Flow stability and transition over finite compliant panels 6

6.1 Concluding remarks The concluding remarks based on the investigations carried out in the previous chapters of this thesis are as follows: a This study started with over the rigid w

Chapter 6 Concluding remarks and recommendations

Various investigations on wavepackets evolution and subsequent breakdown

into incipient turbulent spots for over finite compliant panels in a Blasius boundary layer have been carried out in this thesis work via a direct numerical simulation (DNS) approach The main findings of the investigations described in the previous chapters and recommendations for future works are summarized below

6.1 Concluding remarks

The concluding remarks based on the investigations carried out in the previous chapters of this thesis are as follows:

(a) This study started with over the rigid wall (RW) case simulation with higher number of grid points than before, and this served as a reference case to compare simulation results for over the CP(s) cases in order to appreciate the roles of CP in transition delay RW results (from both spatial and spectral analyses) by way of validation are consistent with the results already published by Yeo et al (2010) (b) Single compliant panel (CP) case simulations were carried out and compared with over the RW case in chapter 3 Simulations were performed directly without any interpolation (as done previously by Zhao (2006)) process in between, as errors due to interpolation are completely avoided With the single CP case, transition distance was delayed farther by ≈ 49% when compared with the RW case with respect to the perturbation source location X = 349.4 Also, the initial

linearization assumption for coupled interaction was rightly justified, as the maximum displacement of CP surface recorded is sufficiently small, which is about 0.24% of the local displacement thickness

In addition, wavepacket amplitude growth curve showed the 2D wave modes being suppressed from growing further by its interaction with the inserted single

CP, thereby impossible for the 3D wave modes to have a base for rapid growth until the later stage Spectral properties of dominant 2D and 3D wave modes frequency ratio ⁄ for both the RW and single CP cases achieve the value near to 0.5, as predicted by resonance triad wavenumber condition (3.10) The propagation angles for both the cases also approached value of 60o when the wavepackets were already in the late-to-post subharmonic stages For the linear simulation part, linear CP wavepacket maintains relatively distinct 2D and 3D wave modes after it had passed beyond the CP Whereas for RW case, the wavepacket was dominated by the 2D wave modes

(c) With transition delay already obtained in chapter 3 with the single CP, we were motivated further to consider two and three compliant panels in chapter 4 to know if better transition delay could be obtained Two types of investigations were carried out namely: (i) Over two-CP arrangement and (ii) Over three-CP arrangement With the two-CP case, transition delay was farther increased by almost 89%, as compared to the RW case wavepacket breakdown location Wavepacket became oblique in shapes as they evolved over the second CP region, and what is responsible for this phenomenon remain unknown at the moment The amplitude growth curve also shows the second CP to suppress the 2D wave modes

farther and that account for the better transition delay than the single CP case Extractions of spectral properties of the dominant 2D and 3D wave modes show that subharmonic resonant wave condition (3.10) is not closely fulfilled over the second CP as both frequency and wavenumber ratios are bit far away from the value of 0.5, as triads of wave’s locations are difficult to discern in the corresponding spectral plots Later, our investigation was extended to over the three-CP case and the aim is to know if much better transition delay could be obtained than the 89% delay already obtained with two-CP case Three different

CP arrangements were first attempted but all these resulted into no or little improvements in transition delay when compared with over the two-CP case result

Later, we considered reducing the separation gap ∆X between CPs and this appears to work well after trying with different ∆Xs With ∆X = 300 between CPs, transition delay improved much better than before to almost 112% increase when compared to the rigid wall case From the amplitude growth curve, first and second CPs kept suppressing the 2D wave modes from growing further However, interaction of wavepacket with the third CP behaved contrary as 2D wave mode amplitudes rather increased sharply as the wavepacket was evolving over the third

CP This may be due to third CP tending rigid (Yeo (1992)) behaviour as highly oblique waves travelling over it Also, none of the spectral properties plots agree with the resonance triad wavenumber condition (3.10) and the reasons behind this need further investigations

(d) In chapter 5, a more systematic approach to selection of properties for finite compliant panel was attempted Chapters 3 and 4 established that finite compliant panels with suitably tailored properties are able to delay the breakdown of wavepacket into incipient turbulent spot(s), which were based on properties selected by Zhao (2006) in her study Safety factors “C and D” were reduced from their initial values of 3.16 and 1.32 respectively with the aim to further tune the

CP properties for a better transition delay than in chapters 3 and 4 Six different compliant panel property cases were investigated and compared with results for the single CP case in chapter 3, and in chapter 4 for over the two-panel case which were dubbed the “reference case” All simulation cases were performed with high number of grid points and allowed to reach the break down stages in order to obtain a comprehensive and overall insights about wavepacket behaviours and dynamics

For over the single CP investigations, cases 1, 2, 4 and 5 broke down earlier than the reference case which broke down at the location X ≈ 1930, but on the other hand, cases 3 and 6 produced better transition delays than the reference case Case 3 wavepacket broke down into incipient turbulent spot at X ≈ 1980, and this translates into almost 3.2% transition delay further if compared with the reference case with respect to the perturbation source location X0 = 349.4 While for case 6 which is characterized with a very low damping, incipient turbulent spot occurred around when X ≈ 2050 and this translates to about ≈ 7.6% further transition delay when compared with the reference case

For over the two-CP case where simulation conditions and configurations remained the same as in chapter 4, case 5 with a damping value half of those cases before it was finally considered best after many trials At the end, case 5 wavepacket finally broke down into more diffused turbulent spots at X ≈ 2600 If compared with the reference case (section 4.1) that broke down at X ≈ 2350, this translates to an almost 12.5% transition delay with respect to perturbation source location X0 = 349.4 Spectral analyses results show case 5 wavepacket to be mainly dominated by the 2D wave modes, especially when the wavepacket was evolving far away from the second CP location Whereas, the reference case in section 4.1 still reveal 3D wave modes that were characterized with very low frequencies

6.2 Recommendations for future works

During the course of carrying out the research works reported in this thesis, more interesting research ideas worthy of further study continued to surface but those could not be investigated due to time constraints In view of this, the following are recommended as possible future works:

(1) A more systematic study on optimizing transition delay with finite compliant panels could be carried out later, as only few studies could be done at the moment due to time constraints Potential areas to study include investigating various CP lengths, inter-panel separation and their overall effects on transition delays Also, wider range of CP properties study could be carried out as what we have done in chapter 5 is not comprehensive enough

(2) All the research investigations reported in this thesis employed fixed perturbation amplitude; therefore, amplitude variation study with finite CPs length could as well be investigated later

(3) Instead of a perturbation point source used in our investigations, a continuous white noise source (a random signal up to a certain magnitude) could be considered also This is to know if the CP(s) abilities in delaying transition farther

as obtained in this thesis could still be preserved if a continuous white noise source is used instead

(4) Another interesting area that could be investigated in the future is anisotropic study This thesis work mainly concerns isotropic study, that is, CP tensions were kept equal (TX = TZ) in both the streamwise and spanwise directions respectively, therefore, anisotropic study is when TX ≠ TZ and to find out if transition delay could be much better than the isotropic case