Two - dimensional unsteady model

Cartesian computational grid

To estimate the potential damage it is important to describe the source of this potential damage as accurate as possible. Often such source represents a danger liquid spill.

PHOENICS was used to determine evaporation rate from a free surface of a liquid spill into stratified atmospheric boundary layer and calculate the variations of this value during an emergency.

The two-dimensional, unsteady differential equations of preservation of airflow mass, its momentum, energy, turbulent characteristics and vapours mass of evaporating liquid make a basis of the mathematical formulation of this problem. Conjugation of heat and mass transfer phenomena, accompanying this process, was taken into account, for what the heat conductivity equation for the ground layer was inserted into the model.

K-e model was employed to describe turbulent transfer within the atmospheric surface layer.

The following basis assumptions were accepted:

The layer of the spreading liquid had infinitesimal thickness, and its temperature was equal to temperature of the ground layer surface;

Liquid was one component that assumed a uniformity of its properties on all volume;

Vapours of an evaporating liquid, air and their mix were considered as ideal gases;

The vapour near to a liquid surface was saturated and its concentration was temperature function only;

Airflow into the atmospheric surface layer had mainly two-dimensional character;

Potential and kinetic temperatures into the atmospheric surface layer were equal.

The initial temperature distribution in a ground layer influencing on its heating rate and, hence, on intensity of evaporation was set with use of connections between the basis components of the heat balance of the ground layer surface. It means that the given distribution was unequivocally defined by setting of five parameters (besides thermal properties of a ground layer): local time, wind speed and air temperature at 10 m height, the Monin-Obukhov length and Bowen ratio.

The boundary conditions consisted of the meteorological values profiles in the surface layer at inlet of computational domain. These profiles were depending on the stability of the atmosphere. At the liquid surface the non-slip condition for the wind speed components was established, and for vapour concentration boundary condition was modified to account for Stephan flow correction. The temperature vertical profile at inlet of computational domain corrected with time, reflecting heating or cooling of the ground surface and, hence, air adjoining with it up to inlet of computational domain. It was reached by that, as considered profile was took the temperature profile at exit of computational domain at previous time step.

The GROUND coding was extensively used to insert various non-standard boundary conditions into PHOENICS.

## Pictures are as follows:

- Figure 1. Normalized evaporation rate depending upon friction velocity at various roughness of wind tunnel floor (points - the experimental data; the experimental error was 10%).
- Figure 2. Normalized evaporation rate depending upon toluene temperature (the experimental error was 10%).
- Figure 3. Calculated benzene evaporation rate from the various bases as a function of time (30 m spill was considered for all presented cases).
- Figure 4. Calculated vertical distribution of temperature within computation domain as a function of time at x=Lspill/2 under benzene evaporation from the various bases (figures at curves - the local time in hours) a) quartz sand; b) asphalt.
- Figure 5. Calculation benzene evaporation rate per unit area depending upon fetch x at various time under evaporation from quartz sand (same notation as shown in fig. 4).
- Figure 6. Calculated mean evaporation rate depending upon spill length at various liquids evaporation from the asphalt surface.
- Figure 7. Normalized benzene evaporation rate from asphalt depending upon 'dispersity' of a roughness layer at various values of geostrophic wind speed, porosity and height of a roughness layer (neutral atmosphere).
- Figure 8. Normalized benzene evaporation rate from asphalt depending upon porosity of a layer at various roughness layer height under Vg=7 m/s, 'dispersity' (N)=0,001 m**(-2).
- Figure 9. Normalized benzene evaporation rate from asphalt depending upon roughness layer height at various porosity and atmospheric stability under Vg=7 m/s, N=0,001 m**(-2) (u - unstable atmosphere; n - neutral one; s - stable one).
- Figure 10. Normalized benzene evaporation rate from asphalt depending upon 10 m wind speed at various atmospheric stability under N=0,001 m**(-2), h=10 m, D=0,9.
- Figure 11. Same as shown in fig. 10 with the exception D=0,6.
- Figure 12. Dimensionless evaporation rate ( - scale size of normalized evaporation rate under neutral stratification in open field conditions) depending upon geostrophic wind speed at various porosity and the atmospheric stability under N=0,001 m**(-2), h=10 m (same notation as shown in fig. 9).
- Figure 13. Dimensionless evaporation rate kR depending upon 'dispersity' (N) of a roughness layer at various values of porosity and roughness layer height for neutral atmospheric stability (figures at curves - geostrophic wind speed, m/s).

Dynamics of change of all basic parameters describing evaporation at emergency liquids spills for a typical set of input parameters occurring in the real atmosphere was obtained and analyzed. The evaporation of water, benzene, ethyl ether from various bases (asphalt, concrete, quartz sand, sandy clay) was examined.

The comparison of results at reduction of grid steps, both in spatial coordinates and in time, has shown good accuracy of the used numerical method adopted in PHOENICS. So, for example, the time step reduction from 1 hour up to 20 min gave increase of evaporation rate from asphalt base on 5%, and the grid condensation in 2 times on each spatial coordinate simultaneously (originally 40x34) resulted in reduction of evaporation rate by 2,5-3%. As a whole, the analysis of results has shown adequacy of the evaporation model in the atmospheric boundary layer conditions.

The comparison of the modeling results with experimental data on toluene evaporation in wind tunnel showed that the results of computations adequately described the evaporation rate both in changing of the flow speed and roughness of the wind tunnel floor and in changing of toluene temperature up to boiling one.

In examined model all main features of evaporation were taken into account including effects of dynamic, thermal and concentration transformation of the airflow at its transition to the liquid surface with other, than at ground, properties.

Besides the benzene evaporation in a roughness layer simulating the various process equipment and a built-up on an industrial area placed in a liquid spillage zone was considered. For this purpose in model on all spill length the vertical profiles of wind speed and eddy viscosity coefficient obtained using the previous model were fixed. Within framework of this approach the influence of wind speed, the atmospheric stability and, first of all, of integrated geometrical characteristics of a roughness layer on the normalized evaporation rate was investigated. On the basis of the carried out investigations of evaporation under these conditions it was established that:

The presence of layer with regular roughness reduces the evaporation rate;

With other things being equal the evaporation rate the higher the less the roughness layer height and the higher its porosity (D);

Influence of the atmospheric stability on the evaporation rate is expressed up to the certain meaning value of wind speed U10 into a roughness layer, and this value of wind speed, with other things being equal, the less the less porosity of a layer and the higher its height (U10=6 m/s, D=0,9 and U10=4,5 m/s, D=0,6).

For practical use it is expedient to present the obtained results in a dimensionless kind being fair for any liquid. As the dimensionless evaporation rate the relation of the evaporation rate in a porous layer to some scale size was used, as which the evaporation rate on open field at neutral stratification appeared in the given work.

The advantage of the given approach is that as scale size can be chosen the evaporation rate obtained through any evaporation model for open field conditions. The obtained relations along with the data on wind speeds in a porous layer can be used as the weight factors which are taking into account the influence of roughness layer parameters on the evaporation rate of any liquid in flows perturbed by obstacles.

Besides the research of evaporation at fixed temperature of a base layer (i.e. with heat exchange not taking into account) was carried out. It is established that the values of the normalized evaporation rate varied insignificantly (2,5%) and the dimensionless evaporation rate remained constant. The change of spill length from 5 up to 100 m gave deviations from the basic results obtained for 30 m spill no more than 3% in both sides. It gives the basis to speak about applicability of the obtained dependencies of dimensionless evaporation rate of volatile liquids from roughness layer parameters for wider range of boundary conditions of evaporation process.

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