Bunsen Burner Flame Modeling: Heat-Loss, Equivalence Ratio, and Chemiluminescence, Slides of Mechanics

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Chapter 7

Bunsen Burner Model

7.1 Purpose of the Bunsen Type Burner Model

The Bunsen type burner with co–flow is a very simple experimental configuration that avoids many complications of modern gas turbine combustors such as complex fluid mechanics and high levels of turbulence. The laminar Bunsen flame is however a non–ideal burning environment that also shows similarities to the gas turbine com- bustor environment. The flame is stabilized by a delicate balance between heat–loss and fluid mechanical strain. The flame is surrounded by a shroud of dilution air that affects the burning. The Bunsen type burner model shows that global chemiluminescence measure- ments can be modeled and understood using simple physical principles without detail information about the exact burning process. Through the understanding of chemi- luminescence several other aspects of the burning process can be elucidated, at the very least at a qualitative level.

7.2 Modeling Approach

A Bunsen flame is illustrated in Figure 7.1 and shown in a photograph at sto- ichiometric conditions in Figure 7.2. The Bunsen type burner model of the flame is illustrated in Figure 7.3. Some elements of the real flame are carried over to the model, others are not. The Bunsen flame curvature is the most significant aspect neglected in the model. Every other important characteristic of the Bunsen burner flame can be represented in the model. The cone is divided into differential segments as shown in Figure 7.3. The flame element is defined by its location relative to the burner rim both in terms of height and radius. The location of the flame element defines the heat–loss from the flame as well as the equivalence ratio of the incoming mixture for the element. The local heat–loss together with the local equivalence ratio determine the burning rate for the element via calculations using the 1-D premixed flame program PREMIX (see Sec- tion 6.1). PREMIX also allows the integration of chemiluminescence yield through

Figure 7.2: Photograph of stoichiometric Bunsen type flame

Figure 7.3: Illustration of Bunsen burner flame model

7.3 Bunsen Type Burner Model Components

To provide closure for the model, relationships between the position of the flame element and all other flame relevant quantities must be obtained. The model will translate the position into both heat–loss and local equivalence ratio using a low- order approximation of the heat–transfer and mixing observed in the flame. The local heat–loss and equivalence ratio will then determine all other flame–related quantities such as chemiluminescence yield and burn–rate through the calculations performed using PREMIX.

7.3.1 Semi-empirical mixing model

The local chemiluminescence measurements revealed that significant mixing be- tween the co–flow of air and the main premixed fuel and air stream exists. To model the effect, a variation of the local equivalence ratio along the height of the flame is prescribed in the model. The form of the variation is given in Equation 7.2. The con- stants in the equation may vary with main–stream equivalence ratio. φl represents the leanest equivalence ratio at the edge of the flame. b is a parameter governing how evenly the equivalence ratio increases from φl to the main stream equivalence ratio φo. b is kept constant for all calculations at a value of 30. hch is the height at which the main stream equivalence ratio is reached. Beyond hch, the equivalence ratio does not change. The formula shown in Equation 7.2 is a crude model of the complex mixing processes that actually occur but the modeling results given in Section 7. will show that the model is sufficient to capture the major experimental influences of the co–flow of air. The model is termed ”semi–empirical” because the variation of parameters φl and hch with equivalence ratio is determined by attempting to match modeling results to experimental data.

φlocal (y) =

e^ φbhoch−^ φ−l 1

eb y^ − 1

• φl for y < hch φo for y > hch

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Flame Temperature (K) Equivalence Ratio = 0.75Equivalence Ratio = 0. Equivalence Ratio = 1.

Figure 7.4: Flame temperature as a function of heat–loss

shown as a function of heat–loss for three equivalence ratios in Figure 7.4. Flame temperature is most sensitive to heat–loss at lower equivalence ratios, as can be expected due to the fact that less heat is liberated at these equivalence ratios.

Flame–speed

The flame–speed as defined here is directly related to the burn-rate per unit area by the dividing the latter by the incoming mixture density. Velocity is shown because it is a more commonly used quantity than burn–rate. The flame–speed as a function of heat–loss is shown in Figure 7.5.

7.4 Bunsen Type Burner Modeling Results

The following paragraphs present the results of the chosen parameter variation, frozen with changes in flow–rate. Results are discussed only with respect to the comparison of experimental data and modeling results of chemiluminescence mea-

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Flame Speed (cm/sec)

Equivalence Ratio = 0.75Equivalence Ratio = 0. Equivalence Ratio = 1.

Figure 7.5: Flame–speed as a function of heat–loss

surements. Detail analysis and evaluation of chemiluminescence as a heat–release rate indicator is given in Section 10.2.1.

7.4.1 Summary of modeling procedure

Before presenting the modeling results, the procedure used to obtain these results is summarized. The parameters defined above in Section 7.3.1 and Section 7.3. are set by matching, to the best of the model’s ability the OH∗^ chemiluminescence experimental data for a flow–rate of 60 cc/sec of air. The conversion factor from the units of experimentally measured chemiluminescence (cV-A) to the yield calculated in PREMIX, is determined at an equivalence ratio of 0.90 and held constant for all other data points. Once the parameter values are determined as a function of equivalence ratio for one flow–rate they are not changed for the other flow–rates.

50 55 60 65 70 75 Air Flow-Rate (cc/sec)

5E-

Chemiluminescence Yield

Experimental Data Modeling Results

Figure 7.7: OH∗^ modeling results and experimental data at an equivalence ratio of

In Section 5.1.1, the collapse of the OH∗^ chemiluminescence experimental data was achieved using the square–root of the Reynolds number. Since the Reynolds num- ber does not vary significantly over the experimental range studied, the square–root dependence of OH∗^ chemiluminescence cannot be readily identified. The modeled chemiluminescence as well would clearly show non-linear behaviour if a wider range of flow–rates were considered. The non–linear variation of chemiluminescence is due to the mixing height which is kept constant with flow–rate and so automatically increases the average equivalence ratio closer and closer to the incoming mixture equivalence ratio. Since chemilumines- cence is not a linear function of equivalence ratio, keeping the mixing height constant causes a non–linearity in the variation of OH∗^ chemiluminescence with flow–rate. In contrast to the experimentally observed non–linearity, the model non–linearity influ- ence is very equivalence ratio dependent. In the model rich equivalence ratios will tend to have lower and lower per unit mass yields of OH∗^ chemiluminescence as the flow–rate is increased. Lean equivalence ratios will tend to have higher per unit mass yields of chemiluminescence as the flow–rate is increased.

Local chemiluminescence

Local OH∗^ chemiluminescence intensity as a function of the radial coordinate is shown in Figure 7.8. Shown with chemiluminescence intensity variation is the variation of the local equivalence ratio. The increase of chemiluminescence over the radius is similar in magnitude to that observed in the experimental data shown in Figure 5.8 for example. The model chemiluminescence variation is however mostly due to the variation of the local equivalence ratio over the radius of the flame. Heat losses appear only to be important in the immediate vicinity of the burner rim. Curvature effects, which contribute significantly to the shape observed experimentally are not considered in the model. Similarly, the local minimum of chemiluminescence intensity observed in the center of the flame is not observed in the model, because the diffusion and pressure influences are not considered by the model. Section 7.5.3 addresses burning at the flame center in greater detail. It is important to reiterate that the goal of the model is not to provide a complete model of the Bunsen flame in air co–flow but rather to model the general behaviour of the flame in order to provide a basis for the interpretation of chemiluminescence measurements in terms of heat–release rate. The modeling success for global chemi- luminescence shows that the level of complexity in the model is adequate to attain the goal of the model. The units of the displayed local chemiluminescence are that of yield intensity since the values have not been integrated over the flame area to give an overall chemiluminescence yield.

7.4.3 CH∗modeling results

Global chemiluminescence

The same conversion factor used above to compare OH∗^ chemiluminescence ex- perimental data with modeling results is used to compare the CH∗^ experimental data to the modeling results. The experimental and modeled variation of CH∗^ chemilumi- nescence is shown in Figure 7.9 for an air flow–rate of 60 cc/sec. The model captures

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1. Equivalence Ratio

5E-

Chemiluminescence Yield

Experimental Data Modelling Results

Figure 7.9: CH∗^ modeling results and experimental data at an air flow–rate of 60 cc/sec

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1E-

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Chemiluminescence Yield

Experimental Data Modeling Results

Figure 7.10: CH∗^ modeling results and experimental data at an equivalence ratio of

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Local Chemiluminescence Intensity

1

Local Chemiluminescence Intensity Local Equivalence Ratio Local Equivalence Ratio

Figure 7.11: Local CH∗^ chemiluminescence intensity modeling results at an equiv- alence ratio of 0.90 and an air flow–rate of 60 cc/sec

radius is similar in magnitude to that observed in the experimental data shown in Figure 5.10 for example. As observed for local OH∗^ chemiluminescence, the increase in chemiluminescence intensity, except for near the burner rim, is due in great part to the equivalence ratio variation over the radius. As observed in the experimental data, there is no significant difference between the shape of the local OH∗^ and CH∗ chemiluminescence intensity variations across the flame.

7.4.4 Chemiluminescence Ratio modeling results

Global chemiluminescence ratio

The variation of the global chemiluminescence ratio of OH∗^ to CH∗^ with main stream equivalence ratio is shown in Figure 7.12 using both experimental data and modeling results at all flow–rates. The modeled chemiluminescence ratio varied very little for variations in flow–rate, whereas there was some noticeable variation in the ratio in the experimental data. Due to the fact that the modeled CH∗^ chemilumi- nescence is lower than the experimental data for CH∗^ chemiluminescence, the model

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Local Chemiluminescence Ratio Local Equivalence Ratio Local Equivalence Ratio

Figure 7.13: Radial variation of the modeled OH∗^ to CH∗^ chemiluminescence ratio at an equivalence ratio of 0.9 with an air flow–rate of 60 cc/sec

7.4.5 Parameter variations used

The model developed for the Bunsen burner is semi-empirical, meaning that the closure of the model was achieved using equations that contain parameters whose value is determined during the course of the modeling effort. The parameters in Equation 7.2 and Equation 7.3 are allowed to vary with equivalence ratio but not with flow–rate. An important feature of the selected parameter variations is that they are internally consistent. Higher standoff distance of the flame, for example, corresponds to a lower burner rim temperature.

Mixing parameter variation

The mixing parameter variation is shown in Figure 7.14. The mixing parameter φl is replaced in the figure by the difference between mainstream and flame edge equivalence ratio, showing more clearly the amount of mixing occurring for each equivalence ratio. The mixing height shown is the actual height in centimeters to which some mixing effects are seen. For an equivalence ratio of 0.75, the mixing height

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Mixing Height (cm)

(Mainstream - Edge) Equivalence Ratio

Mixing height (cm) (Mainstream - Edge) Equivalence Ratio

Figure 7.14: Variation of mixing parameters with mainstream equivalence ratio

shown corresponds to about 30% of the total flame height. The percentage of the total height of the flame affected by mixing is also a decreasing function of equivalence ratio. As the mixing height decreases, the difference between the mainstream and flame edge equivalence ratio increases because a smaller amount of mainstream mixture is presumed to mix with a nearly equal amount of co–flow air. As mentioned in Section 7.4.1, all parameters were frozen for increases in flow– rate. The assumption that the mixing is not a function of flow–rate is very difficult to defend in light of the fact that the mixing is partly shear–layer driven. The use of scaling relationships, for example with the square–root of Reynolds number, was considered but dropped because it was found that the scaling of these parameters only had a very negligible effect on the modeling results. Additionally, the influence of the altered mixing environment on the thermal parameters is difficult to understand. To maintain the model’s low-order character, it was decided to neglect flow–rate variation effects. In a study with a wider range of flow–rate changes in the mixing due to changes in flow–rate must be considered in the modeling effort in order to adequately capture experimental data trends.

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Standoff Distance (cm) Rim Temperature (K)

Figure 7.15: Variation of heat transfer parameters with mainstream equivalence ra- tio

a further physical foundation for the observed chemiluminescence variation in the flame–tip region.

7.5.2 FLUENT implementation of Bunsen type burner model

The procedure used to obtain the results shown in Section 7.5.3 was outlined in Section 6.3. The present section discusses the geometry used in the calculation. The geometry used is shown in Figure 7.16. The computational domain extends from the base of the stainless steel flame holder to the end of the long quartz chimney. At the inlets, a flat velocity profile is used with the velocity magnitude calculated based on the area–average for the given inlet. The center inlet is the premixed gas inlet where the velocity is set to 86 cm/sec to model an air flow–rate of 60 cc/sec and an equivalence ratio of 1.00. The annular air co–flow inlet velocity magnitude is constant for all conditions at 2.9 cm/sec. The stainless steel flame holder is modeled in its entirety with heat conduction within the stainless steel and heat exchange both to and from the surrounding fluid. The stainless steel tube is considered thermally insulated at its upstream end.

Figure 7.16: Schematic of CFD geometry for Bunsen type burner

The calculation is performed under the assumption of laminar flow. The methane reaction mechanism used consists of the Fluent default two–reaction model. The first reaction step is a reaction between methane and molecular oxygen to give carbon monoxide and water. The second reaction step is a reaction between carbon monoxide and molecular oxygen to give carbon dioxide and water. The physical properties of all gases, including viscosity, are a function of temperature. For viscosity and conductivity however, values of air only are used, i.e. gas properties are assumed identical to those of air. All other properties, including diffusion and heat–capacity are calculated for each species separately using a polynomial fit in temperature or molecular theory. The gas average coefficient, when appropriate, is calculated on a mass basis. For more information, the Fluent manuals (Fluent Inc., 1998) offer great detail in the origin and correct use of the correlations and reaction mechanisms already included in the software and used in the present investigation.