Linear Stability Theory Research Articles

Studies on properties of laminar premixed oxygen-enriched NH3/H2/O2/N2 flames at elevated temperature and pressure

In this work, the effects of oxygen enrichment coefficient (Ω = 0.21 − 0.42) and initial temperature (Tu = 298 − 448 K) on the laminar burning properties of NH3/H2/O2/N2 flames are systematically investigated by using the spherical flame propagation method at equivalence ratios (Φ = 0.8 − 1.4) and initial pressure (Pu = 3 atm). LBV is analyzed by obtaining experimental data. In order to analyze flame instability, thermal diffusion and hydrodynamic instability are separated by linear stability theory. The thermal and chemical effects of oxygen enrichment on LBV and its effect on heat release rate are analyzed by numerical simulation. The results show that the laminar burning velocity (LBV) exhibits a positive correlation with both the oxygen enrichment coefficient and the initial temperature. The temperature index (α) exhibits a non-monotonic variation in response to the initial temperature of the NH3/H2/O2/N2 flame. Leeff is insensitive to temperature and positively correlated with the oxygen enrichment coefficient. The NH3/H2/O2/N2 flame is mainly affected by hydrodynamic instability when the oxygen enrichment coefficient is large. The peak NHRR scales positively with the oxygen enrichment coefficient. Oxygen enrichment helps to contribute to the overall net reaction rate.

On the validity of the exchange principle in rotatory electrothermoconvection

Abstract The electrothermoconvection in a rotating dielectric fluid layer heated from below (or above) is studied analytically using linear stability theory. First, we derive the necessary conditions for oscillatory motion when the fluid layer is heated from below and from above. Then as a consequence, sufficient conditions for the validity of the exchange principle are derived for the two configurations in terms of the parameters of the systems alone. The results hold for free boundaries for all wave numbers and for rigid boundaries with some restrictions. Further, the results for electrothermoconvection without rotation, rotatory Rayleigh–Bénard convection and Rayleigh–Bénard convection are also obtained as special cases which validate the existing results. To the best of author’s knowledge such results are not reported in the literature as far as the domain of electrothermoconvection studies is concerned.

Dynamical analysis of coupled curvature-matter scenario in viable f(R) dark energy models at de Sitter phase

We explore the interaction between dark matter and curvature-driven dark energy within viable f(R) gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as Q=αHρ~m(κ23H2ρcurv+1) , into the continuity equations of both sectors, we examine dynamics of two f(R) gravity models that adhere to local gravity constraints and fulfill cosmological viability criteria. In de Sitter phase, our investigation reveals modifications of critical points compared to the conventional form, attributed to the introduced interaction. Through a comprehensive phase-space analysis, we illustrate the trajectories near critical points and outline the constraints on the phase space based on cosmological and cosmographic parameters. Furthermore, we can also observe stable behavior of this interacting system during the de Sitter phase of the Universe.

Roughness-Induced Transition in Supersonic Boundary Layers with Wall Heating and Cooling Effects

The laminar–turbulent transition of a supersonic boundary layer induced by an isolated roughness element is investigated using direct numerical simulation, BiGlobal linear stability theory, and the three-dimensional parabolized stability equation. Cylindrical and diamond-shaped roughness elements are investigated in combination with different wall temperatures. Direct numerical simulations show that the cylinder configuration induces an earlier transition than the diamond configuration, with the interaction between the separated shear layer and the counter-rotating vortices causing the transition. BiGlobal analysis and the parabolized stability equation confirm the existence of two unstable instability modes in the wake region, namely, a symmetric mode and an antisymmetric mode, with the former being strongly dominant. The wall cooling and heating effects are studied by changing the wall temperature. Wall heating lifts the inlet boundary layer and weakens the separated shear layer. This, in turn, weakens the wake instability and delays the transition. The antisymmetric model disappears as the wall heating increases. Wall cooling accelerates the transition by enhancing the distortion of the roughness wake, resulting in stronger instabilities. Finally, the Reynolds number based on the momentum defect is used to define the transition criterion, and this is found to be in good agreement with the present simulation results.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

The accelerated expansion in F(G,TμνTμν) gravity

In this paper, the basic Einstein–Hilbert cosmological model is extended by adding a new functional [Formula: see text] in the fundamental action, encoding specific geometrical effects due to a nontrivial coupling with the Gauss–Bonnet invariant (G), and the energy–momentum squared term ([Formula: see text]). After obtaining the corresponding gravitational field equations for the specific decomposition where [Formula: see text], we have explored the physical features of the cosmological model by considering the linear stability theory, an important analytical tool in the cosmological theory which can reveal the dynamical characteristics of the phase space. The analytical exploration of the corresponding phase space structure revealed that the present model can represent a viable dark energy model, with various stationary points where the effective equation of state corresponds to a de-Sitter epoch, possible explaining the early and late time acceleration of the Universe.

Truncated predictive tracking control design for semi-Markovian jump systems with time-varying input delays

A state tracking control problem for a class of semi-Markovian jump systems (SMJSs) with input delay and disturbances is addressed in this study. In particular, an improved-equivalent-input-disturbance estimator approach (IEIDEA)-based truncated predictive controller is designed to synchronously compensate the effect of unknown external disturbances and time-varying delay. Specifically, by making use of IEIDEA, the unknown disturbances are estimated with high precision and incorporated into the control input channel, which eases the way to achieve the desired tracking performances. Specifically, the state predictor satisfies the delay-free state-space equation and is used in controller design along with prediction. In accordance with linear matrix inequality framework and Lyapunov stability theory, a set of adequate conditions are established to guarantee the state tracking performance of SMJSs. Finally, the numerical examples with simulation results are provided to validate the efficacy and practicability of the established control technique.

Optimization design of forebody shape of an underwater axisymmetric body for transition delay using a genetic algorithm

The forebody shape of an underwater vehicle significantly influences the transition position of the boundary layer, which, in turn, impacts the flow-induced noise that can interfere with the sonar in the head. Typically, underwater vehicle forebodies are axisymmetric. Optimizing the forebody shape of an axisymmetric body can effectively delay the boundary layer transition and reduce the interference caused by flow noise on the sonar. This study applies an artificial intelligence algorithm for the optimization of the forebody shape. Specifically, a genetic algorithm is adopted to establish the optimization design method. The non-uniform rational B-spline (NURBS) method is used to parameterize the forebody shape, and the eN method based on linear stability theory is employed to predict the transition position. The optimization is conducted at the scale of a real vehicle and at a fixed velocity. After 45 generations, the genetic algorithm converges to an optimized shape. The transition position of the optimized shape is significantly delayed in comparison to that of the optimal original shape, with the relative delay amounting to an impressive 20.8%. Furthermore, the optimized shape effectively suppresses wall pressure fluctuation (WPF) in the unstable laminar region, also contributing to a reduction in flow-induced noise.

Pattern formation for a charge transfer model with cross-diffusion

This paper is devoted to a charge transfer model with cross-diffusion under Neumann boundary conditions. By applying the linear stability theory, sufficient conditions for the occurrence of Hopf bifurcation and Turing instability are successfully established. Moreover, the amplitude equations are derived near the critical value of Turing instability according to the standard multiple-scale analysis. Our research indicates that the entire pattern generated by this model is controlled by the cross-diffusion parameter d21. Dynamic pattern formation is described theoretically and numerically, such as changing control parameters for spot pattern, strip pattern, and spot-strip pattern.

Stability of low-pressure turbine boundary layers under variable Reynolds number and pressure gradient

The free-stream turbulence induced transition occurring under typical low-pressure turbine flow conditions is investigated by comparing linear stability theory with wind tunnel measurements acquired over a flat plate subjected to high turbulence intensity. The analysis was carried out, accounting for three different Reynolds numbers and four different adverse pressure gradients. First, a non-similarity-based boundary layer (BL) solver was used to compute base flows and validated against pressure taps and particle image velocimetry (PIV) measurements. Successively, the optimal disturbances and their spatial transient growth were calculated by coupling classical linear stability theory and a direct-adjoint optimization procedure on all flow conditions considered. Linear stability results were compared with experimental particle image velocimetry measurements on both wall-normal and wall-parallel planes. Finally, the sensitivity of the disturbance spatial transient growth to the spanwise wavenumber of perturbations, the receptivity position, and the location where disturbance energy is maximized were investigated via the built numerical model. Overall, the optimal perturbations computed by linear stability theory show good agreement with the streaky structures surveyed in experiments. Interestingly, the energy growth of disturbances was found to be maximum for all the flow conditions examined, when perturbations entered the boundary layer close to the position where minimum pressure occurs.

Modeling dedicated lanes for connected autonomous vehicles with poly-information uncertainties and electronic throttle dynamics

Numerous studies have demonstrated that connected autonomous vehicles and human-driven vehicles are now coexisting throughout a transitional phase. Traffic flow can be improved, the system can be stabilized, and less energy will be used with dedicated lanes for connected autonomous vehicles. Additionally, with few communication resources, no communication delivery is ever perfect, leading to issues with poly-information uncertainty. First, this paper provides a macroscopic model of heterogeneous traffic flow from the perspective of vehicle dynamics employing electronic throttle dynamics and poly-information uncertainty with/without dedicated lanes. Second, the mixed traffic flow linear stability criterion is derived using the linear stability theory. The third portion, which was based on the theoretical analysis, focused on the consequences of dedicated lane configurations on traffic flow as well as a discussion of the effects of various parameters on the stability of mixed traffic flow and energy consumption emissions. Finally, we modeled the Huanshan Road in Jinan, China using the experimental VISSIM platform. The analysis and demonstration of a two-way, four-lane road with or without dedicated lanes. The findings demonstrate that increasing connected autonomous vehicles penetration and dedicated lanes construction can increase traffic capacity, enhance the stability of traffic flow, and lower energy use and additional emissions. It is important to keep in mind that dedicated lanes must be built at an appropriate connected autonomous vehicle penetration rate to boost traffic flow without squandering resources.

Boundary layer transition of hypersonic flow over a delta wing

Cross-flow transition over a delta wing is systematically studied in a Mach 6.5 hypersonic wind tunnel, employing the Rayleigh scattering flow visualisation, high-speed schlieren and fast-response pressure sensors. Direct numerical simulations and analysis based on linear stability theory under the same flow conditions are applied to analyse the transition mechanism. Three unstable modes are identified: the travelling cross-flow instabilities, the second mode and the low-frequency waves. It is shown that the travelling cross-flow vortices first appear in the cross-flow region near the leading edge of the model. These vortices can modulate the mean profile of the flow, which benefits the growth of second mode. A phase-locked interaction mechanism transfers energy from the cross-flow instabilities to the high-frequency second mode, leading to amplification at the expense of the cross-flow instability. As the second mode grows to a critical amplitude, it triggers a $z$ -type secondary instability within a similar frequency range, which introduces secondary finger-like structures connecting to the cross-flow vortex. It is further found that the generation of these finger-like structures is related to the expansion and compression of the second mode. These finger vortices further evolve along the streamwise direction into low-frequency waves and corresponding hairpin-like structures that finally trigger turbulence. An interaction mechanism likely exists between the secondary instability and the low-frequency waves, since their phase speeds are approaching each other. These observations of the interaction mechanism are consistent with those of previous studies on hypersonic boundary layers (Zhang et al., Phys. Fluids, vol. 32 (7), 2020, 071702; Li et al., Phys. Fluids, vol. 32 (5), 2020, 051701).

Separation-induced transition on a T106A blade under low and elevated free stream turbulence

The separation-induced transition on the suction surface of a T106A low pressure turbine blade is a complex phenomenon with implications for aerodynamic performance. In this numerical investigation, we explore an adverse pressure gradient-dominated flow subjected to varying levels of free stream excitation, as the underlying separation-induced transition is a critical factor in assessing blade profile loss. By comprehensively analyzing the effects of free stream turbulence (FST) on the transition process, we delve into the various mechanisms which govern the instabilities underlying bypass transition by studying the instantaneous enstrophy field. This involves solving the two-dimensional (2D) compressible Navier–Stokes equation through a series of numerical simulations, comparing a baseline flow to cases where FST with varying turbulent intensity (Tu=4% and 7%) is imposed at the inflow. Consistent with previous studies, the introduction of FST is observed to delay flow separation and trigger early transition. We explore the different stages of bypass transition, from the initial growth of disturbances (described by linear stability theory) to the emergence of unsteady separation bubbles that merge into turbulent spots (due to nonlinear interactions), by examining the vorticity dynamics. Utilizing the compressible enstrophy transport equation for the flow in a T106A blade passage, we highlight the various routes of bypass transition resulting from different levels of FST, emphasizing the relative contributions from baroclinicity, compressibility, and viscous terms.

Prediction of Onset Temperature in Standing Wave Thermoacoustic Engine with Mesh Screen Stack

A thermoacoustic engine is a engine that converts thermal energy into acoustic energy, which can be used to generate electricity or cooling. This engine is attractive because it consists only of a stack, heat exchangers, and a resonator. The stack serves as the primary component for the energy conversion process and consists of porous materials like an array of stainless steel mesh screens. To generate the acoustic energy, a minimum temperature difference is necessary between the two sides of the stack, called the onset temperature difference. However, the calculation for prediction of onset temperature on the stack made of mesh screen has not been addressed. Therefore, the objective of this paper is to propose a method that can be used to estimate the onset temperature difference in standing wave thermoacoustic engine with stacks made of mesh screen arrays. The onset temperature difference is predicted numerically using linear stability theory and matrix transfer methods. Experimental verification is carried out by using standing wave thermoacoustic engine from pervious study. The results showed that the lowest onset temperature difference (TH - TC = 140ºC) is obtained when rh = 0.497 mm. Furthermore, the numerical and experimental onset temperature difference comparisons show a qualitative agreement, allowing the onset temperature prediction method to be used in designing standing wave thermoacoustic engines with stacks made of mesh screens.

Adaptive security control for uncertain delayed semi-Markov jump systems subject to cyber attacks and actuator failures

This note investigates the adaptive security control issue for uncertain delayed semi-Markov jump systems (DSMJSs) within the framework of sliding mode control (SMC), in which the DSMJSs are affected by generally unknown transition rates (GUTRs), actuator failures (AFs) and cyber attacks. By the virtue of the strong approximation ability of neural network (NN), an adaptive NN-based SMC synthesis is carried out, which could not only force the state trajectories onto the proposed sliding surface but also ensure the DSMJSs operate as demanded in spite of the interference errors, structural uncertainty, hidden AFs, cyber attacks and GUTRs. Then, in view of the reachability of the proposed linear-type sliding mode surface (SMS), linear matrix inequalities (LMIs) and stochastic stability theory, a novel stochastically stable criterion for the resultant DSMJSs is obtained. At last, the single-link robot arm model is offered as an instance with simulation to illustrate the viability of the devised strategy.

Asymptotic boundary condition for numerical modeling of wave packets in a supersonic boundary layer

Within the framework of linear stability theory, a simple non-stationary boundary condition is developed to simulate the far-field asymptotic behavior of linear wave packets propagating in a compressible boundary layer. This condition allows us to skip the linear stage of instability evolution in direct numerical simulations (DNS) of laminar-turbulent transition. It is also suggested to perform numerical simulations of the linear stage without recalculating the Jacobi matrix in the Newton iteration procedure. Robustness and efficiency of the both approaches are evaluated by computations of the first-mode wave packet propagating in the boundary layer on a flat plate at freestream Mach number 2. DNS of the nonlinear stage show that the wave packet quickly breaks down into a turbulent spot, if its hump amplitude is umax′≥0.1U∞. This confirms an amplitude nature of the transition onset criterion. The spectral analysis indicates that the breakdown mechanism differs from the oblique, fundamental or subharmonic resonance and requires additional studies.

Effects of rotation and temperature‐dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

AbstractThe onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions.

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.

On the use of time-dependent fluids for delaying onset of transition to turbulence in the flat plate boundary-layer flow: A passive control of flow

Inelastic time-dependent fluids display continuous and reversible changes in viscosity when subjected to a constant shear-rate. These alterations arise from the gradual modification of the material’s microstructure due to shear-induced effects, known as shear rejuvenation. When this process generates smaller structural units, it is termed thixotropy; conversely, if it produces larger units, it is labeled anti-thixotropy. Aging is another characteristic of such fluids, denoting the capacity of the material to regain its original structure in the absence of shear, thus reversing the initial time-dependent change. This phenomenon often results from thermally activated Brownian motion prompting the reorganization of the material’s microconstituents. Consequently, attractive forces between these components can instigate the reconstruction of a network-like structure within the material. This study centers on investigating how variations in fluid microstructure impact the onset of transition to turbulence in a flat plate boundary-layer flow. Specifically, the focus is on cases where larger structural units emerge during the breakdown process (anti-thixotropy). To represent such fluids, the Quemada model, an inelastic structural-kinetic model, is employed. This model effectively captures thixotropy and anti-thixotropy by appropriately configuring model parameters. The analysis begins with obtaining a local similarity solution for the generalized Blasius equation, representing the base flow. Subsequently, the stability of this flow is assessed using linear temporal stability theory. This involves introducing infinitesimally-small normal-mode perturbations to the base flow, yielding the generalized Orr–Sommerfeld equation. Solving this equation using the spectral method provides insights into stability. Results from this study indicate that for low Deborah numbers, the shear-thickening behavior prevails, causing destabilization. In contrast, higher Deborah numbers lead to stability. This implies that anti-thixotropy effectively delays the onset of transition to turbulence and could hold practical applications for flow control.

Irrotational flow analysis of Rayleigh-Taylor instability in nanofluid layer with tangential magnetic field

The application of nanofluids in the presence of a magnetic field holds promise for advanced drug delivery systems, where controlled manipulation of magnetic nanoparticles within nanofluids can enhance targeted and localized drug delivery. This study explores the instability of a viscous fluid-nanofluid interface arranged in a planar configuration influenced by a tangential magnetic field using the irrotational flow theory. When the nanofluid is positioned above a viscous fluid, the interface is susceptible to the Rayleigh-Taylor instability. Employing linear stability theory, an explicit relationship connecting the perturbation growth parameter with the wavenumber is derived. Different dimensionless quantities such as the Atwood number, Weber number, Froude number, and Reynolds number are analyzed using stability plots. These plots provide valuable information about the behavior of interfaces. Increased magnetic field strength is observed to delay instability onset. Surface tension is found to stabilize the interface, whereas inertial forces destabilize it. This investigation contributes to understanding and controlling the interface dynamics in nanofluid systems.