Fluidisational velocity, resistance of permeable material layer

Transcription

1 Fluidisational velocity, resistance of permeable material layer Fluidisation is a process whereby a granular material is converted from a static solidlike state to a dynamic fluid-like state. This process occurs when a fluid (liquid or gas) is passed up through the granular material. When a gas flow is introduced through the bottom of a bed of solid particles ( mm grain size), it will move upwards through the bed via the empty spaces between the particles. At low gas velocities, aerodynamic drag on each particle is also low, and thus the bed remains in a fixed state. Increasing the velocity, the aerodynamic drag forces will begin to counteract the gravitational forces, causing the bed to expand in volume as the particles move away from each other. Further increasing the velocity, it will reach a critical value (v fmin ) at which the upward drag forces will exactly equal the downward gravitational forces, causing the particles to become suspended within the fluid. At this critical value, the bed is said to be fluidized and will exhibit fluidic behavior. By further increasing gas velocity, the bulk density of the bed will continue to decrease, and its fluidization becomes more violent, until the particles no longer form a bed and are conveyed upwards by the gas flow. (Source: Figure 1: Pressure drop of the material layer v.s. fluidisational velocity Figure 1 depicts an idealised example diagram of the pressure drop ( p) of the gas flowing through the granular layer as a function of its fluidisational velocity (v f ). The curve can be dissected into three regions as follows. 1.) In the velocity region v f < v fmin the material grains are stationary, the pressure drop is directly proportional with the gas velocity. The behaviour is not valid in case of extremely small grain sizes (< 10 mm). 2.) The loosening of the material layer begins near v fmin. The pressure drop in this region (v fmin < v f < v fmax ) is equal with the weight of the particle over a unit area. This may be formulated as follows:

2 p = In Equation 1: V a ( ρ m ρ g )g A ( = 1 ε )V ( ρ m ρ g )g = ( 1 ε) ( ρm ρ A g ) g h Equation 1: Pressure drop of the fluidised layer A [m 2 ] h [m] V [m 3 ] ρ m [kg/m 3 ] ρ g [kg/m 3 ] - the cross section area of the fluidised material layer - height of the material layer - the volume of the theoretical cylinder containing the material layer - density of the solid material - density of the gas ε = V g V = V g V m + V g [-] - porosity of the gas-solid mixture g [m/s 2 ] - gravitational acceleration The porosity is higher at v fmin than in the steady state of the material due to the extension of the material layer described before. 3.) At gas velocity above v fmax the conveying of the grains from the container begins. Measurement exercise The minimum fluidisational velocity of the granulate phase is a unique physical property which will be determined experimentally. This can be done by determining the characteristic curve of the material as seen in Figure 1. The measurement assembly is depicted in Figure 2. The gas is provided by a fluidmachine G (fan, blower or a compressor). The volume flow can be adjusted using valve SZ and measured using the rotameter R (the working principle of a rotameter is briefly described at the end of this preparational document). The fluidisational container K is a transparent tube with a height of L and a diameter of D which contains the material to be examined. The material has to be filled in at closed valve SZ position. The initial layer thickness has to be approximately h 0 = D. The steady material layer height h 0 can be measured after the material layer is slightly loosened by opening the valve SZ and closing it shortly afterwards. This produces a more or less horizontal material layer surface which is easy to examine. The uniform flow of the gas through the material layer is provided by the distributing layer E. The properties and quality of the distribution layer are chosen according to the properties of the particulate material. The pressure inside the fluidisational container K under the distribution layer is measured using a U-tube manometer. The measurement medium in the manometer has to be chosen according to the properties of the solid material and the distribution layer (in the present case it is water).

3 Figure 2: Measurement assembly of fluidisation Prior to the measurement, a volumetric flow rate of the air has to be found by observation at which the whole material layer is fluidised. This helps the accurate measurement of the velocity region around v fmin. Approximately 20 volume flow values are to be measured according to Table 1. No. Q h 01 h 02 p 0 h 1 h 2 p p m v f h [mm] [mm] [Pa] [mm] [mm] [Pa] [Pa] [m/s] [m] Table 1: Header of the measurement table After measuring the common pressure drop p of the distribution and material layer, the pressure drop of the cleaned distribution layer p 0 has to be measured. The characteristics of p 0 can be determined similarly to p.

4 Measurement data evaluation The measured data have to be processed in order to determine a diagram similar to that in Figure 1. In the laboratory only a control diagram has to be drawn to exclude crude errors. These are the deflection differences of the U-tube manometer with the clean distribution layer h 0 (Q), the deflection with the material- and distribution layer together h(q) and the material layer height h(q). The complete diagram has to be prepared at home. The steps to determine the curve are described in detail here. Following these the curve must be drawn and alongside with a lab report it has to be submitted within a week after the measurement session. The steps are as follows (Figure 3). Step 1.: Determine the slope of the distribution layer pressure drop vs. velocity using the method of least squares. By fitting a straight line going through the origin of the diagram the slope can be calculated. This yields the function p(v f ). Step 2.: Separate the two regions of the common pressure drop and decide which measured points belong to the stationary region (region 1) and the fluidisation region (region 2). This can be done by observing the point where a change in the curve slope occurs. Step 3.: Calculate the slope of the line laid on the points in region 1 similarly to Step 1. The fitted line has to go through the origin of the diagram. Step 4.: We assume that our material being an ideally fluidisable material after being fluidised, the rate of pressure change is identical with the pressure change of the distribution layer. Therefore we approximate the measurement points with a line that has the same slope as the distribution layer pressure drop and goes through the center of mass point of the measurement data in region 2. Step 5.: Calculating the intersection point of the lines determined in Step 3 and Step 4 v fmin can be determined. Step 6.: Subtracting the equation of the line describing the distribution layer from both sections of the common pressure loss curves we obtain the required fluidization curve. Figure 3: The steps to determine the pressure drop vs. fluidisation velocity curve of the material layer

5 Data and formulae D = 70 mm ρ v =1000kg/m 3 ρ Hg =13600kg/m 3 0 ( ) v p = h 01 h 02 ρ g [Pa] h 01, h 02 [m] ( ) v p = h 1 h 2 ρ g [Pa] h 1, h 2 p m = p p 0 - internal diameter of the fluidisational container - water density - mercury density - pressure drop of the distribution layer - deflection of the U-tube manometer with clean distribution layer - common pressure drop of the material- and distribution layer - deflection of the U-tube manometer with material layer measurement - pressure drop of the material layer v f = Q A = Q 2 D π 4 - fluidisational velocity Measurement preparations During the measurement 3 pieces of A4 size, previously prepared sheets are needed for calculations. A sample sheet is provided alongside with this document. Additionally an A4 sized mm paper is needed for the fluidisation diagram. The laboratory reports must contain the figure of measurement setup drawn by hand, the short description of the measurement exercise and the formula to be used. Before the measurement one of the control questions will be asked. The answer will be taken into account later in the lab report evaluation. Control questions 1. Sketch the measurement assembly, mark the different parts and characteristic measures! 2. Describe the measurement procedure. 3. Describe the method of determining the fluidisation curve. 4. Using the provided data calculate the porosity! Data: h 0 = 136 mm; h = 10%; p = 102 mmwc; ρ m = 1300 kg/m 3 ; ρ g = 1.25 kg/m 3

6 Working principle of rotameter "A rotameter consists of a tapered tube, typically made of glass, with a float inside that is pushed up by flow and pulled down by gravity. At a higher flow rate more area (between the float and the tube) is needed to accommodate the flow, so the float rises. Floats are made in many different shapes, with spheres and spherical ellipses being the most common. The float is shaped so that it rotates axially as the fluid passes." Source:

7 2009 / 2010 Measurement for Chemical and Environmental Processes Fluidisation Date Name, Neptun code