Fix bug in wave drag derivatives

[A-CGray]

Purpose

Wave drag is zero if the flight Mach number is below the critical Mach number. In this case, the partial derivatives should also be zero. However, the compute_partials method of the wave drag component simply does nothing to the partials arrays if M < Mcrit, leaving whatever values are already in the partial derivative arrays:

Wave Drag Compute Partials:
Mcrit=array([0.79169576])
M=array([0.77])
partials['CDw', 'CL']=array([[1.09376204e+09]])
partials['CDw', 'lengths_spanwise']=array([[-1.88346814e+08, -2.42085539e+08, -2.95707476e+08,
        -3.49292345e+08, -4.02879431e+08, -4.56485145e+08,
        -5.10114915e+08]])
partials['CDw', 'widths']=array([[2.03039031e+08, 2.62837681e+08, 3.23338326e+08, 3.84629052e+08,
        4.46753302e+08, 5.09729247e+08, 5.73562904e+08]])
partials['CDw', 'Mach_number']=array([[8.08674014e+09]])
partials['CDw', 'chords']=array([[-2929614.48597978, -5040768.89678295, -3420983.43417756,
        -1816297.48330755,  -202958.56134173,  1423657.05368816,
         3062503.08397319,  1942355.92887645]])
partials['CDw', 't_over_c']=array([[7.63448035e+08, 9.80843713e+08, 1.19704483e+09, 1.41292912e+09,
        1.62892546e+09, 1.84520841e+09, 2.06183049e+09]])

This PR fixes this issue by explicitly zeroing out the wave drag partial derivatives at the start of compute_partials.

I also made a few code quality improvements to remove some minor differences between code in compute and compute_partials that should be identical:

• Renamed mean_chords in compute and chords in compute_partials to panel_mid_chords
• Switched to using self.ka instead of a hardcoded 0.95 in compute_partials as is done in compute
• Pre compute the summed panel area in compute as is done in compute_partials

Expected time until merged

Type of change

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (non-backwards-compatible fix or feature)
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Documentation update
• Maintenance update
• Other (please describe)

Testing

Successfully converged optimisation that was previously failing. Also tested partial derivatives.

Before this change:

----------------------------------------------------------
Component: WaveDrag 'cruise.wing_perf.aero_funcs.wavedrag'
----------------------------------------------------------

+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| of '<variable>' | wrt '<variable>'   |   calc mag. |  check mag. |  a(cal-chk) |  r(cal-chk) | error desc         |
+=================+====================+=============+=============+=============+=============+====================+
| 'CDw'           | 'CL'               |  1.0938e+09 |  0.0000e+00 |  1.0938e+09 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| 'CDw'           | 'Mach_number'      |  8.0867e+09 |  0.0000e+00 |  8.0867e+09 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| 'CDw'           | 'chords'           |  8.0133e+06 |  0.0000e+00 |  8.0133e+06 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| 'CDw'           | 'lengths_spanwise' |  9.6666e+08 |  0.0000e+00 |  9.6666e+08 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| 'CDw'           | 't_over_c'         |  3.9094e+09 |  0.0000e+00 |  3.9094e+09 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+
| 'CDw'           | 'widths'           |  1.0729e+09 |  0.0000e+00 |  1.0729e+09 |  1.0000e+00 |  >ABS_TOL >REL_TOL |
+-----------------+--------------------+-------------+-------------+-------------+-------------+--------------------+

After this change:

+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| of '<variable>' | wrt '<variable>'   |   calc mag. |  check mag. |  a(cal-chk) | r(cal-chk) | error desc |
+=================+====================+=============+=============+=============+============+============+
| 'CDw'           | 'CL'               |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| 'CDw'           | 'Mach_number'      |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| 'CDw'           | 'chords'           |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| 'CDw'           | 'lengths_spanwise' |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| 'CDw'           | 't_over_c'         |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+
| 'CDw'           | 'widths'           |  0.0000e+00 |  0.0000e+00 |  0.0000e+00 |        nan |            |
+-----------------+--------------------+-------------+-------------+-------------+------------+------------+

If there is an existing test that checks our aero derivatives we should add a case for which M < Mcrit, I couldn't find any such tests though.

Checklist

• I have run flake8 and black to make sure the Python code adheres to PEP-8 and is consistently formatted
• I have formatted the Fortran code with fprettify or C/C++ code with clang-format as applicable
• I have run unit and regression tests which pass locally with my changes
• I have added new tests that prove my fix is effective or that my feature works
• I have added necessary documentation

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.95%. Comparing base (d788e11) to head (c1a3e2a).
Report is 6 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #432      +/-   ##
==========================================
+ Coverage   93.92%   93.95%   +0.02%     
==========================================
  Files         104      104              
  Lines        6472     6468       -4     
==========================================
- Hits         6079     6077       -2     
+ Misses        393      391       -2     

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[eytanadler]

Good catch! Could you add a test that breaks before these changes and succeeds with them? Then it's good to go from me.

[A-CGray]

Good catch! Could you add a test that breaks before these changes and succeeds with them? Then it's good to go from me.

I was initially going to test this fix by enabling wave drag in the scaneagle test (which has a super low Mach number) and then adding a check_totals test. However, the totals there were fine. I kept the new totals derivatives test in there though as I think it's a good addition.

I'm assuming the reason the scaneagle test didn't catch the bug is that the values in the partials arrays that get passed in to compute_partials contain the partials from the last time the method was called, so to trigger this bug you need an case that starts off with M > Mcrit but has an optimum where M < Mcrit. Presumably this is why nobody has run into this bug before.

I managed to engineer a case like this by reducing the Mach number in test_aerostruct_wingbox_wave_fuel_vol_constraint_opt.py from 0.85 to 0.77 and increasing the initial t_over_c values. This ensures that the initial design has wave drag and that the optimum is wave drag free.