Tesla turbine as known as a viscous bladeless turbine, formed by a series of discs parallelly mounted to each other on the shaft, which is closely gap and fitted with rotating shaft [24]. These disks are multiple flat in parallel, thin and spaced along the shaft with thin gaps [26]. The turbine is mainly structured by three main components consists of discs, shaft, casing and accessories (valves and nozzles) [23]. The nozzles of the turbine are designed on the cylindrical casing and tangential to the shaft. The inlet enthalpy is estimated [27] as:

Where T_o, T_inlet denote as ambient temperature and temperature of working fluid inlet the turbine (K), respectively. C_p represent as heating capacity (1005 J/g.K).

The discharge holds are designed on the center of turbine. So that, the diameter of the disk and the inter-disc gap is mainly affected to the working performance of the turbine [28]. Generally, a Tesla turbine is shaped by shaft, discs, housing, collar, nozzle and bearing. The schematic of the Tesla turbine is shown on Figure 2.

Figure 2: 
Configuration of a typical Tesla turbine [18][29]

As for its working principle, the fluid is passed into the nozzles before ejected tangentially to the rotor, the fluid velocity is significantly increased [30]. Subsequently, when working fluids are introduced into the narrow gaps between the discs, the relative velocity between the rotor and the working fluid generates a viscous effect in the boundary layers, resulting in the rotation of the rotor [31]. The geometric parameter which results from disc spacing, converts energy by the fluid in mechanical energy and generates momentum exchange of working fluid and discs, results from torque and power of the turbine. The heat generated during process of converting inlet enthalpy to work, heat and kinetic energy is estimated by:

Where V denotes for outlet velocity of the working fluid.

The shaft power is generated to the rotor, the turbine can be used with function of pump or compressor. The working fluids passed nozzles and ejected into the gap with certain angle. The flow within the Tesla turbine is propelled by a pressure difference that exists between the inlet at the outer radius of the discs and the outlet at the inner radius of the discs. At the disc gap (interdisk spacing), kinetic energy of flow of the working fluid is converted into torque and shaft power. The energy conversion is under the theme of momentum exchange of viscous drag force between flow of working fluid and both walls of each gap. The radial and a tangential velocity component using cylindrical coordinates are two main velocity profile. Torque is produced by shear stress of relative and tangential velocity component. Power is generated in rotation only. The performance efficiency of turbine can be estimated by [32]:

Where m˙ represents mass flow rate of working fluid, h_in, h_out are the total enthalpy inlet and outlet of turbine, respectively.

Besides, the torque is appeared and distributed when the tangential, relative velocity component of flow of working fluid is higher than the circumferential speed of the discs at certain radial position. And, torque can be at negative value in case of circumferential velocity of discs is higher than tangential relative velocity component of flow. Thus, process of kinetic energy conversion into mechanical energy, does not occur constantly across the radius. The flow in the Tesla turbine can exhibit either laminar or turbulent behavior, which is determined by the Reynolds number. The radial velocity component plays a crucial role in determining the flow rate within the system.

In comparisons with the conventional turbine, Tesla turbine has some highlight as simple structure, designation and maintenance cost are low, easy balancing, excellent scalability of shaft power, the competitiveness in small scale turbomachinery, robustness, operating in wide range of fluids and the self-cleaning nature due to centrifugal forces as well. W. Rice wrote in Handbook of Turbomachinery (1991) [33] that Tesla turbomachinery can be quietly and smoothly operation and produce nearly white noise sound signature in comparison with conventional turbomachinery, and, the turbine has competitive efficiency in comparison with miniaturized, conventional turbines in case of small shaft power scales. However, it is limited by power scales because of its restricted-on designation for the energy conversion process. So that, Tesla turbine is widely applying on small scale turbomachinery applications.

The Tesla turbines can be divided into two categories according to the inlet geometry: nozzle type and volute Tesla turbine type [34]. The simple design of the Tesla turbine, combined with the parallel flow of the fluid along the turbine disks, offers a notable advantage over conventional bladed turbines. This design allows for the presence of abrasive particulates and water droplets in the working fluid without the risk of direct impacts that could potentially lead to additional wear and damage to the disks. This characteristic of the Tesla turbine allows it to effectively utilize a wide range of fluids without causing any damage to the blades, thereby offering distinct advantages over traditional turbine designs. Besides, the Tesla turbine shows minus points such as: Efficiency of the turbine is depending on in and outflow of the working fluids, use only for medium and high-power applications, the flow rate must be small for the high efficiency and narrow range of applications as well.

Figure 3 below is a comparison among three basic kinds of turbines. The Tesla turbine (green line) is a highlight with rotational speed and quasi-independency of pressure ratio with rotational speed, proper of dynamic machines. The disadvantage of Tesla turbine can be seen as lower power generation (less than 3.10⁴ W) in compared with volumetric expanders and axial & radial turbines.

Figure 3: 
Characteristics comparison among some kinds of turbines [18]

Initially, the Tesla turbine is not popular as other turbines [35]. However, with the above structure aspects, working principles and performance characteristics, the Tesla turbine is able to use in more and more wide range of applications and effectively serves to compensate for the world’s future energy crisis [31]. Different from other kinds of turbines, the Tesla turbine can be used in working fluids and multiphase without damage [23]. The mains areas of Tesla turbine applications include waste heat recovery, renewable energy resource, distributed generation system, irrigation channels and hybrid electric vehicles as well [36]. As the world trends moving towards renewable sources, Tesla turbine perfectly fits future vision in using renewable fuel at multiple locations and competitive cost as well. However, its major drawback is limited applications over conventional turbines because of their compact and small size.

Due to its exceptionally high efficiency, the Tesla turbine holds great potential to significantly enhance the efficiency of low-performing plants. Specifically, the Tesla turbine can be effectively employed in conjunction with waste heat from thermal power plants, as well as heat obtained from cycles or fuel cells, to generate electricity. Consequently, the utilization of the Tesla turbine for waste heat recovery has garnered considerable attention from scientists due to its substantial impact on performance efficiency and environmental considerations.

The ORC has been applied for decades for recovering waste heat from industrial processes and produce power. Generally, technologies for improvement the system performance can be divided into three main areas: configurations, working fluids and working conditions [37]. As for the ORC system, the waste heat is recovered mainly by power output of the turbine. So that, to maximize the power output, it is necessary to optimize the operation and cost (manufacturing and maintenances) [41]. One of the common method to increase power output and efficiency of ORC is increasing the operation performance of turbine [42][43].

Figure 5 shows the schematic diagram of general ideas of using Tesla turbine as an expander on ORC system. The system consists basically Tesla turbine as an organic expander, condenser, working fluid pump and evaporator. In general, the working principles of the system can be described as follows: the working fluid in liquid form is pumped from the condenser into the evaporator. And, the heat exchange will be occurred here and transfer heat to the working fluid and turned it into saturated or superheated vapor. Then, the organic superheated vapor expands in the Tesla turbine (as an expander) for producing electric power. Subsequently, the exhaust organic vapor is expelled from the Tesla turbine and condensed back into a liquid state in the condenser through the use of cooling water.

Figure 5: 
Schematic diagram of Tesla turbine as an expander on ORC system

In Tesla turbine, process 4-5 (isentropic process) can be calculated by:

Which, h_5s the isentropic enthalpy of the exhaust organic vapor at outlet of Tesla turbine and η_T is its efficiency.

Rusin et al. [32] analyzed and optimized the operation of Tesla turbine in a ORC and compared with experiment results. The research results revealed that Tesla turbine can support to increase from 9-17% of overall efficiency of system.

It is noteworthy to mention that the Tesla turbine exhibits the potential to attain even greater efficiency than the value documented in the research, assuming there are no constraints imposed by constructional limitations or parameter restrictions.

Song et al. [44] analyzed the application of Tesla turbine in small scale size of ORC. The various of configuration and working fluids are tested to examine the ability of generation power of Tesla turbine and proved that Tesla turbine is very potential for small scale ORC. With R245ca as working fluid, Tesla turbine can generate a significant net power output and thermal efficiency in small scale system and got 4% ORC efficiency, with 1.25 kW. The efficiency of the Tesla turbine down at lower evaporation temperature and then increases with the increment of the evaporation temperature (Figure 6).

Figure 6: 
The variation of power output and efficiency of Tesla turbine in ORC [44]

Indeed, the heat exchange that occurs in the evaporator of the Organic Rankine Cycle (ORC) system fluctuates in accordance with the outlet temperature of the heat source. Thus, with each separate heating source temperature, a proper evaporation temperature of the ORC system should be carefully calculated to determine the optimum working area of Tesla turbine and ORC system as well. The power output of the Tesla turbine is dependent on both the mass flow rate of the working fluid and the specific power output. When the evaporation temperature is higher, it leads to a greater power output per unit mass of the working fluid. Additionally, the mass flow rate of the working fluid directly influences the overall power output of the ORC. With an increasing direction of evaporation temperature, the turbine efficiency will first down and up when evaporation temperature reaches 335K. The significant impact of evaporation temperature on the performance of the ORC system is clearly demonstrated by the difference in turbine efficiencies observed at 335 K and 370 K, which amounts to approximately 0.05. The tendency of power of Tesla turbine and system is the same, at the evaporation temperature of 350 K, the ORC system yields 1.27 kW and at the highest net power output and thermal efficiency of the system reaches 0.043. This proves that the Tesla turbine generates a significant net power output and thermal efficiency in small scale system.

In case of upgrading the Tesla turbine with low specific speed n_s (0.001-0.005) and high specific diameter D_s (20-50) and shown very low (0.01-0.1) of right range of flow coefficient for optimum rotor efficiency and increase power output (0.05-0.2). The turbine was sized to effective work around 4000-8000 rpm [10].

In case of, R1233zd(E) as the working fluid, the results obtained the maximum the net power output of ORC system at 371W and the shaft efficiency and maximum adiabatic efficiency was at 9.62% and 30% respectively. This affirmed effectively of utilizing Tesla turbines in ORC applications better than other kinds of expander [18]. The test bench of this system is fully described in Figure 7.

Figure 7: 
Schematic diagram of test bench of Tesla turbine in ORC with R1233zd(E) [18]

Figure 8(a) shows the relationship between thermodynamic power output and expansion ratio. Thermodynamic power reach 906W as the maximum obtained value together with 0.299 kg/s of mass flow rate and 44°C of superheating level at 5000 rpm rotational speed. The obtaining highest power output conditions at high value of superheating levels (data D3 and D5) and high value of mass flow rate conditions (D1 and D6). Figure 8(b) describes the experimental points and power losses of the turbine in comparison with the predicted bearing losses and total of bearings losses and friction losses of the Tesla turbine because of the relationship between the electromagnetic couplings. And, Figure 8c, d, show deviation of 8% of experimental power and efficiency and the corresponding simulated values; the Pearson coefficient of power and efficiency are 0.95 and 0.92 in respectively. The coefficient of correlation of power and efficiency are 0.89 and 0.85. Research obtained a maximum of 9.62% of shaft efficiency and 50% of mechanical efficiency (including generator and torque meter losses) of ORC Tesla turbine.

Figure 8: 
The parametric study with varies of conditions to the powers and efficiencies [18]

L. Talluri et al. developed a Tesla turbine for ORC applications and achieved a total to static efficiency of lower size and larger size version are 52% and 64% respectively [23].

The Tesla turbine exhibited its best performance at an optimal rotational speed and low inlet pressure, with distinct values for power output and efficiency. And, the inlet temperature has not much inflected to the performance of the Turbine. The optimization of turbine efficiency relies heavily on the channel height and the ratio of the inlet and outlet rotor diameters. These parameters play a crucial role in determining the overall efficiency of the turbine.

Figure 9: 
Operating map of Tesla turbine in ORC [23] a) efficiency, b) power output, c) stator–rotor losses, d) kinetic energy

Furthermore, B. Peris et al. [45] evaluated ORC system using a turbine as an expander for harvesting low grade heat sources and resulted that performances ORC system was improved for higher thermal oil temperatures, capturing more thermal power, and obtaining better cycle efficiencies. They received maximum gross electrical efficiency, heat source temperature as 12.32% and 155oC respectively. Furthermore, the Tesla turbine is well-suited for power applications utilizing low-grade heat sources. It has been found to exhibit an electrical isentropic effectiveness of around 65% when operated at an optimal pressure ratio of approximately 7.

Figure 10(a) illustrates the gross electrical efficiency of the cycle, indicating that the efficiency tends to increase with the pressure ratio. It reaches a maximum value of 12.32%, which is higher for higher thermal oil temperatures. Figure 10(b) compares the cycle efficiency with the ideal Carnot efficiency and indicates that the efficiency trend of the cycle becomes attenuated for the highest values. Figure 10(c) is justified this effect in the case of observing referred to the expander. The electrical isentropic effectiveness of the turbine reaches a maximum value above 65% when operating at a pressure ratio around 7, as imposed by the expander 6. This operating range is considered suitable for power applications utilizing low-grade heat sources. This also proved the energy losses produced through conventional expanders.

Figure 10: 
Thermodynamics performance of: (a) gross, (b) net, (c) expander, (d) cycle [23]

The Tesla turbine has also experimented in the ORC combined system including three main loops of ORC, EGMR (Exhaust Gas Mixture Recirculation) and a control loop (Figure 11). In which, the ORC is mainly designed for waste heat recovering from the EGMR which exhausted temperature varies between 300oC and 500oC. The overall energy efficiency of the system increases 0.9% for conventional ORC and 1.5% for the ORC-EGMR system. It is proved that using a Turbine instead of a conventional expander bring much more benefit to the working efficiency of the system [46].

Figure 11: 
the schematic diagram of ORC for waste heat recovery [46]

Among the various components acting as throttle valves for a refrigeration system, Tesla turbine shows a high potential for recovery waste energy and transfer it to power or work. In 2019, Yahya Sheikhnejad et al. [8] introduced the Tesla turbine to substitute the wasting devices of the refrigeration system to increase the coefficient of performance and decrease waste energy of the system. It is effective operating to reduce refrigerant pressure before it enters the evaporator without compromising the system output quality.

Sheikhnejad analyzed thermo-hydrodynamic characteristics of R50 (high-pressure compressible methane) flow in the turbulent regime and proved that the Tesla turbine can be able to produce up to 2 kW (1440 kWh per month) in low angular velocity with R150B1 configuration. Those energies have been already wasted in expanders of the conventional refrigeration systems.

Figure 12: 
Dependency of power on disc angular velocity in different turbine dimension [8]

Among three curves of geometry configuration (disc gaps, outer diameter), the “optimum speed” where the Tesla turbine generated power becomes maximum, will be set up. This optimum speed will vary depends on the dimension (configuration) of the Tesla turbine.

A novel Turbo expander based on the Tesla turbine was innovated and experimented to the expansion of refrigeration cycle for enhancing overall efficiency of the system and waste heat recovery as well [47]. This Tesla turbine is using steam as a working fluid and comprise of a single passage between two discs. Due to dense cloud of liquid droplets in the flow between the discs, considerably, it has produced pressure decrease through the rotor, lead to delay the phase change and a decrease in the performance of Tesla turbine. The purpose of this experiment is to shortly start and confirm the size of droplets and initial modeling as well. This is expected to enhance the efficiency of the Tesla turbine as well as the performance of the refrigeration system.

The Tesla turbine for micro combined heat and power system utilizing low-grade heat sources which archived 1.5 kW electric power and 6.3% of turbine efficiency at 4 of pressure ratio. The parametric study has also shown that an isentropic efficiency of 19.6% and a turbine efficiency of 6.3% and performance of Tesla turbine with more efficient and economical than conventional micro-turbines in using low-grade heat sources areas [48].

The testing system is made from the boiler and small incinerator’s on-off valve, Tesla turbine, a 5 kW-class single-phase generator; and 20 parallel bulbs (100 W for each) as load. The thermal energy source was applied the exhaust waste heat from the small incinerator. The performance of the Tesla turbine working with waste heat using from small-scale incinerator was showed in an experimental result that includes 0.1 kg/s of lower mass flow rate, 419.45 K (146.3oC) of inlet temperature and 0.43 MPa (3.3 bar) of inlet pressure. The collected data and comparison between theoretical and practical were showed in Table 1.

Figure 13 shows a decreasing trend of efficiency in line with the increasing pressure ratio. This can be explained as the increasing pressure ratio lead down loss of the mass flow rate. So that, more loss will lead down the turbine power relative to the increasing input energy as well and become the largest factor to reduce efficiencies.

Figure 13: 
Isentropic and turbine efficiencies of Tesla turbine for pressure ratio [48]

The Tesla turbine performed 5-10% efficiency at 4 kW of electrical output, and 3% less efficiency at 3 kW of electrical output of the heat pipe-turbine. This is proved that Tesla turbine can bring greater economic benefit than the conventional one.

Normally, the exhaust gas from engines counted to 30–35% of total energy [41]. So, engine system is potential for heat recovery and such kind of energy should be utilized by novel solutions such as compressor-exhaust gas turbine group, ORC system, thermo-electric generator and so on. However, for enhancing efficiency of system, the waste heat technologies for engine system should adapt the following requirements [49]:

• - Highlighting efficiency in waste heat using;
• - Easy and safe operating;
• - High ability on response with sink properties and transient heat source;
• - Good adaptable to the changing operation regime of the engine;
• - It can be easily integrated with others power systems;
• - Enough power density for supplying large power as required.

Ji Fenzhu et al. [16] investigated the performance of the Tesla turbine in engine waste heat recovery and stated that the operation of the Tesla turbine was tightly related to the rotation speed and fit to work at 500 rpm-2500 rpm (low and medium rotation speed). The power and thermal efficiency of system increased by 13.2% and 5.2% respectively, on average compared with the original engine.

The general schematic of small-scale engine waste heat recovering using a Tesla turbine is described in Figure 14 below. The working principles as follows: The coolant liquid is supplied to the heat exchanger after exiting the engine. After absorbing heat from the heat exchanger, the liquid flows into the Tesla turbine, where it generates kinetic energy that is subsequently converted into electric energy by a generator. The coolant liquid is then directed to a radiator for cooling, achieving the desired temperature before being fed into the water tank. From there, it is pumped into the cylinder cooling jacket, completing the cycle. This system offers several advantages, including a simple structure, low noise level, and cost-effective manufacturing. This system uses a Tesla turbine with number of discs, outer radius, outer diameter, gap and incident angle are 20, 40mm, 12mm, 0.7mm and 10o respectively. The testing results showed that the experimental results are 8.5% and lower than the simulation and the theoretical results are 12.3% and higher than the simulation results on average and the experimental pressure drops 9.1% higher than the theoretical ones.

Figure 14: 
Schematic of using Tesla turbine for engine waste heat recovery [16]

Figure 15 is a comparison of power before and after recovery. It showed that total power is enhanced at the range of 1000 rpm - 1800 rpm of engine speed, and can be raised by 13.2% on average, despite the improvement of that is not obvious above 2000 rpm, those values are in comparison with the original engine. This clearly showed that the Tesla turbine reflected a greater capacity of energy conversion at the range of low rotation-speed.

Figure 15: 
Comparison of the total power output between the system before and after implementing the recovery process [16]

The Tesla turbine demonstrates effective performance at low and medium rotation speeds. Due to the structural characteristics of the Tesla turbine, working fluids with higher viscosity, larger coefficients of thermal expansion, and lower specific heat capacity are most suitable. The integration of the turbine into an ORC system for waste heat recovery in a diesel engine has resulted in notable enhancements in the overall thermal efficiency. The dual or multi-loop ORC system achieves thermal efficiency enhancements of up to 10% and 60-90% respectively when compared to the 10-25% thermal efficiency of a single-loop ORC system [41].

Figure 16: 
Configuration of engine -ORC system [41]

In view of the fact that, the system for waste heat from engine much depends on its exhaust gas components because of different of specific heat of each component. This will be much effected to operating conditions and efficiency of Tesla turbine. The possible efficiency ranges for different waste heat recovery systems from engines from 5% to 37% [49].