Stability of boundary layer flow based on energy gradient theory

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

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.

Prediction of Laminar to Turbulent Transition in 90° Curved Duct Based on Energy Gradient Theory

Study on laminar to turbulent transition in a 90° curved duct is carried out. Professional mesh generation tool ICEM is used to create geometry model and generate mesh, then the mesh is imported to the fluid dynamics software CFX to simulate three-dimensional flow. The dimensionless parameter K is calculated in the duct with velocity and pressure distribution obtained by numerical simulation. According to energy gradient theory, K is the ratio of energy gradient in the transverse direction to that in the streamwise direction, which can be used to measure stability of the flow field. It is found that fluid is most likely to lose its stability where the maximum K is, and laminar to turbulent transition occurs when K reaches a certain value, corresponding to the critical Reynolds number. The instability and transition characteristics predicted by energy gradient method agree well with former researchers’ results.

On the Instability of Plane Poiseuille Flow of Two Immiscible Fluids Using the Energy Gradient Theory

ABSTRACTIn the present study, the instability of laminar flow of two immiscible fluids is investigated. The theory of energy gradient is employed for the analysis. The distributions of energy gradient for various viscosity ratios, i.e., ratios of lower viscosity to higher one, are obtained and the results for the onset of instability are compared with the available experimental data. The comparison of the results shows excellent agreement with the existing experimental data. It will be also demonstrated that as the viscosity ratio decreases the flow becomes more stable even at high Reynolds numbers.

ENERGY SPECTRUM OF DISTURBANCE AT TURBULENT TRANSITION VIA ENERGY GRADIENT METHOD

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.