Numerical solution of the unsteady navier-stokes equations for the investigation of laminar boundary layer stability

2005 ◽  
pp. 151-160
Author(s):  
Hermann F. Fasel
Keyword(s):  
Boundary Layer ◽  
Numerical Solution ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Boundary Layer Stability ◽  
Navier Stokes Equations

Numerical experiments in boundary-layer stability

1984 ◽  
Vol 392 (1803) ◽  
pp. 373-389 ◽  
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Boundary Layer Stability ◽  
Physical Processes ◽  
Navier Stokes Equations

Numerical solution of the three-dimensional incompressible Navier-Stokes equations is used to study the instability of a flat-plate boundary layer in a manner analogous to the vibrating-ribbon experiments. Flow field structures are observed which are very similar to those found in the vibrating-ribbon experiment to which computational initial conditions have been matched. Stream wise periodicity is assumed in the simulation so that the evolution occurs in time, but the events that constitute the instability are so similar to the spatially occurring ones of the laboratory that it seems clear the physical processes involved are the same. A spectral and finite difference numerical algorithm is employed in the simulation.

scholarly journals A CFD Tutorial in Julia: Introduction to Compressible Laminar Boundary-Layer Flows

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 400
Author(s):  
Furkan Oz ◽  
Kursat Kara
Keyword(s):  
Boundary Layer ◽  
Programming Language ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Navier Stokes ◽  
Aerodynamic Heating ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Navier Stokes Equations

A boundary-layer is a thin fluid layer near a solid surface, and viscous effects dominate it. The laminar boundary-layer calculations appear in many aerodynamics problems, including skin friction drag, flow separation, and aerodynamic heating. A student must understand the flow physics and the numerical implementation to conduct successful simulations in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. Numerical simulations require writing computer codes. Therefore, choosing a fast and user-friendly programming language is essential to reduce code development and simulation times. Julia is a new programming language that combines performance and productivity. The present study derived the compressible Blasius equations from Navier–Stokes equations and numerically solved the resulting equations using the Julia programming language. The fourth-order Runge–Kutta method is used for the numerical discretization, and Newton’s iteration method is employed to calculate the missing boundary condition. In addition, Burgers’, heat, and compressible Blasius equations are solved both in Julia and MATLAB. The runtime comparison showed that Julia with for loops is 2.5 to 120 times faster than MATLAB. We also released the Julia codes on our GitHub page to shorten the learning curve for interested readers.

On laminar boundary-layer blow-off. Part 2

1971 ◽  
Vol 48 (2) ◽  
pp. 209-228 ◽  
Author(s):  
D. R. Kassoy
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Analytical Description ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Similarity Type ◽  
Boundary Layer Equations ◽  
Wall Shear

Several examples of incipient blow-off phenomena described by the compressible similar laminar boundary-layer equations are considered. An asymptotic technique based on the limit of small wall shear, and the use of a novel form of Prandtl's transposition theorem, leads to a complete analytical description of the blow-off behaviour. Of particular interest are the results for overall boundarylayer thickness, which imply that, for a given large Reynolds number, classical theory fails for a sufficiently small wall shear. A derivation of a new distinguished limit of the Navier–Stokes equations, the use of which will lead to uniformly valid solutions to blow-off type problems for Re → ∞, is included. A solution for uniform flow past a flat plate with classical similarity type injection, based on the new limit, is presented. It is shown that interaction of the injectant layers and the external flow results in a favourable pressure gradient, which precludes the classical blow-off catastrophy.

The Laminar Boundary Layer of a Source and Vortex Flow

1971 ◽  
Vol 22 (2) ◽  
pp. 196-206 ◽  
Author(s):  
T. S. Cham
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Pressure ◽  
Layer Flow ◽  
Special Case ◽  
Source Flow

SummaryA study is made of the interaction of a combination of free-vortex and source flow with a stationary surface. The laminar boundary layer flow can be expressed in ordinary differential equations by choosing suitable similarity transforms for the Navier-Stokes equations. When simplifying boundary-layer approximations are included, the equations do not yield any unique solution. Solutions to the complete equations are calculated numerically for the special case of equal source and vortex strengths for a limited range of Reynolds number. The results show the presence of “super” velocities and large pressure variations within the viscous layer.

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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