3.3.1. Aerodynamics of Jet Exhausts Part 1

Goulos, I., Stankowski, T., Otter, J., MacManus, D., Grech, N. and Sheaf, C. (2016) ‘’Aerodynamic Design of Separate-Jet Exhausts for Future Civil Aero-engines - Part 1: Parametric Geometry Definition and Computational Fluid Dynamics Approach`` Journal of Engineering for Gas Turbines and Power, Vol 138.

3.3.1.1. Abstract

  • Output is: integrated approach targeting aerodynamic design of separate-jet exhaust systems for future gas-turbine aero-engines.

  • Framework is a series of fundamental theories applicable to:
    • engine performance simulation
    • parametric geometry definition
    • viscous/compressible flow solution
    • design space exploration (DSE)
  • Method:
    • Mathematical method developed based on:
      • class-shape transformation (CST) functions for geometric design of axi-symmetric engines
      • Standard set of nozzle design parameters
    • Design carried out using:
      • Flow capacities established from 0D cycle analysis
    • Coupled to:
      • ICEM for automatic mesh generation using block structured approach
      • Fluent for RANS solution
    • Validation against:
      • Experimental data on a small-scale turbine powered simulator (TPS)
    • Coupled tool to:
      • DSE Latin-hypercube sampling
    • Applied to two civil engines:
      • Current
      • Future
  • Results:
    • Relation between exhaust systems thrust and discharge coefficient has been quantified
    • Dominant design variables that affect aerodynamic performance of the exhausts have been determined
    • Comparative evaluation of the optimised exhaust design of each engine
  • Conclusions:
    • Enables aerodynamic design of exhausts using only a few design variables
    • Enables quantification and correlation of aerodynamic behaviour of each engine architecture
    • Is an enabling technology to identify fundamental aerodynamic mechanisms for exhaust system performance

3.3.1.2. Introduction

3.3.1.2.1. Background

  • What is the future trend in civil turbofans?
    • The motor of civil turbofan engines will have greater thermal efficiency:
      • Increased TET
      • Increased OPR
    • Maybe leads to intercooled and intercooled-recuperated cycles

    • Future turbofan engines will have lower specific thrust and improved propulsive efficiency:
      • Higher BPR (15+, it is currently ~11)
      • Lower FPR
  • Why is the exhaust important?
    • Higher BPR means higher gross to net propulsive force ratio
    • High BPR designs are therefore more sensitive to gross propulsive thrust
    • Gross propulsive thrust is linearly dependent on the aerodynamics of the exhaust
  • Why is the bypass duct important?
    • High BPR means higher mass flow through bypass
  • Post-exit components are also important

3.3.1.2.2. Performance Prediction of Engine Exhaust Systems

  • Engine housing is not designed by engine manufacturer, so thrust-drag bookkeeping (TDB) is needed to mitigate losses.

  • Exhaust system can cause 1.5 to 2% loss in gross propulsive thrust

  • In TDB \(C_V\) (velocity coefficient) and \(C_D\) (drag coefficient) are used for measuring performance

  • CFD used for aerodynamics analysis of exhaust nozzles

  • What are the flow features?
    • Boundary and shear layer interaction
    • Expansion waves
    • Shock waves
  • What is the accuracy of CFD?
    • less than 1% for \(C_D\) and \(C_V\), largely due to uncertainty in exprimental data

3.3.1.2.3. Scope of Present Work

  • What is unique about the current work?
    • Methodological approach for:
      • Parametric geometry definition
      • Aerodynamic analysis
      • Examination of separate jet exhaust systems
    • Impact of high BPR and lower FPR on exhaust system design

    • Not considering installation geometry then?

  • What are the objectives of the current work?

    • Derive analytical formula for parametric geometry definition of separate jet exhausts
    • CFD model of bypass duct, nozzle and post exit conditions
    • Framework for exploring design space for aerodynamic performance
    • Explore design space for future and current engines
  • How is the parametric geometry defined?

    • CST functions (class function shape function transformation)
    • Axi-symmetric
    • Separate jet exhausts
    • Extends Qin’s aerofoil approach to exhausts and nozzles
    • Parameterisation based on required flow capacities
    • Coupled to ICEM and Fluent
  • How is the CFD model defined?

    • CFD validated against small scale turbine power simulator (TPS)
    • What is the definition of the CFD model? (section below)
    • BCs, discretisation scheme, solver, turbulence model?
  • How is the design space defined?

    • Coupled to framework
    • Explores future and current turbofan
    • How is DSE done (second paper)?

3.3.1.3. Numerical Approach

3.3.1.3.1. Methodological Overview

  • What is GEMINI?

    • Geometric Engine Modeler Including Nozzle Installation

    • Designs separate jet exhaust systems based on key engine hard points

    • Applicable to:
      • Engine performance simulation
      • Exhaust nozzle geometry
      • Parameterisation
      • Viscous compressible flow solution
  • How is the 0D engine performance model defined?

    • Inputs: thermodynamic and geometric design parameters
    • Analyse engine cycle at design point and off design
    • Uses Cranfield’s Turbomatch
    • Outputs: size of bypass and core, average flow properties at inlet and exit of bypass and core
  • How is the GEMINI, ICEM, Fluent and Post processing done?

    • Inputs: flow capacities and size of bypass and core
    • Inverse design approach in Gemini produces 2D axi-symmetric geometry
    • Transfers to ICEM
    • Transfer to Fluent
    • Transfer to Post processor
    • Outputs: \(C_D^{bypass}\) and \(C_D^{core}\) and \(C_V^{overall}\)

3.3.1.3.2. Engine Performance Simulation (Turbomatch)

  • How is the 0D engine performance model done?

    • Turbomatch
    • 0D aerothermal analysis
    • Solves for mass and energy balance between engine components
    • Assumes engine is operating at steady state

3.3.1.3.3. Parametric Geometry Definition of Exhaust Nozzles

  • How is the parametric geometry defined?

    • Kulfans CST functions
    • Qins CST (class shape transformations) extended from aerofoils to exhausts
    • nth order Bernstein polynomial - uses a summation of polynomials to describe the surface with an offset for position
    • The geometry is split into the upstream duct and exhaust nozzle
    • Geometric parameters are specified to achieve design parameters using control points (where geometric information is avaliable)
    • \((n-1) \times (n-1)\) system of linear equations created
    • BCs are established from control points
    • How is the geometric BCs satisfied to be unique? (e.g. is the gradient specified as well?)

3.3.1.3.4. CFD Domain and BCs

  • 2D axi-symmetric

  • Why is the engine intake included?
    • Domain includes engine intake to account for effect of mass flow capture ratio on the nacelle pressure distribution
    • This is required to capture the static pressure aft of the nacelle afterbody and the effect of freestream supression on the aerodynamics
  • Freestream:
    • Pressure far-field
    • static pressure, static temperature, Mach number
    • Position of freestream: 150 maximum nacelle diameters Is this really big enough? (despite sensitivity analysis, maybe ok if inviscid)
  • Fan face:
    • Pressure outlet
  • Bypass:
    • Pressure inlet
  • Core:
    • Pressure inlet
  • Vent:
    • Prescribed mass flow
  • How is the non-uniformity of flow accounted for?
    • Streamline curvature method applied to fan rotor and fan outlet guide vanes

3.3.1.3.5. Automatic mesh generation

  • Block-structured mesh automatically generated using ICEM
  • y+ is unity
  • 50 nodes normal to aeroline surface
  • Expansion ratio 1.2
  • Mesh topology based on MSc thesis?
  • Why not use more efficient hybrid mesh generation?
  • Why not use better scripting language than ICEM e.g. Pointwise?
  • Why not use better quality expansion using hyperbolic PDE in boundary layer using Pointwise?

3.3.1.3.6. Definition of CFD Approach

  • ANSYS Fluent
  • RANS using \(k-\omega\) SST turbulence model
  • Green-Gauss for gradients
  • 2nd order upwind scheme for flow variables, turbulent kinetic energy and dissipation rate
  • Thermal conductivity via kinetic theory
  • Eighth order polynomial for specific heat capacity (\(C_P\))
  • Sutherlands law for dynamic viscosity
  • Why not MUSCL scheme?
  • Why not Riemann solver instead of slow SIMPLE algorithm?
  • Acoustics cannot be included using steady state CFD model
  • Solution won’t be solver independent

3.3.1.3.7. Exhaust System Performance Accounting

  • Discharge coefficient:
\[C_D = {{\dot{m}_{actual} }\over {\left( {\dot{m} \over A }\right)_{ideal} \ A_{throat}}}\]
  • The throat area is taken to be equal to the exit area Is this valid? Is there a vena contracta?
  • It could be like a Venturi meter, where the contraction coefficient is unity, such that \(C_D\) equals \(C_V\) a ratio of velocities for single phase flow
  • \(C_D\) is defined for the core and the bypass separately
  • Gross propulsive force:
\[F_G = F_G^{bypass} + F_G^{core} + F_G^{zone3} - \text{integral of (static pressure term in axial direction aft of max nacelle diameter - viscous shear stress)}\]
  • Overall velocity coefficient (divide a force by a mass flow rate and you get the actual velocity on top):
\[C_V^{overall} = {F_G \over { \left(\dot{m}_{actual}^{bypass} V_{ideal}^{bypass} + \dot{m}_{actual}^{core} V_{ideal}^{core} + \dot{m}_{actual}^{zone3} V_{ideal}^{zone3} \right) }}\]

3.3.1.4. Results and Discussion

3.3.1.4.1. Grid Sensitivity Analysis

  • Numerical predictions at DP mid cruise conditions
  • 5 meshes using uniform refinement
  • Around 100,000 cells for coarse mesh, 1 million cells for fine mesh
  • Non-monotonic behaviour could be caused by turbulence model
  • Non-montone behaviour due to limiter in 2nd order scheme?
  • Investigate the effect of higher order schemes on monotonicity?
  • May be able to use coarser mesh with 3rd order scheme?
  • Big Problem: No AMR - may be able to use even very coarse grid with AMR and high order scheme

3.3.1.4.2. Validation of Employed CFD Approach

  • Pylon blockage in experiment, so CFD must be corrected
  • No correction for 3D nature of flow, CFD is 2D axi-symmetric
  • Used different FPRs and measured normalised mass flow and gross propulsive thrust
  • Difference is around 5% due to 3D nature of flow and possibly uncertainty about pylon
  • Isentropic Mach number is around 10% different in bypass and 6% in core
  • Possibly because of lack of resolution around shock waves?

3.3.1.4.3. Design Space Exploration

  • Design of Experiment approach is Latin Hypercube to mitigate the cost of CFD simulations
  • After a representative database is collected, the beaviour is investigated statistically
  • Design variables are correlated with the performance metrics using Pearson’s product moment of correlation

3.3.1.4.3.1. Case Study Description

  • Two engines, Current (E2) and Future (E1) with BPR of 11 and 16 respectively
  • Each cycle has been optimised wrt FPR to maximise specific thrust and minimise specific fuel consumption
  • How was it optimised?
  • DP mid cruise conditions for both engine models
  • Bypass is choked, core is unchoked

3.3.1.4.3.2. Design Space Definition

  • 11 and 12 parameters for E1 and E2 engines have specified ranges, in agreement with design guidelines and manufacturing constraints

3.3.1.4.3.3. Preliminary Statistical Analysis

  • Each design space was discretised using the Latin Hypercube method
  • 360 exhaust geometries were used per engine
  • Correlation between imposed design variables and performance metrics was investigated
  • Question: Which are the dominant variables?
  • Large percentage variation in core discharge coefficient and zone 3 pressure ratio, due to strong influence of core cowl design on core nozzle exit static pressure
  • E2 has an additional parameter, giving it more degrees of freedom than E1, so the variation in the values is greater
  • Definition of velocity coefficient renders it relatively independent of discharge coefficient to first order, leading to smaller standard deviation for the velocity coefficient.
  • Why did E2 have more degrees of freedom?

3.3.1.4.3.4. Assessment of Apparent Design Space Linearity

  • Plotted charts and determined Pearson correlation coefficient for:

    • \(C_V^{overall}\) versus \(C_D^{bypass}\)
    • \(F_N\) versus \(C_D^{bypass}\)
    • \(F_N\) versus \(C_V^{overall}\)
  • Exchange rates between \(F_N\) and \(C_V^{overall}\) can be almost double for future engines compared to current engines

  • Hinton Diagrams for all performance metrics versus all design variables, coefficients are dependent only on three main design variables

  • Increasing nozzle \(C_P\) to exit length ratio moves low pressure turbine hump upstream and mitigates strong shock

  • This improves discharge coefficient by 0.4 % and velocity coefficient by 0.06% and increases \(F_G\) by 0.45%

  • Why are the improvements so small? But I suppose nearly 0.5% is large for discharge coefficient?

3.3.1.5. Conclusions

  • Integrated approach for aerodynamic design of separate jet exhaust systems

  • Applicable to:
    • Engine performance simulation
    • Parametric geometry definition
    • Viscous compressible flow
  • Analytical approach for parametric geometry using CST functions

  • Validated against experimental data

  • Formulation for design space evaluation

  • Used future and current aero engines

  • Sensitivity to parametric changes has been identified

  • Hinton diagrams are effective in representing behaviour and to identify guidelines for design

  • Can be used to identify fundamental aerodynamic mechanisms