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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
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
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/
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
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
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
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
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.
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.
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
R134a ejector with droplet injection
11S. Croquer
Internal shock structure
Injection location
No injection
1%
5%
10%
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
R134a ejector with droplet injection
13S. Croquer
Shock attenuation
Pressure jump Ma jump
• With increasing injection fraction, the shock pressure and Ma jumps reduce
R134a ejector with droplet injection
14S. Croquer
Effects on performance – Limiting pressure
Injection locationNo injection
10%
u
Injection locationNo injection
10%
R134a ejector with droplet injection
15S. Croquer
Effects on performance – Ejector efficiency
• With increasing injection fraction, the ejector efficiency reduces
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.
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
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
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)
Large-Eddy Simulation of an Air Supersonic Ejector
20S. Croquer
Schlieren images (Experimental)
LES
Preliminary Results
Schlieren images (Experimental)
LES
Large-Eddy Simulation of an Air Supersonic Ejector
21S. Croquer
Q-criterion surfaces colored
by the vorticity sense
Preliminary Results
Large-Eddy Simulation of an Air Supersonic Ejector
22S. Croquer
Preliminary Results
Large-Eddy Simulation of an Air Supersonic Ejector
23S. Croquer
Preliminary Results
24S. Croquer
Thank you!
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