# 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 enginesStandard 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 determinedComparative 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 architectureIs 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

- The
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

- Future turbofan engines will have lower

- 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
- Why is the
**bypass**duct important? High BPR means higher mass flow through bypass

- Why is the
**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 performanceExplore 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 coreInverse 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:

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:

Overall velocity coefficient (divide a force by a mass flow rate and you get the actual velocity on top):

## 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 simulationsAfter 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 greaterDefinition 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