EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...

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EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
VENTILATION 2006, May 13-18 in Chicago, Illinois

  EVALUATION OF NON-ISOTHERMAL
       AIR JET PARAMETERS
FROM RECORDS OF FLOW VISUALIZATION
      USING INTERFEROMETRY

          Milan PAVELEK - Eva JANOTKOVA
    Brno University of Technology – Czech Republic

                                                     1
EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
INTRODUCTION
● Interferometry is a progressive
  visualization method for researching
  non-homogeneities in fluids.
● The non-homogeneities of air
  jets from outlets are due mainly
  to temperature. For this reason,     Candle
                                        flame
  it is only possible to investigate
  non-isothermal jets.
● Ordinary interferometers have a relatively narrow field of view,
  thereby enabling the observation of jets from small outlets used in
  cars, airplanes etc.

● Interferometers are frequently used for measurements of 2D or
  axially symmetrical temperature fields. This contribution, however, is
  aimed at jets, which are often 3D, and from whose interferograms it is
  also possible to derive interesting information.
                                                                       2
EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
EXPERIMENTAL EQUIPMENT
A schematic diagram for the experimental setup used to measure the
initial parameters of jets from ventilation outlets and for measuring the
ambient air state is shown in this figure.

       Ventilator     Heat           Flowmeter          Interferometer
                    exchanger                            field of view
                                     VF
                                             Outlet                          y
                                                                                 x
                                                           w0
                          pF    TF             Ti     T0                 z
                                                                   pi

       Manometer                          Thermometer       Barometer

Ti [K]       ambient air temperature           VF [m3.s-1] is the volumetric
pi [Pa]      barometric pressure               flow for temperature TF [K]
To [K]       initial air temperature           and pressure pF [Pa]
wo [m.s-1]   initial air velocity                                                3
EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
NON-ISOTHERMAL AIR JETS
The research is aimed at:
• strongly non-isothermal jets (Aro > 0.01)
• slightly non-isothermal jets (Aro ≤ 0.001)
Archimedes number is given by the Eq. (1)                do

      g(To − Ti )Lo
Aro =                            (1)
         w o2Ti                                Circular outlet, Ti = 295 K
                                                wo= 14 m.s-1, To= 338 K
g [m.s-2] acceleration due to gravity
Lo [m]    dimension of the outlet
          (diameter do of circular outlets,
          width bo of slot outlets etc.)
                                                         bo
Remark:
To investigate parameters of isothermal
jets, slightly non-isothermal jets must be
generated which have many parameters            Slot outlet, Ti = 296 K
in common with isothermal air jets.            wo= 1.7 m.s-1, To= 323 K
                                                                             4
EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
MACH - ZEHNDER INTERFEROMETER
For visualization and
measurement of 2D                                          MZI
                                     Model

                                             φ 200
temperature fields in
non-isothermal air jets,
a Mach - Zehnder
interferometer (MZI)
was chosen.
                             Mach-Zehnder
                             interferometer
  Model      Field of
 of outlet    view         The size of the interferometer field of
                           view (200 mm) limits the size of object
                           investigated, therefore scale models
    w0                     are needed to investigate larger
    to                     objects.
                           Similarity theory is then applied to the
                           measurement results.
                                                                   5
EVALUATION OF NON-ISOTHERMAL AIR JET PARAMETERS FROM RECORDS OF FLOW VISUALIZATION USING INTERFEROMETRY - VENTILATION 2006, May 13-18 in Chicago ...
INTERFEROGRAM EVALUATION
The interferograms are processed and evaluated by our Interfer-Visual
software [1]. This software automatically evaluates:
• The course of
  interference
  fringes in images
• Fringe distribution
  in selected image
  sections … etc.
Evaluated data may be edited
interactively and transferred
to another program.
The focus is above all on
evaluating:
• Temperatures in jets
• Enthalpy in jets
• Jet boundaries and shapes
                                                                        6
LOCAL TEMPERATURES
The distribution of local temperatures in axial-symmetric or 2D non-
isothermal air jets can be obtained using an ordinary Mach - Zehnder
interferometer.
• Axial-symmetric
  temperature fields
  in the vicinity of circular
  outlets (see figure) are
  evaluated via our own
  equations [2].

• 2D temperature fields
  in the vicinity of slot or
  rectangular outlets are
  evaluated in our work
                                Temperature profiles in an air jet from
  using equations from              a circular outlet, do = 30 mm,
  Hauf, Grigull [3].               x = 30 mm - core area of the jet
                                                                          7
ENTHALPY IN JETS
In lightly non-isothermal jets heat flow and
                                                       y           x = const.
thereby enthalpy flow in direction x will be
constant, and will be equal to the heat
power of the outlet Wo [W]
Wo = w o ⋅ Ao ⋅ ρo ⋅ c p (To − Ti ) =         (2)      0                        x
    = w(x) ⋅ A(x) ⋅ ρ(x) ⋅ c p [T(x) − Ti ]
A [m2]                cross-section of flow
ρ [kg.m-3]            mean flow density                  Rectangular outlet
cp [J.kg-1.K-1]       specific heat (p = const.)        Sides 3:1, Ti = 291 K
                                                       wo=18 m.s-1, To= 326 K
Equation (2) can be modified as follows:
Wo = w(x) ⋅ A(x) ⋅ ρ(x) ⋅ ∆h(x) = w(x) ⋅ A(x) ⋅ ∆hv (x) = w(x) ⋅ ∆hx (x)        (3)

∆h(x) [J.kg-1]       mean specific enthalpy in the cross-section x
∆hv(x) [J.m-3]       mean volumetric enthalpy density in the cross-section x
∆hx(x) [J.m-1]       mean linear enthalpy density in the cross-section x
                                                                           8
ENTHALPY IN 3D JETS
The change in mean linear enthalpy density
in the cross-section x can be obtained                         x = const.
effectively from interferometric records of              y2
non-isothermal air jets [4], see equation (4)

                          y 2 (x)
                c p ⋅Ti
∆hx (x) = − λ
                  K         ∫   ∆S(x, y) dy
                          y 1 (x)
                                              (4)        y1

λ [m]            wavelength of light            Circular outlet, Ti = 288 K
                                                 wo= 3.8 m.s-1, To= 327 K
K [m3.kg-1]      Gladstone - Dale constant
∆S(x,y) [ - ]    change in interference order
y1 , y2 [m]      y co-ordinates of the flow boundaries

The mean flow velocity for 3D jets in cross-                Wo
section x is expressed by equation (5) via          w(x) =                  (5)
                                                           ∆hx (x)
equation (3)
                                                                              9
ENTHALPY IN CIRCULAR JETS
For circular air jets or jets with
known cross-sections A(x)
it is possible to express:
• Mean change in volumetric              w(x)              ∆T(x)
   enthalpy density                                       ≈ ∆h(x)

              ∆hx (x)
  ∆hv (x) =                 (6)         ∆hv(x)                            ∆hx(x)
               A(x)
• Volumetric flow V(x) [m3.s-1]                                            V(x)
                                         A(x)
  V(x) = w(x) ⋅ A(x)        (7)

• Mean temperature                                               −1
                                                   ⎡ r ⋅ ∆hv (x) ⎤        (8)
  difference (r is the      ∆T(x) = T(x) − Ti = Ti ⎢1 −          ⎥ − Ti
  gas constant)                                    ⎢⎣    c  p
                                                           p i   ⎥⎦

• Mean value of                                                           (9)
  specific enthalpy         ∆h(x) = c p ⋅ [T(x) − Ti ] = c p ⋅ ∆T(x)
                                                                                10
AIR JET BOUNDARIES
Interferograms can be obtained
                                                                Finite
using either finite or infinite                                width of
fringe width in a reference area.                              vertical
Finite width enables effective                                 fringes
determination of temperature
boundaries, especially for
smaller ∆To.

                                    Infinite
                                    fringe
                                     width

                                The jet boundaries are the same as the
                                temperature boundaries [5]. See this
  Temperature and jet           interferogram of a smoke and air mixture
     boundaries                 jet from a slot outlet.
                                                                       11
AIR JET SHAPES IN FREE SPACES
Interferograms are used to evaluate the following qualitative and
quantitative data:
• The angle of jet expansion 2ϑ    t
  in the main region of slightly
  non-isothermal air jets
                                                           2ϑ t
• The length xK of the core area
  of the jet where the angle of              xK
  jet expansion is smaller than
  in the main area
• The trajectory y(x) of the jet
  axis of strongly non-isothermal
  air jets                              Local fringe
                                       displacement
• Velocity fluctuations                  in camera
  in turbulent jets                     over 0.01 s
                                                                    12
EVALUATION OF AIR OUTLET C–VALUES
The dependence of the expansion
angle 2ϑ t on air velocity wo and the
temperature ratio ∆To/Ti (∆To = To -
Ti) for a slot outlet with ratio of sides
37:1 is expressed using our
measurements by the equation
                                ∆To
2ϑt = 28.77 − 0.66w o + 34.56         (10)                Expansion   angle
                                                                C-value  for
                                Ti                         for a
                                                             the slot outlet

The evaluation of outlet C-values is carried out according our
equations [6] :
• The C-value for the slot outlet                               To
                                 Cb = 3.492 + 0.031 w o − 0.999          (11)
  is expressed via equation (11)                                Ti

• The C-value for a rectangular
                                                                 To      (12)
  outlet (sides 3:1) is expressed CS = 5.149 + 0.040 w o + 1.006
                                                                 Ti
  using equation (12)
                                                                               13
NON-ISOTHERMAL AIR JETS
The results of jet axis trajectory y(x) measurements of strongly non-
isothermal air jets are expressed by the following relations:

• For the slot outlet with                         y             y(x)
  width bo :
                                      2.5
                         ⎛ x      ⎞
  y(x) = b0 ⋅ Ar0 ⋅ 0.17 ⎜⎜      ⎟⎟         (13)
                         ⎝ b0     ⎠
                                                   0                             x

• For the circular outlet with
  diameter do :

                          ⎛ x    ⎞
                                      2.2          Slot outlet with ratio of sides
  y(x) = d 0 ⋅ Ar0 ⋅ 0.37 ⎜⎜     ⎟⎟         (14)          37:1, Ti = 288 K
                          ⎝ d0   ⎠                   wo = 3.8 m.s-1,To = 327 K

                                                                                     14
AIR JETS IN THE VICINITY OF WALLS
The next figures depict interferograms obtained from measuring the
shapes of non-isothermal jets from circular outlets (do = 30 mm). In the
first figure, the outlet is situated in the vicinity of a ceiling. In the second
figure, the outlet is directed perpendicular to the opposite wall.

       Air jet in the vicinity                Air jet impacting the
     of a ceiling, Ti = 288 K               opposite wall, Ti = 288 K
    wo = 21.5 m.s-1, To = 322 K             wo =21.6 m.s-1, To = 316 K
                                                                             15
AIR JETS FLOWING TO BARRIERS
These figures depict interferograms obtained from measuring the
shapes of non-isothermal jets exiting circular outlets (do = 30 mm) in
spaces containing barriers. In the first figure, the jet axis is directed
over the barrier. In the second figure, the jet axis is directed at the
barrier.

    Jet axis is directed over              Jet axis is directed at
       barrier, Ti = 288 K,                  barrier, Ti = 288 K,
    wo =13.1 m.s-1, To =321 K            wo = 17.7 m.s-1, To = 324 K
                                                                            16
COMPARISON OF VISUALIZATION METHODS
Contact methods are affordable, progressive and suitable for research
on larger air jets. Both laboratory and mobile methods exist:

                         PIV method with
                          particles - for
                            velocities

                         PLIF method with
                           particles - for
 Slot outlet                                  Cross-section of spray
                           temperatures

                         Smoke method -
                         for shapes and
                           stream lines
                            IR camera
                         with a sheet - for
Slot outlet               temperatures        Slot outlet
                                                                       17
COMPARISON OF VISUALIZATION METHODS
Contactless methods are at present suitable for research on smaller
air jets. The following methods are useful:
• Interferometry via                                      Schlieren mobile device
  Mach - Zehnder interferometer
  for measuring temperatures and

                                      0.4 m
                                                 Object
  other values.
  Field of view ~ 0.2 m.
• The schlieren method [7]
                                                          Grid
  with smaller sensitivity as MZI,
  for measuring jet boundaries.
                                        LASER
  Field of view ~ 0.4 m.                              H1            Tomography
                                                                   OS 1
                                              CCD 1         RS 1
• Tomographic interferometry by

                                                                     Object
  holographic interferometer (laser                   H2

                                                                              1m
                                              CCD 2         RS 2
  with greater coherence length
  and optical fibers) for measuring                   H3
                                                            RS 3
  temperatures and other values.              CCD 3
                                                                   OS2             Wall
  Size of object ~ 1 m.                                                                   18
CONCLUSIONS
• Visualization methods are very
  suitable for research on air jets           Smoke              Prof. Dr.
                                                                  Shadow
  from outlets.                               method      Interferometry
                                                            Ernstmethod
                                                                   MACH
• Contactless methods have no                               ∗ 18. 2. 1838
                                                          Mach-Zehnder

  influence on measured jets (give                          Brno - Czech
                                              Schlieren          Republic
  true information about objects)
                                               method       = 19. 2. 1916
  and therefore have a solid future.
                                                          Harr - Germany
• Interferometry has, among
  contactless methods, the greatest
  sensitivity. It is, therefore, best. This
  method serve for research on
  • Jet temperatures
  • Enthalpy in jets - velocities,
    volumetric flow … etc.
  • Jet boundaries and shapes … etc.
• The future of research on larger non-isothermal air jets lies with
  tomographic interferometry.
                                                                             19
CONTACT
    Assoc. Prof. Milan PAVELEK - Assoc. Prof. Eva JANOTKOVA
  Department of Thermomechanics and Environmental Engineering

    Technicka 2, 616 69 Brno, Czech Republic, Tel.: 420 541 143 272,
420 541 143 268, E-mail: pavelek@fme.vutbr.cz, janotkova@fme.vutbr.cz
                 URL: http://ottp.fme.vutbr.cz/~pavelek/
                                                                     20
REFERENCES
[1] M. Pavelek, E. Janotkova: Evaluation of records of flow visualization
    obtained during research on ventilation. Proceedings of 7th Int.
    Symp. Ventilation for Contaminant Control, p. 61-66. Sapporo 2003.
[2] M. Pavelek, M. Liska: Evaluation of interferograms of axial-
    symmetric phase objects. Optica Acta 30, p. 943-954, 1983.
[3] W. Hauf, U. Grigull: Optical methods in heat transfer. In: Advances
    in heat transfer 6, Academic Press, New York, 1970.
[4] M. Pavelek, E. Janotkova: Study of convection heat transfer in free
    non-isothermal air jet by means of interferometry. Int. Congress
    CHISA´2000, Paper No. P1.127. Prague 2000.
[5] H. Goodfellow, E. Tähti: Industrial ventilation design guidebook.
    Academic Press, London, 2001.
[6] E. Janotkova, M. Pavelek: Determination of air outlet C –values by
    means of interferometry. Int. J. of Ventilation 4, p. 311-322, 2006.
[7] R. Postasy, L. I. Kiss, L. Banhidi: The development of a new, mobile
    large field of view schlieren device. Meres es Automatika 37, p. 82-
    85, 1989. (In Hungarian)                                             21
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