This presentation describes a mathematical investigation of turbulent flow around a stepped airfoil. It includes the design of stepped airfoil, airfoil theory, governing equation of turbulence modeling and boundary condition. whereas, results and discussion are shown in second presentation on same topic.

1. Seminar-1
ROSHAN SAH
USN :- 17AE60R01
M.Tech (1st Year)
Dept. of AerospaceEngineering,
Indian Instituteof Technology
Kharagpur(IIT KGP)

2. Topicto be covered :-
• ABSTRACT
• NOMENCLATURE
• LITERATURE REVIEW
• THEORY
• DESIGN OF THE STEPPED AIRFOIL
• GOVERNING EQUATIONS
• TURBULENT MODELLING
• BOUNDARYCONDITION
• RESULT AND DISCUSSION
• CONCLUSION
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3. ABSTRACT
• This paper presents the numerical simulation of flow development around NACA-
2412 airfoil which utilized the backward facing step to enhancing airfoil aerodynamic
performancebytrappedvortex lift augmentation.
• Steps are located on both suction side and pressure side of the airfoil, at different
locations, different lengths and various depths in order to determine their effects on
lift, lift to drag ratioand near stall behavior.
• This article concentrate on the effect of separated flow and following vortex
formation which is created by backward facing step on pressure distribution and
subsequentlyon lift and drag coefficient.
• The results suggest that the steps on the lower surface that extended back to trailing
edge can lead to moreenhancementof lift to drag ratiofor some angles of attack.
• The backward facing step on suction surface offers no discernable advantages over
the conventionalairfoil but showed some positiveeffecton delaying stall.
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4. NOMENCLATURE
C = Airfoilchord CL = Lift coefficient, L/q∞ C
CD =Dragcoefficient, D/q∞ C CP = Pressurecoefficient, (p-p∞)/q∞
DS = Stepdepth K = Turbulentkineticenergy
LR = Reattachmentlength LS = Steplength
Re = Reynolds number, U∞C/ν XS = Steplocation
t = Airfoil local thickness Ui = Meanvelocitycomponent
U∞ = Free streamvelocity α = Angleof attack
μ = Molecularviscosity μt = Turbulentviscosity
ρ = Density ω = Specificdissipationrate
σk, σω= Turbulentmodelconstant
Subscript
L= Lower
R= Reattachment
S = Step
t = Turbulentproperty
U = Upper
∞ = Free streamvalue
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5. LITERATURE REVIEW :-
• The origin of this concept in airfoil design is attributed to a two artists (Kline-
Fogelman) in 1985 that published a book entitled "The Ultimate Paper Plane" in
which theyintroduced theconceptof a stepped airfoil[1].
• A similar NASA sponsored study on the Kline Fogelman airfoil was carried out in
1974 at the Universityof Tennessee for Rotor BladeApplication[2].
• A wedge-like geometry lifted directly from the patent by Fertis in 1994 reported
considerable enhancement of the aerodynamic characteristics for a three
dimensional wing model in terms of lift, drag,and stall angle [3].
• Finaish F, Witherspoon S, in 1998, an airfoil was simulated with the variations of
following parameters: step location, step depth, step configuration and with the
step on either the upper or lower surface by the experimental method and
compared tothe standard value of plainairfoil[4].
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6. Theory :-
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7. Design of Stepped Airfoil
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8. Governing Equations:-
ContinuityEquation:-
Momentum Equations :-
EnergyEquation :-
Reynolds-Averaged Navier-Stokes Equations :-
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9. • The fluid is assumed to be perfectgas and obey the equationof state
for calculationof pressure.
• Shearstress tensorisgiven by:-
Where the laminarand turbulentstress aregiven by :-
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10. Similarly, theconductiveheattransferrateis given by :-
Where the laminarand turbulentconductiveheattransferrate are
given by :-
The fluid is assumed airwith a Prandtl numberof 0.7 and turbulentPrandtl
numberof 0.9
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11. TURBULENCE MODELLING :-
• Among the several variationsof widelyused two-equation turbulence
models, the shear-stress transport(SST) k-ω turbulencemodelis adopted to
properlyresolve the complex flowover the steppedairfoil.
• This model is a two-equation eddy-viscositymodelwhich merges thek-ω
model of Wilcoxwith a high Reynolds number k-ε model (transformed into
the k-ω formulation). The transportequations for the turbulentkinetic
energyand the specificdissipation rateof turbulentin Cartesiancoordinate,
as follows:
Turbulentkineticenergy(K) :-
Specificdissipationrateof turbulent :-
Rate of change of K Convectivetransport Diffusivetransport Rate of productionRate of destruction
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12. Turbulentviscosity,μt is computed by:-
Productionof turbulentkineticenergy, PK
Auxiliaryfunctions (f1,f2) aregiven by
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13. Models constant :-
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14. BoundaryConditions :-
• No slip boundaryconditionsareenforcedon the airfoil surface.
Where, d1 denotes the normal distanceof the first node (cell
centroid)from the airfoil surface
Adiabaticwall boundarycondition is used for temperature
• The far-field boundary conditions follow from the Riemann invariants.
Depending on the sign of the eigenvalues of convective flux Jacobians, the
information is transported out of or into thecomputational domain along
the characteristic. The values of k and ω at the far-field boundary are
calculated from the following equations:
WhereTi is turbulenceintensityand less than 0.1 %, lm is the length
scale constantand is the orderof 0.001.
• Reynolds No. =5.7 *10^6
• AtmosphericTemp. =300K
• AtmosphericPressure= 1.01* 10^5 N/m2
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15. FurtherDiscussion:-
• RESULTS AND DISCUSSION
1. Effectof Step Location
2. Effect of Step Depth
3. Effectof Step Configuration
• CONCLUSION
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16. REFERENCES
[1] Kline R, The ultimatepaperplane. Simonand Schuster, NewYork, N.Y, 1985
[2] LumsdaineE, Johnson W.S, Fletcher L.M, PeachJ.E, Investigationof the
Kline-Fogleman Airfoil Section forRotorBlade Application. 1974, NASA, AE-
74-1054-1
[3] Fertis D. G, Newairfoil designconceptwithimprovedaerodynamic
characteristics. J AerospaceEng, ASCE, 1994; 7:328-339
[4] Finaish F, Witherspoon S, Aerodynamicperformanceof an airfoilwith
step-inducedvortex for lift augmentation. J AerospaceEng, ASCE, 1998; 7:9-16
[5] AbbotI. H, Von Doenhoff A. E, Theory of Wing Sections. McGraw-Hill
Book Company, NewYork, 1949
[6] Adams E. W, Johnston J. P, Eaton J. K, Experimentson the structureof
turbulentreattaching flow. 1984, ReportMD- 43, Departmentof Mechanical
Engineering, Stanford University
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