A Five-Mode System of the Navier-Stokes Equations on a Torus

A five-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented;the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behavior of the new chaos system are revealed.

A Seven-Dimensional System of the Navier-Stokes Equations for a Two-Dimensional Incompressible Fluid on a Torus

A seven-mode truncation system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is considered. Its stationary solutions and stability are presented;the existence of the attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through instability of invariant tori, is simulated numerically by computers with the changing of Reynolds number. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, some basic dynamical behaviors of the new chaos system are revealed.

Theoretical and experimental investigation on the efficiency of a novel roller piston pump

This study presents a novel roller piston pump,in which a cam guide-roller type rolling support is adopted to replace the sliding pair support of the swash plate-slipper pair to achieve the oil suction and discharge of the piston cavity.In addition,the shaft distribution is used to replace the original valve plate distribution and the driving shaft is used as the distribution shaft to remove the valve plate structure,which greatly simplifies the design of the axial piston pump.Such a configuration largely reduces the number of sliding friction pairs of the pump,and avoids the influence of the sliding friction pair on it under high-speed and variable-speed conditions.Firstly,mathematical models of the mechanical and volumetric efficiencies of the roller pump are deduced respectively through force analysis and the compressibility equation.Based on the numerical simulation of MATLAB and AMESim,the effects of load pressure and rotational speed on mechanical and volumetric efficiencies are studied respectively,and it is verified that the roller pump has no structural flow pulsation.The prototype pump is then designed and built,along with a special test rig.The outlet pressure,outlet flow,and torque of the pump under different load pressures and rotational speeds are measured,and the mechanical and volumetric efficiencies of the prototype pump under various load pressures and rotational speeds are obtained.The experimental results are in good agreement with the simulated analysis.When the load pressure is 8 MPa and the speed is 5000 r/min,the mechanical and the volumetric efficiencies are 85.5% and 96.8%,respectively.When the speed is increased to 10000 r/min,the mechanical and the volumetric efficiencies are 66.7% and 95.6%,respectively.The experimental results show that the proposed roller piston pump has excellent efficiency under wide-speed and high-speed conditions and can be a potential solution as a fuel pump in aerospace fuel systems.