Determine (a) the velocity of the steam at the exit, (b) the mass flow rate in kg/s, (c) the power produced by the turbine if the heat los is 1 MW, and (d) the rate of entropy generation if the ambient temperature is 25^oC

What-if scenario: How would the answers change if the exit duct diameter were doubled? 

Step 2: Calculate the i and e States
 
 
 
 
 
 
 
 
 
 

Step 3: Load the States on the Analysis panel, enter device variables, Calculate and Super-Calculate.

Step 4: Change a parameter, Calculate and Super-Calculate.
 

Answering the six questions described  in the Approach   section leads you to the appropriate daemon page:  HOME. Daemons. Systems. Open. SteadyState. Generic. SingleFlow. PhaseChange . Launch the daemon and choose H2O .

Let  State-1 and State-2 represent the i-State and the  e-State  respectively. 

State-1: Enter A1 as '=3.14*.4*.4/4', Vel1 (90 m/s), p1 (14 MPa),  T1 (600 ^oC), and   Calculate. The mass flow rate is calculated as 105 kg/s . 

State-2: Enter A2 as '=3.14*.8*.8/4', p2 (500 kPa),  T2 (180^o C), and Calculate. The exit velocity is calculated as 84.8 m/s . 

On the Analysis panel, load State-1 as the i-State and State-2 as the e-State. Enter the only known device variable Qdot (=-1000 kW) and T_B as 25^o C.  A Calculate and Super-Calculate produce Wdot_ext (Other or electrical work) as 81 MW   and  Sdot_gen=29 kW/K  as well as all other process variables. 

For the what-if study, go to States panel,  choose State-2, change the exit area to '=3.14*1.6^2/4', Calculate and   Super-Calculate . All the answers are updated. Note the exit velocity decreases to 21.2 m/s , while the power output is hardly affected with the new value as 81.5 MW.

What-if scenario:   (a) How would the answers change if the ambient temperature were 15 ^oC instead? (b) How would the answers change if R-12 were replaced with R-134a?

Step 2: Calculate the States.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Step 3: Analyze the Device.
 
 

Step 4: Super-Calculate 
to obtain State-2.
 
 
 
 

Step 5: Calculate the dead state for availability study.
 
 
 
 
 

Step 6: For the what-if study, change the parameters, Calculate and Super-Calculate.
 

Answering the six questions described in the Approach   section leads you to the appropriate daemon page:  HOME. Daemons. Systems. Open. SteadyState. Generic. SingleFlow. PhaseChange . Launch the daemon and choose R12 .

Let  State-1 represent the i-State and State-2 represent the e-State. Because the actual exit state is related to an ideal exit  state through adiabatic efficiency, let  State-3 represent that ideal state isentropic to State-1 and isobaric to State-2. 

State-1: Enter p1 (80 kPa),  x1 (95%), Voldot1 (1m3/min), and   Calculate. Leave Vel1 and z1 at their default value of zero. the mass flow rate is calculated as 0.089 kg/s . Note that the inlet area calculated is ridiculously high. To obtain a realistic A1, Vel1 has to have a realistic value.

State-2: Enter p2 (2 MPa) and leave Vel2 and z2 at their default value of zero. eta_adb=Wdot_ext,s/Wdot_ext = (j1-j3)/(j1-j2). Therefore, j2=j1-(j1-j3)/eta_ad . Enter j2 as '=j1-(j1-j3)/0.75 and  Calculate. The State, obviously cannot be determined because State-3 is completely unknown at this stage. 

State-3: Enter p3  as '=p2',  s3 as '=s1', leave Vel1 and z1 at their default value and   Calculate. The temperature T3 is calculated as 79.4 ^oC .

On the Analysis panel, load State-1 as the i-State and State-2 as the e-State. Enter the only known device variable Qdot (=0) and T_B as 25^oC.  A Calculate and Super-Calculate produce Wdot_ext (the desired compressor power) as -6.44kW   and  Sdot_gen=0.0044 kW/K  as well as all other unknown process and state variables. Go to the States panel to find the final temperature T2 as  100 ^oC. For availability analysis a dead state, State-0, must be evaluated first. 

State-0: Enter p0 (100 kPa) and T0 (25^oC),   and   Calculate. 

On the Availability panel, load State-0 as the dead state. A Calculate produces the second-law efficiency eta_II=79.8% . 
 

For the what-if study, go to States panel,  choose State-0, change T0 to its new value (15^o C) and Calculate . Get back to the Availability panel and do a   Super-Calculate . All the answers are updated. The new value for eta_II=80.4%. 
For the second part, select the working fluid on the States panel to be R-134a. A Super-Calculate yields: Wdot_ext=-6.19 kW   and Sdot_gen=0.0044 kW/K

What-if scenario:   (a) How would the answer change if the air temperature were 40 ^oC instead?

Step 2: Calculate State-1 and State-2. Assume a unit mass flow rate.
 
 
 
 

Step 3: On the Analysis panel, load the calculated states, enter the known device variables. A Calculate and Super-Calculate produce the desired answers.
 
 

Step 4: Change a parameter, Calculate and Super-Calculate the new answer. Show that answers are independent of the mass flow rate
 
 

Answering the six questions described in the Approach   section leads you to the appropriate daemon page:  HOME. Daemons. Systems. Open. SteadyState. Generic. SingleFlow. PerfGas .

Let  State-1 and State-2 represent the i-State and the  e-State  respectively. Note that no mass flow rate is given in the problem. We will assume a mdot of 1 kg/s and check that the answers produced by this analysis do not depend on our choice of flow rate.

State-1: Enter p1 (80 kPa), T1 (0^oC), Vel1 (250 m/s), mdot1 (1 kg/s) and Calculate. The inlet area A1 is calculated as 39.2 cm2 . 

State-2: Enter p2 (100 kPa), initialize Vel2 (unknown),  and Calculate. The state is, obviously, not fully evaluated. 

On the Analysis panel, load State-1 as the i-State and State-2 as the e-State. Enter the known device variable Qdot (0 kW), Wdot_ext (0 kW), and Sdot_gen (=0 because of no irreversibility). The value of  T_B does not affect the entropy balance equation because the diffuser is adiabatic.  A Calculate and Super-Calculate produce the exit State.

Get back to State-2 to find a completely evaluated state (not the gray background of the properties exported from the Analysis panel). The exit area is calculated as 
 51.5 cm2 , an increase of about 31.4 % . Select State-2 , change mdot1 to 2 kg/s. Update all calculations using a Calculate followed by a Super-Calculate . The inlet and exit areas, both double without affecting the answer.

For the what-if study, change T1 to 40^oC. A Calculate and   Super-Calculate  yield A1  and A2 as 44.9 cm2 and 66.0 cm2 respectively, an increase of  47.0 %.
 

What-if scenario: How would the answer change if the supply pressure were reduced to 45 psia?

Step 2: Calculate the States
 
 

Step 3: Analyze the Device
 

Step 4: Calculate and Super-Calculate 
the desired results
 
 
 
 

Step 5: For the what-if study, change p2, Calculate and Super-Calculate.
 

Answering the six questions described in the Approach   section leads you to the appropriate daemon page:  HOME. Daemons. Systems. Open. SteadyState. Generic. SingleFlow. SolidLiquid .

Let  State-1 represent the i-State (at the surface of the liquid in the supply reservoir where the pressure and height are known) and  State-2 (at the surface of the water where the pressure and height are known) the e-State . Let us fix the datum at the pump location, i.e., z1=-25 ft . Switch to English system and choose Oil as the working fluid.

State-1: Enter mdot1 (10 lbm/s), p1 (15 psia), T1(20^oC),  z1 (-25 ft), and   Calculate. Leave Vel1 at its default value of zero (which produces a ridiculously large A1. For a realistic A1 change Vel1 to a reasonable value).

State-2: Enter p2 (60 psia),  z2 (100 ft), and   Calculate. 

On the Analysis panel, load State-1 as the i-State and State-2 as the e-State. Enter the known device variable Qdot (=0),   Sdot_gen (=0 for a pump with no irreversibility or wasted power), and T_B as 25^oC (its value does not affect the calculations as the heat transfer is assumed to be zero).  A Calculate and Super-Calculate produce Wdot_ext=-4.35 hp. Notice that T2 is evaluated as part of the solution. 

For the what-if study, go to States panel,  choose State-2, change p2  to its new value (45 psia) and Calculate . Get back to the Analysis panel and do a   Super-Calculate . All the answers are updated. The new value for Wdot_ext=-3.66 hp.

If the problem involves H2O, the appropriate daemon could be chosen as pure liquid or two-phase mixture. In the second case, liquid can be represented by saturated liquid  (x=0) without any significant error.

What-if scenario:   How would the entropy generation change if the pressure inside the chamber were 200 kPa instead?

Step 2: Calculate the inlet and exit states
 
 
 
 
 
 
 
 
 
 
 
 

Step 3: On the Analysis panel, load the calculated states, enter the known device variables. A Calculate and Super-Calculate produce the desired answers.
 
 

Step 4: Change a parameter, Calculate and Super-Calculate the new answer.

Answering the six questions described in the Approach   section leads you to the appropriate daemon page:  HOME. Daemons. Systems. Open. SteadyState. Generic. FlowMixed. IdealGasMixture .

Let  State-1 and State-2 represent the two inlets, i1-State and the  i2-State  respectively, and State-3 represent the exit inlets, e-State. Choose N2 from the first gas-selector (gas-A) and CO2 from the second gas-selector (gas-B).

State-1: Enter x_A1 (1), T1 (30^oC), p1(100 kPa), Voldot1 (100 m3/min), and Calculate. The mass flow rate is calculated as 1.85 kg/s. 

State-2: Enter x_A2 (0), T2 (200^oC), p2('=p1'), Voldot2 (50 m3/min), and Calculate. The mass flow rate is calculated as 0.93 kg/s. 

State-3: Enter x_A3 ('=mdot1/(mdot1+mdot2)), p3 (=p1), and Calculate. The state cannot be fully evaluated at this stage. 

On the Analysis panel, load State-1 as the i1-State,  State-2 as the i2-State, and  State-3 as the e1-State (note that the daemon can handle up to two exit states). Enter the known device variable Qdot (0 kW) and Wdot_ext (0 kW). The value of  T_B does not affect the entropy balance equation because the chamber is adiabatic.  A Calculate and Super-Calculate produce the exit State and the unknown device variable, Sdot_gen=0.4657 kW/K. Go to the States window to find T3=83.5^oC .

For the what-if study, change p1 to 200 kPa. A Calculate and   Super-Calculate  yield Sdot_gen=0.9307 kW/K. 

The daemon allows two exits, which can be useful for a separator where a single flow enters and separates into two different flows as in a separation chamber used in some refrigeration systems.
 

What-if scenario: How would the answers change if the heat transfer had to be augmented to 5000 kJ/min?

Step 2: Calculate the States.
 
 

Step 3: Analyze the Device.
 

Step 4: Calculate and Super-Calculate 
the desired results.
 
 
 
 

Step 5: For the what-if study, change parameter, Calculate and Super-Calculate.
 

The appropriate daemon is launched from HOME. Daemons. Systems. Open. SteadyState. Generic. FlowUnmixed. IdealGasMixture . Note that a perfect gas is a better choice if the gas is unknown (custom-build with user-specified cp and M ).

In this problem there are essentially three devices.

Device-A : The entire heat exchanger with State-1 representing the i1-State and State-2 the e1-State , State-3 the i2-State and State-4 representing the e2-State . 

Device-B : The air stream with a single inlet and exit, State-1 representing the i1-State and State-2 representing the e1-State.

Device-C : The nitrogen stream with a single inlet and exit, State-3 representing the i2-State and State-4 representing the e2-State.

State-1 (Air inlet): Select Air as gas-A with x_A=1. Enter p1 (1 MPa), T1(600  K), and mdot1 (1000 kg/min) (leave Vel1 and z1 to their default value of 0)  and  Calculate. 2.87 m3/s

State-2 (Air exit): Enter x_A as '=x_A1' , p2 as '=p1', and mdot2 as '=mdot1'.  Calculate. Note that not much is known about this state

State-3 (N2 inlet): To compose pure N2 out of a mixture, choose N2 as Gas-B and enter x_A=0. Enter  p3 (150 kPa) and T3 (800 K),  and   Calculate.   Note that a j3=h3= 540 kJ/kg

State-4 (N2 exit): Enter x_A4=x_A3. Enter p4 (120 kPa), T4 (600 K),  and   Calculate.   Note that a j4=h4= 319 kJ/kg

On the Analysis panel there are three devices.

Device-A : Load State-1 as the i1-State, State-2 as the e1-State,  State-3 as the i2-State and State-4 as the e2-State. Enter  Qdot (=0, heat transfer in the heat exchanger is interanal), and  Wdot_ext (=0).  Calculate.

Device-B : Load State-1 as the i1-State  and  State-2 as the e1-State. Enter  Qdot (=4000 kW) and  Wdot_ext (=0).  A Calculate and Super-Calculate produce  T2= 822 K, mdot3= 1083 kg/min and Sdot_gen= 1.11 kW/K

Note that we do not need Device-C in this problem. However, if you create Device-C with and enter Wdot_ext=0, you will get Qdot=-4000 kW.

For the what-if study, go to Device-B ,  change Qdot to the new value,  Calculate and    Super-Calculate. All the answers are updated. The new value for T2=874 K . Note that p2 remains an unknown as it depends on the friction inside the tube. If p2 were given, the device variable, Sdot_gen would have been determined.
 

What-if scenario: How would the answers change if the heat exchanger looses heat at the rate of 10 kW? Assume the atmospheric temperature to be 25 deg-C.

Modeling the water with the solid/liquid model and air with the ideal gas model, launch the ... Systems. Open. SteadyState. Generic. FlowUnmixed. IG/SL daemon.  

Setup the four states as described in the TEST-Code above. For each state you must select the working fluid carefully. Load the states on the Device Panel, enter Qdot=Wdot_ext=0, Calculate and  Super-Calculate. The mass flow rate of water is found to be 45.78 kg/s and the entropy generation rate 1.71 kW/K .

For the what-if study, go to Device-A ,  change Qdot to -10 kW,  Calculate and    Super-Calculate. The new value for mdot3= 45.6 kg/s. and Sdot_gen= 1.71 kW/K. Could you explain why the entropy generation rate in the system's universe does not show any change?