scholarly journals A CFD-Compatible Amplification Factor Transport Equation for Oblique Tollmien-Schlichting Waves in Supersonic Boundary Layers

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
JiaKuan Xu ◽  
Lei Qiao ◽  
Junqiang Bai
Keyword(s):  
Transport Equation ◽  
Amplification Factor ◽  
Flow Instability ◽  
Supersonic Flows ◽  
Boundary Layer Transition ◽  
Linear Stability Theory ◽  
Two Dimensional ◽  
Layer Transition ◽  
Low Speed ◽  
Tollmien Schlichting

Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, two-dimensional Tollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and Maughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become dominant in flow instability. Inspired by Coder and Maughmer’s NTS amplification factor transport equation for two-dimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are introduced to build the relationships between nonlocal variables and local variables so that all the variables used in the present model can be calculated using local variables. Applications of this new transport equation to the flows over supersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared with the standard LST analysis results.

Numerical simulation of boundary-layer transition and transition control

1989 ◽  
Vol 199 ◽  
pp. 403-440 ◽  
Author(s):  
E. Laurien ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Transition Process ◽  
Numerical Results ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Longitudinal Vortices ◽  
Tollmien Schlichting

The laminar-turbulent transition process in a parallel boundary-layer with Blasius profile is simulated by numerical integration of the three-dimensional incompressible Navier-Stokes equations using a spectral method. The model of spatially periodic disturbances developing in time is used. Both the classical Klebanoff-type and the subharmonic type of transition are simulated. Maps of the three-dimensional velocity and vorticity fields and visualizations by integrated fluid markers are obtained. The numerical results are compared with experimental measurements and flow visualizations by other authors. Good qualitative and quantitative agreement is found at corresponding stages of development up to the one-spike stage. After the appearance of two-dimensional Tollmien-Schlichting waves of sufficiently large amplitude an increasing three-dimensionality is observed. In particular, a peak-valley structure of the velocity fluctuations, mean longitudinal vortices and sharp spike-like instantaneous velocity signals are formed. The flow field is dominated by a three-dimensional horseshoe vortex system connected with free high-shear layers. Visualizations by time-lines show the formation of A-structures. Our numerical results connect various observations obtained with different experimental techniques. The initial three-dimensional steps of the transition process are consistent with the linear theory of secondary instability. In the later stages nonlinear interactions of the disturbance modes and the production of higher harmonics are essential.We also study the control of transition by local two-dimensional suction and blowing at the wall. It is shown that transition can be delayed or accelerated by superposing disturbances which are out of phase or in phase with oncoming Tollmien-Schlichting instability waves, respectively. Control is only effective if applied at an early, two-dimensional stage of transition. Mean longitudinal vortices remain even after successful control of the fluctuations.

Numerical and experimental investigations of oblique boundary layer transition

1999 ◽  
Vol 393 ◽  
pp. 23-57 ◽  
Author(s):  
STELLAN BERLIN ◽  
MARKUS WIEGEL ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Transition ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Layer Transition ◽  
Oblique Waves ◽  
Starting Point ◽  
Incompressible Boundary ◽  
Tollmien Schlichting ◽  
Streamwise Streaks

A transition scenario initiated by two oblique waves is studied in an incompressible boundary layer. Hot-wire measurements and flow visualizations from the first boundary layer experiment on this scenario are reported. The experimental results are compared with spatial direct numerical simulations and good qualitative agreement is found. Also, quantitative agreement is found when the experimental device for disturbance generation is closely modelled in the simulations and pressure gradient effects taken into account. The oblique waves are found to interact nonlinearly to force streamwise vortices. The vortices in turn produce growing streamwise streaks by non-modal linear growth mechanisms. This has previously been observed in channel flows and calculations of both compressible and incompressible boundary layers. The flow structures observed at the late stage of oblique transition have many similarities to the corresponding ones of K- and H-type transition, for which two-dimensional Tollmien–Schlichting waves are the starting point. However, two-dimensional Tollmien–Schlichting waves are usually not initiated or observed in oblique transition and consequently the similarities are due to the oblique waves and streamwise streaks appearing in all three scenarios.

scholarly journals Blind disturbance separation and identification in a transitional boundary layer using minimal sensing

2021 ◽  
Vol 927 ◽  
Author(s):  
I. Gluzman ◽  
J. Cohen ◽  
Y. Oshman
Keyword(s):  
Boundary Layer ◽  
Numerical Study ◽  
A Priori ◽  
Boundary Layer Transition ◽  
Linear Stability Theory ◽  
Plasma Actuators ◽  
Flow State ◽  
Layer Transition ◽  
Novel Approach ◽  
Tollmien Schlichting

A novel approach is presented for identifying disturbance sources in wall-bounded shear flows. The underlying approach models the flow state, as measured by sensors embedded in the flow, as a mixture of disturbance sources. The degenerate unmixing estimation technique is adopted as a blind source separation technique to recover the separate sources and their unknown mixing process. The efficiency of this approach stems from its ability to isolate any, a priori unknown, number of sources, using two sensors only. Furthermore, by adding a single additional sensor, the method is expanded to also determine the propagation velocity vector of each of the isolated sources, based on sensor readings from three sensors appropriately located in the flow field. Theoretical guidelines for locating the sensors are provided. The power of the method is demonstrated via computer simulations and wind-tunnel experiments. The numerical study considers disturbances comprising discrete Tollmien–Schlichting waves and wave packets. Linear stability theory is used to model source mixtures acquired by sensors placed in a Blasius boundary layer. The experimental study investigates the flow over a flat plate, with hot wires as sensors, and a loudspeaker and plasma actuators as source generators. Based on numerical and experimental demonstrations, it is believed that the new approach should prove useful in various applications, including active control of boundary layer transition from laminar to turbulent flow.

The control of boundary-layer transition using a wave-superposition principle

1983 ◽  
Vol 137 ◽  
pp. 233-250 ◽  
Author(s):  
Andrew S. W. Thomas
Keyword(s):  
Boundary Layer ◽  
Superposition Principle ◽  
Three Dimensional ◽  
Feedback System ◽  
Boundary Layer Transition ◽  
Single Frequency ◽  
Two Dimensional ◽  
Layer Transition ◽  
Tollmien Schlichting ◽  
Equal Amplitude

An experimental study has been made of the concept of controlling boundary-layer transition by superimposing in the flow Tollmien–Schlichting waves that are of equal amplitude and antiphased to the disturbances that grow and lead to transition. The cases that have been considered are transition arising from a single-frequency two-dimensional disturbance and transition arising from a nonlinear interaction between two waves of different frequency. A feedback system for controlling transition has also been studied. In each case, both hot-wire surveys and flow visualization have shown that it is possible to delay transition but that the flow cannot be restored completely to its undisturbed state. This appears to be a consequence of interactions between the very weak three-dimensional background disturbances in the flow and the primary two-dimensional waves. The implications of these findings in an implementation of the concept are discussed.

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

2013 ◽  
Vol 732 ◽  
pp. 571-615 ◽  
Author(s):  
I. B. de Paula ◽  
W. Würz ◽  
E. Krämer ◽  
V. I. Borodulin ◽  
Y. S. Kachanov
Keyword(s):  
Boundary Layer ◽  
Modulation Frequency ◽  
Low Frequency ◽  
Natural Disturbance ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Weakly Nonlinear ◽  
Resonant Interactions ◽  
Tollmien Schlichting

AbstractWeakly nonlinear interactions involving amplitude-modulated Tollmien–Schlichting waves in an incompressible, two-dimensional aerofoil boundary layer are investigated experimentally. Selected resonant regimes are examined with emphasis on the regimes where more than one fundamental Tollmien–Schlichting (TS) wave is present in the flow. The experiments were performed on an NLF-type aerofoil section for glider applications. Disturbances with controlled frequency-spanwise-wavenumber spectra were excited in the boundary layer and studied by phase-locked hot-wire measurements. The results show that nonlinear mechanisms connected with the steepening of the primary TS wave modulation do not play any significant role in the transition scenarios studied. It is also shown that modulations of the two-dimensional fundamental waves tend to generate additional modes at modulation frequency. These low-frequency disturbances are found to be produced by a non-resonant quadratic combination of spectral components of the primary, modulated TS wave. The investigations show that the efficiency of the process is higher for three-dimensional low-frequency modes in comparison with two-dimensional modes. Thus, the emergence of three-dimensionality for the low-frequency waves does not require any resonant interactions. In a subsequent nonlinear stage, the self-generated detuned subharmonics are found to be strongly amplified due to resonant interactions with the primary TS waves. The sequence of weakly nonlinear mechanisms found and investigated here seems to be the most likely route to the laminar–turbulent transition, at least for two-dimensional boundary layers of aerofoils with a long extent of laminar flow and in a ‘natural’ disturbance environment.

Linear amplification factor transport equation for stationary crossflow instabilities in supersonic boundary layers

2020 ◽  
pp. 095441002095499
Author(s):  
Jiakuan Xu
Keyword(s):  
Transport Equation ◽  
Boundary Layers ◽  
Amplification Factor ◽  
Reynolds Numbers ◽  
Linear Stability Theory ◽  
Local Flow ◽  
Flow Parameters ◽  
Compressible Boundary Layers ◽  
Non Local ◽  
Flow Variables

Based on the database from linear stability theory (LST) analysis, a local amplification factor transport equation for stationary crossflow (CF) waves in low-speed boundary layers was developed in 2019. In this paper, the authors try to extend this transport equation to compressible boundary layers based on local flow variables. The similarity equations for compressible boundary layers are introduced to build the function relations between non-local variables and local flow parameters. Then, compressibility corrections are taken into account to modify the source term of the transport equation. Through verifications of different sweep angles, Reynolds numbers, angles of attack, Mach numbers, and different cross-section geometric shapes, the rationality and correctness of the new transport equation established in this paper are illustrated.

Effects of Weak Free Stream Nonuniformity on Boundary Layer Transition (Keynote Paper)

2003 ◽  
Author(s):  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Mean Flow ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Distorted Waves ◽  
Thickness Variations

Experiments are described in which well-defined FSN (Free Stream Nonuniformity) distributions are introduced by placing fine wires upstream of the leading edge of a flat plate. Large amplitude spanwise thickness variations are present in the downstream boundary layer resulting from the interaction of the laminar wakes with the leading edge. Regions of elevated background unsteadiness appear on either side of the peak layer thickness, which share many of the characteristics of Klebanoff modes, observed at elevated Free Stream Turbulence (FST) levels. However, for the low background disturbance level of the free stream, the layer remains laminar to the end of the test section (Rx ≈ l.4×106) and there is no evidence of bursting or other phenomena associated with breakdown to turbulence. A vibrating ribbon apparatus is used to demonstrate that the deformation of the mean flow is responsible for substantial phase and amplitude distortion of Tollmien-Schlichting (TS) waves. Pseudo-flow visualization of hot-wire data shows that the breakdown of the distorted waves is more complex and occurs at a lower Reynolds number than the breakdown of the K-type secondary instability observed when the FSN is not present.

A Note on the Transition Observations on an Axisymmetric Body and Some Related Fluctuating Wall Pressure Measurements

1975 ◽  
Vol 97 (1) ◽  
pp. 82-86 ◽  
Author(s):  
V. H. Arakeri
Keyword(s):  
Pressure Transducer ◽  
Critical Frequency ◽  
Dominant Frequency ◽  
Axisymmetric Body ◽  
Boundary Layer Transition ◽  
Linear Stability Theory ◽  
Pressure Measurements ◽  
Schlieren Method ◽  
Layer Transition ◽  
Transducer Signal

Boundary layer transition on an axisymmetric body up to Reynolds number of 1.26 × 106 was observed by schlieren method of flow visualization developed for water tunnel use. The spectrum of the flush mounted pressure transducer signal showed a dominant frequency to exist at transition and further, this frequency was in close agreement with the predicted critical frequency by Smith’s approximate method of transition calculation based on linear stability theory.

Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods

2011 ◽  
Vol 56 (4) ◽  
pp. 1-12 ◽  
Author(s):  
K. Richter ◽  
A. Le Pape ◽  
T. Knopp ◽  
M. Costes ◽  
V. Gleize ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
High Speed ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Boundary Layer Transition ◽  
Dynamic Stall ◽  
Two Dimensional ◽  
Layer Transition ◽  
The Impact

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. To improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction was investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low-speed and high-speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart–Allmaras-type models to state-of-the-art, seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

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