Modeling of External Pressure Gradient Influence on the Stability of Disturbances in the Boundary Layers of Compressed Gas

2013 ◽  
Vol 8 (4) ◽  
pp. 64-75
Author(s):  
Sergey Gaponov ◽  
Natalya Terekhova
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
External Pressure ◽  
Transition To Turbulence ◽  
Compressed Gas ◽  
High Mach ◽  
The Stability ◽  
Very High

This work continues the research on modeling of passive methods of management of flow regimes in the boundary layers of compressed gas. Authors consider the influence of pressure gradient on the evolution of perturbations of different nature. For low Mach number M = 2 increase in pressure contributes to an earlier transition of laminar to turbulent flow, and, on the contrary, drop in the pressure leads to a prolongation of the transition to turbulence. For high Mach number M = 5.35 found that the acoustic disturbances exhibit a very high dependence on the sign and magnitude of the external gradient, with a favorable gradient of the critical Reynolds number becomes smaller than the vortex disturbances, and at worst – boundary layer is destabilized directly on the leading edge

The Influence of Attached Boundary Layers in Determining the Optimum Loading for Blades in Cascade

1965 ◽  
Vol 69 (650) ◽  
pp. 133-135
Author(s):  
B. S. Stratford
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
High Efficiency ◽  
Present Note ◽  
Maximum Efficiency ◽  
Critical Mach Number ◽  
Maximum Loading ◽  
Very High

In the design of cascade blading for compressors and turbines it is often assumed that the maximum efficiency will be attained at the maximum loading that just avoids separation and critical Mach number effects. In a turbine, the overall pressure gradient is favourable so that it should be possible to achieve very high loadings and yet avoid separation. The question then arises as to whether or not such high loadings would produce a high efficiency. The present note suggests that in fact there is an optimum loading, beyond which there would be no improvement in efficiency even though separation and critical Mach number effects were avoided.

Numerical Investigation of the Solidity Effect on Linear Compressor Cascades

2014 ◽  
Author(s):  
J. Sans ◽  
M. Resmini ◽  
J.-F. Brouckaert ◽  
S. Hiernaux
Keyword(s):  
Numerical Investigation ◽  
State Of The Art ◽  
Leading Edge ◽  
Operating Conditions ◽  
Compressor Cascade ◽  
Minimum Loss ◽  
Low Speed ◽  
High Mach ◽  
The Stability ◽  
The Impact

Solidity in compressors is defined as the ratio of the aerodynamic chord over the peripheral distance between two adjacent blades, the pitch. This parameter is simply the inverse of the pitch-to-chord ratio generally used in turbines. Solidity must be selected at the earliest design phase, i.e. at the level of the meridional design and represents a crucial step in the whole design process. Most of the existing studies on this topic rely on low-speed compressor cascade correlations from Carter or Lieblein. The aim of this work is to update those correlations for state-of-the-art controlled diffusion blades, and extend their application to high Mach number flow regimes more typical of modern compressors. Another objective is also to improve the physical understanding of the solidity effect on compressor performance and stability. A numerical investigation has been performed using the commercial software FINE/Turbo. Two different blade profiles were selected and investigated in the compressible flow regime as an extension to the low-speed data on which the correlations are based. The first cascade uses a standard double circular arc profile, extensively referenced in the literature, while the second configuration uses a state-of-the-art CDB, representative of low pressure compressor stator mid-span profile. Both profiles have been designed with the same inlet and outlet metal angles and the same maximum thickness but the camber and thickness distributions, the stagger angle and the leading edge geometry of the CDB have been optimized. The determination of minimum loss, optimum incidence and deviation is addressed and compared with existing correlations for both configurations and various Mach numbers that have been selected in order to match typical booster stall and choke operating conditions. The emphasis is set on the minimum loss performance at mid-span. The impact of the solidity on the operating range and the stability of the cascade are also studied.

Measurements in adverse-pressure-gradient turbulent boundary layers with a step change in surface roughness

1975 ◽  
Vol 70 (3) ◽  
pp. 573-593 ◽  
Author(s):  
W. H. Schofield
Keyword(s):  
Surface Roughness ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Step Change ◽  
Internal Layer ◽  
Mean Velocity ◽  
Law Of The Wall

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

Buoyant convection from horizontal surfaces at const ant pressure

1975 ◽  
Vol 68 (3) ◽  
pp. 609-624 ◽  
Author(s):  
S. C. Traugott
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Line Source ◽  
Leading Edge ◽  
Wall Jet ◽  
Two Dimensional ◽  
Buoyant Plume ◽  
Grashof Number ◽  
Buoyancy Driven Flows ◽  
Streamwise Pressure Gradient

A two-dimensional horizontal flow is discussed, which is induced by other, buoyancy-driven flows elsewhere. It is an adaptation of the incompressible wall jet, which is driven by conditions a t the leading edge and has no streamwise pressure gradient. The relation of this flow to the classical buoyancy-driven boundary layers on inclined and horizontal surfaces is investigated, as well as its possible connexion with a two-dimensional buoyant plume driven by a line source of heat. Composite flows are constructed by patching various such solutions together. The composite flows exhibit$Gr^{\frac{1}{4}}$scaling (Grbeing the Grashof number).

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

2D and 3D Stability of Cavity Flows in High Mach Number Regimes

2019 ◽  
Author(s):  
Parshwanath S. Doshi ◽  
Rajesh Ranjan ◽  
Datta V. Gaitonde
Keyword(s):  
Stability Analysis ◽  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Flame Holder ◽  
High Mach Number ◽  
Eddy Simulation ◽  
High Mach ◽  
The Stability

Abstract The stability characteristics of an open cavity flow at very high Mach number are examined with BiGlobal stability analysis based on the eigenvalues of the linearized Navier-Stokes equations. During linearization, all possible first-order terms are retained without any approximation, with particular emphasis on extracting the effects of compressibility on the flowfield. The method leverages sparse linear algebra and the implicitly restarted shift-invert Arnoldi algorithm to extract eigenvalues of practical physical consequence. The stability dynamics of cavity flows at four Mach numbers between 1.4 and 4 are considered at a Reynolds number of 502. The basic states are obtained through Large Eddy Simulation (LES). Frequency results from the stability analysis show good agreement when compared to the theoretical values using Rossiter’s formula. An examination of the stability modes reveals that the shear layer is increasingly decoupled from the cavity as the Mach number is increased. Additionally, the outer lobes of the Rossiter modes are observed to get stretched and tilted in the direction of the freestream. Future efforts will extend the present analysis to examine current and potential cavity flame holder configurations, which often have downstream walls inclined to the vertical.

scholarly journals The stability of a trailing-line vortex in compressible flow

1994 ◽  
Vol 269 ◽  
pp. 323-351 ◽  
Author(s):  
Jillian A. K. Stott ◽  
Peter W. Duck
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Numerical Results ◽  
Line Vortex ◽  
Mach Numbers ◽  
The Stability ◽  
Vortex Axis ◽  
Very High ◽  
High Wavenumbers

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (azimuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, whilst a new ‘centre mode’ forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex.Throughout the paper comparison is made between our numerical results and results obtained from the various asymptotic theories.

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