# 3.3.2. Aerodynamics of Jet Exhausts Part 2¶

## 3.3.2.1. Introduction¶

### 3.3.2.1.1. Background¶

- Civil aviation traffic will increase in the future, so reduce:
direct operating costs

fuel burn

emissions

noise

- Need to improve design technology in:
Motor

Propulsor

- Improve motor thermal efficiency by:
Increase TET

Increase OPR

- Future architectures:
**Higher BPR**(currently 11, will be 15+)Lower FPR

- This will:
**Lower specific thrust****Improve propulsive efficiency**

- Why is the
**exhaust**important? Increasing

**BPR**will increase**gross to net propulsive thrust**Designs are therefore more

**sensitive to variations in gross propulsive thrust**Gross propulsive thrust is

**linearly dependent**on the**aerodynamic performance of the exhaust**

- Why is the
- Which components will be analysed?
**Bypass duct****Nozzle****Post exit components**

### 3.3.2.1.2. Exhaust system performance accounting¶

- What is separate jet exhausts?
**Core cowl**separates core flow from bypass flow**Protruding core plug**limits the length of core cowl

- What is the problem with separate jet exahusts?
Can be substantial sources of thrust loss (gross thrust reduced by 2%)

- How is performance measured?
Discarge coefficient

Velocity coefficient

### 3.3.2.1.3. Design Optimisation of Engine Exhaust Systems¶

CFD is a reliable performance prediction tool

It is also efficient and used in design optimisation (

**Efficiency is depending on mesh size, geometry complexity, schemes, solvers and models used**)

#### 3.3.2.1.3.1. Heath (2015)¶

Axi-symmetric, dual stream plug nozzle

Parametric geometry via free-form deformation and 3rd order b-splines

RANS solver

**Steady state**Unstructured grid

Adjoint, grid deformation, grid adaption to obtain gradients

Optimisation using sequential quadratic programming (SQP)

Minimise integral of

**near-field pressure disturbances**relative to freestream flowGross thrust gain of 0.2% relative to baseline

#### 3.3.2.1.3.2. Clemen (2012)¶

**Why not use HYDRA for?**Linearised unsteady solver

Non-linear solver

Steady adjoint solver

Harmonic adjoint solver

Integrated framework for high BPR turbofan with core mounted gearbox

**Like Ultrafan?**2nd order splines for parametric geometry

**3D RANS solver HYDRA****Steady state**Hybrid optimisation comprising initial design of experiment coupled with RSM and global optimiser

**RSM**(Response Surface Modelling) based on design of experiment results using interpolations based on radial basis functions**Genetic algorithm**to minimise total pressure loss within bypass duct0.1 % reduction in pressure loss

#### 3.3.2.1.3.3. Haderlie and Crossley (2010)¶

Axi-symmetric supersonic inlet

Modified splitter geometry that separates core and bypass flow

Parametric geometry based on Kulfan’s CST method

RANS flow field

Multiblock structured mesh

Optimisation based on design of experiment - Latin hypercube

Surrogate model using Kriging interpolation

Optimisation from genetic algorithm and local gradient based sequential quadratic programming

Optimisations used total pressure recovery and peak radial distortion intensity at the inlet’s aerodynamic interface plane

Improved splitter design that satisfied imposed geometric constraints

**Current paper is based mainly on this one**

#### 3.3.2.1.3.4. Qiu (2014)¶

Unsteady, continous adjoint-based acoustic propagation method

Optimise the design of a low bypass duct for a civil turbofan

Hick-Henne shape functions for parametric model of bypass and nozzle

Optimisation based on local gradient based algorithm driven by Jacobian from adjoint method

Minimise tonal noise

Reduced overall SPL in far-field by 2.78dB

### 3.3.2.1.4. Scope of Present Work¶

Aerodynamics of the exhaust is important for future high BPR engines

- What is unique about the current work?
Previous authors have looked at optimising exhaust nozzles

A holistic approach for

**separate jet exhausts**including bypass, core duct and post exit components has not been reportedImpact of

**high BPR engines**and lower FPR on exahust system design and optimisation has not been reported

- What is the approach?
Cycle analysis

Geometry parameterisation

Mesh generation

RANS flow solution

- What is new?
Expand optimisation strategy using DOE (Design of Experiment), RSM (Response Surface Modelling) and GA (Genetic Algorithm)

- What is being optimised?
Current and future engine architectures

Large turbofans

Optimise the exhaust designs

## 3.3.2.2. Numerical Approach¶

### 3.3.2.2.1. Aerodynamic Design of Separate-Jet Exhausts¶

- What is GEMINI?
Tool developed is GEMINI

Designs complete exhaust system for designated engine cycle using key engine hardpoints

- Applicable to:
Engine performance simulation

Exhaust duct and nozzle aeroline parameterisation

Viscous compressible flow

- What is the process?
Designate a set of thermodynamic cycles and geometric design parameters

Analyse engine at design point and off design (0D conditions) - Turbomatch, output bypass and core sizes and flow capacities, at steady state conditions

Inverse design to create 2D axi-symmetric model

Automatic generation of grid

Convege CFD solution

Determine discharge and velocity coefficients

### 3.3.2.2.2. Exhaust System Parametric Geometry Definition¶

- How is the parametric geometry defined?
Kulfan’s CST functions

Qin’s CST variations

Bypass, core, duct exhaust are reduced to a set of analytical expressions

The expressions are functions of a standard set of design parameters

- How is the nozzle designed?
Geometric throat area is known

An effective convegent-divergent ratio is defined

Application of the rolling ball area estimation method to nozzle exit plane and upstream CP results in a series of control points that satisfy the prescribed design parameters

- How is the upstream duct defined?
Direct control of a series of control points

- Why is the engine intake considered?
To capture the effect of inlet mass flow capture ratio

To then account for the effect of the static pressure distributionon the nacelle

To then account for the effect of freestream supression on the aerodynamic performance of the exhaust system

- How is the geometry defined?
Upstream duct via specifying position, slope and curvature within a series of control points

Core cowl and plug are modelled as straight lines

Includes a third nozzle

### 3.3.2.2.3. DSE and Optimisation¶

- What is done in this paper?
Extend GEMINI

Implement DSE and optimisation environment

Non-linear nature must be dealt with

Must mitigate the cost of numerous CFD applications

- How is the process of DSE done?
Deployment of

**DOE**method to explore the available design spaceConstruct

**RSMs**from DOE results

- What kind of DOE is used?
**Latin Hypercube**

- What is a RSM?
Hypersurface describing the mathematical relationship between a set of imposed design inputs and outputs

The use of RSMs will avoid a

**prohibatively large number of CFD simulations**Interpolation using Gaussian process regression,

**Kriging interpolation**Performance metrics are

**discharge and velocity coefficient****Leave-one-out cross validation**used to check predictive accuracy of RSMs

- How is the optimisation done?
Global method to avoid being trapped in locally optimal solution - GA (Genetic Algorithm)

## 3.3.2.3. Results and Discussion¶

### 3.3.2.3.1. Definition of Baseline Engines¶

- How are the baseline engines defined?
Optimise low pressure exhaust system design and core afterbody aerolines for current and future aero-engines.

BPR current = 11

BPR future = 15

OPR, TET, component efficiencies selected according to technology guidelines

Each cycle optimised wrt FPR to maximise specific thrust

2D axi-symmetric

Geometry from public domain

Predictions at mid-cruise

Bypass is choked, core is unchoked

### 3.3.2.3.2. Parametric Design Space Definition¶

- How are the parameters designed?
11 to 12 variables for future and current engines

**Outer line angle**is kept constant for future engine

### 3.3.2.3.3. Design Space Exploration¶

How is the design space explored?

Design space discretised using Latin Hypercube

360 exhaust geometries

Correlation between design variables and performance metrics was investigated

Hinton Diagram using Pearson’s product-moment correlation

Shows only a few parameters influence the performance metrics

Within the range of assumptions, the aerodynamic

**performance of the exhaust is decoupled from the intake and nacelle forebody**Changes applied to the exhaust do not influence the intake or nacelle

### 3.3.2.3.4. Response Surface Modelling¶

- How are the RSMs constructed?
Using DOE data

Interpolation using Gaussian processes regression (Kriging interpolation)

Quadratic regression function and squared exponential autocorrelation function

- How are the RSMs checked?
Leave one out cross validation

Employs all the avaliable data apart from one, which is the one to prediction

Prediction is compared with original raw data for accuracy

Surrogate model predictions are correlated against raw data using Pearson’s product moment of correlation

Also assesses averge model error and standard deviation for each performance metric

Result shows that CFD raw data and predicted data has very high correlation.

**Could be improved using a larger amount of data**Low percentage error

Standard deviation is of similar order to error, so data is scattered - shows non-linearity of the system

### 3.3.2.3.5. Exhaust System Design Optimisation¶

- How is the optimisation performed?
Genetic algorithm

Advantage of using RSMs is that they are more efficient than CFD models

- What is the process for the GA?
For current and future engines

Optimise in terms of overall velocity coefficient

Population size is 10 times number of design variables

40 generations

Convergence criterion of \(10^{-12}\)

- What are the results of the optimisation?
Good solution achieved within 500 evaluations

Still contains small number of unfit individuals

Improvement wrt baseline values is large (2-4% in thrust)

CP to exit length ratio is increased (as before) mitigating strong shock

Also flow separations are mitigated

## 3.3.2.4. Conclusions¶

Design optimisation for separate jet exhausts for future civil aero engines

- Modules for:
Cycle analysis

Geometry parameterisation

Mesh generation

Viscous compressible flow solution

Novel analytical geometry tool using CST functions

2D axi-symmetric RANS CFD model

- Extended formulation to include:
DOE

RSM

GA

- Used to optimise:
Current engine

Future engine

Design optimisation can increase net propulsive force by 1.4% or 3.4% for future and current engines

Can identify design guidelines and mitigate undesirable flow features