In this paper some improvements of numerical methods to solve incompressible Navier-Stokes equations in ψ-ω variables are presented. The flow around a cylinder is selected as a test problem. First, the numerical instability due to a central difference approximation for convective terms is discussed, which was found to be strongly related to the pressure gradient in the flow field. Second, in order to remove this instability and treat relatively high Reynolds number flow problems, the third-order accurate upwind finite difference technique based on the GQ (Generalized QUICK) algorithm is incorporated to model the convective terms which yielded stable and reasonable results as expected. The accuracy of the two schemes: the central difference approximation and the GQ algorithm are checked by the calculation of viscous flows on a flat plate for two cases: Re=104 and 105. Both results showed good agreements with Blasius' analytic solutions. The numerical viscosity due to the upwind finite difference approximation in the GQ scheme was rather small. Third, in order to obtain accurate pressure distributions from the calculated velocity field, the Poisson equation with Neumann boundary conditions is solved by the SOR and PCR method. This problem is well known for its difficult convergence. The following things were found. (a) By use of the SOR method, a convergence is very slow. After a number of iterations, the residual distributions in the field become independent of the source distributions. This suggests that the SOR method can not cancel residuals in an effective way. (b) By use of the PCR method, a fast convergence is obtained within a few hundred iterations, but the residual can not be reduced after that. (c) At this time, deleting sources of which absolute values are smaller than some small given value can highly improve the convergence rate of the pressure Poisson equation.
The performance of a kW-order arc-jet thruster is increased experimentally by changing the geometry of the constrictor portion. Out of several test models, the type with two-stage thin throat has shown the best energy efficiency (74%) and the highest specific impluse (1, 200s) under a specified combination of mass flow rate and power supply; over a wide range of power supply (of the order of kW), this type gives the best performance, along with the most stable discharge for the power supply less than even 1kW. Flow visualization using the Schlieren method and quasi-onedimensional analysis are done to understand the phenomena occurring inside the thruster.
Recently, expectation to linear-motor-cars grows up considerably in several countries. However its energy efficiency has scarecely been discussed, until two recent papers appeared in Asahi-shinbun. This paper improves the logic of comparison. According to the present author's opinion, the transportation-efficiency of the linear-motor-cars considered now to be used between Tokyo and Osaka is very close to that of airplanes.