To most people"mathematies"is synonymous(同义词的,类语的) with "figuring". Actually this idea is far from the truth. Aside from the many geometrical qnes-tions which are not at all concerned with a...To most people"mathematies"is synonymous(同义词的,类语的) with "figuring". Actually this idea is far from the truth. Aside from the many geometrical qnes-tions which are not at all concerned with adding, sub-tracting. multiplying. and dividing, there are problems of quite different sorts whose solution are obtained by the direct exercise of the powers of reasoning. without the intervention(插进,介入) of formulas and computations. For mathematics is applied logic in its simplest and purest form. To demonstratc our c...展开更多
Scalar mixing is under the joint control of convection and diffusion.The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number.In the high Schmidt mumber limit.the ...Scalar mixing is under the joint control of convection and diffusion.The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number.In the high Schmidt mumber limit.the scalar scale is much smaller than that of the momentum,which then reguires either special treat ment or ad hoc models for the sealar quantity in mumerical simulations.In order to avoid model uncertainty or unnecessary numerical complexity.the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank.It has been found that in the range of negligible mumerical diffusivity the characteristic scalar mixing time is inversely proportional to the scalar diffusivitv.Analysis based on the dimensional argument justifies such scaling relation as well.from which the unaccepted computational time of the nixing process in the high Schmidt number limit can be efficiently determined,without the use of ad hoc models This scaling idea is also of practical meaningfulness for ot her similar problems.展开更多
文摘To most people"mathematies"is synonymous(同义词的,类语的) with "figuring". Actually this idea is far from the truth. Aside from the many geometrical qnes-tions which are not at all concerned with adding, sub-tracting. multiplying. and dividing, there are problems of quite different sorts whose solution are obtained by the direct exercise of the powers of reasoning. without the intervention(插进,介入) of formulas and computations. For mathematics is applied logic in its simplest and purest form. To demonstratc our c...
文摘Scalar mixing is under the joint control of convection and diffusion.The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number.In the high Schmidt mumber limit.the scalar scale is much smaller than that of the momentum,which then reguires either special treat ment or ad hoc models for the sealar quantity in mumerical simulations.In order to avoid model uncertainty or unnecessary numerical complexity.the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank.It has been found that in the range of negligible mumerical diffusivity the characteristic scalar mixing time is inversely proportional to the scalar diffusivitv.Analysis based on the dimensional argument justifies such scaling relation as well.from which the unaccepted computational time of the nixing process in the high Schmidt number limit can be efficiently determined,without the use of ad hoc models This scaling idea is also of practical meaningfulness for ot her similar problems.
