CONSIDERATIONS IN BUILDING AND USING DREDGE SIMULATORS

Transcription

1 CONSIDERATIONS IN BUILDING AND USING DREDGE SIMULATORS S.A. Miedema ABSTRACT. INTRODUCTION. THE EDUCATIONAL SIMULATOR. THE TRAINING SIMULATOR. THE PREDICTION SIMULATOR. THE PREPARATION SIMULATOR. THE RESEARCH SIMULATOR. THE DREDGE DESIGN SIMULATOR. THE MOTIONS OF THE DREDGE. THE BANK PROFILE. THE CUTTING PROCESS. THE HYDRAULIC TRANSPORT PROCESS. WORKING METHODS AND OPERATIONAL ASPECTS. CONCLUSIONS. REFERENCES. ABSTRACT. Dredge simulators, like simulators in general, are developed with the purpose of simulating real time processes. This may have different reasons: 5. Education Training Prediction Preparation Research file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (1 of 28) [30/4/ :15:07]

2 6. Dredge design The following aspects can be distinguished when designing a simulator for a hydraulic dredge:. b. c. d. e. The motions of the dredge The bank profile, including geometry and soil characteristics The cutting process The hydraulic transport process Working methods and operational aspects This paper takes into consideration the above-mentioned aspects, gives some examples of the mathematical modeling, user interfaces and presentation of the results. INTRODUCTION. When designing a simulator, the first question that should be asked is, what will be the purpose of the simulator. Will it be a simulator for educational purposes, for training of the staff, for the prediction of the dredging process, for preparing a dredging job, for research or for dredge design? The characteristics of the simulator may differ depending on the purpose. It could be possible that not all targets can be met with one and the same simulator. To find out the requirements for the simulator, the purpose of the simulator has to be analyzed. The following analysis is not complete, but gives an impression of different aspects that have to be taken into consideration to show some of the differences between simulators as they should be developed for the different purposes mentioned. In practice however, it often occurs that first a simulator is developed and afterwards the purpose of the simulator is changed, resulting in misuse or no use at all. One should take into consideration that the analysis has been made through the eyes of a scientist. The educational simulator The educational simulator is considered to be a simulator for higher education (B.Sc. or MSc). This type of education requires knowledge of the physics of the dredging processes and a system approach of the equipment and the use of the file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (2 of 28) [30/4/ :15:07]

3 dredge. Dredging processes in a steady state situation can be described mathematical and are not to difficult to solve manually. An example of this is the determination of pipeline resistance in a straight pipeline under steady state conditions, constant flow, constant density, constant grain distribution and constant pump revolutions. When these parameters are not constant and when the hydraulic system consists of more then one pump the system gets to complicated to solve manually. It is however of interest to the engineer to know the dynamical behavior of the dredging system. To see how the different system components interact. To see the dredging limitations in a non-steady state situation. Often problems occur after a certain time. For instance, when a high-density mixture is formed in the cutterhead, sedimentation will not occur immediately. Cavitation of the ladder-pump or main-pump may occur almost instantly, but cavitation of a booster pump may occur after minutes. It is thus very important to anticipate. Figure 1 shows the most important pump parameters. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (3 of 28) [30/4/ :15:07]

4 Fig. 1: The display of the most important pump parameters It is very important to first formulate educational targets, then design an educational program and depending on the targets and the program design, develop a simulator. The main targets are: Teach the different dredging processes individually Teach the dependency of the different dredging processes (system approach) Teach working methods and operational aspects Teach dredge limitations The use of the educational simulator requires: Console and user interface A student and an instructor console, so the instructor can follow the student and interact if necessary Easy to learn and use the simulator, since students have limited time The console and user interface should be focussed on the dredging processes and less on the operations Educational program A well trained instructor Available standard scripts, so the results of different students can be compared Available standard scripts, so predetermined situations can be simulated Mathematical modeling The dredging processes as implemented in the simulator should give correct tendencies, but do not need to be very detailed The simulator has to operate real-time file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (4 of 28) [30/4/ :15:07]

5 The results have to be reproducible when using standard scripts Results and responses Output in relation to input (logging) Output of the cutting process Output of the hydraulic transport process The training simulator The training simulator is considered to be a simulator for training staff members the operations of a dredging vessel. These operations include controlling the pumps, the cutterdrive and the winches, lowering and hoisting the ladder, moving the spud carriage, etc. The student has to learn the function of joysticks, buttons, etc. on the console and has to know how to interpret the different displays. This type of simulator requires that the students have a view from the bridge using video, like in reality. It is also important that the student is able to anticipate on the consequences of his actions, because of time effects. Working methods like dredging a slope or profile, working with spuds and spud carriage, the placement of anchors, etc. are very important for dredge operators. Figure 2 shows the most important operational parameters. The main targets are: Teach the use of console and user displays Teach the response of the dredge on the actions taken Teach and practice the operations of the dredge. Teach working methods and problems file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (5 of 28) [30/4/ :15:07]

6 Fig. 2: The display of the winch, operational and slurry parameters. The use of the training simulator requires: Console and user interface The console and the user interface should match those on the dredge Video facilities should be available There should be an instructors console file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (6 of 28) [30/4/ :15:07]

7 The instructor should be able to monitor the student and influence the dredging process Educational program The educational program focuses on the operational aspects, working methods and problems that may be encountered during dredging A well trained instructor is required Mathematical modeling The simulator has to operate real-time The mathematical modeling of the dredging processes does not have to be detailed, but has to show correct tendencies The mathematical modeling should focus on operational aspects The instructor has to be able to interact Results and responses Especially the man-machine interface actions have to be recorded The display of results and responses should match those on the dredge The instructor requires additional output The prediction simulator The prediction simulator is considered to be a simulator for the prediction of production and for determining dredging limits, like sedimentation in the pipeline and the bulldozer effect on the cutterhead. The prediction simulator has to be operated by a production engineer on regular bases. Since in general with software the rule 'garbage in garbage out' is valid, the production engineer requires knowledge of the dredging processes and working methods. Figure 3 shows an on-screen console. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (7 of 28) [30/4/ :15:07]

8 Fig. 3: The display of an on-screen console, this console has the feature of activating scripts. The main targets are: Predict production Predict the occurrence of process limits Predict the behavior of the dredging processes in time The use of the prediction simulator requires: file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (8 of 28) [30/4/ :15:07]

9 Console and user interface Console and user interface can be combined on one PC (on-screen console) The simulator should be controlled by scripts in combination with manual control Educational program There does not have to be an educational program There has to be a specialist working on a regular basis on the simulator Scripts with standardized working methods have to be available Standardized sets of soil mechanical parameters have to be available Mathematical modeling Detailed mathematical modeling of the dredging processes Detailed mathematical modeling of the bank Less detailed modeling of working methods and operations Possibility to play scripts Results and responses Different parameters as a function of time Statistical values of different parameters Detection of dredging limits The preparation simulator The preparation simulator is considered to be a simulator for preparing dredging projects. Usually when starting a dredging job the operators have to learn how to optimize the working methods for that specific job. If it would be possible to carry out this learning process on a simulator, time would be saved. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (9 of 28) [30/4/ :15:07]

10 The main targets are: Simulate a dredging project Speed up the learning curve of a project on site Detect possible problems The use of the preparation simulator requires: Console and user interface Console and user interface see the training simulator (examples fig. 4 and 5) Display of survey data Fig. 4: The display of the back view of the cutterdredge, also showing the cross-sectional channel profile. Educational program There does not have to be an educational program Training of the dredge operator on a training simulator is required Scripts with standardized working methods have to be available Standardized sets of soil mechanical parameters have to be available file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (10 of 28) [30/4/ :15:07]

11 Mathematical modeling The simulator has to operate real-time The mathematical modeling of the dredging processes does not have to be detailed, but has to show correct tendencies Survey data of real projects have to be able to be used The mathematical modeling should focus on operational aspects Results and responses The display of results and responses should match those on the dredge Additional output in relation to optimization has to be available Survey data has to be made visible Fig. 5: The display of the side view of the cutterdredge, also showing the longitudinal channel profile. The research simulator The research simulator is considered to be a simulator for carrying out desk research on dredging processes and systems. Basic processes can be solved manually, but as soon as the different processes interact and the system starts behaving dynamically it is preferred to use simulation software. Figures 1 to 6 show a combined user-interface and console, including the script feature. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (11 of 28) [30/4/ :15:07]

12 The main targets are: Simulating complex process behavior Simulating complex system behavior The use of the research simulator requires: Console and user interface Console and user interface can be combined on one PC (on-screen console) The simulator must have the ability to be controlled by scripts The simulator must have the ability to be controlled manually An instructors console is not required Educational program There does not have to be an educational program There has to be a specialist working on a regular basis on the simulator There has to be a detailed programmers manual file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (12 of 28) [30/4/ :15:07]

13 Fig. 6: The display of the top view of the cutterdredge, also showing the channel. Mathematical modeling Detailed mathematical modeling of the dredging processes Detailed mathematical modeling of the bank Detailed mathematical modeling of the dynamics Less detailed modeling of working methods and operations file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (13 of 28) [30/4/ :15:07]

14 5. The software should be open Results and responses Dedicated, depending on the subject of the research Output of the input, so the relation input output can be studied Output of dredging process parameters as a function of time complemented with statistics The dredge design simulator The dredge design simulator is considered to be a simulator that predicts system behavior that can be used in the design phase of building a dredge. This type of simulator can also be used for the modification of a dredge for a specific job or for determining the different components and layout for a specific dredging job (for example the choice of a booster pump). The main targets are: Predict complex system behavior Optimize dredging limits Predict loads on specific parts of the dredge The use of the dredge design simulator requires: Console and user interface Console and user interface can be combined on one PC (on-screen console) The simulator should be controlled by scripts Educational program There does not have to be an educational program There has to be a specialist working on a regular basis with the software Mathematical modeling file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (14 of 28) [30/4/ :15:07]

15 Detailed mathematical modeling of dredging processes Detailed mathematical modeling of resulting loads The software has to be reproducible, meaning that one script has reproducible output Results and responses Loads on different parts of the dredge Time series of the dredging processes Production information Detection of limiting conditions The motions of the dredge The dredge motions consist of the six degrees of freedom of the pontoon complemented with the rotation of the ladder around the ladder bearings. This gives a total of 7 degrees of freedom (surge, sway, heave, roll, pitch, yaw and ladder rotation). For a dredge operating in still water, when wave forces are ignored, the motions in the horizontal plane are relevant (surge, sway and yaw) as well as the ladder rotation. The three pontoon motions can be reduced to the rotation around the spud if the spud is considered to be infinitely stiff. If the ladder rotation is considered not to be the result of a mass-spring system, but controlled by the ladder winch, only one equilibrium equation has to be solved, the rotation of the pontoon around the spud. The other 6 equilibrium equations are of interest when working offshore, when wave forces have to be taken into account, but using these equations increases the calculations to be carried out enormous. This may be useful for the training, the preparation and the dredge design simulators for advanced training. For the educational, the prediction and the research simulator these motions are not of interest unless they are subject of research. The equilibrium equation of rotation around the spud is a second order non-linear differential equation, with the following external forces: The inertial forces of pontoon and ladder The water damping on pontoon and ladder The spring forces resulting from the swing wires file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (15 of 28) [30/4/ :15:07]

16 The external forces resulting from the current The external forces resulting from the cutting process The external forces resulting from the swing winches The external forces resulting from the pipeline The reaction forces on the spud The inertial forces (moments) determine whether there is an acceleration or deceleration of the rotation around the spud. These forces are the result of the equilibrium equation and thus of the external forces. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (16 of 28) [30/4/ :15:07]

17 Fig. 7: The output of the winch parameters. The water damping and the current forces depend on the value and the direction of the current and on the rotational speed of the pontoon around the spud. The spring forces resulting from the swing wires and the forces resulting from the swing winches, strongly depend on the characteristics of the winches and the wires and the winch control system. The position of the anchors in relation to the position of the spud and the position of the swing wire sheaves on the ladder determines the direction of the swing wire forces and thus of the resulting moments around the spud. Figure 7 shows the winch output of a research simulator. The forces resulting from the pipeline can be neglected if the position of the swivel elbow is close to the position of the work spud, because in this case this force hardly influences the rotation of the pontoon around the spud. The cutting forces and the cutting torque strongly influence the rotation around the spud, these will be discussed in the paragraph cutting forces. The reaction forces on the spud can be determined by the equilibrium equations of forces and complement this equilibrium. The rotation of the pontoon around the spud is dominated by the cutting forces, the winch characteristics, the inertia of pontoon and ladder and placement of the anchors, while damping and current play a less important role. The equilibrium equation in question is non-linear, while some of the data is produced by interpolation from tables. This implies that the equation will have to be solved in the time domain, using a certain time step. This is also necessary because the simulation program has to interact with the console (the user input). To simulate the motions of the dredge real time, a time step of at least two times per second is required. A time step of 5 to 10 times per second would be preferred. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (17 of 28) [30/4/ :15:07]

18 The bank profile In the modeling of the bank the following aspects can be distinguished: The storage method and resolution The geometry input and presentation of the geometry The number of different soils allowed and the soil mechanical parameters The wall velocity Cave ins Updating the geometry The storage method should be the result of the other 5 aspects, but depending on the computer system used, the storage of the bank profile may use a lot of disk space and use a lot of CPU time. Fortunately the development of computers is going very fast, resulting in cheap multi GB capacity hard disks and very fast CPU's. The bank can be stored as a large matrix (in an array), with one subscript representing the width of the area covered and the other subscript representing the length. The value of each element of the matrix represents the height. If the with is 200 m and the length 1000 m, then a resolution of 1 m gives points. If the height is stored as a floating-point variable of 4 bytes, this requires about 100 kb, which is not a problem with respect to storage. With a resolution of 0.1 m this requires 10 MB, which was a problem 5 years ago. The resolution required can however be determined from the cutting process. The swing velocity will be about 0.3 m/s under normal operating conditions. With a time step of 0.5 seconds, the cutterhead has moved 0.15 m in one timestep. With a time step of 0.1 second, the cutterhead has moved only 0.03 m in one time step. This results in a resolution of 0.01 m, which requires 1 GB of storage and increases the CPU time, since the movement of the cutterhead should always be larger then the resolution. A compromise between time step and resolution has to be chosen. There may be more sophisticated ways to store the bank, but they will usually result in other compromises. Figure 8 shows a 3D picture of the bank, the matrix structure is visible. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (18 of 28) [30/4/ :15:07]

19 Fig. 8: A 3D view on the channel profile. The geometry input should be easy, for instance through a mesh of triangles. Another option is, to use existing survey data to generate a bank. In this case a conversion utility has to be available. The possibility of using existing survey data is especially important for the preparation simulator and also for the training simulator. The geometry presentation is preferred to be 3D, with the possibility to view the geometry from different directions and to zoom in and out. If the bank profile is stored in an independent file, the user has the possibility to write his own bank generating programs. The bank can consist of one type of soil, however to simulate more closely to reality, it is preferred to be able to create a bank consisting of more types of soil. This way layers of different material, like gravel beds or clay layers can be simulated. Since the resolution of these different types of soil does not have to be so fine as the resolution of the bank, it would be a waste of storage space to store the soil data in the bank file. Storing this data in a separate file is preferred. This allows for an almost infinite number of soils. The soil mechanical parameters depend on the type of soil. At least sand and clay should be implemented. By storing the soil types in a database and referring to the record number of the soil type in question, one can use different soils and define standard soil types. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (19 of 28) [30/4/ :15:07]

20 Resuming there are 3 storage files required, one for the geometry of the bank profile, which can be a very large file, one for the storage of the geometry of layers of different types of soil and one for the storage of the soil mechanical parameters. The wall velocity and cave ins are two physical processes that occur independent from the motions of the dredge. Although the dredging process can induce these phenomena, they do not have to occur at the position of the cutterhead and at the same time the cutterhead is at that position. The occurrence of material flowing down on the slopes, depends on the type of material and on the slope angle. The occurrence of cave ins depends on the stability of a slope and thus also on the material properties. With respect to time these phenomena occur almost independent from the dredging process. This requires a second time loop to check for the possible occurrence, determine the displacement of material and update the geometry matrix. It is obvious that the CPU time required is inversely proportional to the resolution of the matrix. This matrix will have to be updated every timestep, when the cutterhead has excavated a certain volume of soil. As mentioned before, the displacement of the cutterhead has to be bigger then the resolution of the matrix, otherwise it is difficult to determine the excavated volume. The matrix only has to be updated for the area covered by the projected area of the cutterhead. A volume balance between excavated volume and hydraulically transported volume can be taken as a verification tool. The cutting process One of the main processes of the cutter dredge is the cutting process. The cutterhead has two functions, excavating the soil and mixture forming. The hydraulic transportation process has the function to transport the mixture to its destination. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (20 of 28) [30/4/ :15:07]

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22 Fig. 9: The output of cutter position, speed and torque. In dredging there is a variety of types of soil to be excavated. Therefore the types of soil are grouped into sand, clay and rock, knowing that this does not cover all the possibilities. Since for solving the equilibrium equations around the spud, the cutting forces need to be known, a cutting model for each type of material has to be implemented, using the soil mechanical and operational parameters as input. Cutting models can be very detailed or global. To determine how detailed the cutting model has to be, the time involved in the detailed cutting process should be compared to the time frame of the motions of the dredge. The time frame of the motions of the dredge can be characterized by the Eigen frequency of the motions of the dredge around the spud. This Eigen frequency is usually 10 to 20 seconds and gives an indication of the speed with which the dredge responds to changes of the loads (forces and moments) on the dredge. Figure 9 shows the results of the cutterhead modeling. The cutting process consists of high frequent cutting of small pieces of soil that break out every few centimeters. With a circumferential cutting speed of several meters per second, this gives a frequency of 50 to 500 pieces per second. The resulting cutting forces will fluctuate around some average with this frequency. It is obvious, that the motions of the pontoon will not be influenced by such high frequency varying forces. The frequency with which cutter blades hit the bank is around 2 to 4 per second. This frequency is also to high to influence the motions of the dredge. Implementing both the forces resulting from pieces breaking out and forces resulting from the blades hitting the bank will cause a tremendous increase in CPU time, without a noticeable effect on the motions of the dredge. The low frequent force variations resulting from a change in the average forces on the cutterhead due to variations in swing speed and variation of the soil to be excavated will influence the motions of the dredge. Those forces should be used in the mathematical model as implemented in simulators. Only the research simulator may require more detailed modeling of the cutting forces if these are the subjects of the research. The hydraulic transport process The hydraulic transport system consists of a multi pump pipeline system (ladder-, main- and booster pump). The pumps are diesel direct or diesel electrical driven. In short, the excavated soil is mixed with water inside the cutterhead and transported through the hydraulic system. Since the excavating process is not stationary, the mixture density, the soil mechanical parameters and the dredging depth all at the position of the cutterhead may vary in time, the mixture density and the soil mechanical parameters will also vary over the length of the pipeline. This results in a varying resistance and thus pressure loss over the length of the pipeline and in time, causing the pump drive to have varying revolutions and the pumps to have varying discharge pressures. Since the mixture travels through the pipeline these effects will occur at different times for the subsequent pumps. Resuming it can be stated that the hydraulic transport process is a very dynamical process. The mathematical model of this file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (22 of 28) [30/4/ :15:07]

23 process should consist of at least a mass, spring, damper model where the torque/revolutions behavior of the pump drive gives input for the external load. The moments of inertia of pump drive, pump and the mass of the mixture in the pipeline give the total mass; the pressure drop in the pipeline gives the damping, while the control system (flow control or diesel injection control) results in spring behavior. The diesel engine behaves however as a second order system, which makes the modeling more complex. To be able to determine the pipeline resistance at every position in the pipeline, it is necessary to know the mixture density and soil mechanical parameters at every position in the pipeline. Since the mixture is moving through the pipeline, a bookkeeping system is required. Then at each small pipe segment the resistance can be determined with Durand, Fuhrboter, Wilson or another model. The total resistance action on a pump can be determined by integration. The number of segments (and thus the size of one segment) determines the CPU time. For the research simulator the segment size should be small. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (23 of 28) [30/4/ :15:07]

24 Fig. 10: The output of the system curves of the pump system. Another modeling problem is pump cavitation. One way of modeling this is, to let the mixture density in the pump decrease as soon as the pump starts cavitating. By letting this density decrease proportional to the time the pump is cavitating the behavior of a cavitating pump can be simulated, because the discharge pressure of a pump is proportional to the mixture density in the pump. Figure 11 gives a good example of the dynamics of the hydraulic transport process, while figure 12 shows the resulting production parameters. In general the CPU time required for the hydraulic transport model can be influenced by the accuracy of the calculations (the number of segments, the number of points on the Q-H curve, etc) and not by the physics of the modeling. Working methods and operational aspects The following aspects are important: Hoisting and lowering the ladder Hoisting and lowering the spuds Stepping in the traditional way Stepping with a spud carriage Starting and stopping the pump drives Controlling the pump revolutions Starting and stopping the cutter drive Controlling the cutter revolutions file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (24 of 28) [30/4/ :15:08]

25 9. Controlling the swing winches Moving the anchors Flow control Etc. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (25 of 28) [30/4/ :15:08]

26 Fig. 11: The output of the most important pump parameters for the main pump of a cutterdredge. Since a student can interact with the simulator at any time, the simulator has to be able to handle this. Most of the above aspects do not give an immediate response in reality, but respond like a first or second order system, so there is a time lap between the action of the student and the reaction of the dredge. This is especially important for the training and the preparation simulator. Conclusions The development of simulators is not just a matter of hardware and software, but should be governed by the use and the targets one wants to achieve. Without a proper 'educational program' a simulator is useless. Only the research simulator can do without, because usually the researcher is often the developer and knows what to do with the simulator. The complexity of the mathematical modeling depends on the use of the simulator. Resuming one can state that a simulator, including hardware, software and educational or training program, can be considered one entity. file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (26 of 28) [30/4/ :15:08]

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28 Fig. 12: The output of the most important production parameters. References IHC-Systems & Miedema, S.A., "CSDS Cutter Suction Dredge Simulator". Delft, 199 Miedema, S.A., "Production Estimation Based on Cutting Theories for Cutting Water Saturated Sand". Proc. WODCON IV, November 1995, Amsterdam, The Netherlands Miedema, S.A., "Modelling and Simulation of the Dynamic Behaviour of a Pump/Pipeline System". 17th Annual Meeting & Technical Conference of the Western Dredging Association. New Orleans, June Last modified Friday February 25, 2000 by: Sape A. Miedema Copyright February, 2000 Dr.ir. S.A. Miedema file:///c /FrontPage Webs/Content/DREDGING/MIEDEMA/1999_WEDA/Weda99.htm (28 of 28) [30/4/ :15:08]