Steady-State VS Transient Propeller Numerical Simulation Comparison

     This post is about the comparison between steady-state and transient computational fluid dynamics analysis of two different propellers. The propellers under investigation are 11x7 and 11x4.7 propellers. The first number in the propeller nomenclature is the propeller diameter and the second number represents the propeller pitch, both parameters are in inch. The transient analysis was carried out using the sliding mesh technique while the steady-state results were obtained by the local rotating region-averaging method. For details about 11x7 propeller click here, for the details about 11x4.7 propeller, click here.

 

     As expected, the propeller efficiencies of transient and steady-state analysis are within 0.9% of each other, as shown in Fig. 1-2. Therefore, it is advised to simulate propellers and horizontal axis wind turbines using the steady-state technique as long as no time-dependent boundary conditions are employed.

 

Fig. 1, Propeller efficiency plot.

  

 Fig. 2, Propeller efficiency plot.

 

     It can be seen from Fig. 3-4 that time taken by the steady-state simulation to converge is on average 42.37% less that the transient analysis.  The steady-state analysis takes considerably less time to give a solution then a transient analysis.

 

Fig. 3, Solution time.

 

Fig. 4, Solution time.

 

Thank you for reading. If you would like to collaborate on research projects, please reach out.

SolidWorks Flow Simulation Premium: Propeller/Horizontal Axis Wind Turbine CFD Tutorial

The tutorial is in the attached video. Analysis such as: 11x7 Aeronautic Propeller Characteristics, 11x4.7 Aeronautic Propeller Characteristics and Wind Turbine SolidWorks Flow Simulation Premium Computational Fluid Dynamics are setup using the same method.

11x7 Aeronautic Propeller Characteristics (Using CFD) (Verified and Validated) (Update 02)

     This post presents the results from an aeronautic propeller CFD analysis.

    
     An 11x7 propeller was modelled using SolidWorks CAD package using the geometry from [1]. The simulations were run at two different rotational velocities and each rotational velocity was simulated at three advance ratios. The mesh for the 3,000 RPM rotational velocity had 213,205 total cells among which 24,048 cells were at the solid fluid boundary. While, the mesh for the 5,000 RPM rotational velocity had 369,963 total cells among which 68,594 cells were at the solid fluid boundary. A mesh control was employed to refine the mesh near the propeller geometry and at the boundary of the rotating region and the stationery domain for all of the cases simulated. This was done to ensure accuracy of the results was within an acceptable range. The results of the numerical simulations are plotted along with the experimental results [1] in Fig. 1.

Fig. 1 J= Advance Ratio, η_prop = propeller efficiency

     It can be seen from Fig. 1 that the trends for the propeller efficiency are in agreement with the experimental results. To increase the mesh density for the mesh independence test, the number of cells in  each of the respective co-ordinate directions was increased by a factor of 1.1. The mesh is shown in the Fig. 2.

Fig. 2 The computational mesh around the propeller.

     The computational domain size was at 2D x 2D x 2.4D, D being the propeller diameter, as shown in Fig. 3. In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity.

 Fig. 3 The computational domain.

Fig. 4 The pressure distribution and the velocity vectors around the propeller.

     The CAD model files and the simulation setup files for the numerical analysis are available here.

     Thank you for reading. If you'd like to collaborate on research projects, please reach out.

[1] Brandt, J. B., & Selig, M. S., “Propeller Performance Data at Low Reynolds Numbers,” 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-1255, Orlando, FL, 2011.

doi.org/10.2514/6.2011-1255

 

Update 01

     Results from the mesh independent study are now available.

Update 02

     CAD model files are now uploaded. The CFD simulation setup files are also included.

11x4.7 Aeronautic Propeller Characteristics (Using CFD) (Verified and Validated) (Update 02)

     This post presents the results from an aeronautic propeller CFD analysis.

     An 11x4.7 propeller was modelled using SolidWorks CAD package using the geometry from [1]. The simulations were run at two different rotational velocities and each rotational velocity was simulated at three advance ratios. The mesh for the 3,000 RPM rotational velocity had 206,184 total cells among which 22,103 cells were at the solid fluid boundary. While, the mesh for the 6,000 RPM rotational velocity had 357,300 total cells among which 64,012 cells were at the solid fluid boundary. A mesh control was employed to refine the mesh near the propeller geometry and at the boundary of the rotating region and the stationery domain for all of the cases simulated. This was done to ensure accuracy of the results was within an acceptable range. The results of the numerical simulations are plotted along with the experimental results [1] in Fig. 1.

Fig. 1 J= Advance Ratio, η_prop = propeller efficiency

 

     It can be seen from Fig. 1 that the trends for the propeller efficiency are in agreement with the experimental results. The fine mesh had the number of cells in each of the respective co-ordinate directions increased by a factor of 1.1. The mesh is shown in the Fig. 2.

 

Fig. 2 The computational mesh around the propeller.

 

     The computational domain size was at 2D x 2D x 2.4D, D being the propeller diameter, as shown in Fig. 3. In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity.

Fig. 3 The computational domain.

Fig. 4 The pressure distribution and the velocity vectors around the propeller.

     The CAD model and numerical simulation setup files are available here.

 

     Thank you for reading. If you'd like to collaborate on research projects, please reach out.

     [1] Brandt, J. B., & Selig, M. S., “Propeller Performance Data at Low Reynolds Numbers,” 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-1255, Orlando, FL, 2011.

doi.org/10.2514/6.2011-1255

 

Update 01

     Mesh independent test results are now available.

 

Update 02

     CAD files for the propeller including the CFD analysis setup are now available.

Marine Propeller Characteristics (Using CFD) (Verified and Validated)

     This post presents the results from a marine propeller CFD analysis. The key thing about this CFD analysis was that the propeller efficiency obtained was within 7% of the experimental results, by using only 112,081 total cells in the computational mesh, of these cells, 21,915 cells were at the solid fluid boundary. The results are, indeed, mesh independent. The software employed was Flow Simulation Premium. The results of the numerical simulations are plotted along with the experimental results in Fig. 1.

Fig. 1 K_T = coefficient of thrust, 10K_Q = coefficient of torque multiplied by a factor of 10, η_prop = propeller efficiency

 

     It can be seen from Fig. 1 that the trends for the thrust and the torque coefficients and the propeller efficiency are in agreement with the experimental results. The experimental data was taken from here. The flow conditions were following. The propeller diameter was at 0.254 m. Propeller rotational velocity was at 15 rev/s. The propeller inclination angle was at 12°. Fluid considered was water. To change the advance ratio, fluid flow velocity was altered. The computational domain size was at 2D x 2D x 3.2D, D being the propeller diameter, as shown in Fig. 3. The mesh is shown in the Fig. 2.

Fig. 2 The computational mesh around the propeller.

 

Fig. 3 The computational domain.

 

     In Fig. 3, the curved teal arrow represents the direction of rotation of the sliding mesh. The blue arrow represents the direction of free stream velocity while the brown arrow represents the force of gravity. The Pressure distribution on the propeller blades and the velocity streamlines are shown in Fig. 4. The streamlines were drawn using line integral convolution, relative to the rotating frame of reference.

 

Fig. 4 The pressure distribution and the velocity profile around the propeller.

 

     If you'd like to collaborate on research projects, please reach out. Thank you for reading.

Bond Graph Representation of the Coaxial Contra-Rotating Propeller (with the Bond-Graph)

A contra rotating propeller, with five gears and seven shafts.

Se	Source of effort; voltage supplied by the power source; a Li-Po battery in this study.
Rw	Motor winding resistance.
Iw	Motor winding inductance.
GY	dc Motor; a Gyrator.
T	Gyrator Modulus.
bs1	Bearing resistance on shaft number one.
Js1	JS1=Js’1+Jg1+Jr.
Js1	Total inertia for shaft number one.
Js’1	Inertia of shaft number one.
Jg1	Inertia of gear number one.
Jr	Inertia for dc motor rotor.
Ks1	Stiffness of shaft number one.
Ms1	Ms1=Ms’1+Mm+Mg1.
Ms1	Total mass for the shaft number one.
Ms’1	Mass for the shaft number one.
Mm	Mass for the dc motor.
Mg1	Mass for the gear number one.
m1	Distance from the center of mass of the Ms1 to the shaft number one; moment arm to transform the torque in to force to be applied to the Ms1.
TF	Transformer, mechanical transformer in this study, spur gear mesh.
Rs12	Transformer Modulus, transmission ratio between shaft number one and two.
bs2	Bearing resistance on shaft number two.
Js2	JS2=Js’2+ Jg2+Jg6.
Js2	Total inertia for shaft number two.
Js’2	Inertia of shaft number two.
Jg2	Inertia of gear number two.
Jg6	Inertia of gear number six.
Ks2	Stiffness of shaft number two.
Ms2	Ms2=Ms’2+Mg6+Mg2.
Ms2	Total mass for the shaft number two.
Ms’2	Mass for the shaft number two.
Mg6	Mass for the gear number six.
Mg2	Mass for the gear number two.
m2	Distance from the center of mass of the Ms2 to the shaft number two; moment arm to transform the torque in to force to be applied to the Ms2.
Rs23	Transformer Modulus, transmission ratio between shaft number two and three.
bs3	Bearing resistance on shaft number three.
Js3	JS3=Js’3+ Jg3+Jg4.
Js3	Total inertia for shaft number three.
Js’3	Inertia of shaft number three.
Jg3	Inertia of gear number three.
Jg4	Inertia of gear number four.
Ks3	Stiffness of shaft number three.
Ms3	Ms2=Ms’2+Mg3+Mg4.
Ms3	Total mass for the shaft number one.
Ms’3	Mass for the shaft number three.
Mg3	Mass for the gear number three.
Mg4	Mass for the gear number four.
m3	Distance from the center of mass of the Ms3 to the shaft number three; moment arm to transform the torque in to force to be applied to the Ms3.
Rs34	Transformer Modulus, transmission ratio between shaft number three and four.
bs4	Bearing resistance on shaft number four.
Js4	JS4=Js’4+ Jg5+Jp1.
Js4	Total inertia for shaft number four.
Js’4	Inertia of shaft number four.
Jg5	Inertia of gear number five.
Jp1	Inertia of propeller number one.
Ks4	Stiffness of shaft number three
Ms4	Ms4=Ms’4+Mg5+Mp1.
Ms4	Total mass for the shaft number four.
Ms’4	Mass for the shaft number four.
Mg5	Mass for the gear number five.
Mp1	Mass for the propeller number one.
m4	Distance from the center of mass of the Ms4 to the shaft number four; moment arm to transform the torque in to force to be applied to the Ms4.
Rs25	Transformer Modulus, transmission ratio between shaft number two and five.
bs5	Bearing resistance on shaft number five.
Js5	JS5=Js’5+ Jg7+Jp2.
Js5	Total inertia for shaft number five.
Js’5	Inertia of shaft number five.
Jg7	Inertia of gear number seven.
Jp2	Inertia of propeller number two.
Ks5	Stiffness of shaft number five.
Ms5	Ms4=Ms’5+Mg5+Mp2.
Ms5	Total mass for the shaft number four.
Ms’5	Mass for the shaft number five.
Mg7	Mass for the gear number seven.
Mp2	Mass for the propeller number two.
m5	Distance from the center of mass of the Ms5 to the shaft number five; moment arm to transform the torque in to force to be applied to the Ms5.
RPS	RPS=KT1/(KQ1*D1)
RPS	Transformer Modulus, for propeller number one.
KT1	Coefficient of thrust for propeller number one.
KQ1	Coefficient of torque for propeller number one.
D1	Diameter for propeller number one.
KT1	KT1=Tp1/(Rho*n12*D14)
KQ1	KQ1=Qp1/(Rho*n12*D15)
Tp1	Thrust from propeller number one.
n1	Speed for propeller number one, in rev/s.
Qp1	Torque required to rotate propeller number one.
P1	Propeller number one, mounted on the shaft number four.
RPH	RPH=KT2/(KQ2*D2)
RPH	Transformer Modulus, for propeller number 2.
KT2	Coefficient of thrust for propeller number two.
KQ2	Coefficient of torque for propeller number two.
D2	Diameter for propeller number two.
KT2	KT=Tp2/(Rho*n22*D24)
KQ2	KQ=Qp2/(Rho*n22*D25)
Tp2	Thrust from propeller number two.
Rho	Density of the fluid, air in this study.
n2	Speed for propeller number two, in rev/s.
Qp2	Torque required to rotate propeller number two.
P2	Propeller number two, mounted on the hollow shaft; only of the system, shaft number five.
mc1	Distance from the center of mass of the chassis to the shaft number one; moment arm to transform torque in to force to be applied to the chassis.
mc2	Distance from the center of mass of the chassis to the shaft number two; moment arm to transform torque in to force to be applied to the chassis.
mc3	Distance from the center of mass of the chassis to the shaft number three; moment arm to transform torque in to force to be applied to the chassis.
mc4	Distance from the center of mass of the chassis to the shaft number four; moment arm to transform torque in to force to be applied to the chassis.
mc5	Distance from the center of mass of the chassis to the shaft number five; moment arm to transform torque in to force to be applied to the chassis.
Mc	Mass of the chassis.