Constraints and Strength Calculations - Interactive Optimization Programs for Initial Propeller

It is ideal to get the maximum output from the engine, without over-extending the engines

capabilities. Therefore, two sets of constraints are constructed, two for each the engine and

thrust capabilities. The first constraint verifies that the engine output is within the engine’s

physical capacity and not over. The second engine constraint is set-up to get the engine output

to within 100% of the engines maximum capabilities. The second set of constraints is used to

verify that the thrust is “as expected” from initial design specifications. The first constraint

verifies that the thrust is positive and the second performs the same analysis as the second

engine constraint.

Along with the thrust and engine constraints, the strength of the propeller must be taken into

account. This is done by looking at each section of the blade as a hydrofoil, as shown in Figure

4.4. In order to calculate the strength of the propeller blade, the propeller type and material is

Figure 4.4:

Radial Blade Section

needed.

MTPROPOPT.py

gives the user two options for blade type along with a few common

blade materials. The blade material is needed to specify a yield stress for the propeller in order

to compare to the calculated blade stress. If the blade’s calculated stress is larger than the yield

stress, the propeller fails. The stress of a propeller is calculated for each radial section with

|σmax|=

M

Chapter 4. Combined Annular Momentum Theory and Blade Element Theory

in whichσmax

is the maximum bending stress,M

is the hydrofoil’s moment, and

SMmin

is the

minimum section modulus. The minimum section modulus is calculated

SMmin

=

I

y

(4.30)

where

I

is the moment of inertia and

y

is the vertical distance from the bending axis to the

centroid of the cross section. These values are calculated uses a program written by Dr. Lothar

Birk calledplasi.py. For a closed figure, as shown in Figure4.4; the area, centroid, and moment

of inertia are calculated. This program is seen in Appendix

B. The hydrofoils moment was

calculated uses beam theory. The propeller’s radial thrust distribution acted as a distributed

load across the propeller, similar to a distributed load on a cantilevered beam.

However, in order to use theplasi.py, the propeller type must be determined.

MTPROPOPT.py

is set-up to calculate the stress for B-series propellers and user defined propellers. For a user

defined propeller, some background information is needed to run the optimization. NACA

propellers were used for tests in this thesis. Abbott and Doenhoff [3] gave all NACA propeller

geometries, as seen in TableA.3.

The GUI written for this analysis,

MTPROPOPT.py, and the results of the optimization are

discussed in Chapter5.

Chapter 5

Results

5.1 Wageningen B-series Optimization

The B-series optimization is coded into a graphic user interface (GUI) calledWageningenOpt.py.

The program’s code is written in wxPython and displayed in AppendixB.2. As shown in Figure

A.1,

WageningenOpt.py

is a GUI, similar to any windows based application. The program

is created with 15 user inputs, 4 user buttons, and a list box of desired optimization tasks.

WageningenOpt.py

runs an optimization with four steps

:

1. Select the desired optimization design task and insert the design inputs into the provided

spaces

2. With the desired task selected and all input values entered, select theSAVEbutton to save

a

.txt

file. The program reads from this file for all calculations within the optimization.

3. After the file is saved, select theRUNbutton which will initiate the optimization.

4. When the optimization is completed, select theView Results

button and the optimum

values will be displayed.

The results for propeller optimization using the B-series have been published in past referenced

works [18,19]. The documentation in these reports select the optimum propeller for a constant

Chapter 5. Results

expanded area ratio (EAR). Also, corrections for the effects of Reynolds number (Re) were

not incorporated.

WageningenOpt.py

verified these results by limiting the

EAR’s maximum

and minimum values to a small tolerance around the designed constant

EAR

and removing

the corrections for

Re. For each task explained in Section

3.3, a propeller with 5 blades and

an

EAR

of 0.65 was used. All other input values are identical to those used in [18,

19]. The

results are displayed in Table

5.1. It can be seen that the values of

WageningenOpt.py

are

Table 5.1:

Results from Constant

EAROptimization

Design Task 1

U niversity of M ichagan

W ageningenOpt.py

η

0.69 J

0.88

0.90 P D

1.20 CT /J

0.278

0.270 Design Task 2

η

0.69

0.695 J

0.88

0.90 P D

1.20

1.18 CT /J

0.0641

0.0623

Design Task 3

η

0.70

0.698 J

0.85

0.878 P D

1.10

1.12 CT /J

0.3611

0.3533

Design Task 4

η

0.70 J

0.85

0.881 P D

1.10

1.11 CT /J

₀_.₀₈₂₂

₀_.₀₈₁₅

very close to the calculated reference values. One reason for the small difference could come

from the fact that even thought the

EAR

is constrained in

WageningenOpt.py, it still is not

true a constant 0.65. Also,WageningenOpt.py

uses a regression equation to calculate kinematic

viscosity and density based on water temperature. The values in the reference material [18,19]

used a standard kinematic viscosity and density, which would cause a small difference in the

final values.

Along with the verification of propeller selection for a constantEAR, the program was checked

against another reference [20] which used a constrainedEARfor an optimal propeller selection.

Radoj˘ci´c [20] used a Sequential Unconstrained Minimization Technique (SUMT) optimization

Chapter 5. Results

algorithm, very similar to the Nelder-Mead (NM) optimization algorithm used for this thesis.

Again, corrections for

Re

were not taken into account. The results from both studies were

similar, as shown in Table5.2. The NM method was able to find higher efficiencies.

Table 5.2:

Results from SUMT vs NM Optimization

Design Task 1

U niversity of Southampton

W ageningenOpt.py

η

0.6849

0.6922

J

0.8617

0.8974

P D

1.1805

1.1988

EAR

0.6398

0.6405

n[RP M]

78.141 75.0377

D[f t]

18.0 Design Task 2

η

0.6866

0.6948

J

0.8679

0.8993

P D

1.1852

1.1824

EAR

0.6432

0.6486

n[RP M]

77.580

74.881 D[f t]

18.0 Design Task 3

η

0.6909

0.6988

J

0.8302

0.8777

P D

1.0882

1.1154

EAR

0.6792

0.6627

n[RP M]

77.000 D[f t]

18.960

17.936 Design Task 4

η

0.6915

0.6992

J

0.8316

0.8783

P D

1.0872

1.1123

EAR

0.6574

0.6633

n[RP M]

77.000 D[f t]

18.927

17.923

In document Interactive Optimization Programs for Initial Propeller Design (Page 41-45)