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Last developments in the modeling of supersonic ejectors 1 Sergio CROQUER a* , Sébastien PONCET a , Zine AIDOUN b a Faculté de génie, Département de génie mécanique, Université de Sherbrooke, Sherbrooke, Canada b CanmetENERGY-Natural Ressources Canada, Varennes, Canada Orford, 11-12 janvier 2018 3ème assemblée annuelle du CREEPIUS

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Page 1: Last developments in the modeling of supersonic ejectors · Last developments in the modeling of supersonic ejectors 1 ... Thermodynamic modeling of supersonic gas ejector ... Large-Eddy

Last developments in the modeling of

supersonic ejectors

1

Sergio CROQUERa*, Sébastien PONCETa, Zine AIDOUNb

aFaculté de génie, Département de génie mécanique, Université de Sherbrooke, Sherbrooke, CanadabCanmetENERGY-Natural Ressources Canada, Varennes, Canada

Orford, 11-12 janvier 2018

3ème assemblée annuelle du CREEPIUS

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Introduction – Supersonic Ejectors

Key benefits:

• No moving parts

• Simple operation

• Low grade energy as input

• Handle single- and two-phase flows

An apparatus which harvests the high energy of a jet (primary flow), to entrain and

compress a secondary flow.

Image: http://www.ertc.od.ua/en/about_ert_en.html 2S. Croquer

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Introduction – Applications

3S. Croquer

Ejector Expansion Ref. Cycle (EERC)

Condenser

Evaporator

Compressor

Valve

SeparatorEjector

Condenser

Evaporator

Ejector

Valve

Generator

Pump

Heat Driven Ref. Cycle (HDRC)

• Desalination

• AC system in electric vehicles

• Emergency systems in nuclear facilities

• Gas wells

• Rebreathers Scuba diving

• Refrigeration

http://www.mazdalimited.com/images/steam-jet-bosster-ejector-header-img.jpg http://articles.sae.org/6741/

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Introduction – Why a numerical study of ejectors?

4S. Croquer

Ejector test benches are limited by:

• Small dimensions

• Thermal insulation

• Hazardous working fluids

• Extreme operating conditions

Numerical modeling:

• Thermodynamic (0D) models

• 1D models

• CFD

Images: R134a ejector test bench at CanmetEnergy

Assembly

Components

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Developments in Numerical Modelling of Ejectors

5S. Croquer

While RANS modelling approaches are already well established for

supersonic ejectors, two new roads are possible:

- Injection of Droplets in the Constant Area Section of a Supersonic

Ejector for Shock Attenuation

- Large-Eddy Simulation of an Air Supersonic Ejector

(In course)

Explore new modelling techniques

Exploit current RANS models

2

1

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R134a ejector with droplet injection

6S. Croquer

Primary Inlet

PP0, TP0

Secondary Inlet

PS0, TS0

Outlet

ShockD

nd

Droplet Injection

de

Dinj

0,0

0,2

0,4

0,6

0,8

26 28 32 33

Po

rtio

n o

f to

tal lo

sse

s

[%]

Section 1 Section 2

Tsatout [oC]

Rationale:

• Shocks and mixing are responsible for about

60% of the exergy lost in the ejector (Croquer

et al. 2016).

• Droplets might attenuate the shock train

intensity and attack this source of losses.

• The effects on a supersonic ejector are

assessed using a combined approach (RANS

+ thermodynamic modelling).

Mixing Shocks

Injection of Droplets in the Constant Area Section of a Supersonic Ejector for

Shock Attenuation

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R134a ejector with droplet injection

7S. Croquer

Operating

Point

Primary Inlet Secondary Inlet Outlet

T [ºC] P [kPa] T [ºC] P [kPa] T [ºC] P [kPa]

1 89.4 2598 20.0 415 29.4 757

2 94.4 2889 20.0 415 32.5 827

3 99.2 3188 20.0 415 35.4 897

1

2

3

Pre

ssu

re

Enthalpy

1

2

3

Ejector geometry and operating conditions

R134a

Reference: Garcia et al. An experimental investigation of a R-134a ejector refrigeration system.

International Journal of Refrigeration, 46 (2014) 105-113

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R134a ejector with droplet injection

8S. Croquer

RANS ModelSecondary inlet:

Total P and Total T

Primary inlet:

Total P and Total T

Outlet: Static

pressure

Smooth, adiabatic walls

2D axi-symmetric domain

• Mesh: structured (650000 elements) with 21

wall-adjacent prismatic layers

• Gas properties: REFPROP Eq. database

• Turbulence model: k-ω SST low-Reynolds

formulation

• Steady state

• Schemes: 2nd order upwind (advection) and

2nd order centered (diffusion)

Numerical Parameters Droplet injection

• Discrete phase (Lagrangian frame)

• Coupling with main flow: two-way

(momentum and thermal energy exchanges)

• Constant properties

• Breakup model: WAVE (We > 100)

RANS model accuracy (w/o droplet injection):

- 5% in terms of entrainment ratio

- 2% in terms of compression ratio

Croquer et al., Turbulence modeling of a single-phase R134a supersonic ejector. Part 1:

Numerical benchmark, Int. J. of Refrigeration, 61, p.140-152, 2016.

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R134a ejector with droplet injection

9S. Croquer http://www.enmodes.de/references/validation/validation-turbulence/

Thermodynamic Model

Outlet

L1

D

nd

L2 L3 L4 L5 L7L6

de

Dinj

Input:

- Geometry: primary throat, constant area section and diffuser diameters

- Operating conditions: inlet P and T, outlet P

- Efficiency coefficients for inlet accelerations, mixing and diffusion

Output:

• Double-choke entrainment ratio

• Limiting compression ratio

Assumptions:

- Real gas equations (CoolProp)

- Uniform values at each cross section

- Entrainment ratio depends on effective area

- Mixing occurs at Constant Area Section

- Normal shock in the Constant Area Section after complete mixing

- Losses represented via isentropic and mixing efficiencies

The model has been extensively validated in single- and two-phase flow operations in Croquer et al.,

Thermodynamic modeling of supersonic gas ejector with droplets, Entropy, 19(579), p.1-21, 2017.

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R134a ejector with droplet injection

10S. Croquer

Comparison between the RANS and Thermodynamic model

Ma number Temperature

Pressure

Inlet conditions: OP2

Injection:

•Diameter: 500 microns

•Temperature: 260 K

•Fraction: 10% of primary mass flow rate

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R134a ejector with droplet injection

11S. Croquer

Internal shock structure

Injection location

No injection

1%

5%

10%

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R134a ejector with droplet injection

12S. Croquer

Changes in flow properties

-100

102030405060

L4 L5 L6 L7

Tem

per

atu

re [

oC

]

Location

0% 1% 2% 5% 10%

Injection fraction

100

300

500

700

900

L4 L5 L6 L7

Pre

ssu

re [

kP

a]

Location

0% 1% 2% 5% 10%

Injection fraction

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R134a ejector with droplet injection

13S. Croquer

Shock attenuation

Pressure jump Ma jump

• With increasing injection fraction, the shock pressure and Ma jumps reduce

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R134a ejector with droplet injection

14S. Croquer

Effects on performance – Limiting pressure

Injection locationNo injection

10%

u

Injection locationNo injection

10%

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R134a ejector with droplet injection

15S. Croquer

Effects on performance – Ejector efficiency

• With increasing injection fraction, the ejector efficiency reduces

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R134a ejector with droplet injection

16S. Croquer

Effects on performance – Exergy accounting

Conclusion:

• Droplet injection attenuates shock, reducing the importance of associated

exergy losses

• Exergy losses associated with injection overcome any potential benefit

• The additional entropy generated with the injection, reduces the maximum

double-choke compression ratio.

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Motive throat 6mm x 50 mm

Constant area section 27 mm x 50mm

Full length 1.52 m

Primary flow 5 bar 300 K

Secondary flow 0.97 bar 300 K

Outlet 1.2 bar

Large-Eddy Simulation of an Air Supersonic Ejector

17S. Croquer

10mm

Secondary:

Ptotal, Ttotal

Pstatic

Primary:

Ptotal, Ttotal

Adiabatic walls

Problem description

Re = 6.6E5, Ma = 1.72

Experimental facility at the Université Catholique de Louvain

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Large-Eddy Simulation of an Air Supersonic Ejector

18S. Croquer

Numerical setup:

- Solver: AVBP (HPC LES code developed by CERFACS)

- Air as perfect gas

- Imposed wall log-laws (Average Y+ = 20)

- Schemes: TTG4A (4th order finite-element scheme)

- Numerical stability: Jameson sensor based on pressure fluctuations

Problem

definition

Meshing and

Numerical setup

Calculations 1:

Flow stabilization

Calculations 2:

Capturing StatisticsPost-processing

Challenges:

- Flow initialization

- Wall treatment

- Shock Handling

- Data storage and post-processing

Roadmap

1.5x Artificial viscosity 2x Artificial viscosity

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Large-Eddy Simulation of an Air Supersonic Ejector

19S. Croquer

Nodes1632 nodes, AMD

Opteron 6172

For each node:

Cores 12

RAM 32GB

Theoretical performance

201.6 Gflops

Computations running in the Mammouth Parallèle 2 cluster (Université de Sherbrooke)

https://wiki.calculquebec.ca/

1 Gflop = 1e9 operations per second

Cluster characteristics

MeshUnstructured –

237 Millions cells (55 Millions nodes)

Simulated time 0.030803 seconds ≈ 10 tc

Computing wall-clock time ≈ 36 days / tc

Nodes 100 (12 cores per node)

https://www.usherbrooke.ca/recherche/en/infrastructure/centre-for-scientific-computing/

Flow stabilization: 8tc

Collecting flow statistics: 2tc (so far)

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Large-Eddy Simulation of an Air Supersonic Ejector

20S. Croquer

Schlieren images (Experimental)

LES

Preliminary Results

Schlieren images (Experimental)

LES

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Large-Eddy Simulation of an Air Supersonic Ejector

21S. Croquer

Q-criterion surfaces colored

by the vorticity sense

Preliminary Results

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Large-Eddy Simulation of an Air Supersonic Ejector

22S. Croquer

Preliminary Results

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Large-Eddy Simulation of an Air Supersonic Ejector

23S. Croquer

Preliminary Results

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24S. Croquer

Thank you!