The efficiency of Rankine cycle and its derivative cycles are severely affected by droplets condensed in the process of vapor expansion, which not only limit its maximum efficiency, but also cause extremely low efficiency around 3% when using low grade heat source. This paper introduces a new theory of Thermodynamic and Gravitational Cycle to explain the concept of MLC, and analyses the reasons MLC OTEC cannot be realized till now. Then The concept of Thermodynamic and Gravitational Closed-Cycle (TGCC) to overcome disadvantage of Rankine and MLC cycle are proposed, and its especial cycle process and efficiency model in detail are discussed. And then we propose a method of combining vapor with mist lift to improve efficiency further, and analyze the new ideal efficiency model (a maximum up to 18.17%) using carbon dioxide sample, indicate the dryness of liquid-vapor mixture is the key factor to improve efficiency. In conclusion, TGCC with mist lift has the potential to significantly improve efficiency and reduce the cost of electricity produced from low grade heat source, such as OTEC and industrial waste heat.
In the field of heat engine, Carnot Cycle and Rankine Cycle are the most important theories guiding us to study thermal machine and its efficiency since they were established in 19th century. The Carnot cycle is a theoretical construct about thermodynamic cycle which provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work. And, the Rankine cycle is the standard model used to predict the performance of steam turbine systems. Here are many factors influencing the efficiency of the real Rankine Cycle, such as the temperature of steam into the superheat region, the temperature of condensing, the dryness and droplets carried by the steam.
In particular the efficiency of the steam turbine will be limited by water droplet formation [
On the other hand, a proper condensation proportion of steam is beneficial to improve thermal efficiency. For example, most enthalpy drop comes from the heat of steam condensing in the last stage of multi-stage steam turbine, the condensation heat from 10% steam accounted for 79% of the total enthalpy drop [
With great different from previous studies, this paper establishes and proposes a new theory named Thermodynamic and Gravitational Cycle (TGC), in order to take full advantages of condensation heat and carrying capability of steam. TGC theory can significantly improve efficiency of energy conversion, and significantly reduce the cost of electricity produced from low grade heat source, such as ocean water and industrial waste heat.
Rankine Cycle and its derivative cycles belong to pure thermodynamic cycle. The earth gravity has no influence on those thermodynamic cycles. On the contrary, if the earth gravity and heat plays a vital role in the conversion process of energy, the conversion cycle is called Thermodynamic and Gravitational Cycle (TGC).
TGC phenomena are common in natural world. For example, water evaporates on the earth surface and rises to upper air due to heated by sun; water steam condenses and forms a cloud while rising; then cloud rains and drop to the earth surface when meeting cold air. The rainwater fallen in highland or mountain is the source to produce hydroelectric power. We can also find TGC phenomenon in some artificiality, such as gravity assisted heat pipe, and MLC (Mist Lift Cycle) experiment devices [
This paper will discuss two kinds of TGC, i.e. Thermodynamic and Gravitational Open-Cycle (TGOC) and Thermodynamic and Gravitational Closed- Cycle (TGCC) to develop the TGC theory.
In particular, MLC is an open-cycle OTEC concept originally developed by Dr. Stuart Ridgway in 1970s [
Obviously, MLC is very different from Rankine Cycle. MLC introduced gravitation to thermodynamic open-cycle. That can be explained by the concept of Thermodynamic and Gravitational Open-Cycle (TGOC) whose process theory is shown in
As we know, Rankine is a close cycle with 4 typical stages shown in
Fundamentally different from Rankine cycle, the concept of TOGC mist lift has 3 primary stages shown in
So, MLC uses little vapor expansion and condensation to lift mass of droplets, while Rankine Cycle uses dry vapor expansion to drive steam turbine. Wet vapor with small dryness can lift to a high altitude, which is the key to develop the theory of TGC. Although the thermodynamic feasibility of mist lift has been established based on much experiments and researches [
In order to avoid the above weaknesses of Rankine Cycle, MLC (TGOC) and other conventional thermodynamic cycles, this paper introduce a better TGC theory, i.e. thermodynamic and Gravitational Closed-Cycle (TGCC), and then combine it with mist lift.
TGCC is a completely closed thermodynamics and gravitational cycle with completely recycling working medium.
A proposed TGCC schematic diagram for OTEC is shown in
medium is heated and evaporated into vapor in evaporator under high pressure and temperature condition, then vapor expand and lift up against gravity to the top condenser. Vapor is completely condensed to cold liquid by lower temperature condenser and that continuously produce lower pressure. Cold liquid is continuously collected into a reservoir and keep the reservoir full, while the cold liquid down to the hydro turbine due to the gravitational force. Liquid gravitational potential energy is conversed to mechanical energy, and then conversed to electric energy.
The process of TGCC cycle contains 5 stages shown in
・ The stage 1 - 2: Cold liquid is heated at constant pressure
・ The stage 2 - 3: The saturated vapor expands and lifts through the lifting pipe to the top against gravity. This decreases the temperature and pressure of the vapor, and some condensation may occur. Here the vapor temperature is
・ The stage 3 - 4: The wet vapor then enters a condenser where it is condensed at the constant pressure
・ The stage 4 - 5: The liquid flow down in the declining pipe to the bottom due to gravitational force, while liquid pressure becomes higher and gets the maximum at the point of hydro turbine. Liquid temperature
enthalpy
・ The stage 5 - 1: The liquid in declining pipe is drained into evaporator through hydro turbine. Liquid temperature
In the stage 2 - 3, the vapor pressure vary with the lift height, its equation is
Herein,
In the stage 2 - 3, the vapor temperature also vary with the lift height, its temperature drop equation without condensation is:
Its temperature drop equation with condensation is:
Herein,
According to the cycle process above, we can get its theoretic efficiency equation:
Herein,
Accordingly, its ideal efficiency depends on the lift height:
Herein,
According to the Equations (1) (2) and (3), the lift height
According to the Equation (5) and
Reducing the height will decrease efficiency, while vapour condensation and mist lift will be easier at the same cooling temperature. That gives a potential way to improve efficiency at a feasible height. So, this paper combine mist lift concept to TGCC theory to significantly improve its efficiency.
Add a mist generator above the evaporator, we can get a new process of TGCC
Item | Vapor in lifting pipe Bottom | Vapor in lifting pipe Top | Liquid in declining pipe Bottom | Unit |
---|---|---|---|---|
High of Lift: | 0 | 1360 | (1360) | meters |
Pressure: | 57.3 | 45.0 | 171.6 | bar |
Condensing Temperature: | 20.0 | 10.0 | -- | Celsius |
Specific Enthalpy fluid: | 255.8 | 225.7 | 225.7 | kJ/kg |
Specific Enthalpy gas: | 407.9 | 422.9 | -- | kJ/kg |
Specific isobar heat capacity fluid: | 4.266 | 2.996 | 2.996 | kJ/kg K |
Specific isobar heat capacity gas: | 4.574 | 2.577 | -- | kJ/kg K |
cycle contains 8 stages shown in
・ The stage 1 - 2: Cold liquid of
・ The stage 1-1’-2’: Cold liquid of
・ The stage 2 - 6: The saturated vapor expands and lifts to the height where mist generator installed. Vapor flow already gets a very fast velocity.
・ The stage (2’, 6)-6’: Vapor meet with mist, and then combine into liquid-vapor mixture at point 6’. Its mass is
・ The stage 6’-3’: the vapor expands through the lifting pipe and lift droplets to the top condenser. This decreases the temperature and pressure of the vapor, and some condensation may occur. The dryness of the mixture will be smaller.
・ The stage 3’-4: The mixture enters a condenser where vapor is condensed at the constant pressure
・ The stage 4 - 5: The liquid of
・ The stage 5 - 1: The liquid in declining pipe is drained into evaporator through hydro turbine. Liquid temperature
Since a mass of
Herein,
If
If
And if
In the condition supposed this paper, efficiency increases with more and more mist combined, at the same time dryness decreases accordingly. We can get the maximum efficiency line as shown in
One the one hand, combining more mist with vapour is the primary method to improve efficiency significantly, which will move the stage of 6’-3’ to a new position (6”-3”) trending to zero dryness as shown in
On the other hand, Mist Lift is significantly influenced by the diameter of mist droplets. Many institutes such as the University of Virginia, Dartmouth College and Solar Energy Research Institute have finished much experiments and researches [
get the maximum velocity at top end of the short lift pipe. We can lengthen the lift pipe to its upper limit so that provide a space for droplet’s moderating process, in order to converse all kinetic energy to gravitational potential energy.
Obviously, thermodynamic and Gravitational Closed-Cycle (TGCC) is completely different with Rankine cycle and other conversional heat engine theory. TGCC is also very different with MLC, MLC depend on injecting mist, and needs no heat exchanger.
TGCC can take full advantage of the condensation during vapor expands and lifts up. The model of TGCC combining with mist lift can significantly improve efficiency of energy process and conversation. For the carbon dioxide case discussed above, with the temperature difference of 10 K, the ideal maximum efficiency may beyond 20% as the mixture dryness decreased to its minimum possible value. This result value is significantly larger than the efficiency (around 3%) of conventional OTEC using Rankine cycle. Thus, TGCC theory gives a new direction to reduce the cost of electricity especially produced from low temperature heat source, such as ocean water and industrial waste heat.
TGC or TGCC theory should be taken seriously and be studied further from now on. The major areas of research required to develop TGC include:
・ To study the lift capability of liquid-vapor mixture with variant dryness, and find the minimum dryness for variant working mediums, such as carbon dioxide, Nitrogen, Freon, water and etc.
・ To study the evolution process of the flow velocity of liquid-vapor mixture, since vapor acceleration process and moderating process are influenced by temperatures, lift pipe diameter, dryness, and lift height.
・ To select feasible temperature difference and the best lift height of TGCC plant, since either too high or too low will decrease the efficiency.
・ To develop better mist generator with narrow spectrum to avoid the disadvantage of large difference of droplets diameter, since multi-group diameter will cause rainout easy.
・ Other technologies related with TGC, some are similar the technologies used in OTEC.
Quan, Z. (2017) Improving Efficiency by Thermodynamic and Gravitational Cycle. Energy and Power Engineering, 9, 250-260. https://doi.org/10.4236/epe.2017.94B030