scholarly journals Decomposition of the temporal growth rate in linear instability of compressible gas flows

2015 ◽  
Vol 778 ◽  
pp. 120-132 ◽  
Author(s):  
Mario Weder ◽  
Michael Gloor ◽  
Leonhard Kleiser
Keyword(s):  
Growth Rate ◽  
Energy Balance ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
Compressible Flows ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Temporal Growth Rate

We present a decomposition of the temporal growth rate ${\it\omega}_{i}$ which characterises the evolution of wave-like disturbances in linear stability theory for compressible flows. The decomposition is based on the disturbance energy balance by Chu (Acta Mech., vol. 1 (3), 1965, pp. 215–234) and provides terms for production, dissipation and flux of energy as components of ${\it\omega}_{i}$. The inclusion of flux terms makes our formulation applicable to unconfined flows and flows with permeable or vibrating boundaries. The decomposition sheds light on the fundamental mechanisms determining temporal growth or decay of disturbances. The additional insights gained by the proposed approach are demonstrated by an investigation of two model flows, namely compressible Couette flow and a plane compressible jet.

scholarly journals Implementation of Linear Stability Theory on Hollow Cone-shaped Liquid Sheet

2020 ◽  
Vol 64 (3) ◽  
pp. 179-188
Author(s):  
Hadiseh Karimaei ◽  
Ramin Ghorbani ◽  
Seyed Mostafa Hosseinalipour
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Rocket Engines ◽  
Hollow Cone ◽  
Liquid Sheets ◽  
Centrifugal Injector

Surface instability of a swirling liquid sheet emanating from a centrifugal injector in presence of external and internal gas flows is studied in this paper. A three-dimensional flow for the liquid sheet and two-dimensional flows for external and internal gas flows are considered. The set of equations involved in this analysis differs from the earlier analyzes. In previous studies, a cylindrical liquid sheet has been considered to implement the linear theory but in this study, the linear stability theory is implemented on a cone-shaped liquid sheet for different cone angles. Actually more over than axial and tangential movements, the radial movements of liquid sheet and gas flows are considered in the present model. Due to complexity of the derived governing equations, semi-analytical and numerical methods were applied to solve them. The case study is oxidizer injector of rocket engines. Implementation of linear stability theory on a hollow cone-shaped liquid sheet better can predict instability phenomenon than the general linear stability analysis for this type of liquid sheets. The results show very close agreement with available experimental data.

scholarly journals Response of a laminar separation bubble to impulsive forcing

2017 ◽  
Vol 820 ◽  
pp. 633-666 ◽  
Author(s):  
Theodoros Michelis ◽  
Serhiy Yarusevych ◽  
Marios Kotsonis
Keyword(s):  
Growth Rate ◽  
Wave Packet ◽  
Linear Stability ◽  
Stability Theory ◽  
Separation Bubble ◽  
Linear Stability Theory ◽  
Laminar Separation Bubble ◽  
Time Resolved ◽  
Laminar Separation ◽  
Response Characteristics

The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive disturbance is introduced with an alternating current dielectric barrier discharge plasma actuator, exciting pertinent instability modes and ensuring flow development under environmental disturbances. Phase-averaged velocity measurements are employed to analyse the effect of imposed disturbances at different amplitudes on the laminar separation bubble. The impulsive disturbance develops into a wave packet that causes rapid shrinkage of the bubble in both upstream and downstream directions. This is followed by bubble bursting, during which the bubble elongates significantly, while vortex shedding in the aft part ceases. Duration of recovery of the bubble to its unforced state is independent of the forcing amplitude. Quasi-steady linear stability analysis is performed at each individual phase, demonstrating reduction of growth rate and frequency of the most unstable modes with increasing forcing amplitude. Throughout the recovery, amplification rates are directly proportional to the shape factor. This indicates that bursting and flapping mechanisms are driven by altered stability characteristics due to variations in incoming disturbances. The emerging wave packet is characterised in terms of frequency, convective speed and growth rate, with remarkable agreement between linear stability theory predictions and measurements. The wave packet assumes a frequency close to the natural shedding frequency, while its convective speed remains invariant for all forcing amplitudes. The stability of the flow changes only when disturbances interact with the shear layer breakdown and reattachment processes, supporting the notion of a closed feedback loop. The results of this study shed light on the response of laminar separation bubbles to impulsive forcing, providing insight into the attendant changes of flow dynamics and the underlying stability mechanisms.

scholarly journals Stability of plane Couette flow for high Reynolds number

1983 ◽  
Vol 24 (3) ◽  
pp. 350-357 ◽  
Author(s):  
G. B. Davis ◽  
A. G. Morris
Keyword(s):  
Reynolds Number ◽  
Experimental Evidence ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
High Reynolds Number ◽  
Numerical Technique ◽  
Linear Stability Theory ◽  
Plane Couette Flow ◽  
High Reynolds

AbstractExperimental evidence shows that plane Couette flow becomes unstable when the Reynolds number R reaches certain critical values. Linear stability theory does not predict these observations and has been unable to locate these instabilities. A Chebyshev/QR numerical technique is used to investigate much higher values of R than those previously tested. In particular, values of R up to 108 are confidently tested, whereas previously values of R up to only 2 × 104 have been considered.

scholarly journals Convolutional neural network for transition modeling based on linear stability theory

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Muhammad I. Zafar ◽  
Heng Xiao ◽  
Meelan M. Choudhari ◽  
Fei Li ◽  
Chau-Lyan Chang ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Transition Modeling

Suppression of Baroclinic Instabilities in Buoyancy-Driven Flow over Sloping Bathymetry

2017 ◽  
Vol 47 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Robert D. Hetland
Keyword(s):  
Growth Rate ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Buoyancy Frequency ◽  
Bottom Slope ◽  
Coriolis Parameter ◽  
Plume Front ◽  
Instability Theory ◽  
Instability Growth ◽  
Flow Configurations

AbstractBaroclinic instabilities are ubiquitous in many types of geostrophic flow; however, they are seldom observed in river plumes despite strong lateral density gradients within the plume front. Supported by results from a realistic numerical simulation of the Mississippi–Atchafalaya River plume, idealized numerical simulations of buoyancy-driven flow are used to investigate baroclinic instabilities in buoyancy-driven flow over a sloping bottom. The parameter space is defined by the slope Burger number S = Nf−1α, where N is the buoyancy frequency, f is the Coriolis parameter, and α is the bottom slope, and the Richardson number Ri = N2f2M−4, where M2 = |∇Hb| is the magnitude of the lateral buoyancy gradients. Instabilities only form in a subset of the simulations, with the criterion that SH ≡ SRi−1/2 = Uf−1W−1 = M2f−2α 0.2, where U is a horizontal velocity scale and SH is a new parameter named the horizontal slope Burger number. Suppression of instability formation for certain flow conditions contrasts linear stability theory, which predicts that all flow configurations will be subject to instabilities. The instability growth rate estimated in the nonlinear 3D model is proportional to ωImaxS−1/2, where ωImax is the dimensional growth rate predicted by linear instability theory, indicating that bottom slope inhibits instability growth beyond that predicted by linear theory. The constraint SH 0.2 implies a relationship between the inertial radius Li = Uf−1 and the plume width W. Instabilities may not form when 5Li > W; that is, the plume is too narrow for the eddies to fit.

On the linear stability theory of Bénard–Marangoni convection

1989 ◽  
Vol 1 (7) ◽  
pp. 1123-1127 ◽  
Author(s):  
Rafael D. Benguria ◽  
M. Cristina Depassier
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Marangoni Convection ◽  
Linear Stability Theory
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