Technical Field

The rapidly growing global need for efficient energy-use and concerns over the environmental impacts of fossil-fuel-based energy call for innovative technologies to provide fast, reliable and inexpensive monitoring tools that enable accurate measurements of the indoor air quality, hazardous leaks in hospitals and factories, as well as the gas emissions from mechanical power systems, such as industrial furnaces and fire-tube boilers. Flue gas analyzers are measurement instruments that can detect and characterize the composition of gas emissions produced during the combustion processes of fossil fuels. These devices further allow the specification of the corresponding air-to-fuel ratios and the determination of whether they fall within the proper limits for maximum heat output and optimal combustion. A typical flue gas essentially contains carbon dioxide (CO ₂ ), carbon monoxide (CO), oxygen (O ₂ ) and nitrogen (N ₂ ), besides minor traces of unburned Hydrocarbons (HCs), nitrogen oxides (NO _x ) and sulfur dioxide

(SO ₂ ).

Background Art

Most of the current flue gas analyzers rely in their principles of operations on the application of either the electrochemical sensors or the non-dispersive infrared (NDIR) sensors.

Electrochemical devices are however based on the oxidation of a target gas at a certain electrode, which results in the circulation of an electric current, within the electrode cell, in proportion with the percent of gas concentration. These sensors are generally compact, consume lesser amount of energy and possess good sensitivity and relatively fast response. However, they suffer from remarkable drift effects besides low overall lifetimes. In contrary with the electrochemical devices, NDIR sensors are spectroscopic sensors that are often used to measure the concentration of carbon monoxide in a certain gas mixture through the calibration of its characteristic absorption of particular wavelengths in response to an emitted infrared light. Although reliable and stable, these infrared sensors are rather expensive, necessitate frequent calibration and their usage is mostly limited to heating, ventilation and air-conditioning applications besides the internal combustion engines.

Few other interesting electro-acoustical gas analyzers were presented by Garrett and Brooks and their collaborators that considered samples of binary (He-Ne) and pseudo-binary gas mixtures (Air-Helium) within either cylindrical or spherical acoustic resonators. In their experiments, the gas concentration was correlated to the relative change in the measured speed of sound. Latter, Polturak et al. were able to build and test a 5-cm-long cylindrical resonator that enabled the determination of the composition of two specific binary-gas mixtures (O ₂ -N ₂ and H ₂ - ⁴ He) through precise measurements of the corresponding resonant frequencies. They further elaborated on the parameters affecting the system performance while reporting an absolute accuracy better than 0.1%. Recently, Yu et al constructed a high-precision acoustic resonator with a remarkable Q- fector of 230 and successfully measured the dependence of the resonance frequency of the ⁴ He-N ₂ gas mixtures on the respective concentrations.

Disclosure of the Invention

The present invention is a fluc-gas analyzer that relies in its operation on the thcrmoacoustic technology. Nowadays, low-GWP thermoacoustic engines are becoming much more reliable and offer attractive and promising path to convert available waste heat at modest temperatures into acoustic power to generate electricity at relatively high efficiency and low cost. These systems are designed to be thermo-acoustical ly unstable such that spontaneous thermofluid interactions between the operating gas and the solid walls of a porous media, referred to as the stack, are taking place within an acoustic, mostly cylindrical, resonator.

The present standing-wave thcrmoacoustic flue-gas analyzer enables the detection of the four main flue-gas components; namely, the CO ₂ , the CO, the O ₂ and the N ₂ gases, typically produced in different fossil-fuel combustion processes. The present device particularly allows for the determination of the combustion efficiencies in many industrial applications through accurate specification of the different gas concentrations while building on the basic principles of thermoacoustics and exploiting the state-of-the-art knowledge of thermoacoustic technology. This new sensor offers a simple, reliable and relatively inexpensive alternative to existing flue-gas analyzers, that helps assess the thermal performance of different fossil-fuel-based energy systems.

In a typical standing-wave thcrmoacoustic engine, heat is added from a high-temperature source and is rejected to a low-temperature sink to generate acoustic power that is equivalent to the net amount of heat added to the system following a thermodynamic cycle similar to that of Brayton engines. In its simplest form, a standing-wave thermoacoustic engine mainly consists of a cylindrical duct 'resonator' that is filled with the working gas. A porous ceramic material 'stack' is carefully positioned within the resonator, as sketched in Fig. 1 , while being heated from one side using an electric heater or preferably a waste-heat source and cooled from the other side through a cold heat exchanger. This helps maintain a nearly uniform temperature gradient along the stack plates.

The stack porosity in a standing-wave engine is consistently chosen such that the spacing between the stack solid walls is approximately 3-4 times the gas thermal penetration depth where a and ω represent the gas thermal diffuisivity and the angular frequency, respectively. While interacting thermally with the stack walls, the temperature gradient of the gas particles within the stack increases gradually till reaching a certain specific limit known as the critical 'onset' temperature gradient ΔT _crit at which the system becomes thermo-acoustical ly unstable and gas-particles oscillations are encouraged inside the resonator.

In contrary with typical thermoncoustic engines, the present resonator is assumed to be filled with a dry mixture of exhaust gases, which are produced -for instance, from water tube boilers- at steam power plants and contain the four main combustion products, namely the O ₂ , N ₂ , CO ₂ and CO gases with negligible traces of nitrogen and sulfur oxides. The gas mixture has a temperature T _H that falls in the range from 500 to 900 degrees Celsius based on the particular application. Hereby, the critical temperature gradient ΔT _crit becomes a function of the effective specific heat ratio γ _mix for the flue gas mixture.

To further proceed, the introduced exhaust gases are allowed to reject their heal content into ambient within the cold duct of the acoustic resonator through the cold heat exchanger sketched in Fig. 1 while the hot duct is insulated to help maintain the initial gas temperature together with the heating coil. The temperature difference between the stack ends increases gradually upon cooling its cold end. It is not until nearly all gas particles within the stack pores are subjected to the critical temperature gradient of Eq. 2, that consistent and continuous oscillations of the gas particles are evident. In addition, the generated acoustic wave has a well-defined fundamental resonant frequency ƒ that varies with the resonator length L, the mean temperature of the entire resonator, the specific heat ratio γ _mix and the molecular weight M _mix of the flue-gas mixture. Here, the specific heat ratio is evaluated at the mean temperature.

Obviously, the usefulness of the present technique for flue-gas analysis depends on the accuracy with which the onset temperature difference between the stack ends and the resonant frequency ƒ of the self-sustainable acoustic oscillations can be determined.

In the design process of the present thermoacoustic flue-gas analyzer, the engine is constrained to operate at low ranges of onset-temperature-difference to help reduce the non-trivial cooling load. However, the preliminary analysis reveals a trade-off between and the engine sensitivity with respect to different flue-gas mixtures. An optimized short stack length (L _s /L = 0.05) is considered to help reduce the viscous losses within the stack solid walls, as consistent with the above theoretical analysis. The selected configuration with L _s /L = 0.05 and x/L = 0.55 has a moderate range of operating onset-temperature-difference together with a corresponding reasonable temperature span of approximately 24 degrees.

Using the determined engine geometry and for L=1m, the above analysis can now be reversed to solve for the flue-gas concentrations assuming knowledge of both operating onsel- tempcrature-difference and resonant frequency. For that purpose, the above equations are solved simultaneously to solve for the unknown mole fractions, namely the and Here, both nitrogen and CO concentrations are initially joined together to form a single component having a specific heat ratio similar to that of pure nitrogen; recalling that both gases have equal molecular weights (≈28 g/gmol). Nevertheless, one extra equation is still required for complete and accurate characterization of the four main flue-gas components, as shall be carefully treated in the following section. For instance, a preliminary estimate can be obtained that enables the determination of the relative importance of both oxygen and carbon dioxide within arbitrary gas mixtures at different operating conditions, as illustrated in the ternary diagrams of Figs. 2 and 3.

The resulting ternary plot shown in Fig. 2 is generic in the sense that it imposes no limits on either or The three axes are clearly extended to include up to 100% of the respective mole fractions using an incremental step of 1% along each axis. However, in this particular flue- gas analyzer, the relative concentrations of the exhausted combustion products are rather limited because of the introduced air-to-fuel ratio. This restricts the CO ₂ -content in flue-gas mixtures mostly to less than 25%, as indicated by the gray-shaded area in Fig. 3. Note that as the carbon content in the fuel to be burnt decreases, the region of possible flue-gas mixtures shrinks, which may affect the sensitivity of the analyzer. Therefore, the present ternary diagram can be employed for general artificial gas mixtures having arbitrary CO ₂ concentration as well as particular fluc-gas mixtures with limited CO ₂ content.

For further distinction between the relative concentrations of both CO and N ₂ , additional information about the type of fuel to be burnt is necessary. Bridging the gap with the combustion science, the combustion equation -along with its mass balance equations- of the known specific hydrocarbon fuel to be burnt shall provide the remaining information. Here, the corresponding balance equations, such as that of the carbon αn = are solved iteratively to allow for accurate determination of the apparent concentrations of both CO and N ₂ . in addition, the molar air-to-fuel ratio β/α can then be straightforwardly estimated.

Furthermore, the analyzer sensitivity associated with the application of the 'low-carbon' natural gas (CH ₄ ) is carefully investigated assuming dry gas analysis at T _H = 900°C. In addition, this fuel is frequently used in power generation. In the present analysis, the flue-gas composition resulting from an ideal 'stoichiometric' combustion process, which has enough oxygen to burn all the fuel, is chosen as the reference point in the corresponding ternary diagram, shown in Fig. 4. Such flue-gas mixture is free from both O ₂ and CO contents, but has approximately 11.74% CO ₂ and 88.26% N ₂ . To further demonstrate the usefulness of the present analyzer, two particular paths, indicated by red and blue dotted lines, are chosen for sensitivity analysis. With reference to the stoichiometric condition, the introduced air-fuel mixtures along the red path become progressively richer such that they have insufficient oxygen to bum all the fuel. However, moving along the blue path, the air-fuel mixtures become increasingly leaner with a rather abundant oxygen.

The present calculations indicate that the combustion of rich mixtures produce a continuous increase in χ _CO along with a consistent decrease in whereas, the concentration results for lean mixtures show a rapid increase in along with a faster drop in as shown in Figs. 5 and 6. The figures also illustrate the potential domains of gas concentrations for either CO ₂ , CO or O ₂ as comprised between the respective rich-mixture (red) and lean-mixture (blue) concentration results. Approximately, the onset temperature difference ranges from 168 to 179.5°C, while the resonant frequency ranges from 317 to 326Hz.

In practical situations of flue-gas analysis, reported χ _CO values are mostly ≤5%, which consequently limits the corresponding domains of interest of CO ₂ and O ₂ , as gray-shaded in Figs. 5 and 6. The figures also show how sensitive the concentrations of different gases are to the induced ΔT _crit and ƒ, respectively, considering CH ₄ . For instance, with the onset-temperature-diffcrence being held constant at 175°C, the present analysis reveals relative increases In both and χ _CO at respective rates of 0.6% and 4%, against a relative decrease in at a rate of 6.7%, per unit shift in ƒ. In contrary, with the frequency being held constant at 320Hz, the results show consistent decreases in both and χ _CO at corresponding rates of 1.9% and 2.2%, respectively, against a relative increase in at a rate of 6.4% per unit shift in ΔT _crit .

Brief Description of the Drawing

Figure (1) represents a schematic drawing of the standing-wave thermoaco.uslic flue-gas analyzer.

Number (1) in Fig.1 represents the body of the device, a tube made of stainless steel with both ends closed and sealed.

Number (2) in Fig.1 represents a stack of thermally non-conducting porous media. Number (3) in Fig.1 represents an electric heater that maintains the stack hot-end temperature.

Number (4) in Fig.] represents a cooling coil that cools the stack cold end.

Number (5) in Fig.1 represents a sealed nut to keep the device closed.

Number (6) in Fig.1 represents a controlled inlet valve to allow for introducing the hot flue gas sample.

Number (7) in Fig.1 represents a filler at the inlet passage to filter the introduced hot flue gas sample.

Number (8) in Fig.1 represents a check valve to prevent the return of air to the analyzer. Number (9) in Fig.1 represents a vacuum pump to pull the air from the tube and allow for sucking a pure flue gas sample.

Number (10) in Fig.1 represents two thermocouples to measure the temperatures of the hot and cold ends of the stack.

Number (11) in Fig.1 represents a pressure sensor to measure the gas-particle oscillations of the generated acoustic wave.

Numbers (12) and (13) in Fig.1 represent an amplifier and DAQ to process the wave frequency, and stack ends temperatures signals.

Number (14) in Fig.1 represents a display to show the molar concentrations of the quaternary-gas components (CO ₂ , CO, O ₂ , and N ₂ ) of the introduced samples.

Figure (2) represents a ternary diagram that helps determine the relative concentrations of CO ₂ , O ₂ , and the combined concentration of CO and N ₂ within arbitrary gas mixtures following the intersections of both ƒ (solid) and ΔT _crit (dashed) lines. The gray area in the bottom-right corner refers to the ranges of typical flue-gas compositions.

Figure (3) represents an enlarged figure of the gray area in the bottom-right comer in Fig. 1 that refers to the expected operational conditions of the proposed thermoacoustic flue-gas analyzer.

Figure (4) represents the ranges of typical flue-gas compositions in case of using natural gas (CH ₄ ) in combustion. The black dots refer to mole fractions of flue-gas species resulting from complete combustion. The red path follows the gas compositions resulting from the richest air-fuel mixtures while the blue path corresponds to the leanest air-fuel mixtures (χ _CO =0%).

Figure (5) represents the variations in different gas concentrations with ΔT _crit for CH ₄ at T _H = 900°C. Symbols: The open circles represent the open squares refer to χ _CO , whereas the crosses correspond to

Figure (6) represents the variations in different gas concentrations with ƒ for CH ₄ at T _H = 900°C. Symbols: The open circles represent the open squares refer to χ _CO , whereas the crosses correspond to