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DESCRIPTION:

 

Recent work by Leverone et al.[1] from TU Delft have proposed a solar thermal propulsion and power system for future satellites. The introduction of their paper states:

“There is an increasing demand for small satellites to have higher on-board electrical power and propulsion capabilities for future interplanetary missions. NASA has suggested that target power densities and specific energies for electrical power system on-board future interplanetary spacecraft are between 150 and 250 W/kg [1] and more than 250 Wh/kg [2]. Conventional small satellite photovoltaic technologies are around 20 to 100 W/kg [3], [4] and Lithium-polymer and -ion batteries have specific energies between 150 to 250 Wh/kg. These systems are currently below the targeted values and call for alternative systems to be investigated.

A possible system proposed to meet these specific mission requirements is a bi-modal integrated solar thermal system for propulsion and electrical power generation [5]–[6][7]. This novel system for small satellites incorporates a solar thermal propulsion (STP) system and a micro-Organic Rankine Cycle (ORC) system. This integration allows sub-systems to share on-board components as shown in Figure 1, by harvesting energy from the STP system to co-generate electrical power, and possibly use the additional waste heat for on-board thermal control. Solar thermal propulsion systems focus solar radiation onto a receiver or the propellant directly using mirrors or lenses to heat the propellant to very high temperatures, generally between 1000 and 2500 K. The vaporized propellant is then expanded through a nozzle to generate thrust.” – Leverone et al. (2020)

They propose to integrate the solar thermal propulsion with a micro-Rankine cycle, as shown in Figure 1.For your analysis, the target output of the power system is 500 W of electrical power. In space, the condenser must be a radiator, and minimizing the weight is critical to achieve the power-to-weight ratio targets.Your job is to analyze this system and identify the best condenser operating pressure based on the minimum condenser size. The project is divided into two parts. First, you will analyze the power cycle under a set of baseline conditions. Then, you will explore an optimum condenser pressure.

 

Figure 1.Schematic of the proposed bi-modal solar thermal system.

 

Part 1 – Baseline Power Cycle Analysis

The power cycle is shown in Figure 1, above. The cycle consists of a boiler, turbine, recuperative heat exchanger, condenser, and a pump. The state points are as follows:

  • State 1 – Boiler Outlet/Turbine Inlet
  • State 2 – Ideal (isentropic) turbine outlet
  • State 3 – Actual turbine outlet/regenerative HX low pressure inlet
  • State 4 – Regenerative HX low pressure outlet/Condenser inlet
  • State 5 – Condenser outlet
  • State 6 – Pump ideal (isentropic) outlet
  • State 7 – Pump actual outlet/regenerative HX high pressure inlet
  • State 8 – Regenerative HX high pressure outlet/boiler inlet

 

You should assume the following your baseline analysis.

  • Toluene is the working fluid (use fluid = ‘toluene’ in EES)
  • The cycle net work output is 500 W
  • Turbine isentropic efficiency = 70%
  • Pump isentropic efficiency = 80%
  • The boiler saturation temperature is 250 degC
  • The turbine inlet temperature is 275 degC
  • The condenser saturation temperature is 75 degC (baseline case)
  • The regenerator low pressure outlet (State 4) is a saturated vapor
  • The condenser outlet (State 5) is a saturated liquid.
  • Neglect pressure drop in all heat exchangers

 

Part 2 – Condenser Optimization

The condenser rejects energy to space via radiation only. The size of the radiator can be estimated by the following equation:

Here, is the Stefan-Boltzmann constant (5.68 × 10-8 W m-2 K-4), and the temperature T must be in Kelvin. Keeping all other assumptions, the same, you should develop a plot of the cycle efficiency, and the condenser area (in m2) for a condenser saturation temperature varying from 0 to 200 degC.

System Analysis Project

 

Part 1 Baseline Analysis Results

  1. Turbine Analysis
    1. Draw an appropriate control volume to calculate the turbine work out and rate of entropy generation.

 

  1. List all assumptions made in analyzing the turbine

 

The following assumptions are made for analysis of turbine.

(i) The mass flow through the system remains constant.

(ii) Fluid is uniform in composition.

(iii) The only interaction between the system and surroundings are work and heat.

(iv) The state of fluid at any point remains constant with time.

(v)  In the analysis only potential, kinetic and flow energies are considered.

 

  1. Starting from the most general form of the 1st and 2nd law for a control volume that you know, simplify down to show the expression you will use in your code to calculate the turbine work.

 

The first law states that energy cannot be created or destroyed, but can be converted from one form to another. As an equation, this is simply:

Esystem = 0 = Ein – Eout

Thermal energy can be increased within a system by adding thermal energy (heat) or by performing work in a system. For a closed system its change in energy will be the balance between the heat transferred to (Qin) and the work done on (Win) the system, and the heat transferred from (Qout) and work done by (Wout) the system. As an equation, this can be expressed by:

 E=(Qin-Qout)-(Wout-Win )=Qnet,in-Wnet ,out

or

Wnet,out =Qin-Qout

Second Law efficiency is a measure of how much of the theoretical maximum (Carnot) you achieve, or in other words, a comparison of the system’s thermal efficiency to the maximum possible efficiency. The Second Law efficiency will always be between the Carnot and First Law efficiencies.

ns =n th /nc

Consider an elemental mass dm flowing through an inlet or outlet port of a control volume, having an area A, volume dV, length dx, and an average steady velocity , as follows.

 

 

  1. Regenerative HX
    1. Draw an appropriate control volume to calculate the high pressure regenerative HX outlet enthalpy (State 8) and the rate of entropy generation within the regenerative HX.

 

 

  1. List all assumptions made in analyzing the regenerative HX
  2. Each component of the working fluid is internally reversible.

ii.All processes of the working fluid are internally reversible.

iii.The pump and turbine operate adiabatically.

iv.Potential and kinetic energy affects are neglected.

v.Condensate leaves the condenser as saturated liquid.

 

  1. Starting from the most general form of the 1st and 2nd law for a control volume that you know, simplify down to show the expression you will use in your code to calculate the enthalpy at state 8, and the rate of entropy generation.

 

 

The energy analysis of regenerative HX is identical to the energy analysis of mixing chambers. The regenerative HX are generally well insulated   (   Q=0          ), and they do not involve any work interactions (W=0). By neglecting the kinetic and potential energies of the streams, the energy balance reduces for a regenerative HX to

 

  1. Fill out following table with given units for the baseline caseFor quality, enter 100 if the state point is superheated vapor, and -100 if the state point is subcooled liquid. *Note, you may have negative values of enthalpy. This is OK. It is related to the reference used in EES.

 

State

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg-K)

 

u(KJ/Kg)

v(m3/kg)

1

250

6.849

602.3

1.715

0

555.1

6.886

2 (ideal)

250

6.849

602.3

1.715

0

555.1

6.886

3

275

7.013

651.2

1.804

1

601.8

7.047

4

275

7.013

651.2

1.804

1

601.8

7.047

5

75

5.556

315.9

1.076

0

284.6

5.638

6(ideal)

75

5.556

315.9

1.076

1

284.6

5.638

7

75

5.556

315.9

1.076

1

284.6

5.638

8

175

6.33

466.8

1.443

1

426.4

6.379

 

 

  1. Show numerical values of following parameters in given units

 

 

1

Working fluid mass flow rate

g/s

1290

2

Condenser heat duty

W

 

259.7

3

Boiler heat duty

W

 

104.9

4

Turbine produced power

W

 

71.48

5

Pump consumed power

W

13.55

 

6

Thermal efficiency of cycle

%

10.4

7

Rate of entropy generation in turbine

W/K

-0.227

8

Rate of entropy generation in regenerative heat exchanger

W/K

0.3211

 

 

 

  1. Show the cycle on a T–s diagram overlaid on tolune property plot. Each state point should be labeledSee the example on Canvas, as well ashttps://youtu.be/HRxRJU6orkE and for more information https://youtu.be/JcxX4SOjPho. It may be easier to only plot the state points, and then manually draw the connecting lines.

 

 

Part 2Parametric Analysis Results

  1. Create a parametric table and generate a plot of the cycle thermal efficiency and condenser area versus the condenser saturation temperature varied from 0 degC to 200 degC. All other variables should be the same as the baseline analysis. Submit as a single plot, using two different y-axes to clearly show the data. The figure can be made in the plotting software of your choice.See the example on Canvas or https://youtu.be/G_xhgkAiw1Y for more information on parametric tables.

 

 

Parametric Table

 

EES Program

 

W_cycle=500 “W”

 

“State 1”

T[1]=250 “C”

P[1]=pressure(Toluene,T=T[1],v=v[1]) “Pa”

x[1]=0 “dim”

v[1]=volume(Toluene,T=T[1],P=P[1]) “m3/kg”

u[1]=intenergy(Toluene,T=T[1],P=P[1]) “kJ/kg”

s[1]=Entropy(Toluene,T=T[1],P=P[1]) “kj/kg-k”

h[1]=enthalpy(Toluene,T=T[1],P=P[1]) “KJ/Kg”

 

“State 2”

T[2]=250 “C”

P[2]=pressure(Toluene,T=T[2],v=v[2]) “Pa”

x[2]=0 “dim”

v[2]=volume(Toluene,T=T[2],P=P[2]) “m3/kg”

u[2]=intenergy(Toluene,T=T[2],P=P[2]) “KJ/Kg”

s[2]=Entropy(Toluene,T=T[2],P=P[2]) “kj/kg-k”

h[2]=enthalpy(Toluene,T=T[2],P=P[2]) “KJ/Kg”

 

“State 3”

T[3]=275 “C”

P[3]=pressure(Toluene,T=T[3],v=v[3]) “Pa”

x[3]=1 “dim”

v[3]=volume(Toluene,T=T[3],P=P[3]) “m3/kg”

u[3]=intenergy(Toluene,T=T[3],P=P[3]) “KJ/Kg”

s[3]=Entropy(Toluene,T=T[3],P=P[3]) “kj/kg-k”

h[3]=enthalpy(Toluene,T=T[3],P=P[3]) “KJ/Kg”

 

“State 4”

T[4]=275 “C”

P[4]=pressure(Toluene,T=T[4],v=v[4]) “Pa”

x[4]=1 “dim”

v[4]=volume(Toluene,T=T[4],P=P[4]) “m3/kg”

u[4]=intenergy(Toluene,T=T[4],P=P[4]) “KJ/Kg”

s[4]=Entropy(Toluene,T=T[4],P=P[4]) “kj/kg-k”

h[4]=enthalpy(Toluene,T=T[4],P=P[4]) “KJ/Kg”

 

“State 5”

T[5]=75 “C”

P[5]=pressure(Toluene,T=T[5],v=v[5]) “Pa”

x[5]=0 “dim”

v[5]=volume(Toluene,T=T[5],P=P[5]) “m3/kg”

u[5]=intenergy(Toluene,T=T[5],P=P[5]) “KJ/Kg”

s[5]=Entropy(Toluene,T=T[5],P=P[5]) “kj/kg-k”

h[5]=enthalpy(Toluene,T=T[5],P=P[5]) “KJ/Kg”

 

“State 6”

T[6]=75 “C”

P[6]=pressure(Toluene,T=T[6],v=v[6]) “Pa”

x[6]=1 “dim”

v[6]=volume(Toluene,T=T[6],P=P[6]) “m3/kg”

u[6]=intenergy(Toluene,T=T[6],P=P[6]) “KJ/Kg”

s[6]=Entropy(Toluene,T=T[6],P=P[6]) “kj/kg-k”

h[6]=enthalpy(Toluene,T=T[6],P=P[6]) “KJ/Kg”

 

“State 7”

T[7]=75 “C”

P[7]=pressure(Toluene,T=T[7],v=v[7]) “Pa”

x[7]=1 “dim”

v[7]=volume(Toluene,T=T[7],P=P[7]) “m3/kg”

u[7]=intenergy(Toluene,T=T[7],P=P[7]) “KJ/Kg”

s[7]=Entropy(Toluene,T=T[7],P=P[7])

h[7]=enthalpy(Toluene,T=T[7],P=P[7]) “KJ/Kg”

 

“State 8”

T[8]=175 “C”

P[8]=pressure(Toluene,T=T[8],v=v[8]) “Pa”

x[8]=1 “dim”

v[8]=volume(Toluene,T=T[8],P=P[8]) “m3/kg”

u[8]=intenergy(Toluene,T=T[8],P=P[8]) “KJ/Kg”

s[8]=Entropy(Toluene,T=T[8],P=P[8])

h[8]=enthalpy(Toluene,T=T[8],P=P[8]) “KJ/Kg”

 

n_T=0.7

n_P=0.8

 

m=1*W_cycle/(W_12+W_34)

 

 

“Work”

W_12=m*h[2]-h[1] “KJ”

W_23=m*h[3]-h[2] “KJ”

W_34=m*h[4]-h[3] “KJ”

W_45=m*h[5]-h[4] “KJ”

W_56=m*h[6]-h[5] “KJ”

W_67=m*h[7]-h[6] “KJ”

W_78=m*h[8]-h[7] “KJ”

W_18=m*h[8]-h[1] “KJ”

 

W_ideal=(W_12+W_23+W_34+W_45+W_56+W_67+W_78+W_18)/n_T

T_b=75 “C”

 

 

“Heat Required”

Q_12=m*u[1]-u[2] “KJ”

Q_23=m*u[2]-u[3] “KJ”

Q_34=m*u[3]-u[4] “KJ”

Q_45=m*u[4]-u[5] “KJ”

Q_56=m*u[5]-u[6] “KJ”

Q_67=m*u[6]-u[7] “KJ”

Q_78=m*u[7]-u[8] “KJ”

Q_18=m*u[8]-u[1] “KJ”

 

“condenser heat duty”

Q_con=(h[4]-h[5])/m “W”

 

“Boiler Heat duty”

Q_boiler=(h[8]-h[1])/m “W”

 

“Turbine produced power”

W_turbine=(h[2]-h[1])/(m*n_T) “W”

 

“Pump consumed power”

W_pump=(h[5]-h[7])/(m*n_P) “W”

 

“Thermal efficiency of cycle”

n_th=W_ideal/Q_boiler

 

“Rate of entropy generation in turbine”

S_gen=(Q_18/m)/T_b+(s[2]-s[1]) “W/K”

 

 

“Rate of entropy generation in regenerative heat exchanger”

S_regen=(Q_18/m)/T_b+(s[8]-s[7]) “W/K”

 

 

 

EES Results

 

 

Results

 

 

[1]Leverone, F., Cervone, A., Pini, M., & Gill, E. (2020, March). Design of a Solar Thermal Propulsion and Power System for Mini-satellite Lunar Orbit Insertion. In 2020 IEEE Aerospace Conference (pp. 1-17). IEEE.