On Hydrodynamic Stability of Dean Flow by Using Energy Gradient Methods

2018 ◽  
Vol 35 (3) ◽  
pp. 405-418 ◽  
Author(s):  
H. Nowruzi ◽  
H. Ghassemi ◽  
S. S. Nourazar
Keyword(s):  
Flow Instability ◽  
Hydrodynamic Instability ◽  
Gradient Methods ◽  
Critical Value ◽  
Dean Number ◽  
Dean Flow ◽  
Energy Gradient ◽  
Entire Flow ◽  
Gradient Function ◽  
Curved Walls

ABSTRACTIn the present paper, we investigate the hydrodynamic instability of Dean flow under different Dean numbers ranging from 1 to 2500, curvature ratios from 0.0001 up to 1000 and temperatures ranging from 273.15 K to 373.15 K. To study of fluid flow instability, analytical velocity profiles under intended conditions and energy gradient function K in the energy gradient method are evaluated. The results of present study show that, as the curvature ratio increases the flow becomes more stable. Moreover, no regular and significant effects on the energy gradient function K were achieved by increasing of temperatures. We found that, the origin of instability in the entire flow field is located on the inner wall of the parallel curved walls, especially for larger curvature ratios. We also reported the critical value of the energy gradient function K for the onset of instability corresponding to the critical Dean number.

scholarly journals A Numerical Study of Natural Convection Heat Transfer in Fin Ribbed Radiator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Hua-Shu Dou ◽  
Gang Jiang ◽  
Lite Zhang
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Flow Instability ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Gradient Theory ◽  
Computational Domain ◽  
Energy Gradient ◽  
Gradient Function ◽  
Fin Shape

This paper numerically investigates the thermal flow and heat transfer by natural convection in a cavity fixed with a fin array. The computational domain consists of both solid (copper) and fluid (air) areas. The finite volume method and the SIMPLE scheme are used to simulate the steady flow in the domain. Based on the numerical results, the energy gradient functionKof the energy gradient theory is calculated. It is observed from contours of the temperature and energy gradient function that the position where thermal instability takes place correlates well with the region of largeKvalues, which demonstrates that the energy gradient method reveals the physical mechanism of the flow instability. Furthermore, the effects of the fin height, the fin number, and the fin shape on the heat transfer rate are also investigated. It is found that the thermal performance of the fin array is determined by the combined effect of the fin space and fin height. It is also observed that the effect of fin shape on heat transfer is insignificant.

scholarly journals Linear Hydrodynamic Stability of Fluid Flow in Curved Rectangular Ducts: Semi-Analytical Study

2019 ◽  
Vol 35 (5) ◽  
pp. 747-765 ◽  
Author(s):  
H. Nowruzi ◽  
H. Ghassemi ◽  
S. S. Nourazar
Keyword(s):  
Fluid Flow ◽  
Aspect Ratio ◽  
Eigenvalue Problem ◽  
Flow Instability ◽  
Wave Number ◽  
Dean Number ◽  
Analytical Technique ◽  
Dean Flow ◽  
Aspect Ratios ◽  
Analytical Results

ABSTRACTIn the current study, for the first time, a semi-analytical technique is used for solving eigenvalue problem arising from linear hydrodynamics stability of fluid flow through the curved rectangular ducts at different curvature ratios and aspect ratios. To this accomplishment, symmetric disturbances are assumed and the Homotopy perturbation method (HPM) is applied to solve our eigenvalue problem for curvature ratios ranging from 0.01 to 0.8 and aspect ratios ranging from 0.05 to 20. Our semi-analytical results are validated through the existing numerical and experimental data, showing good agreement. The semi-analytical results indicate that, as the curvature ratio increases the critical Dean number (Dnc) is increased and the flow becomes more stable, especially for aspect ratios lower than 1.Moreover, for all intended curvature ratios, irregular behavior in variation of Dnc is detected by an increase in the aspect ratio. So that, the Dnc is decreased when the aspect ratio increases from 0.05 up to 1 and the fluid flow becomes unstable. When the aspect ratio is increased from 1 to 5, it causes to increase the Dnc and fluid flow becomes stable. Furthermore, when the aspect ratio increases from 5 to 20, the Dnc is decreased again. In addition, Dnc and eigenvalues of critical complex wave number corresponding to Dnc for the onset of Dean flow instability is reported under different curvature ratios and aspect ratios.

Numerical Investigation of Flow Instability in Centrifugal Pump Based on Energy Gradient Method

2016 ◽  
Author(s):  
Lulu Zheng ◽  
Hua-Shu Dou ◽  
Xiaoping Chen ◽  
Zuchao Zhu ◽  
Baoling Cui
Keyword(s):  
Flow Rate ◽  
Flow Instability ◽  
Flow Stability ◽  
Gradient Theory ◽  
Small Flow Rate ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
Centre Region ◽  
Small Flow ◽  
Gradient Function

Simulation of turbulent flow in a pump is carried out with the RANS equations and the RNG k-epsilon turbulence model. Numerical simulation has been compared with the experimental data. The results show that separating vortex is firstly produced at the pressure side of the impeller passage near the tongue. Then it spreads to the inlet and outlet of the impeller passages and moved to the centre region of impeller passages from the boundaries. Finally, it almost occupies all the impeller passages and multiple vortices exist in impeller passages at small flow rate. It is found that the tongue has large effect on the flow in the impeller passage approaching to it. The impeller passage near the tongue is easily tending to be unstable comparing with others passages. The energy gradient theory is used to analyze the flow stability in the impeller. The region with larger value of energy gradient function K means the bigger turbulence intensity and poor flow stability. At small flow rate the regions with large value of K are enlarged and are mainly located at both sides of blade pressure and suction surfaces where the flow is easily tending to be unstable.

scholarly journals Stability of boundary layer flow based on energy gradient theory

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840003
Author(s):  
Hua-Shu Dou ◽  
Wenqian Xu ◽  
Boo Cheong Khoo
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Flow Instability ◽  
Mechanical Energy ◽  
Navier Stokes ◽  
Gradient Theory ◽  
External Edge ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
Gradient Function

The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier–Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

Study of flow instability in a centrifugal fan based on energy gradient theory

2016 ◽  
Vol 30 (2) ◽  
pp. 507-517 ◽  
Author(s):  
Meina Xiao ◽  
Qing Xiao ◽  
Hua-Shu Dou ◽  
Xiaoyang Ma ◽  
Yongning Chen ◽  
...  
Keyword(s):  
Flow Instability ◽  
Gradient Theory ◽  
Centrifugal Fan ◽  
Energy Gradient Theory ◽  
Energy Gradient

Validation of Hydrodynamic Stability of Supercritical Once-Through Boiler

2008 ◽  
Author(s):  
Bing Wei ◽  
Dong Zhou
Keyword(s):  
Flow Instability ◽  
Hydrodynamic Instability ◽  
Pressure Head ◽  
Operating Conditions ◽  
Hydrodynamic Characteristics ◽  
Boiler Operation ◽  
Calculation Results ◽  
Low Mass ◽  
The Stability ◽  
Heating Loads

Operating safety is one of the most important things to supercritical once-through boilers. To study the hydrodynamic characteristics of fluid in water walls of supercritical once-through boilers and to find out the instable factors will be of great significance to boiler operation. In this paper the mathematical models for hydrodynamic characteristics of fluid in water walls are established. With an example of 600MW boiler, by using the calculation program, the hydrodynamic characteristics curves without and with the throttles at the inlets of the water walls at different operating conditions are presented, the fluid flow instability and the reasons are analyzed. The calculation results show that the boiler operates stably and safely at 100% MCR (Maximum Continuous Rating) condition, the hydrodynamic instability exists at low heating loads of 30% MCR. The method of installing the throttles at the inlets of the water wall pipes will increase the parabola characteristics, help to improve the fluid instability to a certain stable extent, but due to the small curve slopes at low mass flowrates, still need to pay more attention to the low heating loads operation. The existence of gravity pressure head is good to the stability of the vertical upward flow.

scholarly journals Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

2011 ◽  
Vol 3 (2) ◽  
pp. 165-180 ◽  
Author(s):  
Hua-Shu Dou ◽  
Boo Cheong Khoo
Keyword(s):  
Energy Loss ◽  
Gradient Method ◽  
Poiseuille Flow ◽  
Mechanical Energy ◽  
Viscous Friction ◽  
Critical Value ◽  
Plane Couette Flow ◽  
Turbulent Transition ◽  
Energy Gradient ◽  
Total Mechanical Energy

AbstractThe energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function K (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function K for plane Couette flow is derived. The result indicates that K reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain. The critical value of K at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).

SPECTRAL NUMERICAL SIMULATION OF MAGNETO-PHYSIOLOGICAL LAMINAR DEAN FLOW

2014 ◽  
Vol 14 (04) ◽  
pp. 1450047 ◽  
Author(s):  
O. ANWAR BEG ◽  
MD. MAINUL HOQUE ◽  
M. WAHIDUZZAMAN ◽  
MD. MAHMUD ALAM ◽  
M. FERDOWS
Keyword(s):  
Transport Model ◽  
Computational Simulation ◽  
Large Diameter ◽  
Experimental Studies ◽  
Circular Cross Section ◽  
Flow Characteristics ◽  
Axial Flow ◽  
Momentum Conservation ◽  
Dean Number ◽  
Dean Flow

A computational simulation of magnetohydrodynamic laminar blood flow under pressure gradient through a curved bio-vessel, with circular cross-section is presented. Electrical conductivity and other properties of the biofluid (blood) are assumed to be invariant. A Newtonian viscous flow (Navier–Stokes magnetohydrodynamic) model is employed which is appropriate for large diameter blood vessels, as confirmed in a number of experimental studies. Rheological effects are therefore neglected as these are generally only significant in smaller diameter vessels. Employing a toroidal coordinate system, the steady-state, three-dimensional mass and momentum conservation equations are developed. With appropriate transformations, the transport model is non-dimensionalized and further simplified to a pair of axial and secondary flow momenta equations with the aid of a stream function. The resulting non-linear boundary value problem is solved with an efficient, spectral collocation algorithm, subject to physically appropriate boundary conditions. The influence of magnetic body force parameter, Dean number and vessel curvature on the flow characteristics is examined in detail. For high magnetic parameter and Dean number and low curvature, the axial flow is observed to be displaced toward the center of the vessel with corresponding low fluid particle vorticity strengths. Visualization is achieved with the MAPLE software. The simulations are relevant to cardiovascular biomagnetic flow control.

The Instability of a Flexible Sheet in Uniform Parallel Flow

2007 ◽  
Author(s):  
Michael T. Morris-Thomas ◽  
Sverre Steen
Keyword(s):  
Spectral Method ◽  
Ideal Fluid ◽  
Flow Instability ◽  
Fluid Dynamic ◽  
Fluid Velocity ◽  
Critical Value ◽  
Elastic Model ◽  
Elastic Instability ◽  
Mass Ratio ◽  
Unique Aspect

When a flexible sheet immersed in a fluid is under the influence of uniform flow, instability can arise when the fluid velocity reaches some critical value. The fluid-elastic instability known as flutter is the focus of this present work. We present a fluid-elastic model for a flexible sheet whereby the fluid dynamic lift is accounted for by the classical slender body approximation of Lighthill [1] for an ideal fluid. We describe aspects of the system in terms of a mass ratio α and a tension to flexural ratio γ. The model is solved by a spectral method to determine the fluid velocity and frequency at which instability occurs. In addition, we consider the fluid friction and damping on the response of the flexible sheet. Moreover, we compare predictions for the flutter velocity and frequency with published results. The unique aspect of this work is an investigation into the effect of additional tension, in the form of the ratio γ, on stability.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

2014 ◽  
Author(s):  
Kiran Manoharan ◽  
Santosh Hemchandra
Keyword(s):  
Stability Analysis ◽  
Flow Field ◽  
Flow Velocity ◽  
Convective Instability ◽  
Flow Instability ◽  
Hydrodynamic Instability ◽  
Combustion Instability ◽  
Base Flow ◽  
Flow Density ◽  
Backward Facing Step

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms — (1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are co-located. Regions in the space of parameters characterizing the base flow velocity profile, i.e. shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on prior observations of flow instability in other flows such as heated jets and bluff-body stabilized flames is discussed.

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