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(Gas Power, Vapor Power and Refrigeration cycles )
Daemons>Open Cycle> Examples


 
                                                    

 Ex-1: Consider a two-stage R-12 refrigeration system operating between 0.15 MPa and 1 MPa. The refrigerant leaves the condenser as saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The vapor from the flash chamber is mixed with the refrigerant leaving the low-pressure compressor and the mixture is compressed by the high-pressure compressor to the condenser pressure. The liquid in the flash chamber is throttled to the evaporator pressure where the cooling load is handled through evaporation. Assume the refrigerant leaves the evaporator and mixer as saturated vapor.

Determine the COP.

What-if scenario: How would the COP change if the intermediate pressure was increased to 0.6 MPa? 





 

 

# TEST>Daemons>Systems>Open>SteadyState>Specific>
#   RefriCycle>PhaseChange

     States { 
  State-1:  R-12;
  Given:       { p1= 0.15 MPa;   x1= 100.0 %;   Vel1= 0.0 m/s;   z1= 0.0 m;   }

  State-2:  R-12;
  Given:       { p2= 0.4 MPa;   s2= "s1" kJ/kg.K;   Vel2= 0.0 m/s;   z2= 0.0 m;   }

  State-3:  R-12;
  Given:       { p3= "p2" MPa;   x3= 100.0 %;   Vel3= 0.0 m/s;   z3= 0.0 m;   mdot3= "x6*mdot9" kg/s;   }

  State-4:  R-12;
  Given:       { p4= 1.0 MPa;   s4= "s9" kJ/kg.K;   Vel4= 0.0 m/s;   z4= 0.0 m;   }

  State-5:  R-12;
  Given:       { p5= "p4" MPa;   x5= 0.0 %;   Vel5= 0.0 m/s;   z5= 0.0 m;   }

  State-6:  R-12;
  Given:       { p6= "p2" MPa;   h6= "h5" kJ/kg;   Vel6= 0.0 m/s;   z6= 0.0 m;   }

  State-7:  R-12;
  Given:       { p7= "p6" MPa;   x7= 0.0 %;   Vel7= 0.0 m/s;   z7= 0.0 m;   mdot7= "(1-x6)*mdot9" kg/s;   }

  State-8:  R-12;
  Given:       { p8= "p1" MPa;   h8= "h7" kJ/kg;   Vel8= 0.0 m/s;   z8= 0.0 m;   }

  State-9:  R-12;
  Given:       { p9= "p2" MPa;   Vel9= 0.0 m/s;   z9= 0.0 m;   mdot9= 1.0 kg/s;   }
 }

 Analysis {
  Device-A:  i-State =  State-9;  e-State =  State-4; Mixing: true
  Given: { Qdot= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-B:  i-State =  State-4;  e-State =  State-5; Mixing: true
  Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-C:  i-State =  State-5;  e-State =  State-6; Mixing: true
  Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-D:  i-State =  State-6;  e-State =  State-3, State-7; Mixing: true
  Given: { Qdot= 0.0 kW;   Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-E:  i-State =  State-7;  e-State =  State-8; Mixing: true
  Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-F:  i-State =  State-8;  e-State =  State-1; Mixing: true
  Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-G:  i-State =  State-1;  e-State =  State-2; Mixing: true
  Given: { Qdot= 0.0 kW;   T_B= 25.0 deg-C;   }

  Device-H:  i-State =  State-2, State-3;  e-State =  State-9; Mixing: true
  Given: { Qdot= 0.0 kW;   Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }
 }

 



 

Solution

Answering the six questions described in the Navigation   section leads you to the appropriate daemon page for the reverse-Rankine refrigeration cycle: TEST. Daemons. Systems. Open. Steady. Specific.RefriCycles. PhaseChange .

Let us set up the cycle as follows : Device-A: isentropic compression from State-9 to State-4 ; Device-B : constant pressure heat rejection from State-4 to State-5 ; Device-C : isenthalpic expansion from State-5 to State-6 ; Device-D : constant pressure phase separation from inlet at  State-6 to exits at  State-3 ; Device-E : isenthalpic expansion from State-7 to State-8 ; Device-F : constant pressure heat addition from State-8 to State-1 ; Device-G : isentropic compression from State-1 State-2 ; Device-H State-3   into State-9 .

The mass flow rate being an unknown, we will take 1 kg/s through the top loop as the basis for this analysis, i.e.,  mdot9=1 kg/s. In that case mdot3=x6*mdot9 and mdot7=(1-x6)*mdot9. 

In evaluating the states, we can follow two approaches. Utilize known information on devices or put them off until the Device Analysis part and let the daemon export the device info onto the affected States. For instance, in an isentropic device (say, Device-a) operating between State-1 and -2,  we can enter s2 as '=s1'. Or alternatively, we could enter Qdot=0 and Sdot_gen=0 (i.e. adiabatic and reversible) in the analysis of Device-a. The Super-Calculate operation, in that case, would solve the entropy-balance equation for Device-a, conclude that s2=s1, substitute s1 for s2 in State-2, and recalculate State-2. For complex cycles such as this one, we will follow the first approach.

State-1-8: Enter the known values or relations as described in the TEST-codes and Calculate the states fully or partially.  


Fig. 5  Image of Device-D . Solution of the energy equation yields mdot3 which is posted back
on State-3. Super-Calculate calculates State-3 and 7 completely and later solves the entropy
 equation to evaluate Sdot_gen.

 

Device-A through H: For each device select a letter, load the anchor states (see the TEST-codes above), enter the known device variable (Qdot or Wdot_ext) and Calculate. 

Use  Super-Calculate followed by a Super-Iterate  to update all the States and Devices.  The COP is calculated as COP=349%. The mass flow rate for the bottom cycle is calculated as mdot1=0.77 kg/s.

Super-Iterate is sometimes necessary to continue the iterations between the State and Analysis Panels just in case Super-Calculate, with a fixed number of iterations, is not sufficient.
 



For the parametric study, go to the States Panel and change p2  to 0.6 MPa. Calculate the State, Super-Calculate and Super-Iterate to update all calculations. The new COP  is calculated as 332%.
Fig. 4.2  Image of the Cycle Panel. Cycle variables are  automaticaly calculated
once the cycle is complete. 

 
                                              
Ex-2: In a gas refrigeration system air enters the compressor at 10 o C and 50 kPa and the turbine at 50oC and 250 kPa. The mass flow rate is 0.08 kg/s. Assuming variable specific heat, determine (a) the rate of cooling, (b) the net power input and (c) the COP.

What-if scenario:   How would the answers change if the working fluid were helium instead? 


# TEST>Daemons>Systems>Closed>Process>
#          Specific>RefrigCycle>IdealGas;
 

  States { 
               State-1:  Air;
               Given:       { p1= 50.0 kPa;   T1= 10.0 deg-C; 
                          Vel1= 0.0 m/s;   z1= 0.0 m;   mdot1= 0.08 kg/s;   }

               State-2:  Air;
               Given:       { p2= 250.0 kPa;   s2= "s1" kJ/kg.K; 
                          Vel2= 0.0 m/s;   z2= 0.0 m;   }

               State-3:  Air;
               Given:       { p3= "p2" kPa;   T3= 50.0 deg-C; 
                          Vel3= 0.0 m/s;   z3= 0.0 m;   }

               State-4:  Air;
               Given:       { p4= "p1" kPa;   s4= "s3" kJ/kg.K; 
                          Vel4= 0.0 m/s;   z4= 0.0 m;   }
   }

   Analysis {
               Device-A:  i-State =  State-1;  e-State =  State-2; Mixing: true
               Given: { Qdot= 0.0 kW;   T_B= 25.0 deg-C;   }

               Device-B:  i-State =  State-2;  e-State =  State-3; Mixing: true
               Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }

               Device-C:  i-State =  State-3;  e-State =  State-4; Mixing: true
               Given: { Qdot= 0.0 kW;   T_B= 25.0 deg-C;   }

               Device-D:  i-State =  State-4;  e-State =  State-1; Mixing: true
               Given: { Wdot_ext= 0.0 kW;   T_B= 25.0 deg-C;   }
  }
 


Solution

Answering the six questions described in the Navigation   section leads you to the appropriate daemon page for a Brayton cycle: TEST. Daemons. Systems. Open. Steady. Specific.RefriCycles. IdealGas .

Let us set up the cycle as follows: Device-A: compression from State-1 to State-2 ; Device-B: constant pressure heat rejection from State-2 to State-3 ; Device-C : isentropic expansion from State-3 to State-4 ; Device-D : constant pressure heat addition from State-4 to State-1 .

State-1-4: Enter known values or relations and  Calculate
each state fully or partially.



 
Fig. 4.1 Image of the Cycle Panel for a refrigeration/heat pump cycle.

 


Step 4: Analyze the four open and steady devices.

On the Analysis panel, work on the four devices.

Device-A through D: As described in the TEST-codes, identify each device by a unique letter, load the anchor states, enter the known device variables (Qdot and Wdot_ext) and Calculate.   

Use  Super-Calculate to produce the TEST-codes and the detailed output. On the Cycle panel, no further work is necessary. The COP is calculated as 1.72. Now change the gas to helium in the State panel and  Super-Calculate .
The new value for COP is 1.11.




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Copyright 1998-: Subrata Bhattacharjee