An efficient method for predicting zero-lift or boundary-layer drag including aeroelastic effects for the design environment

2015 ◽  
Vol 119 (1221) ◽  
pp. 1451-1460
Author(s):  
J. A. Camberos ◽  
R. M. Kolonay ◽  
F. E. Eastep ◽  
R. F. Taylor
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Near Field ◽  
Field Method ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Design Environment ◽  
Navier Stokes Equations ◽  
Induced Drag ◽  
Flight Regimes

AbstractOne of the aerospace design engineer’s goals aims to reduce drag for increased aircraft performance, in terms of range, endurance, or speed in the various flight regimes. To accomplish this, the designer must have rapid and accurate techniques for computing drag. At subsonic Mach numbers drag is primarily a sum of lift-induced drag and zero-lift drag. While lift-induced drag is easily and efficiently determined by a far field method, using the Trefftz plane analysis, the same cannot be said of zero-lift drag. Zero-lift drag (CD,0) usually requires consideration of the Navier-Stokes equations, the solution of which is as yet unknown except by using approximate numerical techniques with computational fluid dynamics (CFD). The approximate calculation of zero-lift drag from CFD is normally computed with so-called near-field techniques, which can be inaccurate and too time consuming for consideration in the design environment. This paper presents a technique to calculate zero-lift and boundary-layer drag in the subsonic regime that includes aeroelastic effects and is suitable for the design environment. The technique loosely couples a two-dimensional aerofoil boundary-layer model with a 3D aeroelastic solver to compute zero-lift drag. We show results for a rectangular wing (baseline), a swept wing, and a tapered wing. Then compare with a rectangular wing with variable thickness and camber, thinning out from the root to tip (spanwise direction), thus demonstrating the practicality of the technique and its utility for rapid conceptual design.

On reduction of turbulent wall friction through spanwise wall oscillations

1999 ◽  
Vol 383 ◽  
pp. 175-195 ◽  
Author(s):  
M. R. DHANAK ◽  
C. SI
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Wall Friction ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Streamwise Vortices ◽  
Navier Stokes Equations ◽  
Turbulent Wall

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier–Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations.

scholarly journals Numerical Modeling of the Motion and Interaction of a Droplet of an Inkjet Printing Process with a Flat Surface

2021 ◽  
Vol 11 (2) ◽  
pp. 527
Author(s):  
Tim Tofan ◽  
Harald Kruggel-Emden ◽  
Vytautas Turla ◽  
Raimondas Jasevičius
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Field Method ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Stable Form ◽  
Fluid Interface ◽  
Velocity Change ◽  
Navier Stokes Equations ◽  
Inkjet Printhead

The numerical simulation and analysis of the ejection of an ink droplet through a nozzle as well its motion through air until its contact with a surface and taking up of a stable form is performed. The fluid flow is modeled by the incompressible Navier–Stokes equations with added surface tension. The presented model can be solved using either a level set or a phase field method to track the fluid interface. Here, the level set method is used to determinate the interface between ink and air. The presented work concentrates on the demonstration how to check the suitability of ink for inkjet printhead nozzles, for instance, for the use in printers. The results such as velocity, change of size, and volume dependence on time of an ink droplet are presented. Recommendations for the use of specific inks are also given.

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.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Natural convection flow far from a horizontal plate

1999 ◽  
Vol 387 ◽  
pp. 227-254 ◽  
Author(s):  
VALOD NOSHADI ◽  
WILHELM SCHNEIDER
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
The Self ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Self Similar ◽  
Similar Solutions

Plane and axisymmetric (radial), horizontal laminar jet flows, produced by natural convection on a horizontal finite plate acting as a heat dipole, are considered at large distances from the plate. It is shown that physically acceptable self-similar solutions of the boundary-layer equations, which include buoyancy effects, exist in certain Prandtl-number regimes, i.e. 0.5<Pr[les ]1.470588 for plane, and Pr>1 for axisymmetric flow. In the plane flow case, the eigenvalues of the self-similar solutions are independent of the Prandtl number and can be determined from a momentum balance, whereas in the axisymmetric case the eigenvalues depend on the Prandtl number and are to be determined as part of the solution of the eigenvalue problem. For Prandtl numbers equal to, or smaller than, the lower limiting values of 0.5 and 1 for plane and axisymmetric flow, respectively, the far flow field is a non-buoyant jet, for which self-similar solutions of the boundary-layer equations are also provided. Furthermore it is shown that self-similar solutions of the full Navier–Stokes equations for axisymmetric flow, with the velocity varying as 1/r, exist for arbitrary values of the Prandtl number.Comparisons with finite-element solutions of the full Navier–Stokes equations show that the self-similar boundary-layer solutions are asymptotically approached as the plate Grashof number tends to infinity, whereas the self-similar solution to the full Navier–Stokes equations is applicable, for a given value of the Prandtl number, only to one particular, finite value of the Grashof number.In the Appendices second-order boundary-layer solutions are given, and uniformly valid composite expansions are constructed; asymptotic expansions for large values of the lateral coordinate are performed to study the decay of the self-similar boundary-layer flows; and the stability of the jets is investigated using transient numerical solutions of the Navier–Stokes equations.

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.

Расчетно-экспериментальное исследование влияния вдува/отсоса газа через перфорированную поверхность на пограничный слой при сверхзвуковом числе Маха

2021 ◽  
Vol 47 (21) ◽  
pp. 19
Author(s):  
П.А. Поливанов
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Stokes Equations ◽  
Numerical Data ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Piv Method ◽  
Sst Turbulence Model ◽  
Method Analysis

In this paper a numerical and experimental study of the effect of blowing/suction through a perforated surface on a turbulent boundary layer at a Mach number M = 1.4 is carried out. Most of the calculations were performed by Reynolds-averaged Navier-Stokes equations with the k-w SST turbulence model. The calculated geometry completely repeated the experimental one including the perforated surface. The numerical data were compared with experimental measurements obtained by the PIV method. Analysis of the data made it possible to find the limits of applicability of the numerical method for this flow.

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