THE EVAPORATIVE COOLING EFFECTS OF VARYING WATER DROPLET CHARACTERISTICS ON A METAL SURFACE IN A STEADY STATE, HIGH TEMPERATURE AIR FLOW

Project PresentationMANE 6970

Matthew Noll

April 23, 2015

INTRODUCTIONThis project analyzes the effects of changing physical parameters of a water droplet during evaporative cooling of a flat metal plate in a high temperature air flow.

Figure from Reference 1

BACKGROUND• Cooling a high temperature air flow, such as the exhaust

flow from a stationary natural gas turbine generator, normally requires atomized spray cooling.

• System limitations may limit the ability to produce an atomized droplet spray.• Water quality available for cooling spray• Limits in cooling system pressure • Spray nozzle availability• Additives that affect droplet surface tension

• Evaporative cooling provides the potential to have materials and components in high temperature flows be maintained at much lower temperatures without the need for an atomized spray.

METHOD• Evaporative cooling occurs when a gas flows over a liquid

which evaporates the liquid, and the energy associated with phase change is the latent heat of vaporization of the liquid.

• With the conservation of energy:

Steady State Energy Balance:

THEORY• This paper begins with a 2 dimensional droplet modeled

as a half circle on top of a rectangular metal plate in a region of hot air flow. The original droplet diameter is 10mm, and since the droplet is modeled as a half circle, the surface contact angle is 90°.

• The effects of changing the droplet volume, surface contact angle and separation between droplets are studied, but this paper does not research what methods are used to change these properties of the droplet.

• In an effort to simplify the study, the results model the evaporation process as a snapshot in time, and the boundary of the droplet is not moving. Also, the convective heat transfer coefficient (h) is assumed constant for all models.

ASSUMPTIONS• Heat and mass transfer of the system are at steady state.• The properties of the water are assumed to be constant.• The upper “wall” (boundary) of the gas region modeled is

assumed to be a slip conditions so that it will not affect the velocity field over the droplet and bottom wall.

• Pure water is used for the spraying fluid.• Droplet diameter is assumed to be 10mm as the baseline.• = 6.7kg/s (Reference 3)• Tgas = 280°C (Reference 3)• Twater = 40°C• Ugas = 0.44 m/s (scaled from mass ratio of gas and water

spray)• This analysis is assumed to be a snapshot in time.

PRELIMINARY RESULTS

Originally, the wall of the flat plate was modeled as a non-slip condition, which disrupted the velocity field of the hot air flow. The second figure models the droplet in a higher velocity flow and a domain with a smaller height.

TEMPERATURE DISTRIBUTION RESULTS

The same model was used to find the surface plot of the temperature in the system. However, since the bottom wall of the plate was assumed to be at a constant temperature, the heat flux ended up going from the droplet to the plate rater than from the plate to the droplet.

NEXT STEPS

Modeling the bottom of the plate as a constant temperature was the issue. By simplifying the model without a metal surface (only diffusion and convection between exhaust gas and water droplet) the correct heat flux from the droplet can be found, therefore finding the cooling capability of the droplet.

Droplet

Exhaust Gas

Droplet Surface Temperature = Tsat

VELOCITY AND CONCENTRATION FIELDS

The figure on the left shows the wake created in the gas flow by a single droplet, and the right figure shows that the concentration of water in the gas flow increases close to the droplet surface and in the velocity wake.

AVERAGE HEAT FLUX ON DROPLET SURFACES

Hand CalculationFrom Reference 1, the Whitaker Correlation is used to find the heat transfer coefficient from the Nusselt number of the sphere.

Reference (1)

This equation is normally used for Prandtl Number values between and 380, however, the Prandtl Number calculated by this project was .

AVERAGE HEAT FLUX ON DROPLET SURFACES

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0.00550

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Average Normal Heat Flux vs. Droplet Radius

Droplet Radius [m]Avera

g C

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Average Normal Heat Flux vs. Surface Contact Angle

Surface Contact Angle [Degrees]Avera

ge C

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SEPARATION OF DROPLETS

The average heat flux effect of varying the distance between two droplets on a surface was also studied. The figure below shows a case of temperature variation with a droplet separation of 0.05 m

AVERAGE HEAT FLUX ON DROPLET SURFACES

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.0552000

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Average Normal Heat Flux vs. Seperation Distance

Upstream downstream

Droplet Seperation Distance [m]

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The average heat flux of the upstream (blue) droplet is affected very little by the presence of the downstream droplet. However, as the separation increases between the droplets, the average heat flux from the downstream droplet increases.

AVERAGE HEAT FLUX COMPARISON

The average heat flux that was calculated by hand using the Whitaker Correlation was which is approximately 11% lower than the average convective heat flux calculated by COMSOL with a line average plot ().

Although the Prandtl Number does not fall within the range of the Whitaker Correlation, the hand calculation is more accurate since COMSOL must use the average “h” calculated by the hand calculation for the droplet, then again take a line average for the droplet surface heat flux.

FUTURE EFFORTS

If possible, a future project could focus on connecting the conductive heat flux from the metal plate at a specific temperature into this model.

Another step to take would be to model this system with a constantly moving boundary, as an actual evaporating droplet would have.

REFERENCES

1. Fundamentals of Heat and Mass Transfer, Wiley 2011, Hoboken NJ, 07030-5774

2. S.Semenov, V.M. Starov, R.G. Rubio, M.G. Velarde. Instantaneous distribution of fluxes in the course of evaporation of sessile liquid droplets: computer simulations, Loughborough University Institutional Repository, 2010

3. Capstone C1000 Megawatt Power Package – High-pressure Natural Gas, http://www.capstoneturbine.com/_docs/datasheets/C1000%20HPNG_331044F_lowres.pdf