scholarly journals Applying the constant strength doublet method to resolve a steady flow around an airfoil

2021 ◽  
Vol 33 ◽  
pp. 157-166
Author(s):  
Konstantin Metodiev
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Finite Number ◽  
Algebraic System ◽  
Ideal Gas ◽  
Numerical Realization ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Constant Strength ◽  
Two Dimensional Flow

In the paper hereby, a numerical (panel) method is applied to analyze steady two-dimensional flow of ideal gas around an airfoil. Initially, the airfoil is divided into a finite number of panels. Then the panels are replaced by doublets with constant strength. In addition, a wake panel is added to fulfill Kutta condition at the airfoil trailing edge. In order to implement this, a numerical realization is developed and built by means of Tiny C Compiler. To work out a solution to the linear non-homogeneous algebraic system, direct schemes for lower-upper factorization/decomposition of matrix of coefficients were applied, namely Crout, Doolittle, and Cholesky. The obtained results are validated against exact solution and shown for various values of angle of attack and Reynolds number.

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

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.

The Suppression of Shear Layer Turbulence in Rotating Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 229-235 ◽  
Author(s):  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Simple Method ◽  
Coriolis Forces ◽  
Rotating Systems ◽  
Two Dimensional Flow ◽  
High Reynolds

Stabilization of turbulent boundary layer type flows by the action of Coriolis forces engendered by system rotation is studied. Experiments on fully developed, two-dimensional flow in a long, straight channel that was rotated about an axis perpendicular to the plane of mean shear are reviewed to demonstrate the principal effects of stabilization. In particular, the delay of transition to turbulence on the stabilized side of the channel to high Reynolds number (u¯mh/ν) as the rotation number (|Ω|h/u¯m) is increased is demonstrated. A simple method which utilizes the eddy Reynolds number criterion of Bradshaw, is employed to show that rotation-induced suppression of transition may be predicted for the channel flow case. The applicability of the predictive method to boundary layer type flows is indicated.

Resistance of Two Inclined Parallel Flat Plates Placed in Tandem on a Stream-Wise Flat Plate in Two-Dimensional Flow

1993 ◽  
Vol 207 (6) ◽  
pp. 393-397
Author(s):  
R C Mehta ◽  
C R Rao ◽  
Y N Dubey
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Flow Direction ◽  
Considerable Extent ◽  
Appreciable Effect ◽  
Two Dimensional ◽  
Flat Plates ◽  
Dimensional Flow ◽  
Two Dimensional Flow

The paper presents the results of an experimental study on the drag coefficient of two inclined parallel flat plates, placed on a stream-wise flat plate, in tandem, in two-dimensional flow. The effects on the drag coefficient of Reynolds number, the inclination of the plates to the flow direction and the relative spacing between plates were studied. It is observed that, while the Reynolds number has no appreciable effect, the other parameters influence the drag coefficient to a considerable extent. The results are corrected for blockage effect and comparisons are made with the data collected by other investigators.

Hydraulic jumps in a shallow flow down a slightly inclined substrate

2015 ◽  
Vol 782 ◽  
pp. 5-24 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Free Surface Flows ◽  
Hydraulic Jumps ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Surface Flows ◽  
Asymptotic Equations ◽  
Two Dimensional Flow ◽  
Existence Criterion

This work examines free-surface flows down an inclined substrate. The slope of the free surface and that of the substrate are both assumed small, whereas the Reynolds number $Re$ remains unrestricted. A set of asymptotic equations is derived, which includes the lubrication and shallow-water approximations as limiting cases (as $Re\rightarrow 0$ and $Re\rightarrow \infty$, respectively). The set is used to examine hydraulic jumps (bores) in a two-dimensional flow down an inclined substrate. An existence criterion for steadily propagating bores is obtained for the $({\it\eta},s)$ parameter space, where ${\it\eta}$ is the bore’s downstream-to-upstream depth ratio, and $s$ is a non-dimensional parameter characterising the substrate’s slope. The criterion reflects two different mechanisms restricting bores. If $s$ is sufficiently large, a ‘corner’ develops at the foot of the bore’s front – which, physically, causes overturning. If, in turn, ${\it\eta}$ is sufficiently small (i.e. the bore’s relative amplitude is sufficiently large), the non-existence of bores is caused by a stagnation point emerging in the flow.

Wake behaviour and instability of flow through a partially blocked channel

2007 ◽  
Vol 582 ◽  
pp. 319-340 ◽  
Author(s):  
M. D. GRIFFITH ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN ◽  
W. P. ANDERSON
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
Recirculation Bubble ◽  
Dimensional Flow ◽  
Starting Point ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
The Stability

The two-dimensional flow through a constricted channel is studied. A semi-circular bump is located on one side of the channel and the extent of blockage is varied by adjusting the radius of the bump. The blockage is varied between 0.05 and 0.9 of the channel width and the upstream Reynolds number between 25 and 3000. The geometry presents a simplified blockage specified by a single parameter, serving as a starting point for investigations of other more complex blockage geometries. For blockage ratios in excess of 0.4, the variation of reattachment length with Reynolds number collapses to within approximately 15%, while at lower ratios the behaviour differs. For the constrained two-dimensional flow, various phenomena are identified, such as multiple mini-recirculations contained within the main recirculation bubble and vortex shedding at higher Reynolds numbers. The stability of the flow to three-dimensional perturbations is analysed, revealing a transition to a three-dimensional state at a critical Reynolds number which decreases with higher blockage ratios. Separation lengths and the onset and structure of three-dimensional instability observed from the geometry of blockage ratio 0.5 resemble results taken from backward-facing step investigations. The question of the underlying mechanism behind the instability being either centrifugal or elliptic in nature and operating within the initial recirculation zone is analytically tested.

Stability and Scalar Transport in Laminar Non-Newtonian Flow in a Bifurcating T-Junction

2019 ◽  
Author(s):  
Ajay Chatterjee ◽  
Fatemeh Khalkhal
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Volume Averaging ◽  
Scalar Transport ◽  
Linear Perturbation ◽  
Perturbation Equation ◽  
Two Dimensional ◽  
Two Dimensional Flow

Abstract We consider the prototype bifurcating T-junction planar flow and compare the stability of the steady two-dimensional flow field for a Newtonian and a shear thinning inelastic fluid. Global stability of the flow to two-dimensional perturbations is analyzed using numerical solutions of the linear perturbation equation. Calculations are performed for two flow ratios between the main channel and the bifurcating channel, and for two different values of the time constant in the non-Newtonian rheological model. The results show that although the steady flow remains stable to two-dimensional perturbations for Newtonian Reynolds number up to ∼ 400, shear thinning is destabilizing in that the decay rate of the perturbation field is slower. The perturbation growth rate curves for all of the different cases may be correlated by volume averaging the local Reynolds number over the flow domain, indicating that the effect of shear thinning on stability may be described using a suitably defined average Reynolds number. These stability results provide some justification for CFD calculations of steady non-Newtonian two-dimensional flows presented in earlier papers. Since scalar transport is of interest in this flow field, we also present some numerical calculations for the Nusselt number profile along the bifurcating channel wall. The results show that for the shear thinning fluid the scalar transport rate is differentially larger by ∼ 75% across one of the bifurcating channel walls, a consequence of fluid rheology enhancing the effect of flow asymmetry in the entrance region of the bifurcation.

Pressure-driven flow in a two-dimensional channel with porous walls

2009 ◽  
Vol 631 ◽  
pp. 1-21 ◽  
Author(s):  
QUAN ZHANG ◽  
ANDREA PROSPERETTI
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Hydrodynamic Force ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Slip Coefficient ◽  
Staggered Arrangement ◽  
Two Dimensional Flow ◽  
Porous Walls ◽  
Pressure Driven Flow

The finite-Reynolds-number two-dimensional flow in a channel bounded by a porous medium is studied numerically. The medium is modelled by aligned cylinders in a square or staggered arrangement. Detailed results on the flow structure and slip coefficient are reported. The hydrodynamic force and couple acting on the cylinder layer bounding the porous medium are also evaluated as a function of the Reynolds number. In particular, it is shown that, at finite Reynolds numbers, a lift force acts on the bodies, which may be significant for the mobilization of bottom sediments.

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