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Experiments in Fluids

, 54:1542 | Cite as

New correlation of subsonic, supersonic and cryo gas jets validated by highly accurate schlieren measurements

  • J. Gerold
  • P. Vogl
  • M. Pfitzner
Research Article

Abstract

High-speed schlieren visualization at 20,000 fps was performed to investigate the transient penetration depth of helium gas jets into air at 8 different pressure ratios. The injection pressure investigated was between 1.5 and 40 bar. The pressure in the mixing chamber was varied between 1.0 and 4.0 bar. The different pressure ratios were chosen to examine subsonic and underexpanded jets. To investigate the density dependence of the process, cryo injections were performed at injection temperatures of 224, 198 and 173 K at different pressure ratios. Using the image processing technique for detecting the jet tip penetration distance, presented in this article, it can be shown that for a given injector the jet penetration behavior is the same for the same pressure ratio. A new self-similar model was developed, to describe the influence of the injection and chamber gas density on the jet penetration behavior more accurately. The model was verified with the experimental data sets presented in this paper and with literature data.

Keywords

Penetration Depth Pressure Ratio Injection Pressure Nozzle Exit Discharge Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

Unobstructed height of source image (m)

B

Empirical constant (−)

CD

Discharge coefficient (−)

Cf

Fraction of centerline velocity (−)

Ct

Scaling constant (−)

D

Diameter of vortex ball (m)

d

Nozzle diameter (m)

de

Effective diameter (m)

dPMD

Diameter of the PMD (m)

EBG

Background illuminance (lux)

\(\Updelta E\)

Differential illuminance (lux)

f2

Focal length of second mirror (m)

h

Image height (−)

I

Jet image (−)

\(\tilde I\)

Normalized jet image (−)

IBG

Background image (−)

\(\tilde I_{\rm BG}\)

Normalized background image (−)

k

Gladstone-Dale constant (−)

K

Entrainment constant (−)

lK

Kolmogorov length scale (m)

lT

Taylor length scale (m)

Mjet

Momentum of steady-state jet region (kg m/s)

Mvortex

Momentum of jet vortex ball (kg m/s)

MPMD

Mach number downstream of the PMD (−)

Mu,s

Mach number upstream of normal shock (−)

\(\dot M_{\rm n}\)

Momentum flux at nozzle exit (kg m/s2)

\(\dot{m}\)

Massflow (kg/s)

\(\dot{m}_{\rm n}\)

Massflow at nozzle exit (kg/s)

\(\dot m_{\rm m}\)

Measured massflow through nozzle (kg/s)

n

Refractive index (−)

pch

Chamber pressure (bar)

pi

Injection pressure (bar)

pn

Pressure at nozzle exit (bar)

R

Empirical constant (−)

Rch

Specific gas constant of chamber gas (J/kg K)

Rn

Specific gas constant of injected gas (J/kg K)

Re

Reynolds number (−)

ReT

Taylor-scale Reynolds number (−)

Re0

Characteristic jet Reynolds number (−)

r

Radial distance from jet axis (m)

S

Schlieren sensitivity (−)

Tch

Chamber temperature (K)

Ti

Injection temperature (K)

Tn

Temperature at nozzle exit (K)

t

Time (s)

t+

Characteristic time scale (s)

\(\tilde t\)

Non-dimensional time scale (−)

\(\tilde{t}_{\rm P}\)

Normalized time according to Petersen (−)

u

r.m.s. velocity (m/s)

Uc

Centerline velocity (m/s)

Uc,m

Centerline mean velocity (m/s)

Un

Velocity at nozzle exit (m/s)

UPMD

Velocity downstream of the PMD (m/s)

w

Image width (−)

x

Position (m)

x0

Virtual origin (m)

y0.5

Half-width of jet (m)

z

Position along the optical axis (m)

z+

Characteristic length scale (m)

Zt

Penetration depth (m)

\(\tilde{Z}_{\rm t,l}\)

Normalized Z t (\(s^{\frac{1}{2}}\))

\(\tilde{Z}_{\rm t}\)

Non-dimensional Z t (−)

\(\tilde{Z}_{\rm t,H}\)

Normalized Z t according to Hill \((s^{\frac{1}{2}})\)

\(\tilde{Z}_{\rm t,P}\)

Normalized Z t according to Petersen (−)

\(\epsilon\)

Dissipation rate (m2/s3)

\(\hat{\epsilon}\)

Dissipation rate constant (−)

\(\epsilon_y\)

Light ray deflection in y direction (rad)

\(\Upgamma\)

Scaling constant (−)

\(\tilde \Upgamma\)

Scaling constant (−)

γ

Specific heat ratio (−)

γn

Specific heat ratio at nozzle exit (−)

μ

Mean pixel intensity of a image (−)

ν

Kinematic viscosity (m2/s)

νn

Kinematic viscosity at nozzle exit (m2/s)

πi

Injection pressure ratio (−)

ρ

Gas density (kg/m3)

ρch

Chamber gas density (kg/m3)

ρi

Injection gas density (kg/m3)

ρn

Gas density at nozzle exit (kg/m3)

ρPMD

Density downstream of the PMD (kg/m3)

DI

Direct injection

LNG

Liquefied natural gas

PFI

Port fuel injection

PMD

Pseudo-Mach disk

Notes

Acknowledgments

The authors would like to thank F. Gerbig from BMW for providing the cryo system for the low temperature injections.

References

  1. Abraham J (1996) Entrainment characteristics of transient jets. Numer Heat Transf Part A 30:347–364CrossRefGoogle Scholar
  2. Abramovich S, Solan A (1973) The initial development of a submerged laminar round jet. J Fluid Mech 59:791–801CrossRefGoogle Scholar
  3. Anderson J (2003) Modern compressible flow: with historical perspective, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  4. Antonia RA, Satyaprakash BR, Hussain AKMF (1980) Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets. Phys Fluids 23:695–700CrossRefGoogle Scholar
  5. Baert R, Klaassen A, Doosje R (2010) Direct injection of high pressure gas: scaling properties of pulsed turbulent jets. SAE-Paper 2010-01-2253Google Scholar
  6. Birch AD, Brown DR, Dodson MG, Swaffield F (1984) The structure and concentration decay of high pressure jets of natural gas. Combust Sci Technol 36:249–261CrossRefGoogle Scholar
  7. Chen CJ, Rodi W (1980) Vertical turbulent buoyant jets: a review of experimental data. Pergamon Press, OxfordGoogle Scholar
  8. Edwards R, LarivT JF, Beziat JC (2011) Well-to-wheels analysis of future automotive fuels and powertrains in the European context. Well-to-Wheels Rep version 3cGoogle Scholar
  9. Ewan BCR, Moodie K (1986) Structure and velocity measurements in underexpanded jets. Combust Sci Technol 45:275–288CrossRefGoogle Scholar
  10. Gabside JE, Hall AR, Townend DTA (1943) Flow states in emergent gas streams. Nature 748–748Google Scholar
  11. Grabner P, Eichlseder H, Gerbig F, Gerke U (2006) Optimization of a hydrogen internal combustion engine with inner mixture formation. In: First international symposium in hydrogen internal combustion enginesGoogle Scholar
  12. Heller K, Ellgas S (2006) Optimization of a hydrogen internal combustion engine with cryogenic mixture formation. In: First international symposium in hydrogen internal combustion enginesGoogle Scholar
  13. Hill PG, Ouellette P (1999) Transient turbulent gaseous fuel jets for diesel engines. J Fluids Eng 121:93–101CrossRefGoogle Scholar
  14. Kayser JC, Shambaugh RL (1991) Discharge coefficients for compressible flow through small-diameter orifices and convergent nozzles. Chem Eng Sci 46(7):1697–1711CrossRefGoogle Scholar
  15. Merzkirch W (1987) Flow visualization, 2nd edn. Academic Press, New YorkGoogle Scholar
  16. Naber JD, Siebers DL (1996) Effects of gas density and vaporization on penetration and dispersion of diesel sprays. SAE-Paper 960034Google Scholar
  17. Ouellette P (1996) Direct injection of natural gas for diesel engine fueling. PhD thesis, University of British ColumbiaGoogle Scholar
  18. Petersen B (2006) Transient high-pressure hydrogen jet measurements. Master’s thesis, University of Wisconsin-MadisonGoogle Scholar
  19. Petersen B, Ghandhi J (2006) Transient high-pressure hydrogen jet measurements. SAE-Paper 2006-01-0652Google Scholar
  20. Pope SB (2000) Turbulent flows, 1st edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  21. Ricou FP, Spalding DB (1961) Measurements of entrainment by axisymmetrical turbulent jets. J Fluid Mech 11:21–32MATHCrossRefGoogle Scholar
  22. Rizk W (1958) Experimental studies of the mixing processes and flow configurations in two-cycle engine scavenging. Proc Inst Mech Eng 172:417–437CrossRefGoogle Scholar
  23. Schlichting H (1976) Grenzschicht-Theorie, 5th edn. Springer, KarlsruheGoogle Scholar
  24. Settles G (2001) Schlieren and shadowgraph techniques. Springer, BerlinMATHCrossRefGoogle Scholar
  25. Sutherland W (1893) The viscosity of gases and molecular force. Philosoph Mag Ser 5 36(223):507–531MATHCrossRefGoogle Scholar
  26. Turner JS (1962) The ’starting plume’ in neutral surroundings. J Fluid Mech 13:356–368MATHCrossRefGoogle Scholar
  27. Vogl P, Zimmermann I, Pfitzner M (2006) Modelling of hydrogen injection and combustion in internal combustion engines. First international symposium in hydrogen internal combustion enginesGoogle Scholar
  28. Wakuri Y, Fujii M, Amitani T, Tsuneya R (1960) Studies on the penetration of fuel spray in a diesel engine. Bull JSME 3(9):123–130CrossRefGoogle Scholar
  29. Williams TC, Shaddix CR (2007) Simultaneous correction of flat field and nonlinearity response of intensified charge-coupled devices. Rev Sci Instrum 78:1–6Google Scholar
  30. Witze PO (1980) The impulsively started incompressible turbulent jet. SAND80-8617Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for ThermodynamicsUniversität der Bundeswehr MünchenNeubibergGermany

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