An efficient numerical method for calculating the three-dimensional transonic flows in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mi...An efficient numerical method for calculating the three-dimensional transonic flows in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mises coordinate system to reflect the flow feature in turbomachinery. Its main advantage is that it is easier to specify more reasonable initial values, i.e. initial streamsurface position, thus accelerating the convergence rate of the iteration process. Moreover, to use the generalized von Mises coordinates makes the present method capable of incorporating the calculation of the flow field, design and modification of the blade contour into a unified algorithm. A rotated finite difference scheme for the streamsurface-governing equations is constructed, and a new measure is presented to deal with the double-value problem of the velocity and density caused by the application of the stream functions as coordinates in the transonic flow. Three test cases were considered with the present approach to demonstrate the solution method for 3-D inviscid flow analysis. Numerical results confirm that the present method has rapid convergence and high accuracy.展开更多
The non\|oscillatory central difference scheme developed by Nessyahu and Tadmor is modified using a method similar to that in the modified conservation element and solution element scheme (CE/SE scheme). The resulting...The non\|oscillatory central difference scheme developed by Nessyahu and Tadmor is modified using a method similar to that in the modified conservation element and solution element scheme (CE/SE scheme). The resulting scheme is a two\|point second\|order central scheme, which not only retains the advantages of a simple Riemann\|solver\|free recipe, but is also easier to implement near boundaries. Numerical results for several sample flow problems show that the present scheme has higher accuracy and better shock resolution than the original one. 展开更多
文摘An efficient numerical method for calculating the three-dimensional transonic flows in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mises coordinate system to reflect the flow feature in turbomachinery. Its main advantage is that it is easier to specify more reasonable initial values, i.e. initial streamsurface position, thus accelerating the convergence rate of the iteration process. Moreover, to use the generalized von Mises coordinates makes the present method capable of incorporating the calculation of the flow field, design and modification of the blade contour into a unified algorithm. A rotated finite difference scheme for the streamsurface-governing equations is constructed, and a new measure is presented to deal with the double-value problem of the velocity and density caused by the application of the stream functions as coordinates in the transonic flow. Three test cases were considered with the present approach to demonstrate the solution method for 3-D inviscid flow analysis. Numerical results confirm that the present method has rapid convergence and high accuracy.
文摘The non\|oscillatory central difference scheme developed by Nessyahu and Tadmor is modified using a method similar to that in the modified conservation element and solution element scheme (CE/SE scheme). The resulting scheme is a two\|point second\|order central scheme, which not only retains the advantages of a simple Riemann\|solver\|free recipe, but is also easier to implement near boundaries. Numerical results for several sample flow problems show that the present scheme has higher accuracy and better shock resolution than the original one.
