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ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS

GRADUATION PROJECT

A PARAMETRIC STUDY FOR INTAKE FLOWS

Hasan Berk GÜÇLÜ

JULY, 2020

Thesis Advisor: Doç.Dr. Bayram ÇELİK

Department of Aeronautical Engineering

Anabilim Dalı : Herhangi Mühendislik, Bilim

Programı : Herhangi Program

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JULY, 2020

ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS

GRADUATION PROJECT

Hasan Berk GÜÇLÜ

(110150046)

(110150046)

Department of Aeronautical Engineering

Anabilim Dalı : Herhangi Mühendislik, Bilim

Programı : Herhangi Program

Thesis Advisor: Doç.Dr. Bayram ÇELİK

A PARAMETRIC STUDY FOR INTAKE FLOWS

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Thesis Advisor : Doç.Dr. Bayram ÇELİK .............................

İstanbul Technical University

Jury Members : Prof. Dr. Mehmet ŞAHİN .............................

İstanbul Technical University

Prof. Dr. Fırat Oğuz EDİS ..............................

İstanbul Technical University

Hasan Berk Güçlü,student of ITU Faculty of Aeronautics and Astronautics student

ID 110150046, successfully defended the graduation entitled “A Parametric Study

For Intake Flows”, which he prepared after fulfilling the requirements specified in

the associated legislations, before the jury whose signatures are below.

Date of Submission : 13 July 2020

Date of Defense : 21 July 2020

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To my family,

vi

FOREWORD

I would like to express my deepest appreciation to my supervisor, Doç.Dr. Bayram

ÇELİK.

Additionally, I would like to thank to whole lecturers of Aeronautics and Astronautics

Faculty for their valuable efforts that lead to improve my engineering perspective.

I would like to express my special thanks to Turkish Aerospace Industruies and Sergen

UYSAL for invaluable supports for this thesis.

Also, I would like to express thanks to National Center for High Performance

Computing of Turkey (UHeM) for their support

July 2020

Hasan Berk GÜÇLÜ

vii

TABLE OF CONTENTS

Page

ABBREVIATIONS ............................................................................................... ix

NOMENCLATURE ................................................................................................x

GREEK SYMBOLS.............................................................................................. xi

SUBSCRIPTS........................................................................................................ xi

SUPERSCRIPTS .................................................................................................. xi

SUMMARY ........................................................................................................... xv

ÖZ .........................................................................................................................xvi

1. INTRODUCTION ...............................................................................................1

1.1 Objective of Thesis ......................................................................................... 3

2. CHARACTERISTICS OF S-DUCT DIFFUSERS ............................................3

2.1 Pressure Recovery Coefficient (PR) ................................................................ 3

2.2 Distortion Coefficient (DC) ............................................................................ 4

2.3 Contracting Ratio (CR) ................................................................................... 6

3. COMPUTATIONAL FLUID DYNAMICS ANALYSIS ...................................6

3.1 Numerical Approach ...................................................................................... 6

3.2 Flow Solver .................................................................................................... 7

3.3 Turbulence Modelling .................................................................................... 8

4. VALIDATION STUDY ......................................................................................8

4.1 RAE M2129 model details.............................................................................. 9

4.2 Experimental study details .............................................................................10

4.3 Grid Generation .............................................................................................12

4.4 Mesh Independency .......................................................................................13

5. INLET DESIGN STUDY .................................................................................. 16

viii

5.1 Review of several Inlets .................................................................................16

5.2 Grid generation ..............................................................................................18

6. CFD ANALYSIS ............................................................................................... 21

6.1 Selected Flight Phases ...................................................................................21

6.2 Boundary Conditions .....................................................................................21

6.3 Analysis ........................................................................................................22

6.4 Results...........................................................................................................22

7. OPTIMIZATION .............................................................................................. 26

8. CONCLUSION ................................................................................................. 27

REFERENCES ..................................................................................................... 28

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ABBREVIATIONS

AGARD : The Advisory Group for Aerospace Research and Development

AIP : Aerodynamic interface plane

AoA : Angle of attack

ARA : Aircraft Research Association

CFD : Computational fluid dynamics

CFL : Courant number

CFR : Contracting flow ratio

CR : Contracting ratio

DC : Distortion coefficient

HMFR : High mass flow ratio

ISA : International Standard Atmosphere

NACA : National Advisory Committee for Aeronautics

NASA : National Aeronautics and Space Adminstration

PR : Pressure recovery coefficient

RAE : Royal Aircraft Establishment

RANS : Reynolds-Averaged Navier Stokes

TUI : Text user interface

UHeM : National Center for High Performance Computing of Turkey

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NOMENCLATURE

𝐴 : Area

𝑎 : Speed of sound

𝐷 : Diameter

𝐹 : Force

𝐻 : Total enthalpy

𝐽 : Mass flux; diffusion flux

𝐿 : Duct length

L : Reference length

𝑀 : Mach number

𝑃 : Pressure

R : Gas constant

𝑅𝑒 : Reynolds Number

𝑆 : Total entropy

𝑠 : First layer thickness

𝑞 : Dynamic pressure

𝑢, 𝑣, 𝑤 : Cartesian velocity components

𝑥, 𝑦, 𝑧 : Cartesian coordinate system

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GREEK SYMBOLS

Angle of attack

𝛽 Sideslip angle

𝛿 Boundary layer thickness

Δ Change in a variable

∇ Nabla operator

Shear stress

Sector angle

𝛾 Ratio of specific heat

𝜇 Molecular viscosity

Sector angle

Density

SUBSCRIPTS

ℎ𝑙 Condition at engine highlight

𝑡 Local total value i. e. total pressure, 𝑃𝑡

∞ Freestream value i. e. 𝑃∞

SUPERSCRIPTS

− Mean value of component i. e. �̅�

− Time averaged component i. e. ̅

→ Vectoral quantity

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xiii

LIST OF TABLES

Page

Table 2.1 : Table with single row and centered columns ...........................................6

Table 4.1: Geometrical parameters for M2129 ....................................................... 10

Table 4.2: Boundary conditions for experiment DP3532 ........................................ 10

Table 4.3: Additional boundary conditions for experiment DP3532 ........................ 11

Table 4.4: Additional boundary conditions for experiment DP3532 ........................ 12

Table 4.5: Mesh details for independency study. .................................................... 13

Table 4.6: Validation study analysis results.. .......................................................... 15

Table 5.1: Properties of EJ200 turbofan.................................................................. 16

Table 5.2: Values for selected parameters.. ............................................................. 17

Table 5.3: Details of the boundary layer mesh... ..................................................... 18

Table 6.1: Details of boundary conditions for all flight phases. ............................... 21

Table 7.1: Geometrical details and predicted performance values of optimum

geometries.. ............................................................................................................ 26

xiv

LIST OF FIGURES

Page

Figure 1.1: Schematic drawing of an S-duct diffuser.Hata! Yer işareti

tanımlanmamış.

Figure 2.1: Total pressure distribution in AIP- Definition of critical sector .. ......... 5

Figure 2.2: Slices in AIP used for DC(60) calculation. ............................................ 5

Figure 4.1 : M2129 diffuser geometry.. ................................................................... 9

Figure 4.2: Structure of the mesh. ..........................................................................13

Figure 5.1: Highlight area of inlet. .........................................................................17

Figure 5.2: Isometric view of designded inlet geometry. ........................................18

Figure 5.3: Mesh structure of designed inlet.. .........................................................19

Figure 5.4: Wireframe mesh structure of designed inlet. .........................................20

Figure 6.1: Variation of the flow with lip radius. ....................................................23

Figure 6.2: Variation of seperation point with lip radius.. .......................................23

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A PARAMETRIC STUDY FOR INTAKE FLOWS

SUMMARY

The experimental study for RAE2129 subsonic intake model presented in AGARD

advisory report 270 was used for validation study. M2129 is a subsonic inlet model

improved for calibration of CFD codes for S duct diffuser by NASA and UK defense

ministry. AGARD report contains experimental data for high and low mass flow cases

for M2129 which is a S duct inlet. The validation study done by using high mass flow

case. Candidate intake geometries for a jet trainer are created with two geometric

parameters which are lip radius and lip relative length. CATIA V5 generative shape

design module is used to construct candidate inlet geometries. Four values are selected

for each parameter which means total sixteen geometry are created as candidate. Also,

three different flight condition selected for analysis which are take-off, cruise and max

power. Assumptions for flight conditions and geometrical measures are done by

similar jet trainer analysis. EJ200 turbofan engine is selected as reference for required

dimension about engine. ANSYS Fluent 18.2 computational fluid dynamics solver is

used for all analyses. Total 48 analyses are performed with 16 candidate geometry and

3 flight condition. Analysis are performed at National Center for High Performance

Computing of Turkey (UHeM). The effects of the geometrical parameters on the

aerodynamic performance of intake are examined via results of computational fluid

dynamics analysis. The response surface methodology is used to analyze effects of

geometrical parameters. An optimization study is performed in the light of such

information that is taken from response surface analyze. The objective function

importance of the pressure recovery and performance parameters at the takeoff flight

is increased because pressure recovery is the most important parameter and takeoff is

the most critical flight phase. Four optimum geometry is obtained via response surface

analyze.

xvi

HAVA ALIĞI İÇİN PARAMETRİK OPTİMİZASYON ÇALIŞMASI

ÖZ

AGARD 270 numaralı tavsiye raporunda yer alan RAE 2129 ses altı hava alığı

modelinin deneysel çalışma verileri kullanılarak validasyon çalışması

gerçekleştirilmiştir. M2129 modeli S şekilli difüzörler için geliştirilen hesaplamalı

akışkanlar dinamiği yazılımlarının kalibre edilebilmeleri amacıyla NASA ve Birleşik

Krallık savunma bakanlığı tarafından geliştirilen ses haltı hava alığıdır. AGARD

raporunda ‘S şekilli’ difüzöre sahip hava alığı için yüksek ve düşük kütlesel debide

olan deneysel çalışmalar yer almaktadır. Yapılan validasyon çalışmasında yüksek

kütlesel debili deneysel çalışma kullanılmıştır. Bir jet motorlu eğitim uçağı için uygun

olan hava alığı tasarımı yapılmıştır. Bu tasarımda dudak yarıçapı ve dudak bağıl

uzunluğu parametre olarak seçilmiştir. CATIA V5 yazılımının “Generative Shape

Design” modülü kullanılarak aday geometriler oluşturulmuştur. Her bir parametre için

dört farklı değer belirlenmiş ve toplamda 16 adet aday geometri oluşturulmuştur.

Ayrıca kalkış, seyir uçuşu ve maksimum güç durumu olmak üzere üç farklı uçuş

koşulu belirlenmiştir. Geometrisini tasarımı ve uçuş koşullarının belirlenmesi

sırasında yapılan varsayımlar benzer özellikteki eğitim uçaklarının incelenmesi

sonucunda yapılmıştır. EJ200 turbofan motoru, tasarım aşamasında ihtiyaç duyulan

boyut bilgilerinde kullanılmak üzere referans olarak seçilmiştir. Analizler ANSYS

Fluent 18.2 hesaplamalı akış çözücüsü kullanılarak yapılmıştır. 3 farklı uçuş koşulu ve

16 farklı aday geometri için toplamda 48 adet analiz gerçekleştirilmiştir. Tüm analizler

Ulusal Yüksek Başarımlı Hesaplama Merkezi (UHeM) kaynakları kullanılarak

gerçekleştirilmiştir. Hesaplamalı akışkan analizi araçlarıyla, parametrelerin hava alığı

aerodinamik performansı üzerindeki etkileri araştırılmıştır. Bu inceleme yanıt yüzeyi

metodolojisi kullanılarak gerçekleştirilmiştir. Analiz sonucunda elde edilen bilgiler

ışığında optimizasyon çalışması gerçekleştirilmiştir. Optimizasyon çalışması

kapsamında basınç kazanımı oranının eniyileme önemi arttırılmıştır. Benzer şekilde

kalkış durumundaki uçuş için eniyileme önemi de arttırılmıştır. Belirtilen amaç

fonksiyonları doğrultusunda 4 optimum geometri belirlenmiştir.

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1. INTRODUCTION

Jet engines are widely used in both civil and military aviation applications because of their high

efficiency rates and high propulsion characteristics. Jet engines absorbs air from atmosphere

and process it to increase total energy. The final mixture is thrown from the exhaust to produce

required propulsion. One of the most important factors affecting the performance of these

engines is the quality of the air at the compressor face. The main purpose of air inlet is to provide

high quality air stream to the aerodynamic interface plane at specific flow conditions that jet

engine requires via slowing down freestream flow. The quality of the flow at the aerodynamic

interface plane can be measured with uniformity of the flow at that plane and total pressure loss

among inlet. [1]

Air inlets are supposed to be designed as meet the requirements for optimum engine

performance. The total pressure of the air at the aerodynamic interface plane is a crucial

parameter that directly affects the performance of a jet engine. Therefore, it is aimed by inlet

designer that as low as possible total pressure loss among inlet. Also, uniformity of flow at the

compressor face is another objective for inlet performance. In addition of these, there are some

other objectives that affect the inlet design beyond jet engine performance. Especially for

military aviation applications stealth is very important. Rotating compressor blades which are

located at the aerodynamic interface plane can be detected easily by radar system. [2] Besides,

hot sections of jet engine are easily detectable by infrared based systems. [3] Because of these

reasons, the jet engines are usually located at the inside of the aircraft body for military

applications. Another advantage for designers of this configuration is providing more space at

the wings for military instruments. It is required to use S-duct diffusers for inside body jet

engine configurations.

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Figure 1.1: Schematic drawing of an S-duct diffuser. [4]

It is known that using S-duct diffuser causes vortex at the aerodynamic interface plane. [4]

Also, total pressure loss among the inlet will be higher with S-duct diffuser configuration

because of thicker boundary layer relatively. Emerged vortices at the aerodynamic interface

plane affect the flow locally at that plane which results as local increase or decrease at angle of

attacks of compressor blades. In case of dramatic angle of attack increase, stall may occur for

compressor blades which in turn lead to decrease in the engine performance. Also, that change

in the angle of attack causes cyclic loadings on the compressor blades which are root cause for

high-cycle fatigue problem for blades. [4] High-cycle fatigue may cause compressor blades to

failure which intemperately affects the flight performance and engine reliability. [5] Moreover,

failure at the high-speed components like compressor blades endangers passengers, air crew

and surrounding instruments. [6] So, inlet design affects not only performance and efficiency,

but also flight safety and reliability. Briefly, inlet system design and integration of propulsion

system into the aircraft are processes that must be done very precisely because of effects on the

engine performance and flight safety and reliability. The objectives of inlet system design are

minimum loss at the total pressure and uniform flow with minimum vortices possible at the

aerodynamic interface plane.

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1.1 Objective of Thesis

In this thesis, it is aimed to analyze the effects of some selected geometrical parameters which

describes inlet geometry on the aerodynamic performance of the inlet via computational fluid

dynamics tools and conduct an optimization study for a jet trainer inlet in light of such

information.

2. CHARACTERISTICS OF S-DUCT DIFFUSERS

It is difficult to perform measurement at the compressor plane while engine is running. In

experimental studies, measurements are performed on the aerodynamic interface plane (AIP)

which is slightly forward from compressor face but has very similar flow conditions with

compressor face. [7] The most common parameters which describe the performance of the inlet

are pressure recover coefficient, distortion coefficient and mass flow rate. Also, there are

geometrical parameters that describe the inlet geometry like highlight area, throat area and

contraction ratio. The basic formulas and explanations about geometrical and performance

parameters are given in the sections below.

2.1 Pressure Recovery Coefficient (PR)

The most important performance parameter for the turbojet and turbofan engine inlet design

studies is the pressure recovery coefficient. The pressure recovery coefficient is the ratio of

total pressure of the air at aerodynamic interface plane to total pressure of freestream. Pressure

recovery coefficient is significant because it represents the loss in the total pressure among the

inlet which is an indicator for efficiency of the inlet. The aim for the inlet design is to maximize

the pressure recovery because pressure loss is an undesirable condition for optimum engine

performance. [8]

4

Also, pressure recovery coefficient directly affects thrust and the stability of the engine

compressor blades. [9] The pressure recovery coefficient will be calculated as given Equation

2.1.

𝑃𝑅 = 𝑃𝑡,𝐴𝐼𝑃

𝑃𝑡 (2.1)

2.2 Distortion Coefficient (DC)

Distortion coefficient is a parameter that represents the variation of the total pressure at the

aerodynamic interface plane. In other words, distortion coefficient is a measurement for

uniformity of the flow at the engine face. Total pressure distribution may be steady state or

time-variant. [7] High distortion coefficient values represents that the characteristics of the flow

at the aerodynamic interface plane is far away from uniformity. This condition leads to non-

uniform pressure load on the compressor blades which may cause aerodynamic stall for blades

and stability issues. [8] The aim for the inlet design is to minimize the distortion coefficient to

achieve uniform flow at the engine face. There are several forms for distortion coefficient

definition. Propulsion system manufacturers usually develops their own methods for calculation

of distortion coefficient. Although there is no consensus for distortion coefficient method, the

aim for all the definitions is to express variation of the total pressure at the aerodynamic

interface plane. The usual form of definition is given at Equation 2.2.

𝐷𝐶( ) = 𝑃𝑡,𝐴𝐼𝑃̅̅ ̅̅ ̅̅ ̅̅ ̅−𝑃𝑡,̅̅ ̅̅ ̅

𝑞𝑡,𝐴𝐼𝑃̅̅ ̅̅ ̅̅ ̅̅ (2.2)

This definition is developed by Rolls Royce and used in many applications like Tornado and

Eurofighter. [10] Numerator of the equation is the difference between mean total pressure at

the aerodynamic interface plane and mean total pressure of the worst sector, with angle at that

plane. Denominator is mean dynamic pressure of the aerodynamic interface plane which is

used for normalization of pressure difference between AIP and sector that has lowest total

pressure. It is expected that is enough to explain total pressure variation clearly. 60° is

regarded as satisfactory minimum for . Commonly used coefficient for inlet design studies is

DC(60). Besides, DC(90) and DC(120) are used. [11]

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Figure 2.1: Total pressure distribution in AIP- Definition of critical sector .

In this study, DC(60) coefficient is used for investigate total pressure distribution at AIP.

Identical slices with 10° degrees in the AIP which are shown in the Figure 2.2 are used for easy

calculation of DC(60) for symmetrical geometry conditions. Area weighted average of total

pressure for every 10° slices are calculated. Then, average total pressure for each 60° sector,

which is 𝑃𝑡,̅̅ ̅̅ , is calculated with using average total pressures of every six neighbor slices.

Total 36 sectors are used for distortion coefficient calculation. The first sector is [0° - 60°] and

the last sector is [350° - 50°]. There are some limitations for distortion coefficient for different

applications. These limitations are shown in the Table 2.1.

Figure 2.2: Slices in AIP used for DC(60) calculation.

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Table 2.1 : Table with single row and centered columns.

Engine Type DC(60)

Civil Subsonic Transport 0.2

Military Fighter Aircraft 0.9

Industrial, Marine and Automotive Engine Less than 0.1

2.3 Contracting Ratio (CR)

Contracting ratio is an important geometrical parameter for inlet design. It can be defined as

ratio of highlight area to aerodynamic interface plane area and it is shown with Equation 1.3.

This parameter is important to investigate engine demand because it relates directly capture

highlight area to engine area.

𝐶𝑅 = 𝐴ℎ𝑙

𝐴𝐴𝐼𝑃 (2.3)

3. COMPUTATIONAL FLUID DYNAMICS ANALYSIS

3.1 Numerical Approach

The whole calculation domain volume is discretized to simulate fluid flow. Mass (continuity),

momentum and energy conservation equations are applied to each discrete volume. Any

convergence criteria is not defined for conservation equations because defined goals like mass

flow or total pressure at AIP are monitored as convergence criteria. The continuity, momentum

and energy equations are shown in the Equations (3.1 – 3.5). [15]

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Continuity equation:

𝜕𝜌

𝜕𝑡+ ∇ · (�⃗� ) = 0 (3.1)

where 𝜌 is density and �⃗� is velocity vector.

Momentum equations:

𝜕(𝜌𝑢)

𝜕𝑡+ ∇ · (𝑢𝑉⃗⃗⃗⃗ ⃗) = −

𝜕𝑝

𝜕𝑥+

𝜕𝑥𝑥

𝜕𝑥+

𝜕𝑦𝑥

𝜕𝑦+

𝜕𝑧𝑥

𝜕𝑧+𝑔 + 𝐹 (3.2)

𝜕(𝜌𝑣)

𝜕𝑡+ ∇ · (𝑣𝑉⃗⃗⃗⃗ ⃗) = −

𝜕𝑝

𝜕𝑦+

𝜕𝑥𝑦

𝜕𝑥+

𝜕𝑦𝑦

𝜕𝑦+

𝜕𝑧𝑦

𝜕𝑧+𝑔 + 𝐹 (3.3)

𝜕(𝜌𝑤)

𝜕𝑡+ ∇ · (𝑤𝑉⃗⃗⃗⃗⃗⃗ ) = −

𝜕𝑝

𝜕𝑧+

𝜕𝑥𝑧

𝜕𝑥+

𝜕𝑦𝑧

𝜕𝑦+

𝜕𝑧𝑧

𝜕𝑧+𝑔 + 𝐹 (3.4)

where 𝑝 is pressure, 𝜏 is shear stress and 𝐹 external body force.

Euler energy equation:

𝜕(𝜌𝐸)

𝜕𝑡+ ∇ . (�⃗� (𝜌𝐸 + 𝑝)) = −∇ . (∑ ℎ𝑗𝐽𝑗𝑗 ) + 𝑆ℎ (3.5)

3.2 Flow Solver

Pressure-Based solver is used for analysis. Coupled flow solver is selected for pressure velocity

coupling. Coupled flow solver algorithm solves the momentum and continuity equations

simultaneously instead of separately. [16] Because of that algorithm, required solving time per

iteration is higher compared to other coupling methods. [17] However, the advantage of the

coupled flow solver is that the results for conditions with compressible flow and shock waves

is more precise compared to other coupling methods. Flow conditions of inlets are usually very

similar as mentioned above. Therefore, using coupled flow solver is necessary for better results

despite more source is required. Spatial discretization schemes for all variables are adjusted as

iteration dependent. First order upwind scheme is used in the earlier iterations, then second

order upwind scheme is used for rest of the analysis. The reason for that is reduce the

convergence probability at earlier iterations.

8

3.3 Turbulence Modelling

The S duct inlet flow is challenging because of its turbulent characteristics, strong pressure

gradients and complex secondary flow. It is known that the velocity profiles at wall-fluid

interaction region have large gradients which cause to increase shear stress at the wall surface

and to decrease pressure of fluid. [18] The statistical approach named Reynolds-averaged

Navier-Stokes (RANS) proposed by Osborne Reynolds [19] is widely used for turbulence

modelling. Instantaneous quantities in the Navier-Stokes equations are converted to time

averaged and fluctuating quantities in RANS equations.

There are many developed turbulent models to simulate turbulent characteristics of the flow. It

is impossible to say that a turbulence model exist which is proper for all flow conditions. Design

and development of turbulence models are done for specific conditions. Different turbulence

models based on RANS equations are compared for internal flow at Lim, Al-Kayiem ve

Kurnia’s study. [20] The results show that k − ω SST turbulent model can predict the flow

conditions more precisely compared to other turbulent models. Prediction error decreases with

increase of Reynolds number for all turbulent models. However, the most precise results can

be got with k − ω SST turbulent model. Thus, k − ω SST is selected for turbulence modelling.

4. VALIDATION STUDY

The experimental study of AGARD (Advisory Group for Aerospace Research&Development)

published in “Air intakes for High Speed Vehicles” is used for validation study. The experiment

conducted with RAE M2129 S duct diffuser model. The details of geometry and experiment

are given in the sections below.

9

4.1 RAE M2129 model details

Figure 4.1 : M2129 diffuser geometry.

The RAE 2129 subsonic inlet model was designed within a program between NASA and the

United Kingdom defense ministry at the 1900. The aim of the project was to improve the

calibration of the CFD codes for an S duct diffuser. [13] The geometry is defined with two

equations which are centerline curve and radius, given with Equation 4.1 and Equation 4.2.

Geometry of M2129 is given with Figure 4.1.

𝑧 = 0.15𝐿 [1 − cos (𝜋𝑥

𝐿)] (4.1)

(𝑅− 𝑅𝑡

𝑅𝐴𝐼𝑃− 𝑅𝑡 ) = 3(1 −

𝑥

𝐿)4

−4(1 − 𝑥

𝐿)3

+ 1 (4.2)

M2129 model has circular cross section with varying radius all among its length. Geometrical

parameters are normalized with throat radius, 𝑅𝑡. Throat radius is equal to 6.44 cm and AIP

radius is equal to 1.18𝑅𝑡. The ratio of engine face area to throat area is, 𝐴𝐴𝐼𝑃 𝐴𝑡⁄ = 1.40. The

length of the diffuser, L, is 7.1𝑅𝑡. Detailed information about geometrical parameters that

define the M2129 are given in the Table 4.1.

10

Table 4.1: Geometrical parameters for M2129.

Quantity Description Value

L Duct length 45.72 cm

𝑋𝐴𝐼𝑃 Engine face position 48.39 cm

𝑅𝑡 Throat radius 6.44 cm

𝑅𝐴𝐼𝑃 AIP radius 7.6 cm

𝑅𝐶𝑎𝑝𝑡𝑢𝑟𝑒 Capture area radius 7.2 cm

4.2 Experimental study details

There are two data sets for M2129 diffuser model presented in the advisory report 270 of

AGARD. Data sets are for experiments with high and low mass flow rates. The data set for

experiment DP3532, which is experiment with high mass flow rate is used for validation study.

Table 4.2: Boundary conditions for experiment DP3532

Condition Value

Freestream Mach Number 0.21

Freestream Total Pressure 101215.78 Pa

Freestream Total Temperature 293 °K

AIP Mach Number 0.794

Pressure Recovery (PR) 0.92

𝛼 0 °

𝛽 0 °

11

Experiments were conducted at a 13ft x 9ft wind tunnel in the RAE Bedford (UK). This wind

tunnel was designed for low speed cases and has closed circuit. [14] The experiment DP3532

was conducted with a freestream Mach number 0.21. Experiment boundary conditions given in

the AGARD report are Mach number, total pressure and temperature for freestream, pressure

recovery ratio (PR) and AIP Mach number. Boundary conditions are shown in the Table 4.2.The

boundary conditions given in the report are pretty limited. However, additional boundary

conditions that is required for computational fluid dynamics analysis can be calculated with

isentropic flow equations. Isentropic flow equations given below are used to calculate

additional boundary conditions. Additional boundary conditions are shown in the Table 4.3.

𝑃

𝑃𝑡= ( 1 +

𝛾−1

2 M2)

−𝛾

𝛾−1 (4.3)

𝑇

𝑇𝑡= ( 1 +

𝛾−1

2 M2)

−1

(4.4)

Table 4.3: Additional boundary conditions for experiment DP3532

Condition Value

Freestream Static Temperature 290.44 K

Speed of Sound at Freestream 341.61 m/s

Freestream Static Pressure 98152.27 Pa

AIP Static Temperature 277.08 K

Speed of Sound at AIP 333.66 m/s

AIP Static Pressure 77245.56 Pa

Velocity at AIP 178.84 m/s

�̇� 2.953 kg/s

12

4.3 Grid Generation

RAE M2129 is a symmetrical intake model. Half of the inlet geometry with symmetry condition

is used to reduce total computation time. A hemispherical domain is added to forward part of

the inlet. The radius of the domain hemisphere is 50𝑅𝐴𝐼𝑃. Dimension calculations are done by

using Equations (4.5 – 4.8). It is assumed that y+ value is equal to 1. Total turbulent boundary

layer thickness, 𝛿𝑡𝑢𝑟𝑏,, is found as 3.269749 mm. It is calculated that for a growth rate 1.2, 30

layers are required with a first layer thickness, Δs, 2.99705𝑥10−5mm. The details of grid that

represents the boundary layer are given in the Table 4.4.

𝑅𝑒𝑑ℎ = ∗𝑉 ∗𝑑ℎ

𝜇 (4.5)

𝛿𝑡𝑢𝑟𝑏 =0.37∗𝑑ℎ

𝑅𝑒𝑑ℎ1/5 (4.6)

𝛥𝑠 = 5.06 ∗ 𝑑ℎ ∗ 𝑦+ ∗ 𝑅𝑒𝑑ℎ−7/8

(4.7)

𝛿𝑡𝑢𝑟𝑏 = (𝛥𝑠) ∗ (1−(𝐺𝑟𝑜𝑤𝑡ℎ 𝑅𝑎𝑡𝑒)𝐿𝑎𝑦𝑒𝑟 𝑁𝑢𝑚𝑏𝑒𝑟)

1−𝐺𝑟𝑜𝑤𝑡ℎ 𝑅𝑎𝑡𝑒 (4.8)

Table 4.4: Additional boundary conditions for experiment DP3532

Property Value

𝑅𝑒𝑑ℎ 1525321.184

𝛿𝑡𝑢𝑟𝑏 3.269749 mm

𝛥𝑠 2.99705𝑥10−5mm

Growth rate 1.2

Layer number 30

13

Figure 4.2: Structure of the mesh.

4.4 Mesh Independency

Ten different meshes are created between element number 734,813 and 90,823 to determine the

point that dependency to element number is not significant. The details of the candidate meshes

for mesh independency study are given in the Table 4.5.

Table 4.5: Mesh details for independency study.

Mesh no Element Number Nodes Skewness

#1 734,813 313,281 0,80489

#2 667,603 283,420 0,81236

#3 561,292 236,845 0,79673

#4 513,896 195,065 0,79648

#5 409,483 167,341 0,79918

#6 315,406 127,478 0,82134

14

#7 250,275 100,756 0,79564

#8 186,953 76,885 0,79796

#9 131,537 55,814 0,79768

#10 90,823 39,188 0,79919

All the meshes are analyzed with identical conditions and results of analyses are visualized

which are shown with Figure 4.3. According to analysis results, it is shown that approximately

after 500,000 element number the change in the result become negligible. This element number

is normalized with AIP diameter. As result, 3281 elements are needed for an AIP diameter of 1

mm. The results of validation study are given with Table 4.6.

Figure 4.3: Relation between element number and mass flow ratio.

15

Figure 4.4: Flow at AIP- Numerical results

Table 4.6: Validation study analysis results.

Figure 4.6: RAE M2129 Mach contour at symmetry plane.

Property Experimental Result Analysis Result

PR 0.92 0.85

Mass flow (kg/s) 1.476 1.494

DC60 0.398 0.317691

Figure 4.5: Flow at AIP

Experimental results

16

5. INLET DESIGN STUDY

The aim of this study is to analyze and optimize an inlet for a jet trainer aircraft. The inlet

geometry used in this study is designed uniquely via examination of jet trainers which are

currently in operation. It is impossible to reach exact geometry details of aircrafts because of

privacy. The design details are given sections below.

5.1 Review of several Inlets

Several jet trainer aircraft are examined. The design study is based on jet trainer that has single

engine in the body with two pilots. It is seen that for jet trainer aircraft, mostly symmetrical

armpit inlet configuration is used. The advantage of using this type of inlet is providing better

inlet flow for unsymmetrical flight conditions. The cross section of capture areas varying for

each aircraft. It is assumed that capture areas are in circular form for calculation and CAD

simplicity. The EJ200 turbofan engine of Eurojet company is sufficient for the requirements of

a jet trainer. The geometrical parameters that is related with engine are referenced with EJ200

turbofan engine. Features of engine which are used for design study and analysis are given in

the Table 5.1.

Table 5.1: Properties of EJ200 turbofan.

Property Value

Compressor face diameter (AIP) 79 cm

Length 391 cm

Maximum massflow 66 kg/s

The KAI T-50 jet trainer selected as reference aircraft. It is seen that total diffuser length must

be 400 cm. There is no information about centerline of S duct diffuser. Because of that, the

form that is used for RAE M2129 centerline curve is used for inlet design. The variation in

radius among duct is selected as linear for easy drawing unlike RAE M2129. Total capture area

is approximately 0.4 𝑚2. As mentioned before, half circular capture area is used. However, it

is seen that symmetry line leads to highly sharped edges which is not proper for flow

17

smoothness and grid generation. Thus, capture area is created as combination of half circle and

ellipse to improve flow smoothness.

Figure 5.1: Highlight area of inlet.

NACA 1 series are widely used for pitot type subsonic intake lip designs. [21] NACA 1-85-xxx

series is used for lip design. First digit represents series number, following two digits represents

ratio of capture diameter to maximum diameter in percent and last digit group represents the

ratio of lip length to maximum diameter. The normalized dimensions for NACA 1-85 series

given in the [22] are used for creating geometry. Lip radius is an important parameter that

defines the lip geometry. It is defined as 0.025Y. It is known that lip radius has effects on the

flow separation on lip part. [22] Another important parameter is relative lip length which is last

digit group at the NACA 1 series naming system. This parameter affects the smoothness of the

lip section. These two parameters, lip radius and relative lip length, are selected as varying

parameters for inlet design study. Four different values are specified for each parameter. The

values of the parameters are shown in the Table 5.2. The experimental studies [21-22] are

referenced for value specification. Total 16 geometries are created with using Visual Basic

macro for Catia.

Table 5.2: Values for selected parameters.

Property 1. Value 2. Value 3. Value 4. Value

Lip radius(mm) 0.8 1.2 1.4 1.6

Relative lip lenght(%)

45 50 55 60

AIP

Dia

met

er

18

Figure 5.2: Isometric view of designded inlet geometry.

5.2 Grid generation

It was mentioned in mesh independency study that 3281 elements are needed for an AIP

diameter of 1 mm for mesh independency. AIP diameter of designed inlet is 790 mm which is

compressor face diameter of EJ200 engine. Thus, it is seen that approximately 2,500,000

elements are needed for mesh independent results. Identical processes in the section 4.3 are

done for every candidate geometry to generate grid. The boundary layer calculations are done

with same manner. The details of the boundary layer mesh are given in the Table 5.3.

Table 5.3: Details of the boundary layer mesh.

Property Value

𝑅𝑒𝑑ℎ 5,746,271.506

𝛿𝑡𝑢𝑟𝑏 0.013000246

𝛥𝑠 4.8676E-06

19

Growth rate 1.2

Layer number 35

y+ 1

Figure 5.3: Mesh structure of designed inlet.

20

Figure 5.4: Wireframe mesh structure of designed inlet.

21

6. CFD ANALYSIS

6.1 Selected Flight Phases

Three different flight conditions are selected to create boundary conditions which are required

for computational fluid dynamics analysis. The first selected flight condition is takeoff. Takeoff

phase is quite critical for aircraft because the velocity of the aircraft is equal to stall velocity at

that phase. Also, it is critical for inlet because relatively high mass flow demand of engine must

be satisfied although freestream velocity is quite low. The second selected flight condition is

cruise. Cruise flight is critical for optimization because this flight phase is the most time

consumed phase for operation. The last selected flight condition is flight with maximum power.

It is challenging for the inlet to supply very high mass flow rate to the engine. These critic flight

conditions are selected to optimize inlet geometry for all operation conditions.

6.2 Boundary Conditions

In commercial practice, the demand of engine for a given thrust is known through information

taken from software provided by engine manufacturer. But these software are not open to public

because of privacy policy. Thus, some assumptions are done to specify boundary conditions. It

is known that Mach number at the compressor face should not exceed 0.6. [23] Assumptions are

done according to satisfy this limit. Freestream static pressure and temperatures are specified

according to ISA conditions. Flight altitude, speed and angle of attack are specified with

assumptions. The details of boundary conditions for all flight phases are shown in the Table 6.1.

22

Table 6.1: Details of boundary conditions for all flight phases.

6.3 Analysis

ANSYS Fluent 18.2 software is used for both grid generation and computational fluid dynamics

analysis. For 3 different flight conditions and 16 candidate geometries, total 48 analyses were

performed. The journal files as TUI commands were prepared for each analysis. Computing

resources used in this work were provided by the National Center for High Performance

Computing of Turkey (UHeM) under grant number 4007942020. Parallel processing was

performed via CPU’s with clock frequency 2.40 GHz. The number of CPU used for analyses

varied with workload density at UHeM.

6.4 Results

PR, DC(60) and drag force values are monitored to investigate effects of the geometrical

parameters on the aerodynamic performance of the inlet for all analyses. It is seen that lip radius

affects the vortices at AIP dominantly. Vortex structures grow with increase in lip radius. This

phenomenon is shown in the Figure 6.1.

Property Takeoff Cruise Flight Maximum Power

Altitude (m)

0 9200

7500

Flight Velocity (km/s)

225 480

1000

Flight Mach number 0.189

0.45 0.89

Angle of Attack (°) 6

0 0

Freestream Static Temperature (K) 273

220 238

Freestream Static Pressure (Pa)

AIP Mach Number 0.4

0.5 0.6

23

Figure 6.1: Variation of the flow with lip radius.

Figure 6.2: Variation of seperation point with lip radius.

24

Also, flow separation location moves forward with increment in lip radius. This phenomenon is

shown in the Figure Figure 6.2.

Effects of geometrical parameters on PR, DC(60) and drag force are analyzed and visualized

with response surface methodology. For takeoff phase, in other words at flight condition with a

Mach number 0.4 at AIP, it is seen that the effect characteristic of the lip radius on the DC(60)

approximately parabolic. This phenomenon is shown in the Figure 6.3.

Figure 6.3: Variation of DC60 for 0.4 Mach at AIP.

Figure 6.4: Variation of DC60 for 0.5 Mach at AIP.

25

Figure 6.5: Variation of DC60 for 0.6 Mach at AIP.

The characteristics of this effect on the DC60 is changing with increment of Mach number at

AIP which is shown with Figure 6.4 and 6.5. Effects of geometrical parameters on PR and drag

force are approximately linear unlike DC(60).

Figure 6.6: Variation of PR for 0.4 Mach at AIP.

26

Figure 6.7: Variation of drag force for 0.4 Mach at AIP.

7. OPTIMIZATION

An optimization study was performed in the lights of information taken from computational fluid

dynamics analysis. Maximization of PR, minimization of DC(60) and drag force are aimed in

optimization study. The importance degree of takeoff is increased because it is the most critical

flight condition. In similar way, the importance of the PR maximization is increased. According

the objective function mentioned above, four different optimum geometry is obtained in the

scanned region. The geometrical details and predicted performance values of optimum

geometries are shown in the Table 7.1.

27

Table 7.1: Geometrical details and predicted performance values of optimum geometries.

8. CONCLUSION

In this thesis, investigation of effects of geometrical parameters on the aerodynamics

performance of the inlet for a jet trainer and optimization of inlet geometry are aimed.

Experimental study data for subsonic inlet model M2129 in the AGARD Advisory report 270 is

used for validation study. An inlet design is performed with two geometrical parameters which

are lip radius and relative lip lenght. Sixteen candidate geometry is created for optimization

study. Analyses were performed on UHeM. According to CFD results, it is seen that lip radius

affects dominantly the flow at the AIP and the starting point of seperation. An optimization study

was performed in the lights of information taken form CFD analyses with using response surface

methodology. Four optimum geometry is obtained from optimization study. Performance values

are predicted for all optimum geometries.

Optimum

Geometry

Lip Radius

(mm)

Relative

Lenght (%)

PR DC60

Drag Force (N)

#1 0.8 45 0.99 0.072 53.581

#2 0.8 60 0.9897

0.068 84.219

#3 1.18899 48.1449 0.9854 0.057 195.388

#4 1.31655 60 0.9847 0.097 211.129

28

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