Influence Of Magnetic Force On The Flow Stability Based On Energy Gradient Theory

The stability of the flow under the magnetic force is a special problem in fluid mechanics.The investigation of flow of fluids in ducts,diffusers and also other parts of various machines in the existence of the magnetic field is important for many technological processes.In this thesis,the influence of magnetic force on the flow stability in rectangular duct,diffuser,and an airfoil has been studied and the energy gradient theory is used to provide the theoretical analysis of the stability of the magnetohydrodynamics(MHD)flow.In the first part of this thesis,the flow in a rectangular duct with different Hartmann(Ha)number is simulated.The SIMPLE algorithm and the finite volume method are used to solve a system of equations and then the energy gradient theory is used to study the(associated)stability of MHD flow.According to the energy gradient theory,in pressure driven flow,K represents the ratio of energy gradient in the transverse direction and the energy loss due to viscosity in streamline direction.Position with large value of K will lose its stability earlier than that with small value of K.The flow stability of MHD flow for different Hartmann(Ha)number,from Ha=1 to 40,at the fixed Reynolds number,Re=190 are investigated.The simulation is validated firstly against the simulation in literature.The results show that,with the increasing Ha number,the centerline velocity of the rectangular duct with MHD flow decreases and the absolute value of the gradient of total mechanical energy along the streamwise direction increases.The maximum of K appears near the wall in both the coordinate axis of the duct.From the energy gradient theory,this position of the maximum of K would initiate flow instability(if any)more than the other positions.The higher the Hartmann number is,the smaller the K value becomes,which means that the fluid becomes more stable in the presence of higher magnetic force.As the Hartmann number increases,the K value in the parallel layer decreases more significantly than in the Hartmann layer.The most dangerous position of instability tends to migrate towards the wall of the duct as the Hartmann number increases.Thus,with the energy gradient theory,the stability or instability in the rectangular duct can be controlled by modulating the magnetic force.In the second part of this thesis,the flow in a diffuser with different Hartmann(Ha)number is simulated.The SIMPLE algorithm and the finite volume method are used to solve a system of equations and then the energy gradient theory is used to study the(associated)stability of magnetohydrodynamics(MHD).The flow stability of MHD flow for different Hartmann(Ha)number,from Ha=0.5 to 2,at the fixed Reynolds number,Re=114 are investigated.The results show that,with the increasing Ha number,the centerline velocity of the diffuser with MHD flow decreases and the vortices in the boundary layer is suppressed.The maximum of K appears near the wall of the diffuser in the y-axis direction.As the Hartmann number increases,the K value near the wall in the y-axis direction decreases significantly.Thus,with the energy gradient theory,the stability or instability in the diffuser can be controlled by modulating the magnetic force.In the third part of this thesis,the flow around the NACA 0012 airfoil at an angle of attack(AOA)of 7o with different Hartmann(Ha)number is simulated.The SIMPLE algorithm and the finite volume method are used to solve a system of equations and then the energy gradient theory is used to study the(associated)stability of magnetohydrodynamics(MHD)flow.The flow stability of MHD flow for different Hartmann(Ha)number,from Ha=0.01 to 4,at the fixed Reynolds number,Re=5101? are investigated.The results show that,with the increasing Ha number from Ha=0.01 to 0.5,the vortex in the trailing edge is suppressed and eventually the vortex disappeared.The increasing magnetic force pushes the fluid flow in the boundary layer which helps the vortex development and helps it to disappear.The influence of magnetic force becomes larger after increasing the Hartmann number from Ha=0.5 to Ha=4,which changes the flow direction and makes the flow become more unstable.Thus from Ha=0.01 till Ha=0.5,the magnetic force plays a good role for the flow stability.As the Hartmann number increases,the K value in the boundary layer decreases more significantly than the outside of the boundary layer,which makes the fluid flow more stable.Therefore,with the energy gradient theory,the stability or instability of flow around the airfoil can be controlled by modulating the magnetic force.