Accepted Manuscript
Damage prediction of horizontal axis marine current turbines under Hydrody- namic, hydrostatic and impacts loads
M. Nachtane, M. Tarfaoui, A. El Moumen, D. Saifaoui
PII: S0263-8223(17)30664-5
DOI: http://dx.doi.org/10.1016/j.compstruct.2017.03.015
Reference: COST 8333
To appear in: Composite Structures Received Date: 27 February 2017 Accepted Date: 6 March 2017
Please cite this article as: Nachtane, M., Tarfaoui, M., El Moumen, A., Saifaoui, D., Damage prediction of horizontal axis marine current turbines under Hydrodynamic, hydrostatic and impacts loads, Composite Structures (2017), doi:
http://dx.doi.org/10.1016/j.compstruct.2017.03.015
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Damage prediction of horizontal axis marine current turbines under Hydrodynamic, hydrostatic and impacts loads
M.Nachtane1.2, M.Tarfaoui1, A. El Moumen1, D.Saifaoui2
1 ENSTA Bretagne, IRDL/LBMS, Department of Fluid Dynamics Materials and Structures, 29806 Brest, France
2 FSAC - UH2C, Laboratory for Renewable Energy and Dynamic Systems, Morocco Phone number: +33(0) 298348705, e-mail: mostapha.tarfaoui@ensta-bretagne.fr
Abstract
: Marine energy is one of the most exciting emerging forms of renewable energy.Tidal turbines are used to extract this energy and installed on the seabed at locations with catastrophic loading. The present paper employs the finite element method to simulate the behavior of GRP composite nozzle of a tidal turbine under low-velocity impact with implementation of a failure criterion. To investigate this situation, a parametric analysis is conducted which deals with the effect of velocity, energy and geometry of the impactor. The mechanical behavior has been analyzed as both kinematic effect due to deflection of the composite structure and dynamic effect caused by the interaction between the impactor and the hydrodynamic and hydrostatic pressures over the loading. The stress and the deformation distribution are presented. On the other hand, damage modeling was formulated based on Hashin criteria for intra-laminar damage. The effects of the impact velocity and the panel’s flexibility on the initiation and propagation of damage have been investigated.
Keywords:
Renewable marine energy, Composite materials, Current turbine, FEA, Dynamic behavior, Damage criteria.1. Introduction
The kinetic energy available within tidal currents is an untapped source or renewable energy [1]. If an effective method of capturing this energy can be developed, tidal currents could be harnessed to help satisfy the world’s growing energy needs. Several studies have shown that marine currents have a large potential as a predictable sustainable resource for generation of electrical power [2, 3]. Horizontal axis marine current turbines are one favorable technology that is being developed for this purpose.
Generally, the marine industry interests in the use of marine current turbine for electrical power production. The ability to predict the dynamic behavior of these turbines is essential for the design and analysis of such systems.
In use, the nozzle of a tidal turbine can be prone to accidental impact. This phenomenon may be large enough to cause damage in the composite materials. Damage modeling [4] of light weight structure is an active challenge in many applications such as marine, aerospace and naval fields. However, these structures are very susceptible to degradation of their properties and consequently a catastrophic failure can occur with more than one damage modes [5].
This investigation registers as part of research works which aims at the numerical modeling of the composite behavior under dynamic loads for naval applications. This research axle is of a big importance in various domains following the example of renewable marine energy. In this respect composite materials play a central role in the development of renewable marine energy conversion systems such as turbines .
Today, large tidal turbine blades are almost all made of glass fibre reinforced polymer (GFRP) because it currently represents the best way to strike a balance between performance, weight and
structural integrity [6], because the marine environment is particularly require and aggressive (corrosion due to salt, forces of the currents and storms. In this context we used this composite material to analyse the structural integrity of the nozzle. The advantage of GFRP composites is that they relatively inexpensive and provide sufficient strength and stiffness. However, as the turbines size increases, carbon fibre reinforced polymer (CFRP) becomes more popular for developing some parts of the blades and/or the nozzle, such as spar caps and some critical areas such as the trialling edge according to the FEA simulation. On the other hand, carbon fibres normally cost 10-20 times more than glass fibres. In fact carbon fibres provide a much higher modulus and significant weight reduction. Finally GFRP material was selected as a compromise between cost and performance.
In order to meet the needs of the manufacturers of tidal current turbines, which is generally linked to a problem of mass gain, composite materials present a considerable asset on account of their excellent «mass/resistance» and «mass/rigidity» relations. A structural design of ducted tidal current turbines using composite materials has therefore been examined. The duct of the tidal current turbine is especially confronted by the impacts due to its particular position.
The impact damage aspect has also been examined in detail in the present research study.
This paper presents a finite element analysis of dynamic behavior of GFRP marine current turbines. The first part aims to analyze the effect of the shape and the velocity of the impactor on the dynamic response and damage kinetics inducted to the nozzle in service. The second part is concerned with the development of an impact FE model, including Hashin criteria, used for damage prediction. Simulated damage is compared for different impactor geometry and velocity. The improved understanding of these phenomena and the development of predictive tools are part of an ongoing effort to improve the long-term integrity of composite structures for underwater applications.
2. Structure, boundary conditions and materials
2.1.Structure, boundary conditions
Figure 1 shows the profile of the turbine that is used to generate the 3D structure of the tidal turbine. We traced the hydrodynamic profile using the Heliciel software. By extension function of ABAQUS, the 3D structure of marine turbine is obtained as presented on figure 2.
This structure is then introduced in the Abaqus finite element code [7] in order to carry out simulations of impact tests and to analyze the dynamic behavior and to follow the kinetics of the damage.
Marine turbines are subjected to critical loads due to the high density of seawater and the accidental impacts in what they operate. However, adequate strength and stiffness are needed for hydrokinetic and can alone is implemented by the utility of greater enforcement materials so as composite materials, beginning with a design which offers an accommodation between efficiency, endurance, weight, and cost.
We have chosen in our study as boundary conditions a mechanical joint constraint in which the blades are embedded on a rotor itself connected to the stator, the fixed part of the machine see Figure 2 (a) .The mechanical joint constraints fully built-in:
U1 = U2 = U3 = UR1 = UR2 = UR3 = 0.
(a) (b)
Figure 1 : Hydrodynamic profile
(c)
Fig 2: Marine turbine: (a) real turbine, (b) simulated case and (c) final design
For a good design of the turbine and to understand its behavior under dynamic loading, we conducted impact tests. The marine turbine structure was exposed to different impactor forms such as hemispherical and conical, Figure 3. Parametric analysis is conducted which deals with the effect of the velocity, energy and mass of the impactor.
(a) hemispherical (b) conical Fig 3: Impactor forms
2.2.Materials and proprieties
The materials used in this study are the ones taken directly from a real current turbine. They are constituted of biaxial mat of glass fibers in a Polyester resin matrix with 0.286 mm thickness each layer. The composite has been prepared using the vacuum infusion process and cured at room temperature. The composite mechanical properties [8-9] are given in Tables 1 and 2.
Table 1: Properties of glass-polyester composite
Properties Value
Xt(MPa) 1021,3
Xc(MPa) 978
Yt(MPa) 29,5
Properties Value
ρ (kg/m3) 1960
E1(MPa) 48160
E2(MPa)= E3(MPa) 11210
Nu12 0,270
Nu13= Nu23 0,096
G12(MPa)= G13(MPa) 4420
G23 (MPa) 9000
Yc(MPa) 171,8
St(MPa)= Sc(MPa) 35, 3
Table 2: Ultimate stresses of glass-polyester composite
3. Numerical investigation
In this numerical model, the tidal turbine is modeled as a deformable structure and the impactor as the rigid body. In order to reduce computing times, by the reduction in the element number of models without harming the quality of simulation results, one strategy consists in optimizing the mesh model. Therefore, the mesh convergence is studied.
The lists to generate the shroud geometry imported into the finite element computer code (Abaqus) and recorded loads were applied. The fairing is meshed with shell elements of the type quadrangle with four nodes and reduced integration type S4R.
In order to model the dynamic phenomena under ABAQUS, it is possible to solve the problems with an Explicit or Implicit algorithm. Our choice being carried on a modeling with shell elements, the simulation of the elastic impact uses the same geometries as those of Fig.
4a. The impact speed is imposed as an initial condition on the projectile at reference point 20 kg weight.
Numerical simulation of damage in turbine structures can be studied by means of finite element methods [10, 11]. It should be noted that the damage is controlled by Hashin’s criteria to estimate the fiber and matrix damage initiation and propagation. For low impact velocity, no damage was observed.
(a) FE model of the fairing AMM6-12 at 5° (b) Current turbine Layup (10mm) Fig 4: Distribution of material on the nozzle
The finite element model is shown in Figure 4a with hydrostatic and hydrodynamic loads.
Figure 4b shows the composite structure layup [45/-45/0/90/90/0/-45/45] s, used in the model.
To investigate the mesh convergence, we base ourselves on the maximum stress and deflection on the trailing edge of the fairing. The convergence of the finite element model is presented in Figure 5.
(a) Convergence of maximum stress
(b) Convergence of maximum deflection Fig 5: Mesh convergence
The mesh density is defined as the minimum number of elements for which the convergence of properties was started [12]. Fig. 5 shows the results of the mesh convergence study of an elastic impact under the conditions described in the previous section with 5m/s incidental velocity. The evolution of the maximum stress and maximum deflection according to the mesh density is represented in Fig. 5. The generated meshes consist of quadrangular elements S4R of square aspect. The results of successive calculations seem to converge starting from 129490 elements. The mesh size is 100 mm length. The convergence is obtained from a ratio of "mesh size / total size of the structure" of 0.005. This ratio is retained in other fairing modeling geometries. Taking into account the strong evolution of the CPU according to the number of elements, it is not necessary to refine the mesh any further.
In nonlinear structural analyses using quadratic elements is not advisable for this type of modeling because it would entail a very large computing time; therefore in our study we chose a robust, general-purpose 4 noded quadrilateral element with linear interpolation and reduced integration (S4R) that is suitable for a wide range of applications because you will usually obtain better accuracy at less expense if you use a fine mesh of these linear elements rather than a comparable coarse mesh of quadratic elements. Therefore the final selected element in Fig 6 is S4R.
Fig 6: Final mesh for numerical simulation
4. Constitutive models
4.1.Damaged material response
In this section, progressive damage model is discussed explaining the equation of various failure modes implemented. Damage in composites occurs in two phases: damage initiation and damage evolution. Here we adapt the model suggested by Matzenmiller et al. [13]. to compute the degradation of coefficients of the stiffness matrix. In this model, the constitutive relationships for the damaged composite laminates can be written as:
σ = Mσ (1)
Where σ the real stress and M is the damage operator, which has the diagonal form
M =
1
(1 − d) 0 0
0 1
(1 − d) 0
0 0 1
1 − d
(2)
d, d, d are internal variables which characterize the fiber damage, matrix damage and shear damage, respectively. The damaged compliance matrix has the form:
=
1
(1 − ) −
0
−
(1 − 1) 0
0 0 1
(1 − )
(3)
and the corresponding stiffness matrix is obtained from
= 1
! (1 − ) (1 − )(1 − ) 0 (1 − )(1 − ) 1
(1 − ) 0
0 0 !(1 − )
(4)
Where D= 1 − (1 − d)(1 − d)ϑϑ,E, E and G are undamaged material moduli, and ϑ, ϑare undamaged material Poisson’s ratios. The damage variables d, d, d can have different values for tension and compression, which will be denoted by d%, d&, d% , d&
correspond to four following modes:
d= 'd %if σ≥ 0
d& if σ< 0, (5) d= .d % if σ≥ 0
d& if σ< 0, (6)
In addition, we assume that the damage variable corresponding to shear in not independent and can be expressed as function:
= 1 − 01 − 1201 − 32(1 − 1 )(1 − 3) (7)
This criterion permits to detect in the stack the plies in which breakage of fibers and matrix appears.
4.2.Damage initiation criteria
Damage modeling in laminate composites can be studied by a stress or strain-based failure criteria approach or following damage mechanics concepts. Hashin’s has proposed four failure criteria for composites namely: fiber damage in tension and compression and matrix tensile and compressive failure. Hashin’s criterion has been implemented in the majority of the finite element software. Thus, in the present study, this criterion is used to estimate the fiber and matrix damage initiation and proposed as:
• Fiber tensile failure (σ≥ 0):
41= (56
78)+ :(;̂
=>)² (8)
• Fiber compressive failure (σ< 0):
43= (56
78)+ :(;̂
=>)² (9)
• Matrix tensile failure (σ≥ 0) 41 = (56
@8)+ (;̂
=>) (10)
• Matrix compressive failure (σ< 0) FB = Cσ
2SFG+ [IYB
2SFK− 1]σ
YB + (τ6
SN)² (11)
Where
XF: denotes the tensile strengths in the fibers direction, XB: denotes the compressive strengths in the fibers direction, YF: denotes the tensile strengths in the transverse direction, YB: denotes the compressive strengths in the transverse direction, SN: denotes the longitudinal shear strengths of the composite and SF: denotes the transverse shear strengths of the composite.
The coefficient : determines the contribution of shear stress on fiber tensile and σ, σ, τ6 the stress tensor.
4.3. Intralaminar failure based Continuum Damage Mechanic (CDM)
The composite material damage is a cumulative of the microscopic defects in both the fiber and the matrix and other types of failure, the initiation and developments of the micro-cracks with different scale size internal and external of the structure considered the main factor in the fracture mechanism. To simulate the evolution of the damage, modeling must take into account the various forms of damage occurring at the impact tests. It is not necessary that the numerical model take account all the physical phenomena observed if their presence does not affect in a relevant way the current turbine behavior. It was decided to restore only the damage of the matrix and fibers. This choice was dictated by the infiltration of water in the presence of this type of damage and which can lead to the rapid degradation of the material due to aging effect. For that, the Hashin criteria [14] were used.
4.4.Initiation Failure modes approaches in composite
The laminate damage initiation is happening when the true applied stress in the laminate reaches the Ultimate strength of the ply laminate. Explicitly, the debonding interface between the fiber and matrix is occurring due to difference in fiber transverse compressive modulus and matrix modulus that represents the main influence of initiation of the damage, for this reason the stresses are concentrated in local positions. Various failure criteria models have been adapted to predicate the initiation of the fracture based on a combination of the stress as
longitudinal and transverse direction with the fiber axis and the shear stresses, the more satisfy criteria is based on the Hashin theory [14]. Hashin (1980) was introduced a method for failure criteria for unidirectional fiber composite with second degree polynomial expansion.
For more simplicity, failure modes were divided into the four modes based on the failure planes perpendicular and aligned with the fiber direction with six parameters, hence the failure of fiber in the main direction with fiber-axis, and on the other hand the main failure of the matrix in transverse direction [15]. This criteria was widely applicable in the many commercial finite element software, however, many of researchers said that this model not predicted accuracy initial failure, especially in matrix and fiber compression modes.
4.5.Damage progressive Degradation materials models
Despite Satisfied the initiation of the failure modes in the composite materials, the material's stiffness continues to degrade with increasing the load, Figure 7. The phenomena called damage evaluation, the reduction in stiffness material properties is controlled by damage variables corresponding damage modes. The progression of damage evaluation in composite materials consists of the damage of fibers and matrix, equation 12.
d =δQR (δQR− δQRS ) δQR(δQR − δQRS )
(12)
where
δQR : equivalent displacement jump δQRS : onset equivalent displacement jump δQR : final equivalent displacement jump
Fig 2: Hashin’s Failure degradation model
The global model used for simulation is presented in figure 8. This model shows the turbine part and the impactor region. Many situations of accidental impact were treated with the presence of hydrostatic and hydrodynamic loads which are developed using two steps on Abaqus software:
(1)Step 1: A general static step for hydrostatic and hydrodynamic loads
(2)Step 2: An explicit dynamic step for impact on the structure resulting from the calculation of step 1.
Fig 8:Visualization of the overall system
5. Results and discussion
In this part, we have interested to analysis the dynamic response and the damaged area after impact loading with presence of hydrostatic and hydrodynamic loads. Table 3 presents the simulation results of the first step. These photos are the results of the circulation of a fluid with a speed of 2m/s.
Fairing profile AMM 12-6
Hydrodynamic pressure coefficient (Cp)
Hydrostatic pressure (Pa)
Table 3: Hydrodynamic and hydrostatic pressure applied to the fairing
5.1.Global behavior
We will focus in this section to the variation of the impact energy. We have identified: total energy (ETOTAL), kinetic energy (ALLKE), strain energy (ALLSE), internal energy (ALLIE), damaging energy (ALLDMD) and artificial energy (ALLAE). The analysis of energy variation leads to confirm the theory energy conservation of the system. Figure 9 shows the variation of the energies for 20m/s impact velocity. From this figure, it appears that the total energy (ETOTAL) is almost constant throughout the calculation and corresponds to the desired energy impact. Moreover, the summation of kinetic energy (ALLKE) and internal energy (ALLIE) correspond to the total energy. Therefore the conservation of the energy during impact test is obtained. We also observed that the evolution of the deformation energy
(ALLSE) is similar to the internal energy (ALLIE) until 1.5ms of test. But from that moment, the damage energy (ALLDMD) appears and the damage of the structure started. Finally, to confirm the hypothesis of energy conservation, we find that the internal energy of the structure is the sum of the strain energy and energy dissipation damage.
Fig 9: Evolution of impact energies during the period test (m=20kg, V=20m/s)
The evolution of the artificial energy or Hourglass energy (ALLAE) is analyzed. Figure 10 shows the obtained results. It appears that this energy is negligible throughout the test. The hypotheses of impact energy were satisfied. Therefore the created numerical model can estimate the evolution of damage in marine turbine.
Fig 3:Evolution of the interfacial energy during test, M=20kg - V=20m/s
5.1.Damaged structures
In this part, we focus on the damage appeared during the impact test under different scenarios.
Hashin’s criteria for fiber and matrix damages were introduced [15]. Figure 11 shows the force-time curves versus velocity impact for different impactor forms. The effects of impact geometry and velocities impact are noticeable. The maximum force corresponding to each
impactor type is: 450 kN for conical and 350 kN for hemispheric. Initially, the curve was linear and then became non-linear after the peak force due to initiation of damage.
In the case of accidental impact without damage, the force-time history has a parabolic curve, takes a symmetrical form, with a maximum pick. Consequently, the loading and unloading parts are identical. In our case, no symmetry between loading and unloading phases is observed, because the apparition of damage which are marked by the sharp decline of the force. At this moment the damage evolution of composites is started until complete failure.
(a) Hemispheric Impactor
(b) Conical Impactor
Fig 11: Force-time curves vs velocity impact (M=20kg, V=20m/s)
The graphs below show a decrease in the velocity of the projectile with the time during the impact. The general appearance of these curves describes two phases speed variation during impact. In the first phase, a rapid decrease is observed in the speed of the impactor to zero velocity corresponding to the start of the phase of elastic return. The impactor is severely hampered by the nozzle and loses much of its kinetic energy converted into deformation energy of the nozzle. At the end, this phase only the head of the impactor is still in contact with the nozzle. Then comes a second phase of varying the speed of the impactor which slowly believed to reach the residual speed without loss of energy in this case the greater speeds stabilize quickly, Figure 12.
(a) Hemispheric Impactor
(b) Conical Impactor Fig 12: Velocity-time curves (M=20kg)
The damage initiation in marine turbine is controlled. Figure 13 shows a snapshot of the damaged turbine. It appears that the damage initiation depends on the impactor geometry. The maximum damaged zone is obtained by conical geometry because of their tip. A small damaged zone is observed in the case of hemispherical impactor.
Fig 13: Damage of the nozzle under impact, (V=20 m/s, M=20kg) Conical Impactor
Fig 14: Damage of the nozzle under impact, (V=20 m/s, M=20kg) Hemispheric Impactor
The impact was performed on the trailing edge because it is the most sensitive part. One can see that there is an appearance of damage. Hashin criterion for matrix in tension (HSNMTCRT) has been reached for some layers. In the other hand, Hashin criterion for matrix in compression (HSNMCCRT), for fiber in tension (HSNFTCRT) and for fiber in compression (HSNFCCRT) is not checked.
To increase the deflection resistance without adding some significant weight, a sandwich panel construction is used for most of the airfoil area. Our structural design consists of diminishing the deflection at the nozzle trailing edge by trying several spar configurations.
Several spar configurations were tested for the structural core of the nozzle and consist of one or several webs. There are different ways of designing spar/shear webs, either as a girder connected by one or two shear-webs or as a full box like beam structure which is the best spar configuration compared with other configurations according to our numerical simulations (Figure 15). The structural integrity of the nozzle depends on the combination of composites
used to withstand the loads and the highest quality materials which are required for such marine applications.
ρ (Kg/m 3) E1(MPa) E2=E3 (MPa)
Nu12 Nu13= Nu23 G12 (MPa)
G13(MPa) G23 (MPa)
151 3518 50 0.5 0.02 157 157 157
Tableau 4: Material properties used for the sandwich panel core (Balsa AL600/10 CK-100)
Fig 15: Schematic view of the configuration with 32 ribs to the trailing edge
Figure 16 gives the response of the initial and reinforced structure. It can be concluded that the reinforcement of the trailing edge can be beneficial for the nozzle. Indeed, it can be observed that the presence of these spars prevented the occurrence of the damage.
(a) Without spars
(b) With spars
Fig 16: Damage of the nozzle (a) with spars and (b) without spars (M=20kg, V=20 m/s)
6. Conclusion
In this investigation, the numerical simulation of damage progressive in marine current turbine was first performed. The specimens were tested under different loading scenarios including impact with presence of hydrostatic and hydrodynamic loads. The structure consists of E-glass fibers reinforced polymer matrix. A different impactor form has been considered for three impact velocities. The effect of these parameters is noticeable. The variation of impact energy was controlled and analyzed. The notion of energy conservation was satisfied.
Qualitatively good predictions of the energy were shown. The damage is controlled with Hashin’s criteria. The principle conclusions are:
• Performance of impacted marine turbine depends on the fiber properties and especially the matrix formulation
• The maximum damaged area is obtained with a conical impactor
• During test the impact energy is conserved and equivalent to total system energy
• Establishment of numerical models is a first step in integrating the material responses for design of marine structures.
The study of the damage phenomenon of a hydro-turbine under impact has all its interest for the designer. Indeed, even a small damage can have a considerable effect on the durability of the structure. Damage will result in water infiltration which will contribute to the rapid aging of the nozzle and rapid degradation of the structure.
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