# 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**

- Increasing

- 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 flow - Gross 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 reported - Impact 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 space - Construct
**RSMs**from DOE results

- Deployment of

- 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