Flow topology in compressible turbulent boundary layer

2012 ◽  
Vol 703 ◽  
pp. 255-278 ◽  
Author(s):  
Li Wang ◽  
Xi-Yun Lu
Keyword(s):  
Outer Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Flow Topology ◽  
Gradient Tensor ◽  
Navier Stokes Equations ◽  
Velocity Gradient Tensor ◽  
Compressibility Effect ◽  
Unstable Node ◽  
Unstable Focus

AbstractThe flow topologies of compressible turbulent boundary layers at Mach 2 are investigated by means of direct numerical simulation (DNS) of the compressible Navier–Stokes equations, and statistical analysis of the invariants of the velocity gradient tensor. We identify a preference for an unstable focus/compressing topology in the inner layer and an unstable node/saddle/saddle (UN/S/S) topology in the outer layer. The dissipation and dissipation production originate mainly from this UN/S/S topology. The enstrophy depends mainly on an unstable focus/stretching (UFS) topology, and the enstrophy production relies on a UN/S/S topology in the inner layer and on a UFS topology in the outer layer. The compressibility effect on the statistical properties of the topologies is investigated in terms of the ‘incompressible’, compressed and expanding regions. It is found that the locally compressed region tends to be more stable and the locally expanding region tends to be more dissipative. The compressibility is mainly related to unstable focus/compressing and stable focus/stretching topologies. Moreover, the features of the average dissipation, enstrophy, dissipation production and enstrophy production of the various topologies are clarified in the locally compressed and expanding regions.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

Characterization of coherent vortical structures in a supersonic turbulent boundary layer

2008 ◽  
Vol 613 ◽  
pp. 205-231 ◽  
Author(s):  
SERGIO PIROZZOLI ◽  
MATTEO BERNARDINI ◽  
FRANCESCO GRASSO
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Stokes Equations ◽  
Supersonic Boundary Layer ◽  
Navier Stokes ◽  
Hairpin Vortices ◽  
Length Scales ◽  
Navier Stokes Equations ◽  
Vortical Structures

A spatially developing supersonic boundary layer at Mach 2 is analysed by means of direct numerical simulation of the compressible Navier--Stokes equations, with the objective of quantitatively characterizing the coherent vortical structures. The study shows structural similarities with the incompressible case. In particular, the inner layer is mainly populated by quasi-streamwise vortices, while in the outer layer we observe a large variety of structures, including hairpin vortices and hairpin packets. The characteristic properties of the educed structures are found to be nearly uniform throughout the outer layer, and to be weakly affected by the local vortex orientation. In the outer layer, typical core radii vary in the range of 5–6 dissipative length scales, and the associated circulation is approximately constant, and of the order of 180 wall units. The statistical properties of the vortical structures in the outer layer are similar to those of an ensemble of non-interacting closed-loop vortices with a nearly planar head inclined at an angle of approximately 20° with respect to the wall, and with an overall size of approximately 30 dissipative length scales.

Singular treatment of viscous flow near the corner by using matched eigenfunctions

2018 ◽  
Vol 233 (5) ◽  
pp. 1660-1676 ◽  
Author(s):  
Ali Deliceoğlu ◽  
Ebutalib Çelik ◽  
Fuat Gürcan
Keyword(s):  
Stokes Equations ◽  
Careful Analysis ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Flow Topology ◽  
Navier Stokes Equations ◽  
Upper Lid ◽  
Eigenfunction Method ◽  
Numerical And Analytical Methods ◽  
The Stokes Equation

In this paper, the local singular behavior of Stokes flow is solved near the salient and re-entrant corners by the matching eigenfunction method. The flow in a rectangular and an L-shaped cavity are considered as a model for the flow generated by the motion of the upper lid. The solutions of the Stokes equation in polar coordinates are matched with a velocity vector components obtained by analytic or numerical solution for the streamfunction developed for any values of the heights of the rectangular and an L-shaped cavity. Streamline patterns near the corner are simulated for a different aspect ratio A. The techniques are tested on a flow problem undergoing Stokes or Navier–Stokes equations in a square cavity. It is seen that the method appears to be cheaper and more accurate than the numerical and analytical methods. It is expected that the study will lead to useful insights into the understanding of the flow topology near a re-entrant corner from a combined analytical-numerical method. Attention is then focused on the topological behavior near the re-entrant corner of the L-shaped cavity. Careful analysis of the streamlines of streamfunction near the re-entrant corner by using wall shear stress allows us to give a possible flow bifurcation of dividing streamline.

Computations of Unsteady Cavitation With a Pressure-Based Method

2003 ◽  
Author(s):  
Inanc Senocak ◽  
Wei Shyy
Keyword(s):  
Stokes Equations ◽  
Operator Splitting ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Splitting Algorithm ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Compressibility Effect ◽  
Conservative Form ◽  
Geometric Confinement

A computational approach based on the conservative form of the Favre-averaged Navier-Stokes equations, transport equation-based turbulent cavitation models and a pressure-based operator-splitting algorithm is applied to study turbulent cavitating flows through convergent-divergent nozzles. The implications of the compressibility effect, reflected via the speed of sound definition in the two-phase mixture, are assessed with two modeling approaches. Depending on the geometric confinement of the nozzle, compressibility model, and cavitation numbers, auto-oscillations and quasi-steady behaviors are observed. Detailed flow structures and cavitation dynamics are highlighted, and implications of the cavitation model discussed.

Influence of rotation on the near-wake development behind an impulsively started circular cylinder

1985 ◽  
Vol 158 ◽  
pp. 399-446 ◽  
Author(s):  
Madeleine Coutanceau ◽  
Christian Ménard
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Flow Topology ◽  
Near Wake ◽  
Navier Stokes Equations ◽  
Magnus Effect ◽  
Point Trajectories

The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers (Re [les ] 1000). The rotating-to-translating-speed ratio α increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E1 Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies Ei (i = 2,3,…) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter.

Sign in / Sign up

Export Citation Format

Share Document