रँकाइन चक्र

रॅंन्काईनचे चक्र हे एक थर्मोडायनॅमिक एक चक्र आहे. हे उष्णतेचा वापर उर्जा मिळवण्यासाठी करते. उष्णता एका चक्रातून दिली जाते.

वर्णन 

रॅंन्काईनचे चक्र हे औष्णिक विद्युत केंद्रात सर्वसामान्यरित्या वापरल्या जाणाऱ्या वाफचलित ताप इंजिन किंवा वाफेचे इंजिनच्या रुपकाचे वर्णन करते. रॅंन्काईनचे चक्र अवलंबणाऱ्या औष्णिक विद्युत केंद्रात वापरल्या जाणारे जळण म्हणुन कोळसा नैसर्गिक वायू कच्चे खनिज तेल व अणु उर्जा यांचा वापर होतो.
जेंव्हा जेंव्हा एखादे टर्बाईनचा वापर होतो,रॅंन्काईनचे चक्र हे कधी कधी प्रत्यक्ष वापरातले कर्नॉटचे चक्र म्हणुनही ओळखले जाते.

कधी कधी रॅंकाइन चक्र हे कार्नॉट चक्र म्हणून संदर्भित केले जाते, जेव्हा एक कार्यक्षम टर्बाईन वापरली जाते,तेव्हा टी-एस(तापमान विरुद्ध  उष्णताक्षयमान)आक्रुती कार्नॉट चक्रासारखि दिसण्यास सुरुवात होते. मुख्य फरक ह आहे की उष्णतेची भर व त्याग हे रॅंकाइन चक्रामध्ये  आयसोबारिक(दाब स्थिर असणे) असते तर तात्त्विक कार्नॉट चक्रामध्ये आयसोथर्मल(तापमान स्थिर असणे) असते. द्रवाऐवजी वायु दाबानुकुलित करायला पंप वापरला जातो. कॉंप्रेसर(संपीडक) मधे वायू कॉंप्रेस करायला जेवढी ऊर्जा लागते त्यापेक्षा कार्यकारी द्रवाला चक्रामधून pump करायला (ढकलायला) कमी ऊर्जा लागते.

रॅंकाइन चक्राची कार्यक्षमता सामान्यत: कार्यकारी द्रवामुळे मर्यादित राहते. कार्यकारी द्रवाचा दाब अतिक्रांतिक पातळीवर(अशावेळी कार्यकारी द्रवाचे गुणधर्म हे वायु व द्रव यांच्या मधे असतात) पोहोचल्याशिवाय, चक्राची तापमान कक्षा फारच कमी होते: turbine entry temperatures are typically 565°C (the creep limit of stainless steel) and condenser temperatures are around 30°C. This gives a theoretical Carnot efficiency of about 63% compared with an actual efficiency of 42% for a modern coal-fired power station.  This low turbine entry temperature (compared with a gas turbine) is why the Rankine cycle is often used as a bottoming cycle in combined cycle gas turbine power stations.

The working fluid in a Rankine cycle follows a closed loop and is re-used constantly.  The water vapor with entrained droplets often seen billowing from power stations is generated by the cooling systems (not from the closed loop Rankine power cycle) and represents the waste heat that could not be converted to useful work.  Note that cooling towers operate using the latent heat of vaporization of the cooling fluid.  The white billowing clouds that form in cooling tower operation are the result of water droplets which are entrained in the cooling tower airflow; they are not, as commonly thought, steam.  While many substances could be used in the Rankine cycle, water is usually the fluid of choice due to its favorable properties, such as nontoxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties.

One of the principal advantages the Rankine cycle holds over others is that during the compression stage relatively little work is required to drive the pump, the working fluid being in its liquid phase at this point. By condensing the fluid to liquid, the work required by the pump consumes only 1% to 3% of the turbine power and contributes to a much higher efficiency for a real cycle. The benefit of this is lost somewhat due to the lower heat addition temperature. Gas turbines, for instance, have turbine entry temperatures approaching 1500°C. Nonetheless, the efficiencies of actual large steam cycles and large modern gas turbines are fairly well matched.

रॅंन्काईनचे चक्राच्या प्रक्रिया  

There are four processes in the Rankine cycle, these states are identified by number in the diagram to the right.

Process 1-2: The working fluid is pumped from low to high pressure, as the fluid is a liquid at this stage the pump requires little input energy.
Process 2-3: The high pressure liquid enters a boiler where it is heated at constant pressure by an external heat source to become a dry saturated vapor.
Process 3-4: The dry saturated vapor expands through a turbine, generating power. This decreases the temperature and pressure of the vapor, and some condensation may occur.
Process 4-1: The wet vapor then enters a condenser where it is condensed at a constant pressure to become a saturated liquid.

In an ideal Rankine cycle the pump and turbine would be isentropic, i.e., the pump and turbine would generate no entropy and hence maximize the net work output. Processes 1-2 and 3-4 would be represented by vertical lines on the Ts diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the vapor ending up in the superheat region after the expansion in the turbine, which reduces the  energy removed by the condensers.

Variables

समीकरण 
Each of the first four equations is easily derived from the energy and mass balance for a control volume.  The fifth equation defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, equation 5 can be simplified.

रॅंन्काईनचे चक्रReal Rankine cycle (non-ideal) 

In a real Rankine cycle, the compression by the pump and the expansion in the turbine are not isentropic.  In other words, these processes are non-reversible and entropy is increased during the two processes.  This somewhat increases the power required by the pump and decreases the power generated by the turbine.

In particular the efficiency of the steam turbine will be limited by water droplet formation. As the water condenses, water droplets hit the turbine blades at high speed causing pitting and erosion, gradually decreasing the life of turbine blades and efficiency of the turbine. The easiest way to overcome this problem is by superheating the steam. On the Ts diagram above, state 3 is above a two phase region of steam and water so after expansion the steam will be very wet. By superheating, state 3 will move to the right of the diagram and hence produce a dryer steam after expansion.

मुळ रॅंन्काईनच्या चक्रातील बदलणाऱ्या संज्ञा 

The overall thermodynamic efficiency (of almost any cycle) can be increased by raising the average heat input temperature  of that cycle. Increasing the temperature of the steam into the superheat region is a simple way of doing this. There are also  variations of the basic Rankine cycle which are designed to raise the thermal efficiency of the cycle in this way; two of these are described below.

रॅंन्काईनचे चक्र पुनर्तापसहित  

In this variation, two turbines work in series.  The first accepts vapor from the boiler at high pressure.  After the vapor has passed through the first turbine, it re-enters the boiler and is reheated before passing through a second, lower pressure turbine.  Among other advantages, this prevents the vapor from condensing during its expansion which can seriously damage the turbine blades, and improves the efficiency of the cycle, as more of the heat flow into the cycle occurs at higher temperature.

पुनर्निर्माण करणारे रॅंन्काईनचे चक्र 

The regenerative Rankine cycle is so named because after emerging from the condenser (possibly as a subcooled liquid) the working fluid is heated by steam tapped from the hot portion of the cycle. On the diagram shown, the fluid at 2 is mixed with the fluid at 4 (both at the same pressure) to end up with the saturated liquid at 7. This is called "direct contact heating". The Regenerative Rankine cycle (with minor variants) is commonly used in real power stations.

Another variation is where 'bleed steam' from between turbine stages is sent to feedwater heaters to preheat the water on its way from the condenser to the boiler.  These heaters do not mix the input steam and condensate, function as an ordinary tubular heat exchanger, and are named "closed feedwater heaters".

The regenerative features here effectively raise the nominal cycle heat input temperature, by reducing the addition of heat from the boiler/fuel source at the relatively low feedwater temperatures that would exist without regenerative feedwater heating.  This improves the efficiency of the cycle, as more of the heat flow into the cycle occurs at higher temperature.

जैविकाधारीत रॅंन्काईनचे चक्र 

The organic Rankine cycle (ORC) uses an organic fluid such as n-pentane or toluene in place of water and steam. This allows use of lower-temperature heat sources, such as solar ponds, which typically operate at around 70–90 °C. The efficiency of the cycle is much lower as a result of the lower temperature range, but this can be worthwhile because of the lower cost involved in gathering heat at this lower temperature.  Alternatively, fluids can be used that have boiling points above water, and this may have thermodynamic benefits.

The Rankine cycle does not restrict the working fluid in its definition, so the inclusion of an "organic" cycle is simply a marketing concept that should not be regarded as a separate thermodynamic cycle.

संदर्भ 

 ^Van Wyllen 'Fundamentals of thermodynamics' (ISBN 85-212-0327-6)
Moran & Shapiro 'Fundamentals of Engineering Thermodynamics' (ISBN 0-471-27471-2)
Wikibooks Engineering Thermodynamics

बाह्य दुवे 
 Organic Rankine Cycle for electric power generation
 Rankine Cycle on-line calculation
 Cyclone Power another commercial implementation

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