The boundarylayer and disturbance equations are formulated in a general, orthogonal, curvilinear. Taylorgoertler instabilities of tollmienschlichting waves. On the convectively unstable nature of optimal streaks 223 into turbulent spots. Gortler vortices were always present when the wall boundary layers were laminar. Primary and secondary instabilities of the asymptotic. Gortler instability occurs due to the action of centrifugal forces in boundary layers over curved surfaces, where it most commonly results in the generation of steady streamwise vortices. In the rapidexpansion slotted nozzle the vortices persisted far downstream of the transition point when the bleed slot control valves were open. Experimental study of the taylorgortler instability. On the gortler instability of boundary layers progress in aerospace sciences, vol. Boundary layer instabilities in mixed convection and di usion. Gortler instability of boundary layers over concave and convex walls.
The boundarylayer and disturbance equations are formulated in a general. This thesis studies the instability and receptivity of boundary layers over a concave wall and a swept joukowski airfoil. Coriolis effects on gortler vortices in the boundarylayer. The effect of gortler instability on hypersonic boundary layer transition article pdf available in theoretical and applied mechanics letters 62 march 2016 with 65 reads how we measure reads. A simple inviscid stability criterion is developed and used to identify shear layers which are potentially unstable with respect to the gortler. Pdf a formal analysis of goertlertype instability is presented. Instability of a junction vortex princeton university. With the bleed valves closed, the wall boundary layer was tripped by. In particular, it is often observed in boundary layers developing over concave walls in a wide range of freestream speeds and mach numbers. The conjecture is that these waves represent a mode of instability of the bodewadt layer. Under certain conditions particularly with low external turbulence and smooth geometry, perturbations generated through receptivity mechanism get ampli. The most widely used tool for predicting transition is the socalled e n method, which is discussed in chapter 3.
Outside the boundary layer the ow can be considered inviscid i. Cole school of mathematics and statistics, the university of birmingham edgbaston, b15 2tt, united kingdom abstract curved mixing layers are known to be inherently unstable to short wavelength travelling waves due to the. Also, numerical methods to solve the equations of motion in the boundary layer are discussed. Effect of wall temperature on the growth of gortler. It helps to find the most dangerous instability wave in boundary layers. The main interest is in excitation of relevant instability waves by freestream vortical disturbances and in their subsequent linear development. Due to the swept angle of the leading edge, flow on these wings is threedimensional and the pressure gradient across the wing results in a secondary flow. Growth and walltranspiration control of nonlinear unsteady gortler. Gollnera, auniversity of maryland department of fire protection engineering 4356 stadium dr. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically.
Stability of gortler vortices in boundary layers aiaa arc. From the practical standpoint, this phenomenon can be encountered, for example, in flows evolving over the concave part of a wing or turbomachinery blade, or on the walls of divergingconverging nozzles such as those utilized in. Gortler vortices in curved mixing layers and their effect on. Gortler performed no experiments to verify his analysis. Pdf hydrodynamic stability download full pdf book download.
May 17, 2012 american institute of aeronautics and astronautics 12700 sunrise valley drive, suite 200 reston, va 201915807 703. Development and breakdown of goertler vortices in high speed. Primary and secondary instabilities of the asymptotic suction boundary layer on a curved plate. Gortler vortices in curved mixing layers and their effect. Primary and secondary instabilities of the asymptotic suction. Secondary instability of boundary layers secondary instability of boundary layers herbert, t 19880101 00. On the stability of threedimensional boundary layers with application to the flow due to a rotating disk. Stability of gortler vortices in boundary layers aiaa. Secondary instabilities of gortler vortices in highspeed. In order to identify the physical mechanisms responsible for breakdown, it appears essential to determine if the observed oscillations of streaks grow in situ,asinanabsolute instability. The fully nonlinear development of gortler vortices in. Boundary layers are caused by diffusion of momentum.
On secondary instabilities in boundary layers springerlink. We emphasise that a key aspect of boundarylayer theory is the development of singularities. Siam journal on numerical analysis siam society for. The results cover a wide range of sweep angle, pressure gradient, and. Hypersonic boundarylayer transition with ablation and blowing. Gortler vortices in spatially growing boundary layers have been extensively studied analytically by hall and his.
Other instances edit a similar phenomenon arising from the same centrifugal action is sometimes observed in rotational flows which do not follow a curved wall, such as the rib vortices seen in the wakes of cylinders 1 and generated behind moving structures. Linear instability the pioneering work for boundary layers on constantcurvature concave walls was carried out by g. The taylor gortler vortex instability equations are formulated for steady and unsteady interacting boundary layer flows of the type which arise in tripledeck theory. Growth and walltranspiration control of nonlinear unsteady. Boundarylayer flow over a concave wall is subject to the gortler instability. Pdf stability of gortler vortices in boundary layers. Secondary instability in forced wavelength gortler vortices phys. Gortler instability or taylorgortler one in closed rotating streams is widely spread in various shearflows. In this paper, gortler instability is investigated using.
Gortler instability gortler 1940, the centrifugal instability of a boundary layer over a concav e wall, arises due to the imbalance between the centrifugal force and the wallnormal pressure. Aiaa paper 850297, aiaa 23rd aerospace sciences meeting. A formal analysis of gortlertype instability is presented. This book will be appropriate for use in research and in researchrelated courses on the subject. Boundary layer flows over concave surfaces are subject to a centrifugal instability that leads to spatially growing longitudinal vortices known as gortler vortices. The next two instabilities in the cascade are usually called secondary and tertiary instabilities. Boundary layer instabilities in mixed convection and di usion ames with an unheated starting length colin h. Stability of gortler vortices in boundary layers aiaa journal. The instability phenomenon in a laminar boundary layer in the presence of stream wise curvature presents many interesting features, both from a dynamical. Physics of instability and transition with blowing. The leading edge receptivity problem, linear growth and the nonlinear breakdown stage. The boundary layer and disturbance equations are formulated in a general. The effective gortler number is shown to be a function of the all shape in the boundary layer and the possibility of both steady and unsteady taylorgortler modes exists.
The centrifugal instability of the boundarylayer flow. Nonlinear evolution and secondary instability of steady gortler vortices induced by freestream vortical disturbances. For more discussion of this issue see bushnell et al. Gortler vortices in boundary layer flows over concave surfaces are. He found that the linearstability neutral curve has two lobes. Gortler vortices in spatially growing boundary layers have been extensively studied analytically by hall and his coworkers. Zurigat 1 mechanical engineering department university of jordan, amman, jordan m. Pdf the effect of gortler instability on hypersonic. The origins of transition to turbulence in a bounded shear flow within a low disturbance environment are typically found in the instabilities of the basic state. Stability and transition analysis code lastrac version 1.
The new mode of instability in viscous highspeed boundary. The taylorgortler vortex instability equations are formulated for steady and unsteady interacting boundary layer flows of the type which arise in tripledeck theory. However, formatting rules can vary widely between applications and fields of interest or study. Gortler instability of compressible boundary layers aiaa. A simple inviscid stability criterion is developed and used to identify shear layers which are potentially unstable with respect to the gortlertype disturbances. If the boundary layer is thin compared to the radius of curvature of the wall, the pressure remains constant across the boundary layer. The e n method is based on the linear stability theory, which is discussed in this chapter. Gortler instability of turbulent boundary layers centrifugal effects can be categorized into three types, i. Saric arizona state university tempe, usa abstract within the last five years, increased emphasis on secondary instability analysis along with the experimental observations of subharmonic instabilities have changed the picture of the transition process for boundary layers in lowdisturbance. The low skinfriction coefficient of laminar boundarylayer flow is very attractive to those who lay out the engines or pay the fuel for highspeed vehicles such. American institute of aeronautics and astronautics 12700 sunrise valley drive, suite 200 reston, va 201915807 703. On the g6rtler instability of boundary layers 237 instability, section 4 deals with the nonlinear effects, section 5 examines turbulent bound ary layers, section 6 discusses heat transfer effects and section 7 offers some concluding remarks. The effective gortler number is shown to be a function of the all shape in the boundary layer and the possibility of both steady and unsteady taylor gortler modes exists.
The first instability is usually called primary instability and it may consist of a two or threedimensional tollmien schlichting wave, a gortler vortex, or a crossflow instability. Effect of wall transpiration and heat transfer on nonlinear g\o. In this paper, receptivity of gortler and other instability waves in hypersonic boundary layers are investigated using direct numerical simulation dns. The development of gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. Taylorgoertler instabilities of tollmienschlichting. Document, government publication, national government publication, internet resource. Introduction boundarylayer transition to turbulence is often described in terms of the initial ampli. Vortexlike disturbances in a boundary layer flow over a curved wail. Nov 18, 2018 sescu, adrian and elamrani, safae and afsar, mohammed z effect of wall temperature on the growth of gortler vortices in highspeed boundary layers. Gottingen, nachr 1 2, translated as on the threedimensional instability of laminar boundary layers on concave walls.
On the other hand, if the boundary layer thickness is comparable to the radius of curvature, the centrifugal action creates a pressure variation. Experimental study of a hypersonic shock layer stability on a circular surface of compression comptes rendus mecanique, vol. The wellknown gortler instability 7 is an important mode within curved boundary layers. Linear stability theory is used to study the effect of crossflow on gortler instability in incompressible boundary layers. This instability leads to amplification of streamwise elongated vortices steady orand unsteady. On the gortler instability of boundary layers sciencedirect. Request pdf steady and unsteady gortler boundarylayer instability on concave wall the subject of the present combined experimental and theoretical investigation is the steady and unsteady. Direct numerical simulation of gortler instability in. Next, interactive boundarylayer theory is introduced in the context of unsteady separation.
At various levels of modeling the featuring physical phenomena will be described. The centrifugal instability of the boundarylayer flow over slender rotating cones. This discussion leads onto a consideration of largereynoldsnumber asymptotic instability theory. Therefore, gijrtler instability becomes an impor tant topic in fluid dynamics. Boundarylayer stability and transition the proceedings. According to reference 10, the nozzlewall boundary layer in the jpl tunnel can be maintained laminar up to a freestream unit reynolds number of 1. It is not possible to avoid concave surkaces in engineering designs such as engine inlet. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. Boundary layer instabilities in mixed convection and di. Within a few radians of rotation however, the centrifugal instability of the sidewall layer dominates the spindown process and the endwall waves are difficult to examine further. Effect of wall temperature on the growth of gortler vortices. Pdf stability of gortler vortices in boundary layers researchgate. Morkovin also notes that the experimental data as of 1969 was inconclusive for details, see citations below.
Pdf secondary instabilities of gortler vortices in high. Stability of stationary endwall boundary layers during. The streamlinecurvature instability is unstable at much lower reynolds numbers than cross. Stability of gortler vortices in boundary layers article pdf available in aiaa journal 203 april 1982 with 568 reads how we measure reads. Steady and unsteady gortler boundarylayer instability on. Hall 1982b, 1983 has emphasized that it is not legitimate to consider the basic velocity profile as locally parallel unless one restricts attention to the highwavenumber limit.
The streamlinecurvature instability is unstable at much lower. One of those problems is the taylorgortler centrifugal instability that occurs in the boundarylayer flow. It includes chapters on bifurcations in fluid systems, flow patterns, channel flows, nonparallel shear flows, thinfilm flows, strong viscous shear flows, gortler vortices, bifurcations in convection, wavy film flows and boundary layers. Johnstonrollcell structure in a concave turbulent boundary layer. On the convectively unstable nature of optimal streaks in. The data we will use to assess the linear stability of boundary layer. The gortler instability is an important boundarylayer instability that.318 560 410 1652 931 111 643 1038 51 800 831 611 250 1113 1486 1572 1247 259 340 1359 1198 1373 913 700 1 895 517 824 161 127 560 442 1501 957 1570 1640 1588 1089 1427 1275 795 1398 906 858 184 61 94