Validation Case: Drone Propeller Study

This validation case belongs to fluid dynamics. The aim of this test case is to validate the following parameters for a drone propeller:

Thrust and power coefficients.

The simulation results of SimScale were compared to UIUC wind tunnel measurements presented in [1].

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Geometry

The geometry used for this case can be seen below:

It is a two-blade propeller represented using its dimensions in inches. This APC 11×5.5E model is an 11-inch diameter propeller with a pitch of 5.5 inches/revolution used on small UAVs and model aircrafts.

Analysis Type and Mesh

Tool Type: OpenFOAM®

Analysis Type: Steady-state, incompressible analysis with MRF rotating zone, using the k-omega SST turbulence model.

Mesh and Element Types:

The Standard mesher algorithm with tetrahedral and hexahedral cells was used to generate the mesh. Multiple meshes with incrementally increasing refinement were generated in parallel using the automatic meshing functionality.

For each run, the thrust and power coefficients were calculated and plotted below:

mesh sensitivity study testing thrust and power coefficients of propeller — Figure 2: The thrust coefficient remains stable as the amount of cells gradually increases.

A mesh sensitivity analysis has been carried out monitoring the y+ maximum values while using full resolution wall treatment with the standard mesher:

Mesh Name	Element Type	Number of cells/nodes	Max y+
Mesh 1	3D Tetrahedral/Hexahedral	4.3M cells, 1.4M nodes	3.2
Mesh 2	3D Tetrahedral/Hexahedral	6.1M cells, 2.2M nodes	1.5
Mesh 3	3D Tetrahedral/Hexahedral	13.4M cells, 4.1M nodes	0.46

Table 1: The characteristics of the mesh sensitivity analysis with respect to the maximum y+ values for 6473 RPM, which is the highest input tested in this case.

mesh details around the propeller — Figure 3: Details of the mesh used for the validation study. With the mesh clip the user can zoom in and check the generated boundary layer, as well as the different refinement levels inside the domain.

Simulation Setup

Material:

Air
- $(\nu)$ Kinematic viscosity: 1.529 $e^5\ m^2/s$
- $(\rho)$ Density: 1.196 $kg/ m^3$

Boundary Conditions:

Inlet & outlet:
- Total gauge pressure of 0 $Pa$
- Turbulent kinetic energy with an inlet value of 3.75 $e^{-3}$ $m^2 \over\ s^2$
- Specific dissipation rate with an inlet value of 3.375 $1 \over\ s$
Slip walls on the rest of the domain faces to represent an open-air environment

Reference Solution

The UIUC$^1$ data uses the standard definitions for propeller aerodynamic coefficients:

Thrust coefficient:

$$C_T = \frac{T}{\rho \times\ n^2 \times\ D^4}$$

Power coefficient:

$$C_P = \frac{P}{\rho \times\ n^3 \times\ D^4}$$

Where:

$\rho$: the density of the fluid
$n$: revolutions per sec
$D$: the diameter of the propeller

Result Comparison

Comparison of the thrust and power coefficients obtained from SimScale against the experimental results obtained from [1] is given below:

coefficients of power and thrust comparison for propeller — Figure 4: The graph that involves the power and thrust coefficients reveals a good agreement between the SimScale and wind tunnel results.

The SimScale results appear to be on track with the wind tunnel measurements, and below the discrepancies are calculated for each run:

RPM	Thrust Coefficient Discrepancy [%]	Power Coefficient Discrepancy [%]
1868	0.4272	6.5879
4043	7.0814	4.6446
6473	10.6043	7.8704

Table 2: The discrepancy of the thrust and power coefficients for different RPM inputs increases when the rpm input used is also bigger.

In the following images, the results were analyzed in the post-processor. The streamlines tend to concentrate below the propeller, after being drawn by the propeller’s rotation: