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.

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.

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

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.

ENERGY SPECTRUM OF DISTURBANCE AT TURBULENT TRANSITION VIA ENERGY GRADIENT METHOD

2012 ◽  
Vol 19 ◽  
pp. 293-303 ◽  
Author(s):  
HUA-SHU DOU ◽  
BOO CHEONG KHOO
Keyword(s):  
Energy Spectrum ◽  
Flow Instability ◽  
Three Dimensional ◽  
Wave Number ◽  
Gradient Theory ◽  
Turbulent Transition ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
The Difference ◽  
2D And 3D

The energy gradient theory for flow instability and turbulent transition was proposed in our previous work. The theoretical result obtained accords well with some experimental data for pipe and channel flows in the literature. In the present study, the energy gradient theory is extended to examine the effect of disturbance frequency on turbulent transition. Then, the energy spectrum of disturbance at the turbulent transition is obtained, which scales with the wave number by an exponent of –2. This scaling is near to the K41 law of –5/3 for the full developed isentropic homogenous turbulence. The difference for the two energy spectra may be due to the intermittency of turbulence at the transition state. The intermittence causes the distribution of the energy spectrum to take on a steeper gradient (tending to –2 from –5/3). Finally, the flow instability leading to turbulent transition can be classified as two-dimensional (2D) or three-dimensional (3D) in terms of the wave number and the Re. It is found that there is an optimum wave number which separates the 2D and 3D transitions and at which the disturbance energy at transition is minimum.

An adjoint approach for computing the receptivity of the rotating disc boundary layer to surface roughness

2021 ◽  
Vol 926 ◽  
Author(s):  
Christian Thomas ◽  
Christopher Davies
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Stokes Equations ◽  
Flow Instability ◽  
Cross Flow ◽  
Navier Stokes ◽  
Rotating Disc ◽  
Azimuthal Mode ◽  
The Cross ◽  
Adjoint Approach

An adjoint approach is developed to compute the receptivity of the rotating disc boundary layer to surface roughness. The adjoint linearised Navier–Stokes equations, in cylindrical coordinates, are derived and receptivity characteristics are computed for a broad range of azimuthal mode numbers using a fully equivalent velocity–vorticity formulation. For each set of flow conditions (i.e. azimuthal mode number), the adjoint method only requires that the linear and adjoint solutions be computed once. Thus, the adjoint approach offers significant computational and time advantages over alternative receptivity schemes (i.e. direct linearised Navier–Stokes) as they can be used to instantaneously compute the receptivity of boundary layer disturbances to many environmental mechanisms. Stationary cross-flow disturbances are established by randomly distributed surface roughness that is periodic in the azimuthal direction and modelled via a linearisation of the no-slip condition on the disc surface. Each roughness distribution is scaled on its respective root-mean-square. A Monte-Carlo type uncertainty quantification analysis is performed, whereby mean receptivity amplitudes are computed by averaging over many thousands of roughness realisations with variable length and wavelength filters. The amplitude of the cross-flow instability is significantly larger for roughness distributions near the conditions for neutral linear instability, while roughness elements radially outboard have a negligible effect on the receptivity process. Furthermore, receptivity increases sharply for roughness distributions that encompass wavelength scales equivalent to that associated with the cross-flow instability. Finally, mean receptivity characteristics are used to predict the radial range that stationary cross-flow vortices achieve amplitudes sufficient to invalidate the linear stability assumptions.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

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