Chapter Introduction Chapter Introduction 1.1 Background A boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. The boundary layer is characterized by an abrupt change in the transverse direction of velocity (a hydrodynamic boundary layer), temperature (a thermal boundary layer), or concentrations of individual chemical components (a diffusion boundary layer). The viscosity, thermal conductivity, and diffusivity of the fluid are the principal influences on the formation of the flow in a boundary layer. Within a dynamic boundary layer a smooth change in velocity occurs from the velocity of the external stream to zero at the wall as a result of the adhesion of the viscous fluid to the solid surface. Similarly, the temperature and concentration vary smoothly within a boundary layer. The boundary layer is a very critical region of a flow because what happens in that thin regime of flow could have far reaching effects on the global features or disposition of the flow. Boundary layer is known for its transition from smooth laminar state to chaotic, random turbulent state, which occurs where the local flow Reynolds number is sufficiently large. The nature of the boundary layer determines the lift and drag coefficients as well as the stalling and high speed of a wing. The transition of a boundary layer from laminar to turbulent state may occur by two routes namely: the fundamental transition and bypass transition. For the fundamental transition, this is initiated by the amplification of small perturbations. This is the classical Chapter Introduction route of transition, which normally involves the linear amplification of small amplitude two-dimensional Tollmien-Schlichting (TS) waves, the nonlinear wave growth stage, and the final breakdown stage, which leads to fully turbulent flow. Then for the bypass type of transition, the conventional TS waves may be bypassed by nonlinear wave interaction if the initial amplitude of the perturbations is high enough to overpower the initial linear wave development. One thing so common with this type of transition is that, the unsteady fluid flow for this kind of transition goes directly into the late nonlinear instability stage and is connected with direct breakdown by nonlinear wave interactions. Some of the research works already conducted in this area was highlighted inside the book of Schmidt and Henningson (2001). In a real situation, transition from laminar state to turbulent state is something unavoidable, as laminar state cannot be sustained for over a long period of time. From practical viewpoint, laminar boundary layer offers several important advantages over turbulent boundary layer and these include: (1) low skin friction drag, an aspect so important for energy efficiency in modern transportation systems and (ii) low flow noise. These have motivated a considerable lot of research into laminar-turbulent transition and how such transition could be delayed or if possible postponed indefinitely. Then, the need arose for previous researchers to see how transition from laminar state to turbulent state could be controlled or delayed to a certain extent, in order to achieve some favourable and meaningful benefits, such as drag reductions etc. For example, a laminar flow over the surface of a vehicle is often desired since the drag force on the vehicle is Chapter Introduction much lower than had the flow been turbulent. Ample amounts of fuel could be saved if we could control the characteristics of turbulence to reduce drag or even prevent its occurrence. Methods of controlling boundary layer transition are broadly grouped into two categories namely: active control and passive control. Active ways of boundary layer control includes, wall suction, wall cooling (for gases), wall heating (for liquids) and wave cancellation, etc. However, some of the demerits of active transitional control include: (1) sophisticated technical and theoretical supports are usually required for active manipulation of boundary layers to achieve transition control; (2) the technological demands are much higher than passive control means. On the other hand, passive control involves any of the following means: periodic roughness, inclined slots, compliant surfaces, etc. The merits of passive control method includes: (1) It does not require any sophisticated control equipment or feedback system, and (2) less expensive to implement as compared with an active control type. This thesis is concerned with a study of how compliant panels may be devised to delay transition in a Blasius boundary layer flow. 1.2 Boundary layer transitions, instabilities and breakdowns Reynolds (1883) was the pioneer to investigate laminar-turbulent transition problem, where his experiment was carried out in a pipe flow. About twenty one years later, Prandtl (1904) defined the all-important boundary layer through his famous published work. As a result of this Prandtl (1904)’s work, lots of research Chapter Introduction interests began to spring up in the investigations of the laminar-turbulent transition phenomenon within the boundary layers. Some years later, and based on the Orr-Sommerfeld equation, Tollmien (1929) and Schlichting (1933) theoretically computed the small two-dimensional waves in boundary layer these are thus referred to as the Tollmien-Schlichting (TS) waves. Unfortunately, these theoretically computed TS waves could not be verified experimentally at the first instance due to high levels of the free stream turbulence in the wind tunnels of that time. But later, Schubauer and Skramstad (1948) recorded a breakthrough in detecting the TS waves after the free stream turbulence intensity inside the wind tunnel was greatly reduced. Their results were in good agreement with the calculations of TS waves, after they initiated the disturbances by a harmonically oscillating ribbon which was placed on the flat plate. Later on, Emmons (1951) reported intermittent turbulent spots in his experiment of shallow running water. Researchers such as Herbert (1988), Grek et al. (1990), Bakchinov et al. (1995, 1998), Breuer and Haritonidis (1990), Fasel (2002), conducted both numerical simulations and experiments (where most of the studies were based on ribbonexcited harmonic waves) to examine the amplification of two-dimensional TS waves in laminar boundary layers, until their final breakdown into a turbulent flow. But, their results could not verify the important characteristics of naturally occurring boundary layer transition as their resultant transition could show neither the intermittency nor the formation of turbulent spots. Most of the experiments already conducted regarding transition in boundary layers were based on the periodic excited plane waves. These involve artificially introducing a two- Chapter Introduction dimensional (2D) and a three-dimensional (3D) monochromatic disturbance to simulate the initial TS waves. So far from the literature, two main types of wave development and breakdown have been identified and they are: (i) fundamental breakdown (also termed a Ktype breakdown after Klebanoff (1962) and (ii) subharmonic breakdown (which is also termed the C-type breakdown after Craik (1971) or H-type after Herbert (1988). For the fundamental breakdown, this type of transition starts with twodimensional (2D) waves with relatively large amplitude, which typically exceeds 1% of the free stream velocity. As the wave convects downstream, the periodic TS waves develop a three-dimensional configuration after achieving certain amplitude. The nonlinear three-dimensional structures have a frequency equal to that of the primary 2D TS waves and exhibit spanwise periodicity of alternating peaks and valleys, corresponding to the aligned Λ-shaped vortices and spikes. The spanwise wavelength of the aligned structure is about one-half of the streamwise value. Breakdown follows within one wavelength of the spikes. The second type, which is subharmonic breakdown, is the more general type of transition. This kind of breakdown begins with a small initial 2D TS wave, which are typically less than 0.3% of the free stream velocity. With downstream propagation, the growing 2D TS wave evolves nonlinearly into a pattern of staggered Λ-shaped vortices instead. The 3D wave structures grow rapidly to form localized high-shear layers at the peaks. This is then followed by strong localised instability and breakdown into irregular motion. The breakdown is termed subharmonic because the staggered wave structures have a frequency Chapter Introduction close to half the frequency of the primary 2D TS wave. For the C-type breakdown, the spanwise wavelength of the staggered 3D structures is about 1.5 times that of its streamwise wavelength. Craik proposed a theory of wave triad resonance to explain the appearance of the subharmonic 3D structures. H-type breakdown (Herbert (1984)) has a relatively shorter spanwise wavelength that is about 0.7 times that of the streamwise one. Herbert analysed the appearance of the subharmonic wave modes based on a more generalized model of secondary instability. 1.3 Fluid-structure system instabilities and classifications Different kinds of fluid-structure interactions exist whenever a fluid flows over a surface that is capable of interacting with the flow itself. As expected, instability modes multiply rapidly when two wave-bearing media are coupled. Some of these waves could be flow-based (associated with modes that originally exist in the flow), wall-based or combination of both kind of waves as shown in figure 1.1. Some of the volume and surface based models of compliant coatings already used in the past are shown in figure 1.2. The most attractive feature about compliant coatings is their possibility to hinder or promote the dynamical instabilities that characterize both the transitional and turbulent boundary layer flows. Based on Landahl’s (1962) and Benjamin’s (1963) original classification schemes, all the waves arising from the interaction of the flow and the compliant surface can be classified into three categories namely A, B and C depending on the energy needed to activate or excite the disturbance. Chapter Introduction The Class A waves for which the TS wave is an example is characterized by negative activation energy. The class B instability waves for which the traveling wave flutter instability is an example requires positive activation energy for their excitation and growth. For the Class C instability (KH instability for instance) the activation energy is nearly zero. According to Gad-el-Hak (2002), both class A and class B disturbances are essentially oscillations involving conservative energy exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes such as dissipation in the coating or energy transfer to the solid by non-conservative hydrodynamic forces. Class A oscillations are TS type waves in the boundary layer modified by the wall compliance, or to simply say by the motion of the solid in response to the pressure and shear-stress fluctuations in the flow. Another feature is that, the disturbance eigenfunction for class A waves has its maximum amplitude within the fluid region. Such waves are normally stabilized by the irreversible energy transfer from the fluid to the coating, however destabilized by diffusion in the wall. For class B waves, they are to be found in both the fluid and the wall. However, the disturbance eigenfunction has its maximum amplitude at the fluidsolid interface and thus those waves are principally wall-based modes of instability. Such instability would not exist had the wall been rigid. The instability is due to the downstream-running free wave in the solid being modified by the fluid loading. The destabilization of class B waves is affected by the phase difference between the pressure perturbation and the wall deformation, which allows a flow of energy from the fluid into the wall. The behaviour of class B Chapter Introduction waves is the reverse of that for class A waves, that is, stabilized by wall damping but destabilized by the non-conservative hydrodynamic forces. Basically, class B waves are amplified when the flow supplies sufficient energy to counterbalance the coating’s internal dissipation. Lastly, class C waves have something related to the inviscid Kelvin-Helmholtz instability and occur when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid. In that case, Class C waves can grow on the solid surface only if the pressure amplitude is so large as to outweigh the coating stiffness. Class C waves are the result of modal-coalescence instability where the flow speed is sufficiently high that the originally upstream-running wall free waves are turned to travel downstream and merge with the modified downstream-running wall free waves. Irreversible processes in both the fluid and solid and solid have negligible effect on class C instabilities. Another classification is that of Carpenter and Garrad (1985, 1986), who simply divided the waves into fluid-based and solid-based. TS instability (TSI) is an example of fluid-based waves. The solid-based, flow-induced surface instabilities (FISI) are closely analogous to the instabilities studied in hydro-elasticity, and include both the travelling-wave flutter that moves at speeds close to the solid free-wave speed (class B) and the essentially static-and more dangerous-divergence waves (class C). FISI was also termed compliance-induced flow instabilities (CIFI) in the previous study by Yeo (1986). Chapter Introduction 1.4 Research motivations Significant work of research had been done and the balance of evidence points to the ability of compliant (flexible) wall to positively influence laminar turbulence transition. However, there are gaps in this knowledge, especially as it relates to its practical implementation. First to state that the motivations from Zhao (2006) that led to this present work includes: (i) Zhao (2006)’s work over a single membrane panel had shown the ability of membrane panel in suppressing the wavepacket from growing, thereby this suppression accounts for transition delay. With this, we were motivated to consider up to three CPs in this present study and to know if transition could be delayed beyond distance already achieved for the single CP case. (ii) Also we were motivated to extend the study to over more than one compliant panel, and to know if suppressions of 2D wave modes could still be the main mechanism behind transition delay, or any other mechanisms could be responsible for transition delay especially as the wavepacket convects over the subsequent second, third etc. compliant panels. Apart from these, other motivation is based on the economic point of view as the costs of fuelling especially for those in the transportation industries will be reduced, if there is means of delaying transition farther as this will eventually resulted into significant drag reduction. Chapter Introduction 1.5 Major differences between present work and that of Zhao (2006) The major differences between this work and that of Zhao (2006) are: (i) Zhao (2006)’s work was limited in its scope due to then constraints on computing resources, as she could only simulate over the single membrane panel case to the incipient turbulent spot state. However, this same feat could not be repeated for over two compliant panels or more. This present work goes beyond that by simulating over two and three compliant panels until incipient turbulent spots were reached. (ii) Even for over the single membrane panel case, Zhao simulation was carried out in two stages with interpolation process in between. With the number of grid points in the streamwise (X) and spanwise (Z) directions remain fixed, data from coarse Y grid points in stage of her simulation were interpolated into a much denser Y grid points in stage of her simulation. However for this work, all simulations were carried out in a single process without any interpolation process in-between, therefore errors due to interpolation are totally avoided. (iii) More grid points were used in this work compared to those used by Zhao (2006) before, purposely to capture the flow fine details especially near the wall, as this work concerns boundary layer study. (iv) Spectral analyses was taken to a much higher level by extracting the spectral properties for the dominant 2D and 3D wave modes, which were compared to the Craik (1971) type resonance triad. Also, wavepacket amplitude growth curves were also examined in this work in order to appreciate the role of compliant 10 Chapter Introduction panels in suppressing the 2D wave modes. All these were not previously investigated in the work of Zhao (2006). (v) A sub-section of work reported by Zhao (2006) on membrane panel properties was as brief as her simulations were only stopped half way without any concrete conclusions regarding whether transition is delayed or not. However in this work, a more systematic study was carried out on compliant panel properties, where proper tuning of compliant properties resulted into a much better transition delay than before. In addition, this work also investigated effect of compliant panel damping on transition delay which Zhao (2006)’s study did not to cover. 1.6 Research scopes and objectives The work reported in this thesis mainly concerns the use of short compliant panels to delay laminar to turbulent transition within the Blasius boundary layer. Investigations covered the use of single compliant panel to delay transition and later extended to multiple compliant panels so as to delay transition further than before, after the favourable performance exhibited by the single compliant case. Compliant panel cases results are compared with those for over the rigid wall simulation counterparts so as to appreciate the duty of compliant panel(s) in transition delay. In all, short finite compliant panel is considered in order to keep FISI or CIFI modes in check. Study carried out is all about pulse-initiated wavepackets as it provides a plausible model for naturally occurring laminar– turbulent transition because they contain disturbances in a broadband of frequencies and wavenumbers, whose sum of interactions determines the spatio- 11 Chapter Introduction temporal progress of the wavepackets. Post simulation analyses carried out are mainly centered on spatial evolution and spectra analyses with more emphasis on the latter in order to obtain detailed and useful information about the evolving wavepacket before incipience of turbulent spot. Lastly, the investigations ended with further critical studies on compliant panel properties, that is, trying to tune the properties with the aim of making compliant panels to perform better than before. The specific objectives of the present thesis are: (a) With the currently available powerful computational resources at the NUS computer center, this study aims to investigate the possibility of applying more than one single compliant panel to delay laminar to turbulent transition as much further as possible. Previous study by Zhao (2006) on more than one single compliant panel was limited in its scope due to then constraints on computing resource. (b) To search for suitable locations along the streamwise (X) direction, where compliant panels could replace certain sections of the rigid wall, and be able to suppress the rapid growth of the evolving wavepacket, which will result into further transition delay for the Blasius boundary layer. (c) To make sure that any simulation carried out especially those involving more than one compliant panel reach the incipient turbulent spots. Otherwise, transition delay will be difficult to determine and this will amount to waste of time and resources as well. 12 Chapter Introduction (d) To know if compliant panel properties could be further fine-tuned under the compliant panel property study, with the aim of making the compliant panel performing better than what was obtained in the earlier part of this thesis work. (e) Mostly to go deeper in analyses through spectral properties extractions of wavepacket dominant 2D and 3D wave modes, in order to understand more intrinsic mechanisms behind the wavepacket overall behaviours. 1.7 Thesis outline This thesis comprises of six (6) chapters in total. Chapter presents the backgrounds of boundary layer transitions, instabilities, breakdowns and solidfluid interactions. Chapter presents the relevant literature review with the previous works done up to date, from both the numerical and experimental investigations points of view especially for compliant wall fluids interactions problems within the boundary layer. Chapter compares transition delay behaviours of single compliant panel case with that over rigid wall case, purposely to show the ability of single compliant panel in delaying transition. This ended with the linear analysis over the single compliant case; so as to have complete information about the wavepacket behaviours at it evolves over the single compliant panel location. Chapter capitalizes on the motivation obtained from over the single compliant panel case results in Chapter 3, to consider multiple compliant panels and see if transition could be delayed much better than that is already obtained in Chapter before. Simulation results are discussed in detail both in terms of the wavepacket spatial evolution and spectrum analyses. 13 Chapter Introduction Chapter concerns compliant panel (CP) properties study. This chapter shows that by carefully tuning the compliant panel properties further, the compliant panel can perform better in terms of transition delay if compared with the previous properties used by Zhao (2006). Finally, Chapter summarizes all the findings of the present work and capped it all with suggestive recommendations for further investigations. 14 Chapter Introduction Figure 1.1 Classification schemes for fluid-solid instabilities (Gad-el-Hak (2002)). 15 Chapter Introduction Figure 1.2 Volume-based and surface-based models of compliant coatings according to Carpenter (1990). 16 [...]... delay laminar to turbulent transition within the Blasius boundary layer Investigations covered the use of single compliant panel to delay transition and later extended to multiple compliant panels so as to delay transition further than before, after the favourable performance exhibited by the single compliant case Compliant panel cases results are compared with those for over the rigid wall simulation... work and capped it all with suggestive recommendations for further investigations 14 Chapter 1 Introduction Figure 1. 1 Classification schemes for fluid-solid instabilities (Gad-el-Hak (2002)) 15 Chapter 1 Introduction Figure 1. 2 Volume-based and surface-based models of compliant coatings according to Carpenter (19 90) 16 ... carried out on compliant panel properties, where proper tuning of compliant properties resulted into a much better transition delay than before In addition, this work also investigated effect of compliant panel damping on transition delay which Zhao (2006)’s study did not to cover 1. 6 Research scopes and objectives The work reported in this thesis mainly concerns the use of short compliant panels to delay... the numerical and experimental investigations points of view especially for compliant wall fluids interactions problems within the boundary layer Chapter 3 compares transition delay behaviours of single compliant panel case with that over rigid wall case, purposely to show the ability of single compliant panel in delaying transition This ended with the linear analysis over the single compliant case;... evolves over the single compliant panel location Chapter 4 capitalizes on the motivation obtained from over the single compliant panel case results in Chapter 3, to consider multiple compliant panels and see if transition could be delayed much better than that is already obtained in Chapter 3 before Simulation results are discussed in detail both in terms of the wavepacket spatial evolution and spectrum... especially those involving more than one compliant panel reach the incipient turbulent spots Otherwise, transition delay will be difficult to determine and this will amount to waste of time and resources as well 12 Chapter 1 Introduction (d) To know if compliant panel properties could be further fine-tuned under the compliant panel property study, with the aim of making the compliant panel performing better... through spectral properties extractions of wavepacket dominant 2D and 3D wave modes, in order to understand more intrinsic mechanisms behind the wavepacket overall behaviours 1. 7 Thesis outline This thesis comprises of six (6) chapters in total Chapter 1 presents the backgrounds of boundary layer transitions, instabilities, breakdowns and solidfluid interactions Chapter 2 presents the relevant literature... and spectrum analyses 13 Chapter 1 Introduction Chapter 5 concerns compliant panel (CP) properties study This chapter shows that by carefully tuning the compliant panel properties further, the compliant panel can perform better in terms of transition delay if compared with the previous properties used by Zhao (2006) Finally, Chapter 6 summarizes all the findings of the present work and capped it all with... as to appreciate the duty of compliant panel(s) in transition delay In all, short finite compliant panel is considered in order to keep FISI or CIFI modes in check Study carried out is all about pulse-initiated wavepackets as it provides a plausible model for naturally occurring laminar– turbulent transition because they contain disturbances in a broadband of frequencies and wavenumbers, whose sum of... the spatio- 11 Chapter 1 Introduction temporal progress of the wavepackets Post simulation analyses carried out are mainly centered on spatial evolution and spectra analyses with more emphasis on the latter in order to obtain detailed and useful information about the evolving wavepacket before incipience of turbulent spot Lastly, the investigations ended with further critical studies on compliant panel . study of how compliant panels may be devised to delay transition in a Blasius boundary layer flow. 1. 2 Boundary layer transitions, instabilities and breakdowns Reynolds (18 83) was the. turbulent boundary layer flows. Based on Landahl’s (19 62) and Benjamin’s (19 63) original classification schemes, all the waves arising from the interaction of the flow and the compliant surface can. for over two compliant panels or more. This present work goes beyond that by simulating over two and three compliant panels until incipient turbulent spots were reached. (ii) Even for over