Character of simplified Navier-Stokes equations for near the leading edge part of two-dimensional laminar flow past a flat plate

1994 ◽  
Vol 12 (4) ◽  
pp. 351-360
Author(s):  
Tian Ji-wei ◽  
Wang Xin-sheng
Keyword(s):  
Laminar Flow ◽  
Flat Plate ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Edge Part

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

scholarly journals Unsteady Reversed Stagnation-Point Flow over a Flat Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Vai Kuong Sin ◽  
Chon Kit Chio
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Total Flow ◽  
Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

Prediction of Flow Behavior on Diffuser Angle in an Enclosure

2005 ◽  
Author(s):  
B. Tripathi ◽  
R. C. Arora ◽  
S. G. Moulic
Keyword(s):  
Laminar Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Flow Behavior ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Specific Location ◽  
Temperature Distributions ◽  
Diffuser Angle

The present investigation deals with numerical prediction of airflow pattern in a room (enclosure) with a specific location of inlet and outlet with different values of Gr/Re2. Two-dimensional, steady, incompressible, laminar flow under Boussinesq’s approximation has been considered. The velocity and temperature distributions in a room have been found by solving Navier Stokes equations and energy equation numerically by SIMPLE and SIMPLEC algorithms.

The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions

2016 ◽  
Vol 792 ◽  
pp. 499-525 ◽  
Author(s):  
Hui Xu ◽  
Spencer J. Sherwin ◽  
Philip Hall ◽  
Xuesong Wu
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Transmission Coefficient ◽  
Stokes Equations ◽  
Base Flow ◽  
Navier Stokes ◽  
Small Scale ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Tollmien Schlichting

This paper is concerned with the behaviour of Tollmien–Schlichting (TS) waves experiencing small localised distortions within an incompressible boundary layer developing over a flat plate. In particular, the distortion is produced by an isolated roughness element located at $\mathit{Re}_{x_{c}}=440\,000$. We considered the amplification of an incoming TS wave governed by the two-dimensional linearised Navier–Stokes equations, where the base flow is obtained from the two-dimensional nonlinear Navier–Stokes equations. We compare these solutions with asymptotic analyses which assume a linearised triple-deck theory for the base flow and determine the validity of this theory in terms of the height of the small-scale humps/indentations taken into account. The height of the humps/indentations is denoted by $h$, which is considered to be less than or equal to $x_{c}\mathit{Re}_{x_{c}}^{-5/8}$ (corresponding to $h/{\it\delta}_{99}<6\,\%$ for our choice of $\mathit{Re}_{x_{c}}$). The rescaled width $\hat{d}~(\equiv d/(x_{c}\mathit{Re}_{x_{c}}^{-3/8}))$ of the distortion is of order $\mathit{O}(1)$ and the width $d$ is shorter than the TS wavelength (${\it\lambda}_{TS}=11.3{\it\delta}_{99}$). We observe that, for distortions which are smaller than 0.1 of the inner deck height ($h/{\it\delta}_{99}<0.4\,\%$), the numerical simulations confirm the asymptotic theory in the vicinity of the distortion. For larger distortions which are still within the inner deck ($0.4\,\%<h/{\it\delta}_{99}<5.5\,\%$) and where the flow is still attached, the numerical solutions show that both humps and indentations are destabilising and deviate from the linear theory even in the vicinity of the distortion. We numerically determine the transmission coefficient which provides the relative amplification of the TS wave over the distortion as compared to the flat plate. We observe that for small distortions, $h/{\it\delta}_{99}<5.5\,\%$, where the width of the distortion is of the order of the boundary layer, a maximum amplification of only 2 % is achieved. This amplification can however be increased as the width of the distortion is increased or if multiple distortions are present. Increasing the height of the distortion so that the flow separates ($7.2\,\%<h/{\it\delta}_{99}<12.8\,\%$) leads to a substantial increase in the transmission coefficient of the hump up to 350 %.

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

2016 ◽  
Vol 9 (2) ◽  
pp. 239-261 ◽  
Author(s):  
X. He ◽  
C. Vuik
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Flat Plate ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Driven Cavity

AbstractIn this paper we explore the performance of the SIMPLER, augmented Lagrangian, ‘grad-div’ preconditioners and their new variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem the Reynolds number varies from a low to the limiting number for a laminar flow.

Flow Past a Forced Oscillating Cylinder: A Three-Dimensional Numerical Study

2019 ◽  
Author(s):  
Huan Ping ◽  
Yan Bao ◽  
Dai Zhou ◽  
Zhaolong Han
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Two Dimensional Flow

Abstract In this paper, we conducted a three-dimensional investigation of flow past a cylinder undergoing forced oscillation. The flow configuration is similar to the work of Blackburn & Henderson (1999) [1], in which Reynolds number equals to 500 and a fixed motion amplitude of A/D = 0.25. The oscillation frequencies are varied in the range near to the natural shedding frequency of a stationary cylinder. The flow dynamics are governed by Navier-Stokes equations and the solutions are obtained by employing high-order spectral/hp element method. It is found that the flow dynamics are significantly distinguished from the study of two-dimensional flow by Blackburn & Henderson (1999) [1]. The values of hydrodynamic forces are smaller compared to that in the two-dimensional study. However, lock-in boundary we identified is broader. In addition, a different type of hysteresis loop of energy transfer coefficient is obtained.

Input–output analysis, model reduction and control of the flat-plate boundary layer

2009 ◽  
Vol 620 ◽  
pp. 263-298 ◽  
Author(s):  
SHERVIN BAGHERI ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Input Output ◽  
Analysis Model ◽  
Unstable Flow ◽  
Navier Stokes Equations ◽  
And Control

The dynamics and control of two-dimensional disturbances in the spatially evolving boundary layer on a flat plate are investigated from an input–output viewpoint. A set-up of spatially localized inputs (external disturbances and actuators) and outputs (objective functions and sensors) is introduced for the control design of convectively unstable flow configurations. From the linearized Navier–Stokes equations with the inputs and outputs, controllable, observable and balanced modes are extracted using the snapshot method. A balanced reduced-order model (ROM) is constructed and shown to capture the input–output behaviour of the linearized Navier–Stokes equations. This model is finally used to design a 2-feedback controller to suppress the growth of two-dimensional perturbations inside the boundary layer.

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