Performance analysis of a novel small-scale radial turbine with adjustable nozzle for ocean thermal energy conversion

b

impeller inlet height/nozzle height (m)

c

absolute velocity (m/s)

D

diameter (m)

P

power output (kW)

p

pressure (MPa)

Q

mass flow rate (kg/s)

R

radius (m)

T

Temperature (°C)

u

peripheral velocity (m/s)

Z

impeller axial length (m)

Subscript

c

cold water

in

inlet

ise

isentropic

out

outlet

r

radial

$r̄$

relative radial

tot

total

u

peripheral

w

warm water

0

nozzle inlet

1

impeller inlet

1′

nozzle outlet

2

impeller outlet

2s

impeller outlet shroud

2h

impeller outlet hub

3

diffuser outlet

Greek symbol

$D2̄$

ratio of impeller diameter

$ū1$

velocity ratio

α

absolute flow angle (deg)

β

relatively flow angle (deg)

Δ

nozzle-impeller clearance

Ω

degree of reaction

η

efficiency

θ

nozzle vane stagger angle (deg)

φ

nozzle flow velocity coefficient

ψ

impeller flow velocity coefficient

ω

relative velocity (m/s)

Acronyms

CFD

computer fluid dynamics

OTEC

ocean thermal energy conversion

1D

one-dimensional

3D

three-dimensional

With the rapid population growth and technological development in the world, the energy requirement has increased tremendously, and many countries are looking for unconventional energy sources such as solar energy and ocean energy. Ocean thermal energy acts as a combination of solar energy and ocean energy and is regarded as the most valuable and potential exploitation of ocean energy resources in subtropical and tropical regions. OTEC (Ocean Thermal Energy Conversion)^1,2 can effectively convert the ocean thermal energy to electric energy based on the potential energy created by the temperature difference between the sun-warmed surface water and the deep cold seawater in the ocean.

The thermodynamic efficiency of the OTEC system is only about 3%–5%^3,4 due to the essential small temperature difference (of around 20 °C) between the heat and cold sources, which is much lower than that of conventional power generation. To improve the cycle efficiency, much work has been conducted on the OTEC from various aspects such as thermodynamic cycle optimization^5–11 and fluid selection.^12–14 

Apart from optimizing the thermodynamic cycle and working medium, the turbine acts as the core power generation component and plays a significant role, and its overall performance largely influences the power-conversion efficiency of the OTEC system. For the OTEC with a very small-temperature difference, the radial-inflow turbine is the most suitable type of turbine because it has a high-level of overall efficiency. However, the work on the OTEC radial-inflow turbine reported in the open literature is limited. Kim and Kim¹⁵ proposed a new approach to the design and performance analysis of a 200 kW radial-inflow turbine using R152a for OTEC; Nithesh et al.^16,17 designed a 2 kW radial turbine with R134a and R22 as working fluids separately in OTEC. Wu et al.¹⁸ optimized the dual-pressure turbine in OTEC with the total output power for the optimization objective. Alawadhi et al.¹⁹ proposed a turbine design code based on the mean-line method to construct the basic design of a turbine impeller in OTEC. Zhang et al.²⁰ elucidated the effects of blade tip clearance on the flow characteristics of the turbine after the 30 kW radial-inflow turbine was designed and simulated. Liu et al.²¹ proposed a new fully data-based model identification and optimization method for the OTEC radial inflow turbine. Chen et al.^22–24 designed and analyzed the OTEC turbine based on different nozzle installation angles and found that the nozzle installation angle has a greater impact on turbine efficiency.

In addition to the turbine in OTEC, many studies have been performed on the small-scale radial turbine. Al Jubori et al.²⁵ summarized a number of studies on developing and analyzing radial-inflow turbines used in ORC and also accomplished a multi-objective optimization algorithm for a radial-inflow turbine. Fiaschi^26, et al. proposed a 0-D model to design ORC turboexpanders and analyzed different methods for radial turbine design. Lei et al.²⁷ optimized the blade thickness, blade section, and wheel profile in the process of meridian design and structural modeling of a 100 kW class micro turbine unit. Sauret and Gu²⁸ analyzed an organic Rankine cycle radial-inflow turbine with R143a. Li and Gu²⁹ conducted research on radial turbine optimization using the NURBS curve. Song et al.³⁰ optimized the stator and rotor by Bezier splines with several control points with turbine total efficiency as the goal.

The present study is focused on a radial inflow-turbine with ammonia for the 15 kW OTEC system. Its preliminary design is conducted, and flow behavior and overall performance are simulated in the real stage environment. To further improve the turbine design, a parametric study is conducted for the nozzle-impeller radial clearances and nozzle vane stagger angles, and their influences on the flow and overall performance of the turbine are highlighted. Based on this, the performance of the novel small-scale radial turbine with an adjustable nozzle in OTEC is analyzed.

The organic Rankine cycle is used in the OTEC system, as shown in Fig. 1. The Rankine cycle consists of four main components, including an evaporator, turbine, condenser, and pump. In the cycle, the working fluid is heated by the warm seawater in the evaporator to a high-level of pressure and temperature, then enters the turbine, where its enthalpy is converted into shaft output power by the impeller to drive the generator to produce electricity. Subsequently, the working fluid is ejected from the turbine, cooled by the cold deep seawater in the condenser, and then pumped into the evaporator. In such a manner, the OTEC works periodically and produces electricity from the seawater.

As depicted in Ref. 12, R717 (also termed ammonia) is the suitable working fluid and permits high-level efficiency of the OTEC system cycle, which is confirmed by Yoon et al. R717.^13,14 Therefore, R717 is chosen as the working fluid in the present OTEC system, and Table I presents the thermodynamic properties of R717.

In the organic Rankine cycle, the warm sea surface temperature and cold deep sea water temperature are set at 26 and 4.5 °C, respectively, which is identical to that of the South China Sea.³¹ On the basis of such a temperature difference,³² the turbine inlet and outlet parameters are calculated, where its inlet temperature and pressure are respectively 23 °C and 0.83 MPa, and its outlet pressure is 0.58 MPa. The R717 mass flow rate is 0.388 kg/s. The OTEC parameters are summarized in Table II.

In the radial-inflow turbine, the working medium is firstly guided uniformly in the volute and accelerated in the nozzle ring with a large flow velocity, then flows inwards into the impeller and work, and finally discharged by the diffuser, as shown in Fig. 2. The flowchart of the radial turbine design process is illustrated in Fig. 3.

In the preliminary design, flow in the turbine is assumed to be one-dimensional and isentropic. Figure 4 illustrates the velocity triangles at the impeller inlet and outlet of the turbine.

As shown in Eq. (16),³³ the turbine isentropic efficiency is a function of seven parameters: the velocity ratio $ū1$⁠, the degree of reaction Ω, the nozzle flow velocity coefficient φ, the impeller flow velocity coefficient ψ, the ratio of impeller diameter $D̄2$⁠, the absolute flow angle at the impeller inlet α₁, and the impeller outlet relative flow angle β₂. Through a fine-tuning of these seven parameters, a suitable combination is obtained, which permits a high-level of turbine overall efficiency in Table III.

Based on the above-mentioned seven parameters, through the simultaneous solution of the mass continuity equation, the energy equation, and the velocity triangle equations, the one-dimensional geometric parameters of the nozzle and impeller can be calculated. Figure 2 shows the representation of the nozzle and impeller parameters, and Table IV lists the results of the parameters in the turbine.

In order to make the flow into the nozzle smoothly and uniformly, the volute is designed with an asymmetric pear-shaped cross section. The detailed design method is introduced in Ref. 34.

The nozzle vane is designed on the basis of the TC-P series aerodynamic blade developed by the National Research University Moscow Power Engineering Institute.³⁵ The TC-2P blade was chosen as the detail shape, and the final shape was adjusted through rotating and zooming. The basic parameters of the nozzle are shown in Table V.

According to the 1D design results of the turbine, the cylinder parabolic geometrical method is used to design the impeller blade. The design method is implemented by code, and the impeller blade profile is generated. The impeller is composed of the guide wheel and the working wheel. The working wheel is designed as the linear radial blade of high strength and the guide wheel of a cylinder parabolic shape. More details and equations of this method can be referred in Ref. 34.

Downstream the impeller, the diffuser pipe is used to reduce the impeller kinetic energy loss. It is designed with a divergence angle of 6.5° and a circular cross-section.

This paper mainly studies the aerodynamic performance of the turbine by numerical simulation due to the lack of a turbine test in OTEC. Based on the above design of turbine parts, the 3-D model of the turbine is established by SolidWorks with 20 nozzle blades and 12 impeller blades, as shown in Fig. 5.

The governing equations, including the mass conservation equation, momentum conservation equation, energy conservation equation, and turbulence equation, are mainly completed by ANSYS-CFX.³⁶ The SST model is used as the turbulence model suitable for the Re number in the flow of the turbine.³⁷ 

The hexahedral meshing of the impeller and nozzle is established by ANSYS Turbogrid, and the unstructured tetrahedral mesh of the volute and the hexahedral mesh of the diffuser are generated by ANSYS ICEM. Figure 6 shows the overall mesh of the turbine, in which the mesh of the volute tongue is encrypted and the mesh near the impeller and nozzle blade is encrypted by O-grid. In addition, the grid independence verification was carried out by increasing output power with grids to ensure that the grid has almost no effect on the simulation results in Fig. 7. Finally, the turbine mesh number is 3 748 546, including 1 261 128 hexahedral grids of the impeller, 976 000 hexahedral grids of the nozzle, 434 592 hexahedral grids of the diffuser, and 1 076 826 tetrahedral grids of the volute.

To better achieve the simulation of the fluid’s physical properties, the Aungier Redlich Kwong equation of state is applied in the simulation because it has better accuracy near the critical point compared with the Redlich Kwong equation. The impeller domain is connected with the nozzle domain and diffuser domain by the frozen rotor model. The convergence criteria of 10⁻⁵ for rms quantities are used in the simulation, and the mass flow of the inlet and outlet is monitored during the process of convergence. More details of the simulation can be found in the ANSYS CFX theory guide.³⁶ 

Table VI shows the comparison of the main parameters at numerical simulation and the results of the turbine under the design condition. It can be seen that the simulation results for the main parameters are basically less than 2% with the design values, except that the nozzle outlet velocity error is about 3.29%. Although the efficiency and power are a little smaller than those of the design, the error is about 1%–2%, which meets the design requirement well.

Figure 8 shows the overall streamline of the turbine, with the diffuser hidden in order to show the streamline better. It can be seen from the computer fluid dynamics (CFD) result that the overall flow condition of the turbine was performed adequately, and the streamline along the flow is relatively uniform.

Figure 9 depicts the pressure contour and the velocity streamline at 50% spanwise in the nozzle and impeller passages. The pressure distribution at the nozzle and the impeller, except for the leading edge of the blade, is relatively uniform. The pressure gradient direction is along the flow direction, and there is no obvious adverse pressure gradient in the impeller. In the pressure contour, there is a small range of low-pressure area at the suction surface of the blade leading edge, which is shown as a small vortex in the velocity streamline, where the fluid will produce backflow and cause a little flow loss. The formation of vortex is mainly caused by the cutoff leading edge of the impeller blade and the influence of the nozzle stagger angle. Although there is flow loss at the suction surface of the blade, the overall efficiency of the turbine is high, which meets the design requirement well.

Based on the inlet parameters at the design condition and circulation parameters that vary with surface seawater temperature, four other representative working conditions are listed in Table VII. The corrected impeller speed N_c is 1627, 1871, and 1383 r/(min K^1/2), corresponding to the design speed N(28 000 rpm) under the design condition, with the higher speed being 1.15 N and the slower speed being 0.85 N. Turbine efficiency and power output with five inlet conditions under different impeller speeds are shown in Fig. 9.

It can be seen from Fig. 10 that at the design speed, the efficiency of the turbine first increases and then decreases with the increase of the inlet temperature and pressure, reaching its maximum value at the design condition. In the case of low speed, the efficiency of the turbine is maximum when the inlet pressure and temperature of the turbine are lower, and it decreases continuously with the increase in inlet pressure and temperature, and the reduction range is almost linear. At high speed, the efficiency of the turbine increases continuously with the increase in pressure and temperature and reaches its highest point at high temperature and pressure. The power output of the turbine is positively correlated with the turbine inlet temperature and pressure.

As the impeller speed increases, the highest turbine efficiency point moves toward the direction of inlet temperature increasing, but the turbine efficiency at high speed and design speed are basically the same. The reason is that the design speed is already close to the optimal speed, and the change in turbine efficiency at high speed is mainly the result of the improved flow at the suction surface of the impeller blade. Meanwhile, at low speeds, the small eddy currents in the low pressure zone of the impeller will increase sharply, resulting in greater changes in turbine efficiency. The turbine power increases linearly with the increase in impeller speed, mainly because the increase in impeller speed is caused by the increase in mass flow. So when the efficiency of the turbine is between 80% and 88%, the turbine power basically increases linearly with the impeller speed.

The use of an adjustable nozzle can improve the flow condition of a turbine under off-design conditions to a certain extent. In order to solve the problem of turbine efficiency reduction under off-design conditions, the influence of nozzle vane angle change on turbine performance is first studied using two parameters, including nozzle-impeller radial clearance Δr and nozzle vane stagger angle θ shown in Fig. 11.

Figure 12 shows the change in turbine efficiency with different nozzle stagger angles under different nozzle-impeller radial clearances. Figure 13 shows the change in turbine power output with them. It can be seen that the turbine efficiency and power change slightly under different relative radial clearances. The overall trend is that the efficiency of the turbine increases tiny with the decrease in relative radial clearance, while the turbine power has no obvious change. With the increase in nozzle stagger angle, the turbine efficiency increases and then decreases obviously, while the turbine power output increases linearly with the increase in mass flow rate. The maximum efficiency point gradually shifts from the design angle of 32°–36° with the nozzle-impeller clearances decreasing, which indicates the high efficiency point of the turbine is between 32° and 36° of the nozzle stagger angle, while the clearance has no significant effect on the turbine performance.

In order to analyze the above changes better, Fig. 14 shows the streamline and pressure contour of the nozzle-impeller radial clearance at 50% spanwise under different radial clearances when the nozzle angle is 32°. It can be seen that the streamline at the nozzle-impeller radial clearance does not change significantly at the inlet of the impeller with the increase in radial clearance. Figure 14 also shows that although the pressure at the nozzle outlet varies slightly with different radial clearances, the pressure at the impeller inlet is basically the same under different nozzle clearance conditions. It shows that the flow at the nozzle outlet has reached the level of uniform before entering the impeller, which also leads to no obvious impact of the radial clearance on the performance of the turbine.

Figure 15 shows the streamline and pressure contour at 50% spanwise of the nozzle and impeller passages with different nozzle stagger angles. It can be seen that with the decrease in nozzle stagger angle, an obvious low pressure area gradually appears at the suction side of the impeller, and even when the nozzle stagger angle is 22°, there will be two very large vortices, which will lead to an obvious decrease in turbine efficiency. When the nozzle stagger angle increases gradually, the low pressure area at the suction surface of the impeller gradually decreases and finally disappears. However, when the nozzle stagger angle increases to 42°, the flow at the suction side of the nozzle begins to separate, which also explains the reason for the decrease in turbine efficiency at the large nozzle stagger angle.

In reality, the turbine generally drives the generator through a reducer to generate power, and the frequency of the generator is usually constant, 3000 or 3600 rpm, for instance, in the process of an OTEC system. Therefore, if the turbine speed remains the same, the efficiency of the turbine will be greatly affected by internal flow changes in the turbine when the turbine inlet state changes, led by the temperature of the warm seawater. However, the changes in turbine speed with the inlet state will have a certain impact on the operation of the generator or even cause some danger. In order to realize the turbine running at a constant speed under off-design conditions with the efficiency decreasing not so much, an adjustable nozzle is adopted for the turbine to improve its efficiency under all conditions. Based on the simulation results of Sec. V B, when the turbine inlet temperature and pressure are lower, the nozzle installation angle is rotated to a smaller angle, and when it is higher, the angle is increased on the contrary to keep the efficiency stable.

Figure 16 shows the comparison of the typical internal flow diagram of the turbine under three working conditions (Condition B–D) when the adjustable nozzle and the fixed nozzle are used. It can be seen that when the inlet temperature and pressure are lower, the reduction of the adjustable nozzle angle will result in the vortex on the pressure side disappeared and make the streamlines closer to the design condition. When the inlet temperature and pressure are higher under off-design conditions, the vortex on the suction side is significantly reduced. Figure 17 shows the change in turbine operating efficiency under off-design working conditions when using adjustable nozzles and fixed nozzles. It can be seen that the efficiency at off-design conditions by an adjustable nozzle is higher than that by a fixed nozzle but cannot exceed the efficiency of the design point in Fig. 17. Combining Figs. 16 and 17, it can be seen that the turbine efficiency can be improved in non-design working conditions through the use of adjustable nozzles, especially at the maximum and minimum inlet conditions.

The aerodynamic part of the small-scale radial turbine of OTEC is first designed and simulated, and the performance of the nozzle-impeller radial clearance and the nozzle stagger angle are carried out. Finally, the impact of the adjustable nozzle on the performance of the turbine under off-design conditions is studied, and the following conclusions are mainly obtained:

1. The efficiency of the turbine by CFD at the design condition is 86.5%, and the output power is 15.3 kW, which is slightly lower than the design value and meets the design requirements.

2. The optimum point of turbine efficiency gradually moves toward the direction of inlet temperature and pressure, increasing with speed increases under off-design conditions, and the power is positively correlated with the speed and inlet state.

3. The efficiency of the turbine decreases slightly with the increase of the nozzle-impeller radial clearance and increases first, then decreases with the increase of the nozzle stagger angle, and the optimum stagger angle point moves from 32° to 36° gradually with the increase of the nozzle-impeller clearance. The relationship between power and nozzle stagger angle is basically linear.

4. The efficiency of the turbine under off-design conditions can be optimized through the adjustable nozzle, especially when the inlet working conditions deviate greatly from the design conditions. The change in nozzle angle can be adjusted automatically according to the change in inlet condition by adding a controller in future manufacturing work.

This work was supported by the National Natural Science Foundation of China “Study on the mechanism of OTEC thermodynamic cycle and pressure energy utilization of lean ammonia solution” (Grant No. 41976204); Department of Science and Technology of ShanDong Province “Study on heat transfer characteristic mechanism of polar power supply system using ocean thermal energy” (Grant Nos. ZR202111160101 and ZR201910310263); Natural Science Foundation of ShanDong Province “Study on Heat and Mass Transfer Mechanism of Seawater Desalination Based on Ocean Thermal Energy Conversion” (Grant No. ZR2022ME126); and China-Korea Joint Ocean Research Center (CKJORC) “China-Korea Technology Exchange and Cooperation of Ocean Energy Development and Utilization” (Grant No. PI-2023-4).

The authors have no conflicts to disclose.

Yunzheng Ge: Data curation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Jingping Peng: Formal analysis (equal); Validation (equal). Fengyun Chen: Resources (equal). Lei Liu: Data curation (equal); Writing – original draft (equal). Wanjun Zhang: Data curation (equal); Writing – original draft (equal). Weimin Liu: Funding acquisition (equal); Project administration (equal). Jinju Sun: Conceptualization (equal); Project administration (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.