Structures of Skin Friction, Surface Pressure, and Boundary Enstrophy Flux in Attachment-Line Flow

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Tianshu Liu
Keyword(s):  
Exact Solution ◽  
Skin Friction ◽  
Surface Pressure ◽  
Friction Surface ◽  
Navier Stokes ◽  
Wall Structures ◽  
Line Flow ◽  
Distinct Features ◽  
Attachment Line

Abstract The on-wall structures in an attachment-line flow are discussed based on an exact solution of the Navier–Stokes (NS) equations, focusing on distinct features of skin friction, surface pressure, and boundary enstrophy flux (BEF) and intrinsic connections between them.

A solution of the Navier-Stokes and energy equations illustrating the response of skin friction and temperature of an infinite plate thermometer to fluctuations in the stream velocity

1955 ◽  
Vol 231 (1184) ◽  
pp. 116-130 ◽  
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Skin Friction ◽  
Velocity Fluctuation ◽  
Second Harmonic ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Main Stream ◽  
High Frequencies ◽  
Zero Frequency

An exact solution of the Navier-Stokes equations for incompressible flow is derived under the conditions: (i) the flow is two-dimensional and is bounded by an infinite, plane, porous wall; (ii) the flow is independent of the distance parallel to the wall; (iii) the component of velocity parallel to the wall at a large distance from it fluctuates in time about a constant mean; (iv) the component of velocity normal to the wall is constant. It is found that the skin-friction fluctuations illustrate Lighthill’s (1954) theory of the behaviour of boundary layers subject to fluctuating pressure gradients. The amplitude of the skin-friction fluctuations rises with frequency, while the phase lead of the skin-friction over the main-stream-velocity fluctuation rises from zero at zero frequency to 7r/4 at very high frequencies. The velocity profile in the boundary layer fluctuates, and under certain transient conditions resembles that of a separated boundary layer, that is, a boundary layer with reverse flow close to the wall. With viscous dissipation of kinetic energy taken into account, the corresponding exact solution of the energy equation for an incompressible fluid with constant physical properties is derived under a condition of zero heat transfer between the fluid and the wall—the so-called ‘thermometer’ or ‘kinetic temperature’ problem. Whereas the velocity field consists of a mean flow and a first-harmonic fluctuation, the temperature field contains additionally a second-harmonic fluctuation. It is found that the mean temperature of the wall rises with frequency, and is ultimately proportional to the square root of the frequency. The first-harmonic fluctuation of the wall temperature lags behind the main-stream-velocity fluctuation by an amount which rises from zero at zero frequency to 1/4n at high frequencies, while the phase lag of the second-harmonic rises from zero at zero frequency but drops again to zero at high frequencies. The amplitude of the first-harmonic fluctuation tends to zero at high frequencies, whereas the amplitude of the second-harmonic fluctuation tends to a non-zero limit. Thus the residual temperature fluctuation of the wall at high frequencies has a frequency which is twice that of the fluctuating stream.

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.

The Mechanism of Movement and Calculation of Blood Balance in the Flow Channel From the Left Atrium to the End of the Aorta

2020 ◽  
Author(s):  
E. Talygin ◽  
G. Kiknadze ◽  
A. Gorodkov
Keyword(s):  
Exact Solution ◽  
Left Atrium ◽  
Swirling Flow ◽  
Practical Importance ◽  
Sufficient Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Mechanisms Of Formation ◽  
Formation And Evolution ◽  
General Relations

Abstract Today, there are a lot of works studying the mechanisms of formation and evolution of self-organizing tornado-like jets of viscous fluid. In these works, the exact solution of the Navier-Stokes equation for such a class of flows are obtained, the geometry of the generating surface for that flows is established and the necessary and sufficient conditions for the formation and evolution of such swirling jets are formulated. However, important aspects of the mechanics of such flows remain unclear — the structure of the boundary layer, the shape of streamlines in general form, the structure of such flows under a pulsating flow regime, and others. After obtaining the exact solution, attempts were made to obtain relations for streamlines in the corresponding projections. However, due to computational complexity, streamlines were constructed only for regions far from the axis of the swirling flow evolution. In this work, an alternative method of calculating streamlines was used, which made it possible to obtain general relations for these lines at each point in space. Expressions for streamlines contain easily computed functions, which simplifies their practical use Based on the expressions for streamlines, expressions were formulated declaring the conservation of the mass of the swirling blood flow from the left atrium to the aorta and the balance of the medium was calculated. The results of this work are of great theoretical and practical importance. On the one hand, the established expressions for streamlines allow a better study of the mechanisms of formation and evolution of swirling flows in the axial region. On the other hand, obtaining quantitative ratios for the balance of blood in the heart and aorta allows a more accurate study of the mechanics of blood circulation.

Time-Averaged Heat Transfer and Pressure Measurements and Comparison With Prediction for a Two-Stage Turbine

1994 ◽  
Vol 116 (1) ◽  
pp. 14-22 ◽  
Author(s):  
M. G. Dunn ◽  
J. Kim ◽  
K. C. Civinskas ◽  
R. J. Boyle
Keyword(s):  
Surface Pressure ◽  
Space Shuttle ◽  
Three Dimensional ◽  
Stanton Number ◽  
Navier Stokes ◽  
Pressure Measurements ◽  
Two Stage ◽  
Pressure Transducers ◽  
Pressure Distributions ◽  
Main Engine

Time-averaged Stanton number and surface-pressure distributions are reported for the first-stage vane row and the first-stage blade row of the Rocketdyne Space Shuttle Main Engine two-stage fuel-side turbine. These measurements were made at 10, 50, and 90 percent span on both the pressure and suction surfaces of the component. Stanton-number distributions are also reported for the second-stage vane at 50 percent span. A shock tube is used as a short-duration source of heated and pressurized air to which the turbine is subjected. Platinum thin-film gages are used to obtain the heat-flux measurements and miniature silicone-diaphragm pressure transducers are used to obtain the surface pressure measurements. The first-stage vane Stanton number distributions are compared with predictions obtained using a quasi-three dimensional Navier–Stokes solution and a version of STAN5. This same N–S technique was also used to obtain predictions for the first blade and the second vane.

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.

CFD Computation of Fan Interaction Noise

2007 ◽  
Author(s):  
Sheryl M. Grace ◽  
Douglas L. Sondak ◽  
Daniel J. Dorney ◽  
Michaela Logue
Keyword(s):  
Surface Pressure ◽  
Second Harmonic ◽  
Guide Vane ◽  
Power Level ◽  
Broadband Noise ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Fan Noise ◽  
Guide Vanes ◽  
Blade Passage

In this study, a 3-D, unsteady, Reynolds-averaged Navier-Stokes (RANS) CFD code coupled to an acoustic calculation is used to predict the contribution of the exit guide vanes to tonal fan noise downstream. The configuration investigated is that corresponding to the NASA Source Diagnostic Test (SDT) 22-in fan rig. One configuration from the SDT matrix is considered here: the approach condition, and outlet guide vane count designed for cut-off of the blade passage frequency. In this chosen configuration, there are 22 rotor blades and 54 stator blades. The stators are located 2.5 tip chords downstream of the rotor trailing edge. The RANS computations are used to obtain the spectra of the unsteady surface pressure on the exit guide vanes. The surface pressure at the blade passage frequency and its second harmonic are then integrated together with the Green’s function for an annular duct to obtain the pressure at locations in the duct. Comparison of the computed sound power level at the exhaust plane with experiment show good agreement at the cut-on circumferential mode. The results from this investigation validate the use of the CFD code along with the acoustic model for downstream fan noise predictions. This validation enables future investigations such as the effect of duct variation on the exhaust tonal power level and the validity of using this method for predicting broadband noise levels.

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