Received: 27 June 2017 DOI: 10.1002/cae.21883
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Accepted: 8 September 2017
RESEARCH ARTICLE
Developing students’ mathematical and computational knowledge to investigate mooring line in ocean engineering Xiang-Lian Zhou1,2
| Jian-Hua Wang1,3 | Lu-Lu Zhang1,2 | Jun Zhang1,2
1 State
Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, China 2 Geocoastal
Research Group Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, China 3 Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
Correspondence Xiang-Lian Zhou, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. Email:
[email protected];
[email protected] Funding information National Natural Science Foundation of China, Grant numbers: 41572243, 51422905, 41372286
Abstract The rapid development of fast, powerful, and affordable computer technology has provided educators options to introduce innovations in teaching and learning process. The purpose of this study is to investigate the effect of computational simulations on students' understanding of marine mooring line tension in ocean engineering course. Instructional strategies need to incorporate mathematical and computational knowledge into their practice project so that students can use its core concepts to solve interdisciplinary problems. By writing students' own Matlab program, students will demonstrate the effect of mathematical and computational tools on the analysis of ocean structural dynamics. The effectiveness of instructional methods by investigating learning gains, instructional effect, and student perceptions about the course are evaluated. Through the teaching practice, students significantly increase their understanding of ocean engineering concepts. KEYWORDS computational tools, instructional effect, modeling and simulation, mooring line
1 | INTRODUCTION With its applications in the field of education, computers technologies have caused many revolutionary changes in educational processes experienced by both teachers and students. Considering today's conditions, nobody can think about college educational works without support by the computer technology. As a result of rapid improvements in computational hardware and software, it has become more practical to perform teaching and learning activities and easier to achieve desired instruction objectives. Especially employment of advanced software technology has an active role on this situation. There are many case studies and applications in the literature regarding the use of computer-based educational tools indicating optimistic and positive results [3–5,7,8,10,11–13,15,17,18,21,24,27]. Among these, Deliktas [5] presented a novel teaching and learning methodology enhanced with computer technology and 272
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indicated the importance of visual components in education with several very interesting examples. Akkoyun and Careddu [3] gave an example of computer applications for mining as an educational tool to support lectures. The program was designed by using real data obtained from an actual magnesite mine. The results indicated that this program could be used for various lectures in mining engineering such as mining, drilling and blasting. Grunwald et al. [8] developed a similar soil-landscape model implemented in Virtual Reality Modeling Language. Soil and landscape models promoted students' intuitive understanding of soil landscapes. Animation techniques were valuable to high-light specific characteristics of each model. Uribe et al. [24] investigated the effect of computational simulations on student understanding of thermoelectric devices in an advanced online course, which included learning gains, instructional support effect, and student perceptions. The research found that students significantly increased their understanding of thermoelectric devices
wileyonlinelibrary.com/cae
Comput Appl Eng Educ. 2018;26:272–284.
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concepts. Kose and Arslan [12] introduced the intelligent software system and a newly developed optimization algorithm to optimize and improve computer engineering students' self-learning processes. The technical evaluation process for understanding the potential of the used optimization algorithm was explained in order to figure out the success of the software system and the self-learning process. Ramasundaram et al. [21] developed an environmental virtual field laboratory to study the environmental attributes and processes that stimulated students' higherorder cognitive skills. The virtual field laboratory mimicked students' learning processes during real field observations, and provided students with a simulated environment to study the environmental processes that could not be provided on a real field trip. Gutiérrez-Romero et al. [10] presented the teaching and learning processes on offshore engineering design course based on learning approach assisted with Computational Fluid Dynamics (CFD) techniques. The new teaching procedure was proposed for ensuring that students acquired skills related to the ability of analyzing and designing ocean structures. The method increased the satisfaction of the students in a significant manner, and opened their fields in research and development on offshore engineering. Eulogiosá et al. [7] developed a radio access networks design software tools, so that the understanding and the application of theoretical concepts became more simple. Furthermore, as this tool had been applied for the regulation on mobile communications in different countries, students could get some practical knowledge of mobile communications in real world applications. Niazkar and Afzali [18] used Matlab and Excel spreadsheet to solve water distribution networks. The input data was first inserted into Excel spreadsheet while MATLAB codes utilized this data to solve the pipe network. In order to focus on the educational aspects of computer application, a simple pipe network was analyzed using these Q-based methods. Karagiannis et al. [11] presented new web-based educational software (webNetPro) for Linear Network Programming. webNetPro could be viewed as a powerful supplement to traditional instruction techniques and be used without significant difficulties in distance education. Lazaridis et al. [13] discussed some new results on the factors influencing the effectiveness of Algorithm Visualization (AV) applications and the factors influencing the understanding of the revised simplex algorithm. It was found that the most important factors influencing the understanding of the proposed algorithm by the students was the use of animated pseudo-code steps and of textual observation aids during the solution process of a problem in Visual LinProg. Zhou and Wang [27] studied the utilization of interactive computer to teaching and learning Biot poroelasticity modeling in civil engineering. As part
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of the learning method, teaching tools based on interactive computer-based computers had been specifically developed to help students to analyze the Biot poroelasticity equations. The survey found that most students had a basic understanding of pore pressure. When the computational simulations is taken into consideration [14,16,19,20,22,26,28], it can be said that computational technology have a great role on improving educational processes in the context of both teachers and students. One of the most important advantages of such computational technology is enabling users to experience self-learning processes. A well-designed self-learning activity process supports both learners and teachers to achieve educational objectives rapidly. Currently, computational technology has the most effective role on improving selflearning. The purpose of this study is to identify the effects of using computational simulations in civil engineering course. Not only the more efficient approaches are proposed for analyzing of mooring line, but also these programs may also introduce innovative ideas into instructional methods. On the other hand, students can achieve the following aims by using Matlab program: (1) improve students' understanding of the tension evaluation and the shape analysis of the chains and the cables in various underwater systems; (2) introduce and teach how to solve the Morison equation by using Matlab software; (3) prepare students for practical problems they may meet in the future.
2 | THEORY AND CALCULATIONS In general, it is difficult to understand the fundamental concepts and basic principles about the marine mooring line tension under combined wave and current (shown in Figure 1). One possible reason for this learning deficiency may be that the classical teaching mode is not enough to allow students to understand the basic concepts. According to this model, Lumped Mass Method [25] is used to build a two-dimension model that can be calculated by using the formulation of geometric and equilibrium equations. The hydrodynamic loads of current and wave are calculated by using airy wave theory [2] and Morison equation [9].
2.1 | Airy wave theory and Morison equation As shown in Figure 2, in order to calculate the tension and simulate the configuration of cable, the cable can be divided into n segments and (n + 1) nodes with the same by along horizontal direction in the global coordinate system, and all segments are considered to be small massless springs without curvature, loads acting on the segments are equivalent to act on the nodes.
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FIGURE 1
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Marine cable under wave and current
We use Lumped mass method [25] to solve the cable system. Airy wave theory [2] and Morison equation [1] are used to evaluate the load combined with wave and current as shown in Figure 3. The fluid velocity includes the velocity of current and wave. The velocity induced by wave can be calculated by using the Airy theory in shown Figure 4.
FIGURE 2
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Method of analysis of marine cable tension
Assuming the fluid is ideal irrotational fluid with considering gravity only. According to Airy wave theory (as shown in Figure 4), the velocity potential is [9] ϕðx; z; tÞ ¼
gH cosh ½k ðz þ dÞ sinðkx ωtÞ 2 ω cosh ðk dÞ
ð1Þ
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FIGURE 3
Method of calculate wave and current
Morison equation is used to evaluate the fluid hydrodynamic forces acting on the slim tubular members with the results of Airy theory (shown in Figure 5). Consider an arbitrary node i in water. This node is influenced by
FIGURE 4
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Airy theory and equation
submerged weight w (gravity and buoyancy), the force contributed from segment-tension T and the drag force Fn and Fτ. The formulation of geometric and equilibrium relation can be derived:
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FIGURE 5
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Morison equation and solution
dx dli ¼ cosθi
ð2aÞ
xi ¼ xi1 dx
ð2bÞ
zi ¼ zi1 dli sinθi
ð2cÞ
T xði1Þ ¼ T xi þ Fτi dli cosθi þ Fni dli sinθi
ð2dÞ
T zði1Þ ¼ T zi þ Fτi dli sinθi Fni dli cosθi wdli
ð2eÞ
θi1 ¼arctan
T xði1Þ T zði1Þ
ð2fÞ
! ! F n and F τ can be calculated by follows: ! 1 ! F n ¼ CDn Dρω ! v n v n 2
ð3aÞ
! 1 ! v τ v τ F τ ¼ CDτ Dρω ! 2
ð3bÞ
where CDτ and CDn are tangential and normal drag coefficients for tubular member, respectively, CDτ and CDn can choose 1.2 and 0.024; D is the diameter; ρω is the density of fluid; vn and vτ are fluid velocity in the tangential and normal direction, respectively. The fluid velocity includes the velocity of current and the velocity induced by wave. The velocity induced by wave can be calculated by using the airy theory. The surface velocity of
current in working condition is adapted to 2 m/s, and the current velocity varies with depth: u ¼ kz2
2.2 | Soil resistances calculation As shown in Figure 6, an empirical formula is used to calculate frictional resistance (f) and normal resistance (p) of cable embedded in soil [23]. f ¼ Bs ⋅α⋅Su
ð4Þ
where Bs is chain width in shearing; α is a reduction factor, and α = 1 for the soft clay; Su is the undrained shear strength of soil. The normal soil resistance per unit length of chain (p) is derived by the follows p ¼ Bb ⋅q
ð5Þ
where q is the normal ultimate soil pressure; Bb is the chain width. The value of q can be evaluated using the formula given by Skempton [23]. q ¼ N c ⋅Su
ð6aÞ
h N c ¼ 5:14 1 þ 0:2 Bb
ð6bÞ
where Nc is the bearing-capacity factor, for clay Nc = 7.6; h is the depth of the footing.
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FIGURE 6
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Schematic diagram of cable embedded in soil
The value Bb and Bs can be given by BS ¼ S⋅D
ð7aÞ
Bb ¼ B⋅D
ð7bÞ
where S and B are the parameters to express the effective widths in sliding and bearing, respectively, S and B are 8.0 and 2.5. Winkler model is used to evaluate the deflection of soil under the forces from the cable line [9]. Based on the empirical formula and Figure 6, we can derive the formulation of geometric and equilibrium relation: dli ¼
dx cosθi
ð8aÞ
xi ¼ xi1 dx s sin θi
ð8bÞ
zi ¼ zi1 dli sinθi s cosθi
ð8cÞ
T xði1Þ ¼ T xi þ f i dli cosθi pi dli sinθi
ð8dÞ
T zði1Þ ¼ T zi þ f i dli sinθi pi dli cosθi wdli
ð8eÞ
T xði1Þ θi1 ¼arctan T zði1Þ
ð8fÞ
As so far, the controlling equation to calculate the tension and the shape of mooring line have been described and in the next section, we will introduce the numerical process and results.
3 | CALCULATION PROCEDURE As shown in Figure 2, the mooring line is divided into n elements and n + 1 nodes. Flow scheme for mooring line tension calculation can be found in Figure 7. The model of a mooring line includes two segments, mooring line embedded in soil and suspended in water. Algorithmic details of the calculation can be expressed briefly as follows: Step 1 (initialization phase): Set basic parameters of water, mooring line, and soil. And it is necessary to assume the node number of touchdown point i, the initial pretension of the topside and initial angle θ. Step 2: When the iteration process complete, we need to verify the results satisfy the condition of water depth. If jZ nþ1 Z i H 1 j > ε (ε is a small specified quantity), the value of initial angle θ need be adjusted. If jZ nþ1 Z i H 1 j
