A new wave absorbing approach based on the mechanism of gap resonance is proposed in this work. The wave absorber is designed by placing a fixed box in front of the end of a physical wave flume, thereby forming a gap between the box and the end wall. To facilitate matching between the resonant frequency and the incident wave frequency, the gap width, box draft, and box breadth are jointly adjustable. A slatted screen is introduced into the gap to obtain the appropriate damping effect, if necessary. Numerical examinations are conducted to investigate the efficiency and applicability of the proposed resonant wave absorber based on a fully nonlinear finite element numerical wave flume within the modified potential flow theory. The numerical results confirm that the resonant wave absorber can achieve a high efficiency for a wide range of wave frequencies. Small reflection coefficients of KR <5% are obtained for all wave conditions examined in this work. Moreover, the size of the wave absorber (measured in the wave propagation direction) is less than 40% of the incident wave length (for example, the wavelength λ ϵ [1.02 m, 6.55 m] and the water depth h = 0.5 m). The main advantage of the present method is that it can lead to fairly small reflection coefficients for extremely long waves even with relatively small flume sizes, for which the widely used artificial sloping beach generally fails.
At present, along with conventional energy sources continually consumed, renewable energy sources are increasingly favored, especially the clean and inexhaustible geothermal resources have been universally valued both at home and abroad. In particular, the Enhanced Geothermal Systems (EGS), which is mainly aimed to exploit the thermal energy of Hot Dry Rock (HDR) at depths of 3 to 10 kilometers underground, has been full of interest to many countries. However, so far there hasn't been an EGS being successfully put into commercial operation because of its shortcomings such as small scale, low efficiency, etc. In this article, in response to the bottleneck of the study on the development of traditional EGS based on drilling technology (EGS-D), a conceptual model of EGS based upon excavation technology (EGS-E) is innovatively proposed and its main components of underground structure are described in this paper. As for ‘High ground stress, High ground temperature and High osmotic pressure’ initial conditions with regards to deep rock mass, the excavation experience, which is worth being learnt from extensive review of previous study as well as practical experience such as the successful excavation of ultra-deep mines in the gold field of South Africa, is summed up. The underground spatial structure that may be reasonable to the so-called EGS-E is being tried establishing. It is expected to provide with a basis for our subsequent numerical modeling.
Currently, seeking and developing clean new energy is the basic energy exploitation strategy, and the clean and inexhaustible geothermal resources have been universally valued both at home and abroad. Geothermal energy is the heat energy mainly generated by the transmutation of radioactive elements in rocks, which is 2.0934×1018 kJ annually. And the geothermal energy stored at depths of less than 10 kilometers underground was estimated to be 170 million times the amount of heat released from all the coals stored in the earth by Pollack and Chapman in 1977 (Wang Ruifeng, 2002). It can be seen that the reserves of geothermal energy are very considerable.
In spite of its advantages of stability, continuity and high utilization coefficient, the scale of the geothermal energy with temperature less than 150 °C at depths of less than 3 kilometers underground is usually too small to maintain the demand for long-term stable electricity production which is mainly hydrothermal and only accounts for 10% of all the geothermal energy stored in the earth (Guo Jian et al., 2014). Therefore, the enhanced geothermal system (EGS) which aims at exploiting the geothermal energy from hot dry rock (HDR) at depths of 3 to 10 kilometers has gradually attracted people's attention.
The normal stiffness of rock joints is decreased substantially by the opening between joint walls. This paper presents a modified semi-logarithmic relationship to describe the normal deformability of irregular rock joints under varying contact states. The effect of unevenness on the joint closure on opened joint profiles is considered by introducing a dimensionless coefficient. The magnitude of the coefficient highly depends on the joint roughness degree. Experimental data from normal compressive tests on several natural rock joints match well with the analytical results. The constitutive law, after being embedded in a distinct element method code, is able to analyse the stability of rock masses where opened joints exist due to stress relief, nearby blasting and earthquake vibration.
The closure of rock joints governs the overall deformability of rock masses. Critical factors dominating the joint normal deformation include joint wall material, surface roughness and joint matching state. Initially closed rock joints can become dislocated or opened due to underground excavation, nearby blasting and earthquake vibration (Li, 2016, Li et al., 2014, Tang et al., 2016). Under identical degree of normal compressive force, opened rock joints exhibit considerably softer normal stiffness with much higher joint closure, compared to those of closed ones (Li et al., 2016a, Li et al., 2016b, Tang et al., 2013). To predict the movement of rock blocks with opened joint walls, a constitutive law representing the normal deformability of rock joints under distinct contact conditions is required.
It has long been well-recognised that the normal stress-joint closure relationship is typically non-linear. Extensive studies indicated that the normal stiffness of closed rock joints can be shaped by empirical formulations, including hyperbolic equation (Bandis et al., 1983, Goodman, 1976), power equation (Swan, 1983) and logarithmic equation (Evans et al., 1992, Li et al., 2016a, Malama and Kulatilake, 2003, Zangerl et al., 2008, Zhao and Brown, 1992). Investigations into the normal deformation of opened joint walls are much less reported. Bandis et al. (1983) suggested that a semi-logarithmic function could be suitable to interpret the non-linearity of the normal stiffness of unmated rock joints. However, the semi-logarithmic model is incapable to consider the closure under varying degrees of joint opening. Saeb and Amadei (1992) took into account the effect of dislocation on the joint deformation by introducing a dilative component due to opening into the hyperbolic relationship of Bandis et al. (1983). Nevertheless, the assumption that the eventual joint closure equals the summation of the initial aperture created by mismatching and the maximum joint closure of closed joints, conflicts with the experimental observations that mismatched rock joints would never reach the maximum closure state (Bandis et al., 1983, Li et al., 2016a). On the other hand, Xia et al. (2003) and Tang et al. (2013) described the normal closure of mismatched rock joints based on the Hertzian contact theory. Their predictive models involve overly many parameters, making it impossible for practical use. Recently, Li et al. (2016a) proposed a semi-logarithmic formulation that related the normal stiffness variation with the degree of joint opening, the performance of which has been validated against experimental curves of normal compression tests on opened rock joints. The semi-logarithmic equation is merely applicable for idealised rock joints with various initial openings.
Cao, Zhilin (Dalian University of Technology) | Li, Hong (Dalian University of Technology) | Liu, Xiangxin (North China University of Science and Technology) | Wan, Zhen (Chongqing University) | Tang, Chun’an (Dalian University of Technology)
As the exploration and production of conventional reservoirs have passed their peak, the development of unconventional reservoirs including heavy oil are increasingly important. A 3D preliminary numerical model to simulate thermal recovery of oil through mass and heat injection in SAGD technology is developed based on the programs of TOUGH2 as well as its inclusive phase equilibrium library EOS8. The instantaneous distributions of temperature and oil saturation were figured out and the fundamental process of SAGD was studied. It demonstrated that TOUGH2 source codes are potential to model thermal recovery of heavy oil through secondary development.
Steam Assisted Gravity Drainage (SAGD) is an enhanced oil recovery technology (Williams, 2003; Moritis, 2004), which has been widely used in Alberta because of its richest reserves of heavy oil and asphalt sands. In fact, the use of SAGD in the world is also growing not only just in Canada, but also in such as the US and China. It can be seen that SAGD technology has a wide range of application prospects.
To briefly summarize SAGD’s development history, a large amount of literature has been reviewed. From 1979 to 1997 was the first stage: In early 1979, the systematic Lindrain theory firstly started to be published. The gravity drainage equation by percolation mechanics and numerical heat transfer was derivated (Butler and McNab, 1981). Soon after its clear principle, a method named SAGD with up-injection and down-production double horizontal wells (Butler, 1991), which is currently the most commonly used technology in heavy oil recovery, was proposed. In the same period, Tandrain Theory, similarity criteria and Linear Model Theory were proposed successively (Reis, 1992; Butler &; Stephens, 1981; Chung &; Butler, 1989). The second phase is from 1997 to the present: A technology named SAGP (Steam and Gas Push) for recovery oil from thin oil reservoir was developed by Bulter research team (Butler, 1997). In 2000, the FAST-SAGD technology was developed to recovery oil from super heavy oil reservoir. It had been proved that compared with traditional dual horizontal wells it can improve oil-steam ratio and recovery factor (CyrCoates and Polikar, 2001; PolikarCyr and Coates, 2000). In general, the success of steam-assisted gravity drainage has been demonstrated by both field and laboratory studies (Chen, 2009).
Numerical simulation, as an important research method, is also widely used in the field of oil recovery. In this article, firstly, the multi-field and multiphase mechanism in dynamic non-isothermal process during steam injection is elucidated, a non-isothermal three-phase flow model is described based on the mathematical theories of reservoir flow. Secondly, a numerical model of SAGD was established based on TOUGH2 for analyzing the steam injection process. Meanwhile, the parameter sensitivity was analyzed. Lastly, the corresponding summary and outlook are given.
Rock dynamic compressive strength is a most important parameter to evaluate the structural stability. In this study, FEM based numerical code RFPA3D was employed to investigate the inertia and friction effects on the rock dynamic compressive strength using three-dimensional SHPB numerical testing system. Different rock samples, including the solid cylindrical ones with different length to diameter ratios and the ring shaped ones with different inner diameters, were utilized to analyze the axial and radial inertia effects. The friction effect along the interfaces between rock sample and bars was investigated by setting different interfacial static friction coefficients. Simulation results demonstrated that the rock dynamic compressive strength increases with increasing length to diameter ratio or decreasing inner diameter of the testing sample. In addition, the radial inertia effect has a higher impact on the enhancement of the rock dynamic compressive strength compared with the axial one. Moreover, the friction effect along the interfaces between rock sample and bars directly alter the stress state at the rock sample end during the SHPB tests, which further improve the rock dynamic compressive strength. The findings in this study provide a better understanding of the inertia and friction effect on the rock dynamic compressive strength.
The split Hopkinson pressure bar (SHPB) system is widely utilized to test the rock dynamic behaviors. And previous studies have revealed that the rock dynamic compressive strength increases with increasing strain rate (Zhang and Zhao, 2014; Zhao et al., 1999; Li et al. 2005). However, it should be noted that the inertia and friction effects are also involved during the SHPB tests, which may affect the derived rock dynamic compressive strength (Gorham, 1989; Zhu et al., 2016).
The inertia effect is associated with most dynamic events, and can be detailedly divided into axial and radial items in SHPB tests, respectively. A suitable length to diameter ratio testing sample can effectively reduce the axial inertia effect. Davies and Hunter (1963) suggested that the axial inertia effect during the SHPB tests could be obliterated when the length to diameter ratio of the testing sample equals to (equation), where the parameter γ refers to the Poisson’s ratio. For the radial inertia effect, Forrestal et al. (2007) pointed out that the radial inertia effect is largest along the centerline of testing sample, while becomes zero at the surface. However, it should be noted that both of findings above were failed to consider the rock heterogeneous behavior.
Pile group is a commonly used structure in coastal and ocean engineering. The wave action on pile group structures has always been the focus of scholars' research. Because of the vortex shedding around the piles, small scale piles are different from large scale piles. Except inline force, transverse force of a small scale piles cannot be ignored. In order to explore the interaction between different piles, experimental investigations of the interaction of irregular waves with small scale, vertical bottom-mounted pile group which has 9 piles in side by side arrangement have been carried out. Considering the comprehensive influence of the relative pile diameter and KC1/3 number, a new parameter KCLD1/3 is proposed. The influence of relative spacing on the wave force of the pile group is analyzed. The change of pile group coefficient, inline force and resultant force with KCLD1/3 parameter and relative spacing are discussed.
Pile group structures are widely used in the area of coastal and offshore engineering such as crossing bridge and offshore wind turbine platform. However, there are many uncertain issues in the wave force of such piles. Accurate analysis of wave force is essential for designing pile group-supported marine structures. When the distance between the piles in the pile group structures is small, wave force on a single slender pile is significantly affected by the neighboring piles. The formula which is based on the concept of Morison et al. (1950) for calculating the wave force of a single isolated pile is not applicable.
So, a lot of laboratory tests had been conducted to study the interference effects of neighboring piles under the action of irregular waves. Chakrabarti (1981, 1982) measured inline forces on instrumented sections of the piles, the inertia and drag coefficients (Cmand Cd) are determined based on experimental data by applying for instance the least square fit. These coefficients are shown as functions of the KC number which is suggested by Keulegan (1958). The total forces on the piles were computed from the mean curves of the inertia and drag coefficients. The correlation between the maximum calculated forces and the corresponding measured maximum forces is good. However, any relationship with the Reynolds number could not be established primarily because of the small range of Reynolds number covered by the test. Sundar et al. (1998) found that the variations of Cd and Cm with KC for inclined cylinders are significantly wide. Boccotti et al. (2012, 2013) revealed that the inertia and drag coefficients are given as a function of KC number and Reynolds number Re for KC in (0, 20) and Re in (2*104, 2*105). Calculation of wave force of pile group by the Morison equation depends on inertia coefficient, Cm, and drag coefficient, Cd. However, the inertia and drag coefficients are not easy to be determined.
pang, Dan (Dalian University of Technology) | Tang, Guo-qiang (Dalian University of Technology) | Lu, Lin (Dalian University of Technology) | Gao, Rui (China Petroleum Bureau (CPP) No.6 Construction Company) | Zhu, Yan-shun (China Petroleum Bureau (CPP) No.6 Construction Company)
Numerical simulations are performed for the dynamic responses of two identical square cylinders in tandem arrangement oscillating separately in steady current. The results are presented based on a spacing ratio (L/B) ranging from 1.5 to 4 and a reduced velocity (Vr) ranging from 1 to 30 at a low Reynolds number (Re) of 180. The present numerical results show that the responses of both square cylinders are highly dependent on the spacing ratio and reduced velocity. When the spacing ratio is less than 2.5, a critical reduced velocity exists. The responses are dominated by vortex-induced vibration (VIV) when the reduced velocity is smaller than the critical reduced velocity and by galloping when the reduced velocity is larger than the critical reduced velocity. When the spacing ratio is 3.5, only VIV occurs for Vr is less than 20 while a response with combination of VIV and galloping appears for Vr over 20. Additionally, when the spacing ratio reaches 4, only VIV occurs. The results also show that the two square cylinders do not necessarily share the same synchronized mode. Moreover, besides the odd-number synchronized modes, an even-number synchronized mode is also identified.
VIVs of bluff bodies are of significance for both academic and practical applications, which have been widely investigated in recent several decades. In order to study the issue, the previous studies paid much attention to the fluid past an elastically-mounted circular cylinder. A typical phenomenon observed in the VIV of a circular cylinder is lock-in, characterized by the synchronization of vortex shedding frequency which synchronizes with the frequency of body oscillation (Williamson and Govardhan, 2004). Comprehensive investigations have been carried out in various aspects involving the VIV of circular cylindrical structures (e.g. Bearman, 1984; Sarpkaya, 2004; Gabbai and Benaroya, 2005; Williamson and Govardhan, 2008). In addition to circular cylinders, square-cross-section cylindrical structures have also been used in offshore engineering, for instance, the piers of bridges. However, less attention was focused on the dynamic responses of square cylinders in previous studies. Compared to the responses of circular cylinders, besides VIV, the dynamic response of a square cylinder presents another feature, i.e., transverse galloping, where the response amplitude increases with the reduced velocity. The transverse galloping is caused by the fluid force in phase with the body motion due to the change in the angle of attack (Zhao et al., 2014).
An improved multi-phase WCSPH (Weakly Compressible Smoothed Particle Hydrodynamics) model has been established to numerically analyzethe2D sloshing phenomenon in a rectangular tank undergoing the forced rolling motion. The multiphase SPH model is applied taking care on combining the advantages of different SPH models. The application of artificial parameters is avoided in order to simulate physics phenomena realistically. The density re-initialization which is suitable for two-phase flow is applied to obtain smooth pressure field. A coupled dynamic solid boundary treatment (SBT) is adopted here to reduce numerical oscillations of pressure close to the boundary and to prevent particles' unphysical penetration into the solid boundary. Besides, in order to quantitatively study the wave elevation, a wave elevation measurement method based on linear interpolation is proposed.
Sloshing is a typical fluid-structure coupling flow phenomenon with strong nonlinearity and randomness, which is involved in many fields such as marine engineering, aerospace engineering and nuclear engineering, and so on. For instance, in the process of liquefied natural gas and oil transportation, the sloshing of liquid mineral fuels has bad effect on the structure safety of LNG tankers and FPSO vessels. A lot of work has been done for studying the sloshing problem using different methods including the model test (Bass et al., 1985, Liu and Lin, 2009, Pistani and Thiagarajan, 2012), theoretical analysis (Faltinsen, 1978, Faltinsen and Timokha, 2009, Chen et al., 2015) and numerical calculation (Armenio and Rocca, 1996, Wu et al., 1998, Frandsen, 2004).
SPH method which is an effective mesh-free method has been widely concerned for its natural advantages in solving sloshing problems. In SPH, physical objects are represented by a set of particles with individual masses. One particle interacts with nearby ones within a finite area called support domain, and the influence of the neighboring particles depends on the weight function or the smoothing function. The density and the acceleration of the particle are obtained by solving the governing equations descretized according to SPH algorithm (Liu et al., 2004). Much work has been done to improve the efficiency and accuracy for solving the sloshing problem with SPH method. Liu et al. (2012) proposed a kernel gradient correction and a coupled dynamic solid boundary treatment (SBT) which show great advantages in single phase sloshing problems. Chen et al. (2013) presented a boundary pressure correction to improve the measurement precision of the pressure field in boundary origin. Chowdhury and Sannasiraj (2014) compared the effects of different diffusive terms in sloshing problems. Bouscasse et al. (2014) studied the sloshing phenomenon in shallow water with experiment and numerical method of SPH. Delormeet al. (2009) studied the pressure field at the wall with SPH method.
The potential numerical wave flume is applied in this study to estimate the forces and the moment on a submerged plate in the combined wave-current flow by solving the Laplacian equation based on the higher order boundary element method (HOBEM). The free surface motion is tracked by solving the free surface boundary conditions and is advanced in time using the fourth-order Runge-Kutta scheme. The performance of the potential numerical wave flume is assessed by comparing with the published theoretical results and the experimental measurements. The forces and the moment on the submerged plate alternatively increase to the peak value and then decrease to zero with increasing plate breadth, and they are found to increase with increasing water depth. Additionally, it is found that the use of Doppler shifted solutions is not sufficient for considering the effect of depth-uniform current on waves. The generation of higher harmonics due to a sudden change in water depth and the current-induced form drag are found to make significant contributions to the wave loading.
The submerged plate, used as a breakwater device, is less dependent on the bottom topography, more economical and can assure open scenic views. It allows seawater to exchange freely between the sheltered region and the open sea to prevent stagnation, pollution, transport of sediment to maintain the general partition of the natural seabed. It has been applied as an efficient breakwater in coastal and offshore zones Thus, investigations on submerged plate have been focused on their reflection and transmission characteristics (Stamos and Hajj, 2001.), or the generation of higher order bound and free harmonic waves that affects the sailing conditions (Brossard and Chagdali, 2001; Lin et al., 2014). However, the effects of wave-induced forces and moment on submerged structures are of practical importance as well to assure the strength and stability of the structure over the design life. Extensive researches have shown that the mutual influence of waves and currents is intensified in shallow waters/coastal areas (Isaacson and Cheung, 1993; Chen et al. 1999). Methods that can provide accurate predictions of forces and moment on submerged structures in combined waves and currents are required for the safe and cost efficient design of submerged structures in coastal areas.
An anti-sloshing concept for FLNG tanks is investigated by taking advantage of floating foam layers. Physical experiments are conducted in a rectangular tank to investigate the sloshing properties. Effects of the layer thickness on the sloshing dynamics are analyzed. It shows that the floating foam layer can efficiently damp the free surface oscillations and reduce the pressure amplitude in a tank. Higher-order frequency components of the hydrodynamic pressure in the tank gradually vanishes as the foam thickness increases. Considering the economy in practice, the thickness of the foam layer should be as small as possible, as long as the sloshing mitigation effect can be guaranteed. For the present situation, a suitable choice of the foam thickness is recommended to be one-tenth the mean liquid depth.
A proper design of the anti-sloshing technique for FLNG tanks is important for the operation safety. At present, various anti-sloshing techniques have been investigated for liquid cargo tanks. A great proportion of these techniques was based on energy dissipation effects of internal structures (e.g. fixed baffles, flexible baffles, screens, blocks, bulkheads, etc.) in a liquid tank, which has been comprehensively reviewed by Faltinsen and Timokha (2009). There are also some membrane-based techniques used in space technology, and inflatable membranes in trucks (e.g. Accede company, the Netherlands).
Some more recent studies for FLNG tanks include Jung et al. (2012), Wang et al. (2013), Lu et al. (2015), Cho and Kim (2016), Xue et al. (2017), Yu et al. (2017), Sanapala et al. (2018), and so on. The above baffle-based anti-sloshing techniques have been widely adopted by oil or chemical tankers. However, these techniques still require further verification for the special case of LNG tanks. Because the internal surface of an LNG tank is fully covered by thin invar membranes to prevent gas leakage at an extremely low temperature, installing baffles through the membrane surface may affect mechanical properties of the membrane and bring safety risks. Thus, alternative anti-sloshing ideas keep emerging in the recent decade, trying to avoid damaging the membrane surface.