# 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

• 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