To predict the thrust of bubbly water ramjet with a converging-diverging nozzle, the physical processes occurring in the diffuser, mixing chamber and nozzle were analyzed. The mathematical models were constructed sepa...To predict the thrust of bubbly water ramjet with a converging-diverging nozzle, the physical processes occurring in the diffuser, mixing chamber and nozzle were analyzed. The mathematical models were constructed separately under the restrictions of certain assumptions. The bubbly nozzle flow was examined using a two-fluid model and accomplished by specifying the water velocity distribution in the nozzle. The numerical analysis of flow field in the nozzle shows that the Mach number at the throat is 1.009, near unity, and supersonic bubble flow appears behind the throat. There is greater thrust produced by bubbly water ramjet, compared with single-phase air ramjets. Subsequently, the influences of vessel velocity, air mass flow rate, inlet area Ai, area ratio （i.e., mixing chamber to inlet area Am/Ai）, and initial bubble radius on the thrust were emphatically investigated. Results indicate that the thrust increases with the increase of air mass flow rate, inlet area and the area ratio, and the decrease of initial bubble radius. However, the thrust weakly depends on the vessel velocity. These analytical and numerical results are useful for further investigation of bubbly water ramjet engine.展开更多
The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geom...The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids.The results are compared to previously derived expressions for the same geometries using the lubrication approximation.The results of the one-dimensional Navier–Stokes are identical to those obtained from the lubrication approximation within a nondimensional numerical factor.The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration.Moreover,they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.展开更多
文摘To predict the thrust of bubbly water ramjet with a converging-diverging nozzle, the physical processes occurring in the diffuser, mixing chamber and nozzle were analyzed. The mathematical models were constructed separately under the restrictions of certain assumptions. The bubbly nozzle flow was examined using a two-fluid model and accomplished by specifying the water velocity distribution in the nozzle. The numerical analysis of flow field in the nozzle shows that the Mach number at the throat is 1.009, near unity, and supersonic bubble flow appears behind the throat. There is greater thrust produced by bubbly water ramjet, compared with single-phase air ramjets. Subsequently, the influences of vessel velocity, air mass flow rate, inlet area Ai, area ratio （i.e., mixing chamber to inlet area Am/Ai）, and initial bubble radius on the thrust were emphatically investigated. Results indicate that the thrust increases with the increase of air mass flow rate, inlet area and the area ratio, and the decrease of initial bubble radius. However, the thrust weakly depends on the vessel velocity. These analytical and numerical results are useful for further investigation of bubbly water ramjet engine.
文摘The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids.The results are compared to previously derived expressions for the same geometries using the lubrication approximation.The results of the one-dimensional Navier–Stokes are identical to those obtained from the lubrication approximation within a nondimensional numerical factor.The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration.Moreover,they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.
