Article Information

Rabiu Ahamd Abubakar^1*, Nuhu Ibrahim²

¹Institute of Mechanical engineering Design, Mechanical Engineering Department, Zhejiang University, Hangzhou, China

^*Corresponding Author: Rabiu Ahamd Abubakar, Institute of Mechanical engineering Design, Mechanical Engineering Department, Zhejiang University, Hangzhou, China.

Received: 16 May 2024; Accepted: 30 May 2024; Published: 06 June 2024

Citation: Rabiu Ahamd Abubakar, Nuhu Ibrahim. Thermal Energy Conversion Using NITI Shape Memory Alloy Material. International Journal of Plant, Animal and Environmental Sciences. 14 (2024): 20-30.

Abstract

Keywords

NiTi SMA; Thermomechanical; Phase transformation; Heat engine

Article Details

1. Introduction

Thermal energy is a form of energy that occurs by temperature difference [1]. It can also be defined as the energy possessed by an object due to the particle movements within the object. It is the kinetic energy of an object due to random movements of the body molecules and atoms. It occurs naturally in many different kinds like ocean thermal energy caused by the direct sunlight radiation conversion to heat energy [2,3], and geothermal energy [4,5], which naturally occurs beneath the earth crust. Many technologies are used to convert such thermal energy to generate electricity for human and industrial use. Ocean energy has existed since earth creation. It recently attracted research attention for the possible harvesting and used as an alternative source of green energy. Ocean thermal energy occurs due to the temperature differences between the ocean depth and surface [6], usually (100m). Energy demand is increasing every day, and the energy depends on is mostly non-renewable and depleting every day. These energy sources include the following: petroleum, firewood, solar [2,3] biomass [7-9], hydropower [10,11], nuclear, coal, wind [12,13] and many more [14-18]. These energy sources [19] are dangerous to our environment due to harmful carbon footprint emissions [20]. Therefore, alternative, cheaper, safer, and renewable sources are welcome [21,22]. In our ecosystem, different energy sources exist. Hence, converting these energies would help our domestic and industrial activities [23].

Sixty percent of this energy is at 100°C or less[21]. Solar radiation is closed to 8×10¹⁶watt energy flux, with 70% heating like sea and ocean, which may be converted to usable energy when explored carefully [24]. Ocean thermal Energy (OTE) is one of these types that can be converted to mechanical energy [25]. OTE is the second largest (1000TW/a) [26] and is stable at low temperature [23]. This can be harvested using the NiTi SMA Heat engine. This will give additional energy sources and help control carbon emissions [27-29]. The temperature difference between the ocean bottom, which is cold, and its top can cause austenite-martensite phase transformation that will result in thermos-mechanical energy conversion for electricity generation [25].

Many devices are used for thermos-mechanical energy conversion, but they are not up to the level of commercialization. Research on the Rankine cycle has been recently used for ocean thermal energy conversion. A low boiling medium is used. The Rankine cycle uses a low boiling medium which requires a small temperature difference. It can be used in a tropical region where large solar is converted to thermal energy [2,3], thus warming the ocean water to 28-35°C [30]. Rankine cycle technology has very low efficiency due to the following reason. Because of the low-temperature difference, the process of heat exchange is very restricted. This technology needs a large amount of water to be pumped up from the bottom of the sea to the top. This requires energy, and the pipe needs thermal insulation. Parasite tends to grow on the heat exchanger; thus, it has to clean up from time to time, and all this is energy demanding, which will be very difficult. This makes the Rankine cycle technology inefficient, therefore, it makes it unsustainable due to energy loss.

There is an alternative to the problems mentioned above associated with Rankine technology. That is by applying NiTi SMAs for the energy conversion. NiTi SMA has an outstanding shape memory effect (SME) behavior, which results in thermos-mechanical energy conversion through martensitic phase transformation. Since its invention, there have been many attempts to apply it in energy harvesting, yet it is not up to the level of commercialization [31,32].

A synchronized pulley SMA heat engine is proposed. The engine has two actives pulley and two idle pulleys. Two-timing gears are mounted on the acting pulleys with a synchronizing timing belt.

This research intends to convert both ocean thermal and geothermal energy based on phase transformation.

Research shows that there are synchronized and unsynchronized SMA pulley heat engines [33-35]. In the synchronized type the, due to synchronization, the development resolved to ease tension, so it favors ratio in one direction [36,37]. In unsynchronized pulley type, each pulley rotates independently.

2. The Conceptual Design and Kinematics

It can be used as an ocean thermal energy harvester or a geothermal energy harvester. The active pulleys are Pulleys 1 & 2 and have the same radius a. SMA spring makes contact wrap angle ϕ. The timing belt connects the two active pulleys. Pulley 3 & 4 are idle pulleys. When using the engine as an ocean energy harvester, the pulley 3 is immersed in bathwater, simulating the ocean surface top, while pulley4 is in a cold-water chamber, simulating the cold ocean bottom. When used as a geothermal energy harvester, the pulley 3 is left in the open air or immersed in cold water simulating the low-temperature sink, while pulley 4 is immersed in a hot water chamber simulating the hot water from the earth crust. An opposing external load like an alternator can be mounted on pulley 2. The SMA spring has F_CD in cold water_, and in hot water, it has F +ΔF. The gear for synchronization has unequal radii b₁ and b₂. The timing belt on top has F_t and on the bottom, F_t +Δ F_t. Assuming no frictional force and no sliding on the pulleys, then Eq. 1 obtained as:

Where M_loodis the external load, a is the radius of the pulley1 & 2, b₁ is the radius of timing gear1 on, and b₂ is the radius of timing gear 2. Using equilibrium equations  is eliminated, resolving into a single equation 3.

The ratio b₁/b₂ is (0< b₁/b₂<1). This restoring SMA spring force is a function of temperature as:

In this research, the SMA Spring is made to acquire the shape memory effect through heat treatment. The critical austenite to martensite transformation temperature is set at 30^oC. This means if the spring is extended and heated, it will instantly return to its original shape at 30^oC. An SMA wire with 1.5 mm diameter is wound around a cylindrical rod of 16mm, then put in a heating furnace and heated up to 500^oC for 30 minutes. It is brought out and cooled at ambient temperature. This process sets the SMA spring to the above critical temperature of 30^oC [38-41].

Figure 1 shows the SMA spring with installation length L and initial length L_o

Where x₀ is the initial stretch ratio.

Figure 1: Represents a thermo-mechanical energy converter.

3. The relationship between temperature and time

SMA depends largely on the shear modulus (G) of the material. Therefore G has the following relationship with temperature (T):

where, Ms, M_f, As, A_f, represent the start and finish martensite and austenite temperature. G_A and G_M are the austenite and martensite shear modulus, respectively. In the absence of stress, when: (M_f≤ T ≤ A_f), the SMA shear modulus is:

Therefore during heating

And during cooling,

When the SMA spring is heated, the equation for heat balance is an ordinary differential equation:

Where m'is the SMA Spring mass linear density, C_s is SMA spring specific capacity, V is its total volume, H_his coefficient of heat exchange A SMA spring surface area, and T_w is water temperature.

When T=T₀, at t=0, then the temperature variation of SMA spring with time is:

Where T₀ is the initial temperature and φ is the time constant of SMA spring,

4. The force generation

The following numbers of turns are observed associated with the engine:  is SMA spring number of turns in AB region,  is SMA spring number of turns in the CD region. Assuming and the stretch ratio (x₁/x₂ ) of 1:3 is used.

Where n₁ and n₂ are the numbers of turns of SMA spring in the heating and cooling chamber, respectively; L_AB and L_CD are the length of AB and CD.

When M_f< T₂< A_f, the force developed in hot water can be expressed as:

And the axial force at a low temperature of cold water can be expressed as:

Where T_c is the temperature at cold water before heating.

Therefore,

The axial displacement is restricted since the SMA spring acts as a belt with a head-to-tail connection. Therefore, the length of the SMA spring remains the same.

Therefore,

The axial load developed during cooling is expressed as:

Where D is the SMA spring diameter, d_w is the SMA wire diameter, and G_L is the shear moduli of SMA spring at low temperature.  

5. Torque

The engine driving force is:

From Equation 3, the torque/moment generated is:

6. The Engine Speed

The angular acceleration is gotten as:

Where l_eis the effective mass moment of inertia of the pulley But, the moment of inertia of the pulley is:

where m is the mass of the pulley with radius a.

Therefore,

To get the angular velocity, Eqt. 30 is integrated with respect to time.

Where C is the constant of integration, and is here taken as zero. Hence Eq. 32 reduced to:

Substituting Eqt. 24 in 29,

The T(t), x(t), and F(t) are periodic. And period is:

From experimental data, pulley1 has 14rpm; therefore, the engine period τ is 4.3s.

Under engine steady operation, there is zero acceleration and no slippage on the pulley, hence there is constant mass flow rate. Let the reference and current velocity be V_o and V, then the linear mass density is:

Therefore at point B and D, the mass flow is as:

Where θ_iis rotation speed, x₁ and x₂ are the stretch ratio. The timing ratio b¯is expressed as:

Using parameters in Table 1, Figure 2(a) shows the nonlinear relationship between the force generated versus temperature. As the heating starts, the curve goes nonlinearly from 20 to 30°C, and then it goes linearly up to around 60°C and then ends nonlinearly from 60 to 70°C. A reverse happens during cooling.

Figure 2: simulation of result (a) forces during heating and cooling versus temperature (b) moment versus temperature, (c) rotation rate versus output torque at pulley 1 for heating chamber.

7. Output Power of OTEH

The output power of the engine is computed as:

Figure 3: Simulation of power (a) verse temperature (b) verse angular velocity.

8. Efficiency of the Engine

The engine efficiency is calculated as:

Where R_w is wire radius; R_sis SMA spring radius; m_totalis the total mass; m'is the wire linear density; l is SMA spring current length; H_h is the convection heat transfer coefficient for heating, τ is the total time taken; P_totalis the total power produced; P_specis the specific power. 

Using parameters from Table 1, the following simulations are performed:

Figure 4: Simulation of efficiency (a) versus temperature (b) versus angular speed.

9. Fitting

The behavior of the SMA spring of (x-T) is modeled using Eq. 49.

Where T₀, T₁, x₀, x _A, x _M are obtained from the experiment, x_A, x_M are austenite and martensite stretch ratios. T₀, T₁, and x₀ are also parameters for shaping and positioning. The equation above will simulate the behavior of the SMA spring under the influence of temperature change. Using the estimated parameters, the following simulations are performed:

Figure 5: (a) stretch ratio verse temperature (b) simulation of force (c) temperature versus time (d) stretch ratio distributions along the SMA spring loop.

Table 1: Simulation parameter for Ti-49, 51Ni SMA material is used in this OTEH.

10. Experiment

The NiTi SMA heat engine prototype shown in Figure 6 was tested, and it developed at 110 rpm at 70^oC. In real practice, when the engine is used for geothermal energy conversion, the water temperature may be up to 90^oC. But when the engine is used for ocean thermal energy conversion, the seawater will be further heated up to a sufficient temperature using a solar heater. The arrangement of the NiTi SMA heat engine after construction is shown in Figure 7, and a series of experiments were conducted.

Figure 6: The SMA heat engine.

11. Comparison Between Experimental and Simulated Data

Using the experimental data and the parameters from Table 1, the moment generated is plotted in Figure 7 (a), and the angular speed versus moment in Figure 7(b).

Figure 7: (a) moment versus temperature (b) rotation rate versus output torque at pulley 1.

12. Discussion

Figure 2 (a) shows the simulation of force verse temperature during cooling and heating processes. It shows that the relationship is a nonlinear one. Figure 2 (b) simulates the torque generated by the engine with maximum torque of 0.9 Nm at the corresponding zero value of angular velocity. And also, it is a nonlinear one. Figure 3 (a) shows the graph of power versus temperature. As heating starts, there is zero power until after the critical phase transformation temperature of (30^oC). Power then increases with temperature change with a nonlinear relationship. Figure 3 (b) represents the simulation of power versus angular speed. The curve goes with a nonlinear relationship for a maximum power of 3.2 watts at 3.2 revolutions per second, then decreases. Figure 4 (a) demonstrates the thermodynamic engine efficiency as a function of temperature, and in Figure 7 (b) as a function of rotation speed which is a nonlinear curve. Figure 5 represents the simulation of stretch ratio as a function of temperature for the full engine operation cycle. The graph forms a hysteretic one. Figure 6 (b) shows the force along the SMA spring loop. It indicates that there is a constant force between the two active pulleys. Figure 5 (c) shows the stretch ratio as a function of time, and Figure 5 (d) shows the stretch ratio distributions along the spring length. Both two graphs show a nonlinear nature. Figure 7 represents a comparison between model and experimental data. There is good fitting in both (a) and (b).

13. Conclusion

A heat engine based on NiTi SMA is designed, modeled, constructed and tested. The simulated data are compared with the experimental one with good fitting. The engine developed a power of 2.4 watts, with maximum efficiency of 4.51 %. This shows that the engine can harvest both ocean thermal and geothermal energy.

14. Declarations

Availability of data and materials: Not applicable

Competing interests: Ocean thermal energy conversion

Funding:

Chineese government Scholarship (CSC)   

Authors' contributions:

Modeling of Ocean thermal energy Harvester

Acknowledgements:

I sincerely express my appreciation and gratitude to the Chinese Scholarship Council (CSC) for its sponsorship to accomplish this program.

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