Skip to main content
SpringerLink
Log in

Time-resolved, 3D, laser-induced fluorescence measurements of fine-structure passive scalar mixing in a tubular reactor

  • Original
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A three-dimensional, time-resolved, laser-induced fluorescence (3D-LIF) technique was developed to measure the turbulent (liquid-liquid) mixing of a conserved passive scalar in the wake of an injector inserted perpendicularly into a tubular reactor with Re=4,000. In this technique, a horizontal laser sheet was traversed in its normal direction through the measurement section. Three-dimensional scalar fields were reconstructed from the 2D images captured at consecutive, closely spaced levels by means of a high-speed CCD camera. The ultimate goal of the measurements was to assess the downstream development of the 3D scalar fields (in terms of the full scalar gradient vector field and its associated scalar energy dissipation rate) in an industrial flow with significant advection velocity. As a result of this advection velocity, the measured 3D scalar field is artificially “skewed” during a scan period. A method to correct for this skewing was developed, tested and applied. Analysis of the results show consistent physical behaviour.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1a, b
Fig. 2
Fig. 3a, b
Fig. 4 a
Fig. 5
Fig. 6 a
Fig. 7 a
Fig. 8a–c
Fig. 9a, b
Fig. 10
Fig. 11
Fig. 12 a
Fig. 13a–c
Fig. 14a, b
Fig. 15a–d
Fig. 16a, b
Fig. 17
Fig. 18a, b
Fig. 19a, b
Fig. 20
Fig. 21a, b
Fig. 22a, b
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

Notes

  1. For isotropic turbulence, both the strain rate, S, and the energy dissipation, ε, can be related to the Taylor micro scale, λ g, by \(S^{2} = 2{u^{2}_{l} } \mathord{\left/ {\vphantom {{u^{2}_{l} } {\lambda ^{2}_{{\text{g}}} }}} \right. \kern-\nulldelimiterspace} {\lambda ^{2}_{{\text{g}}} } \) and \(\varepsilon = {15vu^{2}_{l} } \mathord{\left/ {\vphantom {{15vu^{2}_{l} } {\lambda ^{2}_{{\text{g}}} }}} \right. \kern-\nulldelimiterspace} {\lambda ^{2}_{{\text{g}}} } \) (Hinze 1975). Elimination of u l /λ g yields S 2=2ε/(15ν), which, in combination with λ ν =c 1(ν/S)1/2, leads to λ ν =(c 115ν 3/(2ε))1/4~η.

  2. In the present article, the width of a laser sheet will be based on the (1/e) intensity decay position, while the thickness will be based on the (1/e2) position. The definitions are in a ratio of \({\sqrt 2 } \).

  3. For every discrete grid position, x′, of the output concentration field, ζ′, the value is retrieved from the input concentration field, ζ, at the corresponding position, x, given by Eqs 12 and 13. Since x is generally located within the fixed grid, a bi-linear interpolation is applied using the values at the eight surrounding grid points to estimate ζ(x).

  4. The mixing fraction distribution is obtained from the SED pdf, f logχ (Fig. 24), by plotting the volume fraction \(1 - {\int_{ - \infty }^{s = \chi } {f\chi {\left( s \right)}} }{\text{d}}s \) against the mixing fraction \(1 - \frac{1}{{\langle \chi \rangle }}{\int_{ - \infty }^{s = \chi } {sf\chi {\left( s \right)}} }{\text{d}}s \), where the conditional distribution, f χ , is obtained via the transformation f χ =f log(χ)/(χln(10)).

Abbreviations

A :

Deformation tensor

D t, D f :

Reactor and injector diameter

L x, L y, L z :

Dimensions of the 3D-LIF measurement volume

N x, N y, N z :

Number of data samples per measurement volume

Re m :

Reynolds number based on mean velocity

Sc :

Schmidt number

f :

Focal length

f c,lens, f c,array :

Cut-off frequency for camera lens and sensor array

f θ , f φ :

Marginal probability density function for θ and φ

f θφ :

Joint probability density function of θ and φ

\(\Delta t \) :

Temporal separation of the 2D data planes

\(\Delta T \) :

Temporal resolution of the measurement volume

\(\Delta x,\;\Delta y,\;\Delta z \) :

Spatial resolution of the measurement volume

γ, α :

Deformation angle and deformation, where α=tanγ

ε :

Fluid energy dissipation rate

λ ν , λ Γ :

Strain limited vorticity and scalar diffusion layers

ζ :

Scalar concentration

η, η B :

Kolmogorov and Batchelor length scale

θ, φ :

Spherical angles of the scalar gradient vector, \(\nabla \zeta \)

ν :

Kinematic viscosity

σ e –2 :

Half-thickness (1/e2) of the laser sheet

τ, τ a :

Kolmogorov and Kolmogorov advection time scales

χ :

Scalar energy dissipation rate

Γ :

Scalar diffusivity

2D, 3D:

Two- and three-dimensional

DNS:

Direct numerical simulation

LIF:

Laser-induced fluorescence

SED:

Scalar energy dissipation rate

TR:

Tubular reactor

References

  • Bakker RA (1996) Micromixing in chemical reactors: Models, experiments and simulations. PhD thesis, Delft University of Technology

    Google Scholar 

  • Bakker RA, Van den Akker HEA (1996) A Lagrangian description of micromixing in a stirred tank reactor using 1D-micromixing models in a CFD flow field. Chem Eng Sci 51(11):2643–2648

    Article  CAS  Google Scholar 

  • Baldyga J, Bourne JR (1984) A fluid mechanical approach to turbulent mixing and chemical reaction. Part 2: Micromixing in the light of turbulence theory. Chem Eng Commun 28:243–258

    CAS  Google Scholar 

  • Brethouwer G (2001) Mixing of passive and reactive scalars in turbulent flows. PhD thesis, Delft University of Technology

  • Castleman KR (1979) Digital image processing. In: Openheim AV (ed) Prentice Hall signal processing series. Prentice-Hall, Englewood Cliffs, NJ

  • Colucci PJ, Jaberi FA, Givi P, Pope SB (1998) Filtered density function for large eddy simulation of turbulent reacting flows. Phys Fluids 10(2):499–515

    Article  CAS  Google Scholar 

  • Dahm WJA, Southerland KB, Buch KA (1990) Four-dimensional laser induced fluorescence measurements of conserved scalar mixing in turbulent flows. In: Proceedings of the 5th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1990

  • Dahm WJA, Southerland KB, Buch KA (1991) Direct, high resolution, four-dimensional measurements of the fine scale structures of Sc>>1 molecular mixing in turbulent flows. Phys Fluids A-Fluid 3(5):1115–1127

    Google Scholar 

  • Derksen JJ, Van den Akker HEA (1999) Large eddy simulations on the flow driven by a Rushton turbine. AIChE J 45(2):209–221

    CAS  Google Scholar 

  • Fox RO (1997) The Lagrangian spectral relaxation model of the scalar dissipation in homogeneous turbulence. Phys Fluids 9(8):2364-2386

    Article  CAS  Google Scholar 

  • Frank JB, Lyons KM, Long MB (1991) Technique for three-dimensional measurements of the time development of turbulent flames. Opt Lett 16(12):958–960

    CAS  Google Scholar 

  • Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York

  • Hoffmann A, Zimmerman F, Schultz C (2002) Instantaneous three-dimensional visualization of concentration distribution in turbulent flows with a single laser. In: Proceedings of the 1st international conference on optical and laser diagnostics, London, England, December 2002

  • Hopkins H (1955) The frequency response of a defocused optical system. P Roy Soc A 231:91–106

    Google Scholar 

  • Knaus DA, Gouldin FC, Hinze PC, Miles PC (1999) Measurement of instantaneous flamelet normals and the burning rate in a SI engine. Technical report 1999–01–3543, SAE

  • Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13:82–85

    Google Scholar 

  • Landenfeld T, Kremer A, Hassel EP, Janicka J, Schäfer T, Kazenwadel J, Schultz C, Wolfrum J (1998) Laser-diagnostic and numerical study of strongly swirling natural gas flames. P Combust Inst 27:1023–1029

    Google Scholar 

  • Maas HG, Stefanidis A, Gruen A (1994) From pixels to voxels: Tracking volume elements in sequences of 3-D digital images. In: ISPRS commission III: Intercongress symposium, Munich, Germany

  • Nygren J, Hult J, Richter M, Aldén M, Christensen M, Hultqvist A, Johansson B (2002) Three-dimensional laser-induced fluorescence of fuel distribution in a HCCI engine. P Combust Inst 29 (in press)

  • Overholt MR, Pope SB (1996) Direct numerical simulations of a passive scalar with imposed mean gradient in isotropic turbulence. Phys Fluids 8(11):3128–3148

    Article  CAS  Google Scholar 

  • Paul PH, Van Cruyningen I, Hanson RK, Kychahoff G (1990) High resolution digital flowfield imaging of jets. Exp Fluids 9:241–251

    CAS  Google Scholar 

  • Prasad RR, Sreenivasan KR (1990) Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows. J Fluid Mech 27:507–521

    Google Scholar 

  • Su LK, Clemens NT (1999) Planar measurements of the full three-dimensional scalar dissipation rate in gas-phase turbulent flows. Exp Fluids 27:507–521

    Article  CAS  Google Scholar 

  • Ten Cate A (2002) Turbulence and particle dynamics in dense crystal sluries. PhD thesis, Delft University of Technology

  • Van Vliet E, Derksen JJ, Van den Akker HEA (2000a) Four-dimensional laser induced fluorescence measurements of micro-mixing in a tubular reactor. In: Proceedings of the 10th European conference on mixing, Delft, July 2000

  • Van Vliet E, Derksen JJ, Van den Akker HEA (2000b) Measurements of micro-mixing in a tubular reactor using a four-dimensional laser induced fluorescence technique. In: Proceedings of the 10th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 2000

  • Van Vliet E, Derksen JJ, Van den Akker HEA (2001) Modelling of parallel competitive reactions in isotropic homogeneous turbulence using a filtered density function approach for large eddy simulations. In: Proceedings of the 3rd international symposium on computational technologies for fluid/thermal/chemical systems with industrial applications, Atlanta, Georgia, USA, September 2001

  • Van Vliet E, Derksen JJ, Van den Akker HEA (2003) Turbulent reactive mixing in a tubular reactor: An LES/FDF approach. AIChE J (to be submitted)

    Google Scholar 

  • Walker DA (1987) A fluorescence technique for measurement of concentration in mixing liquids. J Phys E Sci Instrum 20:217-224

    Article  CAS  Google Scholar 

  • Yip B, Lam JK, Winter M, Long MB (1987) Time resolved three-dimensional concentration measurements in a gas jet. Science 235:1209–1211

    Google Scholar 

  • Yip B, Long MB (1986) Instantaneous planar measurements of the complete three-dimensional scalar gradient in a turbulent jet. Opt Lett 11:64–66

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kramers Laboratorium voor Fysische Technologie, Faculty of Applied Sciences, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW, Delft, The Netherlands

    E. Van Vliet, S. M. Van Bergen, J. J. Derksen, L. M. Portela & H. E. A. Van den Akker

Authors
  1. E. Van Vliet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. Van Bergen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. J. Derksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. M. Portela
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. E. A. Van den Akker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Van Vliet.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van Vliet, E., Van Bergen, S.M., Derksen, J.J. et al. Time-resolved, 3D, laser-induced fluorescence measurements of fine-structure passive scalar mixing in a tubular reactor. Exp Fluids 37, 1–21 (2004). https://doi.org/10.1007/s00348-004-0779-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-004-0779-1

Keywords

Search

Navigation