boundary layer effects on the critical nozzle of …

BOUNDARY LAYER EFFECTS ON THE

CRITICAL NOZZLE OF HYDROGEN SONIC

JET

Marius Paraschivoiu

Farbod Vakilimoghaddam

Mohammadamin Afroosheh

Concordia University

The 6th International Conference on Hydrogen Safety (ICHS)

Yokohama (Japan)

October 19-21, 2015

- 2 -

Research Goal

Study the Mach number at the nozzle exit of

the under-expanded jet

Objectives

Study the viscous effects which create a fluid throat

which acts as a converging-diverging nozzle;

Study the initial transient effect on the Mach number

inside the exit throat;

Quantify the effect on the mass flow and velocity of the

under-expanded jet.

Model| Objectives | Boundary layer effect| Axisymmetric model| Transient results | Conclusion

- 3 -

Previous Work

Kubo, K., Miyazato, Y., and Matsuo, K., Study

of choked flows through a convergent Nozzle,

Journal of Thermal Science, 19, no. 3, 2010,

pp. 193-197.

Experimental work, Low Reynolds number, Steady

flow; “the main flow Mach number at the nozzle exit is supersonic

when the back pressure ratio is equivalent to the choking

condition, and the Mach number increases as the boundary

layer thickness increases.”


- 4 -

Navier-Stokes Equations with Large Eddy Simulation model for turbulence

Model| Objectives | Boundary layer effect|

Transport (Advection) Equation: 𝝏𝒄

𝝏𝒕+𝝏(𝒄(𝒖 − 𝒘𝒙))

𝝏𝒙+𝝏(𝒄(𝒗 − 𝒘𝒚))

𝝏𝒚+𝝏(𝒄(𝒘 − 𝒘𝒛))

𝝏𝒛= 𝟎

Abel Nobel Real Gas Law: 𝒑 = (𝟏 − 𝒃𝝆)−𝟏𝝆𝑹𝒎𝒊𝒙𝑻, 𝒃 = 𝟎. 𝟎𝟎𝟕𝟕𝟓 𝒎𝟑 𝒌𝒈

• 𝑐=0 a cell full of hydrogen

• 0<𝑐<1 discontinuity (hydrogen-air interface)

• 𝑐=1 a cell full of air

Spatial Discretization (Convection Flux)

𝟐𝒏𝒅 order Roe-MUSCL scheme

Temporal Discretization

𝟏𝒔𝒕 order Implicit Scheme

Linear Solver

Iterative Method : GMRES

Axisymmetric model| Transient results | Conclusion

- 5 -

Computational

Domain

3D unstructured

tetrahedral mesh

2D slices of the mesh

small cylindrical orifice

diameter D=1 mm and a

length L=2 mm

14.8 million grid points


- 6 -

Mach number in the Nozzle

Viscous Mach number distribution

inside the release pipe after 15

micro-second of release for

1) 10 MPa and 2)70 MPa


Radial Mach number distribution

- 7 -

Near Jet Region

Centerline values of

hydrogen jet release

from 1mm orifice after

15 microsecond of

release for A) Mach

number, B) density, C)

pressure, and D)

temperature


- 8 -

Euler Simulation

Inviscid Mach number distribution inside

the release pipe after 15 micro-second of

release

Mach Distribution

Inviscid 10MPa Inviscid 70MPa


- 9 -

Geometry : 3D CAD Model

Full 3D CAD Model

Axisymmetric Model : 10 Degree

modelling

Circular orifice diameter : 0.5 mm Hydrogen High Pressure

Chamber

Air Chamber

Hydrogen High Pressure

Chamber

Air Chamber


- 10 -

Computational Domain

Mesh Statistic

Viscous Case Euler Case

Number of Elements

2,715,484 2,490,247


- 11 -

Boundary Layer Mesh

AR=1

Boundary Layer Meshing Characteristics

First Layer Height (mm) 2.E-05

y+ 0.7 Aspect Ratio 1.1

Number of Layers 40


- 12 -

Inviscid simulation based on Euler Equations.

Viscous simulation based on Reynolds Averaged Navier-Stokes (RANS)

Equations.

One transport equation for concentration.

Turbulence Model:

K–omega (k–ω) –SST

Two transport equations (PDE) for :

Turbulence Kinetic Energy (k)

Specific Rate of Dissipation (ω)

Redlich Kwong Real Gas Law:

𝒑 = (𝟏

𝝆− 𝒃 + 𝒄)−𝟏𝑹𝒎𝒊𝒙𝑻 −

𝒂 𝑻

𝟏𝝆

𝟏𝝆 + 𝒃


Solution Characteristic

Discretization

Order Second Order

CFL Adaptive time

stepping method

Convergence

criteria 1.0 E-05

Initial

Timestep 5.0 E-09

- 13 -

Initial and Boundary Conditions

Initial Reservoir Pressure 70MPa &

10MPa

Initial Temperature 300 K

Air mixture fraction 1

Hydrogen mixture fraction 0

Hydrogen & air isentropic exponent (γ) 1.4

Molecular mass of hydrogen (𝑴𝑯𝟐) 2.016 g/mol

Molecular mass of air (𝑴𝒂𝒊𝒓) 28.96 g/mol

Convergence Criteria 𝟏𝟎−𝟓

Time step adaptive

The effect of the gravity on the fluid is neglected.

No-slip and adiabatic solid walls.

Non-reflecting farfield boundary conditions.


- 14 -

Flow at after 15 micro seconds


- 15 -

Transient Flow Simulation

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

-0.002 -0.0015 -0.001 -0.0005 0

Mach Number

5µs 10µs 15µs 20µs 30µs

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

5.50E+06

6.00E+06

-0.002 -0.0015 -0.001 -0.0005 0

Pressure

5 µs 10 µs 15 µs 20 µs 30 µs

Euler Case Study


- 16 -


1

1.01

1.02

1.03

1.04

1.05

1.06

-0.002 -0.0015 -0.001 -0.0005 0

Mach Number

100 µs 200 µs 300 µs

4.80E+06

4.85E+06

4.90E+06

4.95E+06

5.00E+06

5.05E+06

5.10E+06

5.15E+06

5.20E+06

-0.002 -0.0015 -0.001 -0.0005 0

Pressure

100 µs 200 µs 300 µs

Euler Case Study


- 17 -


0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

-0 .002 -0 .0015 -0 .001 -0 .0005 0

MACH NUMBER

5 µs 10 µs 15 µs 25 µs

Viscous-SST Case Study

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

5.50E+06

6.00E+06

6.50E+06

-0 .002 -0 .0015 -0 .001 -0 .0005 0

PRESSURE

5 µs 10 µs 15 µs 25 µs


- 18 -


Euler-Viscous Case Comparison ( t =15µs)

0.9

0.95

1

1.05

1.1

1.15

-0 .002 -0 .0015 -0 .001 -0 .0005 0

MACH-NUMBER

VISCOUS-SST-15 µs EULER-15 µs

4.50E+06

4.70E+06

4.90E+06

5.10E+06

5.30E+06

5.50E+06

5.70E+06

5.90E+06

6.10E+06

-0 .002 -0 .0015 -0 .001 -0 .0005 0

PRESSURE

VISCOUS-SST-15µs EULER-15µs


- 19 -

Conclusion

Boundary layer in the nozzle leads to lower mass flow

rate;

Boundary layer is difficult to capture accurately;

Importance of transient effect in the first 100

micro-seconds;

Euler solution provides a worse case scenario compared

with a Navier-Stokes solution.


- 20 -

Thank You

- 21 -

- 22 -


Converging Diverging Boundary Layer


- 23 -



boundary layer effects on the critical nozzle of …

Documents