Stokes Layers in Horizontal-Wave Outer Flows

1996 ◽  
Vol 118 (3) ◽  
pp. 537-545 ◽  
Author(s):  
J. E. Choi ◽  
M. K. Sreedhar ◽  
F. Stern
Keyword(s):  
Boundary Layer ◽  
Computational Study ◽  
Perturbation Expansion ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Additional Parameter ◽  
Small Disturbance ◽  
Wave Speeds ◽  
Wide Range ◽  
Horizontal Wave

Results are reported of a computational study investigating the responses of flat plate boundary layers and wakes to horizontal wave outer flows. Solutions are obtained for temporal, spatial, and traveling waves using Navier Stokes, boundary layer, and perturbation expansion equations. A wide range of parameters are considered for all the three waves. The results are presented in terms of Stokes-layer overshoots, phase leads (lags), and streaming. The response to the temporal wave showed all the previously reported features. The magnitude and nature of the response are small and simple such that it is essentially a small disturbance on the steady solution. Results are explainable in terms of one parameter ξ (the frequency of oscillation). For the spatial wave, the magnitude and the nature of the response are significantly increased and complex such that it cannot be considered simply a small disturbance on the without-wave solution. The results are explainable in terms of the two parameters λ−1 and x/λ (where λ is the wavelength). A clear asymmetry is observed in the wake response for the spatial wave. An examination of components of the perturbation expansion equations indicates that the asymmetry is a first-order effect due to nonlinear interaction between the steady and first-harmonic velocity components. For the traveling wave, the responses are more complex and an additional parameter, c (the wave speed), is required to explain the results. In general, for small wave speeds the results are similar to a spatial wave, whereas for higher wave speeds the response approaches the temporal wave response. The boundary layer and perturbation expansion solutions compares well with the Navier Stokes solution in their range of validity.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

Magnus Effect: Physical Origins and Numerical Prediction

2011 ◽  
Vol 78 (5) ◽  
Author(s):  
Roxan Cayzac ◽  
Eric Carette ◽  
Pascal Denis ◽  
Philippe Guillen
Keyword(s):  
Boundary Layer ◽  
Turbulence Modeling ◽  
Lateral Force ◽  
Numerical Prediction ◽  
The Body ◽  
Navier Stokes ◽  
Flow Topology ◽  
Vortex Sheets ◽  
Magnus Effect ◽  
Wide Range

An overview of the Magnus effect of projectiles and missiles is presented. The first part of the paper is devoted to the description of the physical mechanisms governing the Magnus effect. For yawing and spinning projectiles, at small incidences, the spin induces a weak asymmetry of the boundary layer profiles. At high incidences, increased spin causes the separated vortex sheets to be altered. Vortex asymmetry generates an additional lateral force which gives a vortex contribution to the total Magnus effect. For finned projectiles or missiles, the origin of the Magnus effect on fins is the main issue. There are two principal sources contributing to the Magnus effect. Firstly, the interaction between the asymmetric boundary layer-wake of the body and the fins, and secondly, the spin induced modifications of the local incidences and of the flow topology around the fins. The second part of the paper is devoted to the numerical prediction and validation of these flow phenomena. A state of the art is presented including classical CFD methods based on Reynolds-averaged Navier–Stokes (RANS) and unsteady rans (URANS) equations, and also hybrid RANS/LES approach called ZDES. This last method is a recent advance in turbulence modeling methodologies that allows to take into account the unsteadiness of the flow in the base region. For validation purposes computational results were compared with wind tunnel tests. A wide range of angles of attack, spin rates, Reynolds and Mach numbers (subsonic, transonic and supersonic) have been investigated.

The flat plate boundary layer. Part 1. Numerical integration of the Orr–-Sommerfeld equation

1970 ◽  
Vol 43 (4) ◽  
pp. 801-811 ◽  
Author(s):  
R. Jordinson
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Plate Boundary ◽  
Mean Flow ◽  
Comparison With Experiment ◽  
Wide Range ◽  
The Mean ◽  
Sommerfeld Equation ◽  
Range Of Values ◽  
Flat Plate Boundary Layer

Numerical space-amplified solutions of the Orr-Sommerfeld equation for the case of a boundary layer on a flat plate have been calculated for a wide range of values of frequency and Reynolds number. The mean flow is assumed to be parallel and given by the appropriate component of the Blasius solution. The results are presented in a form suitable for comparison with experiment and are also compared with calculations of earlier authors.

Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations

1990 ◽  
Vol 221 ◽  
pp. 311-347 ◽  
Author(s):  
H. Fasel ◽  
U. Konzelmann
Keyword(s):  
Boundary Layer ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Detailed Comparison ◽  
Problem Formulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Difference ◽  
Direct Numerical Integration

Non-parallel effects which are due to the growing boundary layer are investigated by direct numerical integration of the complete Navier-Stokes equations for incompressible flows. The problem formulation is spatial, i.e. disturbances may grow or decay in the downstream direction as in the physical experiments. In the past various non-parallel theories were published that differ considerably from each other in both approach and interpretation of the results. In this paper a detailed comparison of the Navier-Stokes calculation with the various non-parallel theories is provided. It is shown, that the good agreement of some of the theories with experiments is fortuitous and that the difference between experiments and theories concerning the branch I neutral location cannot be explained by non-parallel effects.

Numerical Verification of Scaling Laws for Shock-Boundary Layer Interactions in Arbitrary Gases

1997 ◽  
Vol 119 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. Cramer ◽  
S. H. Park ◽  
L. T. Watson
Keyword(s):  
Boundary Layer ◽  
Scaling Laws ◽  
Plate Boundary ◽  
Strong Support ◽  
Ideal Gas ◽  
Numerical Verification ◽  
Dense Gases ◽  
Ideal Gas Law ◽  
Dimensional Interaction ◽  
Wide Range

The steady, two-dimensional interaction of an oblique shock with a laminar flat-plate boundary layer has been examined through use of the Beam-Warming implicit scheme. A wide range of fluids is considered as are freestream pressures corresponding to dense gases, i.e., gases at pressures which are so large that the ideal gas law is no longer accurate. The results, when combined with the triple-deck theory of Kluwick (1994), provides strong support for the idea that the classical scaling laws can be extended to dense gases.

Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer

2011 ◽  
Vol 687 ◽  
pp. 503-528 ◽  
Author(s):  
Luca Brandt ◽  
Denis Sipp ◽  
Jan O. Pralits ◽  
Olivier Marquet
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Resolvent Operator ◽  
Plate Boundary ◽  
Singular Values ◽  
Base Flow ◽  
Stokes Operator ◽  
Navier Stokes ◽  
Strong Impact ◽  
The Resolvent Operator

AbstractNon-modal analysis determines the potential for energy amplification in stable flows. The latter is quantified in the frequency domain by the singular values of the resolvent operator. The present work extends previous analysis on the effect of base-flow modifications on flow stability by considering the sensitivity of the flow non-modal behaviour. Using a variational technique, we derive an analytical expression for the gradient of a singular value with respect to base-flow modifications and show how it depends on the singular vectors of the resolvent operator, also denoted the optimal forcing and optimal response of the flow. As an application, we examine zero-pressure-gradient boundary layers where the different instability mechanisms of wall-bounded shear flows are all at work. The effect of the component-type non-normality of the linearized Navier–Stokes operator, which concentrates the optimal forcing and response on different components, is first studied in the case of a parallel boundary layer. The effect of the convective-type non-normality of the linearized Navier–Stokes operator, which separates the spatial support of the structures of the optimal forcing and response, is studied in the case of a spatially evolving boundary layer. The results clearly indicate that base-flow modifications have a strong impact on the Tollmien–Schlichting (TS) instability mechanism whereas the amplification of streamwise streaks is a very robust process. This is explained by simply examining the expression for the gradient of the resolvent norm. It is shown that the sensitive region of the lift-up (LU) instability spreads out all over the flat plate and even upstream of it, whereas it is reduced to the region between branch I and branch II for the TS waves.

Direct numerical simulation of controlled transition in a flat-plate boundary layer

1995 ◽  
Vol 298 ◽  
pp. 211-248 ◽  
Author(s):  
U. Rist ◽  
H. Fasel
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Direct Numerical Simulation ◽  
Flat Plate ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flat Plate Boundary Layer

The three-dimensional development of controlled transition in a flat-plate boundary layer is investigated by direct numerical simulation (DNS) using the complete Navier-Stokes equations. The numerical investigations are based on the so-called spatial model, thus allowing realistic simulations of spatially developing transition phenomena as observed in laboratory experiments. For solving the Navier-Stokes equations, an efficient and accurate numerical method was developed employing fourth-order finite differences in the downstream and wall-normal directions and treating the spanwise direction pseudo-spectrally. The present paper focuses on direct simulations of the wind-tunnel experiments by Kachanov et al. (1984, 1985) of fundamental breakdown in controlled transition. The numerical results agreed very well with the experimental measurements up to the second spike stage, in spite of relatively coarse spanwise resolution. Detailed analysis of the numerical data allowed identification of the essential breakdown mechanisms. In particular, from our numerical data, we could identify the dominant shear layers and vortical structures that are associated with this breakdown process.

scholarly journals A class of exact Navier–Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

2014 ◽  
Vol 752 ◽  
pp. 462-484 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Linear Stability ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Transition Prediction ◽  
Neutral Curves ◽  
Tollmien Schlichting

AbstractWe introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Identification of a Pressure-Strain Correlation Based Bypass Transition Onset Marker

2021 ◽  
Author(s):  
Shanti Bhushan ◽  
Satish Muthu ◽  
Dibbon K. Walters
Keyword(s):  
Boundary Layer ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Transition Flow ◽  
Free Stream Turbulence ◽  
Transitional Boundary Layer ◽  
Layer Region ◽  
Rapid Pressure

Abstract Temporally developing direct numerical simulations are performed for bypass transition flow with zero pressure gradient over a flat plate boundary layer for a range of free-stream turbulence intensities (Tu) of 1.4% to 6%. The objective is to understand the role of pressure-strain terms on bypass transition onset, and to propose and validate a phenomenological hypothesis for the identification of a robust transition onset marker for use in transition-sensitive Reynolds-averaged Navier-Stokes (RANS) simulations. Results show that transition initiates at a location where the slow pressure-strain term becomes more dominant than the rapid term in the pre-transitional boundary layer region. A simple transition onset marker based on one-point statistical quantities is derived from the scaling of the ratio of the slow and rapid pressure fluctuation source terms. The critical value of the marker is found to vary within a narrow range (+/- 3.2%), and satisfies previously identified criteria for a robust transition onset marker.

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