scholarly journals Effect of compressibility on the global stability of axisymmetric wake flows

2010 ◽  
Vol 660 ◽  
pp. 499-526 ◽  
Author(s):  
P. MELIGA ◽  
D. SIPP ◽  
J.-M. CHOMAZ
Keyword(s):  
Mach Number ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Global Instability ◽  
Linear Dynamics ◽  
Wake Flows ◽  
Sensitivity Functions ◽  
Flow Profiles ◽  
Subsonic Regime ◽  
Compressibility Effects

We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence suggesting that the onset of unsteadiness in this class of flows results from a global instability. We determine the boundary separating the stable and unstable domains in the (M, Re) plane, and show that an increase in the Mach number yields a stabilization of the afterbody flow, but a destabilization of the sphere flow. These compressible effects are further investigated by means of adjoint-based sensitivity analyses relying on the computation of gradients or sensitivity functions. Using this theoretical formalism, we show that they do not act through specific compressibility effects at the disturbance level but mainly through implicit base flow modifications, an effect that had not been taken into consideration by previous studies based on prescribed parallel base flow profiles. We propose a physical interpretation for the observed compressible effects, based on the competition between advection and production of disturbances, and provide evidence linking the stabilizing/destabilizing effect observed when varying the Mach number to a strengthening/weakening of the disturbance advection mechanism. We show, in particular, that the destabilizing effect of compressibility observed in the case of the sphere results from a significant increase of the backflow velocity in the whole recirculating bubble, which opposes the downstream advection of disturbances.

Compressibility effects on the structural evolution of transitional high-speed planar wakes

2016 ◽  
Vol 796 ◽  
pp. 5-39 ◽  
Author(s):  
Jean-Pierre Hickey ◽  
Fazle Hussain ◽  
Xiaohua Wu
Keyword(s):  
Mach Number ◽  
Linear Stability ◽  
High Speed ◽  
Three Dimensional ◽  
Structural Evolution ◽  
Base Flow ◽  
Length Scale ◽  
Two Dimensional ◽  
Linear Mode ◽  
Compressibility Effects

The compressibility effects on the structural evolution of the transitional high-speed planar wake are studied. The relative Mach number ($Ma_{r}$) of the laminar base flow modifies two fundamental features of planar wake transition: (i) the characteristic length scale defined by the most unstable linear mode; and (ii) the domain of influence of the structures within the staggered two-dimensional vortex array. Linear stability results reveal a reduced growth (approximately 30 % reduction up to $Ma_{r}=2.0$) and a quasilinear increase of the wavelength of the most unstable, two-dimensional instability mode (approximately 20 % longer over the same $Ma_{r}$ range) with increasing $Ma$. The primary wavelength defines the length scale imposed on the emerging transitional structures; naturally, a longer wavelength results in rollers with a greater streamwise separation and hence also larger circulation. A reduction of the growth rate and an increase of the principal wavelength results in a greater ellipticity of the emerging rollers. Compressibility effects also modify the domain of influence of the transitional structures through an increased cross-wake and inhibited streamwise communication as characteristic paths between rollers are deflected due to local $Ma$ gradients. The reduced streamwise domain of influence impedes roller pairing and, for a sufficiently large relative $Ma$, pairing is completely suppressed. Thus, we observe an increased two-dimensionality with increasing Mach number: directly contrasting the increasing three-dimensional effects in high-speed mixing layers. Temporally evolving direct numerical simulations conducted at $Ma=0.8$ and 2.0, for Reynolds numbers up to 3000, support the physical insight gained from linear stability and vortex dynamics studies.

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

scholarly journals The onset of compressibility effects for aerofoils in ground effect

2007 ◽  
Vol 111 (1126) ◽  
pp. 797-806 ◽  
Author(s):  
G. Doig ◽  
T. J. Barber ◽  
E. Leonardi ◽  
A. J. Neely
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Subsonic Flow ◽  
Flow Characteristics ◽  
Ground Effect ◽  
Aerodynamic Performance ◽  
Computational Studies ◽  
Pressure Gradients ◽  
Cfd Simulations ◽  
Compressibility Effects

Abstract The influence of flow compressibility on a highly-cambered inverted aerofoil in ground effect is presented, based on two-dimensional computational studies. This type of problem has relevance to open-wheel racing cars, where local regions of high-speed subsonic flow form under favourable pressure gradients, even though the maximum freestream Mach number is typically considerably less than Mach 0·3. An important consideration for CFD users in this field is addressed in this paper: the freestream Mach number at which flow compressibility significantly affects aerodynamic performance. More broadly, for aerodynamicists, the consequences of this are also considered. Comparisons between incompressible and compressible CFD simulations are used to identify important changes to the flow characteristics caused by density changes, highlighting the inappropriateness of incompressible simulations of ground effect flows for freestream Mach numbers as low as 0·15.

scholarly journals Global stability of buoyant jets and plumes

2017 ◽  
Vol 835 ◽  
pp. 654-673 ◽  
Author(s):  
R. V. K. Chakravarthy ◽  
L. Lesshafft ◽  
P. Huerre
Keyword(s):  
Global Stability ◽  
Richardson Number ◽  
Base Flow ◽  
Shear Instability ◽  
Absolute Instability ◽  
Global Instability ◽  
Buoyant Jets ◽  
Physical Mechanisms ◽  
Basic Shear ◽  
Density Ratios

The linear global stability of laminar buoyant jets and plumes is investigated under the low-Mach-number approximation. For Richardson numbers in the range $10^{-4}\leqslant Ri\leqslant 10^{3}$ and density ratios $S=\unicode[STIX]{x1D70C}_{\infty }/\unicode[STIX]{x1D70C}_{jet}$ between 1.05 and 7, only axisymmetric perturbations are found to exhibit global instability, consistent with experimental observations in helium jets. By varying the Richardson number over seven decades, the effects of buoyancy on the base flow and on the instability dynamics are characterised, and distinct behaviour is observed in the low-$Ri$ (jet) and in the high-$Ri$ (plume) regimes. A sensitivity analysis indicates that different physical mechanisms are responsible for the global instability dynamics in both regimes. In buoyant jets at low Richardson number, the baroclinic torque enhances the basic shear instability, whereas buoyancy provides the dominant instability mechanism in plumes at high Richardson number. The onset of axisymmetric global instability in both regimes is consistent with the presence of absolute instability. While absolute instability also occurs for helical perturbations, it appears to be too weak or too localised to give rise to a global instability.

scholarly journals Optimal streaks in the circular cylinder wake and suppression of the global instability

2014 ◽  
Vol 752 ◽  
pp. 572-588 ◽  
Author(s):  
Gerardo Del Guercio ◽  
Carlo Cossu ◽  
Gregory Pujals
Keyword(s):  
Circular Cylinder ◽  
Maximum Amplitude ◽  
Reynolds Numbers ◽  
High Energy ◽  
Linear Instability ◽  
Sensitivity Analyses ◽  
Cylinder Wake ◽  
Global Instability ◽  
Streamwise Streaks ◽  
Energy Amplification

AbstractThe steady, spanwise-periodic, symmetric (varicose) optimal blowing and suction that maximizes energy amplification in the circular cylinder wake is computed at Reynolds numbers ranging from 50 to 100. It is found that the cylinder wake can sustain large energy amplifications that are associated with the generation by the optimal blowing and suction of streamwise vortices near the cylinder, which then induce the transient spatial growth of high-energy streamwise streaks further downstream. The most amplified perturbations have spanwise wavelengths ranging from five to seven times the cylinder diameter at the Reynolds numbers considered, with the corresponding optimal streaks reaching their maximum amplitude in the near wake, inside the pocket of absolute instability which sustains the global instability. The optimal blowing and suction is shown to stabilize the global linear instability. The most stabilizing spanwise wavelengths are in good agreement with previous findings. The amplitude of optimal blowing and suction required to suppress the global instability decreases when the Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}$ is increased from 75 to 100. This trend reveals the key role played by the non-normal amplification of the streaks in the stabilization process, which is able to overcome the increase of the uncontrolled global growth rate with $\mathit{Re}$. Finally, it is shown that the global instability can be suppressed with control amplitudes smaller than those required by 2-D (spanwise-uniform) control. This result is not what would be expected from first-order sensitivity analyses, which predict a zero sensitivity of the global instability to spanwise-periodic control and, in general, a non-zero sensitivity to spanwise-uniform control.

Theory of low Mach number compressible flow in a channel

1996 ◽  
Vol 313 ◽  
pp. 131-145 ◽  
Author(s):  
A. Shajii ◽  
J. P. Freidberg
Keyword(s):  
Steady State ◽  
Mach Number ◽  
Aspect Ratio ◽  
Compressible Flow ◽  
Applied Pressure ◽  
Subsonic Flows ◽  
Low Mach Number ◽  
Large Channel ◽  
Channel Aspect Ratio ◽  
Compressibility Effects

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.

On the benefits of lower Mach number aircraft cruise

2007 ◽  
Vol 111 (1122) ◽  
pp. 531-542 ◽  
Author(s):  
A. Filippone
Keyword(s):  
Mach Number ◽  
Fuel Consumption ◽  
Long Range ◽  
Optimal Operation ◽  
Environmental Benefits ◽  
Sensitivity Analyses ◽  
Commercial Aircraft ◽  
Transport Aircraft ◽  
Marginal Delay ◽  
Heat Released

Abstract The paper reviews the issue of cruise Mach number and addresses the benefits of operating subsonic commercial aircraft at speeds below the long-range cruise speed. The case considered is the flight of transport aircraft for flight segments up to 1,000nm. It is shown that the fuel burned is decreased by as much as 1·8% on a nominal 1,000nm stage length for operation around the long-range cruise Mach number, or below. This is achieved at a cost of a marginal delay on each flight segment (less than three minutes). The longer flight time is likely not to affect the daily operation of the aircraft. The fuel saving is compounded, because the gross take-off weight (GTOW) is recalculated to take into account the reduced fuel consumption at each flight segment. The analysis into the environmental benefits includes the reduction in,andemissions, and the heat released in the high atmosphere. Sensitivity analyses are carried out on the take-off weight, on the aerodynamic coefficients, on the transonic drag rise and the weight uncertainty. It is predicted that the optimal operation of the example aircraft over a nominal 1,000nm route can reduce the fuel consumption by as much as 150,000kg per year in comparison with an operation at the long-range Mach number. The aircraft model has a maximum take-off weight of 170,000kg and is powered by two GE CF6-80C2 engines.

scholarly journals Investigation of base flow for an axisymmetric suddenly expanded nozzle with micro JET

2018 ◽  
Vol 7 (3.29) ◽  
pp. 236 ◽  
Author(s):  
Zakir Ilahi Chaudhary ◽  
Vilas B. Shinde ◽  
S A. Khan
Keyword(s):  
Mach Number ◽  
Pressure Range ◽  
Base Flow ◽  
Base Pressure ◽  
Small Scale ◽  
Sectional Area ◽  
Circulation Zone ◽  
Cross Sectional ◽  
D Values ◽  
The Given

This investigation presents the outcome of the tests conducted to control the pressure in the re-circulation zone. Also, the efficiency of the flow controllers to govern the pressure at the base in a rapidly expanded pipe has been investigated. Tiny jets our in number of 1 mm diameter are positioned at the interval of 90 degrees at 6.5 mm from the central axis of the main jet. The Mach numbers of the abruptly expanded flows studied for base pressure range from 1.1 to 3 and the obtained wall pressure distribution is depicted for Mach number 1.6 and 1.8 respectively. Axi-symmetric round brass tubes were used to join jets; and cross-sectional area of those tubes are 2.56. L/D ratio of the broadened pipe was differed from 1 to 10 and NPR was shifted from 3 to 11. Notwithstanding, the outcomes displayed were for Low L/D values of 4, 3, 2 and 1 individually. Also, when the stream was released to the pipes of the given area ratios, it stayed connected with the channel divider for all the inertial levels and the NPRs tried in the present case. Further it is understood that level of expansion assumes a noteworthy part to choose the pressure at the base and its control adequacy. At whatever point, the stream is over expanded, it leads to the formation of an oblique shock at the nozzle lip, prompting improvement of the pressure in the base locale. Shock waves formation, reflection and recombination proceeded till the pressure winds up noticeably environmental and seen that the stream stays intact for low L/D ratio of 4. Very small scale (micro) jets proved to fit in as controllers for the base pressure.  

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.

Sign in / Sign up

Export Citation Format

Share Document