CFD Modelling of Regenerative Pre-heating Systems for Recycled Glass Raw Material

The glass industry is one of the major sources of energy consumption. It is estimated that in 2004 in Italy this industrial sector absorbed about 5 % of all industrial energy consumption (1.33 Mtoe) without the addition of all the related activities (transport, packaging, etc.). For this reason, the research and the development of techniques to save energy and to increase the efficiency of the entire glass production system is very important. One of the main concerns is the effective exploitation of the exhaust gases from the combustion in the glass furnace. First of all the regenerative chambers composed of a series of refractory bricks are used to preheat the combustion air. The efficiency of this process has reached almost 70 % thanks to the numerous studies carried out recently [1-3]. The research group from the University of Genoa has gained a relevant expertise in the field by developing different numerical models for the design of regenerative chambers [4-6] and gas recirculation strategies for the reduction of NO_x emissions [7].

An additional method to exploit the residual heat from the combustion gases after the heat transfer process inside the regenerative chambers is to preheat the recycled glass raw material that is increasingly used into the glass composition. In fact the gas at the exit of the regenerative chamber has still a considerable heat content having a temperature of about 450 °C that could be exploited. Since the 1960 several glass raw material pre-heating systems have been patented [8-10]. In the foundries pre-heating systems for scrap material have been studied using the heat of the waste gases [11]. Similar pre-heating systems of the scrap are used in the steelmaking process [12]. In this regard, the size of the grain or the porosity of the scrap have been modelled [13]. Finally, some numerical analysis has been carried out on the raw material in solidification of pure iron [14].

The main purpose of this work is the development of numerical models for the pre-heating of raw materials. A simplified model that represents the core of a pre-heater for glass raw material has been used. A sensitivity analysis on the main characteristics of the raw material has been carried out. This turns out to be very useful for the preliminary selection of raw material size and properties to be effectively used in a pre-heater design. This analysis can estimate the impact fuel saving in the glass melting process. Two different methods of heat exchange are considered: the direct and the indirect methods. In the former, the exhaust gases flow through the raw material (direct contact) in the latter the hot gases flow in channels and the raw material is heated by conduction. Although the first approach is more efficient in terms of temperature reached by the raw material under the same conditions, it can create pollution problems to the gases that will requires post treatment before reaching the chimney. The indirect model has therefore been explored. Analytical and numerical (CFD) models are presented together with a design optimization process for the system design. These models have been used and validated in a research project where an experimental campaign has been carried out on a specific test rig [15].

3.1 Granulometry model

The first aspect to consider is the modelling of the size of the material. For simplicity, it has been assumed that the pieces of scrap glass have a parallelepiped shape of size L₁×L₂×S. The average length defined with the Eq. (1), neglecting the thickness S, is considered:

$L_m=\frac{L_1+L_2}{2}$ (1)

The raw material does not occupy the entire volume inside the pre-heater but a percentage is empty volume. For this reason the parameter R_g is introduced to define the ratio between the volume of glass and the total volume, Eq. (2):

$R_h=\frac{V_g}{V_T}=1-\varepsilon=1-\frac{V_g}{V_T}$ (2)

Given the size of a scrap of glass (50×50×5 [mm]), the percentage (50 %) of volume that the raw material occupy compared to the total one (R_g), it is possible to derive a relationship between L_m and R_g. This relation has been obtained by performing the regression of the curve passing for the following three points, according to the idea that in a raw material of small size the air percentage is lower than the one of the glass pieces:

A (R_g;L_m)=(0.5; 50)

B (R_g;L_m)=(0.01; 300)

C (R_g;L_m)=(0.99; 1)

The curve reported in the Eq. (3) and in the Figure 2 is obtained:

$L_m=alnR_g+b(a=-64.67;b=2.568)$ (3)

2.png

Figure 2. Relationship between the glass volume ratio and the size of the raw material

3.2 Indirect method

The preheating system with indirect heat exchange consists of a tube bundle, immersed into the raw material, where hot gas flows. The heat is transferred by conduction and radiation. In this model the raw material is treated as an equivalent solid composed of air and glass. So appropriate thermo-physical properties have been defined for the equivalent solid. For the equivalent density the mass conservation has been used, Eq. (4):

$\dot{m}_{eq}=\rho_{eq}V_T=\dot{m}_g+m_a=\rho_{g}V_g+\rho_{a}V_a=\rho_g(1-\varepsilon)V_T+\rho_{a}V_a $ (4)

in order to define the equivalent density, Eq. (5) and the equivalent conductivity, Eq. (6):

$\rho_{eq}=(1-\varepsilon)\rho_g+\varepsilon \rho_a$ (5)

$K_{eq}=(1-\varepsilon)K­_g+\varepsilon K_a$ (6)

the specific heat has been calculated as the weighted average between the specific heat of glass and air, Eq. (7):

${{C}_{p,eq}}=\frac{{{m}_{g}}}{{{m}_{eq}}}{{C}_{p,g}}+\frac{{{m}_{a}}}{{{m}_{eq}}}{{C}_{p,a}}\simeq {{C}_{p,g}}$ (7)

where the specific heat of the glass (independent of the raw material size) is dominant.

3.3 Direct method

The preheating system with direct heat exchange consists of a tube bundle with several holes on the tube surface and capped on the upper surface. The exhaust gases flow through the raw material. The heat exchange takes place by not only conduction and radiation, but also by convection and higher temperatures can be reached in a shorter time. In this case a porous domain has been used, in order to model the domain containing the raw material, with the properties of the glass for the solid part and the properties of the exhaust gases for the fluid part (C_p,f=1290 [J/kgK], K_f=0.0454 [W/mK] e r_f=0.53 [kg/m³]). The permeability loss coefficient C₁ and the inertial loss coefficient C₂ to determine the pressure drop of the exhaust gases in the porous matrix are introduced. One technique for deriving the appropriate constants involves the use of the Ergun equation [16], applicable over a wide range of Reynolds numbers and for many types of packing. This correlation has been validated in several works dealing with packed bed [17, 18], but also by the authors in applications of regenerative chambers [4, 5] and thermal storage CSP [19]. The coefficients C₁ e C₂ have been defined as follows, Eq. (8-9):

$C_1=\frac{1}{a}=\frac{150}{D_P^2}\frac{(1-\varepsilon)^2}{{\varepsilon }^3}$ (8)

$C_2=\frac{3.5}{D_P}\frac{(1-\varepsilon)}{ {\varepsilon }^3}$ (9)

These coefficients depend on the porosity e and on the diameter D_P of the equivalent sphere of a piece of raw material that is assumed equal to L_m.

In the following sections several CFD analysis are shown to understand the effects of the main parameters and to compare the different solutions and models. The time history of the average temperature of the raw material volume is used as monitor value to compare. 

5.1 Direct model

A parametric analysis has been carried out to gain a sensitivity on the impact of the main parameters on the system response. In the direct model the size of raw material (related to the porosity and consequently the porous resistance) has been varied following Eq. (8-9). Figure 4 compares the volumetric temperature trends over time for different dimensions L_m of the raw material.

It is clear that as the size of the scrap increases, the system has a faster thermal response. In fact, when the raw material is larger, there is less volume of the exchanger actually filled by raw material and the gases can find their way through the packed bed. The effect is more pronounced when e increases. A variation from e=0.1 to 0.2 gives about 5 [K] difference while a negligible temperature change is observed in the range e=0.01 - 0.1.

4.png

Figure 4. Raw material size analysis on direct model

5.2 Indirect model

In Figure 5 the temperature trend over time are reported for different dimensions of the raw material (influence on the equivalent solid properties - density and thermal conductivity).

5.png

Figure 5. Raw material size analysis on indirect model

6.png

Figure 6. Comparison between the indirect and direct CFD model–thermal response

As for the direct case a quicker response is obtained by increasing the raw material size. The difference concerns the temperature values achieved in the two different thermal modes. With the same raw material properties and e=0.05 a temperature higher than 200 [K] is obtained in the direct case, at the end of the pre-heating time while, as expected, a much slower thermal response is obtained with the indirect case. The difference is quantified in the comparison of Figure 6.

The direct method is clearly more efficient than the indirect case. However, since the direct method requires appropriate filtering systems for the gases which can release harmful substances and powder, it requires special post treatment systems and it is therefore less attractive. For this reason the attention has been focused on the indirect approach in order to develop models and tools for its optimal design. Attention has been given to the individual properties of the scrap glass. In order to make the comparisons easier a baseline case has been identified (Table 1).

Table 1. Baseline case properties

Table 2 summarizes the set of cases considered with the percentage variations of the individual properties of the respective raw material.

Table 2. Dataset of cases with the properties variations

7.png

8.png

Figure 8. Raw material specific heat effect - indirect model

In Figure 9 the temperature trends over the time with different thermal conductivity of the scrap glass are compared.

9.png

Figure 9. Raw material thermal conductivity effect -indirect model

In this case a variation of almost 5 [K] has been highlighted by varying the conductivity of 20 %. A faster thermal response is obtained by increasing the thermal conductivity.

5.3 Energetic considerations

From the parametric analysis the impact of each individual parameter in a raw material pre-heater is identified and with the CFD model can be quantified. The designer can use the results in order to understand the impact on the energetic balance of the system (combustion fuel gain) for a given raw material characteristic. The heat flux that the fuel (methane) have to provide to the glass bath following the observed temperature change compared to the baseline case, at the end of the pre-heating time is:

$\dot{m}_Gc_{p,g}\Delta T_{baseline}=\delta q=\delta \dot{m}_{{CH}_4}Hi$ (10)

Assuming that in a generic glass furnace 356 tons/day (or 4.12 [kg/s]) of raw material to melt are introduced and that a generic glass bath absorbs 8.3 [MW] [20], the percentage variations of the fuel massflow rate can be predicted; consequently the economy savings in the furnace management can be estimated. Assuming that the percentage of recycled material is in the range 20 and 80 %, the impact on fuel is reported in Table 3, for all the cases previously simulated.

Table 3. Fuel percentage variation for the several cases

This section describes an analytical model based on the lumped parameters approach developed for a quick analysis of raw material pre-heating system in the indirect heat transfer case. The results of the analytical model are compared to those from CFD in order to tune the 0D approach. To calculate the heating rate of the raw material, the energy balance is imposed, Eq. (11). The internal energy variation of the raw glass is equal to the variation of the thermal heat flow through the system. The incoming heat flow includes the heat entering from the pipes, Eq. (12), and the heat entering from the lower and upper base of the box; the heat dispersed in the environment is clearly a loss, Eq. (13).

${{\rho }_{g}}{{V}_{g}}{{C}_{p,g}}\frac{\delta {{T}_{g}}}{\delta t}=({{q}_{tubes}}+{{q}_{bottom}}+{{q}_{top}})-{{q}_{loss}}$ (11)

${{q}_{tubes}}={{U}_{tot}}{{A}_{tubes}}({{T}_{f}}-{{T}_{g}})$ (12)

${{q}_{loss}}={{U}_{box}}{{A}_{box}}({{T}_{g}}-{{T}_{amb}})$ (13)

The upper and lower base have been neglected. The average dispersion efficiency has been introduced, Eq. (14). In this way Eq. (11) can be simplified in Eq. (15).

${{\eta }_{loss}}=1-\frac{{{q}_{loss}}}{{{q}_{tubes}}}$ (14)

${{\rho }_{g}}{{V}_{g}}{{C}_{p,g}}\frac{\delta {{T}_{g}}}{\delta t}={{\eta }_{loss}}{{U}_{tot}}{{A}_{tubes}}({{T}_{f}}-{{T}_{g}})$ (15)

The analytical solution of the previous equation is reported in the Eq. (16). It gives the temperature trend of the equivalent solid over time, where the exponent is the ratio between the time and the characteristic time of the system, as reported in Eq. (17).

${{T}_{g}}={{T}_{f}}+({{T}_{g,0}}-{{T}_{f}}){{e}^{-\left( {}^{t}/{}_{{{\tau }_{id}}} \right)}}$ (16)

${{\tau }_{id}}=\frac{{{\rho }_{g}}{{V}_{g}}{{C}_{p,g}}}{{{\eta }_{loss}}{{U}_{tot}}{{A}_{tubes}}}$ (17)

The characteristic time depends on the thermal inertia of the equivalent solid, on the tube exchange surface, on the box dispersion efficiency and finally on the transmittance (Eq. 18), that considers the conductive resistance of the tube and the internal convective resistance.

${{U}_{tot}}=\frac{1}{{}^{{{A}_{e}}}/{}_{{{A}_{i}}{{h}_{f}}}+\frac{{{A}_{e}}}{2\pi {{K}_{tubes}}L}\ln {}^{{{r}_{e}}}/{}_{{{r}_{i}}}}$  (18)

Forced convection in pipes is described by the following dimensionless parameters: Reynolds number, Eq. (19), Prandtl number, Eq. (20) and Nusselt, Eq. (21).

${{R}_{{{e}_{D}}}}=\frac{{{\rho }_{f}}{{v}_{f}}D}{{{\mu }_{f}}}$  (19)

${{P}_{r}}=\frac{{{\mu }_{f}}{{C}_{p,f}}}{{{K}_{f}}}$ (20)

${{N}_{{{u}_{x}}}}=\frac{{{h}_{f}}D}{{{K}_{f}}}=f({{R}_{{{e}_{D}}}},{{P}_{r}})$ (21)

As the flow regime inside the tubes is similar to a not fully developed motion, the correlations for the calculation of the local Nusselt number have been reported in Eq. (22), the first line is valid when

${{N}_{{{u}_{x}}}}=\left\{ \begin{matrix}   1077x_{*}^{-{}^{1}/{}_{3}}-0.7  \\   3.657+6.874{{({{x}_{\phi }}\times {{10}^{3}})}^{-0.488}}{{e}^{-57.2{{x}_{\phi }}}}  \\ \end{matrix} \right.$ (22)

${{x}_{\phi }}=\frac{{}^{x}/{}_{D}}{{{R}_{{{e}_{D}}}}{{P}_{r}}}$ (23)

${{x}_{\phi }}(H)<{{\bar{x}}_{\phi }}=0.05$ (24)

This analytical 0D model has been applied to three different sizes of raw material (different e). In Figure 12 the temperature distributions are compared to those obtained by the CFD.

12.png

Figure 12. Comparison between 0D and CFD models

13.png

Figure 13. Correlation factor vs size of raw material

Using the above curves, a calibration factor for the 0D analytical model can be obtained. The characteristic time from CFD results has been estimated. Table 4 shows the numerical values of the calibration factors F defined as the ratio

The above relation is introduced to use the 0D model for quick parametric analysis for the preliminary design phases before a CFD simulation campaign.

Table 4. Calibration factors for different size of raw material

Several models have been presented for the pre-heating of raw material for both direct and indirect heating processes. The attention has been actually focused on the indirect process because it is safer with respect to environmental problems related to the exhaust gases. The numerical models can be used to quantitatively compare the effects of the main design parameters taking into account the raw material dimensions and physical properties. The parametric analysis can be used either for design purposes or to support the decision making process according to the economic savings associated to the pre-heater with a given raw material and hot gas conditions.

With a reference raw material in mind, it has been estimated that a variation of 25 % of specific heat leads to a variation of 0.5 % of fuel. With the estimated fuel consumption from an average furnace [20] giving an annual cost of the order 14 M€, a saving of 70 k€ can be expected with the above solution. A lower advantage is obtained with the variation of the density and the lowest impact is predicted the change of thermal conductivity of the raw material. As far as the raw material size is concerned, it has been observed that only for values of L_m>10 [mm] there is a pronounced impact. It has been also verified that a CFD model with stationary raw material is representative and accurate because the velocity of the raw material (with values compatible with an actual design v_g=0.002 [m/s]) gives no thermal effects on the system response.

An optimization procedure, based on CFD models and response surfaces, has been developed to support the design process of the system.