水中颗粒孔洞流的最大休止倾角和流量公式

Maximum ceasing angle of inclination andflux formula for granular orifice flow in water

实验测量了完全浸泡在水中的玻璃珠颗粒样品在重力驱动下通过不同倾角和孔径的圆形孔洞的流量.发现与空气中的情形类似,不同孔径时的流量均与倾角余弦呈良好的线性关系;线性外推得到的零流量角,即流量休止临界角,随颗粒粒径与孔洞直径之比d/D的减小而线性增加;在无穷大孔径极限下,此临界角在实验误差范围内与样品的休止角一致.此外,所有测量都可用Beverloo公式Q=C0ρg^1/2(D-kd)^5/2很好地拟合;其中参数C0和k仅与倾角余弦有关,分别呈线性和平方反比关系.与文献报道的空气孔洞流测量结果对比,发现差别主要来自浮力和流体拖曳力对参数C0的影响.这些结果表明用倾斜孔洞流测量颗粒材料休止角的方法和Beverloo公式具有一定的普适性.无论颗粒间隙中填充的是水还是空气,孔洞流的行为在定性上是一样的.

In previous work [Acta Phys.Sin.60 054501(2011)],we found that for inclined Granular Orifice Flow(GOF) in air,regardless of the orifice size,the flow rate Q had a good linear relationship with the cosine of the inclination cos θ,i.e.Q/Q0=1-cosθ-1/cosθc-1,where Q0 is flow rate at θ=0°,and θ c is the critical angle of flow ceasing obtained by linear extrapolation.Moreover,θc increased linearly with ratio between grain and orifice diameter d/D,and at the limit of d/D going to zero(that is,D going to infinity),the angle of repose of the sample θr(=180°-θc∞) was obtained.Since the flow of GOF is very stable,we believe that the linear extrapolation of the above-mentioned inclined GOF provides a novel method for accurately measuring the angle of repose of granular materials.This method has been proved to be effective in a wider orifice size range by another work [Acta Phys.Sin.65 084502(2016)];and three angles,namely the repose angle measured by GOF,the free accumulation angle of a sandpile and the internal friction angle of the granular material measured by Coulomb yielding,are confirmed to be consistent.In this work,we extend this method to underwater,measuring the mass flow rate of a granular sample(glass beads) which completely immersed in water and driven by gravity,discharged from an inclined orifice for various inclination angles and orifice diameters.It is found that similar to the case in air,regardless of the orifice size,the flow rate increase linearly with the cosine of the inclination;the critical angle of flow ceasing increases linearly with ratio between grain and orifice diameter;at the limit of infinite orifice,this critical angle is consistent with the repose angle of the underwater sample within the experimental error range.In addition,all measurements can be well fitted by using the Beverloo formula Q=C0ρg^1/2(D-kd)^5/2,where the parameters C0 and k are only related to the cosine of the inclination,and are linear and inversely squared,respectively.Compared with the results of GOF in air reported by previous work,it is found that the difference mainly comes from the influence of buoyancy and fluid drag forces on the parameter C0.These results show that both the method of measuring angle of repose with the inclined GOF and the Beverloo formula have certain universality.The behavior of GOF is qualitatively the same whether the interstitial fluid is water or air.