Fuel Combustion and Heat Transfer in a Furnace

Fuel Combustion and Heat Transfer in a Furnace

Heat is needed in a furnace for heating of the furnace charge (material to be heated in the furnace) and sometimes for the chemical reactions. The three sources of heat energy are (i) combustion of fuels, (ii) electric energy, and (iii) chemical energy available through the exothermic reactions. Other than the electro-thermal furnaces, this requirement of heat (excluding the chemical energy) is met through the combustion of a fuel. The fuel can be a gaseous fuel (e.g. by-product gases like coke oven gas, blast furnace gas, and converter gas, natural gas, and liquid petroleum gas etc.), a liquid fuel (e.g. fuel oil, and tar etc.), or a solid fuel (e.g. coal, and coke etc.).

All fuels contain potential energy. On combustion, this potential energy is released in the products of combustion (POC). Combustion is normally considered to be the controlled release of heat and energy from the chemical reaction between a fuel and an oxidizer. Nearly all of the combustion in industrial processes uses a hydrocarbon fuel. A generalized combustion reaction for a typical hydrocarbon fuel is given by the equation fuel + oxidizer = carbon di-oxide (CO2) + water vapour (H2O) + other species. The ‘other species’ depends on the type of the oxidizer used and the ratio of the fuel to oxidizer. The most commonly used oxidizer is air, which consists of nearly 79 % nitrogen (N2) by volume and is generally carried through in the combustion process. If the combustion is fuel rich, meaning there is not enough oxygen (O2) to fully burn the fuel, then there exists unburned hydrocarbons in the exhaust products and little, if any, excess O2. If the combustion is fuel lean, meaning there is more O2 than required to fully burn the fuel, and then there is excess O2 in the exhaust products.

The fuel has a significant influence on the heat transfer in the furnace combustion system. One of the most important properties is the heating value of the fuel. This is used to determine how much fuel is to be burned to process the desired production rate of material which is being heated. The heating value is specified as either the higher heating value (HHV) or the lower heating value (LHV).

The LHV excludes the heat of vaporization, which is the energy required to convert liquid water to steam. This means that the LHV assumes all of the POC are gaseous, which is usually the case for nearly all industrial combustion applications. If the combustion products are to leave the process at a temperature low enough that all of the water is converted from a gas to a liquid, then the heat of condensation is to be released into the process as an additional source of energy. The HHV of a fuel includes this additional energy.

The composition of the fuel is important in determining the composition of the POC and the amount of oxidizer which is needed to burn the fuel. The density of the fuel is needed to determine flow rates through the fuel delivery system of the furnace and the associated pipe sizes.

The exhaust gas composition is very important in determining the heat transfer in the furnace. Unburned hydrocarbons in the exhaust indicate that the fuel has not been fully burned and hence all of the available heat has not been released. High excess O2 levels in the exhaust gas usually indicate that too much oxidizer has been supplied. The excess oxidizer carries sensible energy out through the exhaust gas. This again means that some of the available heat of the fuel has not been fully utilized to heat the furnace charge. If the oxidizer is air, then a large proportion of the available energy in the fuel is carried out in the flue with the exhaust products.

The POC transfer the heat energy to the furnace charge to raise its temperature to the required value and then leave the furnace. The sensible heat in POC at the critical process temperature is not available to the furnace. The higher the process critical temperature, higher is the sensible heat in POC. This sensible heat in POC is very important from the point of view of fuel utilization.

There are two common types of oxidizers used in industrial combustion processes. The majority of the processes use air as the oxidizer. However, many of the higher temperature processes use an oxidizer containing a higher concentration of O2 than available in the air (around 21 % by volume). This type of combustion is referred to as O2 enhanced combustion. In many cases, the production rate in a heating process can be significantly increased with only relatively small amounts of O2 enrichment.

In several cases, air/fuel burners can successfully operate with an oxidizer containing upto around 30 % O2 with little or no modifications. At higher O2 concentrations, the flame can become unstable or the flame temperature can become too high for a burner designed to operate under air/fuel conditions. In higher temperature applications, where the benefits of higher purity O2 justify the additional costs, higher purity oxidizers can be used (greater than 90 % O2). The heating process is greatly intensified by the high purity O2. The oxidizer purity has a significant influence on the heat transfer in a combustion system.

An important aspect in a combustion system is the ratio of the fuel to the oxidizer. There are many ways by which this can be specified. These are deliberated here in short. A global combustion reaction using CH4 (methane) as the fuel can be written as CH4 + (xO2 + yN2) = CO, CO2, H2, H2O, N2, NOx, O2, trace components. The stoichiometry of a reaction indicates the ratio of O2 to fuel for a given combustion system. One method of quantifying the stoichiometry is to only consider the O2 in the oxidizer, since the inerts in the oxidizer are not needed for the reaction. Hence, considering CH4 as a fuel, the global simplified stoichiometric reaction with air can be written as CH4 + (2O2 + 7.52N2) = CO2 + 2H2O + 7.52N2. In this reaction, air is represented as 2O2 + 7.52N2. Here the stoichiometric ratio is 2 since 2 molecules of O2 are required to burn one molecule of CH4.

This method of specifying stoichiometric ratio is generally used for combustion systems incorporating O2 enrichment. This is since the amount of O2 supplied to the combustion system is of importance.

Actual flames generally require some excess O2 for complete combustion of the fuel. This is due to incomplete mixing between the fuel and oxidizer. For the fuel-rich combustion of CH4, stoichiometric ratio is less than 2. In case of fuel-lean combustion of CH4, the stoichiometric ratio is greater than 2. Hence, the oxidizer composition is important. A common way of specifying the oxidizer composition is by calculating the O2 mole fraction in the oxidizer.

Many industrial combustion processes run with around 3 % more O2 than is theoretically needed for perfect combustion. This is often the amount of excess O2 needed to minimize the emissions of unburned hydrocarbons and ensure the complete combustion of the fuel. This can be due to mixing limitations between the fuel and the oxidizer, especially in non-premixed systems.

Too much excess O2 means that energy is being wasted in the heating up of the excess combustion air, instead of the furnace charge. Hence, it is desirable to only use just enough excess O2 to get low CO (carbon mono-oxide) emissions. An example of a simplified global reaction for CH4 with 3 % of excess O2 is the reaction CH4 + (2.06O2 + 7.75N2) = CO2 + 2H2O + 0.06O2 + 7.75N2.

Most industrial flames are turbulent which is generally determined by a turbulent Reynolds number (Re). The turbulent characteristic length scale is normally called the Kolmogorov length. The Kolmogorov length is representative of the dimension where dissipation occurs. The Taylor length scale can be defined as the ratio of the strain rate to the viscous forces. The various lengths can be used to characterize a flame. A flame can be (i) a wrinkled flame, (ii) severely wrinkled flame, (iii) flamelets in eddies, and (iv) distributed reaction front. A non-dimensional Damköhler number (Da) indicates the type of reaction time which is significant for the specific type of combustion reaction. This number is the ratio of the reaction time to the flow rate.

Combustion properties

The normal combustion properties generally used in industrial applications are (i) combustion product composition, (ii) flame temperature, (iii) available heat, and (iv) flue gas volume after combustion.These are important in calculating the heat transfer from the flame and exhaust gases to the furnace and to the furnace charge.

Combustion products

There are a number of variables which can have a significant impact on the products of combustion. Some of the important variables include the oxidizer composition, mixing ratio, preheat temperatures of air and fuel, and fuel composition. These are briefly discussed below.

Oxidizer composition – Taking the example of CH4 combustion, the stoichiometric combustion of CH4 with air can be represented by the global equation CH4 + 2O2 + 7.52N2 = CO2, 2H2O, 7.52N2, and trace components. It can be seen that over 70 volume percent of the exhaust gases is N2. Similarly, a stoichiometric O2/CH4 combustion process can be represented by the equation CH4 + 2O2 = CO2, 2H2O, and trace species.  The volume of exhaust gases is considerably reduced by the elimination of N2. In general, a stoichiometric O2-enhanced CH4 combustion process can be represented by the equation CH4 + 2O2 + xN2 = CO2 + 2H2O + xN2 + trace components.

The actual composition of the exhaust products from the combustion reaction depends on several factors, including the oxidizer composition, the temperature of the gases, and the equivalence ratio. The equivalence ratio is defined as the ratio of the actual fuel/air ratio to the stoichiometric fuel/air ratio. Stoichiometric combustion occurs when all the O2 is consumed in the reaction, and there is no molecular O2 in the products.

An adiabatic process means that no heat is lost during the reaction, or that the reaction occurs in a perfectly insulated chamber. This is not the case in an actual combustion process where heat is lost from the flame by radiation. The predicted major product for the adiabatic equilibrium combustion of CH4 is a function of the oxidizer composition.

An equilibrium process means that there is an infinite amount of time for the chemical reactions to take place, or the reaction products are not limited by chemical kinetics. However, in actual conditions, the combustion reactions are completed in fractions of a second. Further, as N2 is removed from the oxidizer, the concentration of N2 in the exhaust products decreases correspondingly. Likewise, there is an increase in the concentrations of CO, CO2 and H2O. For this adiabatic process, there is a significant amount of CO at higher levels of O2 in the oxidizer.

The radical products H, O, and OH all increase with the O2 in the oxidizer. NO (nitric oxide) initially increases and then decreases after around 60 % O2 in the oxidizer as more N2 is removed from the system. When the oxidizer is pure O2, NO is not formed since no N2 is available. Unburned fuel in the form of H2 and unreacted oxidizer in the form of O2 also increase with the O2 concentration in the oxidizer. This increase in radical concentrations, unburned fuel in the form of CO and H2, and unreacted O2 are all due to chemical dissociation which occurs at high temperatures.

The actual flame temperature is lower than the adiabatic equilibrium flame temperature due to the imperfect combustion and radiation from the flame. The actual flame temperature is determined by how well the flame radiates its heat and how well the combustion system, including the furnace charge and the refractory walls, absorbs that radiation.

A highly luminous flame generally has a lower flame temperature than a highly nonluminous flame. The actual flame temperature is also lower when the furnace charge and the walls are more radiatively absorptive. This occurs when the furnace charge and walls are at lower temperatures and have higher radiant absorptivities.

As the gaseous combustion products leave the flame, they usually lose more heat by convection and radiation as they travel through the combustion chamber. The objective of a combustion process is to transfer the chemical energy contained in the fuel to the furnace charge, or in some cases to the combustion chamber. The more thermally efficient is the combustion process, the more heat is transferred from the combustion products to the furnace charge and to the combustion chamber. Hence, the gas temperature in the exhaust stack is desirably much lower than in the flame in a thermally efficient heating process. The composition of the combustion products then changes with gas temperature.

Mixture ratio – The O2 and N2 concentrations in the exhaust gases strictly decrease with the equivalence ratio. The H2O and CO2 concentrations peak at stoichiometric conditions. This is important as both of these gases produce nonluminous gaseous radiation. The unburned fuels in the form of H2 and CO both increase with the equivalence ratio. This gets reflected in the available heat as not all of the fuel is fully burned.

Air and fuel preheat temperature – In many industrial combustion processes, heat is recovered to improve the overall thermal efficiency of the process to reduce the operating costs. The recovered heat is normally used to preheat the incoming combustion air and is sometimes used to preheat the incoming fuel. Preheating either the air or the fuel affects the composition of the combustion products. CO2, H2O, and N2 with all decreasing in the exhaust gas with air preheat, due to chemical dissociation. Due to the safety considerations and the possibility of sooting up the fuel supply piping, higher fuel preheat temperatures are not practical or recommended under most of the conditions. It is generally seen that there is only a slight decrease in the concentrations of the major components and a slight increase in the concentrations of the minor components of the exhaust gases. This is because of the fact that the mass of fuel is relatively small compared to the mass of combustion air supplied to the combustion system. This means that preheating the combustion air has a much more significant impact than preheating the fuel for a given preheat temperature.

Fuel composition – Combustion products depends on the fuel composition.  The predicted combustion product compositions for different fuel under a variety of operating conditions can be calculated. Most common gaseous fuels being used are H2 (hydrogen), CH4, C3H8 (propane), and blends of H2 and CH4. These are intended to be representative of fuels normally used in industrial applications. In terms of luminosity, H2 produces non-luminous flames, CH4 produces low-luminosity flames, and C3H8 produces higher luminosity flames.

Flame temperature – The flame temperature is a critical variable in determining the heat transfer from the flame to the furnace charge. The adiabatic flame temperature is affected by the oxidizer and fuel compositions, the mixing ratio, and the air and fuel preheat temperatures. However, the real flame temperatures are not as high as the adiabatic flame temperature, but the trends are comparable and representative of actual conditions.

Oxidizer and fuel composition – The flame temperature increases significantly when air is replaced with O2 since N2 acts as a diluent which reduces the flame temperature. The flame temperature normally varies for air and pure O2. There is a rapid rise in the flame temperature from air upto around 60 % O2 in the oxidizer. The flame temperature increases at a slower rate for higher O2 concentrations. Also, the fuel composition has a strong impact on the flame temperature. In a fuel blend of H2 and CH4, the temperature increases as the H2 content in the blend increases. It is important to note that the increase is not linear, with a more rapid increase at higher levels of H2. Because of the relatively high cost of H2 compared to CH4 and C3H8, it is not used in many industrial applications. However, high H2 fuels are often used in many of the hydrocarbon applications. These fuels are by-products of the chemical manufacturing process and therefore much less expensive than purchasing H2 from an industrial gas supplier and more cost effective than using other purchased fuels.

Mixing ratio – The peak flame temperatures occur at stoichiometric conditions. The lower the O2 concentration in the oxidizer, the more the flame temperature is reduced by operating at non-stoichiometric conditions (either fuel rich or fuel lean). This is due to the higher concentration of N2, which absorbs heat and lowers the overall temperature. At stoichiometric conditions, there is just enough oxidizer to fully burn all the fuel. Any additional oxidizer absorbs sensible energy from the flame and reduces the flame temperature. In most real flames, the peak flame temperature often occurs at slightly fuel lean conditions. This is due to the imperfect mixing where slightly more O2 is needed to fully burn all the fuel. Nearly all industrial combustion applications are run at fuel-lean conditions to ensure that the CO emissions are low. Hence, depending on the actual burner design, the flame temperature can be close to its peak, which is often desirable for maximizing heat transfer. One problem frequently encountered when maximizing the flame temperature is that the NOx (oxides of N2) emissions are also maximized since NOx increases approximately exponentially with gas temperature. This has led to many design concepts for reducing the peak flame temperature in the flame to minimize NOx emissions. This also affects the heat transfer from the flame.

Oxidizer and fuel preheat temperature – The adiabatic flame temperature varies and is a function of the preheat temperature of the oxidizer for air/CH4 and O2/CH4 flames. The increase in flame temperature is relatively small for the O2/CH4 flame because the increased sensible heat of the O2 is only a fraction of the chemical energy contained in the fuel. For air/CH4 flames, preheating the air has a more dramatic impact since the increase in sensible heat is very significant due to the large mass of air in the combustion reaction. The adiabatic flame temperature increases rapidly for air/fuel flames in many fuels.

Available heat – The available heat in the furnace combustion system is important in the determination of the overall thermal efficiency and is hence a factor when calculating the heat transfer in the process. It is less effective to try to maximize the heat transfer in the system which inherently has a low available heat. Available heat is defined as the gross heating value of the fuel, less the energy carried out of the combustion process by the hot exhaust gases.

The gross available heat (GAH) in the furnace is given by equation GAH = calorific value of the fuel + sensible heat of the reactants – heat carried by POC leaving the furnace. GAH represents the heat available at the critical process temperature. It does not represent the heat available to perform a given function due to the various types of losses. It can be used as a criterion for comparing different fuel‐combustion system.

Further, in a furnace, there are heat losses which are governed by the process critical temperature, refractory lining thickness and thermal conductivity of the refractory. Hence the net available heat (NAH) in the furnace is given by the equation NAH = GAH − heat losses. NAH can be used as a criterion for comparing the smelting/melting/heating efficiency of different furnaces.

The heat lost from the process through openings in the furnace, through the furnace walls, or by air infiltration is not considered in the calculation of the theoretical available heat as these are dependent on the process. The theoretical available heat is to be proportional to the amount of energy actually absorbed by the furnace charge in an actual process, which is directly related to the thermal efficiency of the system. Hence, the theoretical available heat is generally used to show the thermal efficiency trends as functions of exhaust gas temperature, oxidizer and fuel compositions, mixing ratio, and air and fuel preheat temperatures.

The available heat varies as a function of the exhaust gas temperature and decreases rapidly with the exhaust gas temperature and is relatively independent of the fuel composition. Hence, to maximize the thermal efficiency of the process, it is desirable to minimize the exhaust gas temperature. This is usually done by maximizing the heat transfer from the exhaust gases to the furnace charge (and furnace walls) and by recovering some of the heat in the exhaust gases by preheating the oxidizer and/or thefuel.

As the exhaust gas temperature increases, more energy is carried out of the combustion system and less remains in the system. The available heat decreases to zero at the adiabatic equilibrium flame temperature where no heat is lost from the gases. The available heat of a CH4/O2 combustion system even at the exhaust gas temperature of around 2000 deg C, the available heat is still is 57 %. Also, it is usually not very economical to use CH4/air systems for high-temperature heating and melting processes. At an exhaust temperature of around 1300 deg C, the available heat for the CH4/air system is only a little over 30 %. Heat recovery in the form of preheated air is generally used for higher temperature heating processes to increase the furnace thermal efficiency.

As the exhaust gas temperature increases, the available heat decreases because more energy is carried out with the exhaust gasses. There is an initial rapid increase in available heat as the O2 concentration in the oxidizer increases from the 21 % found in air. This is one reason why O2 enrichment has been a popular technique since the incremental increase in efficiency is very significant. The thermal efficiency of the CH4/air system is two times when air is preheated to around 1100 deg C.

For the CH4/O2 system, the increase in efficiency is much less dramatic by preheating the O2. This is since the initial efficiency with no preheat is already 70 % and since the mass of the O2 is not nearly as significant in the combustion reaction as compared to the mass of air in an fuel/air system. There are also safety fears when flowing hot O2 through pipeline, heat recuperation equipment, and a burner. The fuel savings for a given technology can be calculated using the available heat curves.

Volume of exhaust gas – The flow rate of gases through a furnace combustion chamber is proportional to the convective heat transfer to the furnace charge. There are several factors which influence this flow rate. One is the gas temperature since higher temperature gases have higher actual flow rates ( cubic metres per hour) due to the thermal expansion of the gases. This means that preheating the fuel or the oxidizer, which both normally increases the flame temperature, produces higher actual flow rates. However, the flow rate of the gases is the same when corrected to standard temperature and pressure conditions (STP).

Another factor which has a very strong influence on the gas flow rate through the combustion system is the oxidizer composition. O2 enhanced combustion basically involves removing N2 from the oxidizer. A major change compared to air/fuel combustion is the reduction in the flue gas volume. This means that for each unit volume of fuel, 3 normalized volumes of gas are produced for O2/fuel combustion compared to 10.5 volumes for air/fuel combustion. This reduction can have both positive and negative effects, but the effect on convective heat transfer is a reduction in the average gas velocity through a furnace chamber and a resulting reduction in the convection heat transfer to the furnace charge.

Exhaust gas transport properties

The transport properties of the gaseous components in the furnace chamber are important for determining the heat transfer and fluid dynamics. The properties are highly dependent on the temperature and the gas components. The important gas properties for heat transfer in industrial furnace chambers vary as functions of the fuel and oxidizer composition, mixing ratio, and air preheat temperatures. The property variation as a function of the fuel preheats temperature has a minimal effect. The gas composition and temperature are needed to calculate nonluminous gaseous radiation. The gas transport properties are needed to calculate the convection heat transfer coefficient, which is often given in the form Nusselt number (Nu). Nu is calculated from the Prandtl number (Pr) and the Reynolds number (Re). The convection heat transfer coefficient ‘h’ is then calculated from the Nusselt number using Nu = hd/k where d is a characteristic dimension for the flow system and k is the fluid thermal conductivity. The gas properties are needed to calculate the Nu, Pr, and Re numbers are given below.

Density – The gas density can be used to calculate the Re number, which is generally needed to compute the convective heat transfer coefficient. The density is also used to calculate the average gas velocity through the furnace chamber, which is also normally needed to compute the convection coefficient. The gas density is inversely proportional to the gas temperature so that as the temperature increases, the density decreases. The reduction in the gas density is roughly proportional to the inverse of the absolute gas temperature. Also, the gas density decreases rapidly as the O2 content in the oxidizer increases. This is because of the increased flame temperatures. A lower gas density means a lower Re number and hence reduced convective heat transfer, if all other variables remain the same. However, the mass flow rate of gases is also decreasing. Hence, the average gas velocity is not significantly impacted as a result of the combined effect of lower density and lower mass flow rate so that the impact on convection due to gas velocity is minimal.

The gas density reaches a minimum at intermediate equivalence ratios. This again can be attributed to the adiabatic equilibrium flame temperature. Further, the gas density decreases nearly linearly as the air preheat temperature increases, which correlate inversely with the curves for the flame temperature. Also, the gas density does not decrease linearly as a function of the gas blend composition, as is generally expected instinctively. Again, the density corresponds inversely to the adiabatic flame temperatures.

Specific heat – The gas specific heat, sometimes referred to as the gas heat capacity, is another transport property which has an impact on the convective heat transfer in the furnace system. It is used to calculate the Pr number, which is often used to calculate the convective heat transfer coefficient.  There is a nonlinear increase in the gas specific heat with respect to the exhaust product temperature. The specific heat increases more rapidly at higher temperatures. Further, the exhaust gas specific heat increases almost linearly as the O2 percent in the oxidizer increases. All other things being the same, this improves the convective heat transfer from the combustion product gases to the furnace charge.

However, there is a much more complicated relationship between the specific heat and the equivalence ratio, including strong fuel dependence as well. All the fuels show an initial increase in the specific heat as the equivalence ratio increases, reaching a local maximum at stoichiometric conditions. Beyond stoichiometric conditions, the specific heat then decreases, plateaus, and increases again. In the case of CH4, the specific heat increases very rapidly at high equivalence values. Although the relationship between specific heat and equivalence ratio is fairly complicated, the reality is that most industrial combustion processes are operated at slightly fuel-lean conditions where there is a strong but more linear relationship between the equivalence ratio and the specific heat. In case of H2/CH4 fuel blends, the specific heat increases rapidly at high H2 contents in the fuel blend. The flame temperature shows a very similar relationship to the H2 content in the blend.

Thermal conductivity – Like the specific heat, the gas thermal conductivity affects the Pr number, which in turn affects the convective heat transfer coefficient. In this case, there is an inverse relationship between the thermal conductivity and the Pr number. As the thermal conductivity increases (decreases), the Pr number decreases (increases) along with the convection coefficient, assuming all other variables remaining constant. The thermal conductivity of a gas is roughly dependent on the square root of the absolute temperature. A similar non-linear increase in thermal conductivity takes place with gas temperature as for the specific heat.

Further, the thermal conductivity increases rapidly as the O2 content in the oxidizer increases. The relationship is almost linear although there is a faster increase at lower O2 contents compared to that at higher O2 content in the oxidizer. However, there is a complicated relationship between a transport property and the equivalence ratio. There is a local maximum at stoichiometric conditions. For H2, the local maximum also is the overall maximum for a wide range of equivalence ratios. For CH4, there is a rapid increase in the thermal conductivity at very fuel-rich conditions (high equivalence ratios), with the conductivity exceeding the local maximum value at stoichiometric conditions. Although not as dramatic, there is a similar phenomenon for C3H8. Although most industrial processes are run at slightly fuel-lean conditions, there is still a rapid change in thermal conductivity on the fuel-lean side of stoichiometric conditions.

A much simpler relationship exists between conductivity and combustion air-preheat temperature. The conductivity increases slightly faster than linearly as the preheat temperature increases. Also, the thermal conductivity increases much more rapidly as the H2 content in the H2/CH4 fuel blend increases.

Viscosity – The absolute or dynamic viscosity is a measure of momentum diffusion. Gas viscosity is having a similar relationship to the thermal conductivity. The viscosity is important in calculating both the Pr and Re numbers, but in opposite ways. As the gas viscosity increases (decreases), the Pr number increases (decreases) and the Re number decreases (increases) assuming that all the other variables are constant. The kinematic viscosity is related to the dynamic viscosity.

There is a nearly linear increase in gas viscosity with the exhaust product temperature. The gas viscosity increases as the O2 content in the oxidizer increases, similar to the adiabatic flame temperature. The gas viscosity peaks at an equivalence ratio of 1.0 (stoichiometric conditions) and declines as the mixture becomes either more fuel rich or more fuel lean. The gas viscosity also increases with the air preheat temperature, comparable to the flame temperature. The viscosity increases as the H2 content increases in an H2/CH4 fuel blend. The increase in the viscosity is more rapid at higher H2 contents.

Pr number – The Pr number is frequently used to calculate the convection heat transfer coefficient. The components of Pr include the specific heat, viscosity, and thermal conductivity. The combination of these variables which forms the Pr number changes as functions of the fuel and oxidizer compositions, the mixing ratio, and the air preheat temperature. However, there is little change in Pr number as a function of the fuel preheat-temperature. The Pr number decreases as a function of temperature, but in a non-uniform way. Initially, it decreases moderately quickly, then decreases more slowly, and finally decreases rapidly at higher temperatures.

There is also a highly nonlinear relationship between the Pr number and the oxidizer composition. For CH4 and C3H8, the Pr number decreases rapidly at first and then levels off at higher O2 contents. For H2, the Pr number actually has a minimum at around 50 % O2 content. Also, a highly nonlinear relationship exists between the Pr number and the equivalence ratio. Most of the fuels show local maximum and minimum. The Pr number also declines almost linearly with the air preheat temperature. The Pr number declines as the H2 content in an H2/CH4 fuel blend decreases, and decreases rapidly at high H2 contents.

Lewis number – The Lewis number (Le) is the ratio of the thermal diffusivity to the molecular (mass) diffusivity. The Le number is important for the heat transfer in combustion systems. In general, for Le values greater than 1, there are some enhancements in convective heat transfer due to chemical recombination reactions. The Le number is 1 for temperatures below 1200 deg C, depending on the fuel, and then rises fairly rapidly at higher temperatures. The Le number is greater than one for all oxidizer compositions under adiabatic equilibrium conditions, which equates to the highest flame temperature possible for those conditions. The values of Le number peaks at intermediate oxidizer compositions and declines at higher O2 contents. There is a dramatic peak in the Le number at stoichiometric conditions, with the Le number going below 1.0 at higher equivalence ratios. The Le number increases almost linearly with the air preheat temperature for adiabatic equilibrium conditions. It increases more rapidly as the H2 content in a fuel blend of H2/CH4 increases.

Heat transfer in a furnace

Factors affecting the heat transfer in a furnace to the furnace charge are described below.

Flow of heat within the furnace charge – In case of an electrically heated furnace charge where the charge is used as a resistance in a circuit or by induction heating, the flux lines concentrate just inside the surface. In a fuel-fired heating process, heat enters the charge through its surface (by radiation or by convection) and diffuses throughout the charge by conduction. This heat flow requires a difference in temperature within the charge. Steady heat flows through a flat furnace charge. For other than flat charge, heat flux lines are seldom parallel and rarely steady. In transient heat flow, determination of the temperature at a given time and point within the charge necessitates use of the finite element method. Increasing the furnace temperature (a high ‘thermal head’) or ‘high-speed heating’ often results in non-uniform heating, which necessitates a longer soak time, sometimes defeating the purpose of high-speed heating.

Thermal conductivity and diffusion – There is normally wide variation in thermal conductivities of various metals, which has a direct bearing on the ability of heat to flow through or diffuse throughout them, and hence has a very strong effect on temperature distribution or uniformity in solids. The factor which affects temperature distribution is the thermal diffusivity. It is thermal conductivity divided by the volume specific heat of the solid material and is represented by the equation thermal diffusivity = thermal conductivity/ (specific heat x density). In this equation, the numerator is a measure of the rate of heat flow into a unit volume of the material while the denominator is a measure of the amount of heat absorbed by that unit volume. With a higher ratio of numerator to denominator, heat gets conducted into, distributed through, and absorbed.

Thermal conductivities and diffusivities of solids vary greatly with temperature. Specific heats and densities vary little, except for steels at their phase transition point. The thermal conductivities of solid pure metals drop with increasing temperature, but the conductivities of solid alloys generally rise with temperature.

Lag time – The effect of thermal conductivity on heat flow and internal temperature distribution is shown in Fig 1 for three same-size slabs of ferrous alloys heated from two sides. The surface temperatures in all the three cases generally rise very quickly, but the interior temperatures of rise differentially because of their poorer diffusivities. The slabs take different time to come to the equilibrium condition with the furnace temperature.

Fig 1 Effect of thermal conductivity on heat flow and internal temperature distribution

Solid materials which are heated in industrial furnaces are not necessarily continuous. Many times, the charge consists of coiled strip material or separate pieces piled to various depths or close side by side. In such cases, heat only can flow from one piece to the adjacent piece through small contact points on their surfaces, or through gas filled spaces, the thermal conductivity of which is very small. A stack of flat plates is an example of very low conductance. Even very small gaps constitute a big thermal resistance than solid metal. A stack cannot be treated as a solid, since thin air spaces are insulators. The differing air gaps in a stack result in bad non-uniformities in temperatures.

Rapid heat flow in each piece of a piled charge is obtained only by circulation of hot gases through the piled material by convection and gas radiation. These gas masses are to be constantly replaced with new hot gas since they have low mass, low specific heat, and thin gas beam thickness, so they cool quickly without delivering much heat to the loads. For uniform heating and precise reproducibility, piling of pieces of materials are to be avoided.

Heat transfer to the surface of the furnace charge – In furnace practice, heat is transferred by three modes namely (i) conduction, (ii) convection, and (iii) radiation. There are some essentials of heat transfer which are helpful to designers and operators of industrial furnaces. Most industrial furnaces, ovens, kilns, incinerators, boilers, and heaters use combustion of fuels as their heat source. Combustion, as used in industrial furnaces, comes from rapid and large chemical reaction kinetics and this result into conversion of chemical energy to sensible heat (thermal) energy. Increasing fuel and oxidizer (usually air) mixing surface area or increasing temperature of the reactants can cause faster combustion reactions, usually resulting in higher heat source temperatures. Fuel oxidation reactions are exothermic, so they can develop into a runaway condition (e.g. thermal energy being released faster than it can be carried away by heat transfer). This positive feedback can cause an explosion.

A flame is a thin region of rapid exothermic chemical reaction. An example is a Bunsen burner flame. In a Bunsen burner, a thoroughly premixed laminar stream of fuel gas and air is ignited by an external heat source, and a cone-shaped reaction zone (flame front) forms. Turbulence increases the thickness and surface area of the reaction zone, resulting in higher burning velocity. Laminar burning velocity for natural gas is around 18 metres per minute (mpm) while the turbulent burning velocity can be two to ten times faster. In a laminar flame, thermal expansion from chemical heat release can combine with increased reactivity caused by higher temperatures, resulting in acceleration to a turbulent flame. Except for long luminous flames, most industrial flames are turbulent.

Conduction heat transfer – Conduction heat transfer is molecule-to-molecule transfer of vibrating energy, usually within solids. Heat transfer solely by conduction to the charged load is rare in industrial furnaces. It occurs when cold metal is laid on a hot hearth. It also occurs, for a short time, when a piece of metal is submerged in a salt bath or a bath of liquid metal.

If two pieces of solid material are in thorough contact (not separated by a layer of scale, air, or other fluid), the contacting surfaces instantly assume an identical temperature somewhere between the temperatures of the contacting bodies. The temperature gradients within the contacting materials are inversely proportional to their conductivities (Fig 2).

Fig 2 Effect of conductivity and time on temperature gradients in two solids of different temperatures and conductivities, in firm contact with one another

The heat flux (rate of heat flow per unit area) depends not only on the temperatures of the two solids but also on the diffusivities and configurations of the contacting solids. In practice, comparatively little heat is transferred to (or abstracted from) a charge by conduction, except in the flow of heat from a billet to water-cooled skids.

When a piece of cold metal is suddenly immersed in liquid salt, lead, zinc, or any other liquid metal, the liquid freezes on the surface of the cold metal, and heat is transferred by conduction only. After a very short time, the solid jacket, or frozen layer, remelts. From that time on, heat is transferred by conduction and convection.

Convection heat transfer

Convection heat transfer is a combination of conduction and fluid motion, physically carrying heated (or cooled) molecules to another surface. If a stream of gaseous fluid flows parallel to the surface of the solid, the vibrating molecules of the stream transfer some thermal energy to or from the solid surface.

A ‘boundary layer’ of stagnant, viscous, poorly conducting fluid tends to cling to the solid surface and acts as an insulating blanket, reducing heat flow. Heat is transferred through the stagnant layers by conduction. If the main stream fluid velocity is increased, it scrubs the insulating boundary layer thinner, increasing the convection heat transfer rate. The conductance of the boundary layer (film coefficient) is a function of mass velocity (momentum, Re number).

In furnaces which operate below 600 deg C, heat transfer by convection is of major importance since radiation is weak there. Modern high-velocity (high-momentum) burners give high convection heat transfer coefficients. High velocities often provide more uniform temperature distribution around a single piece charge, or among multiple piece charges, since more mass flow carries additional sensible heat at more moderate temperatures. At low furnace temperatures, high rates of total heat transfer can be obtained only by high gas velocities since heat transfer by radiation at around 550 deg C is less than one-tenth of what it is at around 1200 deg C. High-velocity (high momentum) burners are widely used to fill in where radiation cannot reach because of shadow problems.

Radiation heat transfer

Radiation between solids – Heat is radiated by solids even at low temperatures. The net radiant heat actually transferred to a receiver is the difference between radiant heat received from a source and the radiant heat re-emitted from the receiver to the source. The net radiant heat flux between a hot body (heat source) and a cooler body (heat receiver) can be calculated by Stefan-Boltzmann equations.

Emissivity and absorptivity of materials are important properties for radiation between solids. Emissivity is the radiant heat emitted (radiated) by a surface, expressed as a decimal of the highest possible (black body) heat emission in a unit time and from a unit area. Emittance is the apparent emissivity of the same material for a unit area of apparent surface which is actually much greater, due to roughness, grooving, and so on. Absorptivity is the radiant heat absorbed by a surface per unit time and unit area, expressed as a decimal of the most possible (black body) heat absorption.

Engineers use emissivity value of 0.85 in conventional refractory lined furnaces. However, the temperature, surface condition, and alloy can make considerable difference. As an example, if stainless-steel strip is heated in less than three minutes in a catenary furnace, the emissivity may not change even though the temperature increases from ambient to 1100 deg C. By measuring both strip surface temperature and furnace temperature, it has been possible to revise heating curve calculations, assuming that oxidation has not changed the emissivity or absorptivity during the heating cycle.

Radiation from clear flames and gases – There are two origins of radiation from the products of combustion to solids. The two origins of radiation are (i) from clear flame and from gases, and (ii) from the micron-sized soot particles in luminous flame. Radiation from clear gas does not follow the Stefan-Boltzmann fourth-power law. The only clear gases which emit or absorb radiation appreciably are those having three or more atoms per molecule (triatomic gases) such as CO2, H2O, and SO2 (sulphur di-oxide). An exception is diatomic CO, which gives off less radiation. The other diatomic gases, such as O2, N2 (and their mixture, air), and H2 have only negligible radiating power.

Gaseous radiation does not follow the fourth-power law since gases do not radiate in all wavelengths, as do solids (gray bodies). Each gas radiates only in a few narrow bands. Radiation from clear gases depends on their temperature, on the partial pressure or percent volume of each triatomic gas present, and on the thickness of their gas layer.

The temperature of a radiating gas gets lower in the direction of gas travel. To maintain active gas radiation, the gas is to be continually replaced by new hot gas, which also improves convection. Higher gas feed velocities reduce the temperature drop along the gas path. This factor is very critical in maintaining good temperature uniformity in high temperature industrial furnaces.

The furnaces are often designed on the basis of refractory radiation heating the charge, with usually reasonable results, but some situations cannot be explained by refractory radiation alone. Direct radiation from furnace gases generally delivers 62 % (+/- 2 %) of the heat to the charge, and refractories transfer the remaining 38 % (+/- 2 %). Gas temperatures needed to transfer the heat to refractory and charge are generally much higher than generally assumed.

Radiation from luminous flames – If a fuel-rich portion of an air/fuel mixture is exposed to heat, as from a hotter part of the flame, the unburned fuel molecules polymerize or suffer thermal cracking, resulting in formation of some heavy, solid molecules. These soot particles glow when hot, providing luminosity, which boosts the flame’s total radiating ability.

If fuel and air are not thoroughly mixed promptly after they leave the burner nozzle, they can be heated to a temperature at which the hydrocarbons crack (polymerize). Further heating brings the resulting particles to a glowing temperature. As O2 mixes with them, they burn. As the flame proceeds, formation of new soot particles can equal the rate of combustion of previously formed particles. Farther along the flame length, soot production diminishes, and all remaining soot is incinerated. This series of delayed-mixing combustion processes are to be completed before the combustion gases pass into the flue. If the flame is still luminous at the flue entry, smoke can appear at the stack exit. Smoke is soot that has been cooled (chilled, quenched) below its minimum ignition temperature before being mixed with adequate air.

The added radiating capability of luminous flames causes them to naturally cool themselves faster than clear flames. This is performing their purpose—delivering heat. The cooling phenomenon can negate some of the gain from the higher luminosity (effective emissivity).

Luminous flames often have been chosen because the added length of the delayed mixing luminous flames can produce a more even temperature distribution throughout large combustion chambers. As industrial furnaces are supplied with very high combustion air preheat or more oxy-fuel firing, luminous flames can enable increases in heat release rates.

Fuels with high C/H2 ratios (most oils and solid fuels) are more likely to burn with luminous flames. Fuels with low C/H2 ratios (mostly gaseous fuels) can be made to burn with luminous flames namely (i) by delayed mixing, injecting equally low-velocity air and gas streams side-by-side, and (ii) by using high pressure to ‘shoot’ a high-velocity core of fuel through slower moving air so that the bulk of the air cannot ‘catch up’ with the fuel until after the fuel has been heated (and polymerized) by the thin ‘sleeve’ of flame annular interface between the two streams.

Flames from solid fuels can contain ash particles, which can glow, adding to the flame’s luminosity. With liquid and gaseous fuels, flame luminosity usually comes from glowing C and soot particles. The effective flame emissivity, as measured is usually between that of the POC gases and a maximum value of 0.95, depending on the total surface area of solid particles. Normally, heat transfer from a luminous flame is greater than that from a clear flame having the same temperature. The difference in the rate of heat transfer is quite noticeable in furnaces for reheating steel and metals. The difference becomes more pronounced at high temperature, where the radiating power of each triatomic gas molecule increases, but the gain is partially canceled by the decreasing density of radiating molecules per unit volume.

In another phenomenon, the bands of gaseous radiation hold their wavelengths regardless of temperature. At higher temperatures, however, the area of high intensity of solid radiation (glowing soot and C particles) moves toward shorter wavelengths (away from the gas bands). In higher temperature realms, radiation from clear gases does not increase as rapidly as radiation from luminous flames.

Flame radiation is a function of many variables such as C/H2 ratio of the fuel, air/fuel ratio, air and fuel temperatures, mixing and atomization of the fuel, and thickness of the flame. Some of these can change with distance from the burner. Fuels with higher C/H2 ratio, such as oils, tend to make more soot, so they usually create luminous flames, although blue flames are possible with light oils. Many gases have a low C/H2 ratio, and tend to burn clear or blue. It is difficult to burn tar without luminosity. It is equally difficult to produce a visible flame with blast furnace (BF) gas or with H2.

When comparing luminous and nonluminous flames, it is important to remember (i) soot radiation (luminous) usually ends where visible flame ends because soot is most often incinerated at the outer surface or skin of the flame, where it meets secondary or tertiary air, and (ii) gas radiation (nonluminous) occurs from both inside and outside the visible flame envelope, greatly increasing the uniformity and extent of its coverage, although gas radiation within the flame is somewhat shadowed by any surrounding soot particles or triatomic gases, and gas radiation outside the flame can be from cooler gases.

The effect of excess fuel on flame radiation is considerably greater than the effect of less excess air. The merits and demerits of clear flames versus long luminous flames have been debated for years. Modified burners and control schemes are helping to utilize the best of both. A problem common to several burner types is change of the flame characteristic as the burner input is turned down. Problems with some clear flame burners are (i) movement of the hump in the temperature profile closer to the burner wall as the firing rate is reduced, and (ii) at lower input rates, temperature falls off more steeply at greater distances from the burner wall (e.g., the temperature profile of a burner firing at 50 % of its rated capacity or below is at its peak temperature (maximum heat release at or near the burner wall, falling off further from the burner wall). At lower firing rates, the temperature drop off gets worse. At higher firing rates, the burner wall temperature decreases as the peak temperature moves away from it. In some steel reheating furnaces at maximum firing rate, the temperature difference between the burner wall and the peak can be 150 deg C.

The problem of a temperature peak at the far wall during high fire is aggravated by spur of furnace gases into the base of the flame, delaying mixing of fuel with O2. If the burner firing rate is increased, the spur of the products of complete combustion increases exponentially. Resulting problems are many. When side-firing a furnace at low firing rate, the peak temperature is at the burner wall, but at maximum firing rate, the peak temperature can be at the furnace centre or the opposite wall. Thus, the location of a single temperature control sensor is never correct. If the temperature sensor is in the burner wall, low firing rates have peak temperature hugging the furnace wall and driving the burner to low fire rate resulting into the rest of the furnace width receiving inadequate input. At high firing rates, a sensor in the burner wall is cool while the temperature away from the burner wall is very high, perhaps forming liquid scale on the surfaces of the charge pieces at the centre and/or far wall. To remedy this issue, inexperienced operators can lower the set point, reducing the furnace heating capacity.

Another example of the effect of the problem occurs with the bottom zone of a steel reheating furnace when fired longitudinally counter flow to the load movement, and with the control sensor installed 3 metre (m) to 6 m from the (end-fired) burner wall. At low-firing rates, with the zone temperature set at 1300 deg C, the burner wall can rise to higher than 1370 deg C. At that temperature, scale melts and drips to the floor of the bottom zone where it can later solidify as one big piece. At high firing rates, the peak temperature can move beyond the bottom zone T-sensor, possibly melting scale some distance toward the charge end of the furnace. Again, to avoid the problem, operators can lower temperature control settings, reducing the furnace capacity.

Control of the aforementioned problems requires an additional temperature sensor in each zone and a means for changing the mixing rate characteristic of the burner in response to the temperature measurements. Burners with adjustable spin (swirl) can be set to prevent much of the problem, especially if combined with a low-fire, forward-flow gas or air jet through the center of the burner. Such a jet is typically sized for 5 % of maximum gas or air flow.

Long, luminous flames, either laminar type or turbulent type, tend to have much less temperature hump and do not change length as rapidly when input is reduced. They can be great ‘levelers’, providing better temperature uniformity.

This information on in-flame soot radiation and triatomic gas radiation has been known for some time, but recent developments may be changing the picture. Use of oxy-fuel (100 % O2), both of which elevate flame turndown. The major gain from oxy-fuel firing is from more intense radiation heat transfer because of the higher concentration of triatomic gases, due to the elimination of N2 from the POC. This also decreases the mass of gas carrying heat out the flue (reducing stack loss). In another development, some lean premix gas flames (designed for low NOx emissions) make a ubiquitous flame field (seemingly transparent) through much of the chamber.

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