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 Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

2019 ◽  
Vol 877 ◽  
pp. 1163-1185 ◽  
Author(s):  
Junhao Ke ◽  
N. Williamson ◽  
S. W. Armfield ◽  
G. D. McBain ◽  
S. E. Norris
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Linear Stability ◽  
Transition Point ◽  
Three Dimensional ◽  
Base Flow ◽  
Convection Boundary Layer ◽  
Two Dimensional ◽  
Integral Boundary ◽  
Convection Boundary

The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a ‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$, where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$, according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.

scholarly journals Quasi-two-dimensional approximation for numerical simulation of flows in engine ducts

2019 ◽  
Author(s):  
V. Vlasenko ◽  
A. Shiryaeva
Keyword(s):  
High Speed ◽  
Fuel Injection ◽  
Three Dimensional ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Combustion Chambers ◽  
New Approach ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
3D Flows

New quasi-two-dimensional (2.5D) approach to description of three-dimensional (3D) flows in ducts is proposed. It generalizes quasi-one-dimensional (quasi-1D, 1.5D) theories. Calculations are performed in the (x; y) plane, but variable width of duct in the z direction is taken into account. Derivation of 2.5D approximation equations is given. Tests for verification of 2.5D calculations are proposed. Parametrical 2.5D calculations of flow with hydrogen combustion in an elliptical combustor of a high-speed aircraft, investigated within HEXAFLY-INT international project, are described. Optimal scheme of fuel injection is found and explained. For one regime, 2.5D and 3D calculations are compared. The new approach is recommended for use during preliminary design of combustion chambers.

Study of High Speed Turbulent Flow Over Rotating Two Stage Three Dimensional Double Wedge

2006 ◽  
Author(s):  
Khaled Alhussan
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Mach Number ◽  
Shock Waves ◽  
High Speed ◽  
Three Dimensional ◽  
Oblique Shock ◽  
Wave Interactions ◽  
Double Wedge ◽  
Slip Surfaces

In this paper some characteristics of non-steady, compressible, flow are explored, including compression and expansion wave interactions and creation. The work to be presented herein is a Computational Fluid Dynamics investigation of the complex fluid phenomena that occur inside three-dimensional region, specifically with regard to the structure of the oblique shock waves, the reflected shock waves and the interactions of the shock waves. The flow is so complex that there exist oblique shock waves, expansion fans, slip surfaces, and shock wave interactions and reflections. The flow is non-steady, turbulent, viscous, compressible, and high-speed supersonic. The work to be presented herein is a Computational Fluid Dynamics analysis of flow over a 15-degree angle double wedge for a compressible air, with spin angle of 10-degree and Mach number of 2.5. The problem to be solved involves formation of shock waves, expansion fans and slip surfaces, so that the general characteristics of supersonic flow are explored through this problem. Shock waves and slip surfaces are discontinuities in fluid mechanics problems. It is essential to evaluate the ability of numerical technique that can solve problems in which shocks and contact surfaces occur. In particular it is necessary to understand the details of developing a mesh that will allow resolution of these discontinuities. Results including contour plots of pressure, temperature, and Mach number will show that CFD is capable of predicting accurate results and is also able to capture the discontinuities in the flow, e.g., the oblique shock waves and the slip surfaces. Through this computational analysis, a better interpretation of the physical phenomenon of the three-dimensional shock waves interaction and reflection can be achieved.

Experimental Study on Gravity Driven Discharging of Quasi-Two-Dimensional Pebble Bed Based on Mathematical Morphology

2020 ◽  
Author(s):  
Yujia Liu ◽  
Sifan Peng ◽  
Nan Gui ◽  
Xingtuan Yang ◽  
Jiyuan Tu ◽  
...  
Keyword(s):  
Experimental Study ◽  
Mathematical Morphology ◽  
High Speed ◽  
Three Dimensional ◽  
Reactor Core ◽  
Engineering Application ◽  
Discharge Process ◽  
Two Dimensional ◽  
Pebble Bed ◽  
Gravity Driven

Abstract The pebbles flow is a fundamental issue for both academic investigation and engineering application in reactor core design and safety analysis. In general, experimental methods including spiral X-ray tomography and refractive index matched scanning technique (RIMS) are applied to obtain the identification of particles’ positions within a three-dimensional pebble bed. However, none of the above methods can perform global bed particles’ position identification in a dynamically discharging pebble bed, and the corresponding experimental equipment is difficult to access due to the complication and high expense. In this research, the experimental study is conducted to observe the gravity driven discharging process in the quasi two-dimensional silos by making use of the high-speed camera and the uniform backlight. A mathematical morphology-based method is applied to the pre-processing of the captured results. After being increased the gray value gradient by the threshold segmentation, the edges of the particles are identified and smoothed by the Sobel algorithm and the morphological opening operation. The particle centroid coordinates are identified according to the Hough circle transformation of the edges. For the whole pebble bed, the self-programmed process has a particle recognition accuracy of more than 99% and a particle centroid position deviation of less than 3%, which can accurately obtain the physical positions of all particles in the entire dynamically discharge process. By analyzing the position evolution of individual particles in consecutive images, velocity field and motion events of particles are observed. The discharging profiles of 5 conditions with different exit are analyzed in this experiment. The results make a contribution to improving the understanding of the mechanism of pebbles flow in nuclear engineering.

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.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

1997 Best Paper Award—Turbomachinery Committee: A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1998 ◽  
Vol 120 (3) ◽  
pp. 393-401 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Short Length ◽  
Operating Conditions ◽  
Length Scale ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms in a low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short length-scale disturbance known as a “spike,” and the second with a longer length-scale disturbance known as a “modal oscillation.” In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented that relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: Long length-scale disturbances are related to a two-dimensional instability of the whole compression system, while short length-scale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed that explains the type of stall inception pattern observed in a particular compressor. Measurements from a single-stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

scholarly journals On the stability of plane Couette–Poiseuille flow with uniform crossflow

2010 ◽  
Vol 656 ◽  
pp. 417-447 ◽  
Author(s):  
ANIRBAN GUHA ◽  
IAN A. FRIGAARD
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Energy Production ◽  
Base Flow ◽  
Two Dimensional ◽  
Wall Velocity ◽  
Resonant Interactions ◽  
Flow Stabilization ◽  
Tollmien Schlichting ◽  
The Stability

We present a detailed study of the linear stability of the plane Couette–Poiseuille flow in the presence of a crossflow. The base flow is characterized by the crossflow Reynolds number Rinj and the dimensionless wall velocity k. Squire's transformation may be applied to the linear stability equations and we therefore consider two-dimensional (spanwise-independent) perturbations. Corresponding to each dimensionless wall velocity, k ∈ [0, 1], two ranges of Rinj exist where unconditional stability is observed. In the lower range of Rinj, for modest k we have a stabilization of long wavelengths leading to a cutoff Rinj. This lower cutoff results from skewing of the velocity profile away from a Poiseuille profile, shifting of the critical layers and the gradual decrease of energy production. Crossflow stabilization and Couette stabilization appear to act via very similar mechanisms in this range, leading to the potential for a robust compensatory design of flow stabilization using either mechanism. As Rinj is increased, we see first destabilization and then stabilization at very large Rinj. The instability is again a long-wavelength mechanism. An analysis of the eigenspectrum suggests the cause of instability is due to resonant interactions of Tollmien–Schlichting waves. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality. The stabilization at very large Rinj appears to be due to decay in energy production, which diminishes like Rinj−1. Our study is limited to two-dimensional, spanwise-independent perturbations.

A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1997 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms a in low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short lengthscale disturbance known as a ‘spike’, and the second with a longer lengthscale disturbance known as a ‘modal oscillation’. In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented which relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: long lengthscale disturbances are related to a two-dimensional instability of the whole compression system, while short lengthscale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed which explains the type of stall inception pattern observed in a particular compressor. Measurements from a single stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

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