Session X26: Flow Instability: Transition to Turbulence

Chaos and unstable periodic orbits in subcritical Taylor-Couette flow

Although spectral approximation of turbulence typically requires a large number of modes, for relatively low Reynolds numbers the turbulent attractor lies on a low-dimensional manifold in phase space. The most extreme case is when the main features of the chaotic attractor can be quantified by a one-dimensional map on Poincaré section. We find this can indeed happen in subcritical Taylor-Couette flow, which should offer an important test case for connecting turbulence and periodic orbit analysis.   

Modal decomposition analysis to extract the coherent behaviors in transitional pulsatile pipe flows

Investigation of mechanisms triggering the transition to turbulence in pulsatile pipe flows are of interest due to the detrimental effect of intermittent flow structures on hemodynamics behaviors. However, conventional metrics such as critical Reynolds number or turbulence intensity fail to represent these intermittent flow mechanisms adequately because of the time-varying nature of pulsatile flow as well as the interdependent mechanism between mean and oscillatory flow components. Data driven modal decomposition methods such as proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) have generally been found to be well-suited for extracting the underlying coherent interdependent mechanism in the data. In this work, we perform several modal decomposition analyses on 2D particle image velocimetry (PIV) data of transitional pulsatile pipe flow to extract the spatial, temporal, and spectral coherent mechanisms triggering the transition to turbulence. Furthermore, we explore the relation between the resulting modes to traditionally obtained coherent structures as well as our novel instantaneous frequency structures of the flow field.   

Developing a universal metric to assess the progression of transition to turbulence in pulsatile pipe flow

Transition to turbulence in pulsatile flow has been observed to occur in the left ventricle of the heart, cerebral aneurysms, etc. The intermittent and fluctuating flow behavior associated with it has been shown to affect key hemodynamic metrics such as wall shear stress (WSS) and pressure, as well as contribute to disease progression. Unfortunately, despite the clear need, no metrics or analysis tools exist to assess the magnitude of transitional flow behavior present for a given flow. In this work, we aim to address this gap by identifying and establishing a metric capable of estimating the progression of transition within a flow environment. We developed a continuous wavelet transform (CWT)-based time-frequency analysis (TFA) method capable of evaluating the instantaneous frequency of the flow. We apply our TFA method to 2D planar particle image velocimetry (PIV) data of transitional flow collected in-house. The 2D PIV data includes both steady and pulsatile flow cases with mean Reynolds numbers (Re_m) ranging from 500-5000. Specifically, we examine the temporal evolution of spatial frequency structures across different waveforms and Re_m. We show that the spatial structures undergo a transformation from coarser to finer spatial scales and serve as a metric in identifying progression of transition to turbulence.   

A deterministic analysis of effects of external body forces on transition to turbulence

The present study investigates the impact of externally-applied traveling-wave body forces on the transition to turbulence of plane Poiseuille flow through direct numerical simulation. The friction Reynolds number ranges from 85 to 400. As expected, higher Reynolds numbers escalate the likelihood of transition, and the likelihood is further intensified as the frequency of the external body force decreases. To comprehensively analyze the effects of the body force on transition, we apply it to the nonlinear traveling-wave solutions of the Navier-Stokes equations, also known as exact coherent structures. Two solution families are considered, namely a core mode and a critical-layer mode, depending on flow structure. Similar observations are made in which the body force triggers an early transition. However, the critical-layer mode exhibits a faster transition compared to the core mode. Additionally, an increase in Reynolds number augments the bursting magnitude during transition, commonly referred to as the transition instability. We further express the transition and bursting magnitude in terms of a drag reduction map, which allows us to characterize the optimal parameters for achieving the desired transition. Lastly, flow dynamics and structures of the traveling-wave solutions during transition are investigated to provide a deeper insight into the underlying mechanisms at play.   

Transition without puffs and slugs in curved pipes

Spatio-temporal intermittency, i.e. the coexistence of laminar and turbulent domains, is one of the central characteristics of the transition to turbulence in pipe and other shear flows. As shown in recent studies this transition is continuous, i.e. with decreasing Reynolds number the fraction of the flow that is turbulent decreases gradually and reaches zero at a critical point. In this talk we present experiments in curved pipes where for certain parameter regimes spatio-temporal intermittency is shown to be marginalized. That is, with decreasing Reynolds number the flow transitions from fully turbulent to laminar and the transition appears to become discontinuous. As we show localized turbulent structures such as puffs and slugs are unstable and below critical they shrink in size and the flow relaminarizes, whereas above critical they continue to expand until the flow is turbulent throughout.   

Experimental investigation of intermittency in transitional channel flows with drag-reducing polymers

The unforced transition from laminar to turbulent flow with increasing Reynolds number (Re) is compared between water and various aqueous solutions of drag-reducing flexible polymers in a channel flow. Time-resolved and double-frame particle image velocimetry are used to measure the velocity field and compare the transition process of the Newtonian and polymeric channel flows. For the channel flows of water, the transition to turbulence occurs between Re of 1500 and 1965. Between these Re, the transitional Newtonian channel flows exhibit intermittent zones of laminar and turbulent flow, and the fraction of time for which the flows are turbulent varies between 40% to 80%. For all polymeric flows, the transition to turbulence is delayed and the critical Re at which the flow turns chaotic increases as the polymer concentration grows. Moreover, the range of Re where flows exhibit intermittent laminar-turbulent patches increases with increasing polymer concentration. For flows with a polymer concentration of 150 ppm, transitional flow begins at Re of 2810 and persists until Re of 5370. At this large polymer concentration, transitional flows exhibit laminar zones with larger fluctuations due to growing instabilities.   

DNS of laminar-to-turbulent transition over a cooled/heated supercritical wing

Effects of cooling and heating supercritical airfoil surface on laminar-to-turbulence transition and drag are investigated through high-fidelity DNS. The DNS is performed by our high-order structured-grid-based flow solver and state-of-the-art supercomputer Fugaku, with the number of grid points of approximately 3.1 billion. Through the DNS, it is found that airfoil surface cooling induces delayed transition while heating promotes the transition. Moreover, we clarify that the transition process over the supercritical wing is the same as the traditional one over a flat plate observed in prior DNS, while cooling airfoil surface cooling makes the Λ vortices sharp and extended, which results in the downstream shifted location of the transition. Furthermore, the resultant friction drag is reduced by cooling the airfoil surface due to the delayed transition and decreased viscosity.    

Transition Measurements on NLF(1)-0416 Airfoil Using Infrared Thermography

Accurate determination of transition location is of critical importance for a wide range of engineering applications from natural laminar-flow wing designs to wind turbine blade aerodynamics. There has been significant progress in transition prediction over the years but the efforts to advance the prediction capability are still on-going. One of the test cases used in a recent transition prediction workshop (The 1st AIAA CFD Transition Modeling and Prediction Workshop 2021) is the flow over NLF(1)-0416 airfoil, which is a 16% thick natural laminar-flow airfoil designed in early 1980s and tested at NASA Langley Low Turbulence Pressure Tunnel (LTPT) in a Reynolds number range of 1E6 to 9E6 and for a Mach number range from 0.1 to 0.4. In that study, transition measurements were conducted using oil flow visualization and by connecting a microphone to orifices on the model. In this presentation we will show the results of recent transition measurements on the same airfoil using infrared thermography. The measurements are performed in the new large-scale wind tunnel of the Center for Wind Energy Research (RÜZGEM) at the Middle East Technical University (METU) in Ankara, Turkey. The tests are performed in the 2.5 m x 2.5 m cross-section test section of the wind tunnel using a 0.9 m chord and 2.5 m span model for various Reynolds numbers from 1E6 to 4E6. Current transition measurement results will be compared to the previously obtained data from the NASA Langley LTPT.   

Effects of Injection Gas Composition on High-Speed Boundary Layer Instability and Transition

High-speed vehicles experience severe aero-thermal loads, especially around the stagnation region and leading edges. To protect the underlying structure, transpiration cooling can be incorporated by employing gas injection which can dramatically reduce the heat transfer to the vehicle surface. Transpiration cooling first reduces the wall temperature through convection when the coolant passes through the porous media and secondly, it also forms a protective gas film reducing the heat transfer from the hot outside gas. Our work aims at understanding how transpiration cooling applied only in the nose region affects the stability characteristics of a Mach 9.81 flow around a blunt cone as compared to downstream injection. We will consider different injection gases and analyze how changing the composition of the gas mixture affects the flow transition to turbulence. Gas injection alters the boundary layer profiles by changing the peak temperature in addition to affecting the boundary layer thickness. We observe that the N-factors are not affected significantly if the injection of air is limited only in the nose region. However, if the injection is applied further downstream too, it can stabilize or severely destabilize the flow depending on the injection rates and types of gases used. In the case of air injection, we observe that increasing the blowing rates shifts the unstable flow region to a lower frequency range due to an increase in the boundary layer thickness. We also notice the appearance of the supersonic mode, in addition to the dominant second mode in the flow field at certain blowing rates.   

Hypersonic CFD Solutions for Boundary-Layer Transition Sled Test Track Experiment

In this study, we have performed simulations on blunt ogive geometries at various hypersonic speeds. The primary objective of conducting these simulations is to obtain the shapes of shock waves and pressure distributions, which are intended for use with the Harris Boundary-Layer Code developed by NASA. By leveraging the synergy between the Computational Fluid Dynamics (CFD) simulations, the Harris Code, and a 1D Heat Conduction Code, we aim to predict the surface roughness that leads to Boundary-Layer Transition. Specifically, we have evaluated the blunt ogive geometries at Mach 6 and 8 speeds. The details of this process, from geometry generation to post-processing of the results, will be explained in depth, utilizing the ANSYS Fluent Software as our primary tool.   

Magnetised turbulent-laminar dynamics in shear flows

Turbulence is ubiquitous in nature, however, the characterisation of the transition that gives rise to turbulence in shear flows is yet to be accomplished. Intermittency is a defining feature of the initial onset of turbulence in wall-bounded flows, in which chaotic regions, often in the form of bands or spots, coexist and compete with laminar motion. Connections between the behaviour of this laminar-turbulence transition have been made with both the dynamics of excitable media in addition to predator-prey dynamics, although it is hard to differentiate between these two models since there is only one control parameter, namely the Reynolds number. In this study, we attempt to unfold this problem by adding a magnetic field, the presence of which suppresses the excitability of the medium, making the turbulence less intermittent and modifying the form of the bands. By considering the low magnetic Reynolds number approximation, we introduce a second control parameter, the Hartmann number, thereby enabling this transition to be explored in a systematic manner. Specifically, we study the idealised shear between stress-free boundaries driven by a sinusoidal body force. This system, known as Waleffe flow, is further reduced by constructing a model that uses only four Fourier modes in the wall-normal direction, thus substantially reducing the computational cost of simulations whilst retaining the fidelity of the essential physics. Conclusions are drawn based on a series of carefully designed numerical simulations.   

Towards a Rational Approach to Transition Modeling

Existing transition sensitized RANS models rely on ad-hoc ramping functions and fits to experimental data. We propose a new modeling approach which takes on the fact that the exact, unclosed, second-order moment equations are valid for all flows, including those in transition. In order to develop a closure which is valid in the transition region, we attempt to impose the constraint that the linear response of the model equations to small disturbances should match the predictions of linear stability theory. Our analysis results in two critical conclusions. First, the scaling of the turbulent kinetic energy production is not physically consistent with the common intermittency scaling. Second, the non-local behavior of the Orr-Sommerfeld equation must arise in the model through a properly behaved explicit rapid-pressure diffusion model. In addition, we show that the normal rapid pressure-strain term, which assumes homogeneity, is a poor model for linear instability waves. Finally, we present a new model for transition in Rayleigh-Taylor and Kelvin-Helmholtz unstable flows.