Improving Efficiency by Thermodynamic and Gravitational Cycle

Transcription

1 Energy and Power Engineering, 07, 9, htt:// ISSN Online: ISSN Print: 949-4X Imroving Efficiency by Thermodynamic and Gravitational Cycle Zhang Quan Shanghai Kongtai Energy Techonolgy Co., Ltd, Shanghai, China How to cite this aer: Quan, Z. (07) Imroving Efficiency by Thermodynamic and Gravitational Cycle. Energy and Power Engineering, 9, htts://doi.org/0.46/ee.07.94b00 Received: February 6, 07 Acceted: March 0, 07 Published: Aril 6, 07 Abstract The efficiency of Rankine cycle and its derivative cycles are severely affected by drolets condensed in the rocess of vaor exansion, which not only limit its maximum efficiency, but also cause extremely low efficiency around % when using low grade heat source. This aer introduces a new theory of Thermodynamic and Gravitational Cycle to exlain the concet of MLC, and analyses the reasons MLC OTEC cannot be realized till now. Then The concet of Thermodynamic and Gravitational Closed-Cycle (TGCC) to overcome disadvantage of Rankine and MLC cycle are roosed, and its esecial cycle rocess and efficiency model in detail are discussed. And then we roose a method of combining vaor with mist lift to imrove efficiency further, and analyze the new ideal efficiency model (a maximum u to 8.7%) using carbon dioxide samle, indicate the dryness of liquid-vaor mixture is the key factor to imrove efficiency. In conclusion, TGCC with mist lift has the otential to significantly imrove efficiency and reduce the cost of electricity roduced from low grade heat source, such as OTEC and industrial waste heat. Keywords Thermodynamic and Gravitational Cycle, Mist Lift, Height, Drolet, Low Grade Heat Source. Introduction In the field of heat engine, Carnot Cycle and Rankine Cycle are the most imortant theories guiding us to study thermal machine and its efficiency since they were established in 9th century. The Carnot cycle is a theoretical construct about thermodynamic cycle which rovides an uer 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 DOI: 0.46/ee.07.94B00 Aril 6, 07

2 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 redict the erformance of steam turbine systems. Here are many factors influencing the efficiency of the real Rankine Cycle, such as the temerature of steam into the suerheat region, the temerature of condensing, the dryness and drolets carried by the steam. In articular the efficiency of the steam turbine will be limited by water drolet formation []. As the water condenses, water drolets hit the turbine blades at high seed causing itting and erosion, gradually decreasing the life of turbine blades and efficiency of the turbine. Obviously, the efficiency of Rankine Cycle and its derivative cycles are severely affected by drolets condensed in the rocess of vaor exansion, which not only limit its maximum efficiency, but also cause extremely low efficiency when used in low grade heat source, such as the best efficiency of OTEC (Ocean Thermal Energy Conversion) cycle is around %. On the other hand, a roer condensation roortion of steam is beneficial to imrove thermal efficiency. For examle, most enthaly dro comes from the heat of steam condensing in the last stage of multi-stage steam turbine, the condensation heat from 0% steam accounted for 79% of the total enthaly dro []. Thus, the largest humidity of exhaust steam is suggested 0% - %. Obviously, the condensation heat of steam is beneficial to imroving thermal efficiency, while drolets are very harmful to turbine life and its efficiency. Therefore, most scientists focused on studying how to control dryness of steam and the liquid-vaor two hase flow [] []. With great different from revious studies, this aer establishes and rooses a new theory named Thermodynamic and Gravitational Cycle (TGC), in order to take full advantages of condensation heat and carrying caability of steam. TGC theory can significantly imrove efficiency of energy conversion, and significantly reduce the cost of electricity roduced from low grade heat source, such as ocean water and industrial waste heat.. The TGC Theory.. The TGC Concet Rankine Cycle and its derivative cycles belong to ure thermodynamic cycle. The earth gravity has no influence on those thermodynamic cycles. On the contrary, if the earth gravity and heat lays a vital role in the conversion rocess of energy, the conversion cycle is called Thermodynamic and Gravitational Cycle (TGC). TGC henomena are common in natural world. For examle, water evaorates on the earth surface and rises to uer air due to heated by sun; water steam condenses and forms a cloud while rising; then cloud rains and dro to the earth surface when meeting cold air. The rainwater fallen in highland or mountain is the source to roduce hydroelectric ower. We can also find TGC henomenon in some artificiality, such as gravity assisted heat ie, and MLC 5

3 (Mist Lift Cycle) exeriment devices []. This aer will discuss two kinds of TGC, i.e. Thermodynamic and Gravitational Oen-Cycle (TGOC) and Thermodynamic and Gravitational Closed- Cycle (TGCC) to develo the TGC theory... The TGOC Concet In articular, MLC is an oen-cycle OTEC concet originally develoed by Dr. Stuart Ridgway in 970s []. MLC uses a finely erforated titanium late (mist generator) at the bottom of vacuum chamber. Warm seawater is introduced into the vacuum chamber through 0. mm diameter holes in the titanium late. The low ressure in the vacuum chamber is maintained such that some of the water flash evaorates-creating a fine mist. Farther u the column, cold seawater is injected into the chamber. The cold seawater lowers the ressure in the to of the chamber. This creates a ressure gradient that drives the mist from the bottom of the chamber to the to. The vaor comonent of the mist is comletely condensed into the cold water by the time the lift is comlete. The lift height is such that water is lifted above sea level, and then the water is drained into the ocean. Obviously, MLC is very different from Rankine Cycle. MLC introduced gravitation to thermodynamic oen-cycle. That can be exlained by the concet of Thermodynamic and Gravitational Oen-Cycle (TGOC) whose rocess theory is shown in Figure comaring with Rankine Cycle. Figure. MLC and Rankine cycle s P-S diagram. 5

4 As we know, Rankine is a close cycle with 4 tyical stages shown in Figure. The stage - : The working fluid is umed from low to high ressure. As the fluid is a liquid at this stage, the um requires little inut energy. The stage - : The high ressure liquid enters a boiler where it is heated at constant ressure by an external heat source to become a dry saturated vaor. The stage - 4: The dry saturated vaor exands through a turbine, generating ower. This decreases the temerature and ressure of the vaor, and some condensation may occur. The stage 4 - : The wet vaor then enters a condenser where it is condensed at a constant ressure to become a saturated liquid. Fundamentally different from Rankine cycle, the concet of TOGC mist lift has rimary stages shown in Figure. The stage - : warm seawater from sea surface get a high ressure at bottom of vacuum chamber, seawater is injected into low ressure vacuum chamber through the mist generator. Here is a very large ressure dro. The stage - : the mist contains a mass of drolets and some vaor generated by flash evaoration; vaor exands through the vacuum chamber, and lift drolets to the to. The stage - 4: The vaor comonent of the mist is comletely condensed into cold water by cooler sraying water at the to. So, MLC uses little vaor exansion and condensation to lift mass of drolets, while Rankine Cycle uses dry vaor exansion to drive steam turbine. Wet vaor with small dryness can lift to a high altitude, which is the key to develo the theory of TGC. Although the thermodynamic feasibility of mist lift has been established based on much exeriments and researches [5]-[], its characteristics are oorly understood and there is no sound theoretical suort. The most critical issue of OTEC MLC is ignored till now, i.e. without heat exchanger, the temerature difference (7 K) is not enough to lift all warm seawater introduced into vacuum chamber. As we know, the latent heat of water evaoration is 500 kj/kg, while the secific isobar heat of water is 4. kj/kg K. One unit mass of water evaoration need the heat of 5. unit mass of seawater with 7 K dro of temerature. Obviously, the dryness of mist (X < 0.08) is extremely small. Although some researches show that it is realizable to lift 0.0 unit mass of mist to high altitude using unit mass of vaor if rovide a much bigger inlet ressure [7]. It is indeed imossible to lift the.5 unit mass of mist using unit of steam. That is the reason MLC haven t been realized in OTEC till now from the oinion of this aer. MLC should be realized with higher temerature difference. In order to avoid the above weaknesses of Rankine Cycle, MLC (TGOC) and other conventional thermodynamic cycles, this aer introduce a better TGC theory, i.e. thermodynamic and Gravitational Closed-Cycle (TGCC), and then combine it with mist lift... The TGCC Concet TGCC is a comletely closed thermodynamics and gravitational cycle with comletely recycling working medium. A roosed TGCC schematic diagram for OTEC is shown in Figure, working 5

5 Figure. The schematic diagram of TGCC for OTEC. medium is heated and evaorated into vaor in evaorator under high ressure and temerature condition, then vaor exand and lift u against gravity to the to condenser. Vaor is comletely condensed to cold liquid by lower temerature condenser and that continuously roduce lower ressure. Cold liquid is continuously collected into a reservoir and kee the reservoir full, while the cold liquid down to the hydro turbine due to the gravitational force. Liquid gravitational otential energy is conversed to mechanical energy, and then conversed to electric energy..4. TGCC Process and Efficiency The rocess of TGCC cycle contains 5 stages shown in Figure. The stage - : Cold liquid is heated at constant ressure by an external heat source to become a saturated vaor at bottom. The vaor temerature is T, the vaour secific enthaly is H, the quantity of heat absorbed from external heat resource is Q x. The stage - : The saturated vaor exands and lifts through the lifting ie to the to against gravity. This decreases the temerature and ressure of the vaor, and some condensation may occur. Here the vaor temerature is T, the vaor ressure is, and the secific enthaly of vaor is H. The stage - 4: The wet vaor then enters a condenser where it is condensed at the constant ressure to become a saturated liquid with the same temerature T. Here the secific enthaly of liquid is H, the quantity of heat released to external cold resource is Q f. The stage 4-5: The liquid flow down in the declining ie to the bottom due to gravitational force, while liquid ressure becomes higher and gets the maximum at the oint of hydro turbine. Liquid temerature T and secific 54

6 Figure. The P-H diagram of TGCC. enthaly H is almost invariant. The stage 5 - : The liquid in declining ie is drained into evaorator through hydro turbine. Liquid temerature T and secific enthaly H is almost invariant. But the liquid ressure is lunged from 4 to. The outut work W g of liquid almost equals to the roduced electric energy. In the stage -, the vaor ressure vary with the lift height, its equation is ( 000 ) ehgm T N k =, () Herein, is the original ressure at bottom (h = 0), is the ressure at the height of h, e is the natural constant, g is the acceleration of gravity, M is molar mass of gasmolecular, T is the degree kelvin (K), N is the Avogadro constant, and k is the Boltzmann constant. In the stage -, the vaor temerature also vary with the lift height, its temerature dro equation without condensation is: g T = h () C Its temerature dro equation with condensation is: g L T = s h q C + C () Herein, T is the degree of temerature dro, g is acceleration of gravity, C is secific isobaric heat caacity, h is the lift height, L is latent heat, q is the mass of condensation. Normally, the temerature dro values comly with the sequence Ts < T < T T. According to the cycle rocess above, we can get its theoretic efficiency equation: 55

7 Qf H H η = = Q H H x (4) Herein, H is secific enthaly of saturated vaour, H is secific enthaly of wet vaour lifted to the to, H is secific enthaly of condensed liquid. Accordingly, its ideal efficiency deends on the lift height: V ( ρ gh + ) ηh = mh ( H) Herein, V the volume of liquid, ρ is density of liquid, m= ρv is the mass of liquid (or vaour), g is acceleration of gravity, h is the lift height, is the vaour ressure at bottom, is the vaour ressure at to. According to the Equations () () and (), the lift height h is limited by the temerature difference T T. For the examle, given T = 0, T = 0, then the maximum condensation height of carbon dioxide gas is 60 meters. Otherwise, higher than 60 meters, the carbon dioxide will not condensate at the same temerature T since ressure will become lower with higher lift height. Table show detail attributes and arameters of carbon dioxide samle. According to the Equation (5) and Table, we can get the maximum efficiency ηh 5.08 % that seems to be a little better comaring with conversional OTEC efficiency (around %). Considering building a TGCC ie system reach u to the height of 60 meters is extremely hard and exensive. If the real lift height is reduced to 600 meters, the efficiency η h is less than %. Thus, the efficiency still need be imroved further in order realize more economic and ractical. Reducing the height will decrease efficiency, while vaour condensation and mist lift will be easier at the same cooling temerature. That gives a otential way to imrove efficiency at a feasible height. So, this aer combine mist lift concet to TGCC theory to significantly imrove its efficiency..5. Method of Imroving TGCC Efficiency Add a mist generator above the evaorator, we can get a new rocess of TGCC (5) Table. Attributes and arameters of carbon dioxide. Item Vaor in lifting ie Bottom Vaor in lifting ie To Liquid in declining ie Bottom Unit High of Lift: 0 60 (60) meters Pressure: bar Condensing Temerature: Celsius Secific Enthaly fluid: kj/kg Secific Enthaly gas: kj/kg Secific isobar heat caacity fluid: kj/kg K Secific isobar heat caacity gas: kj/kg K 56

8 cycle contains 8 stages shown in Figure. The stage - : Cold liquid of m mass is heated at constant ressure by an external heat source to become a saturated vaor at bottom. The vaor temerature is T, the vaour secific enthaly is H, the quantity of heat absorbed from external heat resource is Q x. Saturated vaor dryness is near to.0. The stage - - : Cold liquid of m mass is heated at constant ressure, then is umed into mist generator with a higher ressure (oint ), and then is srayed at a lower ressure (oint ). Mist is roduced at oint, mist dryness is near to 0. The stage - 6: The saturated vaor exands and lifts to the height where mist generator installed. Vaor flow already gets a very fast velocity. The stage (, 6)-6 : Vaor meet with mist, and then combine into liquid-vaor mixture at oint 6. Its mass is ( m + m). The stage 6 - : the vaor exands through the lifting ie and lift drolets to the to condenser. This decreases the temerature and ressure of the vaor, and some condensation may occur. The dryness of the mixture will be smaller. The stage -4: The mixture enters a condenser where vaor is condensed at the constant ressure. The mixture comletely become a saturated liquid at temerature T. Here the secific enthaly of liquid is H, the quantity of heat released to external cold resource is Q f. The stage 4-5: The liquid of ( m + m) mass flows in the declining ie down to the bottom due to gravitational force, while liquid ressure becomes higher and gets the maximum at the oint of hydro turbine. Liquid temerature T and secific enthaly H is almost invariant. The stage 5 - : The liquid in declining ie is drained into evaorator through hydro turbine. Liquid temerature T and secific enthaly H is almost invariant. But the liquid ressure is lunged from 4 to. The outut work W g of liquid almost equals to the roduced electric energy. Since a mass of m mist is added into vaor of m, the ideal efficiency is different from Equation (5), its new equation is as below: V ( ρ gh + ) ηh = (6) m H H + mc T ( ) Herein, V the liquid volume, ρ is the density of liquid, ( m + m) = ρv is the mass of all working medium, g is acceleration of gravity, h is the lift height, is the vaour ressure at bottom, is the vaour ressure at to, H is secific enthaly of saturated vaour, H is secific enthaly of condensed liquid. C is the secific isobar heat caacity of liquid, T is the temerature rise. mc T is the heat absorbed by the liquid for roducing mist. If m = m, the dryness of mixture is X According to Equation (6) and the arameters in Table, the ideal maximum efficiency is η h = 8. 55% 8.55%. 57

9 If m m =, the dryness of mixture is X 0.. The maximum efficiency will be η =.06%.06%. h And if m = 8m, The dryness of mixture is X 0., the maximum efficiency will be η = 8.7% 8.7%, which is an exciting value comaring with h conventional OTEC efficiency (% - 4.5%). Even we reduce the lift height to the half (680 m), η h is still larger than 9%. In the condition suosed this aer, 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 Figure 4. Obviously, to left the cycle efficiency trends to a closed MLC without vaor, and to right the cycle efficiency trends to a closed Rankine cycle without mist. One the one hand, combining more mist with vaour is the rimary method to imrove efficiency significantly, which will move the stage of 6 - to a new osition (6 - ) trending to zero dryness as shown in Figure. On the other hand, Mist Lift is significantly influenced by the diameter of mist drolets. Many institutes such as the University of Virginia, Dartmouth College and Solar Energy Research Institute have finished much exeriments and researches [7]-[] on mist lift flow rate, velocity, drolet diameter, and inlet ressure, which give full evidences and summarize laws of mist lift. Exeriments show that inlet ressure influences mist lift erformance [7]. Bigger inlet ressure can get a bigger maximum flow rate before rainout aears. If inlet ressure is 0. bar, then the maximum flow rate is 8 kg/s without rainout, dryness is 0.. If inlet ressure is 5.0 bar, then the maximum flow rate is 945 kg/s without rainout, the dryness is about Figure 5 shows the drolet velocity and temerature changing rules in mist lift stage [7]. Drolets velocity can be accelerated by the vaor exanding at bottom and condensing at to. Figure 5 shows drolets Figure 4. Maximum efficiency line of TGCC. 58

10 Figure 5. Samle oututs from single-grou models. get the maximum velocity at to end of the short lift ie. We can lengthen the lift ie to its uer limit so that rovide a sace for drolet s moderating rocess, in order to converse all kinetic energy to gravitational otential energy.. Conclusions Obviously, thermodynamic and Gravitational Closed-Cycle (TGCC) is comletely different with Rankine cycle and other conversional heat engine theory. TGCC is also very different with MLC, MLC deend on injecting mist, and needs no heat exchanger. TGCC can take full advantage of the condensation during vaor exands and lifts u. The model of TGCC combining with mist lift can significantly imrove efficiency of energy rocess and conversation. For the carbon dioxide case discussed above, with the temerature difference of 0 K, the ideal maximum efficiency may beyond 0% as the mixture dryness decreased to its minimum ossible value. This result value is significantly larger than the efficiency (around %) of conventional OTEC using Rankine cycle. Thus, TGCC theory gives a new direction to reduce the cost of electricity esecially roduced from low temerature 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 develo TGC include: To study the lift caability of liquid-vaor mixture with variant dryness, and 59

11 find the minimum dryness for variant working mediums, such as carbon dioxide, Nitrogen, Freon, water and etc. To study the evolution rocess of the flow velocity of liquid-vaor mixture, since vaor acceleration rocess and moderating rocess are influenced by temeratures, lift ie diameter, dryness, and lift height. To select feasible temerature difference and the best lift height of TGCC lant, since either too high or too low will decrease the efficiency. To develo better mist generator with narrow sectrum to avoid the disadvantage of large difference of drolets diameter, since multi-grou diameter will cause rainout easy. Other technologies related with TGC, some are similar the technologies used in OTEC. References [] Guha, A. (998) Comutation, Analysis and Theory of Two-Phase Flows. The Aeronautical Journal,, 7-8. [] Li, L. and Li, Yu.(008) Study of Wet Steam Two Phase Flow with Condensation in Steam Turbine. Thermal Turbine, 7, [] Ridgway, S.L. (977) The Mist Flow OTEC Plant.Proceedings of 4th OTEC Conference. [4] Lockheed, M. (0) Ocean Thermal Energy Conversion Life Cycle Cost Assessment. Bethesda: Lockheed Martin Cororation. [5] Ridgway,S.L. and Charwat,A.F.(978) The Design of Laboratory Scale Exeriment on Vertical Two Phase Flow with Alication to the Mist Flow OTEC Cycle.Proceedings of 5th OTEC Conference. [6] Ridgway,S.L.,Lee,C.K.B. and HammondR.P.(98)Exerimental Demonstration of the Feasibility of the Mist Flow Ocean Thermal Enerty Process.Proceedings of 8th OTEC Conference. [7] Davenort, R.L. (980) The Mist Lift Analysis Summary Reort. USA Colorado: Solar Energy Research Inst.htts://doi.org/0.7/5474 [8] Charwat, A.F. (978) Studies of the Vertical Mist Transort Process for an Ocean Thermal Energy Cycle. SAN Los Angeles, CA: University of California. [9] Ridgway, S.L., Hammond, P.R. (978) Mist Flow Ocean Thermal Energy Process.RDA-TR Marina del Rey, CA: Research and Develoment Assoc. [0] Joseh, V.R., Steven, R. and Stuart, R. (00) Develoment of Mist Lift: A Cost Breakthrough for OTEC. DE-PS0-09ER09-7. [] Wallis,G.B.,Richter,H.J. andbharathan,d. (979) Analysis of the OTEC Mist Lift Process. SERI-87-. Hanover, NH: Thayer School of Engineering, Dartmouth College. [] Abbott,C.E. (977) A Survey of Waterdro Interaction Exeriments. Reviews of Geohysics and Sace Physics, 5, htts://doi.org/0.09/rg05i

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