Fundarmentalof two-phase flow 810-3 Resistance of mobile 1. Character of solid material Two-phase flow often involves physical and geometrical character of solid 1. 1 Main physical character of solid material Main physical character of solid material is mass(ps), specific weight (rs) and specific gravity 2. 2 Main geometrical character of solid material 2. 2. 1 Particle diameter. In fact the shape of solid material is anomalistic Adopt equal volume particle diameter express its size (taking particle as sphere with equal volume a6W√36G√/3 10-1)
11 1.Character of solid material Two-phase flow often involves physical and geometrical character of solid. 1.1 Main physical character of solid material. Main physical character of solid material is mass (rs), specific weight（gs）and specific gravity 。 2.2 Main geometrical character of solid material 2.2.1 Particle diameter. In fact the shape of solid material is anomalistic. Adopt equal volume particle diameter express its size (taking particle as sphere with equal volume ): ) (10 1) 6 ) ( 6 ( 1/3 1/3 s s V G d g §10-3 Resistance of mobile
祖流动 §10-3运动物体的阻力 一、固体物料的性质 两相流中常涉及的是固体的物理性质和几何性质。 1、固体物料的主要物理性质 固体物料的主要物理性质有质量(),重度()和比重 。应注意比重是无因次物理量,与重度的物理概念不同 2、固体物料的几何性质 1)粒径实际固体物料的形状一般是不规则的,可采用 等体积粒径来表示颗粒的大小,即把颗粒看作等体积球体, 可得等体积粒径为: 6136G√/3 10-1) 12
12 一、固体物料的性质 两相流中常涉及的是固体的物理性质和几何性质。 1、固体物料的主要物理性质 固体物料的主要物理性质有质量（rs）,重度（gs）和比重 。应注意比重是无因次物理量，与重度的物理概念不同。 2、固体物料的几何性质 （1）粒径 实际固体物料的形状一般是不规则的，可采用 等体积粒径来表示颗粒的大小，即把颗粒看作等体积球体， 可得等体积粒径为： ) (10 1) 6 ) ( 6 ( 1/3 1/3 s s V G d g §10-3 运动物体的阻力
Fundarmentalof two-phase flow 2. 2. 2 Shape of particle: Get sphere as standard; scaling different shape but same particle and specific weight, called shape coefficient o s(10-2) where: Spb surface area of cylinder; b f6 surface area of particle Because surface area of sphere is least, so 0<o<1 2. Basic type of resistance of mobile When a object moves in liquid, force that P F liquid act to object is component of forces plumb with speed P(ascending force )and component of forces adverse with speed r ( resistance ), as in 10-1 moreover r is made of friction R resistance Rm produced by shear stress and press Fig.10—1 resistance Rp produced by press: R=Rm+ Rp Object streamline chart 13
13 2.2.2 Shape of particle:Get sphere as standard;scaling different shape but same particle and specific weight, called shape coefficient f (10 2) where surface area of cylinder; surface area of particle pb pb fb fb S S S S f ： － － Because surface area of sphere is least, so 0< f <1 。 2. Basic type of resistance of mobile When a object moves in liquid, force that liquid act to object is component of forces plumb with speed, P (ascending force)and component of forces adverse with speed R （resistance）,as in 10—1. Moreover R is made of friction resistance Rm produced by shear stress and press resistance Rp produced by press: R＝ Rm＋ Rp P F R Fig.10－1 Object streamline chart
(2)颗粒的形状取球形作标准,衡量颗粒和重度相同但形 状不同的颗粒,称作球形度或形状系数,用￠表示 o= (10-2) 力b 式中:Sm一圆柱体的表面积;Sb一颗粒的表面积 由于球形表面积最小,故其它形状颗粒球形度0<女1。 二、运动物体阻力的基本类型 当一物体在流体中运动时,流体对 物体的作用力可分为与速度垂直的分力 P F P(简称为升力)和与速度相反的分力 R R(称为阻力),如图10-1所示。而阻力 R又分为由切应力产生的摩擦阻力R和图10-1物体的流线谱 由压力产生的压力阻力Rn,即 R=R +R
14 （2）颗粒的形状 取球形作标准，衡量颗粒和重度相同但形 状不同的颗粒，称作球形度或形状系数，用f表示 式中： pb－圆柱体的表面积； fb－颗粒的表面积。 fb pb S S S S f (10 2) 由于球形表面积最小，故其它形状颗粒球形度 0< f<1 。 二、运动物体阻力的基本类型 当一物体在流体中运动时，流体对 物体的作用力可分为与速度垂直的分力 P （简称为升力）和与速度相反的分力 R （称为阻力），如图10—1所示。而阻力 R 又分为由切应力产生的摩擦阻力 Rm 和 由压力产生的压力阻力 Rp，即 R＝ Rm＋ Rp P F R 图10－1 物体的流线谱
Fundarmentalof two-phase flow When object moves in fluid, action force law is connected with Renault When Renault is great, it means inertia force is far large than viscosity force; in reverse, viscosity is larger than inertia force 3. Resistance of spherical object with great Reynolds number When renault is great, object with bad streamline will produce vortex resistance as attached layer separating. Resistance account formula get by modifying the Newton-Reutlingen resistance formula, it is suitable as 500<Re<105 od l (10-3) 6 4. Resistance of spherical object with minor Reynolds number In many practical project, particle diameter is very small, moving speed is slow, mostly resistance produced is friction resistance belong to generic laminar flow movement Translate formula(10-3) into generic resistance formula: 15
15 When object moves in fluid, action force law is connected with Renault. When Renault is great,it means inertia force is far large than viscosity force; in reverse ,viscosity is larger than inertia force. 3. Resistance of spherical object with great Reynolds number When Renault is great，object with bad streamline will produce vortex resistance as attached layer separating. Resistance account formula get by modifying the Newton-Reutlingen resistance formula, it is suitable as 500<Re<10 5 . (10 - 3) 16 2 2 R rd u 4. Resistance of spherical object with minor Reynolds number In many practical project,particle diameter is very small,moving speed is slow,mostly resistance produced is friction resistance, belong to generic laminar flow movement. Translate formula（10－3）into generic resistance formula: