WAKE/GROUND INTERACTIONOsama A. Kandil1 and Ihab G. Adam2
Aerospace Engineering DepartmentOld Dominion University, Norfolk, VA 23529, USA
ABSTRACT
The effect of exhaust plume temperatureon the vortex-wake decent, separation andrebound near the ground is investigated. Thethree-dimensional, compressible Navier-Stokes(NS) equations are solved numerically. Theimplicit, upwind, Roe flux-differencing, finitevolume scheme is used. The computations ofvortex-wake/exhaust plume interaction with theground are carried out using overlapping zonalmethod for long distances downstream. Typicalvelocity profiles of a tip vortex for Boeing 757and Boeing 747, with and without exhaust plumetemperature profiles are used for inflow boundaryconditions. The vortex-wake is subjected tocrosswind flow and both upwind and downwindvortices are considered. The results of the vortex-wake decent, separation and rebound with andwithout exhaust plume are compared with eachother.
INTODUCTION
With the civil air traffic growth ofsubsonic aircraft, an increase in the runwaycapacity is needed. On the other hand, strongwake vortices emanating from large aircraft arenecessary to generate the lift needed to sustain theaircraft in flight, but also it can be hazardous tofollowing aircraft. The trailing aircraft, under theinfluence of those vortex trails could suffer highrolling moments, loss of climb and structuredamages. These vortex trails are characterized
with high intensity and turbulence, and theirkinematical and dynamical characteristics areaffected by ground, atmospheric turbulence,stratification and wind shear; among others. Thevortex-wake interaction with the ground causesthe vortex pair to separate and rebound back to theflight path of the following aircraft. These vortextrails may persist up to several miles and for longperiods of time before they decay, and hence theyplay a major role in sequencing landing and take-off operations at busy airports. Safety is currentlymaintained by keeping a minimum safe-separationdistance between aircraft to avoid hazardousvortex encounters.
The literature shows several wind tunneland flight measurements1"4 made in the 1970s toanalyze the roll-up of a tip vortex, the vortex-wakeinteraction with the ground including merging anddecay, as well as the hazardous effects of thesephenomena on trailing aircraft. All of these testsconfirmed the phenomena of wake-vorticesseparation and rebound by interacting with theground, which was first reported by Dee andNicholas1.
Recently, several other field datameasurements5"7 of wake vortices emanating fromlarge variety of take-off and landing aircraft, suchas B-747 and B757 were conducted. These datawere to study the effects of crosswind on thevortex transport. Hallock, Sigona and Burnham7
showed that a suitable ambient crosswind velocitycould lead to vortex stalling near extended runway
centerline. It might cause one vortex to remain onthe flight path of the following aircraft. Kopp5
and Burnham and Hallock6 emphasized on theimportance of monitoring the aircraft exhaustplume in airport vicinity. A significant jump intemperature was reported by Burnham andHallock6 and was attributed to the entrainedengine exhaust plume.
Various computational modeling studiesof aircraft wake vortices used different type ofnumerical /techniques; Direct NumericalSimulation8"12 (DNS), Large-Eddy Simulation13"16
(LES), two-dimensional Reynolds AveragedNavier-Stokes Simulations17"19 (RANS) and three-dimensional RANS20. Most of these modelsinvestigated the effects of crosswind velocity,ambient turbulent and stratification on the vortextrajectories and decay.
In this paper, three-dimensionalcomputational investigations of the vortexwake/exhaust plume interaction with the groundand under crosswind flow influence, are carriedout in an attempt to study the effect of the plumetemperature on the descent, separation andrebound. The effect of the flow velocity in theaxial direction on the results is also investigated.An overlapping zonal method is used to carry outthe computations for long distance downstream. Inthe previous paper20, the computed results werevalidated with the available experimental data byKopp5.
FORMULATION
The implicit, upwind, Roe flux-differencesplitting, finite-volume scheme is used to solve thecompressible Navier-Stokes equations. Upwind-based spatial differencing is used for the inviscidterms, and flux limiter is not used. The viscousterms are differenced using second-order accuratecentral differencing. The resulting differenceequations are solved implicitly in time with theuse of the three-factor approximate factorizationscheme. This code is known as FTNS3D, which isa modified version of the well-known CFL3Dcode. An overlapping zonal method is used to
carry out the computations far downstream. Thismethod has been described and successfully usedby the authors in References 20 and 21.
BOUNDARY AND INITIALCONDITIONS
Boundary conditions are explicitlyimplemented. They include inflow-outflowconditions and solid boundary conditions. At theinflow boundaries, the velocity profiles areprescribed and the Riemann-invariant boundary-type conditions are used. At the outflowboundaries, pressure profile is extrapolated frominterior domain, while variables are determined aspart of the solution. The ground is treated asviscous surface with no-slip, no-penetration andadiabatic conditions. The initial conditionscorrespond to those of the free-stream flow and aconstant crosswind velocity. It should be notedthat the crosswind direction is parallel to the y-axis when viewed by an observer lookingupstream. At the inflow boundaries and in order tosatisfy the no-slip and no-penetration conditionson the ground, a vortex pair located at (y0,Zo) and(y0,-Zo) is used, to prescribe the velocitycomponents (v,w) in the cross flow plane (y,z).Using same sign of vortex pair, the velocitycomponent in y-direction with no-slip condition atthe ground (z=0) is obtained. While using oppositesign of vortex pair, the velocity component in z-direction with no-penetration condition at theground (z=0) is obtained.
RESULTS AND DISCUSSION
Two different vortex-wake flow cases areconsidered. The first case is that of a Boeing 757vortex-wake flow, with and without single engineexhaust plume temperature field subjected to acrosswind velocity of 0.085, which corresponds toa dimensional value of 5.8 m/s. In the second casea Boeing 747 vortex-wake flow, with and withoutexhaust plume temperature fields of two engines(per side), subjected to a crosswind velocity of0.054, which corresponds to a dimensional valueof 3.7 m/s is used. For the first, case and in orderto study the effect of axial flow velocity, twodifferent cases, with axial velocity and without
axial velocity, are considered. The crossflowvelocity, temperature and vorticity contours in theinflow plane for both cases are shown in Figs. 1and 2, receptively.
1. Boeing 757 Vortex Wake/Exhaust Plume ofSingle Engine
The NS equations are used to compute thedevelopment of this vortex wake/exhaust plumeinteraction with the ground for a long downstreamdistance, up to x=X/2s=140, where s is thesemispan. The computations are carried out usingan overlapping zonal method that was explained indetails in Ref. 20.
A rectangular grid of 14x201x153 grid pointsin x, y and z directions, respectively, is used foreach of the 1.3x30x12 semi-span unitcomputational stage. The grid points areredistributed at the end of the computations foreach stage to capture the vortex-wake resolutionwith a fine grid.
Computations are carried out for the right andleft side of the computational domain and no flowsymmetry is assumed. Figure 1 shows thecrossflow velocity, temperature and vorticitycontours in the inflow plane with the tip-vortexcenters located at y=±0.5 and z=2.333. The swirlratio of the tip-vortex is 0.2. The centers ofexhaust plume of the engines are located on thez=2.25 plane at y=±0.219 as shown in Fig. 1. Theflow is assumed laminar, with a Reynolds numberof 50,000, based on the span, 2s, and the flowMach number is 0.2. The inflow velocitycomponents in y and z directions are similar tothose used as initial conditions by Proctor14 in histwo-dimensional studies.
The results for this case with and without theexhaust plume are shown in Figs. 3, 4 and 5. Allthe results are plotted in reference to the originand the corresponding axes at the inflow plane.All variables are dimensionless using the free-stream values. Figures 3a, b and c show the vortexwake center trajectories in (y-z), (x-y) and (x-z)planes, respectively. Figures 3d and e show theplume maximum temperature, maximum vorticity
variations along the axial direction, respectively.Figure 3f shows the average circulation variationalong the axial direction, calculated based on twodifferent radii (r = R/2s = 1/3 and 1/6). In Fig. 3the left column corresponds to the upwind vortex,while the right corresponds to the downwind one.Figures 4 and 5 show the vorticity contours andstreamlines, respectively, at selected downstreamstations. In Figs 4 and 5 the left columncorresponds to the case with exhaust plume, whilethe right corresponds to the case without exhaustplume.
The tip-vortex descends and moves outwardas expected. During the tip-vortex motion, theexhaust plume is wrapped around it and its flow isentrained in the tip-vortex. As the tip vortexmoves closer to the ground, the boundary layerstarts to separate, generating another vortex withopposite sense of rotation (known as thesecondary vortex) as shown in Figs. 4 and 5. Nextthe tip vortex starts to rebound. For the downwindvortex, the height at which the vortex starts toseparate and then rebound is slightly lower for thecase with exhaust plume (z=0.68 at x=80) thanthat of the case without exhaust plume (z=0.72 atx=80). On the other hand, for the upwind vortex,the vortex starts to separate and then tend torebound later on at (x=95 and z=0.628) for thecase with exhaust plume and (x=95 and z=0.61)for the case without exhaust plume. The secondaryvortex generated from the boundary-layerseparation was weaker than that of the upwindvortex separation as seen in Figs. 4 and 5, andcould not force the main downwind vortex torebound at once. The main downwind vortexstalled at z=0.62 for axial distance of 10 for thecase without exhaust plume and of 30 for the casewith exhaust plume. For the case with exhaustplume, the secondary vortex rises due to theconvective force and wraps around the main one,pushes it to move down again instead of reboundback as happened in the case without plume.
2. Boeing 747 Vortex Wake/Exhaust Plume ofTwo Engines
In this case, the solution is carried out up tox=X/s=150, where s is the semispan. The same
grid with the overlapping zonal method used inthe previous case is implemented. Computationsare carried out for the right and left side of thecomputational domain and no flow symmetry isassumed. Figure 2 shows the crossflow velocity,temperature and vorticity contours in the inflowplane with the tip-vortex centers located at y=±1.0and z=2. The swirl ratio of the tip-vortex is 0.2.The centers of exhaust plume of the engines arelocated on the z=1.9 plane at y=±0.333 andy=±0.667 as shown in Fig. 2. The flow is assumedlaminar, with a Reynolds number of 50,000, basedon the semi-span, s, and the flow Mach number is0.2. The inflow velocity components in y and zdirections are calculated using Gaussian method.
The results for this case with and without theexhaust plume are shown in Figs. 6, 7 and 8. Allthe results are plotted in reference to the originand the corresponding axes at the inflow plane.All variables are dimensionless using the free-stream values. Figures 6a, b and c show the vortexwake center trajectories in (y-z), (x-y) and (x-z)planes, respectively. In Fig. 6 the left column iscorresponding to the upwind vortex, while theright is corresponding to the downwind one.Figures 7 and 8 show the vorticity contours andstreamlines, respectively, at selected downstreamstations. In Figs 7 and 8 the left column iscorresponding to the case with exhaust plume,while the right is corresponding to the casewithout exhaust plume.
The same vortex motion, separation andrebound scenario, described in the previoussection is repeated. During the tip-vortex motion,the exhaust plume is wrapped around it and itsflow is entrained in the tip-vortex, starting firstwith the outboard part and followed by theinboard part of the exhaust plume. For thedownwind vortex, the height at which the vortexstarts to separate and then rebound is slightlylower for the case with exhaust plume (z=1.18 atx=65) than that of the case without exhaust plume(z=1.22 at x=65). On the other hand, for theupwind vortex, the vortex starts to separate andthen rebound later on at (x=70 and z=0.995) forthe case without exhaust plume. While for thecase with exhaust plume, the boundary layer
separation did not occur until x=l 15. At x=l 15 thegenerated secondary vortex was very weak anddid not alter the main downwind vortex which inturns stalled for a long axial distance (about 30) ata height of z=l.09.
In order to validate the computed results,experimental data reported by Kopp5 have beenused. Figure 6a shows a comparison of the vortex-wake trajectory for the present computationalresults, with and without exhaust plume, with theexperimental data. It is observed that thecomputed and measured trajectories are in goodagreement. The computed results, taking intoconsideration the exhaust plume temperature fieldeffect, shows better agreement with theexperimental data than those without exhaustplume during the rebound process. The vortexwake reaches a maximum descent of z=1.18 forthe case with plume and z=1.22 for the casewithout plume, while the experimental date showsa maximum descent of z=0.95. The disagreementmay be attributed to several computational andexperimental inconsistencies; 1. in thecomputational study, a constant averagedcrosswind velocity is assumed along the axialdirection, while, in the experimentalmeasurements, the crosswind velocity is naturallyvarying along the axial direction, 2. only, laminarflow has been studied in the computationalinvestigation and flow turbulence is not modeled,and 3. the exhaust plume is represented as atemperature field with maximum temperature oftwice that of the free-stream temperature, and nochemical reaction was considered.
3. Effect of Axial Inflow Velocity
To investigate the effect of the flow inaxial direction on the vortex, two different runs(using same configuration as in case 1) wereconducted, one with axial velocity and the otherwithout axial velocity. A set of results similar tothose presented in case 1 is shown in Figs. 9, 10and 11. In Figs 10 and 11 the left column iscorresponding to the case without axial velocity,while the right is corresponding to the case withaxial velocity. For the downwind vortex, the casewith axial velocity shows stronger separation,which yields stronger secondary vortex causing
the main vortex to rebound higher than the casewithout axial velocity. The downwind vortexstarts to rebound at x=70 and z=0.78 for the casewith axial velocity and at x=80 and z=0.68 for thecase without exhaust plume. This may attributedto the existence of the axial boundary layer for thecase with exhaust plume. For the upwind vortex,the same phenomenon is repeated. The separationfor the case with axial velocity is stronger, asshown in Fig. 10, and causes the vortex torebound. While for the case without axial velocity,the weak separation generates a weak secondaryvortex, which causes the main vortex to stall forsometime and then continue descending.
CONCLUDING REMARKS
The computational solution of the compressible,three-dimensional, full Navier-Stokes equations isused to predict the effect of exhaust plumetemperature field on the far-field vortex-wakeinteraction with the ground. An overlapping zonalmethod is used to carry out the computations fardownstream. The effect of exhaust plume on bothportions of the vortex pair is studied. Twodifferent cases have been studied. The first case isthat of a Boeing 757 vortex-wake flow, with andwithout exhaust plume of single engine subjectedto a crosswind velocity. In the second case, avortex-wake flow corresponding to Boeing 747with and without two engines exhaust plume isconsidered.
The exhaust plume causes the upwindvortex to decent more before rebound. On theother hand, The existence of the exhaust plumeforces the downwind vortex to stall at a certainheight and it might descent more after that.
To investigate the effect of the axialvelocity, two different runs were conducted withand without axial velocity. The results with theaxial velocity show a stronger separation, whichyields stronger secondary vortex, and hence asudden rebound at higher elevation.
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