ESDU Transonic Aerodynamics Series
The information is concerned with the flow around aerofoils, wings, bodies and cowls at high subsonic, transonic and (in a few cases) low supersonic speeds. The transition from high subsonic to transonic flow is marked by the development of a local region of supersonic flow embedded in the otherwise wholly subsonic flow and the consequent development of shock waves and shock wave drag.
Methods in computational fluid dynamics (CFD) are important in the study of transonic aerodynamics, and information is provided concerning the use of such methods. Example results are given that demonstrate the accuracy that can be achieved for both inviscid and viscous flow. The Sections provide methods of calculating the pressure distribution and loading on aerofoils and wings in high subsonic flow, provide methods of calculating the dragrise Mach number and/or the wave drag of aerofoils, wings and bodies, and provide exchange rates between pertinent aerofoil and wing design parameters at the dragrise condition. For aerofoils and wings, particular attention is paid to the prediction of shockinduced separation and both direct (CFD) prediction and semiempirical methods are given.
CFD has also been used to provide data for the wave drag coefficient for families of low fineness ratio forebodies and for an extensive family of axisymmetric forecowls. The data demonstrate how the pressure distribution and shock waves develop on the forebodies and forecowls considered as the Mach number is increased and as detailed changes in geometry are made.
A unique feature is the extensive treatment of the application of vortex generators to the control of shockinduced separation, particularly on wings, which includes consideration of the aerodynamic principles involved, a design guide and case studies of the use of vortex generators.

Section 1: Explanatory and General Guidance

ESDU 99034
Transonic Aerodynamics Series organisation: preface, location schedule, amendment record. 
ESDU 90008
Introduction to transonic aerodynamics of aerofoils and wings.

ESDU 99034

Section 2: Aerofoils  Estimation of Pressure Distribution

ESDU TD MEMO 6511
A method for estimating the pressure distribution between the crest and the trailing edge on the surface of an aerofoil section in a sonic stream. 
ESDU 69013
A method for estimating the pressure distribution on the surface of a twodimensional aerofoil in a sonic stream. 
ESDU 72025
Secondorder method for estimating the subcritical pressure distribution on a twodimensional aerofoil in compressible inviscid flow. 
ESDU 76002
Firstorder method for estimating the subcritical pressure distribution on a twodimensional aerofoil in compressible viscous flow.

ESDU TD MEMO 6511

Section 3: Aerofoils  Computational Methods

ESDU 79009
Numerical methods for solving the potential flow equations for twodimensional aerofoils in subsonic and transonic flows: brief details, test cases and examples. 
ESDU 81019
Methods for estimating the pressure distribution on a twodimensional aerofoil in viscous transonic flow.

ESDU 79009

Section 4: Aerofoils  Drag Rise, Designs, Separation

ESDU TD MEMO 6407
A method of estimating dragrise Mach number for twodimensional aerofoil sections. 
ESDU 71019
Dragrise Mach number of aerofoils having a specified form of uppersurface pressure distribution: charts and comments on design. 
ESDU 71020
Aerofoils having a specified form of uppersurface pressure distribution: details and comments on design. 
ESDU 78010
The lift achievable by aerofoils having a particular form of supercritical uppersurface pressure distribution that yields only small wave drag. 
ESDU 81020
A method of estimating a separation boundary for twodimensional aerofoil sections in transonic flow. 
ESDU 92008
Direct prediction of a separation boundary for aerofoils using a viscouscoupled calculation method.

ESDU TD MEMO 6407

Section 5: Aerofoils  Excrescence Drag Magnification

ESDU 87004
Calculation of excrescence drag magnification due to pressure gradients at high subsonic speeds. 
ESDU TM 181
An assessment of methods for estimation of turbulent boundarylayer profiles

ESDU 87004

Section 6: VGK Aerofoil Method

ESDU 96028
VGK method for twodimensional aerofoil sections. Part 1: Principles and results. 
ESDU 96029
VGK method for twodimensional aerofoil sections. Part 2: user manual for operation with MSDOS and UNIX systems. 
ESDU 97030
VGK method for twodimensional aerofoil sections. Part 3: estimation of a separation boundary in transonic flow. 
ESDU 98031
VGK method for twodimensional aerofoil sections. Part 4: estimation of excrescence drag at subsonic speeds. 
ESDU 99032
VGK method for twodimensional aerofoil sections. Part 5: design to a specified uppersurface pressure distribution. 
ESDU 01033
VGK method for twodimensional aerofoil sections. Part 6: aerofoil with simple hinged flaps. 
ESDU 03015
Transonic data memorandum. VGK method for twodimensional aerofoil sections. Part 7: VGK for Windows.

ESDU 96028

Section 7: Wings  Aerodynamic Design

ESDU 97017
Guide to wing aerodynamic design. 
ESDU 98013
Aerodynamic principles of winglets.

ESDU 97017

Section 8: Wings  Spanwise Loading

ESDU TD MEMO 6309
Graphical method for estimating the spanwise distribution of aerodynamic centre on wings in subsonic flow. 
ESDU TD MEMO 6403
Method for the rapid estimation of theoretical spanwise loading due to a change of incidence. 
ESDU 73012
Method for predicting the pressure distribution on swept wings with subsonic attached flow.

ESDU TD MEMO 6309

Section 9: Wings  Drag Rise, Wave Drag, Separation

ESDU 72027
Adaptation of dragrise charts in T.D. Memor. 71019 to the midsemispan portion of swept and tapered planforms. 
ESDU 78009
A framework relating the dragrise characteristics of a finite wing/body combination to the those of its basic aerofoil. 
ESDU 87003
A method of determining the wave drag and its spanwise distribution on a finite wing in transonic flow. 
ESDU 91021
A method of estimating a flow breakdown boundary for aerofoils and swept wings in transonic flow.

ESDU 72027

Section 10: VFP Wing Method

ESDU 02013
Fullpotential (FP) method for threedimensional wings and wingbody combinations  inviscid flow. Part 1: Principles and results. 
ESDU 02014
Fullpotential (FP) method for threedimensional wings and wingbody combinations  inviscid flow. Part 2: Use of FP and related programs. 
ESDU 06015
Fullpotential method for threedimensional wings and wingbody combinations  inviscid flow. Part 3: Method with improved estimates of body lift and drag contributions (FPIBE). 
ESDU 06016
Fullpotential method for threedimensional wings and wingbody combinations  inviscid flow. Part 4: Evaluation of trailingvortex drag and wave components. 
ESDU 10014
Fullpotential method for threedimensional wings and wingbody combinations Part 5: Preprocessor to represent effect of fore and aftbody shape on wing flow 
ESDU 11007
Fullpotential method for threedimensional wings and wingbody combinations Part 6: Fullpotential with frozen boundary layer 
ESDU 13013
Viscous fullpotential (VFP) method for threedimensional wings and wingbody combinations. Part 1: Validation of VFP results with experiment and comparisons with other methods. 
ESDU 13012
Viscous fullpotential (VFP) method for threedimensional wings and wingbody combinations. Part 2: Use of VFP and related programs. 
ESDU 13014
Viscous fullpotential (VFP) method for threedimensional wings and wingbody combinations. Part 3: VFP error messages, failures and suggested remedies.

ESDU 02013

Section 11: Vortex Generators

ESDU 93024
Vortex generators for control of shockinduced separation. Part 1: introduction and aerodynamics. 
ESDU 93025
Vortex generators for control of shockinduced separation. Part 2: guide to use of vane vortex generators. 
ESDU 93026
Vortex generators for control of shockinduced separation. Part 3: examples of applications of vortex generators to aircraft.

ESDU 93024

Section 12: Axisymmetric Bodies  Drag Rise

ESDU 74013
A method for estimating dragrise Mach number at zero incidence of smooth or bumpy nonducted axisymmetric bodies without or with fins.

ESDU 74013

Section 13: Axisymmetric Forebodies  Wave Drag, Pressure Distribution

ESDU 79004
Forebodies of fineness ratio 1.0, 1.5 and 2.0, having low values of wave drag coefficient at transonic speeds. 
ESDU 80008
Axial pressure coefficient distributions for forebodies of fineness ratio 1.0, 1.5 and 2.0 at zero incidence in transonic flow. 
ESDU 83017
The wave drag coefficient of spherically blunted secant ogive forebodies of fineness ratio 1.0, 1.5, and 2.0 at zero incidence in transonic flow. 
ESDU 83018
Axial pressure coefficient distributions for spherically blunted secant ogive forebodies of fineness ratio 1.0, 1.5 and 2.0 at zero incidence in transonic flow. 
ESDU 89033
Pressure drag and lift contributions for blunted forebodies of fineness ratio 2.0 in transonic flow (M_{∞} ≤ 1.4).

ESDU 79004

Section 14: Axisymmetric Forecowls  Wave Drag, Pressure Distribution

ESDU 94013
NACA 1series geometry representation for computational fluid dynamics. 
ESDU 94014
Wave drag coefficient for axisymmetric forecowls at zero incidence (M_{∞} ≤ 1.5). 
ESDU 94015
Surface pressure coefficient distributions for axisymmetric forecowls at zero incidence (M_{∞} ≤ 1.5)

ESDU 94013

Section 15: Design Optimisation

ESDU 99019
Constrained multivariate optimisation techniques for the design of aerofoil sections 
ESDU 99020
Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: single, geometry variation: LE and TE flap deflection or camber line vars, initial aerofoil: RAE 2822 
ESDU 99021
Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: dual, geometry variation: LE and TE flap deflection and camber line vars, initial aerofoil: RAE 2822, 
ESDU 00022
Example of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: single, geometry var: LE and TE flaps, initial aerofoil: combat aircraft section, CFD: BVGK (viscous flow) 
ESDU 00023
Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: single, geometry var: LE and TE flaps, initial aerofoil: combat aircraft section, CFD: BVGK (inviscid), Euler code. 
ESDU 01024
Example of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Dual design point, upper and lower surface shape geometry, leading and trailing edge flap deflections, RAE 2822, Euler code and BVGK. 
ESDU 01025
Examples of the application of constrained multivariate optimisation techniques to the design of aerofoil sections. Design point: single, upper and lower surfaces geometry and camber line variations, initial aerofoil: NACA 0012 and RAE 2822, CFD: BVGK.

ESDU 99019

Section 16: Surface Flow Visualisation

ESDU 03014
Surface flow visualisation in aircraft design

ESDU 03014

Section 17: Extrapolating WindTunnel Data

ESDU 05022
Extrapolating windtunnel data to fullscale Reynolds number. Part 1: Principles 
ESDU 07010
Extrapolating windtunnel data to fullscale Reynolds number Part 2: Procedures 
ESDU 09015
Extrapolating windtunnel data to fullscale Reynolds number Part 3: Example (i) Choice of simulation criteria and transitionstrip locations for the F4 Wing/Body combination at the design condition 
ESDU 11006
Extrapolating windtunnel data to fullscale Reynolds number Part 3: Example (ii) Comparison of extrapolated lowReynoldsnumber lift measurements on the F4 wing/body with highReynoldsnumber measurements 
ESDU 09016
Use of localflow conditions for calculation of roughnessparticle height in transition strips on wings 
ESDU 14007
Selection of roughness bands to induce boundarylayer transition in windtunnel testing 
ESDU 12006
Method to determine surface finish required to minimise local skin friction in the presence of a turbulent boundary layer.

ESDU 05022

Section 18: Wind Tunnel Interference

ESDU 95014
Upwash interference for wings in solidliner wind tunnels using subsonic linearisedtheory.

ESDU 95014
Users of this Series may find the following apps useful.
 International Standard Atmosphere app
The app evaluates, at a given pressure altitude, pressure, temperature and density (and their corresponding relative values) together with the absolute values of the speed of sound, kinematic and dynamic viscosity and thermal conductivity. It also determines V_{TAS}, V_{EASM}, kinetic pressure and unit Reynolds number for a specified Mach number at the given pressure altitude. Calculations are limited to the troposphere and stratosphere in the ISA.
 Wing liftcurve slope app
A modified version of the HelmboldDiederich equation is used to obtain the liftcurve slope of a wing of trapezoidal planform, provided the wing is thin and has an aspect ratio greater than 1.5. The wing may be planar or have only moderate camber and twist. Compressibility effects are catered for by means of the classic PrantlGlauert factor, but the flow must remain both attached and wholly subcritical. The original HelmboldDiederich equation was often used before there was general access to more soundly based methods such as the liftingsurface theory that has been used as the basis of ESDU 70011. However, the modified version used in this calculator provides estimates accurate to within a few per cent of those obtained by ESDU 70011. The full background to this method, and that of ESDU 70011, is given in ESDU TM 169 in the ESDU Aerodynamics Series.
ESDU Series:
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 Transonic Aerodynamics
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