**The Investigation of the Hydrodynamics of an Artificial Reef**

Yan Liu1, Guohai Dong1, Yunpeng Zhao1, Changtao Guan2,3 and Yucheng Li1 *1Dalian University of Technology 2Yellow Sea Fisheries Research Institute 3Key Laboratory of Fishery Equipment and Engineering China* 

#### **1. Introduction**

78 Aquaculture and the Environment - A Shared Destiny

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Marine resources have been declining all over the world in recent decades. The natural reefs of the world are experiencing higher use and pressures, resulting in anthropogenic influences that are deteriorating coral reefs and causing poor water quality. Artificial reefs are manmade structures that are placed on the seabed deliberately to mimic some characteristics of a natural reef. **(Jensen, 1998)**. Both Japan and the United States have been using artificial reefs for at least 200 years. The first artificial reef was deployed in Japan in the 1700s, and the primary goal was to increase fish-catch. Nowadays, artificial reefs in Japan involve diversified types, integrated materials, complicated structures and large-scale design. The first documented artificial reef in the United States dates from 1830, when logs and rocks were sunk off the coast of South Carolina to improve fishing **(Williams, 2006)**. In many countries, artificial reefs have become important elements in the plans for integrated fishery management. Diverse shapes for artificial reefs, such as cube reefs, circular reefs, cross-shaped reefs and so on, provide favorable circumstances for fish perching, foraging, breeding and defense from enemies. Most artificial constructions in the marine environment consist of a variety of non-natural materials. At present, concrete is most commonly employed as a reef material, including cubes, blocks and pipes. Concrete has also been used in combination with other reef materials such as steel, quarry rock, tires and plastic **(Baine, 2001)**. Many of the world's largest artificial reefs have been deployed as part of a national fisheries program in Japan, where large steel and concrete frameworks have been carefully designed to withstand strong ocean currents **(Seaman, 2007)**. Other popular reef building materials include natural stone and rock, the latter constructed from wide-ranging materials including canvas, anchor blocks, and others. The different faunal assemblages associated with artificial reefs are determined by the physical and chemical nature of the reef materials. **Walker, et al (2002)** quantitatively compared the fish abundance, fish species richness and fish biomass on artificial reef modules constructed of various materials.

There are several proposed mechanisms to explain how artificial reefs increase total biomass production. First, an artificial reef can provide additional food and increase feeding efficiency, and many studies have reported observations of fishes feeding at artificial reefs.

The Investigation of the Hydrodynamics of an Artificial Reef 81

invasive PIV measurements were conducted to measure the flow patterns around the artificial reef. On the basis of the numerical model validation, the flow fields of hollow cube artificial reefs with different altitudes were analyzed using the numerical model. The effects of spacing on the flow field around the parallel and vertical two hollow cube artificial reefs

Computational fluid dynamics (CFD) are generally used by engineers to solve fluid dynamics problems that involve solving some form of the Navier-Stokes equations. The numerical simulation analysis of flow fields around artificial reef is based on a dynamic, full 3D model elaborated with the aid of FLUENT 6.3 commercial code. The finite volume method are used in the study to solve the three-dimensional Reynolds-averaged Navier-

4. The water surface is modeled as a "moving wall" with zero shear force and the same

The equations solved are the momentum equation, also known as the Navier-Stokes equation, and the continuity equation. This approach is useful for solving laminar flows, but, for turbulent flows, the direct solving of all the vortices in a turbulent flow is expensive. Therefore, a model for turbulence must be added. There are several types of turbulence models available. The most common are the RANS models and large eddy simulation models. In the present study, the two-equation RANS models were chosen to resolve the ensemble averaged flow and model the effect of the turbulent eddies. In the RANS equations, various instantaneous physical parameters are replaced by the time-averaged

' ' () ( ) *<sup>i</sup>*

μ

*i j i j*

<sup>0</sup> *uvw xy z* ∂∂∂ ++ =

For Eq. (1), *ρ* is the mass density; *u*i is the average velocity component for x, y, z; *P* is a body of fluid pressure on the micro-volume; *μ* is the viscosity; *u*′ is the fluctuation velocity; and *i*,

*P u u u uu S*

*i*

 ρ

=− + − + ∂ ∂∂ ∂ (1)

∂∂ ∂ (2)

value. Incompressible flow is assumed such that the equations are as follows:

*j ij j*

*x xx x*

∂ ∂∂ ∂

were also analyzed in detail.

**2. Numerical methods** 

**2.1 Hypotheses** 

Momentum equation

Continuity equation

Stokes (RANS) equations for incompressible flows.

3. Flow is in the non-steady state.

speed as the incoming fluid.

**2.2 Hydrodynamic equations solved** 

ρ

*j*=1, 2, 3 (x, y, z). *S*i is the source item.

1. Incompressible, viscous, Newtonian fluid for the water. 2. Isothermal flows, regardless of heat exchange in the water.

Secondly, affording shelter from predation implies higher survival at artificial reefs than in natural habitats, which is supported by some early experimental studies. **Hixon & Beets, (1989)** tested two corollaries of the limited shelter hypothesis by conducting the experiments in Perseverance Bay, St. Thomas, U.S. Virgin Islands. They suggested that artificial reefs designed for persistent fisheries should include both small holes for small fishes (as refuges from predation) and large holes for predatory species (as home sites). **Leitao, et al (2008)** studied the effect of predation on artificial reef juvenile demersal sh species. The results indicated that interspecic interactions (predator–prey) are important for conservation and management and for the evaluation of the long-term effects of reef deployment. Third, artificial reefs increase the production of natural reef environments by creating vacated space. **Einbinder, et al. (2006)** experimentally tested whether artificial reefs change grazing patterns in their surrounding environment. The results suggest that herbivorous fishes are attracted to the artificial reefs, creating a zone of increased grazing. It is necessary to consider their overall influence on their natural surroundings when planning deployment of artificial reefs. Fourth, artificial reefs have been demonstrated a potential tool for the restoration of marine habitats. The proper role of artificial habitats in aquatic systems continues to be a topic of debate among ecological engineers. A detailed description of the role of artificial reef habitats in the restoration of degraded marine systems has been given by **Seaman, (2007)**. Finally, an important aspect of artificial reefs includes the flow pattern effect. Recent studies have demonstrated the value of investigating the flow field effect in and around artificial reefs as a means of identifying their ecological effect on the proliferation of fishery resources **(Lin & Zhang, 2006)**. When an artificial reef is deployed at the bottom of the sea, many kinds of flow patterns characterized by intense velocity gradients, flow turbulence, vortices, and so on are aroused and develop depending on the shapes, sizes and the different arrangements of artificial reefs. **Zhang & Sun, (2001)**  discovered that considerable local upwelling current fields and eddy current fields are generated at the front and the back of artificial reefs, respectively. Upwelling enhances biological productivity, which feeds fisheries, and it is richer in nutrients. Meanwhile, a geometric shaded area is distributed within and around the reef. Consequently, algae and plankton thrive, and therefore, the reefs not only provide a shelter from predators but also an abundant food source.

In view of the above, flow field research is key to the research of artificial reef eco-efficiency. **Liu, et al. (2009)** simulated the flow fields around solid artificial reefs models with different shapes, including cubes, pyramids and triangular prisms, by mean of wind tunnel experiments and numerical simulation methods. **Su, et al. (2007)** conducted particle image velocimetry (PIV) measurements to study the flow patterns within and around an artificial reef. The PIV results were then used to verify the numerical results obtained from finite volume method (FVM) simulations. In engineering practice, the stability of artificial reefs is an important issue in preventing the failure of reef units due to current action. The stability of reefs and sediment erosion on the bottom of artificial reefs rely on the interactions among the current-bottom material-reef system. In this study, the flow field patterns around a hollow cube artificial reef were investigated by employing FVM simulation with unstructured tetrahedral grids for solution of three-dimensional incompressible Reynoldsaveraged Navier-Stokes equations. A renormalization group (RNG) *k-ε* turbulence model was embedded in the Navier-Stokes solver. The pressure and velocity coupling was solved with the SIMPLEC algorithm at each time step. To validate simulation predictions, noninvasive PIV measurements were conducted to measure the flow patterns around the artificial reef. On the basis of the numerical model validation, the flow fields of hollow cube artificial reefs with different altitudes were analyzed using the numerical model. The effects of spacing on the flow field around the parallel and vertical two hollow cube artificial reefs were also analyzed in detail.

#### **2. Numerical methods**

80 Aquaculture and the Environment - A Shared Destiny

Secondly, affording shelter from predation implies higher survival at artificial reefs than in natural habitats, which is supported by some early experimental studies. **Hixon & Beets, (1989)** tested two corollaries of the limited shelter hypothesis by conducting the experiments in Perseverance Bay, St. Thomas, U.S. Virgin Islands. They suggested that artificial reefs designed for persistent fisheries should include both small holes for small fishes (as refuges from predation) and large holes for predatory species (as home sites). **Leitao, et al (2008)** studied the effect of predation on artificial reef juvenile demersal sh species. The results indicated that interspecic interactions (predator–prey) are important for conservation and management and for the evaluation of the long-term effects of reef deployment. Third, artificial reefs increase the production of natural reef environments by creating vacated space. **Einbinder, et al. (2006)** experimentally tested whether artificial reefs change grazing patterns in their surrounding environment. The results suggest that herbivorous fishes are attracted to the artificial reefs, creating a zone of increased grazing. It is necessary to consider their overall influence on their natural surroundings when planning deployment of artificial reefs. Fourth, artificial reefs have been demonstrated a potential tool for the restoration of marine habitats. The proper role of artificial habitats in aquatic systems continues to be a topic of debate among ecological engineers. A detailed description of the role of artificial reef habitats in the restoration of degraded marine systems has been given by **Seaman, (2007)**. Finally, an important aspect of artificial reefs includes the flow pattern effect. Recent studies have demonstrated the value of investigating the flow field effect in and around artificial reefs as a means of identifying their ecological effect on the proliferation of fishery resources **(Lin & Zhang, 2006)**. When an artificial reef is deployed at the bottom of the sea, many kinds of flow patterns characterized by intense velocity gradients, flow turbulence, vortices, and so on are aroused and develop depending on the shapes, sizes and the different arrangements of artificial reefs. **Zhang & Sun, (2001)**  discovered that considerable local upwelling current fields and eddy current fields are generated at the front and the back of artificial reefs, respectively. Upwelling enhances biological productivity, which feeds fisheries, and it is richer in nutrients. Meanwhile, a geometric shaded area is distributed within and around the reef. Consequently, algae and plankton thrive, and therefore, the reefs not only provide a shelter from predators but also

In view of the above, flow field research is key to the research of artificial reef eco-efficiency. **Liu, et al. (2009)** simulated the flow fields around solid artificial reefs models with different shapes, including cubes, pyramids and triangular prisms, by mean of wind tunnel experiments and numerical simulation methods. **Su, et al. (2007)** conducted particle image velocimetry (PIV) measurements to study the flow patterns within and around an artificial reef. The PIV results were then used to verify the numerical results obtained from finite volume method (FVM) simulations. In engineering practice, the stability of artificial reefs is an important issue in preventing the failure of reef units due to current action. The stability of reefs and sediment erosion on the bottom of artificial reefs rely on the interactions among the current-bottom material-reef system. In this study, the flow field patterns around a hollow cube artificial reef were investigated by employing FVM simulation with unstructured tetrahedral grids for solution of three-dimensional incompressible Reynoldsaveraged Navier-Stokes equations. A renormalization group (RNG) *k-ε* turbulence model was embedded in the Navier-Stokes solver. The pressure and velocity coupling was solved with the SIMPLEC algorithm at each time step. To validate simulation predictions, non-

an abundant food source.

Computational fluid dynamics (CFD) are generally used by engineers to solve fluid dynamics problems that involve solving some form of the Navier-Stokes equations. The numerical simulation analysis of flow fields around artificial reef is based on a dynamic, full 3D model elaborated with the aid of FLUENT 6.3 commercial code. The finite volume method are used in the study to solve the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations for incompressible flows.

#### **2.1 Hypotheses**


#### **2.2 Hydrodynamic equations solved**

The equations solved are the momentum equation, also known as the Navier-Stokes equation, and the continuity equation. This approach is useful for solving laminar flows, but, for turbulent flows, the direct solving of all the vortices in a turbulent flow is expensive. Therefore, a model for turbulence must be added. There are several types of turbulence models available. The most common are the RANS models and large eddy simulation models. In the present study, the two-equation RANS models were chosen to resolve the ensemble averaged flow and model the effect of the turbulent eddies. In the RANS equations, various instantaneous physical parameters are replaced by the time-averaged value. Incompressible flow is assumed such that the equations are as follows:

Momentum equation

$$
\rho \frac{\partial}{\partial \boldsymbol{\alpha}\_{j}} (\boldsymbol{u}\_{i} \boldsymbol{u}\_{j}) = -\frac{\partial P}{\partial \boldsymbol{\alpha}\_{i}} + \frac{\partial}{\partial \boldsymbol{\alpha}\_{j}} (\mu \frac{\partial \boldsymbol{u}\_{i}}{\partial \boldsymbol{\alpha}\_{j}} - \rho \overline{\boldsymbol{u}\_{i} \dot{\boldsymbol{u}}\_{j}}) + \mathbf{S}\_{i} \tag{1}
$$

Continuity equation

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 \tag{2}$$

For Eq. (1), *ρ* is the mass density; *u*i is the average velocity component for x, y, z; *P* is a body of fluid pressure on the micro-volume; *μ* is the viscosity; *u*′ is the fluctuation velocity; and *i*, *j*=1, 2, 3 (x, y, z). *S*i is the source item.

The Investigation of the Hydrodynamics of an Artificial Reef 83

The boundaries of the computational domain are categorized as inlet, outlet, and wall. The mean velocity is specified at the inlet where the turbulent kinetic energy and specific dissipation rate are calculated according to the computational formulas of the turbulence parameter. The flow at the outlet is not defined and is allowed to change as the hydrodynamic pressure at all the boundaries is calculated from inside the domain. A stationary no-slip boundary condition is prescribed on the flume and artificial reef, and the undisturbed free surface is treated as a "moving wall", which has zero shear force and the same speed as the incoming fluid. For coarse meshes, boundary layers cannot be discretized in sufficient detail. The standard wall functions based on the proposal of Launder and Spalding was used to bridge the solution variables in the cell next to the wall to the values at

The computational grids are shown in Fig. 1. Meshes for modeling flow fields of artificial reefs using FLUENT were created in GAMBIT. In this work, all grids used were unstructured, and the TGrid meshing scheme was used to generate unstructured tetrahedral grids. Grids around the artificial reef were generated densely, and other domains were

The equations were solved using a FVM, where the equations were integrated over a control volume. The control volume integrals were discretized into sums, which yielded discrete equations. The discrete equations were applied to each control volume. The values of the variables in the equations were solved by upwind discretization schemes. The basic concept of upwind schemes is that the face value of a given variable is defined from the cell center value in the cell upstream of the face. Upstream is defined relative to the fluid velocity normal to the face. The second-order upwind schemes were employed for the turbulent kinetic energy and turbulent energy dissipation rate here. In FLUENT6.3, all computational work was performed with the 3D pressure-based solver in a first-order implicit unsteady formulation. Gradients were estimated by the Green-Gauss cell-based method. The

generated sparsely to reduce unnecessary calculations.

Here, *η*=*Sk*/*ε* and *η*0 and *β* are constants equal to 4.380 and 0.012, respectively.

**2.3 Boundary conditions** 

the wall.

**2.4 Meshing** 

Fig. 1. Computational grids

**2.5 Finite volume discretization** 

In eddy viscosity turbulence models, the Reynolds stresses are linked to the velocity gradients via the turbulent viscosity, and this relation is called the Boussinesq assumption, where the Reynolds stress tensor in the time averaged Navier-Stokes equation is replaced by the turbulent viscosity multiplied by the velocity gradients. The two-equation models assume an eddy-viscosity relationship for the Reynolds stresses in Eq. (1) given by

$$-\rho \overline{\boldsymbol{u}\_{i}\boldsymbol{\dot{u}\_{j}}} = \mu\_{\text{t}} (\frac{\partial \boldsymbol{u}\_{i}}{\partial \boldsymbol{x}\_{j}} + \frac{\partial \boldsymbol{u}\_{j}}{\partial \boldsymbol{x}\_{i}}) - \frac{2}{3} \rho k \mathcal{S}\_{\text{ij}} \tag{3}$$

where *μ*t is the eddy viscosity and *δ*ij is the Kronecker delta.

The *k–ε* two equations model has become the workhorse for practical engineering modeling of turbulent flows due to its robustness, economy and reasonable accuracy for a wide range of flows. In the derivation of the *k–ε* model, it is assumed that the flow is fully turbulent and that the effects of molecular viscosity are negligible. Therefore, the model is only valid for fully turbulent flows. An improved version of the *k–ε* turbulence model, the renormalization group (RNG) *k–ε* model, is adopted here, which is derived from the transient Navier-Stokes equation and employs a new mathematical method called a "renormalization group". RNG *k–ε* model provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately

The new turbulent equations for "*k*" and "*ε*" are introduced as follows.

*k* equation

$$\frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial \mathbf{x}\_i}(\rho k \overline{u\_i}) = \frac{\partial}{\partial \mathbf{x}\_j}(\alpha\_k \mu\_{\text{eff}} \frac{\partial k}{\partial \mathbf{x}\_j}) + \mathbf{G}\_k - \rho \varepsilon \tag{4}$$

*ε* equation

$$\frac{\partial}{\partial t}(\rho \varepsilon) + \frac{\partial}{\partial x\_i}(\rho \varepsilon \overline{u\_i}) = \frac{\partial}{\partial x\_j}(\alpha\_\varepsilon \mu\_{\varepsilon \overline{f}} \frac{\partial \varepsilon}{\partial x\_j}) + C\_{1\varepsilon} \frac{\varepsilon}{k} G\_k - C\_{2\varepsilon} \rho \frac{\varepsilon^2}{k} - R\_\varepsilon \tag{5}$$

In Eqs. (4-5), *α*k and *α*ε are the inverse effective Brandt numbers for the *k* and *ε* equations, respectively; *G*k is expressed by the mean flow velocity gradient arising from the turbulent kinetic energy; *C*1ε and *C*2ε are constants with values of 1.42 and 1.68, respectively; and *μ*eff is the validity viscosity coefficient defined as follows:

$$
\mu\_{\rm eff} = \mu\_{\rm t} = \rho \mathcal{C}\_{\mu} \frac{k^2}{\varepsilon} \tag{6}
$$

*C*μ is a constant equal to 0.0845.

The additional term *R*ε is the major difference between the RNG *k-ε* model and the standard *k-ε*, which significantly improves the accuracy for a high strain rate and large degree of crook flows. This term is given as

$$R\_{\varepsilon} = \frac{C\_{\mu}\rho\eta^{3}(1-\eta/\eta\_{0})}{1+\beta\eta^{3}}\frac{\varepsilon^{2}}{k} \tag{7}$$

Here, *η*=*Sk*/*ε* and *η*0 and *β* are constants equal to 4.380 and 0.012, respectively.

#### **2.3 Boundary conditions**

82 Aquaculture and the Environment - A Shared Destiny

In eddy viscosity turbulence models, the Reynolds stresses are linked to the velocity gradients via the turbulent viscosity, and this relation is called the Boussinesq assumption, where the Reynolds stress tensor in the time averaged Navier-Stokes equation is replaced by the turbulent viscosity multiplied by the velocity gradients. The two-equation models

> <sup>2</sup> ( ) <sup>3</sup> *i*

*j*

*i*

*ij*

= +− (3)

 ρε

> ε

= = (6)

2

 ε

ρ

 ε

(7)

∂∂ ∂ ∂ (4)

ε

εε

2

*k* ρ*C*μ ε

3 2 0 3 (1 / )

 η η ε

βη

*k*

+ = +−− ∂∂ ∂ ∂ (5)

 ρ*k*δ

*j*

The *k–ε* two equations model has become the workhorse for practical engineering modeling of turbulent flows due to its robustness, economy and reasonable accuracy for a wide range of flows. In the derivation of the *k–ε* model, it is assumed that the flow is fully turbulent and that the effects of molecular viscosity are negligible. Therefore, the model is only valid for fully turbulent flows. An improved version of the *k–ε* turbulence model, the renormalization group (RNG) *k–ε* model, is adopted here, which is derived from the transient Navier-Stokes equation and employs a new mathematical method called a "renormalization group". RNG *k–ε* model provides an option to account for the effects of swirl or rotation by modifying the

> () ( ) ( ) *<sup>i</sup> k eff <sup>k</sup> i jj <sup>k</sup> k ku <sup>G</sup>*

α μ

+ = + −

*tx x x*

1 2 () ( ) ( ) *<sup>i</sup> eff <sup>k</sup> i jj*

*eff t*

 μ

The additional term *R*ε is the major difference between the RNG *k-ε* model and the standard *k-ε*, which significantly improves the accuracy for a high strain rate and large degree of

1

ρη

<sup>−</sup> <sup>=</sup> <sup>+</sup>

*C*

μ

*R*

ε

μ

 α μ

*<sup>u</sup> C GC R tx x xk k* ε

In Eqs. (4-5), *α*k and *α*ε are the inverse effective Brandt numbers for the *k* and *ε* equations, respectively; *G*k is expressed by the mean flow velocity gradient arising from the turbulent kinetic energy; *C*1ε and *C*2ε are constants with values of 1.42 and 1.68, respectively; and *μ*eff is

∂∂ ∂ ∂

<sup>∂</sup> <sup>∂</sup> <sup>−</sup> ∂ ∂

assume an eddy-viscosity relationship for the Reynolds stresses in Eq. (1) given by

t

μ

*<sup>u</sup> <sup>u</sup> u u x x*

' '

*i j*

The new turbulent equations for "*k*" and "*ε*" are introduced as follows.

 ρ

ρ

 ρε

the validity viscosity coefficient defined as follows:

∂∂ ∂ ∂

ρ

where *μ*t is the eddy viscosity and *δ*ij is the Kronecker delta.

turbulent viscosity appropriately

ρε

*C*μ is a constant equal to 0.0845.

crook flows. This term is given as

*k* equation

*ε* equation

The boundaries of the computational domain are categorized as inlet, outlet, and wall. The mean velocity is specified at the inlet where the turbulent kinetic energy and specific dissipation rate are calculated according to the computational formulas of the turbulence parameter. The flow at the outlet is not defined and is allowed to change as the hydrodynamic pressure at all the boundaries is calculated from inside the domain. A stationary no-slip boundary condition is prescribed on the flume and artificial reef, and the undisturbed free surface is treated as a "moving wall", which has zero shear force and the same speed as the incoming fluid. For coarse meshes, boundary layers cannot be discretized in sufficient detail. The standard wall functions based on the proposal of Launder and Spalding was used to bridge the solution variables in the cell next to the wall to the values at the wall.

#### **2.4 Meshing**

The computational grids are shown in Fig. 1. Meshes for modeling flow fields of artificial reefs using FLUENT were created in GAMBIT. In this work, all grids used were unstructured, and the TGrid meshing scheme was used to generate unstructured tetrahedral grids. Grids around the artificial reef were generated densely, and other domains were generated sparsely to reduce unnecessary calculations.

Fig. 1. Computational grids

#### **2.5 Finite volume discretization**

The equations were solved using a FVM, where the equations were integrated over a control volume. The control volume integrals were discretized into sums, which yielded discrete equations. The discrete equations were applied to each control volume. The values of the variables in the equations were solved by upwind discretization schemes. The basic concept of upwind schemes is that the face value of a given variable is defined from the cell center value in the cell upstream of the face. Upstream is defined relative to the fluid velocity normal to the face. The second-order upwind schemes were employed for the turbulent kinetic energy and turbulent energy dissipation rate here. In FLUENT6.3, all computational work was performed with the 3D pressure-based solver in a first-order implicit unsteady formulation. Gradients were estimated by the Green-Gauss cell-based method. The

The Investigation of the Hydrodynamics of an Artificial Reef 85

The basic optical devices of the PIV system were designed according to the experimental configuration specified by TSI Inc (USA). The light sheets were generated by an Nd: YAG laser capable of producing 3-5 ns, 120 mJ pulses at a repetition frequency of 15 Hz. The digital images were captured using a high-resolution CCD camera with two million pixels. The maximum frame rate of the camera was 32 f/s. A CCD camera (Power View 4MP) coupled to PC image acquisition software was used to acquire images. The operation of the laser and the camera was synchronized by a digital delay pulse generator. Selecting reflective polyvinyl chloride powder with a mean diameter of 10 *μ*m and density of 1050

It is known that the structure of flow field within and around artificial reefs plays an important role in their ecological effects. The flow field effect is one of the most important ecological effects, therefore making artificial reefs with configurations specifically designed to induce suitable flow field structures has been of great interest to marine ecologists and engineers in recent decades. The upwelling and back vortex flow is the major flow field character, which is an important hydrodynamic characteristic of artificial reefs. Some nomenclatures are listed for analyzing and discussing these flow field characteristics qualitatively and quantitatively. The upwelling field is defined where the flow velocity of

*U*in: inlet current velocity (cm/s) *h*: the height of artificial reef model (cm) *H*: the depth of water (cm) r: the ratio of reef height to water-depth *H*up: the height of upwelling field (cm) *S*up: the area of upwelling field (cm2) *S*e: the area of back vortex flow (cm2) *L*e: the length of back vortex flow (cm)

(cm/s)

upwelling

upwelling field

*V*a: the average upwelling current velocity

*L*rp: the length of water current reattachment point from the end of reef model (cm)

*S*upA: unit reef effect for the area of

*H*upA: unit reef effect for the height of

Fig. 3. Schematic diagram of the experimental apparatus and the PIV system

**4. Flow field characteristics of a single hollow cube artificial reef** 

kg/m3 was added to the water as a trace particle.

Nomenclature

velocity (cm/s)

vortex flow field

vortex flow field

model (cm2)

*V*max: the maximum upwelling current

*S*: the incident flow area of artificial reef

*S*eA: unit reef effect for the area of back

*L*eA: unit reef effect for the length of back

SIMPLEC algorithm was employed for pressure-velocity coupling. High-resolution discretization schemes were used for the discretization of mass and momentum equations. The equations were linearized using an implicit solution and iterated to achieve a converged solution. Convergence was assumed for each time step when all residuals fall below 10−3, and a maximum of 100 iterations per time step was considered if the residuals failed to pass these thresholds.

#### **3. Experimental methods**

In recent decades, PIV has become a powerful technique for measuring instantaneous velocity fields. Highly reflective particles are thrown into the flume, and a light sheet produced by a laser is projected into the flow field of interest. Then, the light reflected by these particles is captured by a high-speed camera. The calculation of the speed of the particles in the raw particle images is based on the cross-correlation, and techniques such as the erroneous vector correction are also employed to reduce the computing error. The PIV systems are described in detail below.

The structure and arrangement of a single hollow cube artificial reef model are shown in Fig. 2. In this study, the reef block model was scaled by a factor of 1:20 to satisfy the physical constraints of the flume measuring area and avoid inducing an undesirable channel wall effect. The hollow cube artificial reef model was composed of five Plexiglas faces, with a width of 7.5 cm and 4.5 cm square openings. The artificial reef model was arranged at 900 and 450 angles at the bottom of the flume. All of the test sections are based on the axial plane of the artificial reefs.

Fig. 2. Structure and arrangements of a single hollow cube artificial reef model

As shown in Fig. 3, a three-dimensional coordinate system (x-y-z) was set up to build the PIV experiment with the origin at the center of the artificial reef. The internal dimensions of the flume were 22.00×0.45×0.60 m (length ×width ×height), and the water depth of test (*H*) was 0.4 m. The maximum test section was 45 cm wide, 60 cm deep and 100 cm long. The sides and bottom of the test area in the center of the water channel were composed of glass to facilitate PIV measurement of the flow fields at various positions around the artificial reef model. A centrifugal pump was fixed on the left of the flume and affords flow velocities of U1=6.7, U2=11.0 and U3=18.0 cm/s. The experimental flow velocities were chosen according to the characteristic flow rate of the practical sea area, and the corresponding physical values were 0.3 m/s, 0.5 m/s and 0.8 m/s. The inlet flow velocity was measured using acoustic Doppler current velocimetry.

SIMPLEC algorithm was employed for pressure-velocity coupling. High-resolution discretization schemes were used for the discretization of mass and momentum equations. The equations were linearized using an implicit solution and iterated to achieve a converged solution. Convergence was assumed for each time step when all residuals fall below 10−3, and a maximum of 100 iterations per time step was considered if the residuals failed to pass

In recent decades, PIV has become a powerful technique for measuring instantaneous velocity fields. Highly reflective particles are thrown into the flume, and a light sheet produced by a laser is projected into the flow field of interest. Then, the light reflected by these particles is captured by a high-speed camera. The calculation of the speed of the particles in the raw particle images is based on the cross-correlation, and techniques such as the erroneous vector correction are also employed to reduce the computing error. The PIV

The structure and arrangement of a single hollow cube artificial reef model are shown in Fig. 2. In this study, the reef block model was scaled by a factor of 1:20 to satisfy the physical constraints of the flume measuring area and avoid inducing an undesirable channel wall effect. The hollow cube artificial reef model was composed of five Plexiglas faces, with a width of 7.5 cm and 4.5 cm square openings. The artificial reef model was arranged at 900 and 450 angles at the bottom of the flume. All of the test sections are based on the axial plane

Fig. 2. Structure and arrangements of a single hollow cube artificial reef model

As shown in Fig. 3, a three-dimensional coordinate system (x-y-z) was set up to build the PIV experiment with the origin at the center of the artificial reef. The internal dimensions of the flume were 22.00×0.45×0.60 m (length ×width ×height), and the water depth of test (*H*) was 0.4 m. The maximum test section was 45 cm wide, 60 cm deep and 100 cm long. The sides and bottom of the test area in the center of the water channel were composed of glass to facilitate PIV measurement of the flow fields at various positions around the artificial reef model. A centrifugal pump was fixed on the left of the flume and affords flow velocities of U1=6.7, U2=11.0 and U3=18.0 cm/s. The experimental flow velocities were chosen according to the characteristic flow rate of the practical sea area, and the corresponding physical values were 0.3 m/s, 0.5 m/s and 0.8 m/s. The inlet flow velocity was measured using

these thresholds.

of the artificial reefs.

**3. Experimental methods** 

systems are described in detail below.

acoustic Doppler current velocimetry.

Fig. 3. Schematic diagram of the experimental apparatus and the PIV system

The basic optical devices of the PIV system were designed according to the experimental configuration specified by TSI Inc (USA). The light sheets were generated by an Nd: YAG laser capable of producing 3-5 ns, 120 mJ pulses at a repetition frequency of 15 Hz. The digital images were captured using a high-resolution CCD camera with two million pixels. The maximum frame rate of the camera was 32 f/s. A CCD camera (Power View 4MP) coupled to PC image acquisition software was used to acquire images. The operation of the laser and the camera was synchronized by a digital delay pulse generator. Selecting reflective polyvinyl chloride powder with a mean diameter of 10 *μ*m and density of 1050 kg/m3 was added to the water as a trace particle.

#### **4. Flow field characteristics of a single hollow cube artificial reef**

It is known that the structure of flow field within and around artificial reefs plays an important role in their ecological effects. The flow field effect is one of the most important ecological effects, therefore making artificial reefs with configurations specifically designed to induce suitable flow field structures has been of great interest to marine ecologists and engineers in recent decades. The upwelling and back vortex flow is the major flow field character, which is an important hydrodynamic characteristic of artificial reefs. Some nomenclatures are listed for analyzing and discussing these flow field characteristics qualitatively and quantitatively. The upwelling field is defined where the flow velocity of


The Investigation of the Hydrodynamics of an Artificial Reef 87

Fig. 5. *H*up/h, *S*up/*S*, *L*e/*h* and *V*a of experimental and simulation results at a 90 degree angle

tracing particles is weakened and causes a larger error. The mean error of upwelling and back vortex flow between the experiment and simulation is lower than 11%, and both of the results have an identical variation trend with the increase of the incoming flow velocity.

Figs. 6(a) and 6(b) present the experimental and numerical results obtained for the velocity vector diagrams of a hollow cube artificial reef with 45° angle. The flow structures observed at this angle are not the same as those for a 90° angle, especially inside the artificial reef. At this angle, the water flow is obstructed by the side face of the artificial reef, and no fluid can directly enter the reef in the middle. In the upstream, the slow flow velocity field is mainly distributed at the bottom or close to the reef side face. The flow velocity, both in the experiment and simulation, in most regions within the reef, is less than 2.0 cm/s, and the maximum velocity is only half of the inlet flow velocity. There is a large difference for the flow field structure in the rear of the artificial reef between the two arrangements. A large and complicated vortex is formed immediately downstream of the reef. The low flow velocity conditions in this region indicate the presence of a desirable shading effect, i.e., fish can rest and seek shelter in this suitable environment. For Fig. 6 (a) and (b), the numerical simulation predicts a flow field that is comparatively similar with the experimental results.

**4.1.2 A single hollow cube artificial reef at a 45 degree angle** 

(a) Experimental results (b) Simulation results

angle

Fig. 6. Flow field velocity vector diagram of a hollow cube artificial reef with a 45 degree

Fig. 7 shows the comparisons of the scale and intensity of the upwelling and back vortex flow field that are derived from the experiment and numerical simulation at a 45 degree angle. A good agreement was found between the two results. Nonetheless, there is a large

the axis z (height) orientation is equal to or greater than ten percent of inlet flow velocity. A clockwise rotation vortex is generated at the rear of the artificial reef and is called the back vortex flow field. Compared with the inlet flow velocity, the flow velocity in the back vortex flow field is slower. Therefore, the back vortex flow field is also called the slow flow region. The water current reattachment point is an important characteristic quantity and is located downstream of the artificial reef where the flow velocity is on the verge of zero. All of the arguments for the upwelling current and back vortex flow are on the vertical twodimensional central plane.

#### **4.1 Flow field of a single hollow cube artificial reef**

#### **4.1.1 A single hollow cube artificial reef at a 90 degree angle**

Figs. 4(a) and 4(b) show the experimental and numerical results for the flow field velocity vector diagram of a single hollow cube artificial reef with a 90 degree angle, respectively. In front of the artificial reef, the flow velocities slow down due to the reef resistance causes. Several narrow regions with different values of flow velocities spread in the upstream field, and the flow velocities increase gradually with height. Within the reef, the upper and bottom regions of the flow field have a low velocity, while the regions in the opening have a high velocity, which is approximately the incoming flow velocity. The reason is that the flow into the reef is obstructed by the two vertical members on both sides of the cube side face but can enter freely through the opening located in the center of the face. Figs. 4(a) and 4(b) also show that a low velocity flow field is formed in the area downstream of the reef. Experimental and simulation results show a similar velocity distribution around the artificial reef. The overall velocity vector diagrams of the two figures are in good agreement.

Fig. 4. Flow field velocity vector diagram of a hollow cube artificial reef with a 90 degree angle

Fig. 5 compares the scale and intensity of upwelling and back vortex flow field between the experimental and simulation results at a 90 degree angle. The height (*H*up) and the area (*S*up) of upwelling field by simulation are close to the experimental data. The computational average upwelling current velocities (*V*a) are slightly higher than the experimental results. A major gap exists in the length of the back vortex flow (*L*e), especially with a lower inlet flow velocity. In the field of the back vortex flow, the flow velocity is very slow and is on the verge of zero at the water current reattachment point, such that the performance of the

the axis z (height) orientation is equal to or greater than ten percent of inlet flow velocity. A clockwise rotation vortex is generated at the rear of the artificial reef and is called the back vortex flow field. Compared with the inlet flow velocity, the flow velocity in the back vortex flow field is slower. Therefore, the back vortex flow field is also called the slow flow region. The water current reattachment point is an important characteristic quantity and is located downstream of the artificial reef where the flow velocity is on the verge of zero. All of the arguments for the upwelling current and back vortex flow are on the vertical two-

Figs. 4(a) and 4(b) show the experimental and numerical results for the flow field velocity vector diagram of a single hollow cube artificial reef with a 90 degree angle, respectively. In front of the artificial reef, the flow velocities slow down due to the reef resistance causes. Several narrow regions with different values of flow velocities spread in the upstream field, and the flow velocities increase gradually with height. Within the reef, the upper and bottom regions of the flow field have a low velocity, while the regions in the opening have a high velocity, which is approximately the incoming flow velocity. The reason is that the flow into the reef is obstructed by the two vertical members on both sides of the cube side face but can enter freely through the opening located in the center of the face. Figs. 4(a) and 4(b) also show that a low velocity flow field is formed in the area downstream of the reef. Experimental and simulation results show a similar velocity distribution around the artificial reef. The overall velocity vector diagrams of the two figures are in good agreement.

dimensional central plane.

angle

**4.1 Flow field of a single hollow cube artificial reef** 

**4.1.1 A single hollow cube artificial reef at a 90 degree angle** 

(a) Experimental results (b) Simulation results

Fig. 4. Flow field velocity vector diagram of a hollow cube artificial reef with a 90 degree

Fig. 5 compares the scale and intensity of upwelling and back vortex flow field between the experimental and simulation results at a 90 degree angle. The height (*H*up) and the area (*S*up) of upwelling field by simulation are close to the experimental data. The computational average upwelling current velocities (*V*a) are slightly higher than the experimental results. A major gap exists in the length of the back vortex flow (*L*e), especially with a lower inlet flow velocity. In the field of the back vortex flow, the flow velocity is very slow and is on the verge of zero at the water current reattachment point, such that the performance of the

Fig. 5. *H*up/h, *S*up/*S*, *L*e/*h* and *V*a of experimental and simulation results at a 90 degree angle

tracing particles is weakened and causes a larger error. The mean error of upwelling and back vortex flow between the experiment and simulation is lower than 11%, and both of the results have an identical variation trend with the increase of the incoming flow velocity.

#### **4.1.2 A single hollow cube artificial reef at a 45 degree angle**

Figs. 6(a) and 6(b) present the experimental and numerical results obtained for the velocity vector diagrams of a hollow cube artificial reef with 45° angle. The flow structures observed at this angle are not the same as those for a 90° angle, especially inside the artificial reef. At this angle, the water flow is obstructed by the side face of the artificial reef, and no fluid can directly enter the reef in the middle. In the upstream, the slow flow velocity field is mainly distributed at the bottom or close to the reef side face. The flow velocity, both in the experiment and simulation, in most regions within the reef, is less than 2.0 cm/s, and the maximum velocity is only half of the inlet flow velocity. There is a large difference for the flow field structure in the rear of the artificial reef between the two arrangements. A large and complicated vortex is formed immediately downstream of the reef. The low flow velocity conditions in this region indicate the presence of a desirable shading effect, i.e., fish can rest and seek shelter in this suitable environment. For Fig. 6 (a) and (b), the numerical simulation predicts a flow field that is comparatively similar with the experimental results.

Fig. 6. Flow field velocity vector diagram of a hollow cube artificial reef with a 45 degree angle

Fig. 7 shows the comparisons of the scale and intensity of the upwelling and back vortex flow field that are derived from the experiment and numerical simulation at a 45 degree angle. A good agreement was found between the two results. Nonetheless, there is a large

The Investigation of the Hydrodynamics of an Artificial Reef 89

Fig. 8. Distribution of the upwelling field with different heights of hollow cube artificial

Fig. 9. Normalized maximum and average upwelling velocities with different heights of

(Inlet velocity is 11.0 cm/s)

reefs

artificial reefs

Fig. 7. *H*up/*h*, *S*up/*S*, *L*e/*h* and *V*a of experimental and simulation results at a 45 degree angle

difference in the comparison of the height of upwelling field when the inlet flow velocity is 6.7 cm/s, which may be caused by the lack of particle concentration in the experiment. The mean error between the experiment and simulation was within 8%. In this arrangement, the resistance to the water flow is intensified, and a large pressure gradient is generated around the reef so that a large-scale back vortex flow is produced.

#### **4.1.3 Brief conclusion**

In this small chapter, the flow field around a single hollow cube artificial reef is analyzed qualitatively and quantitatively by physical experiment and numerical simulation. The flow field within and in back of the artificial reef with a 45 degree angle has a lower flow velocity than a 90 degree angle. The scale and intensity of the upwelling field of artificial reef with a 90 degree angle are larger than a 45 degree angle. However, a biggish area of slow flow field is obtained at a 45 degree angle. The results of numerical simulation show good agreements with experimental measurements which provide powerful support for the next numerical analysis with regard to the effect of reef height on the flow field of a single artificial reef and the effect of spacing on the parallel and vertical binary combined artificial reefs.

#### **4.2 Effect of reef height on the upwelling field and back vortex flow field**

#### **4.2.1 Distributions of the upwelling field**

Fig. 8 shows that, with the same inlet velocity, the variation of reef height have nearly no effect on the general structure of the upwelling field. The upwelling field is mainly distributed at the top left corner of the artificial reef and has a fan shaped. The values of the upwelling flow velocity gradually decrease from inside to outside. Generally speaking, the height, breadth and area of the upwelling field always increase with the height of the artificial reef, and these rules are the same as those of a solid cube artificial reef (Pan et al., 2005).

#### **4.2.2 The effect of the reef height on the intensity of the upwelling field**

The effect of the reef height on the intensity of the upwelling field was measured by using *V*max and *V*a. The normalized maximum and average upwelling flow velocities are defined as the ratio of the flow velocity to the inlet current velocity, i.e., *V*max/*U*in and *V*a/*U*in.

According to Fig. 9, the normalized maximum upwelling flow velocity first increases and then decreases with increasing reef height and peaks at 8.0~9.0, where the value of *V*max is close to inlet flow velocity. The maximum upwelling flow velocity remains stable when the reef height is less than 7.0; afterwards, it increases rapidly until 9.0. The normalized average

Fig. 7. *H*up/*h*, *S*up/*S*, *L*e/*h* and *V*a of experimental and simulation results at a 45 degree angle

difference in the comparison of the height of upwelling field when the inlet flow velocity is 6.7 cm/s, which may be caused by the lack of particle concentration in the experiment. The mean error between the experiment and simulation was within 8%. In this arrangement, the resistance to the water flow is intensified, and a large pressure gradient is generated around

In this small chapter, the flow field around a single hollow cube artificial reef is analyzed qualitatively and quantitatively by physical experiment and numerical simulation. The flow field within and in back of the artificial reef with a 45 degree angle has a lower flow velocity than a 90 degree angle. The scale and intensity of the upwelling field of artificial reef with a 90 degree angle are larger than a 45 degree angle. However, a biggish area of slow flow field is obtained at a 45 degree angle. The results of numerical simulation show good agreements with experimental measurements which provide powerful support for the next numerical analysis with regard to the effect of reef height on the flow field of a single artificial reef and

Fig. 8 shows that, with the same inlet velocity, the variation of reef height have nearly no effect on the general structure of the upwelling field. The upwelling field is mainly distributed at the top left corner of the artificial reef and has a fan shaped. The values of the upwelling flow velocity gradually decrease from inside to outside. Generally speaking, the height, breadth and area of the upwelling field always increase with the height of the artificial reef, and these rules are the same as those of a solid cube artificial reef (Pan et al.,

The effect of the reef height on the intensity of the upwelling field was measured by using *V*max and *V*a. The normalized maximum and average upwelling flow velocities are defined

According to Fig. 9, the normalized maximum upwelling flow velocity first increases and then decreases with increasing reef height and peaks at 8.0~9.0, where the value of *V*max is close to inlet flow velocity. The maximum upwelling flow velocity remains stable when the reef height is less than 7.0; afterwards, it increases rapidly until 9.0. The normalized average

as the ratio of the flow velocity to the inlet current velocity, i.e., *V*max/*U*in and *V*a/*U*in.

the effect of spacing on the parallel and vertical binary combined artificial reefs.

**4.2 Effect of reef height on the upwelling field and back vortex flow field** 

**4.2.2 The effect of the reef height on the intensity of the upwelling field** 

the reef so that a large-scale back vortex flow is produced.

**4.2.1 Distributions of the upwelling field** 

**4.1.3 Brief conclusion** 

2005).

(Inlet velocity is 11.0 cm/s)

Fig. 8. Distribution of the upwelling field with different heights of hollow cube artificial reefs

Fig. 9. Normalized maximum and average upwelling velocities with different heights of artificial reefs

The Investigation of the Hydrodynamics of an Artificial Reef 91

The length of the back vortex flow is almost equal to the distance of the water flow reattachment point from the original point, which is a significant characteristic quantity for back vortex flow. Consequently, *L*rp and *S*e are used to measure the scale of the back vortex flow field. The unit artificial reef effect relative to the length and area of the back vortex flow

In Fig. 12, the length from the water current reattachment point to the artificial reef and the area of back vortex flow increase continually with increasing reef height. *L*rp with *h* (in x axis) presents an exponential growth relationship, and the relevant relational equation is y=1.09ex/5.46+0.20. A good correlation coefficient of 0.9976 is acquired. The quadratic polynomial fitted equation for the area of the back vortex flow (y) and reef height (x) is expressed by y=0.21x2-1.11x+3.03, and the homologous correlation

As shown in Fig. 13, the variation curves of *L*eA and *S*eA with reef height are similar to some degree. The values of *L*eA and *S*eA are the minimum at the reef height of 6.0 cm; after that point, there is a relatively fast increase, and a steady value is maintained until 9.0. There are three large values appearing at the heights of 4.0, 7.5 and 10.0, which can be used for the

Considering the economical problems and the stability of artificial reef in a certain depth of water, the height of artificial reef cannot be raised excessively. According to the results

**4.2.4 The effect of reef height on the back vortex flow field** 

Fig. 12. *L*rp and *S*e with different heights of artificial reefs

Fig. 13. *L*eA and *S*eA with different heights of artificial reefs

artificial reef designers as a reference.

**4.2.5 Brief conclusion** 

field is represented by *L*eA and *S*eA.

coefficient is 0.9973.

upwelling flow velocity does not always increase with the reef height, and the maximum value is obtained at 8.0. The maximum average upwelling flow velocity is nearly a quarter of the inlet flow velocity.

#### **4.2.3 The effect of reef height on the scale of the upwelling field**

To find the best size of the artificial reef, a new conception unit artificial reef effect is introduced. It is weighed by length and area, and the unit artificial reef effect relative to the height and area of the upwelling field is represented by *H*upA=*H*up/*h* and *S*upA=*S*up/*S*.

As shown in Fig. 10, the result of regression found that the height of the upwelling field and the reef height have a positive linear relationship. The best fit equation between *H*up (axis y) and *h* (axis x) is y=1.76x-0.62, which is obtained by the linear regression analysis method, and the R² (correlation coefficient) is 0.9997. According to Fig. 10, when the reef height is 7.5 cm and 10.0 cm, *H*upA (the ration of *H*up to *h*) is large. Thus, the preferable unit artificial reef effect relative to *H*up was acquired at the reef height of 7.5 cm and 10.0 cm.

Fig. 10. *H*up and *H*upA with different heights of artificial reefs

The area of the upwelling field and the reef height were fitted by the nonlinear regression analysis method, i.e., a second-order polynomial regression. The relationship between *S*up (y) and *h* (x) can be expressed by the equation y=0.86x2-2.51x+3.87 and R² = 0.9979. Fig. 11 shows that the curves of *S*upA are the same as those for *H*upA, and both of them acquire a large value at the reef heights of 7.5 cm and 10.0 cm. Thus, a preferable unit artificial reef effect relative to *S*up is acquired at the reef heights of 7.5 cm and 10.0 cm.

Fig. 11. *S*up and *S*upA with different heights of artificial reefs

upwelling flow velocity does not always increase with the reef height, and the maximum value is obtained at 8.0. The maximum average upwelling flow velocity is nearly a quarter

To find the best size of the artificial reef, a new conception unit artificial reef effect is introduced. It is weighed by length and area, and the unit artificial reef effect relative to the

As shown in Fig. 10, the result of regression found that the height of the upwelling field and the reef height have a positive linear relationship. The best fit equation between *H*up (axis y) and *h* (axis x) is y=1.76x-0.62, which is obtained by the linear regression analysis method, and the R² (correlation coefficient) is 0.9997. According to Fig. 10, when the reef height is 7.5 cm and 10.0 cm, *H*upA (the ration of *H*up to *h*) is large. Thus, the preferable unit artificial reef

The area of the upwelling field and the reef height were fitted by the nonlinear regression analysis method, i.e., a second-order polynomial regression. The relationship between *S*up (y) and *h* (x) can be expressed by the equation y=0.86x2-2.51x+3.87 and R² = 0.9979. Fig. 11 shows that the curves of *S*upA are the same as those for *H*upA, and both of them acquire a large value at the reef heights of 7.5 cm and 10.0 cm. Thus, a preferable unit artificial reef

height and area of the upwelling field is represented by *H*upA=*H*up/*h* and *S*upA=*S*up/*S*.

**4.2.3 The effect of reef height on the scale of the upwelling field** 

effect relative to *H*up was acquired at the reef height of 7.5 cm and 10.0 cm.

Fig. 10. *H*up and *H*upA with different heights of artificial reefs

Fig. 11. *S*up and *S*upA with different heights of artificial reefs

effect relative to *S*up is acquired at the reef heights of 7.5 cm and 10.0 cm.

of the inlet flow velocity.

#### **4.2.4 The effect of reef height on the back vortex flow field**

The length of the back vortex flow is almost equal to the distance of the water flow reattachment point from the original point, which is a significant characteristic quantity for back vortex flow. Consequently, *L*rp and *S*e are used to measure the scale of the back vortex flow field. The unit artificial reef effect relative to the length and area of the back vortex flow field is represented by *L*eA and *S*eA.

In Fig. 12, the length from the water current reattachment point to the artificial reef and the area of back vortex flow increase continually with increasing reef height. *L*rp with *h* (in x axis) presents an exponential growth relationship, and the relevant relational equation is y=1.09ex/5.46+0.20. A good correlation coefficient of 0.9976 is acquired. The quadratic polynomial fitted equation for the area of the back vortex flow (y) and reef height (x) is expressed by y=0.21x2-1.11x+3.03, and the homologous correlation coefficient is 0.9973.

Fig. 12. *L*rp and *S*e with different heights of artificial reefs

As shown in Fig. 13, the variation curves of *L*eA and *S*eA with reef height are similar to some degree. The values of *L*eA and *S*eA are the minimum at the reef height of 6.0 cm; after that point, there is a relatively fast increase, and a steady value is maintained until 9.0. There are three large values appearing at the heights of 4.0, 7.5 and 10.0, which can be used for the artificial reef designers as a reference.

Fig. 13. *L*eA and *S*eA with different heights of artificial reefs

#### **4.2.5 Brief conclusion**

Considering the economical problems and the stability of artificial reef in a certain depth of water, the height of artificial reef cannot be raised excessively. According to the results

The Investigation of the Hydrodynamics of an Artificial Reef 93

The horizontal flow velocities along the line of y=0 at the horizontal cross-sections of z=1/2*h* are shown in Fig. 15. Similar distributions of flow velocities are found within and around artificial reefs at different heights. In front of the artificial reef, the horizontal flow velocities are approximate and decrease gradually when approaching the artificial reefs. Within artificial reefs, the flow velocities are larger than the inlet flow and peak at the center of the reefs. In addition, with the increase of the reef height, the maximum horizontal flow velocity within the reef is also on the increase. At the rear part of the artificial reefs, the flow velocities show a long-distance attenuation until the locations are sufficiently far away from

Fig. 15. Distribution of the horizontal flow velocities along the line of Y=0 at the horizontal

the reefs, which are the slow flow regions as mentioned earlier. The smaller the artificial reef is, the lower the horizontal flow velocity is at the rear of artificial reefs. However, there is a special phenomenon where the lowest velocity occurs when the reef height is 7.0 cm. In

The arrangements of two models of artificial reef are shown in Fig. 16. The spacing of two parallel combined models is 0.5*h*, 1.0*h*, 2.0*h* and 3.0*h*. The spacing of two vertical combined

other words, a preferable slow flow effect is acquired at the reef height of 7.0 cm.

**5. Flow field characteristics of two hollow cube artificial reefs** 

models is 1.0*h*, 2.0*h*, 4.0*h*, 6.0*h*, 8.0*h*, 10.0*h* and 12.0*h* (*h*=7.5 cm).

Fig. 16. The arrangements of two hollow cube artificial reefs

cross-section of Z=1/2*h* (*h*=5.0, 6.0, 7.0, 8.0, 9.0, 10.0 cm)

calculated in the numerical simulation, when the reef height is 7.5cm, the efficiency of the reef unit performs best.

#### **4.3 Flow field velocity vector diagram in the horizontal cross-section**

The velocity vector diagrams in the horizontal cross-section that is located at the height of 1/2*h* are listed in Fig. 14. Similar structures of the flow field are obtained with different heights of artificial reefs. Within the reef, the flow velocity is close to the inlet velocity. In the area on either side of the artificial reef, the horizontal flow velocity is larger than the inlet flow velocity, and the maximum values are 11.5, 11.9, 11.9, 12.3, 12.9 and 12.9 cm/s, respectively, with increasing reef height. It is apparent that a higher artificial reef will have a wider area in which the horizontal flow velocity is greater than the inlet velocity. The slow flow field is distributed in the front and the back of the reef, where the structures of flow fields vary with the reef height.

Fig. 14. Velocity vector diagrams in horizontal cross-section with different heights of artificial reefs (the inlet velocity is 11.0 cm/s)

calculated in the numerical simulation, when the reef height is 7.5cm, the efficiency of the

The velocity vector diagrams in the horizontal cross-section that is located at the height of 1/2*h* are listed in Fig. 14. Similar structures of the flow field are obtained with different heights of artificial reefs. Within the reef, the flow velocity is close to the inlet velocity. In the area on either side of the artificial reef, the horizontal flow velocity is larger than the inlet flow velocity, and the maximum values are 11.5, 11.9, 11.9, 12.3, 12.9 and 12.9 cm/s, respectively, with increasing reef height. It is apparent that a higher artificial reef will have a wider area in which the horizontal flow velocity is greater than the inlet velocity. The slow flow field is distributed in the front and the back of the reef, where the structures of flow

Fig. 14. Velocity vector diagrams in horizontal cross-section with different heights of

artificial reefs (the inlet velocity is 11.0 cm/s)

**4.3 Flow field velocity vector diagram in the horizontal cross-section** 

reef unit performs best.

fields vary with the reef height.

The horizontal flow velocities along the line of y=0 at the horizontal cross-sections of z=1/2*h* are shown in Fig. 15. Similar distributions of flow velocities are found within and around artificial reefs at different heights. In front of the artificial reef, the horizontal flow velocities are approximate and decrease gradually when approaching the artificial reefs. Within artificial reefs, the flow velocities are larger than the inlet flow and peak at the center of the reefs. In addition, with the increase of the reef height, the maximum horizontal flow velocity within the reef is also on the increase. At the rear part of the artificial reefs, the flow velocities show a long-distance attenuation until the locations are sufficiently far away from

Fig. 15. Distribution of the horizontal flow velocities along the line of Y=0 at the horizontal cross-section of Z=1/2*h* (*h*=5.0, 6.0, 7.0, 8.0, 9.0, 10.0 cm)

the reefs, which are the slow flow regions as mentioned earlier. The smaller the artificial reef is, the lower the horizontal flow velocity is at the rear of artificial reefs. However, there is a special phenomenon where the lowest velocity occurs when the reef height is 7.0 cm. In other words, a preferable slow flow effect is acquired at the reef height of 7.0 cm.

#### **5. Flow field characteristics of two hollow cube artificial reefs**

The arrangements of two models of artificial reef are shown in Fig. 16. The spacing of two parallel combined models is 0.5*h*, 1.0*h*, 2.0*h* and 3.0*h*. The spacing of two vertical combined models is 1.0*h*, 2.0*h*, 4.0*h*, 6.0*h*, 8.0*h*, 10.0*h* and 12.0*h* (*h*=7.5 cm).

Fig. 16. The arrangements of two hollow cube artificial reefs

The Investigation of the Hydrodynamics of an Artificial Reef 95

Fig. 18. Horizontal flow velocity contour plots of a single and two parallel artificial reefs

The mutual effect of two reefs is very strong, and the slow flow velocity fields in the front and the back of two artificial reefs nearly connect when the spacing is 0.5*h*. Thus, a larger area of slow velocity flow field is produced for a 0.5*h* gap distance. When the spacing increases to 1.0*h*, downstream of the reefs, the flow speed begins to increase, and the construction of the flow field presents a trend of separation. The slow velocity flow fields behind two artificial reefs are separated from each other by and large when the spacing is 2.0*h*. After that point, the structure of the flow field for each artificial reef becomes the same as the single condition, and the interaction between the two reefs is slight when the distance

Fig. 19 compares the upwelling field of two vertical artificial reefs with different spacings. As shown in the graphs, for different spacings, the latter artificial reef causes little impact on the upwelling field of the first artificial reef. With different spacings, the scales of the upwelling field of the first reef are the same as that of a single reef. Nevertheless, with the increase of the vertical spacing from 2.0*h* to 12.0*h*, the height of the upwelling field of the second incident flow artificial reef increases gradually. When the spacing is 12.0*h*, the height

of the upwelling field of two artificial reefs is close, but the area gap is greater.

with different spacings (the horizontal cross-section is z=1/2*h*, *h*=7.5 cm)

increases to 3.0*h*.

**5.2 Two vertical hollow cube artificial reefs** 

#### **5.1 Two parallel hollow cube artificial reefs**

Fig. 17 presents the numerical results for the upwelling field of single and two parallel artificial reefs with different spacings. Compared to a single artificial reef, the heights of the upwelling field increase with spacing at first and then decrease until steady. When the spacing is 0.5*h*, the height of the upwelling field reaches the maximum value of 13.8 cm, and the corresponding area is 49.0 cm2. When the spacing is equal to or larger than 2.0*h*, the height of upwelling field has a steady value of 12.5 cm, and the steady value of the area is 35.0 cm2.

Fig. 17. Distribution of the upwelling field of a single and two parallel hollow cube artificial reefs with different spacings by simulation (the inlet velocity is 11.0 cm/s)

Fig. 18 shows a long and narrow slow flow field spread at the rear of a single artificial reef. Along the forward direction of the x-axis, the maximum horizontal flow velocity appears within the artificial reef, and after that, the flow velocity first decreases and then increases.

Fig. 17 presents the numerical results for the upwelling field of single and two parallel artificial reefs with different spacings. Compared to a single artificial reef, the heights of the upwelling field increase with spacing at first and then decrease until steady. When the spacing is 0.5*h*, the height of the upwelling field reaches the maximum value of 13.8 cm, and the corresponding area is 49.0 cm2. When the spacing is equal to or larger than 2.0*h*, the height of upwelling field has a steady value of 12.5 cm, and the steady value of the area is

Fig. 17. Distribution of the upwelling field of a single and two parallel hollow cube artificial

Fig. 18 shows a long and narrow slow flow field spread at the rear of a single artificial reef. Along the forward direction of the x-axis, the maximum horizontal flow velocity appears within the artificial reef, and after that, the flow velocity first decreases and then increases.

reefs with different spacings by simulation (the inlet velocity is 11.0 cm/s)

**5.1 Two parallel hollow cube artificial reefs** 

35.0 cm2.

Fig. 18. Horizontal flow velocity contour plots of a single and two parallel artificial reefs with different spacings (the horizontal cross-section is z=1/2*h*, *h*=7.5 cm)

The mutual effect of two reefs is very strong, and the slow flow velocity fields in the front and the back of two artificial reefs nearly connect when the spacing is 0.5*h*. Thus, a larger area of slow velocity flow field is produced for a 0.5*h* gap distance. When the spacing increases to 1.0*h*, downstream of the reefs, the flow speed begins to increase, and the construction of the flow field presents a trend of separation. The slow velocity flow fields behind two artificial reefs are separated from each other by and large when the spacing is 2.0*h*. After that point, the structure of the flow field for each artificial reef becomes the same as the single condition, and the interaction between the two reefs is slight when the distance increases to 3.0*h*.

#### **5.2 Two vertical hollow cube artificial reefs**

Fig. 19 compares the upwelling field of two vertical artificial reefs with different spacings. As shown in the graphs, for different spacings, the latter artificial reef causes little impact on the upwelling field of the first artificial reef. With different spacings, the scales of the upwelling field of the first reef are the same as that of a single reef. Nevertheless, with the increase of the vertical spacing from 2.0*h* to 12.0*h*, the height of the upwelling field of the second incident flow artificial reef increases gradually. When the spacing is 12.0*h*, the height of the upwelling field of two artificial reefs is close, but the area gap is greater.

The Investigation of the Hydrodynamics of an Artificial Reef 97

Fig. 20. Horizontal flow velocity contour plots of a single and two artificial reefs with

minimum, a larger spacing leads to a lower flow velocity.

Fig. 21 shows that the flow velocity within and in the front of the first artificial reef with different spacings is approximately equal to that of a single reef; however, the flow velocities in the rear of two reefs are less than that of the single condition. The same distribution regularity of the flow velocity between two artificial reefs is obtained for different spacings. The flow velocity decreases first and then increases suddenly in the front field of the second artificial reef. The same distribution rules for flow velocities also exist in the rear of the two reefs for different spacings. When the spacing is 4.0*h,* the minimum flow velocity in the area between the two artificial reefs has a minimum value; after that point, it increases with spacing. It was also found that the minimum velocity in the back of the two reefs is acquired at the spacing of 2.0*h*, and a large gap was found compared with other conditions. After the key point in the back field of two reefs where the flow velocity is the

different spacings (Z=0.5*h*)

Fig. 19. Distribution of the upwelling field of a single and two vertical hollow cube artificial reefs with different spacings by simulation (the inlet velocity is 11.0 cm/s)

As shown in Fig. 20, the flow fields between two reefs are constantly changing with increasing spacing. The horizontal flow field structure of two artificial reefs with 1.0*h* spacing is similar to that of a single reef. With the spacing of two reefs added to 2.0h, the construction of the flow field presents a trend of separation. When the spacing is 4.0*h*, the flow velocity in most areas between the two reefs is slow after that the flow velocity increase gradually with the spacing. The interactions of two artificial reefs are first strengthened and then weakened with increasing distance.

Fig. 19. Distribution of the upwelling field of a single and two vertical hollow cube artificial

As shown in Fig. 20, the flow fields between two reefs are constantly changing with increasing spacing. The horizontal flow field structure of two artificial reefs with 1.0*h* spacing is similar to that of a single reef. With the spacing of two reefs added to 2.0h, the construction of the flow field presents a trend of separation. When the spacing is 4.0*h*, the flow velocity in most areas between the two reefs is slow after that the flow velocity increase gradually with the spacing. The interactions of two artificial reefs are first strengthened and

reefs with different spacings by simulation (the inlet velocity is 11.0 cm/s)

then weakened with increasing distance.

Fig. 20. Horizontal flow velocity contour plots of a single and two artificial reefs with different spacings (Z=0.5*h*)

Fig. 21 shows that the flow velocity within and in the front of the first artificial reef with different spacings is approximately equal to that of a single reef; however, the flow velocities in the rear of two reefs are less than that of the single condition. The same distribution regularity of the flow velocity between two artificial reefs is obtained for different spacings. The flow velocity decreases first and then increases suddenly in the front field of the second artificial reef. The same distribution rules for flow velocities also exist in the rear of the two reefs for different spacings. When the spacing is 4.0*h,* the minimum flow velocity in the area between the two artificial reefs has a minimum value; after that point, it increases with spacing. It was also found that the minimum velocity in the back of the two reefs is acquired at the spacing of 2.0*h*, and a large gap was found compared with other conditions. After the key point in the back field of two reefs where the flow velocity is the minimum, a larger spacing leads to a lower flow velocity.

The Investigation of the Hydrodynamics of an Artificial Reef 99

This work was financially supported by the National Natural Science Foundation (NSFC) Project No.50809014 and 50921001, the National 863 High Technology Project No.2006AA100301, the Specialized Research Fund for the Doctoral Program of Higher Education No.200801411094 and Special Fund for Agro-scientific Research in the Public

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spacing of 2.0*h*, and, at a larger spacing, there was a lower flow velocity.

**7. Acknowledgments** 

Interest Project NO.201003068.

365-371

No.4, pp. 406-412

University, America.

**8. References** 

spacing was 4.0*h*, the flow velocity in the area between the two reefs obtained the minimum value. Behind the two reefs, the lowest flow velocity was achieved at a

Fig. 21. Distribution of the horizontal flow velocities of two vertical artificial reefs along the line of Y=0 at the horizontal cross-section of Z=1/2*h* (*h*=7.5 cm)

#### **6. Conclusions**

Some main conclusions can be drawn as follows:


spacing was 4.0*h*, the flow velocity in the area between the two reefs obtained the minimum value. Behind the two reefs, the lowest flow velocity was achieved at a spacing of 2.0*h*, and, at a larger spacing, there was a lower flow velocity.

#### **7. Acknowledgments**

98 Aquaculture and the Environment - A Shared Destiny

Fig. 21. Distribution of the horizontal flow velocities of two vertical artificial reefs along the

1. The flow field within and around a single hollow cube artificial reef was investigated by physical experiments and numerical simulations. The upwelling and back vortex flow fields that arose from artificial reefs were analyzed by using qualitative and quantitative analysis methods. According to the comparisons, there is a good

2. Based on the experimental verification, a detailed numerical study was conducted to investigate the effect of reef height on the structure of the flow field. The height and area of upwelling current region increased linearly and nonlinearly with increasing reef height, respectively. When the value of r (the reef height to water-depth) was 0.2, the normalized maximum and average upwelling flow velocities reached their maximum values. An exponential growth relationship existed between the length of the back vortex flow and the reef height. The flow field on either side of artificial reef was also discussed. A preferable unit artificial reef effect was achieved when the ratio of the reef

3. In the meantime, the influence of the arrangement (parallel and vertical) and spacing on the flow field of the two artificial reefs were discussed using the results of the numerical method. In the parallel combination, the scale of the upwelling field reached the maximum value, and a larger area of slow velocity flow field was obtained. The interaction between the two reefs was slight after the spacing became larger than 2.0*h.*  In the vertical combination, the latter artificial reef had a weaker effect on the distribution of flow velocities within and in the front of the first artificial reef. When the

line of Y=0 at the horizontal cross-section of Z=1/2*h* (*h*=7.5 cm)

agreement between the numerical and experimental results.

Some main conclusions can be drawn as follows:

height to water-depth was 0.2.

**6. Conclusions** 

This work was financially supported by the National Natural Science Foundation (NSFC) Project No.50809014 and 50921001, the National 863 High Technology Project No.2006AA100301, the Specialized Research Fund for the Doctoral Program of Higher Education No.200801411094 and Special Fund for Agro-scientific Research in the Public Interest Project NO.201003068.

#### **8. References**


**Water Management** 

Zhang, H.H. & Sun L. (2001). Resources Science. *On reproduction increase of the sea aquatic resources by artificial fish-reef engineering*. Vol.23, No.5, pp. 6-10 **Part 2** 
