Large-eddy simulation of separated-flow transition under elevated free-stream turbulence and pressure gradient

The primary focus of this PhD thesis is to enhance current understanding on The primary focus of this PhD thesis is to enhance current understanding on boundary layer separated-flow transition under elevated free-stream turbulence (FST). Due to the applied free-stream turbulence, streaks are formed and propagate inside the boundary layer. These play an important role in the transition process. Previous studies have revealed that transition can occur due to both inviscid Kelvin-Helmholz (K-H) instability and streak-related instability mechanisms. Also, in an elevated FST environment, such as under 1.99% FST, streaks are found to contribute higher energy than the K-H instability during transition. Nevertheless, important questions such as, “How can streaks lead to transition-onset?”, and “What is the transition mechanism with both streaks and K-H instability?”, remain unanswered.

The main discussion of this thesis has been divided into four sections. First, the numerical set-up for the current investigation is discussed in chapter 4. The Large Eddy Simulation (LES) approach, with a dynamic subgrid-scale (SGS) turbulence model, is employed to investigate the current flow field. The predicted time-mean flow field has a good agreement with the experimental observations and previous numerical predictions. Stability analyses have shown that the separated-flow transition in the 0%-FST case possessed a K-H frequency peak, whereas no frequency peak is detected in the 3%-FST case. Instead, streaks exist in the boundary layer up to the transition-onset location. From the flow visu- alisation, the span-wise K-H rollers found in the 0%-FST case have been severely disrupted in the 3%-FST case. This has resulted in part-span 2D rollers, rapidly developing into a 3D motion. Consequently, the usual secondary instability stage is bypassed, followed by weaker vortex shedding. Current analyses have revealed that both K-H instability and streak-related instability are at work.

Second, the effect of free-stream turbulence intensity (FSTI) on separated-flow transition is investigated in Chapter 5. In total, four levels of FST are studied and compared. The separation bubble characteristics are found to be sensitive to the increased FSTI. Both separation bubble length and height reduce when FSTI increases. A similar relation with FSTI is observed from the transition onset location. It moves forward when FSTI in- creases, which is believed to be caused by the reduced length of the separated shear layer. This is due to streaks propagating inside the boundary layer and through the transition process, interrupting growth of the separated share layer and promoting early transition. In the highest FSTI case (8.0% FST) under investigation, a separation bubble and vortex shedding can be observed, indicating the coexistence of both streak instability and K-H instability in the transition process. However, the former is found to be a much stronger transition mechanism than the latter.

In the third discussion, Proper Orthogonal Decomposition (POD) has been employed to analyse the current separated-flow transition in Chapter 6. From the POD analyses, results have confirmed the coexistence of both streak instability and K-H instability in the 3%-FST case. The streak instability is found to dominate in the current separated- flow transition. In the power spectral density analyses of the POD corresponding time- coefficients, the K-H frequency peak has been detected. Nevertheless, the K-H instability is considered as a localised activity. Both the outer- and inner-streak instability modes normally found in the bypass transition exist in the current separated-flow transition. The differences between these two streak instability modes have been clearly demonstrated by the POD mode visualisation.

In Chapter 7 of the final discussion, flow visualisation and 2D particle tracking have been employed to investigate the two modes of streak instability in the current separated- flow transition. Differences between the current two streak instability modes and those from the bypass transition have been identified. Analogous to the bypass transition, the inner mode originates from shear between a high-speed streak and below low-speed fluid, whereas the outer mode is caused by shear between a lifted low-speed streak and the high-speed free-stream flow. In contrast to the bypass transition, the inner mode streak instability is found to have a similar instability mechanism to the K-H instability. Part- span K-H roller can be a result of inner mode streak instability. For the outer mode, instability arises due to the formation of ring-like vortices warping around the low-speed streak. These vortices are believed to be the precursor to the hairpin vortices. Initial breakdowns of both streak instability modes are via the varicose breakdown pattern.

under elevated free-stream turbulence (FST). Due to the applied free-stream turbulence, streaks are formed and propagate inside the boundary layer. These play an important role in the transition process. Previous studies have revealed that transition can occur due to both inviscid Kelvin-Helmholz (K-H) instability and streak-related instability mechanisms. Also, in an elevated FST environment, such as under 1.99% FST, streaks are found to contribute higher energy than the K-H instability during transition. Nevertheless, important questions such as, “How can streaks lead to transition-onset?”, and “What is the transition mechanism with both streaks and K-H instability?”, remain unanswered.

The main discussion of this thesis has been divided into four sections. First, the numerical set-up for the current investigation is discussed in chapter 4. The Large Eddy Simulation (LES) approach, with a dynamic subgrid-scale (SGS) turbulence model, is employed to investigate the current flow field. The predicted time-mean flow field has a good agreement with the experimental observations and previous numerical predictions. Stabil- ity analyses have shown that the separated-flow transition in the 0%-FST case possessed a K-H frequency peak, whereas no frequency peak is detected in the 3%-FST case. Instead, streaks exist in the boundary layer up to the transition-onset location. From the flow visualisation, the span-wise K-H rollers found in the 0%-FST case have been severely disrupted in the 3%-FST case. This has resulted in part-span 2D rollers, rapidly developing into a 3D motion. Consequently, the usual secondary instability stage is bypassed, followed by weaker vortex shedding. Current analyses have revealed that both K-H instability and streak-related instability are at work.

Second, the effect of free-stream turbulence intensity (FSTI) on separated-flow transition is investigated in Chapter 5. In total, four levels of FST are studied and compared. The separation bubble characteristics are found to be sensitive to the increased FSTI. Both separation bubble length and height reduce when FSTI increases. A similar relation with FSTI is observed from the transition onset location. It moves forward when FSTI in- creases, which is believed to be caused by the reduced length of the separated shear layer. This is due to streaks propagating inside the boundary layer and through the transition process, interrupting growth of the separated share layer and promoting early transition. In the highest FSTI case (8.0% FST) under investigation, a separation bubble and vortex shedding can be observed, indicating the coexistence of both streak instability and K-H instability in the transition process. However, the former is found to be a much stronger transition mechanism than the latter.

In the third discussion, Proper Orthogonal Decomposition (POD) has been employed to analyse the current separated-flow transition in Chapter 6. From the POD analyses, results have confirmed the coexistence of both streak instability and K-H instability in the 3%-FST case. The streak instability is found to dominate in the current separated- flow transition. In the power spectral density analyses of the POD corresponding time- coefficients, the K-H frequency peak has been detected. Nevertheless, the K-H instability is considered as a localised activity. Both the outer- and inner-streak instability modes normally found in the bypass transition exist in the current separated-flow transition. The differences between these two streak instability modes have been clearly demonstrated by the POD mode visualisation.

In Chapter 7 of the final discussion, flow visualisation and 2D particle tracking have been employed to investigate the two modes of streak instability in the current separated- flow transition. Differences between the current two streak instability modes and those from the bypass transition have been identified. Analogous to the bypass transition, the inner mode originates from shear between a high-speed streak and below low-speed fluid, whereas the outer mode is caused by shear between a lifted low-speed streak and the high-speed free-stream flow. In contrast to the bypass transition, the inner mode streak instability is found to have a similar instability mechanism to the K-H instability. Part- span K-H roller can be a result of inner mode streak instability. For the outer mode, instability arises due to the formation of ring-like vortices warping around the low-speed streak. These vortices are believed to be the precursor to the hairpin vortices. Initial breakdowns of both streak instability modes are via the varicose breakdown pattern.