial diffusion equations must be solved to correctly capture damping effects due to mass and thermal diffusion. The latter are too computationally intensive to implement into a continuum model for bubbly cavitating flows, since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive a reduced-order model that accounts for thermal and mass diffusion. Motivated by results of applying the Proper Orthogonal Decomposition to data from full radial computations, we derive a model based upon estimates of the average heat transfer coefficients. The model captures the damping effects of the diffusion processes in two ordinary differential equations, and gives better results than previous models

A Reduced-Order Model of Heat Transfer Effects on the Dynamics of Bubbles

The Rayleigh-Plesset equation has been used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Radial diffusion equations may be solved for a single bubble, but these are too computationally expensive to implement into a continuum model for bubbly cavitating flows since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive reduced-order models that account for thermal and mass diffusion. We present a model that can capture the damping effects of the diffusion processes in two ODE's, and gives better results than previous models

A reduced-order model of diffusive effects on the dynamics of bubbles

We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity

A Numerical Investigation of Unsteady Bubbly Cavitating Nozzle Flows

The effects of unsteady bubbly dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. these latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubbly dynamics are not important, but show that in many instances the neglect of bubbly dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubbly raidal motion is restricted to a simple "effective" viscosity, but many features of the flow are shown to be independent of the specific damping mechanism

Bounds for Invariance Pressure

This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.Comment: 16 page

Direct Numerical Simulations of Three-Dimensional Cavity Flows

Three-dimensional direct numerical simulations of the full compressible Navier–Stokes equations are performed for cavities that are homogeneous in the spanwise direction. The formation of oscillating spanwise structures is observed inside the cavity. We show that this 3D instability arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. In general, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than 2D Rossiter (flow/acoustics) instabilities. The 3D mode properties are in excellent agreement with predictions from our previous linear stability analysis. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. We connect these results with the observation of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows. Preliminary results on the connections between the 3D centrifugal instabilities and the presence/suppression of the wake mode are also presented

Three-Dimensional Linear Stability Analysis of Cavity Flows

Numerical Simulations of the two- and three-dimensional linearized Navier–Stokes equations are performed to investigate instabilities of open cavity flows that are homogeneous in the spanwise direction. First, the onset of two-dimensional cavity instability is characterized over a range of Mach numbers, Reynolds numbers and cavity aspect ratios. The resulting oscillations are consistent with the typical Rossiter flow/acoustic resonant modes. We then identify the presence of three-dimensional instabilities of the two-dimensional basic flow and study their dependence on the parameter space. In general, the most amplified three-dimensional mode has a spanwise wavelength scaling with the cavity depth, and a frequency typically an order-of-magnitude smaller than two-dimensional Rossiter modes. The instability appears to arise from a generic centrifugal instability mechanism associated with a large vortex in the two-dimensional basic flow that occupies the downstream portion within the cavity

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core