Modelling of solid concentration and solid flow fields

,

, , ,

,

(3.3)

Ash and sand are not taking part to any reactions, thus, the solution process is simplified and the mass change due to comminution is included to zero-dimensional balance equations and determined for total fractional masses mi. The total net mass flow due to comminution for particle size i is

, ,

,

,

, (3.4)

Examples of determined comminution rate coefficients for different solid materials are found in works by Loschkin (2001) and Pikkarainen (2001).

3.4 Modelling of solid concentration and solid flow fields

The SolveRhosProf module determines three-dimensional weight fraction fields for different materials and particle size fractions by applying empirical equations for solid concentration profiles. The total vertical solid concentration profile as a function of height follows an equation given by Johnsson and Leckner (1995):

, , , (3.5)

The parameters include volume fraction of solids at bottom and top of the furnace (εs,btm, εs,top), coefficients for transient and dilute section (ctr, cdi), and total height (H). These

are based on measured vertical pressure profiles or separate correlation models, which have been developed from field measurements.

The material and particle size fraction specific profiles of inert materials and total sorbent have similar shape as the total profile, but the equation parameters are adjusted so that the total integrated masses over the total height match the different masses solved from furnace mass balance. The solid concentration fields of fuel and sorbent species have been solved separately as described in Chapters 4 and 5.

In horizontal direction, the solid concentration is assumed flat, except for a denser wall layer, which is solved as superimposed over the main furnace model. The volume fraction of solids at wall layer is determined as a function of the local average volume fraction of solids (εs) across the cross-section of the furnace:

, 1 exp (3.6)

In the above equation, the term εmax is the maximum volume fraction (e.g. packing density) of solids and the term a is an empirical constant. Figure 3.5 compares the equation with literature data from Zhang et al. (1993) and Nicolai et al. (1993).

Figure 3.5. Volume fraction of solids at wall layer vs. average volume fraction of solids.

The internal circulation of solids due to downflow of solids at the walls is modelled by a wall layer model, which is superimposed over the main furnace model. A wall layer is formed to all vertical walls in the furnace, including the internal heat exchanger structures. It is reasonable to assume that large internal panels, e.g. hanging superheaters, have the same effect as the furnace walls on the solids flow (Reh, 2003), thus they have been modelled by the same principles.

The mass balance of a wall layer cell is defined by Equation 3.7 and illustrated in Figure 3.6. The solid mass flow entering the wall layer (qm,ic) and the back mixing from wall

0 0.2 0.4 0.6 0.8 1

0.0001 0.001 0.01 0.1 1

Volume fraction of solids  at wall layer (‐)

Average volume fraction of solids (‐) Zhang et al., 1993

Nicolai et al., 1993 This work (a = 5) εmax= 0.6

layer to main flow (qm,ib) are proportional to local solid concentration, which has been determined from empirical correlations (Equations 3.5 and 3.6). The down flowing mass flow at the wall layer is determined from Equation 3.7. This is solved from roof to bottom of the furnace, each wall layer cell receiving mass flow from above and exchanging mass with the main furnace domain.

, , , , , , (3.7)

Figure 3.6. Mass flows in wall layer.

At the bottom of the furnace, the accumulated mass flow at wall layer is released back to main furnace flow. In the case of internal walls, which are not extending to the bottom of the furnace, e.g. hanging superheaters, the wall layer flow is released back to main furnace flow at the lower edge of the internal wall.

Figure 3.7 illustrates the mass flows by internal and external circulation of solids. The internal flow of solids through the wall layers has a large effect on the thermal balance of the furnace. Similar to external circulation of solids through the separators, the internal circulation of solids creates a heat capacity flow or a thermal wheel, which reduces the temperature gradients and results in a more uniform vertical temperature profiles. Thus, the model parameters, which define the local mass flow values to and from wall layer, are determined experimentally based on vertical temperature profile measurements.

The flow of solids through the wall layer and the heat exchange from wall layer to heat transfer walls produces a heat transfer model similar to mechanistic heat transfer models based on cluster renewal model (Dutta and Basu, 2003), but allowing for a more accurate description of the local temperatures by the three-dimensional description of the flow.

Wall Main cell

Wall layer cell ε_s,c ε_s,wl

q_m,ic q_m,ib q_m,wl,top

q_m,wl,btm

Figure 3.7. Internal and external circulation of solids in the model.

As the model only requires the knowledge of solid mass flows and heat capacity flows through the internal circulation and the wall layer model is superimposed over the main furnace model, the thickness or the velocity of the wall layer does not need to be solved.

The solid concentration of the wall layer (Equation 3.6) is applied in the correlations defining the heat transfer coefficients.

The external circulation of solids entering the separators, i.e. the net solid flux across the furnace is determined by an empirical correlation, which is a function of superficial fluidization velocity and the average solid concentration at the upper part of the furnace, just below the furnace outlets. This sets the velocity of the solids at the furnace outlets.

The velocity is assumed constant at all outlet faces and used for determining the boundary condition for solid flow model.

The solid mass flows to fly ash are determined by fractional collection efficiencies of the separators. The fractional collection efficiencies are based on measured fractional mass balances of circulating solids and fly ash. The remaining mass flow from separators is then released to downcomer legs and further to return legs or to external heat exchangers located in the return loop.

Accumulating

The solid mass flow from furnace to external heat exchangers is controlled by empirical correlation, which sets the velocity of solids and the maximum solid mass flux at the interfaces. The solid mass flow entering an external heat exchanger is then added to the circulating mass flow coming from a separator.

As the three-dimensional solid concentration field has been fixed by the empirical correlations and the different solid sources and sinks are known, the solution of the net velocity field of solids is possible by a potential flow approach. This is a steady state description of the flow field without the effects of vortices or transient mixing of solids.

In the future, the target is to apply more comprehensive CFD flow model approaches (cf. Shah et al., 2009) , but for the moment, this is a simple method to produce an approximation of the solid convection to be applied in the energy equation. The local mixing effects due to vortices and fluctuating flow are considered by dispersion terms.

A flow potential Pfs is defined according to Equation 3.8, i.e. the gradient of Pfs is equal to mass flux of solids. The continuity equation for total solids includes convection, a source term and a reaction term (Equation 3.9).

(3.8)

· (3.9)

The source term includes the sources due to flow from return legs and solid feeds and sinks due to flow to bottom ash, wall layer and possible external heat exchangers connected to the furnace. The reaction rate term includes the mass changes due to different reactions. The potential difference across the furnace outlet faces is set based on the determined constant outlet velocity. This is necessary to set a reasonable velocity profile at the outlets. With a constant potential at the outlet, the mass flow would be much higher through the bottom section of the outlets, which would be contrary to the experience from measurements and modelling results by CFD models.

Combining the above equations, the potential field Pfs is solved, after which the solid velocity field is defined from Equation 3.8. The solved solid velocity field represents the net velocity of total solids, i.e. combined solid materials and particle size fractions.

The flow fields for fuel and sorbent are solved separately – these are presented in Chapters 4 and 5. However, at the furnace outlets, all solid materials are assumed to flow at the same velocity, which has been solved from the total solid flow field. This assumption does not have a large effect on the solved flow fields inside the furnace: if a solid material has been able to flow to the furnace outlet, it can be removed at the same velocity as all the other solids.

The bottom ash is removed from the furnace at the specified locations and according to specified discharge rates or according to solved mass balance. The composition of the

bottom ash flow depends on the composition of solids at the bottom discharge points.

Classification of bottom ash can be included, i.e. returning certain particle size fractions back to furnace at the discharge points.

The solution of the total mass balance can be based on two optional methods. In the first method, the total bed mass is known, in which case the total bottom ash flow rate is solved in module SolveBtmAshFlow from the overall mass balance. In the second method, the bottom ash flow rate is known and the total bed mass is solved based on the solution of the total mass of each solid material (fuel, ash, sand, sorbent). Both methods produce the same results, but either the total bed mass or the total bottom ash flow rate must be fixed to reach the steady state result.