STATE OF ART OF DIFFERENT KINDS OF FLUID FLOW INTERACTIONS WITH PIEZO FOR ENERGY HARVESTING CONSIDERING EXPERIMENTAL, SIMULATIONS AND MATHEMATICAL MODELING

In this work, the different kinds of fluid flow interactions with piezo smart materials have been discussed for energy harvesting. The present work has been classified into the following categories: (i) experimental investigations (ii) simulation and (iii) mathematical modelling. In section (i) different experimental set-ups such as harvesting of energy with the help of vortex flow, turbulent flow, cross flow, flow in an open channel and closed channel and flow through nozzles have been examined. In section (ii) simulations studies performed with different tools/software like ANSYS/fluent, COSMOL etc. have been detailed. Lastly, in section (iii) different mathematical equations such as Navier-Stokes equation of motion, Continuity equation, finite element method, numerical methods, transport equations, Bernoulli equation, equation of linear elasticity, fluid structural equations, piezoelectric equations and coupled-wave equations are described for generation of energy with fluid’s interaction. The present work has to fulfil two aims: (i) active engineers can choose the best appropriate methodology for their work in the same field (ii) researchers can know about how the area of energy harvesting has been grown in various decades, what are the practical application of this field with real life and the literature gaps of the field.


INTRODUCTION
Energy generation is a phenomenon of employing the existing unexploited energy from the atmosphere, converting it suitably and utilize it for upcoming purposes.The obtained energy can be reserved as electrical energy which can be used to operate micro-powered devices in real time or can be stored in the battery for later use. Nowadays, two forms of the battery have been utilized for low-power electronics, specifically primary and secondary. A primary battery is a single-use or "throwaway" battery that is not reusable in the environment, whereas the secondary battery can be recharged yet again. While these storage devices are harmless and ecologically friendly, their bounded phase cycle, deceptive utility and inadequate life span reduce their utility. So, investigators are discovering a viable solution to generate and utilized energy in real-time as an automatic resource in handy devices, where the power is regularly harvested and utilized. It is vital to offer a different solution to the current requirement of micro-power so that individuals can create their self-supply of power. Some of the micro-scale energy harvesting system discussed by different researchers is an electromagnetic energy generating system, electrostatic energy generating system, thermo-electric energy generating system, solar energy generating system, piezo-electric energy generating system.  [1]. A model of compressible flowing fluid with turbulent characteristics and in this model, the equations for Reynolds Averaged Navier Stokes and piezo-electrics are used by [2]. They also mentioned the mechanical behaviour using a solid mechanical linear basic strain tensor, stress tensor equations.
In the present work, experimental set-ups, simulation studies, and mathematical modelling of

Open Channel Based Interaction
Fluid energy harvesting using the open channel is a rapidly growing area of research, especially for environmentally friendly and renewable resources, as shown in Figure 2. One of the most important model is constructed by placing a PVDF piezo-film in an open channel system having water flow at different rates [3,4,5]. The PEHF (piezoelectric energy harvesting with fluid) model is composed of a water tank (66x66x30cm), an open channel (117x23x23cm) with the proper gating system. Two motor pumps to circulate the water, PVDF film hung inside the channel, an electric circuit (four diodes of IN4007 MIC, 1 capacitor of 63v 1 eF), a battery to store the harvested energy. The piezo film connections are properly insulated with the rubber tape to increase their durability and also to make the circuit waterproof. The piezo patch is connected to a rectifier circuit to convert AC (alternating current) into DC (direct current). The layout of the open channel system for PEHF is shown in Figure 2. As the water discharge rate increases, the current and voltages also increase at all stages of experiments. The experimental model produced a 1.03µW power with a voltage of 0.83V and current 1.24µampere , when the fluid strikes at a rate of 55.24 litre/min on the patch. The output of the system is measured with the help of a multi-meter with both voltage doubler circuit and full bridge rectifier circuit. This energy harvesting model can be used where the water supply is continuous, ranging from low flow discharge as in household kitchen drains, brook, etc. to high flow water discharge sources such as rivers, lakes, bridges, waterfall, industrial waste disposal, etc.

Closed Channel Based Interaction
Interaction of fluid-structure through the closed channel has arisen in last few decades since it is easy to cope with other systems, as shown in Figure 3. The investigation has been carried out to generate energy at a micro-scale in different kinds of water flows on piezo-smart materials [6]. In close channel system, applied load is either impact load or continuous fluid force (with turbulent flow). A model for a fluid flowing in a close channel is proposed using different rectifier circuits and piezo patches as shown in Figure 3. The designed model consist a single ceramic piezo patch and produced a maximum voltage with voltage doubler circuit is 5.5V at 33m 3 /min flow rate, while for the full wave rectifier circuit it is 2.86V [7]. Same model for two patches, the maximum voltage for full wave rectifier circuit and doubler circuits is 2.3V device at the inlet side, and the piezo-patch at the outlet [8]. It has been noticed that when the fluid strike with a speed of 20.25 litre/min on a single patch and the most eminent voltage of 3.34 V is produced while double piezo-patch is produced is 2.42 V for an optimal flow speed of 31.26 litre/min.
Further, Akaydin carried out the experimental investigations by placing the PVDF piezoelectric beam in the wind tunnel [9,10]. They analysed the output in the wake of the cylinder and turbulent boundary layer. The power generated from the circular cylinder is 4µW when the flow speed is 7.23 m/s and in the boundary layer flow power is 0.06µW over a different load resistance of 100kΩ and 10MΩ respectively.

Vortex Based Interaction
Interaction of fluid structure with vortices is a powerful tool for generation of energy at micro level. Goushcha has done a lot of research in this field by subjecting vortices in the form of the wake of bluff bodies to generate electric power with a piezo-electric beam [11]. A power of 5.5 flow-induced vibration [12]. They pumped up the tap water in the circular pressure chamber which has PVDF patch arrangement. It is observed with National Instruments data acquisition system that 2.2 V and 0.2µW be generated when 1.19 kPa is applied under 26 Hz frequency from the proposed set-up.

Flags Based Interaction
Generation of energy using various placements of piezo-electric flags is a keen area of research. In this aspect scientist Michelin & Doare worked on the energy harvesting effectiveness of the piezo-electric flags placed in axial flow by using numerical technique [13]. A flexible piezo-electric energy generator has been placed in the cross-flow. Hence it caused the strain in structure and output power is produced. The effect of various factors like turning ratio, flow velocity, mass ratio and piezo-electric coupling on the efficiency of harvester has been investigated. According to output, it has been observed that high fluid flow can advance the efficiency and robustness of the energy generating process.

Nozzle Based Interaction
This is one of the most valuable voltage generation's system using smart materials. Different factors like number of nozzles with different arrangements, circuits, and distance of nozzles from smart materials can influence the voltage produced by the system [14]. Nozzle Based Interaction model has been developed by Rani & Chhabra with number of varying factors like the distance of patch from the nozzle, number of nozzles, angle of the nozzle with horizontal and different circuits. The voltage is generated using dynamic pressure of the fluid flowing through the nozzle and PVDF patch is used for converting this pressure energy into electrical energy [15,16,17]. It has been investigated that the highest voltage of 17.54 V has been generated by voltage doubler circuit at 16.92 m/s is the fluid flowing rate at 75 cm far away from the nozzle at an angle of 35 • .

Other Piezoelectric Based Interaction
Some other important mechanism of energy harvesting has been achieved by various researcher. Among these mechanisms one of the classical techniques of generating voltage in which construction of pressure chamber has been done with one side of the chamber is composed of a piezo-electric beam and the smart material piezoceramics are works as a control instrument [18,19]. Circuit generates voltage with the help of piezoceramic patches and the sensor [20] measured the voltage produced between the piezoceramics materials. A strong proportional relation has been obtained between voltage produced and strain accumulated over the piezoceramics patches. One of the experimental tasks of generating voltage is dynamic [21,22] loading with patches. Yadav M et al. generated electric energy by using dynamic periodic loading on piezo-smart materials [23]. For this purpose, an experimental model of proposed set-up is constructed by using circular supported boundary conditions for three different loads 33 N, 42 N and 46 N with 20 numbers of strokes. The piezo patch is attached with a voltage doubler circuit and full bridge rectifier circuits. 6.10 V is the highest voltage obtained for 46 N applied load in the circular boundary condition. The energy generation in a fluidic environment by using strips and piezo-smart materials at different frequency ranges is an emerging field of investigation for various researchers in order to generate the energy-yielding capabilities of ionic polymer-metal composite (IPMCS) in the fluid environment [24]. An experiment set up has been modelled and designed with IPMCS strip immersed in water with a resonance frequency in the range of 2-50 Hz under the resistance of 10Ω ,the power obtained through base excitation frequency of polymer is of 1nW. Further piezo-electric micro pumps are acting as a boon for energy harvesting because of their advanced features. Neto [25] developed a self-exciting Poly-methyl-methacrylate valve, less piezo-electric micro pump. It has been observed that the highest value of flow rate is 4.53m 3 /min with a frequency of 25.2 Hz and correspondingly a voltage of 150 V is generated.

SIMULATION OF FLUID FLOW WITH PIEZO
In the previous few decades, various techniques of energy harvesting have come into play [26]. Harvesting of energy from the fluid is the great need of the world because of its ecofriendly behaviour, easy to integrate with other systems and readily available in the environment [27]. So, researchers are swinging towards the pre determination of the interaction between fluid flows with piezo-patches in virtual environment. Using simulation software, we pre-determine the results related to the energy harvesting model using virtual environment.
Simulation has been done by various modern software like ANSYS, COMSOL Multiphysics software and FLUENT [28]. The important techniques used in this software for simulation purposes are like finite element method, finite difference method and numerical methods such as the Galerkin method of time and space discretization. Many researchers have used various ways of simulation for different energy harvesting models and for various types of flow analysis.

Simulation of Piezo-Fluid Interaction with ANSYS/FLUENT
In ANSYS based simulation, a user-defined function code has been created between piezocircuit and the fluid in ANSYS/FLUENT software. Stress strain analysis, Impact force variation, voltage generation, power production using the constructed model has been pre-analysed using simulation [30,31]. Simulation has been done with the method of volume meshing in ANSYS software. A comparative analysis between the experiment and simulated models has been done to validate the model.
One of the important ways of generation of power by interaction of unsteady turbulent flow with a piezo-electric generator. In this simulation technique the piezo-electric beam has been located within the turbulent boundary and waked of a circular cylinder, hence the highest output power of 60µW is recorded by using FLUENT software for flowing speed of 7.12 m/s with pressure of striking fluid, while this power differs from electric power 7µW obtained from alternating current [29,30]. Models are refined numerically and analytically to realize the consequence of material criteria on energy producing efficiency of more than one-layer construction [33]. The solution of an equation is done by the technique of variables separation. ANSYS software is used for numerical simulation.

Simulation of Piezo-Fluid Interaction with COMSOL
Various researchers in today's era heavily investigate different types of flows in different types of channels and fluid-structure interaction mechanism using different simulation tools. Researchers also discussed the ways to deal with the shear over the surface of the structure using COMSOL. Navier-Stokes equations and stress tensor equations are used for simulation while Green's formula and Dirichlet boundary value problem are used for numerical calculations for an incompressible fluid. Sin et al. performs the elastic eel's motion from the wake of deceiving structure in a cross-flow. Collaboration between eels and vortex shedding behind a deceive structure is investigated mathematically [34]. The motto of the research is to upgrade the eel's oscillation by pairing with the varying vortices. COMSOL software is used for simulation in the fluid-structure interaction (FSI) model. In order to generate energy by designing and simulating a valve-less diaphragm based piezo-electric micropump with the interaction of fluid [35]. All

Simulation of Piezo-Fluid Interaction with Eulerian and Lagrangian Technique
Sanders et al. did further advancement, by presenting a recent important technique for simulating stiff structure motion in two-phase flow for an incompressible fluid [36]. The investigation aims to numerically define an algorithm for the simulation of stiff structure reacting with incompressible two-phase viscous flowing fluid in the occurrence of liberates surfaces. Numerical simulation has been carried out with the finite element technique and time integration method.
The finite difference method is used in the Eulerian and Lagrangian domain of grids structure to calculate the velocity and pressure of the two-phase fluid flowing structure.
To maximize the amount of power, many factors such as the thickness and stiffness of the eel materials, eel length, the bluff body width, the spacing between the body and eel head are considered. Further, the interaction of the fluid with vibrating structures is also the main source for energy harvesting. Afrasiab & Movahhedy carried out the interaction of fluid flowing model with vibrating solid structure in two different micro-pumping devices with various boundary conditions by using the formulation of the Lagrangian-Eulerian approach with VMS finite element simulation technique and thus calculated the efficiency of system [37].
Further advancement in this technique is attained by Ravi & Zilian by proposing a consistent and simultaneous investigation of small-scale energy harvesting systems, which aim toward flowinduced vibrations with trustworthy sensitivity toughness and efficient study of the coupled non-linear system [38]. It includes fluidic energy harvesting at various boundary conditions, structural piezoceramics and electric circuit equations. Simulation is done with the help of the finite element method (FEM) and the Galerkin method of time and space discretization.

Other Simulation Technique
Interaction between fluid and oscillators is also played a key role in energy generating. Matsiev operated flexural mechanical resonators at a high rate of flowing liquid [39]. Interaction between the oscillator and surrounding fluid is theoretically considered. For numerical simulation, Navier-Stokes equations and continuity equations with suitable boundary restrictions on the surface of the resonator and at infinity are used for ideal fluid.
The interaction of fluid-structure with propagating wave in 3D is also investigated by various researchers [40,41,42]  To generate energy using a diffuser nozzle through a piezo-electric micropump with two dissimilar models, the contrast has been made by Jeong [44]. The obtained results are showing that the model is extremely significant for calculating the performance of the diffuser nozzle with piezo-electric micropump. The fluid flowing rate is 2.83 under the deformation of 2.05 µl/s/cm at 50Hz frequency while the flowing rate under the deformation of 3.61 µl/s/cm is 3.76 at 90Hz frequency.
A further investigation has been carried out for the generation of energy from a vertical flow by using a passive heaving foil [45,46]. An immersed boundary method with the interaction of incompressible fluidic structure is used for doing numerical simulation.

MATHEMATICAL MODELING OF FLUID FLOW WITH PIEZO
Generating of energy through piezo-smart materials with the striking of fluid includes various mathematical equations for numerical calculation of electrical voltage [47,48,49]. Different types of fluid interaction model different governing equations of mathematics are used as per the requirement of structure.

PEHF Modelling with Analytical Equations (Navier-Stokes and Continuity Equations)
One of the most familiar techniques of energy generation is the two-phase flow which is mostly used by researchers. Sanders presented a recent technique for simulating stiff structure motion for two-phase flow in an incompressible fluid [36]. The investigation aims to define an algorithm numerically for the simulation of stiff structure, which is reacting with incompressible two-phase viscous flowing fluid in occurrence of liberates stop layers. Equation of conservation of momentum in two-phase incompressible flow is used, and Navier-Stokes equations for incompressible Newtonian viscous fluid is also applicable for numerical calculation. Equation of conservation of momentum in two-phase incompressible flow is given as where ρ f is the fluid's density,u is the fluid's velocity and σ f is the fluid's stress.
In the case of the incompressible Newtonian viscous fluid equation is where p is the hydrostatic pressure of the fluid and µ f is the viscosity of the fluid.
Navier-Stokes equations for fluid is where g is the gravity.
Momentum conservative equation is Transport equation between turbulence kinetic energy k and turbulence dissipation rate ε 1 is given by The piezo-electric equation for Cauchy stress tensor and electrical displacement is given by where S is the strain symmetric tensor, − → E is the electric velocity field,T is the stress symmetric tensor,β is the elasticity tensor and d T is the piezoelectric coupling tensor for a strain -charge form.
Further advancement in this field has been done by Akayein by investigating the energy harvesting technique for the unsteady turbulent flow of fluid with a piezo-electric generator [9]. The where ρ D Dt = − ∂ ∂t +V K ∂ ∂ x K is total derivative operator Where, p is the pressure in the fluid, ρ is the density of the fluid, V i is the fluid velocity, τ i j is the stress vector and S KK is strain rate tensor.
The generation of energy with the nozzle by using a PZT micropump is a vital area of research for investigation. Further, Jeong numerically simulates the diffuser nozzle, which occupying a piezo-electric micropump having two dissimilar models [44]. A numerical solution of models has been carried out and comparison has been made among them [59,60,61]. The results show that the model is extremely significant for calculating the diffuser nozzle-occupying piezo-electric micropump performance. Navier-Stokes equations and continuity equation in the curvilinear coordinates are used. The piezo-electric equations for the piezo-disk are also used.

Equation of Navier-Stokes and continuity in the curvilinear coordinates are
where ρ is the fluid density, p is pressure, t is time, x i is cartesian coordinates, µ is the effective dynamic viscosity, U j is velocity component in ξ j direction, J is Coordinate transformation Jacobian and u i is Cartesian velocity component. With the help of various arrangements of fluid structure different researchers have done tremendous work in this field. Rojas designed and simulated valve-less, diaphragm based piezoelectric micropump [35]. All the simulation was made using COMSOL Multiphysics software. Using the piezo-electric device module simulates the deformation of the membrane under different voltage, using different arrangements of the membrane. Piezo-electric constitutive strain-charge relation and Navier-Stokes equations for incompressible fluid are used.
Bernoulli's equation and Newton's 2nd law are also used in simulation.
Newton's 2 nd law is where ρ is the density of the solid, u is solid displacement vector, σ is stress tensor, F v is body force per unit volume.
Navier-Stokes equations describe incompressible fluid motion as: where ρ is density of the fluid,u is fluid velocity vector,p is pressure, F is body force, I is identity tensor, η is viscosity and F is vector that represents all external forces.

Continuity equation is
where h P is sum of head gains of the pump, h f is sum of head losses due to pipe friction and h L is sum of head losses in accessories. In this sequence of generating energy through PZT valve-less micropump, Johari carried out the periodical flow performance in the valve-less piezo-electric micropump with the Fluid-Structure Interaction (FSI) simulation technique [52].
Their investigation was based on boundary motion, equations of fluid, equations of structural equations, and actuator equations as given below. Navier-Stokes equations: where u i is the velocity of fluid, ρ is density of fluid, σ i, j is stress tensor, f i is body force per unit mass andû j is mesh velocity. The method of placing piezo-electric flags in a fluidic medium comes in the process from the last few decades. Li investigated the process of how the ocean wave energy or the energy from the fluid has been converted into electricity [32].
where − → u f is velocity for flowing of fluid, − → u s is velocity of the solid mechanics and − → F is volume force field.

The transport equation for fluid is
where ε is turbulent dissipation factor, G k is turbulent kinetic energy produced by average velocity gradient, G b is turbulent kinetic energy produced by buoyancy, Y m is effect of pulsating expansion on total turbulent kinetic energy incompressible turbulence.
Flow-induced vibrations play a key role in piezo-electric energy generation system in present society. In this field, Ravi proposed a constant and simultaneous concurrent investigation of elegant small-scale energy harvesting techniques aiming for flow-induced vibrations [38]. Their purpose of allowing trustworthy sensitive toughness and efficient study of a coupled non-linear system that includes fluid structural piezoceramics and electric circuits. Simulation is done with the help of the finite element method (FEM). Navier-Stokes equations for incompressible fluid flow are also used.
The incompressible Navier-Stokes equations for fluid flow as The Cauchy stress tensor T is given by where ρ is density of fluid, f is external body forces, u is fluid's velocity, µ is kinematic viscosity, p is hydrostatic pressure, D is strain rate tensor and I is identity tensor.
Flowing of fluid through various kinds of channels is a task that takes revolution in the world of energy harvesting. Particularly the flow arises due to recirculation in a channel is used by many of the researchers for energy generation. Bank carried out the controlling of recirculation flow in a channel using the fluid-structure interaction mechanism [18]. Experimentalists have discussed the ways to deal out the shear over the surface of the structure. For an incompressible fluid, Navier-Stokes equations are used for simulation purposes. The stress tensor equation is also used for numerical calculations.
Incompressible Navier-Stokes equations is Stress tensor is given as where u is velocity field, p is pressure, ρ • is mass density, µ is viscosity of the fluid, f is density of external forces.
Matsiev has made further improvements by taking the interaction between the oscillators and surrounding fluid and operated flexural mechanical resonators at high rate throughout liquid [39]. For numerical simulation, Navier-Stokes equations and continuity equations with suitable boundary restrictions on the surface of the resonator and at infinity are used. The concept of Navier-Stokes equations for ideal fluid is also used. Equations of Navier-Stokes and continuity with appropriate boundary conditions on the resonator surface and in infinity are as Navier-Stokes equations for ideal fluid is ρ is fluid density, t is time, p is pressure, η is fluid viscosity, − → u • (s)is velocity distribution along resonator surface, − → u is fluid velocity and S is indexes.
Interaction of fluid-structure with propagating wave is an interesting topic for research in three dimensional [41]. The finite element method is used for this purpose. For numerical simulation, Navier-Stokes equations and continuity equations are used. Four coupled wave equation for displacement and voltage is also used.
Navier-Stokes equations for fluid as: The Continuity equation is given as where ρ is the fluid density, v f is fluid velocity, f 1 is body forces, P is pressure and T is Deviatoric stress tensor.
Four coupled wave equation for displacement and voltage is given as where c is structural elasticity matrix, e is piezo-electric stress matrix and ε is Dielectric matrix at constant electric field.
A further achievement in the field of voltage generation is carried out by Zhu through the interaction of the dynamic fluid with a flapping foil power producer in a linear shear flow environment [53]. Since the concept of linear shear arrived, so 2-D Navier-Stokes equations in vorticity-stream function format is used.
Navier-Stokes equations in vorticity-stream function format is given as where J is the Jacobian of the transformation, u is the velocity of the fluid,R e is Reynolds number, ψ is stream function and ω is vorticity.

Mathematical modelling of PEHF with applied fluid mechanics
Another recent widely used technique of energy generation is the interaction of vortices with a deformable beam [11]. An experimental method is closed to produce numerous controllable vortices for measuring their interaction with an elastic beam. Distribution of pressure is found out for various instants. Numerical simulation is done by the equation of linear elasticity for a mesh moving model.

Equation of linear elasticity for mesh moving model is
where σ is Cauchy stress tensor and f is external force.
The inclusion of passive foil has arrived with further achievement in this field. The technique of generation of energy from a vortex flow by using a passive foil has been investigated [45]. An immersed boundary technique with the interaction of the fluid network is used for doing numerical simulation. The governing equation for numerical simulation in the case of incompressible flowing fluid is also used as where v is velocity of the fluid, R e is Reynold number, P is instantaneous power input to the foil and f is the body forces.
The concept of cross-flow is equally crucial in fluid-structure interaction mechanisms as other methods. Sin performed the elastic eel's motion from the wake of deceiving structure in a cross-flow. In this paper, the collaboration between eels and vortex shedding behind a deceive structure is investigated mathematically. The motto of the paper is to upgrade the eel's oscillation by pairing with the varying vortices. COMSOL software is used for simulation. The equations for fluid-structure interaction (FSI) model are also used.
The governing equation for the FSI model given as ∇ · u f = 0 (41) where u f is velocity of fluid flowing field, u s is velocity of solid mechanics field, p is pressure, I is identity tensor, F is volume force field, µ is viscosity of fluid and σ is Cauchy stress tensor.

PEHF Modelling with Other Methods
Further improvement in this area has done by Neto by planning a technique for a self-exciting PMMA valve-less piezo-electric micropump [26]. A software-based on the finite element is considered for studying the feasibility system configuration. The experimental test shown that planned, constructed path harvest a less expenditure and extremely efficient micro pump. Simulation is done by using the finite element method (FEM). Piezo-electric strain charges constitutive relation is also used for simulation are as per equation (13) and (14). Modified control matrix singular value decomposition approach and optimal placement of the piezoelectric pieces enhance the output performance of the system [62,63,64].
Zhang investigated a piezo-electric polymer having more than one layer of construction on the elastic substrate in a fluidic environment for mechanical energy harvesting with a bending approach [33]. Models are refined numerically and analytically to realize the effect of material criteria on the energy producing efficiency of more than one-layer construction. The solution of an equation is done by the method of variable's separation. ANSYS software is also playing a vital role in numerical simulation. Basic equation of piezo-electric materials is also used. Further in case of generation of energy at micro level various vital hybrid techniques like Taguchi and heterogeneous 3-D has been used for optimization, simulation, modelling and fabrication in case of low-level vibration applications [54,55,56,57,58].

CONCLUSIONS
The present work efficiently classified the different kinds of fluid flow interactions with piezo smart materials for energy harvesting into three categories: (i) experimental investigations (ii) simulation and (iii) mathematical modeling. Experimental investigation results that the piezopolymers are more flexible and durable as compared to piezoceramics, and also act as better energy harvester. As compared to linear flow, turbulent flow generated by various means like the wake of a circular cylinder, creating vorticity act as an efficient energy harvester. Simulation investigation efficiently elaborates the advantages of Multiphysics simulations/programming methods than computer graphics of any software/tools for various energy harvesting systems.
For mathematical modeling of the energy harvesting through piezo material with fluid flow, it is easier to use numerical methods using the Navier-Stokes equation of motion than analytical methods.In case of Bernoulli's equation, considering various losses like friction losses, bend losses, net head on the piezo material can be calculated and using piezoelectricity equation indicates the energy generated by the system.It can be concluded that, harvesting of energy from the sources such as ocean wave, rain water, human muscles and hydraulic pressure of fluid with much density are very hopeful source of energy generation at a micro level in upcoming time with eco-friendly, durable, economical and easily integrated nature.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.