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
  • 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 duct

  • 0.1 % 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
  • 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