User Manual for the Sizing Model

Welcome to the fluid loop sizing model!

- The model can be used in two different modes: o Manual mode (1)

o Optimization mode (2)

- There is also an auxiliary function for formulating requirements based on the disturbance environment of the satellite. This is not explained as this is self-explanatory.

- The model has some important limitations (3).

- The model has been verified by tests with a fluid loop prototype.

- This manual refers to the Excel worksheet “Fluid Loop Sizing Model.xml”.

1. Manual Mode

The Manual Mode gives the fluid loop‟s performance parameters based on manually specified design parameters. It can be used to:

- Manually and iteratively size a fluid loop and compare its performance to the given requirements.

- Tweak the design after the Solver (2) has found optimized results.

1.1 Instructions

1. [Optional] Fill in the REQUIREMENTS fields, to compare the fluid loop to the required specifications. This can be based on:

a. Customer requirements; b. Reaction wheel specifications;

c. Other specifications that need to be matched.

2. Fill in the FLUID LOOP DESIGN PARAMETERS fields.

a. For unknown values, there are suggested values in the respective cell comments. b. For most missions, a square loop shape is advised, because it fits best along the

outer edges of the satellite bus. A corner radius of at least 3 times the channel diameter is advised, in order to prevent friction losses associated with sharp elbows. This can be automated by entering in cell J34 “=3*J31”.

c. The loop diameter should be chosen as large as possible, so that the angular momentum and torque are maximized.

d. The “Assumptions” fields do not have to be changed often. Each cell has a comment with some suggested typical values.

i. The “Maximum pump flow rate acceleration” determines the torque capability of the fluid loop. Unfortunately, pumps are only rated for flow rate rather than acceleration. Some reverse-calculated values can be used here. However, since fluid loops generally have a high torque capability it can be assumed that a fluid loop sized for a certain angular momentum will also fulfil the torque requirements. Based on previous research, centrifugal pumps may not fulfil the torque requirements [26], whereas MHD [91] and gear pumps (Section 5.3.2; or other positive displacement pumps) do have a high acceleration/torque capability, so most likely will. ii. The channel wall thickness and material density are used to calculate the

total mass of the actuator. This can be tweaked according to the expected channel properties. Suggested values are 0.5 – 1 mm thick Aluminium (2700 kg/m³) or plastic (1100 kg/m³).

iii. The channel surface roughness can remain on smooth (0.0015 mm) for standard plastic tubing. It marginally influences viscous friction losses in turbulent flow.

3. Assess the resulting FLUID LOOP PERFORMANCE PARAMETERS.

a. If unrealistic values turn up, check the design parameters for correctness.

2. Optimization Mode

The Optimization Mode finds optimal FLUID LOOP DESIGN PARAMETERS based on given REQUIREMENTS and constraints. This mode uses the Solver function in Excel. It can be used to:

- Optimize the mass, angular momentum or power consumption of a fluid loop, while matching the customer requirements

2.1 Setting up the Solver

1. Install Solver: File > Options > Add-ins > Manage > Excel Add-ins > Go > OK 2. Open Solver: Data tab > Analysis > Solver.

3. Set Objective Cell to be optimized.

a. Maximize (e.g. angular momentum of fluid loop)

b. Minimize (e.g. mass or power consumption of fluid loop)

4. Set Variables. Select the cells that should be changed by the Solver until it arrives at the optimal solution. Typically, the variables are:

a. Loop diameter b. Channel diameter c. Number of coils d. Pump flow rate

5. Set constraints by clicking “Add”. Constraints set the boundaries between which the Solver will allow solutions. This ensures that requirements are met and values remain realistic. The constraints below are used for optimizing mass, while matching the angular momentum requirement, within the power budget. Slightly different constraints should be used for other optimization modes!

a. Add constraints so that the customer requirements are met.

i. Fluid loop angular momentum should match the required angular momentum (X6 = J6).

ii. Fluid loop power consumption should be smaller than the power budget (X10 >= J10). The smallest calculated power is used here, because the tests found that these are the most accurate (except for sharp elbows, in which case the maximum value should be used).

iii. Fluid loop outside dimension should be equal to the Maximum outside dimension (X16 = I16). Using a “<=” instead of a “=” is technically correct, but should not be done because this results in the Solver giving a near-zero loop diameter with thousands of coils (because this optimizes the mass).

b. Add constraints so that the values remain realistic.

i. Number of coils should be a whole number (J25 = int). ii. Number of coils should be larger than 1 (J25 >= 1). iii. Loop diameter should be larger than 0 (J30 >= BM4). iv. Channel diameter should be larger than 0 (J30 >= BM4).

v. Pump flow rate should be larger than 0 (J30 >= BM4).

vi. The corner radius should be smaller than half the loop diameter (J34 <= J16/2)

c. Add constraints between which values the solver can attempt solutions.

i. The Pressure drop Δp(min) should not exceed the Maximum pump pressure (X31 <= J42)

ii. The Pump flow rate should be not exceed the Maximum pump flow rate (J38 <= J41)

2.2 Instructions

6. Fill in the REQUIREMENTS fields with, for instance: a. Customer requirements;

b. Reaction wheel specifications;

c. Other specifications that need to be matched. 7. Set a loop shape.

a. For most missions, a square loop shape is advised, because it fits best along the outer edges of the satellite bus. If it is square, a corner radius of at least 3 times the channel diameter is advised, in order to prevent friction losses associated with sharp elbows. This can be automated by entering in cell J34 “=3*J31”.

8. Set the Channel shape to “circular”.

a. The “rectangular” channel option can only be used in Manual mode. 9. Set fluid properties (values in the cell comments).

10. Set the pump properties (suggested values in the cell comments).

a. The Maximum pump flow rate and Maximum pump pressure serve as constraints, so are useful to fill in. If this is not done, it is possible that the Solver suggests very high flow rates or pressures that no spacecraft-sized pump can match.

11. Set the Channel wall material and Channel wall thickness.

a. These values can be tweaked after solving to optimize the mass further.

12. Open Solver.

13. After setting all boundary conditions (step 1–5 and 6–11), click Solve. 14. Assess whether the results are realistic.

a. If negative values are given, enter a positive value and try solving again.

b. Sometimes, Solver gives an error message. This can be the result of too stringent requirements or constraints. Adjust accordingly.

15. If satisfied with the results, copy the desired parameters into a table. Register parameters that are interesting or necessary to recreate the configuration, such as:

a. Type of fluid

b. Loop and channel diameter; number of coils

c. Angular momentum, mass, power consumption (and used efficiency) d. Flow rate, pressure drop

16. Repeat this process for different fluids, pumps, dimensional constraints, etc. Register results.

17. Compare the results of all configurations to one another. 18. Pick the best one for further design or analysis.

3. Limitations

1. The calculation of the fluid loop torque is based on an assumed flow rate acceleration, obtained from reverse-calculated reported values of MHD-pumped fluid loops. This means that the model is not very useful for torque sizing. However, based on reported results, the torque of (MHD-pumped) fluid loops is expected to be much higher than a reaction wheel with a similar angular momentum. Gear pumps too appear to have a high torque capability. Centrifugal pumps less so. This means that a fluid loop sized for angular momentum will most likely also fulfil the torque requirement (except for centrifugal pumps, which should be assessed separately).

2. The electrical power consumption of the fluid loop is based on an assumed overall pump efficiency. The suggested efficiency values are based on typical values of mechanical pumps, reverse-calculated values from existing and simulated MHD pumps. Although the suggested values are quite accurate, the real values vary widely with pump and system parameters. More accurate results can be obtained by characterizing individual pumps. The power component that is needed to push the liquid through the channel (hydraulic power consumption) does remain correct, because it only depends on flow rate and pressure drop.

3. The orbital disturbance environment calculation is based on many assumptions and simplifications. It can therefore only give rough order-of-magnitude requirements. The results resemble real mission values most accurately for 10 - 200 kg satellites.

4. The orbital disturbance environment requirement calculation only works for LEO satellites.