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渣漿泵液混合物在旋轉流道中的相對運動
   推導固液混合物液流在旋轉流道內相對運動的伯努利方程具有實際意義。固體顆粒沿其軌線運動，液體則沿流線運動。固液混合物在旋轉流道出口的總能最大于入口的總能量因而，所研究的液流運動，只有從外面將能量引入固液泥合物液流中才有可能。

一、固液混合物在固定流道內的運動

研究固液混合物相對運動，即認為流道是固定的，同時混合物全體以角速度-w (此處o為流道角速度)繞軸線旋轉。因為運動是定常的，在研究它時，在每一點上必須引用向心加速度和哥氏加速度。哥氏力方向垂直于固體顆粒軌線和液體流線，所以不做功。與固液混合物單位質量有關的離心力，與其是否作用在固體顆?；蛘咭后w上無關，做功為
    流經葉輪的固液混合物流量用Q表示，固體顆粒和液體的流量分別用Q,和Q。表示，于是， 單位時間內消耗在克服固液混合物流過時流道內壓降(n- p) 的功T一Q. (p:-pi)。. 

假定在流道入口固體顆粒和和液體相對速度相問，并等于w.在流道出口它們不同，分別為UT和wo.固體顆粒和液體固體顆粒、液體和混合物的密度分別為P.P和p.在流過人口運動到出口時動能變化為

固液混合物在旋轉流道內運動時靜水頭變化。

從得到的等式中看出，在旋轉流道內靜水頭變化，等于單位重量固液混合物的壓降，與相同密度與質液體在旋轉流產內運動時的靜水頭不同之處在于，混合物的固相和液相動能差乘以固體顆粒質量濃度K和附加水力損失，在固體顆粒和液體相對速度差值不大時，與均質液體液流壓降相比，固液混合物液流壓降的減少，只與水力損失增加有關。
    第二種情況具有實際意義， 就是具有不同粒度固體顆粒的混合物液流繞軸線旋轉流逃內的運動。

    二、固液混合物在旋轉流道內的運動
    下面研究現象定性方面，即相同粒度固體顆粒在固定流道內的分布。假定固體顆粒相當小并且其速度與載體局部速度相等。假定流體流動為絮流流動，同時在重力作用下，休顆粒以等于其沉降速度W'從液體中下降，這個速度不同于顆粒在靜止水中自由下沉的沉降速度W.由于在液流中速度U的脈動作用，固體顆粒將參與絮流混合過程。
    研究兩個平行于液流運動方向的平面，它們相互處在混合路徑長度的距離上。采用處在單位體積流體內上平面區域內顆粒數量等于n,在下平面區域內為m. +On..固體顆粒從上層運動到下層，是受到重力作用和液流紊流度的雙重影響。而固體顆粒從下層運動到上層，只有依靠紊流運動才能實現。
    單位時間內經過單位面積從上層進入下層的固體顆粒數量等于n,u' +n,W'.在從液體下層到上層交換的穩定過程時，應該進人同樣數量的顆粒(n, + An,)v'=n,v' +nW'.因而，在下層和上層之間顆粒數量變化，可以根據A1/n, =W'/u'求出，這種變化表明，懸浮顆粒沉降速度越大，它們在液流中分布均勻性越差。脈沖速度v增大，將導致An,減少，因而導致固體顆粒在液流中分布更加均勻。
    當絮流中沉降速度 W變為等于脈中速度。時，比值Sn/n,=1,就是說處在上層所有顆粒下降到下層，即固體顆粒液流大部分不再懸浮，并且它們將不多加紊流混合過程。
    下面研究繞軸線施轉的流道，它垂直于縱斷面的平面。在相對運動時，液流在流道中速度等于1。固體顆粒與液體起在旋轉流道內， 例如在葉輪葉片之間空間內運動，它們處在離心力場中。加速度法向分量(在相對運動時)為
    為了估算這加速度值，給出下列吸入短管直徑為125mm挖泥深幾何多數和運動參數: "o=8m/s，斷面平均半徑R= 150mm,w= 150L/s, cosp=0.85, r,= 150mm。在這種情況下1a1 >0也就是說比重力加速度大50多倍。因此懸浮在液體中固體顆

粒的沉降速度大于混合物在固定流道中運動的速度。

在估算混合物在流道中運動所產生的水力損失，具有重要意義的是粒徑級配分為兩類的可能性:細顆粒，雖然存在很強的加速度場但仍然參加絮流混合過程:較大顆粒，在離心力場影響下，不再參加紊流交換并在液流中沿單獨軌線運動。在所有固體顆粒參加絮流交換時，固液混合物可以作為均質液體進行研究，認為在液說中的損失與密度相同的均質液體一樣。在存在不參加絮流交換過程的固體顆粒時，液體不能作為均質液體來研究，確定流道中的水力損失，必須考慮非均質液流。
  懸浮顆粒處在加速度場中，其沉降速度由下列等式確定

式中d-一粒徑;

C- 顆粒迎面阻力系數。

對于細顆粒，可以認為迎面阻力系數(報據斯托克斯定律)為

式中，v一載體運動黏度。

因此，在旋轉流道中運動的固體顆粒沉降速度為

決定已知粒徑徑固體顆粒在液流中分市特性的因素: 可以這樣估價

認為混合物液流在流道中平均相對速度為w，根據與脈沖速度的關系

對于旋轉流道中運動相似工況，液流中加速度與n2D成正比（式中，n為流道轉速，D為流道特征尺寸），而速度與nD成正比。

  假定dr是對于給定的混合物粒徑級配時顆粒界限直徑，所有粒徑d<dr的顆粒稱為細顆粒，而粒徑d>dr的顆粒稱為粗顆粒。這就意味細顆粒參加液流的紊流混合，而粗顆粒沿著完全確定的單獨軌跡運動，不參加紊流交換。
  如果沉降速度小于脈沖速度，那么顆粒就懸浮，如果沉降速度大于脈沖速度，那么顆粒就逐漸下沉?？梢约俣?，對于界限直徑的顆粒，比值Wr/v' (式中， Wr為粒徑d:顆粒的沉降速度)，即它們可以從給定層均勻地下沉，與處在懸浮狀態一樣。
  我們估算界限粒徑所采用判據之值dr n人，采用pr=2650kg/m3, Po =1000kg/m3，

對渣漿泵混合物在旋轉流道中運動特征的分析表明，在相同混合物粒徑及配對，旋轉流道中的損失不能模擬。如果模型的軸轉速等于1450r/min，而實型的轉速為600r/min，那么顆粒界限尺寸在模型試驗時比實驗小1/1.55倍。因此，利用與實際條件相同的粒徑級配固體顆粒進行模型泵試驗，不能給出有關實型泵在抽關送固液混合物時實際特性的正確概念。

應該考慮砂礫圓液混合物顆粒界限尺寸相當小。例如，如果采用泵轉速n=600r/min。即10r/s.那么d,=0.4mm.在砂礫混合物中粒徑小于0.4mm顆粒含量一般不大，所以通常不能認為在砂礫固液混合物流動時在旋轉流道中的損失與具有相同密度的均質液體的情況一樣。
    從所得到的顆粒界限尺寸判據看出，在確定dr時主要參數是流道轉速，因為用挖泥泵抽送固液混合物的載體介質黏度一般變化很小。

Relative Motion of Slurry Pump Mixture in Rotating Channel

It is of practical significance to derive Bernoulli equation for the relative motion of liquid-solid mixture in a rotating channel. Solid particles move along their tracks, while liquids move along streamlines. The total energy of solid-liquid mixtures at the outlet of the rotating channel is greater than that at the inlet. Therefore, it is only possible to introduce energy from the outside into the solid-liquid sludge flow.

I. The Movement of Solid-liquid Mixtures in Fixed Channels

The relative motion of solid-liquid mixtures is studied. It is considered that the runner is fixed and the mixtures rotate around the axis at an angular velocity of - w (where o is the angular velocity of the runner). Because motion is steady, centripetal acceleration and Coriolis acceleration must be used at every point in studying it. Coriolis force is perpendicular to solid particle trajectory and liquid streamline, so no work is done. The centrifugal force related to the unit mass of a solid-liquid mixture has nothing to do with whether it acts on solid particles or liquids.

The flow rate of solid-liquid mixture through impeller is expressed by Q, and the flow rate of solid particles and liquid is expressed by Q, and Q, respectively. Thus, work T-Q. (p:-pi) is consumed per unit time to overcome the pressure drop (n-p) in the outdated flow passage of solid-liquid mixtures. .

It is assumed that the relative velocities of solid particles and liquids at the entrance of the runner are interrelated and equal to w. They are different at the exit of the runner. The densities of solid particles and liquid solid particles, liquids and mixtures are P.P and P.

Static Head Change of Solid-liquid Mixture in Rotating Channel

From the equation obtained, it can be seen that the change of static head in the rotating channel is equal to the pressure drop of solid-liquid mixture per unit weight. The difference between the static head of the same density and mass liquid moving in the rotating abortion is that the kinetic energy difference between the solid phase and the liquid phase of the mixture is multiplied by the mass concentration of solid particles K and the additional hydraulic loss in the solid phase. When the relative velocity difference between particles and liquids is small, the pressure drop of solid-liquid mixture decreases only because of the increase of hydraulic loss compared with that of homogeneous liquid.

The second case has practical significance, that is, the liquid flow of mixtures with different particle sizes flows around the axis of rotation to escape.

2. The Movement of Solid-liquid Mixture in the Rotating Channel

The following qualitative aspects of phenomena are studied, i.e. the distribution of solid particles with the same particle size in a fixed channel. It is assumed that the solid particles are fairly small and their velocities are equal to the local velocities of the carrier. It is assumed that the fluid flow is a flocculating flow, and that under the action of gravity, the suspended particles decrease from the liquid at a settling velocity equal to W', which is different from the settling velocity W of particles in stationary water. Because of the pulsation of velocity U in the liquid flow, the solid particles will participate in the flocculating mixing process.

Two planes parallel to the direction of fluid flow are studied. They lie at the distance of the length of the mixing path. The number of particles in the upper plane region of a unit volume fluid is equal to n, and in the lower plane region is m. +On.. The movement of solid particles from the upper layer to the lower layer is influenced by gravity and turbulence. The movement of solid particles from the lower layer to the upper layer can only be achieved by turbulent motion.

The number of solid particles per unit time passing from the upper layer to the lower layer is equal to n, u'+n, W'. In the stable process of exchange from the lower layer of liquid to the upper layer, the same number of particles (n,+An,) v'=n, v'+nW'. Therefore, the change of the number of particles between the lower layer and the upper layer can be calculated according to A1/n,= W'/u'. The results show that the larger the settling velocity of suspended particles, the worse the uniformity of their distribution in liquid flow. The increase of pulse velocity V will lead to A and decrease, which will lead to more uniform distribution of solid particles in liquid flow.

When the settling velocity W in the flocculation becomes equal to the velocity in the pulse. When the ratio of Sn/n is equal to 1, that is to say, all the particles in the upper layer descend to the lower layer, that is, most of the solid particles are no longer suspended, and they will not add much turbulent mixing process.

Next, we study the flow path running around the axis, which is perpendicular to the plane of the longitudinal section. In relative motion, the velocity of liquid flow in the channel is equal to 1. Solid particles and liquids move in a rotating channel, such as in the space between impeller blades, and they are in the centrifugal force field. The normal component of acceleration (in relative motion) is

In order to estimate this acceleration value, the following geometric majority and movement parameters of the dredging depth with the diameter of the suction short pipe 125 mm are given: "o = 8 m/s, the average cross-section radius R = 150 mm, w = 150 L/s, cosp = 0.85, r, = 150 mm". In this case, 1A1 > 0 is more than 50 times the acceleration of gravity. So solid particles suspended in liquids

The settling velocity of particles is faster than that of mixture moving in a fixed channel.

In estimating the hydraulic loss caused by mixtures moving in the channel, it is important to divide the particle size distribution into two categories: fine particles, although there is a strong acceleration field, still participate in the flocculation mixing process: larger particles, under the influence of centrifugal force field, no longer participate in turbulent exchange and along a single trajectory in the fluid flow. Sports. When all solid particles participate in flocculation exchange, solid-liquid mixtures can be used as homogeneous liquids. It is considered that the loss in liquid theory is the same as that in homogeneous liquids with the same density. When there are solid particles which do not participate in the flocculation exchange process, the liquid can not be studied as homogeneous liquid. To determine the hydraulic loss in the channel, the heterogeneous liquid flow must be considered.

The settling velocity of suspended particles in acceleration field is determined by the following equation

D-1 particle size in the formula;

C- particles