The ratio of the pressure drop force to the drag force,C_(P),is concerned for a non-closely fitting spherical particle settling along the central line in long rectangular tubes with different A_(r)(A_(r)is W/H,where W...The ratio of the pressure drop force to the drag force,C_(P),is concerned for a non-closely fitting spherical particle settling along the central line in long rectangular tubes with different A_(r)(A_(r)is W/H,where W,H is length of the longer and shorter side of the rectangle respectively).Under Stokes flow conditions,C_(P0)for an infinitely small sphere in long rectangular tubes and C_(P)for a sphere in a long channel between two parallel layered barriers are both calculated.Then C_(P)of a sphere settling in long rectangular tubes are conducted with the direct-forcing fictitious domain(DF/FD)method.At large Reynolds number,the sphere settles unstably with a fluctuating velocity and C_(P).The fluctuation of Cp is much stronger than that of velocity and both fluctuations are stronger for less confined sphere.The influences of the particle Reynolds number(Re_(p))on C_(P)is similar to the existing experimental results in long circular tubes.At low Re_(p),C_(P)is a determined value and is calculated.For a given d/H(d sphere diameter),Cp gets its maximum value at one A_(r)in the range of[1,1.5].For a given A_(r),C_(P)is a quadratic function of d/H similar to that in a circular tube,and parameters of the quadratic function are got by curve fitting from numerical data.The constant term coefficients got have almost no difference with C_(P0)and are furtherly replaced by the latter to get new quadratic coefficients C_(P1).Lastly,an algebraic correlation of C_(P1)to A_(r)is developed.The predictions of Cp are good with a maximum relative error about 1.5%for a sphere with d/H not greater than0.7,compared to numerical results.展开更多
The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-sp...The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-space or a suitable dense sub-space for the ,especially the later is valuable.It has been proved in [1] (Theorem 10) that,if ~∞展开更多
基金supported by the National Natural Science Foundation of China(12132015,12332015)。
文摘The ratio of the pressure drop force to the drag force,C_(P),is concerned for a non-closely fitting spherical particle settling along the central line in long rectangular tubes with different A_(r)(A_(r)is W/H,where W,H is length of the longer and shorter side of the rectangle respectively).Under Stokes flow conditions,C_(P0)for an infinitely small sphere in long rectangular tubes and C_(P)for a sphere in a long channel between two parallel layered barriers are both calculated.Then C_(P)of a sphere settling in long rectangular tubes are conducted with the direct-forcing fictitious domain(DF/FD)method.At large Reynolds number,the sphere settles unstably with a fluctuating velocity and C_(P).The fluctuation of Cp is much stronger than that of velocity and both fluctuations are stronger for less confined sphere.The influences of the particle Reynolds number(Re_(p))on C_(P)is similar to the existing experimental results in long circular tubes.At low Re_(p),C_(P)is a determined value and is calculated.For a given d/H(d sphere diameter),Cp gets its maximum value at one A_(r)in the range of[1,1.5].For a given A_(r),C_(P)is a quadratic function of d/H similar to that in a circular tube,and parameters of the quadratic function are got by curve fitting from numerical data.The constant term coefficients got have almost no difference with C_(P0)and are furtherly replaced by the latter to get new quadratic coefficients C_(P1).Lastly,an algebraic correlation of C_(P1)to A_(r)is developed.The predictions of Cp are good with a maximum relative error about 1.5%for a sphere with d/H not greater than0.7,compared to numerical results.
文摘The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-space or a suitable dense sub-space for the ,especially the later is valuable.It has been proved in [1] (Theorem 10) that,if ~∞
