Micro model for the single droplet and experiments for the spray by u70DVy

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									   Experimental and theoretical investigation of spray cooling heat transfer on
                            macro and micro level
           Mariya Nacheva*, Teodor Todorov, Dimitar Dontchev, Juergen Schmidt
                      Institute of Fluid Dynamics and Thermodynamics
                 Otto-von-Guericke-University, 39106 Magdeburg, Germany
  *
   DFG-Graduiertenkolleg “Micro-Macro Interactions in Structured Media and Particle Systems”

Many technical processes in the metallurgy, process engineering and minimum cooling technology
demand a rapid cooling of hot surfaces. Such a cooling can be obtained by different liquids and
techniques. The spray cooling is often preferred because of the good adaptability to different cooling
requirements.

The realization of defined cooling conditions requires the knowledge of the heat transfer coefficient
(HTC) on macro level. The cooling fluid, its mass flux and the spray characteristics (velocity and
size of the droplets) influence the HTC in the spray cooling. In most research works, the HTC is
correlated as a function of the mass flux. However, other studies consider as well its dependence on
the droplet size, droplet velocity, material properties and the temperature of the wall. Significant
discrepancies can be observed while comparing results obtained by different authors. These differ-
ences can be explained by the employment of different test conditions and different nozzles. In the
majority of the scientific works, the parameters that influence the HTC were not varied independent-
ly from one other. In the present work, the influence of the spray characteristics on the HTC is in-
vestigated for stable film boiling above the Leidenfrost point. In this regard, each parameter (mass
flux, droplet velocity and droplet size) is varied while keeping the others constant. Previous results
were already presented5.

Two experimental methods (quasi-stationary and transient) are used for the estimation of the HTC.
The quasi-stationary method can be applied only when the fluid impingement density is uniform. If
this condition is not fulfilled the vapor film collapses rapidly. The employed experimental set-up is
sketched in Fig. 1. A Phase-Doppler-Anemometer (PDA) was used to determine the spray character-
istics-the volume mean diameter and the mean velocity of the droplets. Distilled water was used as
the cooling liquid. The mass flux was measured by patternator. An electrically heated metal sheet
(60 x 43 x 0.3 mm) was used for the heat transfer experiments. The constant electrical current supply
(up to 400 A) provides a nearly constant heat flux. The HTC was calculated from the temperature
field of the “dry” side of the surface when the calibration of the heat losses on the same side is taken
into account. The temperature field of the metal plate was determined by means of the IR-
Thermography. The test section was coated, Fig. 2, using a high temperature resistant laquer, whose
emissivity was determined as a function of the temperature.

An inverse heat conduction algorithm based on the Beck’s function specification procedure1 was
used to analyze the experimental data. The HTC can be calculated at the „spray” side since the
boundary conditions at all other sides are known and the temperature history at the “coated” side,
Fig. 2, can be obtained by means of the IR-Thermography. The computation of the 2D-temperature
field, where the surface coating is taken into account, is based on the Finite–Difference–Method
(FDM). The inverse method is applicable to both steady and unsteady measurements. The calcula-
tions in the case of a nearly uniform impingement density can be simplified.

Full cone (Bete CW 25, Lechler 460.406) and flat spray (Lechler 432.404, Lechler 432.366) water
nozzles were used. Large variations in the impingement density, droplet diameter and mean droplet
                                                                                                                                                                                                                                               Neumann boundary condition

                                                                                                                                                                                                                               spray side                           IR- camera side
                                                               PDA
                                                               Unit                 PDA
                                                                                    Unit                                                  Water                                                                                                                 surface coating
                                                                                                                                          Nozzle                                                                               sheet steele

                                                                                                              +                                                                                                                                                  Newton boundary
                                                                                  Transmitter Current                               Metal
                                                                                                                                                                                                                                                                 condition
                                                                                                             --
                                                                                                                                    Sheet        Receiver
                                                                                                                                                                                                                           unknown
                                        IR                                                                                                                                                                                 temperatu
                                                                             IR
                                        Unit                                 Unit                                     IR                                                                                                   re
                                                                                                                      Camera                                  Pump                                                                                                                          r
                                                                                                                                                                                                                                                       couple condition
                                                                                                                                                                                                                                  Neumann
                                                                                                                                                                                                                                  boundary                      y
                                                                                                                               Water                                                                                              condition
                                                                                                                               Tank

                                                                                    Figure 1 Experimental set-up                                                                Figure 2 Scheme of the test section and conditions
                                                                                                                                                                                           for the mathematical model

                                                                                                                                                                        velocity are necessary for a systematical studies. Each
                                                                                                                                                                        spray parameter has to be varied nearly independently
                                            nt [W/m K]




                                                                         800
                                            2




                                                                          700                                                                                           while keeping the other two approximately fixed. Pres-
                                                                          600
                                                                                                                                                                        sure (0.1-0.9 MPa), water flow rate (28-105 l/h), nozzle
                                              Heat transfer coefficie




                                                                          500
                                                                           400                                                                                          distance (0.04-0.5 m) and temperature of the test sec-
                                                                           300                                                                                          tion (200-600 °C) were the varied experimental pa-
                                                                            200
                                                                                                                                                              ]
                                                                                                                                                            m




                                                                                                                                                                        rameters.
                                                                                                                                                         [m




                                                                            100                                                               30
                                                                                                                                                        h
                                                                                                                                                     dt




                                                                              0                                                          25
                                                                                                                                                   wi




                                                                                     20
                                                                                                                                                    t
                                                                                                                                                 ee




                                                                                            25                                      20
                                                                                                                                              sh




                                                                                                 30
                                                                        P ar t                          35                                                              Typical results are presented in Fig.3 for the nozzle
                                                                                                                                             e




                                                                                 of th                        40
                                                                                                                                          th




                                                                                         e sh                         45       15
                                                                                             eetle
                                                                                                                                         of




                                                                                                     ngth                                                               Bete CW 25, which produces nearly uniform water dis-
                                                                                                                                     rt




                                                                                                            [mm
                                                                                                                                    Pa




                                                                                                                  ]
                                                                                                                                                                        tribution. At the rims of the area the vapor film begins
                                                                                                                                                                        to collapse. For the data reduction a small area (25 x 15
                                      Figure 3 Local distribution of HTC over                                                                                           mm) of the centre of the plate was selected. The HTC
                                                    the surface                                                                                                         was calculated for each point of the chosen area.

                                      350                                                                                                                                                                            450
                                                                          Nozzles:                                                                                                                                               w = 450 °C
                                      300                                  432.404, d_30 = 107 µm; v = 3.7 m/s             m = 8 kg/(m²min)                                                                          400
Heat tramsfer coefficient [W/(m²K)]




                                                                                                                                                                                Heat transfer coefficient [W/m 2K]




                                                                           460.406, d_30 = 46 µm; v = 3.7 m/s
                                                                                                                                                                                                                     350
                                      250                                  432.366, d_30 = 71 µm; v = 3.7 m/s

                                                                                                                                                                                                                     300
                                      200
                                                                                                                                                                                                                     250                                                                             v = 3,5 m/s
                                      150                                                                                                                                                                                                                                                            v = 5,5 m/s
                                                                                                                                                                                                                     200
                                                                                                                                                                                                                                                                                                     v = 8 m/s
                                      100
                                                                                                                                                                                                                     150                                                                             v=4,3-4,8 m/s

                                      50                                                                                                                                                                                                                                                             v=6,8-7,2 m/s
                                                                                                                                                                                                                     100
                                                                                                                                                                                                                                                                                                     v=7,5-8 m/s
                                       0                                                                                                                                                                             50
                                        200                                250             300         350      400       450      500                  550       600     650                                              0          5         10      15          20     25         30        35      40         45
                                                                                                             Wall temperature [°C]                                                                                                                   Water impingement density [kg/m2min]


                                                                        Figure 4 Influence of the droplet size                                                                                                             Figure 5 HTC vs. impingement density

                                      The behavior of the HTC with the wall temperature, Fig. 4, shows that the influence of the droplet
                                      diameter is negligible. Two sets of data illustrating the effects of the droplet velocity, Fig. 5, were
                                      obtained by using both experimental methods. The full points in Fig. 5 correspond to the unsteady
                                      state method. The droplet velocity is varied from 3.5 to 8 m/s. It can be seen that the impingement
                                      density has the strongest effect on the HTC in comparison to other parameters. The HTC increases
                                      also clearly with increase in the droplet velocity. Similar results for dependence of the HTC on the
                                      velocity ware presented for unstable film boiling by Chen3.
                                                                              24
                                                                                                                                         Simulation
                                                                                                                                         Wruck/Renz
                                                                              20
                                                                                                                                         Bolle/Moureau
                                                                                                                                         Puschmann




                                                 Evaporation efficiency [%]
                                                                              16


                                                                              12


                                                                              8


                                                                              4


                                                                              0
                                                                                   0   0.02   0.04   0.06     0.08      0.1       0.12   0.14     0.16   0.18
                                                                                                            Droplet radius [mm]


Figure 6 Micro-Macro-Interaction by spray        Figure 7 Model comparison for the evaporation effi-
                cooling                                      ciency of a single droplet

For a better theoretical explanation of the influence of the droplet size and velocity observed our aim
is to model the spray cooling on micro level. The direct interaction of single droplets with the wall is
considered firstly for dilute sprays. One single drop and a characteristic part of the surface, which
dependences on the spray parameters, constitute a representative volume element (RVE), Fig. 6. As
the droplet reaches the surface, most of the heat is transferred in the first stage, when the liquid is in
direct contact with the material and before a vapor film is formed. After the impact, the drop spreads
out to its maximum diameter. Time-dependent droplet propagation is considered and a first approach
is presented. From this function and the numerical solution of the transient 2D-heat conduction prob-
lem using the enthalpy method and FDM, the heat delivered by the wall can be calculated. This heat
is characteristic for a certain drop type and permits the calculation of the HTC by considering of the
droplet flux. Results are compared with those of Bolle/Moureau2, Puschmann4, and Wruck6, Fig. 7,
                                               Q drop
based on the evaporation efficiency  v                  of a single droplet.
                                            M drop  h v

Acknowledgment
The financial support of the German Research Foundation (DFG-Graduate College 828
“MicroMacro Interactions in Structured Media and Particle Systems”) is gratefully acknowledged.


                                             References
1.   Beck, J., Blackwell B., Inverse heat conduction, Wiley-Interscience Publ., 1985.
2.   Bolle, L. and Moureau, J. C., Spray cooling of surfaces, in: Multiphase science and technolo-
     gy, Vol. 1, pp 1-97, McCraw-Hill, New York, 1982.
3.   Chen, R.H., Chow, L.C., Navedo, J.E., Effects on Critical Heat Flux in subcooled Water Spray
     Cooling, Int. J. Heat Mass Transfer, 45 (2002), 4033- 4043.
4.   Puschmann, F., Experimentelle Untersuchung der Sprühkühlung zur Qualitätsverbesserung
     durch definierte Einstellung des Wärmeübergangs. PhD Thesis, Otto-von-Guericke-
     Universität, Magdeburg, 2003.
5.   Schmidt J. and Boye H., Influence of Velocity and Size of Droplets on the Heat Transfer in
     Spray Cooling, Chem. Eng. Technol., Vol. 24, pp 255- 260, 2001.
6.   Wruck, N., Transientes Sieden von Tropfen beim Wandaufprall, PhD Thesis, Shaker Verlag,
     Aachen, 1999.

								
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