scholarly journals Theory and Simulation of Asymmetrically Perturbed Radiatively Cooled Jets

1997 ◽  
Vol 163 ◽  
pp. 575-579
Author(s):  
P. E. Hardee ◽  
J. M. Stone ◽  
J. Xu
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Weak Shock ◽  
Body Waves ◽  
Low Frequencies ◽  
Non Linear ◽  
Protostellar Jets ◽  
Ambient Gas ◽  
Cooling Function ◽  
Low Amplitude

AbstractResults of a spatial stability analysis and of numerical simulations of a “slab” jet in which optically thin radiative cooling is dynamically important are presented. Two different cooling curves are used. Unstable Kelvin-Helmholtz modes are significantly different from the adiabatic limit, and the form of the cooling function strongly affects the results. The numerical simulations are in excellent agreement with the linear stability analysis. In the non-linear regime growth of the surface wave at low frequencies results in sinusoidal oscillation which can disrupt the jet, while non-linear body waves produce low amplitude wiggles within the jet that can result in shocks within the jet. In cooling jets, these shocks can produce dense knots and filaments of cooling gas within the jet, and weak shock “spurs” in the ambient gas. Acceleration of ambient gas can be produced by these “spurs”, or by rapid entrainment if the jet is disrupted. For parameters typical of protostellar jets perturbations with a period of < 100 yrs should excite body waves which produce internal shocks and small amplitude wiggles. The lack of large amplitude wiggles in most observed systems is consistent with the suggestion that jets arise from the inner regions (r < 1 AU) of accretion disks.

Characterisation of a Wavy Convective Instability in Poiseuille-Rayleigh-Be´nard Flows: Linear Stability Analysis and Non Linear Numerical Simulations Under Random Excitations

2010 ◽  
Author(s):  
Xavier Nicolas ◽  
Shihe Xin ◽  
Noussaiba Zoueidi
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Random Excitation ◽  
Time Development ◽  
Direct Numerical Simulations ◽  
Channel Inlet ◽  
Non Linear

The aim of the present paper is to characterize a secondary convective instability of Poiseuille-Rayleigh-Be´nard (PRB) mixed convection flows in air that takes the shape of wavy thermoconvective rolls, for 70≤Re≤300 and 3000<Ra<15000. At first, the linear stability analysis by Clever and Busse [JFM, 1991] in the case of PRB flows between two infinite plates is extended to the case of confined channels with a 10 transversal aspect ratio. In the second part, using 3D non linear direct numerical simulations, the space and time development of the chaotic wavy rolls obtained by maintaining a permanent random excitation at channel inlet is analyzed. As the perturbation is designed to cover all the modes, it is possible to detect the modes that are naturally amplified by the flow and those that are damped. It is shown that the wavy roll characteristics obtained in this way vary a lot with Ra increasing and stabilize for Ra>3Ra*. Comparisons with the experiments by Pabiou et al. [JFM, 2005] are proposed.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

Numerical Simulations as a Reliable Alternative for Landmine Explosion Studies: The AUTODYN Approach

2010 ◽  
Author(s):  
Stephanie Follett ◽  
Amer Hameed ◽  
S. Darina ◽  
John G. Hetherington
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Reasonable Agreement ◽  
Specific Impulse ◽  
Numerical Procedure ◽  
Ground Surface ◽  
Time Of Arrival ◽  
Linear Dynamics ◽  
Non Linear

In order to validate the numerical procedure, the explosion of a mine was recreated within the non-linear dynamics software, AUTODYN. Two models were created and analysed for the purposes of this study — buried and flush HE charge in sand. The explosion parameters — time of arrival, maximum overpressure and specific impulse were recorded at two stand-off distances above the ground surface. These parameters are then compared with LS-DYNA models and published experimental data. The results, presented in table format, are in reasonable agreement.

The Effects of Small Sinusoidal Load Variations in Elastohydrodynamic Line Contacts

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
C. J. Hooke ◽  
G. E. Morales-Espejel
Keyword(s):  
Pressure Distribution ◽  
Maxwell Model ◽  
Total System ◽  
Low Frequencies ◽  
Load Variations ◽  
Entrainment Velocity ◽  
Line Contacts ◽  
Sinusoidal Load ◽  
Voigt Model ◽  
Low Amplitude

A method of determining the response of elastohydrodynamic line contacts to low amplitude, sinusoidal variations in load is presented. It is shown that the load variations alter the Hertz width, cyclically increasing and reducing the effective entrainment velocity. This produces clearance variations in the inlet, which are transported through the conjunction altering the pressure distribution as they pass. The resulting pressure and clearance changes can be many times greater than when the load changes slowly. The results are used to determine the flexibility and damping of the conjunctions. These vary depending on the number of transported waves inside the contact. It is shown that a Maxwell model rather than the usual Voigt model is required to define the contact's behavior. While the Voigt model may be used at low frequencies, it has a damping coefficient that is not unique to the contact but depends on the total system stiffness.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

scholarly journals Effect of Variable Viscosity and Gravity Modulation on Linear and Non-Linear Rayleigh-Benard Convection in Viscoelastic Ferromagnetic Liquids

2020 ◽  
Vol 9 (3) ◽  
pp. 3482-3488
Keyword(s):  
Stability Analysis ◽  
Heat Transport ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Variable Viscosity ◽  
Low Frequency ◽  
Physical Parameters ◽  
Gravity Modulation ◽  
Non Linear ◽  
The Individual

The combined effect of various parameters of gravity modulation on the onset of ferroconvection is studied for both linear and non-linear stability. The effect of various parameters of ferroconvection is studied for linear stability analysis. The resulting seven-mode generalized Lorenz model obtained in non-linear stability analysis is solved using Runge -Kutta-Felberg 45 method to analyze the heat transfer. Consequently the individual effect of gravity modulation on heat transport has been investigated. Further, the effect of physical parameters on heat transport has been analyzed and depicted graphically. The low-frequency gravity modulation is observed to get an effective influence on the stability of the system. Therefore ferro convection can be advanced or delayed by controlling different governing parameters. It shows that the influence of gravity modulation stabilizes system.

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