The effect of compressibility on the critical swirl of vortex flows in a pipe

2002 ◽  
Vol 461 ◽  
pp. 301-319 ◽  
Author(s):  
Z. RUSAK ◽  
J. H. LEE
Keyword(s):  
Mach Number ◽  
Eigenvalue Problem ◽  
Swirling Flow ◽  
Base Flow ◽  
Vortex Flows ◽  
Flow State ◽  
Flow Perturbation ◽  
Limit Value ◽  
High Reynolds ◽  
Pressure Perturbations

The effect of compressibility on the critical swirl level for breakdown of subsonic vortex flows in a straight circular pipe of finite length is studied. This work extends the critical-state concept of Benjamin (1962) to include the influence of Mach number on the flow behaviour. The analysis is based on a linearized version of the equations for the motion of a steady, axisymmetric, inviscid and compressible swirling flow of a perfect gas. The relationship between the velocity, density, temperature and pressure perturbations to a base columnar flow state are derived. An eigenvalue problem is formulated to determine the first critical level of swirl at which a special mode of a non-columnar small disturbance may appear on the base flow. It is found that when the characteristic Mach number of the base flow tends to zero the eigenvalue problem and the critical swirl are the same as defined by Wang & Rusak (1996a, 1997a) in their study of incompressible swirling flows in pipes. As the characteristic Mach number is increased, the critical swirl level increases and the flow perturbation expands in the radial direction. As the Mach number is increased toward a certain limit value related to the core size of the vortex, the critical swirl reaches very large values and becomes singular. The present results indicate that the axisymmetric breakdown of high-Reynolds-number compressible vortex flows may be delayed with the increase of the flow Mach number.

scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

Receptivity of the boundary layer to vibrations of the wing surface

2013 ◽  
Vol 723 ◽  
pp. 480-528 ◽  
Author(s):  
A. I. Ruban ◽  
T. Bernots ◽  
D. Pryce
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Stokes Equations ◽  
Wing Surface ◽  
Main Concern ◽  
Elastic Vibrations ◽  
Stokes Layer ◽  
Characteristic Wavelength ◽  
Tollmien Schlichting ◽  
Pressure Perturbations

AbstractIn this paper we study the generation of Tollmien–Schlichting waves in the boundary layer due to elastic vibrations of the wing surface. The subsonic flow regime is considered with the Mach number outside the boundary layer $M= O(1)$. The flow is investigated based on the asymptotic analysis of the Navier–Stokes equations at large values of the Reynolds number, $\mathit{Re}= {\rho }_{\infty } {V}_{\infty } L/ {\mu }_{\infty } $. Here $L$ denotes the wing section chord; and ${V}_{\infty } $, ${\rho }_{\infty } $ and ${\mu }_{\infty } $ are the free stream velocity, air density and dynamic viscosity, respectively. We assume that in the spectrum of the wing vibrations there is a harmonic that comes in to resonance with the Tollmien–Schlichting wave on the lower branch of the stability curve; this happens when the frequency of the harmonic is a quantity of the order of $({V}_{\infty } / L){\mathit{Re}}^{1/ 4} $. The wavelength, $\ell $, of the elastic vibrations of the wing is assumed to be $\ell \sim L{\mathit{Re}}^{- 1/ 8} $, which has been found to represent a ‘distinguished limit’ in the theory. Still, the results of the analysis are applicable for $\ell \gg L{\mathit{Re}}^{- 1/ 8} $ and $\ell \ll L{\mathit{Re}}^{- 1/ 8} $; the former includes an important case when $\ell = O(L)$. We found that the vibrations of the wing surface produce pressure perturbations in the flow outside the boundary layer, which can be calculated with the help of the ‘piston theory’, which remains valid provided that the Mach number, $M$, is large as compared to ${\mathit{Re}}^{- 1/ 4} $. As the pressure perturbations penetrate into the boundary layer, a Stokes layer forms on the wing surface; its thickness is estimated as a quantity of the order of ${\mathit{Re}}^{- 5/ 8} $. When $\ell = O({\mathit{Re}}^{- 1/ 8} )$ or $\ell \gg {\mathit{Re}}^{- 1/ 8} $, the solution in the Stokes layer appears to be influenced significantly by the compressibility of the flow. The Stokes layer on its own is incapable of producing the Tollmien–Schlichting waves. The reason is that the characteristic wavelength of the perturbation field in the Stokes layer is much larger than that of the Tollmien–Schlichting wave. However, the situation changes when the Stokes layer encounters a wall roughness, which are plentiful in real aerodynamic flows. If the longitudinal extent of the roughness is a quantity of the order of ${\mathit{Re}}^{- 3/ 8} $, then efficient generation of the Tollmien–Schlichting waves becomes possible. In this paper we restrict our attention to the case when the Stokes layer interacts with an isolated roughness. The flow near the roughness is described by the triple-deck theory. The solution of the triple-deck problem can be found in an analytic form. Our main concern is with the flow behaviour downstream of the roughness and, in particular, with the amplitude of the generated Tollmien–Schlichting waves.

Spatial stability analysis of subsonic corrugated jets

2019 ◽  
Vol 876 ◽  
pp. 766-791 ◽  
Author(s):  
F. C. Lajús ◽  
A. Sinha ◽  
A. V. G. Cavalieri ◽  
C. J. Deschamps ◽  
T. Colonius
Keyword(s):  
High Reynolds Number ◽  
Base Flow ◽  
Flow Profile ◽  
Azimuthal Direction ◽  
Instability Mechanism ◽  
Helmholtz Instability ◽  
Circular Jets ◽  
Unstable Solutions ◽  
High Reynolds ◽  
Axis Switching

The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin–Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin–Helmholtz instability.

scholarly journals On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

2014 ◽  
Vol 747 ◽  
pp. 518-544 ◽  
Author(s):  
Jan Östh ◽  
Bernd R. Noack ◽  
Siniša Krajnović ◽  
Diogo Barros ◽  
Jacques Borée
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Eddy Viscosity ◽  
Initial Conditions ◽  
Base Flow ◽  
Reduced Order ◽  
State Dependent ◽  
Galerkin Models ◽  
High Reynolds ◽  
Ahmed Body

AbstractWe investigate a hierarchy of eddy-viscosity terms in proper orthogonal decomposition (POD) Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to large eddy simulation (LES) data for a flow around a vehicle-like bluff body called an Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (J. Fluid Mech., vol. 260, 1994a, pp. 351–375; J. Fluid Mech. vol. 275, 1994b, pp. 257–283). Robustness of the model solution with respect to initial conditions, eddy-viscosity values and model order is achieved only for state-dependent eddy viscosities as proposed by Noack, Morzyński & Tadmor (Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol. 528, 2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier–Stokes-based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown

1998 ◽  
Vol 366 ◽  
pp. 211-237 ◽  
Author(s):  
Z. RUSAK ◽  
S. WANG ◽  
C. H. WHITING
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Swirling Flows ◽  
Axisymmetric Vortex ◽  
Burgers Vortex ◽  
Theoretical Predictions ◽  
Necessary And Sufficient Criteria ◽  
High Reynolds ◽  
Necessary And Sufficient

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown is studied through numerical computations. These unique simulations are guided by a recent rigorous theory on this subject presented by Wang & Rusak (1997a). Using the unsteady and axisymmetric Euler equations, the nonlinear dynamics of both small- and large-amplitude disturbances in a swirling flow are described and the transition to axisymmetric breakdown is demonstrated. The simulations clarify the relation between our linear stability analyses of swirling flows (Wang & Rusak 1996a, b) and the time-asymptotic behaviour of the flow as described by steady-state solutions of the problem presented in Wang & Rusak (1997a). The numerical calculations support the theoretical predictions and shed light on the mechanism leading to the breakdown process in swirling flows. It has also been demonstrated that the fundamental characteristics which lead to vortex instability and breakdown in high-Reynolds-number flows may be calculated from considerations of a single, reduced-order, nonlinear ordinary differential equation, representing a columnar flow problem. Necessary and sufficient criteria for the onset of vortex breakdown in a Burgers vortex are presented.

Internal Aerodynamic Performance Evaluation of Double Entrance S-Duct Intake at Moderately High Subsonic Mach Number

2021 ◽  
Author(s):  
Satpreet Sidhu ◽  
Asad Asghar ◽  
William D. E. Allan ◽  
R. A. Stowe ◽  
R. Pimentel
Keyword(s):  
Mach Number ◽  
Total Pressure ◽  
Swirling Flow ◽  
Essential Element ◽  
Aerodynamic Performance ◽  
Geometric Constraints ◽  
Pressure Recovery ◽  
Data Set ◽  
Similar Work ◽  
And Performance

Abstract Inlets are an essential element of aircraft propulsion systems. Aircraft with fuselage-embedded engines require intake ducts with bends to direct oncoming air into the engine. Consequently they often experience flow separation, losses, total pressure distortion, and swirling flow near the engine faces, all of which are detrimental to engine stability and performance. In some aircraft, double-entrance ducts are used to meet geometric constraints and maintain the required airflow. The present paper investigated aerodynamic performance of a bifurcated Y-duct with S-bends in both horizontal and vertical planes. Intake performance was evaluated at inlet Ma = 0.63 by measuring the surface static pressure along the four stream-wise rows of pressure taps and total pressure and 3D velocities using 5-hole probe across the exit plane of the intake duct. The data were used to determine the static and total pressure recovery, together with associated radial and circumferential distortion coefficients and swirl intensity. This work provides a rare experimental data-set for a twin-entrance, moderately high-subsonic, double S-duct intake. It compared reasonably with the most similar work published, that of single-entrance ducts at higher Mach number. Pressure recovery was on par while swirl was noted to be reduced when compared with those geometries. Complementary computational fluid dynamics was useful in the qualitative comparisons as well.

Effect of Longitudinal Vortex on Boundary Layer State and Separation on NACA Symmetric Foil

2010 ◽  
Author(s):  
Sebastien Prothin ◽  
Henda Djeridi ◽  
Jean-Yves Billard
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shape Factor ◽  
Base Flow ◽  
Vortex Generators ◽  
Longitudinal Vortex ◽  
Velocity Measurements ◽  
Number Range ◽  
Fluid Displacement ◽  
High Reynolds

Vortex generators have been widely used in aerodynamics to control the separation of boundary layers. In such application (Angele and Muhammad, 2005) vortex generators are embedded in the boundary layer and the vortex height, with regards to the wall, is of the boundary layer thickness. The objective of this configuration is obviously far from being the effects of a single longitudinal vortex (generated upstream by an elliptical plan form profile) on the turbulent boundary layer shape over a Naca0015 symmetric foil at different incidences at high Reynolds number 5 105. The vortex is situated outside the boundary layer (ten times the BL thickness over the wall) taking into account the small value of the thickness in our hydrodynamic application. Obviously, this situation is optimum as the vortex delays separation and increases the maximum lift but introduces drag penalty at small incidence. This is nevertheless frequently encountered in hydrodynamic applications (hub vortex upstream of a rudder) and of interest. To point out the mechanism of the boundary layer manipulation, both global efforts using gauge balance and velocity measurements using LDV and PIV have been performed and compared with and without vortex. The base flow is an APG boundary layer characterized by a predominant wake area. Effect of the vortex is analyzed via the shape factor both in inflow and outflow regions. The longitudinal vortex suppress the hysteretic loop classically described in this Reynolds number range (Djeridi et al., 2009) but an increase of the drag is observed in the range of incidence just before stall. Velocity measurements indicated that, for incidences near the stall appearance, the shape factor is decreased both in the inflow and in the outflow regions. Even for large incidences, in the inflow region the value of the shape factor is equivalent to the one found in the turbulent BL over a flat plate. In this region the vortex modifies the equilibrium state of the BL as attested by the Clauser parameter. Even for large distances between the vortex and the wall, the ability of the vortex to suppress the detachment of the BL is observed on the evolution of the backflow coefficient. This effect is greater pronounced in inflow area near the trailing edge region where the flow is locally reattached due to the high momentum fluid displacement.

Non-constant Superluminal Velocities in AGN

1990 ◽  
Vol 8 (04) ◽  
pp. 353-356
Author(s):  
Colin S. Coleman
Keyword(s):  
Standing Wave ◽  
Perturbation Analysis ◽  
Large Scale ◽  
Swirling Flow ◽  
Active Galaxies ◽  
Line Of Sight ◽  
Beam Model ◽  
Radio Structure ◽  
Flow Perturbation ◽  
Relativistic Beam

AbstractLarge apparent superluminal velocities are observed in nuclear jets in Active Galaxies, indicating the presence of relativistic velocities almost along the line of sight. If the flow is well collimated, as suggested by the large scale radio structure, the inferred alignment leads to difficulties with source statistics. Here a modification of the usual relativistic beam model is proposed, in which the jet is assumed to contain azimuthal (swirling) flow. Perturbation analysis is used to show that the jet is unstable to a Kelvin-Helmholtz helical standing wave, the wavelength of which increases without bound in the limit of vanishing swirl. This instability may cause a cylindrical jet to follow a helical path in space, thereby reducing the implied alignment of a superluminal source, and providing a natural interpretation of non-constant superluminal velocities.

A local scattering approach for the effects of abrupt changes on boundary-layer instability and transition: a finite-Reynolds-number formulation for isolated distortions

2017 ◽  
Vol 822 ◽  
pp. 444-483 ◽  
Author(s):  
Zhangfeng Huang ◽  
Xuesong Wu
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Abrupt Change ◽  
Base Flow ◽  
Wall Suction ◽  
S Waves ◽  
Boundary Layer Instability ◽  
Abrupt Changes

We investigate the influence of abrupt changes on boundary-layer instability and transition. Such changes can take different forms including a local porous wall, suction/injection and surface roughness as well as junctions between rigid and porous walls. They may modify the boundary conditions and/or the mean flow, and their effects on transition have usually been assessed by performing stability analysis for the modified base flow and/or boundary conditions. However, such a conventional local linear stability theory (LST) becomes invalid if the change occurs over a relatively short scale comparable with, or even shorter than, the characteristic wavelength of the instability. In this case, the influence on transition is through scattering with the abrupt change acting as a local scatter, that is, an instability mode propagating through the region of abrupt change is scattered by the strong streamwise inhomogeneity to acquire a different amplitude. A local scattering approach (LSA) should be formulated instead, in which a transmission coefficient, defined as the ratio of the amplitude of the instability wave after the scatter to that before, is introduced to characterize the effect on instability and transition. In the present study, we present a finite-Reynolds-number formulation of LSA for isolated changes including a rigid plate interspersed by a local porous panel and a wall suction through a narrow slot. When the weak non-parallelism of the unperturbed base flow is ignored, the local scattering problem can be cast as an eigenvalue problem, in which the transmission coefficient appears as the eigenvalue. We also improved the method to take into account the non-parallelism of the unperturbed base flow, where it is found that the weak non-parallelism has a rather minor effect. The general formulation is specialized to two-dimensional Tollmien–Schlichting (T–S) waves. The resulting eigenvalue problem is solved, and full direct numerical simulations (DNS) are performed to verify some of the predictions by LSA. A parametric study indicates that conventional LST is valid only when the change is sufficiently gradual, and becomes either inaccurate or invalid when the scale of the local distortion is short. A local porous panel enhances T–S waves, while a local suction with a moderate mass flux significantly inhibits T–S waves. In the latter case, a comprehensive comparison is made between the theoretical predictions and experimental data, and a satisfactory quantitative agreement was observed.

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