Aerodynamics and Flight Mechanics - University Of...

Smart Icing Systems NASA Review, May 18-19, 1999

Aerodynamics and Flight Mechanics

Principal Investigators: Mike BraggEric Loth

Graduate Students: Holly Gurbacki (CRI support)

Tim Hutchison Devesh Pokhariyal (CRI support)

Ryan Oltman

SMART ICING SYSTEMS Research Organization

Core Technologies

Flight SimulationDemonstration

FlightMechanics

Controls and Sensor

Integration

HumanFactors

AircraftIcing

Technology

Operate andMonitor IPS

EnvelopeProtection

AdaptiveControl

CharacterizeIcing Effects

IMS Functions

Safety and EconomicsTrade Study

Aerodynamicsand

Propulsion

Aerodynamics and Flight Mechanics

Goal: Improve the safety of aircraft in icing conditions.

Objective: 1) Develop a nonlinear iced aircraft model. 2) Develop steady state icing characterization

methods and identify aerodynamic sensors. 3) Identify envelope protection needs and

methods.

Approach: First use Twin Otter and tunnel data to developa linear clean and iced model. Then develop anonlinear model with tunnel and CFD data. Usethe models to develop characterization and envelope protection.

THE AERODYNAMICS ANDFLIGHT MECHANICS GROUP

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Aircraft - FlightMechanicsAnalysis

Steady StateCharacterization

Flight Mechanics Model

Devesh Pokhariyal, Dr. Bragg

Tim Hutchison, Dr. Bragg

Ryan Oltman, Dr. Bragg

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Smart Icing System Research

Holly Gurbacki, Dr. Bragg AerodynamicSensors

Outline

• Flight Mechanics Model• Development of Clean Aircraft Model• Development of Iced Aircraft Model• Flight Mechanics Analysis of Clean and Iced Aircraft• Steady State Characterization• Hinge-Moment Aerodynamic Sensor• Summary and Conclusions• Future Plans/CFD Analysis

Equations of Motion

• 6 DoF equations of motion :

xx TA FFsinmg)WQVRU(m ++−=+− θθ&

yy TA FFcossinmg)WPURV(m ++=−+ θθφφ&

zz TAz FFcoscosmg)VPUQW(m ++=+− θθφφ&

TAyyzzxzxzxx LLRQ)II(PQIRIPI +=−+−− &&

xzzzxxyy MM)RP(IPR)II(QI +=−+−−&

TAxzxxyyxzzz NNQRIPQ)II(PIRI +=+−+− &&

Equations of Motion (cont.)

• The longitudinal equations of motion areconsidered initially the forces along theaircraft body axes are resolved into lift anddrag forces to yield:

TcosT)cosDsinL(sinmg)WQVRU(m φφααααθθ +−+−=+−•

TsinT)sinDcosL(coscosmg)VPUQW(m φφααααθθφφ +−−+=+−•

xzzzxxyy MM)RP(IPR)II(QI +=−+−−•

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Twin Otter Clean Model (v1.0)

• Longitudinal model is derived from flightdynamics data in AIAA report 86-9758, AIAAreport 89-0754 and AIAA 93-0754

• Dimensional parameters:Parameter Value UnitsWing Area 39.02 m2Wing Span 19.81 mAspect Ratio 10Mean Aerodynamic Chord 1.981 mMass 4150 kgAirspeed 61.73 m/sAltitude 1524 mMoments of Inertia: Ixx, Iyy, Izz, Ixz 21279, 30000,44986, 1432 kg.m2Flap Deflection 0 deg

Clean Dimensional Derivatives (v1.0)

Nondimensional Clean Dimensional CleanParameter Value Parameter Value UnitsCL 0.5 Mδ -10.45 /s2

CLo 0.2 Mu 0 /ft-s

CLq 19.97 Mq -3.06 /s

CLα 5.66 Mαdot -0.804 /s

CLαdot 2.5 MTu 0 /ft-s

CLδE 0.608 Mα -7.87 /s2

CD0 0.0414 Zδ -40.33 ft/s2

K 0.0518 Zα -379.03 ft/s2

Cm 0 Zu -0.31 /sCmo 0.15 Zαdot -2.446 ft/s

Cmq -34.2 Zq -19.7 ft/s

Cmα -1.31 Xα 13.72 ft/s2

Cmαdot -9 XTu 0.0149 /s

CmδE -1.74 Xu -0.033 /sXδ 0 ft/s2

Empirical Clean Model Method

• The clean aircraft model is developed using methodsoutlined in NASA TN D-6800 for twin-engine,propeller-driven airplanes.

• Lift, pitching moment, drag and horizontal tail hingemoments are modeled.

• Method is based on theoretical and empiricalmethods (USAF Datcom handbook and NACA/NASAreports)

• Model requires mainly aircraft geometry and thus canbe applied to different aircraft at minimal cost.

• Waiting for Twin Otter data

Empirical Clean Model (NASA TN D-6800)

• Representative equations:

powere)hf(hwfn)C()C(CCC LLLLL ∆+∆++=

powertabe)hf(hwfn)C()C()C(CCC MMMMMM ∆+∆+∆++=

powersystemcoolingnifihiwi0)C()C()C()C()C()C(CC DDDDDDDD ∆++++++=

0tab)f(h)f(h)C(

)xx()C(

)xx()C(C M

4/chingeL

achingeLh δδδδδδ

′∆+−

∆+−

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Icing Effects Model

To devise a simple, but physically representative, modelof the effect of ice on aircraft flight mechanics for use inthe characterization and simulation required for theSmart Icing System development research.

Objective:

Linear Icing Effects Model

• = Arbitrary coefficient (CLα, Cmδe, etc.)

• = icing severity factor

• = coefficient icing factor

)A(Ciceiced)A( C)k1(CA

ηη+=

iceηη

Icing Factors

• is the icing severity factor

where: = freezing fraction

= accumulation parameter

= collection efficiency

• is the coefficient icing factor

( )EA,nf cice =ηη

)conditionsicing.,configandgeometryaircraft,IPS(fk )A(CA=

iceηηn

ηηice Formulation

• ∆Cd fit as a function of n and AcE− ∆Cd data obtained from NACA TM 83556

• ∆Cdref calculated from ∆Cd equation usingcontinuous maximum conditions

• ηice formulated such that ηice=0 at n=0 or AcE=0

( )( )min45t,conditions.max.cont,0012NACAC

dataIRT,'3c,0012NACAC

dice =∆

=∆=ηη

∆∆Cd Curve Fit of NASA TM 83556 Data

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

∆∆C

n=.33 Data

n=.33 Curve Fit

n=1 Data

n=1 Curve Fit

ηηice Reference Value

• To nondimensionalize the ∆Cd equation, a referencecondition was chosen based on FAA Appendix CMaximum Continuous conditions.

• NACA 0012 c = 3 ft.

MVD = 20 µm V∞ = 175 knotsLWC = 0.65 g/m3 t = 45 minT0 = 25 °F

• These conditions yielded a ∆Cd = 0.1259 at ηice=1

Final ηηice Equation (v1.0)

( ) ( )2c2c1ice EAZEAZ +=ηη

n176.3Z1 = 432

2 hngnfnen1dncnbnan

26.179810d

58.248690c

52.54370b

33.4547a

697.36h

595.250g

295.33f

322.4e

−=−=

Variation with n and AcE

0 0.2 0.4 0.6 0.8 1n

η ice

AcE=.01

AcE=.02

AcE=.03

AcE=.04

Cont. Max. Case

Glaze Ice Rime Ice

ηηice Variation with AcE and n

0.000 0.010 0.020 0.030 0.040 0.050

ηηic

Iced Model (v1.0)

• Equations:

)k1()C()C( iceCAA Acleaniceηη+= 1

AiceC −=ηη 2

L0DD KCCC +=

CL CLo CLq CLα CLαdot CLδE CD0 Kclean 0.5 0.2 19.97 5.66 2.5 0.608 0.041 0.052iced 0.5 0.2 19.7 5.094 2.5 0.55 0.062 0.057kCAηice 0 0 -0.014 -0.1 0 -0.095 0.5 0.1

Cm Cmo Cmq Cmα Cmαdot CmδE

clean 0 0.15 -34.2 -1.31 -9 -1.74iced 0 0.15 -33 -1.18 -9 -1.566kCAηice 0 0 -0.035 -0.099 0 -0.1

Comparison of Clean and Iced Model (v1.0)

Parameter Clean Iced Units Mδ -10.44 -9.4 /s2

Mu 0 0 /ft-s

Mq -3.055 -2.948 /s

Mαdot -0.804 -0.804 /s

MTu 0 0 /ft-s

Mα -7.863 -7.083 /s2

Zδ -40.29 -36.45 ft/s2

Zα -378.72 -342.67 ft/s2

Zu -0.31 -0.31 /sZαdot -2.446 -2.466 ft/s

Zq -19.697 -19.431 ft/s

Xα 13.706 13.898 ft/s2

XTu 0.0149 0.0266 /s

Xu -0.033 -0.0463 /sXδ 0 0 ft/s2

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Flight Dynamics and Control Toolbox

• Flight Dynamics Code 1.3– FDC 1.3 is a free source code written by Marc

Rauw (based in the Netherlands)– Code developed using MATLAB and SIMULINK– 6 DoF equations:

• Assumptions– The body is assumed to be rigid during motions– The mass of the aircraft is assumed to be constant during

the time-interval in which its motions are studied– Earth is assumed to be fixed in space & the curvature is

neglected

• 12 - Nonlinear differential equations used to describe themotion

Velocity

Forces & Moments

FDC Equations

( ) ββααββββααββααββββαα cossinwqupvsinvrupwcoscosurvqwsinsinFsinFcoscosFm1

V wwwwwwwwwzyx

+−−

+−−++=

••••

],,,,,,,,,r,q,p,,,,,,,0[CScVM

],,,,,,,,,r,q,p,,,,,,,0[CSVF2

earfrafe3232

N,M,L2

2earfrafe

3232z,y,x

ββββδδαδαδαδαδαδαδδδδδδδδδββββββααααααρρ

ββββδδαδαδαδαδαδαδδδδδδδδδββββββααααααρρ&

⋅⋅⋅⋅⋅=

⋅⋅⋅⋅=

( ) ( ) ββααααααααααααββ

αα tansinrcospqsinurvqwcoswqupvcosFsinFm1

wwwwwwzx +−+

+−−+−=

•••

( ) ααααββααββββααββααββββααββ cosrsinpsinsinwqupvcosvrupwsincosurvqwsinsinFcosFsincosFm1

wwwwwwwwwzyx −+

+−+−+−=

••••

Pitch, Roll & Yaw Rates

FDC Equations (cont.)

( )( )( )

( )( )( ) ( ) ( )

( ) ( )

( )( ) ( )( )( ) ( ) ( ) N

JxzIzzIxxIxx

LJxzIzzIxx

JxzIzzIxxJxzIzzIyyIxx

pJxzIyyIxxIxxr

rpIyyIxz

IxxIzzq

NJxzIzzIxx

JxzIzzIxxIzz

qpJxzIzzIxx

JxzIzzIyyIxxr

JxzIzzIxxJxzIzzIzzIyy

⋅−⋅

+⋅−⋅

−⋅⋅+−

−⋅+−⋅=

+−⋅−⋅⋅−

⋅−⋅

+⋅−⋅

−⋅⋅+−

+⋅−⋅

−⋅−=

Euler Angles

Position

( ) θθψψθθϕϕϕϕϕϕϕϕϕϕθθ

θθϕϕϕϕ

sinptancosrsinqp

sinrcosqcos

cosrsinq

+=++=−=

( ){ } ( )( ){ } ( )( ) θθϕϕϕϕθθ

ψψϕϕϕϕψψθθϕϕϕϕθθ

coscoswsinvsinuz

cossinwcosvsinsincoswsinvcosuy

sinsinwcosvcossincoswsinvcosux

eeeeee

++−=

−−++=

The current aircraft model (without turbulence) is usingthe following equations for the longitudinal mode:

( )ββααββαα sinsinFcoscosFm1

V zx +=•

( ) ( ) ββααααααααββ

αα tansinrcospqcosFsinFm1

zx +−+

( ) ( )IyyM

rpIyyJxz

IxxIzzq 22 +−⋅−⋅⋅

ϕϕϕϕθθ sinrcosq −=&

( ){ } ( )( ) θθϕϕϕϕθθ

ψψϕϕϕϕψψθθϕϕϕϕθθ

coscoswsinvsinuz

sinsinwcosvcossincoswsinvcosux

eeeeee

++−=

−−++=&

Open Loop Analysis Tool for Nonlinear Twin Otter Model

Closed Loop Analysis Tool for Nonlinear Twin Otter Model

Validation of the FDC (TIP flight p5220)

• Code is validated by comparing the responseof a doublet to published NASA data (AIAA99-0636) for the Twin Otter aircraft.

• Flight conditions:• V = 187 ft/s

• alt. = 5620 ft

• α = 3.53 deg

• δF = 0 deg

Clean and Iced Model (v2.0 TIP)

CX0 CXα CXα2 CXδe

Clean -0.076 0.390 2.910 0.096Iced -0.090 0.714 1.744 0.068ηice.kC(A) 0.182 0.831 -0.401 -0.290

CZ0 CZα CZα2 CZq CZδe

Clean -0.311 -7.019 4.111 -3.182 -0.234Iced -0.318 -7.510 6.573 -7.395 -0.3541ηice.kC(A) 0.020 0.070 0.599 1.322 0.513248

Cm0 Cmα Cmα2 Cmq Cmδe

Clean -0.011 -0.879 -3.852 -19.509 -1.8987Iced -0.026 -0.790 -3.930 -21.480 -1.8629ηice.kC(A) 1.361 -0.101 0.020 0.101 -0.01886

Ref: Robert Miller and W. Ribbens, AIAA 99-0636

Validation of FDC 1.3

• Validation of the FDC (TIP flight p5220, no ice)

0 5 10 15Time, sec

Flight DataFDC

-10-8-6-4-202468

0 5 10 15Time, sec

Flight DataFDC

Validation of FDC 1.3 (cont.)

181182183184185186187188189190

0 5 10 15Time, sec

Flight DataFDC

• Validation of the FDC (TIP flight p5220, no ice)

5610561556205625563056355640564556505655

0 5 10 15Time, sec

Flight DataFDC

Validation of FDC 1.3 (cont.)

• Validation of the FDC (TIP flight p4601, iced)

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Clean and Iced Dynamic Comparison

Initial trimmed flight conditions:• Altitude = 5600 ft• Velocity = 187.5 ft/sec• Angle of Attack = 3.52°• Aircraft Model v2.0Clean:

ηice = 0.0Iced:

ηice = .15

Dynamic Analysis, Clean & Iced

Dynamic Analysis, Clean & Iced (cont.)

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Steady State Characterization

Goal:• Analyze quasi-steady data characterized by control

inputs and disturbances insufficient to excite dynamicmodes to characterize the icing encounter.

Objectives:• Determine onset of icing on an aircraft in real-time

during flight.• Estimate the severity of ice accretion in terms of its

effect on performance, stability and control.• Identify location of ice accretion on the A/C and the

potential safety hazards.

Steady State Characterization (cont.)

Approach:• Acquire flight data, using onboard sensors.• Process aircraft data to obtain nondimensional

parameters in iced and equivalent clean conditions.• Compare iced and clean models to back out “useful

flight parameters” such as ∆CL, ∆δE, ∆CD, and ∆Ch.• Set threshold values to determine onset of icing.

• Analyze the ∆’s and other sensor information to determine the type and location of ice accretionand the potential safety hazards.

S. S. Characterization Results

• Use FDC 1.3 auto-pilot configuration set at:– constant altitude– constant power

• Analyze the effects of icing on:– angle of attack– elevator deflection– velocity and drag characteristics

• The clean and iced configurations have beencompared for conditions with and without turbulence.

• The icing simulations are set at ηice = .15 and thesimulations are run for 22 minutes.

Steady State Flight Conditions

The initial conditions for the steady state analysis are:• Altitude = 9000 ft• Velocity = 268 ft/sec• Angle of Attack = 0.5°• Elevator Deflection = -0.6°

ηice(t = 0) = 0ηice(t = 22 min.) = 0.83

Clean and Iced Model v2.1 is used.

Turbulence Model

• The turbulence model used in the FDC 1.3 steadystate analysis is based on the Dryden spectraldensity distribution.

• The turbulence intensity produces an aircraft z-acceleration of 0.13g RMS with typical variations of+/- 0.5g encountered over the 22 minute flight.

Comparison for αα and δδE (No turbulence)

0ice =ηη

83.0ice =ηη

0ice =ηη

83.0ice =ηη

Comparison for CD and V (No turbulence)

83.0ice =ηη

0ice =ηη

0ice =ηη 83.0ice =ηη

Comparison for αα and δδE (turbulence)

0ice =ηη

83.0ice =ηη

0ice =ηη

83.0ice =ηη

Comparison for CD and V (turbulence)

0ice =ηη

83.0ice =ηη0ice =ηη

83.0ice =ηη

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Wind Tunnel Testing

Sensing Unsteady Hinge Moments

• Objective: Use unsteady hinge moment to sense potentialcontrol problems and nonlinearities due to ice-induced flowseparation

• Approach:– NACA 23012 airfoil model with simple flap and forward-facing

quarter round simulated ice

– Steady-state Cl, Cd and Cm from balance and pressures andCh from hinge-moment balance and pressures

– Time series and frequency spectra of unsteady Ch from hinge-moment balance

– Time series and frequency spectra of flow unsteadiness fromhot-wire anemometer placed within and aft of separationbubble, in shear-layer, and over flap

Unsteady Ch RMS

-10 -5 0 5 10 15 20

AOA (degrees)

Clean x/c = .02 x/c = .10 x/c = .20

Cl , max

NACA 23012, Re = 1.8 million, δδ f = 0

99 00 01 03

Federal Fiscal Year98 02

Aerodynamics and Flight Mechanics Waterfall Chart

Linear Iced Aircraft Model

Wind Tunnel Testing

Nonlinear Iced Aircraft Model

Determine Need for and SelectAerodynamics Sensors

Steady State Characterization of Icing Effects

S. S. Char. Method

Summary and Conclusions

• Clean twin otter linear models developed.• Method for including icing effects in linear

model developed.• Flight mechanics computational method

available.• Iced twin otter models for TIP studies

available and performs well.• Steady state characterization formulated and

initial results promising.

Future Research

• Complete and refine linear models, icing effectsmodel and perform icing accident analysis

• Complete steady state characterization method• Study and develop envelop protection schemes• Identify aerodynamic and other sensors• Develop fully nonlinear model

– Experiment & CFD for AE data bases– Neural Networks for AE interrogation

• Assess Feasibility of a VIFT (Year 4)

Wind TunnelData

IcedAerodynamics

ComputationalFluid

Dynamics

Iced AircraftModel

Clean AircraftModel

to be decided, Dr. Loth

Characterization

Flight Simulation

Envelope Protection

Fully Non-Linear APC Overview

Fully Non-Linear Model

• Objective:For flight mechanics, we would like non-linear Aero-Performance Curves (APC): CL, CD, Cm, Ch as afunction of α , δ , etc. and environmental conditions

• Method:– Use high-quality previous and new data sets

(experimental and computational) to construct All-Encounters (AE) data bases

– Construct neural networks for use in interrogation ofany condition atmospheric/flight condition

– Apply neural networks to flight mechanics

All Encounters Data Bases

• Method:– Collect data of ice-shape characteristics (x/cice, k/cice) as

a function of flight conditions (α , d, LWC, T0, Re, etc.):• Icing Research Tunnel Shapes

• In-Flight Icing Shapes

• LEWICE shapes

– Collect data of 2-D APC (Cl, Cm,..) as a function of ice-shape characteristics (x/cice, k/cice) and α and δ :

• Icing Research Tunnel Aerodynamic Tests

• Wind Tunnel Tests for various Ice Shapes

• CFD for various Ice Shapes

Computational Fluid Dynamics

• NSU2D will be the primary code for CFD– unstructured adaptive triangulated grid– Can handle complex shapes & multi-element– Spallart-Almaras turbulence model– Employs en transition model– Unsteady capabilities for flow shedding

• To improve prediction fidelity• To investigate unsteady aerodynamic sensing

– To be parallelized for SG Origin 2000

Sample CFD

• NSU2D LE ice-shape predictions

Neural Network Approach

• Construct Separate Neural Networks for:– Ice-shape characteristics as a function of environmental

conditions– 2-D APC as a function of ice-shape characteristics and

flight conditions

• Train Neural Networks with AE databases• Use analytical methods to convert 2-D APC to

CL,CD,Cm, Ch

• Replace Linear Model with Non-Linear NeuralNetworks for Flight Mechanics

Neural Network for Ice-Shape

• Sample neuron: Y= f(Σ Wi xi) with x i = (α , d, LWC, etc.)

• Wi are trained with data (f refers to a sigmoidal function)

• Y refers to output of a neuron; final output: x/cice, k/cice

x/cice, k/cice

OutputLayer

HiddenLayer 2

HiddenLayer 1

InputLayer

Neural Network Interrogation

• Input are ice-shape characteristics & flight condition• Final output are the 2-D APC: Cl,Cd,Cm, or Ch

Cl ,Cd ,Cm ,Ch

x/cice

OutputLayer

HiddenLayer 2

HiddenLayer 1

InputLayer

k/cice

Feasibility of a Virtual Icing Flight Test

• Objective:Assess Feasibility of a VIFT (for a follow-on study) whichwould simulate a complete icing encounter includingtemporal resolution of ice accretion, pilot input, IMS, etc.

• Goal: Consider requirements for integrating– Ice Accretion (LEWICE)– Aerodynamic Predictions (NSU2D)– A/C Flight Dynamics Model (Selig)– Pilot Input / Flight Simulator Output (Sarter/Selig)– IMS Control (Basar/Perkins)

Virtual Icing Flight Test Configuration?

a) receive input from pilot, IM S,

and aerodynamic performance

b) computes A /C dynamic state

c) displays cockpit viewincluding IM S warnings/info

" Aero Workstation" for

simulated A/C performance" A/C Workstation" for virtual airplane state & pilot I/O

Computes as function. of time

a) ice shape from LEW ICE

b) instantaneous aero forces &

moments as a function of

angle-of-attack & flap defl.

A tmospheric model: real time conditions: pressure, temperature, humidity, L W C of clouds

aero forces/moments,

virtual ice sensor output

" I M S Workstation" for icing

ID and IMS decision making:

modify display/IPS/contr ol

From A /C state data can:

a) issue warnings to pilot

b) initiate IPS operation

c) modify flight envelope

d) institute control adaptation

Dedicated NC SA

Supercomputer

A /C dynamic state, IPS on?

IPS initiating

A /C state, pilot input

icing sensor data

Send appropriate IM S output:

see levels a)-d) listed below

H 1H 0

Aerodynamics and Flight Mechanics - University Of...

Documents

Transcript of Aerodynamics and Flight Mechanics - University Of...

AUG06 - DTIC · Oscillation in the Flow Over a NACA0012 Airfoil with an 'Iced' Leading Edge", Low Reynolds Number Aerodynamics, T. J. Mueller (Editor), Springer-Verlag Berlin, Heidelberg,

ISSUE two For true ... · Lychee Ginger Iced Tea 3 Mixed Berry Iced Tea 3 Kiwi Iced Tea Rose Iced Tea 3 200 180 180 180 180 Iced Tea Americano, French Press, Latte, Mocha, Cappuchino,

A virtual mass model in train aerodynamics › Secure › elibrary › papers › CR... · A virtual mass model in train aerodynamics I. Tanackov1,2, J. Tepić1, M. Kostelac3, G.

AIAA Applied Aerodynamics Technical Committee APA … Aerodynamics... · AIAA Applied Aerodynamics Technical Committee APA-TC Minutes ... Supersonic and Hypersonic Aerodynamics ...

2 - Iced-Airfoil Aerodynamics

45331520 Model Aircraft Aerodynamics m Simons

Introduction to AERODYNAMICS Aerodynamics is an applied ...

RAREFIED-FLOW SHUTTLE AERODYNAMICS FLIGHT MODEL

Chapter 2 Aerodynamics Model - Virginia TechCHAPTER 2. AERODYNAMICS MODEL 21 Center [44] were also costly, requiring a 12 block grid with 876 ;912 cells. It is abun-dantly clear that

Iced Organic Coffee

Aerodynamics Model for a Generic ASTOVL Lift-Fan Aircraft€¦ · Aerodynamics Model for a Generic ASTOVL Lift-Fan Aircraft LOURDES G. BIRCKELBAW, WALTER E. MCNEILL, AND DOUGLAS A.

ICED INN RUSSIA

Model Aircraft Aerodynamics

Unsteady aerodynamics of low-pressure steam … aerodynamics of low-pressure steam turbines operating under low volume flow conditions thÈse no 6096 (2014) ... 4.3 steam model turbine

ICED November

delivery order form delivery address€¦ · mocha 5.0 additional espresso shot 1.0 iced americano 3.5 iced cappuccino 4.0 iced latte 4.5 iced caramel latte 5.0 iced vanilla latte

ICED Magazine March

Alcoholic Beverages Beverages C 5 - Yoshimatsu · Beverages C le・Iced Tea 3.5 ・Iced Green Tea 3 ・Iced Matcha 3.5 ・Iced Matcha Float 5 ・Iced Black Tea 3 ・Ginger Honey Tea

KARTA PIĆA · homemade iced tea breskva.....190.00 din homemade iced tea malina.....190.00 din homemade iced tea jagoda.....190.00 din homemade iced tea kivi.....190.00 din homemade

Validation of a Low-Cost Transitional Turbulence Model for Low-Reynolds-Number External Aerodynamics