scholarly journals STABILITY CHARACTERISTICS OF COMPRESSIBLE BINARY PLANAR JETS

2020 ◽  
Vol 19 (1) ◽  
pp. 80
Author(s):  
M. T. Mendonca ◽  
M. M. Vargas
Keyword(s):  
Density Gradient ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Chemical Species ◽  
Phase Speed ◽  
Linear Stability Theory ◽  
Density Gradients ◽  
Lower Phase ◽  
External Mode ◽  
The Stability

The present work investigates the stability of compressible binary planar jets. Different from a homogeneous jet, where a single chemical species is present, the binary jet may have strong density gradients due to the choice of the chemical species considered in each stream. The goal is to identify the possible instability  modes for simple and co-flowing jets and investigate the effect of density gradients on the flow structure, growth rates, unstable frequency range and disturbance phase speed for each mode. The effect of species concentration on free shear layer stability has been reported previously in the literature, but detailed comparisons between stability modes and characteristics for a range of density ratios typical of oxygen and hydrogen mixtures as well as the identification of inner and outer sinuous and varicose modes are new. Linear stability theory is used to determine the stability characteristics of the different configurations. For the co-flowing jet four different modes are found, the inner and outer shear layers both have sinuous and varicose modes. Both for the sinuous and varicose modes the simple jet is more unstable when the fluid with the highest density is at the inner jet, with amplification rates twice as high as the lowest density ratio considered, but the range of unstable frequencies can be four times lower. The sinuous mode is less dispersive than the varicose and the disturbance speeds may vary by one order of magnitude with density ratio. For co-flowing jets the external mode is up to seven times more unstable, but this is due to the choice of the velocity ratio considered. For the inner mode the density gradient has a stabilizing effect regardless of which species is at the center. The co-flowing jet is more dispersive, except for the varicose inner mode. The variation of phase speed with density gradient is not as strong as in the simple jet. The ratio of larges to lower phase speeds are of the order of 2 for the co-flowing jet and 4 for the simple jet.

Bubbling and jetting regimes in planar coflowing air–water sheets

2011 ◽  
Vol 682 ◽  
pp. 519-542 ◽  
Author(s):  
R. BOLAÑOS-JIMÉNEZ ◽  
A. SEVILLA ◽  
C. GUTIÉRREZ-MONTES ◽  
E. SANMIGUEL-ROJAS ◽  
C. MARTÍNEZ-BAZÁN
Keyword(s):  
Velocity Ratio ◽  
Density Ratio ◽  
Water Film ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Absolute Instability ◽  
Control Parameters ◽  
Air Velocity ◽  
The Mean

The dynamics of a plane air sheet surrounded by a coflowing water film, discharging into stagnant air, is investigated by means of experiments and linear stability theory. For fixed values of the water-to-air thickness ratio, h = hw,0*/ha,0* ≃ 5.27, and of the air-to-water density ratio, S = ρa/ρw ≃ 0.0012, two different flow regimes are experimentally observed depending on the values of two control parameters, namely the Weber number, defined as We = ρwuw,0*2ha,0*/σ, and the velocity ratio, Λ = uw,0*/ua,0*, where uw,0* and ua,0* are the water velocity and the mean air velocity at the exit slit, respectively, and ha,0* and hw,0* are the half-thicknesses of the air and water sheets at the exit. The study focuses on the characterization of the transition between the two regimes found experimentally: a bubbling regime, leading to the periodic breakup of the air sheet, and a jetting regime, where both sheets evolve slowly downstream without breaking. With the aim of exploring whether the transition from the jetting to the bubbling regime is related to a convective/absolute instability transition, we perform a linear spatiotemporal stability analysis. The base flow is described by a simple model that incorporates the downstream evolution of the sheets, which shows excellent agreement with our experiments if the existence of a sufficiently long region of absolute instability, of the order of one absolute wavelength evaluated at the nozzle exit, is imposed as an additional requirement. Finally, we show that the transition is also properly captured by two-dimensional numerical simulations using the volume of fluid technique.

Ribbing Instability Analysis of Forward Roll Coating

2009 ◽  
Vol 25 (2) ◽  
pp. 167-175
Author(s):  
K. N. Lie ◽  
Y. M. Chiu ◽  
J. Y. Jang
Keyword(s):  
Surface Coating ◽  
Velocity Ratio ◽  
Rolling Process ◽  
Linear Stability Theory ◽  
Wave Number ◽  
Roll Coating ◽  
Critical Capillary Number ◽  
Roll Velocity ◽  
Forward Roll Coating ◽  
Numerical Program

AbstractThe ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Numerical Investigation of Coolant-to-Mainstream Scaling Parameters With Film Cooling on Pressure and Suction Side of a Gas Turbine Blade

2017 ◽  
Author(s):  
Lingyu Zeng ◽  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Gas Turbine ◽  
Film Cooling ◽  
Momentum Flux ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Flux Ratio ◽  
Suction Side ◽  
Pressure Side ◽  
Blowing Ratio ◽  
Adiabatic Effectiveness

Most experiments of blade film cooling are conducted with density ratio lower than that of turbine conditions. In order to accurately model the performance of film cooling under a high density ratio, choosing an appropriate coolant to mainstream scaling parameter is necessary. The effect of density ratio on film cooling effectiveness on the surface of a gas turbine twisted blade is investigated from a numerical point of view. One row of film holes are arranged in the pressure side and two rows in the suction side. All the film holes are cylindrical holes with a pitch to diameter ratio P/d = 8.4. The inclined angle is 30°on the pressure side and 34° on the suction side. The steady solutions are obtained by solving Reynolds-Averaged-Navier-Stokes equations with a finite volume method. The SST turbulence model coupled with γ-θ transition model is applied for the present simulations. A film cooling experiment of a turbine vane was done to validate the turbulence model. Four different density ratios (DR) from 0.97 to 2.5 are studied. To independently vary the blowing ratio (M), momentum flux ratio (I) and velocity ratio (VR) of the coolant to the mainstream, seven conditions (M varying from 0.25 to 1.6 on the pressure side and from 0.25 to 1.4 on the suction side) are simulated for each density ratio. The results indicate that the adiabatic effectiveness increases with the increase of density ratio for a certain blowing ratio or a certain momentum flux ratio. Both on the pressure side and suction side, none of the three parameters listed above can serve as a scaling parameter independent of density ratio in the full range. The velocity ratio provides a relative better collapse of the adiabatic effectiveness than M and I for larger VRs. A new parameter describing the performance of film cooling is introduced. The new parameter is found to be scaled with VR for nearly the whole range.

Dendritic competition in the developing retina: Ganglion cell density gradients and laterally displaced dendrites

1993 ◽  
Vol 10 (2) ◽  
pp. 313-324 ◽  
Author(s):  
Rafael Linden
Keyword(s):  
Density Gradient ◽  
Cell Density ◽  
Time Course ◽  
Ganglion Cells ◽  
Lateral Displacement ◽  
Optic Tract ◽  
Density Gradients ◽  
Temporal Asymmetry ◽  
Dendritic Arbors ◽  
Contralateral Eye

AbstractDendrites of retinal ganglion cells (RGCs) tend to be distributed preferentially toward areas of reduced RGC density. This, however, does not occur in the retina of normal pigmented rats, in which it has been suggested that the centro-peripheral gradient of RGC density is too shallow to provide directional guidance to growing dendrites. In this study, laterally displaced dendrites of RGCs retrogradely labeled with horseradish peroxidase were related to cell density gradients induced experimentally in the rat retina. Neonatal unilateral lesions of the optic tract produced retrograde degeneration of contralaterally projecting RGCs, but spared ipsilaterally projecting neurons in the same retina. These lesions created an anomalous temporal to nasal gradient of cell density across the decussation line, opposite to the nasal to temporal gradient found along the same axis in either normal rats or rats that had the contralateral eye removed at birth. RGCs in rats that received optic tract lesions had their dendrites displaced laterally toward the depleted nasal retina, while in either normal or enucleated rats there was no naso-temporal asymmetry. The lateral displacement affected both primary dendrites and higher-order branches. However, the gradient of cell density after optic tract lesions was less steep than the gradient in either normal or enucleated rats. To test for the presence of steeper gradients at early stages of development, RGC density gradients were also examined at postnatal day 5 (P5). In normal rats, the RGCs were homogeneously distributed throughout the retina, while rats given optic tract lesions at birth already showed a temporo-nasal density gradient at P5. Still, this anomalous gradient was less steep than that found in normal adults. It is concluded that the time course, rather than the steepness of the RGC density gradient, is the major determinant of the lateral displacement of dendritic arbors with respect to the soma in developing RGCs. The data are consistent with the idea that the overall shape of dendritic arbors depends in part on dendritic competition during retinal development.

An extended optimal velocity difference model in a cooperative driving system

2015 ◽  
Vol 26 (05) ◽  
pp. 1550054
Author(s):  
Jinliang Cao ◽  
Zhongke Shi ◽  
Jie Zhou
Keyword(s):  
Traffic Flow ◽  
Linear Stability Theory ◽  
Difference Model ◽  
Optimal Velocity ◽  
Driving System ◽  
Cooperative Driving ◽  
Proposed Model ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

scholarly journals A mass-conserving and multi-tracer efficient transport scheme in the online integrated Enviro-HIRLAM model

2013 ◽  
Vol 6 (4) ◽  
pp. 1029-1042 ◽  
Author(s):  
B. Sørensen ◽  
E. Kaas ◽  
U. S. Korsholm
Keyword(s):  
Prediction Model ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Chemical Species ◽  
Numerical Weather Prediction Model ◽  
Computationally Efficient ◽  
Long Time ◽  
Dimensional Version ◽  
The Stability ◽  
Lagrangian Scheme

Abstract. In this paper a new advection scheme for the online coupled chemical–weather prediction model Enviro-HIRLAM is presented. The new scheme is based on the locally mass-conserving semi-Lagrangian method (LMCSL), where the original two-dimensional scheme has been extended to a fully three-dimensional version. This means that the three-dimensional semi-implicit semi-Lagrangian scheme which is currently used in Enviro-HIRLAM is largely unchanged. The HIRLAM model is a computationally efficient hydrostatic operational short-term numerical weather prediction model, which is used as the base for the online integrated Enviro-HIRLAM. The new scheme is shown to be efficient, mass conserving, and shape preserving, while only requiring minor alterations to the original code. It still retains the stability at long time steps, which the semi-Lagrangian schemes are known for, while handling the emissions of chemical species accurately. Several mass-conserving filters have been tested to assess the optimal balance of accuracy vs. efficiency.

Flow and Density Difference Lattice Model and its Numerical Simulations Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 2461-2465
Author(s):  
Hao Dai ◽  
Zhen Zhou Yuan ◽  
Jun Fang Tian
Keyword(s):  
Numerical Simulations ◽  
Lattice Model ◽  
Density Difference ◽  
Linear Stability Theory ◽  
Traffic Jam ◽  
Car Following ◽  
Car Following Model ◽  
Traffic Flow Stability ◽  
The Stability ◽  
Difference Effect

Based on Nagatani’s model, an extended car following model named flow and density difference lattice model (FDDLM) was proposed. Using the linear stability theory, the stability condition of the new model was obtained. The phase diagram presents that density difference effect is more efficiently than flow difference effect in improving the traffic flow stability and FDDLM could suppress traffic jam effectively. The numerical simulations are consonant with the analytical results and show that considering the flow and density difference leads to the stabilization of the system.

Analysis of drivers' characteristics in car-following theory

2014 ◽  
Vol 28 (24) ◽  
pp. 1450191 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Hui Liu ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Car Following ◽  
Car Following Model ◽  
The Stability ◽  
The Impact

In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.

Stability of the Prandtl model for katabatic slope flows

2019 ◽  
Vol 865 ◽  
Author(s):  
Cheng-Nian Xiao ◽  
Inanc Senocak
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Slope Angle ◽  
Transverse Mode ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Vortical Flow ◽  
Longitudinal Modes ◽  
Prandtl Model ◽  
The Stability

We investigate the stability of the Prandtl model for katabatic slope flows using both linear stability theory and direct numerical simulations. Starting from Prandtl’s analytical solution for uniformly cooled laminar slope flows, we use linear stability theory to identify the onset of instability and features of the most unstable modes. Our results show that the Prandtl model for parallel katabatic slope flows is prone to transverse and longitudinal modes of instability. The transverse mode of instability manifests itself as stationary vortical flow structures aligned in the along-slope direction, whereas the longitudinal mode of instability emerges as waves propagating in the base-flow direction. Beyond the stability limits, these two modes of instability coexist and form a complex flow structure crisscrossing the plane of flow. The emergence of a particular form of these instabilities depends strongly on three dimensionless parameters, which are the slope angle, the Prandtl number and a newly introduced stratification perturbation parameter, which is proportional to the relative importance of the disturbance to the background stratification due to the imposed surface buoyancy flux. We demonstrate that when this parameter is sufficiently large, then the stabilising effect of the background stratification can be overcome. For shallow slopes, the transverse mode of instability emerges despite meeting the Miles–Howard stability criterion of $Ri>0.25$. At steep slope angles, slope flow can remain linearly stable despite attaining Richardson numbers as low as $3\times 10^{-3}$.

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