PC-Based Teaching Tools for Fluid Mechanics

PC-Based Teaching Tools for Fluid Mechanics S. U. Rahman *, N. M. Tukur and I. A. Khan Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran-31261, Kingdom of Saudi Arabia Abstract In this work an interactive teaching tool in the form of virtual fluid mechanics laboratory has been developed. This lab consists of four experiments dealing with losses in piping systems, flow meters, packed and fluidized beds. The labs can be run on any PC running a 32-bit operating system and could be made available through Internet. With the ability to vary different parameters in the experiments, students can develop an intuitive sense of cause-and-effect. Keywords Virtual laboratory, Fluid Mechanics, Engineering education INTRODUCTION The advancement in the fields of computers and information technology have influenced every sphere of human life, education and training are no exception. As the microcomputer gained popularity, a plethora of computer programs have appeared to help teachers educate students from kindergarten to postgraduate schools. These computer programs, often termed as teaching tools, are commercially available either with textbooks or as independent products. Virtual laboratory is relatively a newer concept, which essentially is a computer program that allows students to run simulated experiments. The benefit of a virtual lab as a teaching tool is evident. The installation, running and maintenance cost of chemical engineering teaching laboratory are usually high. Once a real experiment is installed, it is difficult to modify it. It limits the students to performing experiments within a narrow range of parameters. In addition, experiment running time is too long to repeat a run or to vary parameters in a bigger range. A simulated laboratory removes these difficulties allowing students to perform virtual experiments effortlessly on a microcomputer. In fact, one can create situations, which are impossible in real life but are pedagogically important. Once a virtual laboratory is installed on a website, more students can benefit. Students can perform experiments from any location and at any time. The ease of running allows them to repeat an experiment with varying parameters, exploring what would happen under different scenarios. Readily available multimedia based help enhances the basic understanding of the subject. The students can learn the basic concepts without getting * Coressponding author (E-mail: srahman@kfupm.edu.sa ) 1

lost into performing details of a real experiment. A virtual laboratory will prove useful for students, those who have access to a real laboratory and those who do not. Virtual labs provide students with the means to use laboratories on a 24-hour basis. They also help to overcome as well, experiment-related hazards and safety concerns and therefore could be used for practicing before running actual experiment. Besides, rarely are traditional laboratories truly interactive. A student conducts a series of pre-planned experiments and heads home to perform the analysis. This experience does not leave the students with an intuitive feel for the nature of the process. These shortcomings can be overcome through proper use of computer-based experiments. Some prototype virtual laboratories are already opened to users via the Internet e.g., the physics virtual lab at the University of Oregon [1], and the oscilloscope experiment at the Electrical Engineering Department of the National University of Singapore [2], among others. The Centre for Water Research, Department of Environmental Engineering at the University of Western Australia has a virtual lab for Fluid Mechanics [3], where students conduct experiments and write their reports online. In the chemical engineering discipline, efforts have been made in this direction. The chemical engineering department at John Hopkins University has a lab at their website [4] where students are trained in virtual experimentations. A number of chemical engineering virtual experiments have also been created by the Purdue University [5-11]. Additionally, a host of computer-based process simulation packages (e.g. Aspen plus, Pro Vision, HYSYS) are now commonplace in most modern Chemical Engineering curriculum, although these software were not designed as teaching aids. WHAT HAS BEEN DONE? We have created a PC-based teaching tool for Virtual Fluid Mechanics Laboratory. Presently, it consists of four important experiments of process fluid mechanics currently taught in one of the laboratory courses at KFUPM. The experiments were written in Microsoft Visual Studio version 6.0, and the multimedia based help files were developed using macromedia flash 5.0. The experiments can be run on any PC with a 32-bit operating system (e.g. Windows Me, Windows 98 or 95, Windows NT) with a display capability of at least 256 colors. The first experiment is on losses in piping systems. In this experiment, pressure loss measurements are carried out as a function of flowrate on seven (7) pipe components namely;straight Pipe, Sudden Expansion, Sudden Contraction, Standard Elbow Bend, 90 o Mitre Bend, Globe Valve, and Gate Valve. The second experiment has as its objective the study of some of the more common flow meters, in particular, Pitot Tube, Venturimeter, and Orifice plate. 2

While the third and fourth experiments deal with flow through packed and fluidized beds respectively. The main objective is to investigate the relationship between flowrate and the pressure drop through the beds. [3] EXPERIMENTS Once the software is installed, the option window appears upon clicking the software link. It allows one to select among six (6) laboratories which to run. Figure 1 is a snap shot of the option window. Once a specific lab is selected, the main window of that particular lab shows up. The main window of each of the lab is where virtual experiments are run. The main windows are designed to be highly interactive, with enhanced multimedia features. Figure 1: The Virtual Lab Interface 3

EXPERIMENT # 1: LOSSES IN PIPING SYSTEMS One of the most common problem in fluid mechanics is the estimation of pressure loss. Pipe losses in a piping system result from a number of system characteristics, which include among others; pipe friction, changes in direction of flow, obstructions in flow path, and sudden or gradual changes in the cross-section and shape of flow path. In this experiment, pressure loss measurements are made as a function of flowrate on seven (7) pipe components namely;straight pipe, sudden expansion, sudden contraction, standard elbow bend, 90 o mitre Bend, globe valve, and gate valve. The display in Figure 2 shows the main window when the losses in piping systems experiment is selected. One can then select the component of interest to run.. Figure 2: Losses in piping Systems Main Window 4

For experiment #1, the straight pipe virtual experiment is selected to demonstrate how to run the virtual lab. But first of all, a brief theoretical background to flow through straight pipe is given. When a fluid flows inside a pipe, fluid elements in the center of the pipe will move at a higher speed than those closer to the wall. This movement of fluid elements relative to each other is associated with pressure drop, called friction losses or viscous losses. At low flow rates, the pressure drop per unit length is proportional to the volumetric flow rate (laminar region). At intermediate flow rates, there is a region where the experimental results are not reproducible (transient region). Finally, at very high flow rates, the pressure drop becomes proportional to the flow rate raised to a power, which varies from 1.8 to 2.0 (turbulent regime) [15]. Knowledge of the magnitude of viscous losses is of great importance because it determines the power requirements of the pump forcing the fluid through the pipe. For example, in refining and petrochemical industries, these losses have to be calculated accurately to determine where booster pumps have to be placed when pumping crude oil or other fluids in pipes to distances thousands of kilometres away. Using dimensional analysis, it is possible to show that flow in smooth pipes is a function of only two dimensionless groups, the Reynolds number and the friction factor. D v ρ Re = (1) η p D = (2) 2ρ v L f 2 In smooth pipe, the friction factor-reynolds number relationship for laminar region is: 16 f =, for Re < 2100, laminar (3) Re In the range 4000 < Re < 10 5, the relationship follows closely the Blasius equation: 1 / 4 f = 0.079 Re, for 4000 < Re < 10 5, turbulent (4) The Blasius equation is purely an empirical equation and has no theoretical basis, but it is a convenient form for application. The entire turbulent region can be represented by the von Kármán-Nikuradse equation: 1 f ( Re ) 0. 4 = 4.0 log f 10, for Re > 4000, turbulent (5) 5

The Virtual Experiment: When the Flow in Straight Pipe virtual experiment is selected, a display similar to Figure 3 below appears: Figure 3: Straight Pipe Virtual Experiment Main Window The flow control valve is opened to allow water to flow through the test pipe. The Rotameter on the left hand side gives the value of the flow rate. While the corresponding pressure drop readings are indicated on the pressure gauge. One is expected to specify the pipe and fluid specifications via the 'View Specs' button. Default values have already been entered. Users can adjust the values by deleting existing values and typing new ones. Once the pipe and fluid specifications are entered, flowrate can be varied via the flow control valve. The valve is located near the entrance of the pipe. The positive (+) and the negative signs (-) are used to increase or decrease the flow rate respectively. As the experiment is run by increasing the flow rate, data are generated which can be retrieved via the 'View Data' button. A sample data is shown in Figure 4 below. 6

Figure 4: Sample Data Plot of friction factor versus Reynolds number can be seen via the 'View Plot' button. Sample plot is shown in Figure 5 below. 7

Figure 5: Sample Plot EXPERIMENT # 2: FLOWMETERS Expansion and contraction losses can be exploited to measure volumetric flow rate. For example, an orifice meter consists of a plate with a hole in the center that is placed between flanges of two adjoining sections of pipe. The fluid contracts and then expands as it moves through the orifice and this results in a pressure drop across the orifice, which can be measured. The magnitude of the pressure drop can be related to the volumetric flow rate. This is also the case with the other flow meters to be studied in this experiment, venturimeter and Pitot tube. Venturi meter, orifice meter, and Pitot tube are widely used as flow measuring devices in the industry. The Pitot-static tube is the standard device for measuring airspeed of airplanes [15], and is often used for measuring the local velocity in pipes or ducts. One can easily identify the Pitot-static probes projecting form the front of modern commercial airplanes. For measuring flow in enclosed ducts or channels, the Venturi meter and orifice meters are more convenient and more frequently used. The Venturi is widely used particularly for large volume liquid and gas flows since it exhibits little pressure loss. However, for smaller pipes orifice meter is a suitable choice. Pitot Static Tube: Pitot-Static tube is an instrument for measuring velocity by means of pressure measurement. It is assumed that the presence of the tube will not affect the upstream flow field. It consists of an inner tube, which is open at the end, and outer tube that is sealed at the end but contains several openings along the side. Each tube is filled with the flowing 8

fluid, and the tubes are connected to a manometer. By applying Bernoulli s equation to the streamline leading to the stagnation point (tip of the inner tube where the velocity is zero) leads to an equation of the following form [14]: V 1 ( p ) 2 2 p3 = (6) ρ where, p 2 is the stagnation pressure, while p 3 is the pressure acting on the side holes in the outer tube, so it is the pressure of the fluid in the outer tube. Thus, the manometer measures directly the pressure difference and hence the velocity. Orifice meter: An orifice is a flat plate with a centrally drilled hole machined to a sharp edge. The orifice plate is inserted between two flanges perpendicularly to the flow, so that the flow passes through the hole with the sharp edge of the orifice pointing to the upstream. The relationship between flow rate and pressure drop can be determined using Bernoulli s equation as: ( p1 p2 ) 2 ( A / A) 2 Q = Co Ao (7) ( 1 )ρ where, Q is the volumetric flow rate, A o is the orifice cross sectional area, A is the pipe cross-sectional area, p 1 and p 2 are the pressure measured at the upstream and downstream and C o is the orifice coefficient, which has a value of approximately 0.62. Venturi meter: One of the disadvantages of orifice meters is the large irreversible pressure loss across the orifice, which results in substantial pumping costs in case of large diameter pipes. However, the same principle can be exploited with only minimal pressure loss with the use of a Venturi meter. In this case, the meter consists of a section with both a smooth contraction and a smooth expansion. Because of the smoothness of the contraction and expansion, the irreversible pressure loss is low. However, in order to obtain a significant measurable pressure drop, the downstream pressure tap is placed at the throat of the meter; i.e., at the point of the smallest diameter. The equation relating flow rate to pressure drop is the same as equation (7) except that the value of the coefficient is about 0.98 for a well-designed Venturi. o The Virtual Experiment: When the Flowmeters virtual experiment is selected, a display similar to Figure 6 appears. 9

Figure 6: Flowmeters Main Window The flow control valve is opened to allow water to flow through the different flow meters. The Rotameter on the left hand side gives the value of the flow rate. While the corresponding pressure drop readings are indicated on the pressure gauge. One is expected to specify the flow meters and fluid specifications via the 'View Specs' button. Default values have already been entered. Users can adjust the values by deleting existing values and typing new ones. As the experiment is run by increasing the flow rate, data are generated which can be retrieved via the 'View Data' button. Plots of pressure drop (delp) versus flowrate(q) are also generated. They can be viewed via the 'Plot delp vs Q' button. EXPERIMENTS 3 AND 4:PACKED & FLUIDIZED BEDS Flow in packed beds is a subject of great interest to chemical engineers for their importance in fluidized-bed catalytic cracking, which is a standard petroleum refining operation. As fluid moves between the individual packed particles, it experiences friction at the surface of the packing as well as numerous changes in direction. This results in a drag force, which manifests itself as a pressure drop across the bed [13]. In this 10

experiment, the fluid flow rate is varied and the corresponding effect on the pressure drop is observed. Fluidized beds are packed beds where the fluid flows upwards over the packing at highenough velocity to suspend the solid particles, and the two-phase mixture behaves very much like a liquid. The most important parameters in packed and fluidized beds are the particle diameter, Dp, the superficial velocity, v, and the void fraction, ε. Superficial velocity is the flow rate through the bed per unit area. The void fraction is the volume fraction of the packed bed that is not occupied by the packing material. Ergun s equation is generally used to relate pressure drop across the bed and superficial velocity: Where, f p 150 f p + 1.75 (8) Re = p 3 D pε p = and 2 ρv (1 ε L ) Re D = p v p ( 1 ε )η p. In the Ergun s equation, the first term dominates at low Reynolds number while the last term is dominant in turbulent regime [14]. According to this equation, pressure drop across a packed bed increases with increasing flow rate. This continues until the superficial velocity reaches a point where the product of the bed s cross sectional area and the pressure drop equals the gravitational force exerted on the mass of the bed particles. At this point, the incoming fluid is able to lift the solids, resulting in marked expansion in the bed volume, and the solid particles become individually suspended. The superficial velocity of the fluid at this point is called the minimum fluidizing velocity, v mf. As the superficial velocity is increased further beyond this point the pressure drop does not significantly change. Two expressions for the minimum fluidizing velocity can be obtained, one at low Reynolds number (Re P <10) and the other at high Reynolds number (Re P >1000): ( ρ ρ ) 2 3 p f g D p ε v mf = (9) 150η (1 ε) v mf D = p 3 ( ρ ρ ) ε p 1.75 ρ f f g 1 / 2 (10) The Virtual Experiment: 11

When the flow through packed beds or fluidization experiment is selected, a display similar to Figure 7 appears. Figure 7: Packed Beds Main Window The flow control valve is opened to allow liquid to flow through the packed beds. The Rotameter on the left hand side gives the value of the flow rate. While the corresponding pressure drop readings are indicated on the pressure gauge. One is expected to specify the bed, particle and fluid specifications via the 'View Specs' button. Default values have already been entered. Users can adjust the values by deleting existing values and typing new ones. Once the bed, particle and fluid specifications are entered, flow rate can be varied via the flow control valve. And the corresponding pressure drop readings are indicated on the pressure gauge. 12

Plots of pressure drop (delp) versus flow rate(q) and fp vs. Rep can be obtained from the data generated. [4] CONCLUSIONS Using Microsoft Visual Studio, we have designed an interactive teaching tool for fluid mechanics experiments. Four experiments have been added to the virtual lab consisting of packed and fluidized beds, flow in smooth pipe and flowmeters. The virtual experiments will help students understand the fundamentals of fluid flow and provide a novel method of learning new processes and concepts. More experiments will be added to the software covering such areas as Heat Transfer, Mass Transfer, Unit Operations, Process Control and Reaction Kinetics as soon as additional support is secured. ACKNOWLEDGEMENT The authors wish to acknowledge the use of information and facilities of the King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia and financial support through the Academic Development Center of the same university. REFERENCES [1] http://jersey.uoregon.edu/vlab/index.html [2] http://vlab.ee.nus.edu.sg/vlab. [3]http://www.cwr.uwa.edu.au/cwr/teaching/fmLabs/fm_labs.html [4] http://www.jhu.edu/~virtlab/virtlab.html [5] Squaires, R. G., G. V. Reklaitis, N. C. Yeh, J. F. Mosby, I. A. Karimi, and P. K. Anderson, Purdue-Industry Computer Simulation Modules: The Amoco Resid Hydrotreater Process, Chem. Eng. Ed., 25(2), 98 (1991). [6] Squaires, R. G., P. K. Anderson, G. V. Reklaitis, S. Jayakumar, and D. S. Carmichael, Multimedia-Based Educational Applications of Computer Simulations of Chemical Engineering Processes, Comp. Appls. In Eng. Ed., 1(1), 25 (1992). [7] Jayakumar, S., R. G. Squaires, G. V. Reklaitis, P. K. Anderson, K. R. Graziani, and B. C. Choi, The Use of Computer Simulations in Engineering Capstone Courses: A Chemical Engineering Example-The Mobil Catalytic Reforming Process Simulation, Internat. J. of Eng. Ed., 19(3), 243 (1993). 13

[8] Jayakumar, S., R. G. Squaires, G. V. Reklaitis, P. K. Anderson, and L. R. Partin, Purdue-Industry Computer Simulation Modules 2: The Eastern Chemical Reactive Distillation Process, Chem. Eng. Ed., 27(2), 136 (1993). [9] Jayakumar, S., R. G. Squaires, G. V. Reklaitis, P. K. Anderson, and B. K. Dietrich, The Purdue-Dow Styrene-Butadiene Polymerization Simulation, J. Eng.Ed., 84(3), 271(1995). [10] Jayakumar, S., R. G. Squaires, G. V. Reklaitis, K. S. Grassi, Simulating the Air Products Cryogenic Hydrogen reactive cooling Process, Chem. Eng. Ed., 29(1), 26 (1995). [11] Squaires, R. G., K. Kuiyan, S. Jayakumar, G. V. Reklaitis, M. Evans, B. Morrato, and R. Gutwein, The Procter and gamble Decaffeination Project: A multimedia Instruction Module, Comp. Appls. in Eng. Ed., 4(4), 269 (1996). [12] Waller, J. C., and N. Foster, Training via the Web: A Virtual Instrument, Computers & Education, 35, p. 161-167, 2000. [13] Thomson, W. J., Introduction to Transport Phenomena, Prentice-Hall, Inc., Upper Saddle River, N. J., 2000. [14] Denn, M. M., Process Fluid Mechanics, Prentice-Hall, Inc., Englewood Ciffs, N. J., 1980. [15] de Nevers, N., Fluid Mechanics for Chemical Engineers, McGraw-Hill, Inc., Singapore, 1991. 14