Zero-Pressure-Gradient Turbulent Boundary Layer

1997 ◽  
Vol 50 (12) ◽  
pp. 689-729 ◽  
Author(s):  
William K. George ◽  
Luciano Castillo
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Navier Stokes Equations ◽  
Theoretical Concepts

Of the many aspects of the long-studied field of turbulence, the zero-pressure-gradient boundary layer is probably the most investigated, and perhaps also the most reviewed. Turbulence is a fluid-dynamical phenomenon for which the dynamical equations are generally believed to be the Navier-Stokes equations, at least for a single-phase, Newtonian fluid. Despite this fact, these governing equations have been used in only the most cursory manner in the development of theories for the boundary layer, or in the validation of experimental data-bases. This article uses the Reynolds-averaged Navier-Stokes equations as the primary tool for evaluating theories and experiments for the zero-pressure-gradient turbulent boundary layer. Both classical and new theoretical ideas are reviewed, and most are found wanting. The experimental data as well is shown to have been contaminated by too much effort to confirm the classical theory and too little regard for the governing equations. Theoretical concepts and experiments are identified, however, which are consistent-both with each other and with the governing equations. This article has 77 references.

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.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

The structure of two-dimensional separation

1990 ◽  
Vol 220 ◽  
pp. 397-411 ◽  
Author(s):  
Laura L. Pauley ◽  
Parviz Moin ◽  
William C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Shedding Frequency

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

scholarly journals A Modified Gas-Kinetic Scheme for Turbulent Flow

2014 ◽  
Vol 16 (1) ◽  
pp. 239-263 ◽  
Author(s):  
Marcello Righi
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Turbulent Stress ◽  
Navier Stokes Equations

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

Steady streaming in a turbulent oscillating boundary layer

2007 ◽  
Vol 571 ◽  
pp. 265-280 ◽  
Author(s):  
PIETRO SCANDURA
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Time Average

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

scholarly journals Effect of uniform and non-uniform mesh on the development of turbulent boundary layer

2021 ◽  
Author(s):  
Lokesh Kalyan Gutti ◽  
◽  
Bhupendra Singh Chauhan ◽  
Hee-Chang Lim ◽  
◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Uniform Mesh ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Grid Points ◽  
Long Channel

For incompressible flow simulation, it is commonly accepted to use uniform meshes to solve the governing equation of turbulent boundary layer. It follows the laws of conservation stabilizing the flow field in the domain and preventing odd-even decoupling in the pressure field. In this study, Large Eddy Simulation (LES) has been conducted in a long channel. In order to calculate the turbulent boundary layer in the channel, the unsteady Navier-Stokes equations has been adopted at a Reynolds number =180, which is based on mean centerline velocity and the half-width of the channel. The mesh used in this study was based on both stretch and uniform mesh having grid points, which is corresponding to . Turbulence statistics were also calculated to compare to the existing results. In the results, the turbu lent boundary layer was fully developed at around . In addition, fully developed channel flow was achieved at the non-dimensional time of .

Multi-Airfoil Navier–Stokes Simulations of Turbine Rotor–Stator Interaction

1990 ◽  
Vol 112 (3) ◽  
pp. 377-384 ◽  
Author(s):  
M. M. Rai ◽  
N. K. Madavan
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Spatial Dimensions ◽  
Rotor Stator Interaction ◽  
Pitch Ratio ◽  
Experimental Ratio

An accurate numerical analysis of the flows associated with rotor–stator configurations in turbomachinery can be extremely helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier–Stokes equations in two spatial dimensions are solved on a system of patched and overlaid grids for an axial-turbine rotor–stator configuration. The governing equations are solved using a finite-difference, upwind algorithm that is set in an iterative, implicit framework. Results are presented in the form of pressure contours, time-averaged pressures, unsteady pressures, amplitudes, and phase. The numerical results are compared with experimental data and the agreement is found to be good. The results are also compared with those of an earlier study, which used only one rotor and one stator airfoil. The current study uses multiple rotor and stator airfoils and a pitch ratio that is much closer to the experimental ratio. Consequently, the results of this study are found to be closer to the experimental data.

Prediction of Sudden Expansion Flows Using the Boundary-Layer Equations

1984 ◽  
Vol 106 (3) ◽  
pp. 285-291 ◽  
Author(s):  
O. K. Kwon ◽  
R. H. Pletcher ◽  
J. P. Lewis
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Finite Difference ◽  
Stokes Equations ◽  
Computational Effort ◽  
Sudden Expansion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Difference Calculation

A finite-difference calculation method based on the boundary-layer equations is described for the prediction of laminar, developed channel flow undergoing a symmetric sudden expansion. The scheme requires only a fraction of the computational effort required for the numerical solution of the full Navier-Stokes equations that are usually employed for this flow. Predictions of the method compare very favorably with experimental data and solutions of the full Navier-Stokes equations.

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