Patent Publication Number: US-2018038589-A1

Title: Flame holders with fuel and oxidant recirculation, combustion systems including such flame holders, and related methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage Entry under 35 U.S.C. 371 of International Application No. PCT/US2015/000219 filed on 23 Dec. 2015, which claims priority to U.S. Provisional Application No. 62/096,612 filed on 24 Dec. 2014, the disclosures of which are incorporated herein, in their entirety, by this reference. 
    
    
     BACKGROUND 
     Flame stabilization can be dependent upon a speed at which a fuel-air mixture enters a flame holder where propagation of a flame is desired. For example, fuel injection at high speed toward a flame holder may contribute to or cause instabilities in flame position and shape of a flame. 
     High fuel injection speeds can result in non-uniform fuel distribution, insufficient mixing of the fuel with an oxidant, and unstable flame propagation within the flame holder, which can cause such problems such as poor combustion (e.g., a low percentage of the fuel oxidant mixture is combusted), failure to combust leaner fuels (e.g., low fuel to oxidant mixture), increased emissions of pollutants, combustion outside of the flame holder, poor heat transfer, reduced component life, and potential system damages among others. Additionally, fuel injection at low speeds into the flame holder may cause a flashback that can damage structures within the fuel-oxidant mixing region of the combustion system. 
     Therefore, developers and users of combustion systems continue to seek improvements to the flame holders. 
     SUMMARY 
     Embodiments disclosed herein include flame holders that can provide fuel and oxidant recirculation, combustion systems that include such flame holders, and related methods. A fuel and/or fuel-oxidant mixture may pass through one or more openings in a flame holder and, after combustion, the resulting flame may be held inside the flame holder and/or at or near a surface of the flame holder. Generally, the configuration of the flame holders disclosed herein (e.g., the one or more openings of the flame holders) may recirculate and/or regulate (e.g., decrease and/or increase) the flow of fuel and/or oxidant therethrough, at least limit flame flashback, improve fuel/oxidant mixing, increase flame stability, regulate where the flame is located in the flame holder, improve the operational stability window of the combustion system, or combinations of the foregoing. The openings may be shaped to promote vortex formation in the fuel, oxidant, and flame; with the vortex or vortices providing the recirculation. 
     In an embodiment, a flame holder is disclosed. The flame holder includes a refractory body defining a proximal side, a distal side spaced downstream from the proximal side, and a plurality of openings extending therethrough. Each of the plurality of openings extends between an inlet on the proximal side and an outlet on the distal side. The inlet has a first area in plan view. Each of the plurality of openings includes a bulging region located downstream from the inlet thereof. The bulging region has a second area in plan view that is greater than the first area. 
     In an embodiment, a combustion system is disclosed. The combustion system includes a flame holder. The flame holder includes a refractory body defining a plurality of openings therein. Each of the plurality openings includes an inlet and a bulging region located downstream from the inlet. The flame holder also includes one or more nozzles configured to dispense fuel toward the flame holder and into the plurality of openings thereof. The flame holder further includes one or more flame holder supports supporting the flame holder above the one or more nozzles to define a standoff between the one or more nozzles and the flame holder. 
     In an embodiment, a method of operating a combustion system is disclosed. The method includes dispensing fuel from one or more nozzles toward inlets of a plurality of openings of a flame holder and further toward outlets of the plurality of openings of the flame holder. The method also includes decreasing a velocity of the fuel as the fuel passes through at least a portion of the plurality of openings. Finally, the method includes igniting at least a portion of the fuel in the flame holder. 
     Features from any of the disclosed embodiments may be used in combination with one another, without limitation. In addition, other features and advantages of the present disclosure will become apparent to those of ordinary skill in the art through consideration of the following detailed description and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings illustrate several embodiments, wherein identical reference numerals refer to identical or similar elements or features in different views or embodiments shown in the drawings. 
         FIG. 1A  is an isometric view of a combustion system according to an embodiment. 
         FIG. 1B  is an isometric cutaway view of the combustion system shown in  FIG. 1A  taken along plan  1 B- 1 B. 
         FIGS. 2A-2D  are partial cross-sectional views of flame holders having at least one opening therein, according to different embodiments. 
         FIG. 3  is an isometric cutaway view of a combustion system, according to an embodiment. 
         FIGS. 4A-4F  are partial cross-sectional views of flame holders, according to different embodiments. 
         FIG. 5  is a partial cross-sectional view of a flame holder defining an opening, according to an embodiment. 
         FIGS. 6A and 6B  are partially cross-sectional views of flame holders that include one or more mechanisms disposed in an opening thereof that increase mixing of a fuel/oxidant, according to an embodiment. 
         FIG. 7  is a partial cross-sectional view of a flame holder including a sleeve that is attachable to a refractory plate, according to an embodiment. 
         FIGS. 8A-8D  are top plan views of a distal side of flame holders, according to different embodiments. 
         FIG. 9  is a top plan view of a flame holder assembly that includes a plurality of flame holders, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments disclosed herein include flame holders that may provide fuel and oxidant recirculation, combustion systems that include such flame holders, and related methods. A fuel and/or fuel-oxidant mixture may pass through one or more openings in a flame holder and, after combustion, the resulting flame may be held at or near a surface of the flame holder including in the one or more openings. Generally, the configuration of the flame holders disclosed herein (e.g., the one or more openings of the flame holders) may recirculate and/or regulate (e.g., decrease and/or increase) the flow of fuel and/or oxidant therethrough, at least limit flame flashback, improve fuel/oxidant mixing, increase flame stability, regulate where the flame is located in the flame holder, improve the operational stability window of the combustion system, or combinations of the foregoing. The openings may be shaped to promote vortex formation in the fuel, oxidant, and flame; with the vortex or vortices providing the recirculation. 
     For example, openings of the flame holder may recirculate and/or regulate flow of the fuel, oxidant, fuel-oxidant mixture, or combinations thereof (any of which may be referred to as “fuel/oxidant” herein for convenience) flowing through the openings in the flame holder. In an embodiment, the flame holder may reduce the velocity of the fuel/oxidant flowing through the openings. For example, the flame holder may initially decrease the velocity of the fuel/oxidant flowing through the openings from a first location (e.g., the inlet  118  of  FIG. 1B , the narrowed region  576  of  FIG. 5 ) toward and/or to a second location (e.g., the outlet  120  of  FIG. 1B , the bulging region  322  of  FIG. 3 ). Subsequently, the flame holder may increase the velocity thereof as the fuel/oxidant from the second location (e.g., the bulging region  322  of  FIG. 3 ) flows towards and/or to an outlet of the openings in the flame holder. In some embodiments, the flame holder may cause the fuel and/or oxidant to initially exhibit a relatively high velocity at and/or near an inlet of the openings to thereby substantially prevent flashback. In some embodiments, the flame holder may cause the fuel/oxidant to form eddies or vortices therein that increase flame stability. In some embodiments, the flame holder may regulate a velocity of the fuel/oxidant therein, thereby regulating where flame is combusted in the flame holder. In some embodiments, the flame holder may trap the flame in the opening and/or improving the mixing of the fuel and/or oxidant. In some embodiments, regulating and/or modulating fuel/oxidant through the openings may improve flame stabilization, flame robustness, improve heating efficiency, reduce NO x  formation, improve mixing of fuel and oxidant, prevent flashback, or combinations of the foregoing. 
       FIGS. 1A and 1B  are isometric and isometric cutaway views, respectively, of a combustion system  100 , according to an embodiment. The combustion system  100  includes a flame holder  102  and one or more nozzles  106  spaced from and oriented toward the flame holder  102 . The flame holder  102  includes a plurality of openings  104  therein. The nozzles  106  may dispense a fuel/oxidant, which may generally flow toward the flame holder  102  and/or through the openings  104  of the flame holder  102 . 
     In an embodiment, the flame holder  102  may be supported above the nozzles  106  by one or more elements or components. For example, flame holder supports  108  and/or an optional burner tile  110  may support and/or secure the flame holder  102  at a suitable distance above the nozzles  106 . Generally, the burner tile  110  may encircle a combustion air passage  112  (e.g., the burner tile  110  may at least partially surround at least some of the nozzles  106 ). For instance, the burner tile  110  may have an approximately conical (e.g., a truncated cone) or cylindrical shape, and the encircled space of the burner tile  110  may define the combustion air passage  112 . It should be appreciated that the burner tile  110  may have any suitable shape (e.g., cross-sectional shape) and/or size, which may vary from one embodiment to the next. For example, the burner tile  110  may have a rectangular, square, triangular, irregular, or any other suitable cross-sectional shape. In some embodiments, the burner tile  110  is omitted. 
     Furthermore, the nozzles  106  may be positioned at any number of suitable locations and/or in any number of suitable arrangements, which may vary from one embodiment to the next. In some embodiments, one, some, or all of the nozzles  106  may be located in the combustion air passage  112 . Additionally or alternatively, one, some, or all of the nozzles  106  may be located outside of the combustion air passage  112  (e.g., arranged about the perimeter or periphery of the burner tile  110 ). 
     The nozzles  106  and the flame holder  102  may be arranged to provide at least partial premixing of the dispensed fuel with an oxidant (e.g., air or flue gas) in a premixing region between the nozzles  106  and the flame holder  102 . In one or more embodiments, the fuel and an oxidant may mix or at least partially mix in the combustion air passage  112 . For example, the fuel exiting nozzles  106  may mix with an oxidant in the combustion air passage  112 . As such, the fuel at least partially mixed with an oxidant may flow toward the flame holder  102  and/or into the openings  104  therein. The fuel/oxidant may be at least partially ignited (e.g., in the openings  104  of the flame holder  102  and/or above the flame holder  102 ). 
     In any event, as shown in  FIG. 1B , the nozzles  106  may be located near and/or inside the burner tile  110 . In an embodiment, the burner tile  110  may support an intermediate flame between the flame holder  102  and the nozzles  106  (e.g., between an upper surface  113  of the burner tile  110  and a proximal side  114  of the flame holder  102 ) to pre-heat the flame holder  102  prior to transfer of combustion to the flame holder  102 . For example, the upper surface  113  of the burner tile  110  may be configured to support the flame (not shown) during at least one of start-up, low fuel flow, or ignition by a pilot flame. 
     Generally, the flame holder  102  may include and/or be formed from any number of suitable high-temperature resistant materials, such as a refractory material as discussed in more detail below. Also, as described below in more detail, the flame holder  102  may have any suitable shape and/or size. For instance, a periphery or perimeter of the flame holder  102  may have a generally circular shape. Alternatively, the flame holder  102  may be, in plan view, generally rectangular, generally triangular, etc. 
     The flame holder  102  may be partially or completely formed from a refractory plate  115  or other type of refractory body. For example, the refractory plate  115  may define a proximal side  114  and a distal side  116  spaced downstream from the proximal side  114 . The refractory plate  115  may have generally a plate-like shape. For example, the proximal side  114  and/or the distal side  116  may be approximately planar. In alternative or additional embodiments, the proximal side  114  and/or the distal side  116  may be non-planar. In an embodiment, the proximal side  114  and the distal side  116  may be substantially parallel to each other. Alternatively, at least a portion of the proximal side  114  and at least a portion of the distal side  116  may have a non-parallel orientation relative to each other. 
     The proximal side  114  is closer to the nozzles  106  than the distal side  116 . The openings  104  may extend from and between the proximal side  114  and the distal side  116 . One, some, or each of the openings  104  may include an inlet  118  on the proximal side  114  and an outlet  120  on the distal side  116 . In other words, the fuel and/or fuel-oxidant mixture can enter the openings  104  at the inlets  118  thereof and exit at the outlets  120  thereof. 
     In some embodiments, the openings  104  may be configured to facilitate mixing of the fuel/oxidant therein (e.g., as the fuel/oxidant passes through the openings  104 ). As such, the openings  104  may improve combustion fuel/oxidant and/or stability of the flame produce during or after combustion. For example, one, some, or all of the openings  104  may be configured to initially decrease the velocity of the fuel/oxidant flowing through a portion of the openings  104 . Decreasing the velocity of the fuel/oxidant may increase the time the fuel/oxidant has to mix and may create turbulent flow. In an embodiment, one, some, or all of the openings  104  may include a bulging region  122  downstream from the inlet  118 , which has a larger area than the inlet  118  thereby decreasing the velocity of the fuel/oxidant. 
     Furthermore, in some embodiments, the openings  104  may include a sudden and/or discontinuous transition or increase in the area (unless otherwise stated, any of the areas disclosed herein are in plan view), along the downstream direction (e.g., between the inlet  118  and the bulging region  122 ). Hence, when the fuel/oxidant flows downstream and through the openings  104 , the nominal velocity of the fuel/oxidant may at least initially decrease in the downstream direction when the area of the opening  104  increases. A nominal decrease in flow velocity in the downstream direction may be accompanied by vortex formation that can recirculate reactants and heat within the openings  104 . For instance, a portion of one, some, or each of the openings  104  may be generally stepped from an intermediate location (e.g., from the bulging region  122 ) of the opening  104  toward and/or to the inlet  118  thereof (e.g., such that the opening  104  is wider at the bulging region  122  and may discontinuously narrow toward and/or to the inlet  118 ). For example, one or more of the openings  104  may include one or more steps between the bulging region  122  and the inlet  118 . 
     As such, in some embodiments, one, some, or all of the openings  104  may include the bulging region  122  that may be located downstream from the inlet  118 . In an embodiment, the bulging region  122  may be located at and/or near the outlet  120 . For example, the bulging region  122  may extend from the outlet  120  to an intermediate location between the inlet  118  and the outlet  120 . As such, the bulging region  122  may be located at and/or near the distal side  116  of the refractory plate  115 . 
     The bulging region  122  may be defined by or have a maximum area A B  (as measured transversely to length L of the opening  104 ), which may be greater than an area A I  of the inlet  118  that is also measured transversely to the length L. In the illustrated embodiment, the maximum area A B  may be substantially the same as the area A O  of the outlet  120  that is also measured transversely to the length L. 
     Generally, the area A I  of the inlet  118 , the area A O  of the outlet  120 , the area A B  at or near the bulging region  122 , the length L, the cross-sectional shape of the opening(s)  104 , or combinations thereof may vary from one of the openings  104  to another as well as from one embodiment to another. As described above, the inlet  118  and the outlet  120  may have respective areas A I  and A O . The area of at least one of A I  or the area A O  may be in one or more of the following ranges: about 0.002 in 2  to about 0.01 in 2 ; about 0.008 in 2  to about 0.014 in 2 ; about 0.012 in 2  to about 0.019 in 2 ; about 0.018 in to about 0.25 in 2 ; or about 0.024 in 2  to about 0.040 in 2 . It should be appreciated, however, that the areas of at least one of A I  or A O  may be less than 0.002 in 2  or more than 0.040 in 2 . In some embodiments, the area A I  and the area A O  may be selected at least partially based on the expected fuel/oxidant flow rate or volume, the expected flame propagation rate (e.g., the velocity at which the fuel/oxidant burns), the amount of heat to be absorbed by the refractory plate  115 , the percent of fuel/oxidant to be ignited within the flame holder  102 , or combinations thereof. 
     The bulging region  122  may have an area A B  that may be greater than the area A I  and/or area A O . For example, the area A B  may be greater than the areas A I  and/or A O  by a percentage in one or more of the following ranges: about 5% to about 15%; about 10% to about 25%; about 20% to about 60%; about 50% to about 100%; about 80% to about 200%; about 150% to about 300%; about 250% to about 500%; or about 400% to 800%. In some embodiments, the area A B  may be greater than any of the areas A I  or A O  by less than 5% or by more than 800%. In another embodiment, the area A B  may be substantially the same as A O . The area A B  may be selected at least partially based on: the expected fuel/oxidant flow rate, the type of fuel/oxidant, the desired amount of mixing between the fuel and oxidant, the amount of heat to be absorbed by the refractory plate  115 , the percent of fuel/oxidant to be ignited within the refractory plate  115 , or combinations of the foregoing. 
     The areas A I  and A O  at one, some, or each of the openings  104  may be different from one another. In an embodiment, areas A I  or the area A O  (for the same opening  104  and/or at different openings  104 ) may be different from each other by a percentage in one or more of the following ranges: about 1% to about 5%; about 8% to about 15%; about 10% to about 25%; about 20% to about 50%; about 45% to about 75%; about 70% to about 150%; or about 100% to about 200%. In some embodiments, the difference between the areas A I  and A O  may be less than 1% or greater than 200% (e.g., about 200% to about 500% or about 400% to about 800%). In some embodiments, the areas A I  and A B  may be different from each other by a percentage that is less than 1% or greater than 800%. 
     As described above, the openings  104  may also have the length L. The length L may be the same as the thickness of the refractory plate  115 . In an embodiment, the length L may also be selected at least partially based on the largest dimension of the inlet  118  and/or of the outlet  120  (e.g., based diameter of the inlet  118  and/or diameter of the outlet  120 ). For example, the length L may be greater than the largest dimension of the inlet  118  and/or of the outlet  120  by a percentage of about 350% to about 2000%. The length L may be selected at least partially based on the flow of fuel/oxidant, the amount of heat to be absorbed by the refractory plate  115 , the amount of fuel to be ignited within the flame holder, the area A B , combinations of the foregoing, etc. 
     As previously discussed, the flame holder  102  may be partially or entirely formed from the refractory plate  115 . In an embodiment, the refractory plate  115  may be monolithic and formed from a single piece. In an embodiment, the refractory plate  115  may include two or more portions stacked (e.g., positioned, abutted, connected, attached, coupled, etc.) together that collectively form the refractory plate  115 . In the illustrated embodiment, the refractory plate  115  may include a first portion  128  positioned downstream from a second portion  129 , which collectively form the refractory plate  115 . For example, the first portion  128  may abut and/or may be attached to the second portion  129 . 
     In an embodiment, the first portion  128  may include a first proximal side  132  spaced upstream from a first distal side  134  (e.g., distal side  116 ). The first proximal side  132  may include a plurality of first entrances  136  formed therein and the first distal side  136  may include a plurality of first exits  138  (e.g., outlets  120 ) formed therein. The areas of the first entrances  136  and the first exits  138  may be substantially the same or may be different. A portion of the openings  104  may extend through the first portion  128 . For example, the first portion  128  may define a plurality of first perforations  140  extending between the first entrances  136  and the first exits  138 . In the illustrated embodiment, at least one of the first perforations  140  may exhibit a substantially constant area between the first entrances  136  and the first exits  138 . In another embodiment, at least some of the first perforations  140  may exhibit an area that varies (e.g., increases and/or decreases) between the first entrances  136  and the first exits  138 . For example, the first perforation  140  may exhibit an area that continuously (e.g., tapered) or discontinuously (e.g., stepped) increases and/or decreases. In the illustrated embodiment, the bulging region  122  may be located within the first perforation  140 . 
     In the illustrated embodiment, the second portion  129  may be configured substantially similar to the first portion  128 . For example, the second portion  129  may include a second proximal side  142  (e.g., the proximal side  114 ) that is spaced upstream from a second distal side  144 . The second distal side  144  may contact the first proximal side  132  to form an interface therebetween. The second portion  129  may include a plurality of second entrances  146  (e.g., inlets  118 ) formed in the second proximal side  142  and a plurality of second exits  148  formed in the second distal side  144 . At least a portion of the openings  104  may extend through the second portion  129 . For example, the second portion  129  may define a plurality of second perforations  149  extending between the second entrances  146  and the second exits  148 . The second perforations  149  may exhibit a substantially constant or varied area between the second entrances  146  and the second exits  148 . In other embodiments, the second portion  129  may not include the second perforation  149 . Instead, for example, the second portion  129  may include a plank ( FIG. 2D ). 
     In the illustrated embodiment, the second exits  148  may exhibit an area and/or shape (in plan view) that is different (e.g., smaller) than the first entrances  136 . For example, the area of the openings  104  may suddenly and/or discontinuously vary when the second exits  148  exhibit an area and/or shape that is different than the first entrances  136 . In another embodiment, the second exits  148  may exhibit an area and shape (in plan view) that is substantially the same as the first entrance  136 . For example, the area of the openings  104  may smoothly and/or continuously vary when the second exits  148  exhibit an area and/or shape that is substantially the same as the first entrances  136 . 
     Referring to  FIG. 1B , in the illustrated embodiment, the streamwise velocity of the fuel/oxidant is highest where the area of the opening  104  is smallest. In the illustrated embodiment, the area of the opening  104  is smallest within the second perforation  149  (e.g., at and/or near the inlet  118 ). For example, the velocity of the fuel/oxidant within the second perforation  149  may be greater than or equal to the rate of flame propagation to prevent the flame from leaving the refractory plate  115  and entering a space between the flame holder  102  and the nozzles  106  (e.g., flashback). 
     The velocity of the fuel/oxidant may decrease when the area of the opening  104  increases. In the illustrated embodiment, the area of the openings  104  increases suddenly from the second exit  148  to the first entrance  136 . As such, the velocity of the fuel/oxidant may decrease when the fuel/oxidant enters the first perforation  140 . In an embodiment, the velocity of the fuel/oxidant in the first perforation  140  may be less than the flame propagation rate of the fuel/oxidant. In such an embodiment, combustion of the fuel/oxidant may be trapped in the first perforation  140  so long as the velocity of the fuel/oxidant in the first perforation  140  is less than the flame propagation rate. As such, the fuel/oxidant may substantially maintain combustion of at least some of the fuel/oxidant within the first perforation  140 . For instance, about 20% to substantially all of the fuel/oxidant may ignite within the first perforation  140 . Additionally, the lower fuel/oxidant flow rate within one or more of the openings  104  may improve fuel oxidant mixing (e.g., as compared with openings of substantially constant area), increase the amount of fuel ignited in the openings  104 , decrease the amount of NO x  emissions, or combinations thereof. 
       FIG. 1B  illustrates that the sudden increase in the area of the opening  104  from the second exit  148  to the first entrance  136  may create eddies or vortices in the first perforation  140 . For example, the eddies or vortices may form throughout the first perforation  140 . The eddies decrease the streamwise velocity and cause heat recycling into the incoming cold fuel/oxidant. As such, the eddies may improve the flame stability of the fuel/oxidant combusted therein. 
     In an embodiment, the portion of the refractory plate  115  that includes the bulging region  122  may be thicker than the portion of the refractory plate  115  that does not include the bulging region  122 . Hence, the fuel/oxidant is more likely to ignite in, at, and/or near the bulging region  122 . For example, the first portion  128  may be thicker than the second portion  129  (e.g., about 10% to about 500% thicker or at least about 500% thicker). In another embodiment, the first portion  128  may be thinner than the second portion  129  (e.g., about 10% to about 500% thinner or at least about 500% thinner). Alternatively, the first and second portion  128 ,  129  may have approximately the same thickness. 
     It should be appreciated, however, that the first and/or second portions  128 ,  129  may have any suitable thickness, which may vary from one embodiment to another. In an embodiment, the first and second portions  128 ,  129  may have respective thicknesses of about 2 inches (5 centimeters) and about 0.5 inches (1.3 centimeters). In another embodiment, the first and second portions  128 ,  129  may have respective thicknesses of about 6 inches (15 centimeters) and about 1 inch (2.5 centimeters). In another embodiment, the first and second portions  128 ,  129  may both have thicknesses of about 2 inches (5 centimeters). 
     The flame holder  102  (e.g., the refractory plate  115 ) may be formed in any suitable manner. In an embodiment, the flame holder  102  may be formed from two or more portions stacked together (e.g. the first and second portions  128 ,  129 ) that are connected and/or joined together. For example, the first and second portions  128 ,  129  may be fastened, welded, or otherwise secured together. Alternatively or additionally, a portion of or the entire flame holder  102  may be substantially monolithic or formed from three or more portions. In an embodiment, at least a portion of the flame holder  102  (e.g., each of the two or more portions) may be manufactured from a solid plate by machining the openings  104  therein, such as by at least one of wire electro-discharge machining, water jet drilling, laser drilling, mechanically drilling, or any other suitable technique. In another embodiment, the first portion  128  may be supported by the second portion  129  by the force of gravity. In another embodiment, the first and second portions  128 ,  129  may be clamped together. In another embodiment, the first and second portions  128 ,  129  may be fastened together by refractory cement. 
     One or more components of the combustion system  100  (e.g., the flame holder  102 ) may be formed from any number of suitable high-temperature resistant materials or various combinations thereof. In an embodiment, the flame holder  102  may include refractory metals (e.g., niobium, molybdenum, tantalum, tungsten, rhenium, alloys thereof, or combinations thereof). In an embodiment, the flame holder  102  may include alumina silicate, cordierite, other suitable high-temperature resistant ceramics, or combinations thereof. For example, the flame holder  102  may comprise high-temperature resistant ceramic fibers, such as alumina silicate fibers. In an embodiment, the flame holder  102  may comprise any metallic material or non-metallic material exhibiting a melting temperature greater than an expected operating temperature of the flame holder  102 . For example, the expected operating temperature of the flame holder  102  may be about 1600° C. to about 3500° C. In some instances, the expected operating temperature may be about 2000° C. to about 3000° C., or about 2800° C. In one or more embodiments, the flame holder  102  may include an electrically conducting material, an electrically insulating material, or combinations thereof. In an embodiment, the flame holder  102  may include a combination of any of the materials discussed herein. 
     In an embodiment, the flame holder  102  (e.g., the refractory plate  115 ) may be heated at one, some, or all of the openings  104  during combustion of the fuel/oxidant in openings  104 . For example, the flame holder  102  may absorb heat by combusting the fuel/oxidant therein. The bulging region  122  may improve the heat absorption of the flame holder  102  (as compared with openings having approximately uniform areas). In another example, as will be discussed in more detail later, the flame holder  102  may be heated another device, such as an electric heating element. In an embodiment, heating the flame holder  102  may provide improved ignition of a fuel/oxidant therein (e.g., as compared with an unheated flame holder and/or with a flame holder with openings having approximately uniform areas along lengths thereof). For example, the heated flame holder  102  may be heat such that a surface of the flame holder  102  (e.g., at least one inner surface  126  defining the openings  104 ) may exhibit a surface temperature greater than a threshold temperature required to ignite the fuel/oxidant (e.g., an autoignition temperature). The flame holder  102  may be configured to ignite the fuel/oxidant and, thereby, may facilitate the use of a leaner fuel/oxidant and/or may not require an ignition source, such as a flame or a spark. Additionally, the heated flame holder  102  may increase a percentage of fuel/oxidant ignited in the openings  104  (as compared with an unheated flame holder and/or with a flame holder with approximately uniform openings). 
     For example, the average velocity of fuel/oxidant flow through the openings  104  that include the bulging region  122  may be characterized by increased vorticity compared to openings having substantially uniform area throughout. 
     In an embodiment, the flame holder  102  may be preheated to a temperature above the threshold temperature before the fuel is dispensed from the nozzles  106 . For example, the flame holder  102  may be preheated using a flame. In another embodiment, the flame holder  102  may be preheated using an electric heating element, by an electric current passing through the flame holder  102 , a laser irradiating the flame holder  102 , combinations thereof, etc. 
     The percentage of fuel/oxidant ignited in the openings  104  may be about 20% to substantially all of the fuel. In an embodiment, greater than 50% of the fuel/oxidant that enters the inlets  118  may ignite before exiting the outlets  120  of the openings  104 . In another embodiment, more that 75% of the fuel/oxidant may ignite in the openings  104 . Under some conditions, a significant portion of uncombusted fuel/oxidant may ignite beyond the distal side  116  of the flame holder  102 . According to embodiments, the openings  104  having a bulging region may have an increased portion of the combustion reaction occurring in the openings  104  compared to straight openings. 
     The heat absorbed by the flame holder  102  may be transferred to a selected location. For example, heat absorbed by the flame holder  102  may be radiated to a furnace wall or may be used to warm the fuel before the fuel is ejected by the nozzle  106  (e.g., fuel oil). 
     The openings  104  of the flame holder  102  may define a void fraction of the flame holder  102  (e.g., the refractory plate  115 ) of about 0.1 to about 0.9. Void fraction is a ratio of volume of the openings  104  to total volume of flame holder  102 . In an embodiment, the flame holder  102  may have a void fraction in one or more of the following ranges: about 0.3 to about 0.8; about 0.5 to about 0.7; or about 0.60 to about 0.9. The void fraction of the flame holder may be selected at least partially based on the type of fuel, the desired temperature of the refractory plate  115 , the percentage of fuel targeted for ignition within the flame holder, the fuel/oxidant flow rate, combinations of the foregoing, etc. 
     The nozzles  106  may be configured to dispense fuel away from an orifice thereof towards the proximal side  114 . The nozzles  106  may be configured to dispense a hydrocarbon gas, such as natural gas (mostly CH 4 ) or propane, or hydrocarbon liquids such as fuel oil, diesel oil, etc. Additionally or alternatively, the nozzles  106  may be configured to dispense other fuels such as hydrogen or mixtures of gaseous fuels such as methane, carbon monoxide, and hydrogen. The nozzles  106  may additional dispense an oxidant and/or an additive that assists combustion. The nozzles  106  dispense the fuel at an angle and at a specific speed. For example, the nozzles  106  may dispense the fuel at about a 15° angle as measured from opposing edges of the fuel stream. 
     In some embodiments, the nozzles  106  may dispense the fuel at a sufficiently high velocity to prevent the flame from leaving one or more of the openings  104  and entering the space between the flame holder  102  and the nozzles  106 . In an embodiment, the nozzles  106  may dispense the fuel at a velocity greater than the flame propagation velocity. Additionally, the nozzles  106  may dispense the fuel at a sufficiently low rate, such that the fuel may sufficiently mix with the oxidant prior to combustion. The combustion system  100  may be formed to be aligned with a fuel dispensed from a single nozzle  106 . Alternatively, in at least one embodiment, the flame holder  102  of the combustion system  100  may be formed to be aligned with fuel dispensed from a plurality of nozzles  106 . 
     The flame at or near the upper surface  113  may heat the flame holder  102 . However, the flame at the upper surface  113  of the burner tile  110  may prevent adequate mixing of the fuel and the oxidant. Extinguishing the primary flame may facilitate movement of the flame from at or near the upper surface  113  to the flame holder  102 . Systems including primary and secondary nozzles that may be used in combination with any of the embodiments disclosed herein are disclosed in U.S. Provisional Patent Application No. 61/765,022 entitled “Perforated Flame Holder and Burner Including a Perforated Flame Holder” filed on Feb. 14, 2013, the entire content of which is incorporated herein by this reference. 
     In some embodiments, the combustion system  100  includes a premixing region between the proximal side  114  and the nozzles  106  that allows for mixing of the fuel and an oxidant source. While the premixing region may extend from the nozzles  106  to the proximal side  114  of the flame holder  102 , it will be understood that this is an approximation made for ease of understanding. Under some operating conditions, a flame may occasionally and/or briefly extend downward from the proximal side  114  of the flame holder  102 . For instance, eddies in the premixing region may be temporarily bounded by a flame front and premixing may temporarily stop. However, such flame extensions may be transient, and on a time-averaged basis, the premixing region may still be considered to support premixing of the secondary fuel stream with air or flue gas. The premixing region may have a length of about 1 inch (2.54 centimeters) to about 24 inches (61 centimeters) (e.g., about 3 inches to about 8 inches (about 7.62 centimeters to about 20.32 centimeters), about 8 inches to about 16 inches (about 20.32 centimeters to about 40.64 centimeters), about 16 inches to about 24 inches (about 40.64 centimeters to about 60.96 centimeters)). The length of the premixing region may depend on the diameter of the fuel nozzle orifice, etc. 
     As described above, the combustion system  100  may include one or more flame holder supports  108 , which may be configured to support the flame holder  102  in a furnace, boiler, or other combustion volume aligned to receive the fuel stream. The flame holder supports  108  may be configured to support the flame holder  102  substantially completely around the periphery or perimeter of the flame holder  102 . The flame holder supports  108  may be fabricated from steel, from the same materials as the flame holder  102 , from refractory brick, etc. For example, the flame holder supports  108  may include or be formed from a metallic superalloy, such as Inconel. In an embodiment, the flame holder supports  108  may support the flame holder  102  such that the proximal side  114  may be substantially perpendicular to the expected fuel/oxidant stream. In alternative or additional embodiments, the flame holder  102  may be supported at an angle such that the proximal side  114  may be not substantially perpendicular to the expect fuel/oxidant stream. 
     The flame holder supports  108  may be designed to support the flame holder  102  at a predetermined distance above the nozzles  106 . In one or more embodiments, the distance between the proximal side  114  and the nozzles  106  may be about 0.5 inches to about 48 inches (about 1.27 centimeters to about 121.92 centimeters). For example, the distance between the proximal side  114  and the nozzles  106  may be about 8 inches to about 16 inches (about 20.32 centimeters to about 40.64 centimeters), or about 16 inches to about 24 inches (about 40.64 centimeters to about 60.96 centimeters). In at least one embodiment, an orifice of the one or more nozzles  106  may have a maximum orifice width and the distance between the proximal side  114  and the nozzles  106  that may be about 20 times to about 250 times greater than the maximum fuel nozzle orifice width (e.g., about 20 time to about 100 times, about 100 time to about 245 times). 
     The combustion system  100  may include additional equipment not shown in the illustrated embodiment. For example, the combustion system  100  may include one or more control valves that are capable of controlling the fuel and/or oxidant flow to the nozzles  106 . In an embodiment, the control valves may include at least one of a manually actuated valve, a hydraulically actuated valve, or a pneumatically actuated valve.  FIGS. 2A-2D  are partial cross-sectional views of flame holders having at least one opening therein, according to different embodiments. Except as otherwise described herein, the flame holders shown in  FIGS. 2A-2D  and their materials, components, or elements may be similar to or the same as the flame holder  102  ( FIGS. 1A-1B ) and its respective materials, components, or elements. Any of the openings illustrated in  FIGS. 2A-2D  may be used in any of the flame holder embodiments disclosed herein. It is noted that while  FIGS. 2A-2D  illustrate only a single opening, the illustrated flame holders may include a plurality of openings formed therein arranged according to any suitable pattern including any of the patterns disclosed herein. 
       FIG. 2A  illustrates a flame holder  202   a  that is formed from a single portion (e.g., monolithic). Alternatively, the flame holder  202   a  may be formed from a plurality of portions that are stacked or joined together. The flame holder  202   a  includes one or more openings  204   a  that extends from an inlet  218   a  to an outlet  220   a . The area of the outlet  220   a  is greater than the area of the inlet  218   a . The opening  204   a  is defined by at least one inner surface  226   a  that extends from the inlet  218   a  to the outlet  220   a . The at least one inner surface  226   a  exhibits a suitable convex curvature, such as a generally convex curvature, such as a parabolic, ellipsoidal, or circular curvature. As such, the opening  204   a  exhibits a generally funnel-shaped opening in which an area of the opening  204   a  generally smoothly and continuously increases from the inlet  218   a  to the outlet  220   a  (e.g., a bulging region  222   a  of the opening  204   a  is at and/or near the outlet  220   a ). In another embodiment, the at least one inner surface  226   a  may exhibit a concave curvature (e.g., the bulging region  422   c  of  FIG. 4C ). 
     The shape of the opening  204   a  may increase the stability and robustness of a flame combusted therein. For example, the velocity of a fuel/oxidant flowing through the opening  204   a  may be greatest at and/or near the inlet  218   a  and may generally decrease with distance from the inlet  218   a . The relatively high velocity of the fuel/oxidant at and/or near the inlet  218   a  may prevent flashback. Additionally, the shape of the opening  204   a  may facilitate combustion of the flame therein at a range of fuel/oxidant velocities and/or the velocity of the fuel/oxidant may be used to regulate where the fuel/oxidant combusts within the opening  204   a , which increases an operational stability window for a combustion system incorporating the flame holder  202   a . For example, combustion of the fuel/oxidant may occur when the velocity of the fuel/oxidant is about equal to the flame propagation rate. As such, combustion of the fuel/oxidant may move closer to the inlet  218   a  when the velocity of the fuel/oxidant decreases and may move closer to the outlet  220   a  when the velocity of the fuel/oxidant increases. 
       FIG. 2B  illustrates a flame holder  202   b . For example, the flame holder  202   b  includes one or more openings  204   b  that extends from an inlet  218   b  to an outlet  220   a . The opening  204   b  is defined by at least one inner surface  226   b  that is substantially planar and tapers from the outlet  220   b  to the inlet  218   b . Therefore, the opening  204   b  exhibits a generally truncated conical shape in which an area of the opening  204   b  generally smoothly and continuously increases from the inlet  218   b  to the outlet  220   b.    
     The flame holder  202   b  may improve flame stability and robustness in substantially the same manner as the flame holder  202   a  of  FIG. 2A . For example, combustion of the fuel/oxidant may move closer to the inlet  218   b  when the velocity of the fuel/oxidant decreases and may combust closer to the outlet  220   b  when the velocity of the fuel/oxidant increases. 
       FIG. 2C  illustrates a flame holder  202   c  that is formed from a plurality of portions stacked together. For example, in the illustrated embodiment, the flame holder  202   c  includes a proximal side  214   c ; a distal side  216   c ; and a first, second, third, fourth, and fifth portions  228   c ,  229   c ,  250 ,  252 , and  254 , respectively. However, the flame holder  202   c  may include less or more than five portions and/or may be monolithic. 
     Similar to the flame holder  102 , each of the plurality of portions defines an entrance and an exit. Each of the plurality of portions defines a perforation extending from the entrance to the exit. The perforations collectively form an opening  204   c  that extends from an inlet  218   c  to an outlet  220   c . In the illustrated embodiment, each of the perforations exhibits a different area and/or shape relative to each other. As such, the area of the opening  204   c  suddenly and/or discontinuously increases from the inlet  218   c  to the outlet  220   c  (e.g., includes a plurality of steps) when the plurality of portions are stacked together. In another embodiment, the perforations may be configured to form an opening exhibiting an area that smoothly and/or substantially continuously increases from the inlet  218   c  to the outlet  220   c.    
     The flame holder  202   c  may improve flame stability and robustness in substantially the same manner as the flame holder  202   a  of  FIG. 2A . For example, combustion of the fuel/oxidant may move closer to the inlet  218   c  when the velocity of the fuel/oxidant decreases and may combust closer to the outlet  220   c  when the velocity of the fuel/oxidant increases. Additionally, similar to flame holder  102  of  FIGS. 1A-1B , the sudden increase in the area of the opening  204   c  may create eddies or vortices when the fuel/oxidant flows through the opening  204   c . For example, the eddies may facilitate combustion of fuel/oxidant over a range of fuel/oxidant velocities, which increases the operational stability window for a combustion system incorporating the flame holder  202   c.    
       FIG. 2D  illustrates a flame holder  202   e  that is formed from a plurality of portions. For example, the flame holder  202   e  includes a first portion  228   e  that is downstream from a second portion  229   e . The first portion  228   e  defines an entrance  236   e , an exit  238   e  downstream from the entrance  236   e , and a perforation  240   e  extending therebetween. The entrance  236   e  may exhibit a maximum width W F . The second portion  229   e  may exhibit a plank-like structure having a length (e.g., measured traverse to the maximum width W F ) sufficient to span across the entrance  236   e . The second portion  229   e  may also exhibit a maximum width W S  that is measured is a direction substantially parallel to the maximum width W F . The maximum width W F  of the perforation  240   e  is greater than the maximum width W S  of the second portion  229   e . As such, the second portion  229   e  cannot completely obscure the entrance  236   e.    
     The second portion  229   e  may be stacked relative to the first portion  228   e  to completely span across the perforation  240   e  and only partially obstruct the entrance  236   e . For example, in the illustrated embodiment, the second portion  229   e  may obstruct a middle section of the entrance  236   e . As such, the entrance  236   e  includes a first section  260  and a second section  262  located on either side of the second portion  229   e  that are not obstructed by the second portion  229   e . As such, the first and second section  260 ,  262  may collectively form an inlet  218   e  having an area that is less than the area of the entrance  236   e . In another embodiment, the second portion  229   e  may only obstruct a side section of the entrance  236   e . As such, the entrance  236   e  only includes a single section that is located on one side the second portion  229   e . In another embodiment, the second portion  299   e  may be staked relative to the first portion  228   e  to only partially span across the entrance  236   e . In another embodiment, the second portion  229   e  may not exhibit a length sufficient to span across the entrance  236   e . As such, the second portion  229   e  may only span across a portion of the entrance  236   e  or be supported in the middle of the entrance  236   e  (e.g., using wires made out of any of the high-temperature resistant materials disclosed herein). In another embodiment, the entrance  236   e  may be partially obstructed by a plurality of second portions  229   e.    
     In operation, the flame holder  202   e  may operate substantially similar to the flame holder  102   a  ( FIGS. 1A-1B ). For example, the sudden increase in the area of the opening  204   e  may create eddies or vortices when the fuel/oxidant flows through the opening  204   e.    
       FIG. 3  is an isometric cutaway view of a combustion system  300 , according to an embodiment. Except as otherwise described herein, the combustion system  300  and its materials, components, or elements may be similar to or the same as the combustion system  100  ( FIGS. 1A-1B ) and its respective materials, components, or elements. For instance, the combustion system  300  may include one or more nozzles  106  spaced from and oriented toward a flame holder  302 . The nozzles  106  may dispense a fuel/oxidant, which may generally flow toward the flame holder  302  and/or at least some of the fuel/oxidant may flow through a plurality of openings  304  defined by the flame holder  302 . 
     The flame holder  302  includes a proximal side  314  and/or a distal side  316 . The proximal side  314  may be closer to the one or more nozzles  106  than the distal side  316 . The proximal side  314  and the distal side  316  may define a plurality of inlets  318  and a plurality of outlets  320  therein, respectively. One, some, or each of the plurality of openings  304  may extend from an inlet  318  to an outlet  320 . The fuel/oxidant emitted from the one or more nozzles  106  may enter the openings  304  at the inlets  318  and exit at the outlets  320  thereof. In the illustrated embodiment, the flame holder  302  is collectively formed from two or more portions (e.g., a first portion  328  and a second portion  329  upstream from the first portion  328 ). In another embodiment, the flame holder  302  may be monolithic. 
     In some embodiments, the openings  304  may be configured to facilitate mixing and combustion of a fuel/oxidant flowing therein. As such, the openings  304  may improve the stability and robustness of the flame produced during or after combustion. For example, one, some, or all of the openings  304  may be configured to initially reduce the velocity of the fuel/oxidant flowing through a portion of the openings  304  using any of the methods disclosed herein. For example, one, some, or all of the openings  304  may exhibit a bulging region  322  that is positioned downstream from the inlet  318 , which has a larger area than the inlet  318 . 
     Furthermore, in some embodiments, the openings  304  may include a gradual or substantially continuous transition or increase of the cross-section area along the downstream direction, between the inlet  318  and an intermediate location (e.g., the bulging region  322 ) of the opening  304 . For example, a portion of one, some, or each of the openings  304  may be generally tapered from the bulging region  322  toward and/or to the inlet  318  thereof (e.g., such that the opening  304  is wider at the bulging region  322  and may substantially continuously narrows toward and/or to the inlet  318 ). In other embodiments, as will be discussed in more detail below, the openings  304  may include a sudden and/or discontinuous transition or increase of the area along the downstream direction (e.g., stepped). 
     In additional or alternative embodiments, at least a portion of one, some, or each of the openings  304  may be configured to facilitate velocity increase of the fuel/oxidant flow in the downstream direction through another portion of the openings  304  (e.g., from the bulging region  322  toward and/or to the outlet  320  of the opening). For example, the area of the opening  304  at the bulging region  322  may be greater than the area of the outlet  320 . In an embodiment, the area of the opening  304  may gradually or substantially continuously decrease from the bulging region  322  toward and/or to the outlet  320  (e.g., tapered). In another embodiment, the area of the opening  304  may suddenly and/or discontinuously decrease from the bulging region  322  toward and/or to the outlet  320 . (e.g., stepped). 
     In at least one embodiment, at least a portion of one, some, or all of the openings  304  may have a generally circular shape in plan view. Hence, for example, one or more portions of one, some, or each of the openings  304  may have approximately conical shapes (e.g., a shape of a truncated cone). In an embodiment, one, some, or each of the openings  304  may have two conical portions that may have bases thereof connected to each other and forming the bulging region  322  of the opening  304 . As described in more detail below, the openings  304  may have any number of suitable configurations and shapes, which may vary from one embodiment to the next. 
     In some embodiments, one, some, or all of the openings  304  may include a bulging region  322  that is spaced from the inlet  318  and the outlet  320 . The bulging region  322  may be defined by or have a maximum area A B  (as measured transversely to length L of the opening  304 ), which may be greater than area Ai of the inlet  318  and area A O  of the outlet  320 . 
     In an embodiment, the bulging region  322  may be located midway between the proximal and distal sides  314 ,  316  of the flame holder  302 . Hence, the maximum area A B  may be located approximately at the centerline between the proximal side  314  and the distal side  316 . In another embodiment, the bulging region  322  may be located more proximate the distal side  316  than the proximal side  314  or more proximate the proximal side  314  than the distal side  316 . 
     As previously discussed, the openings  304  illustrated in  FIG. 3  may improve flame stability and robustness. For example, the initial velocity of the fuel/oxidant may be relatively high at and/or near the inlets  318 . The relatively high velocity of the fuel/oxidant may be greater than the flame propagation rate, thereby substantially preventing flashback. The velocity of the fuel/oxidant may decrease from a location at and/or near the inlets  318  toward and/or to the bulging regions  322  and/or increase from the bulging regions  322  toward and/or to the outlets  320 . Decreasing and/or increasing the velocity of the fuel/oxidant may improve mixing thereof, regulate where the fuel/oxidant combusts in the openings  304  (e.g., combustion of the fuel/oxidant moves towards the outlet  320  when the velocity of the fuel/oxidant increases), improve combustion of a fuel/oxidant having relatively high velocities, improve combustion of a leaner fuel/oxidant, better trap combustion of the fuel/oxidant within the openings  304  over a range of fuelioxidant velocities compared to an opening having a constant area, or combinations thereof. In another embodiment, the relatively small area A I  and A O  of the inlets  318  and outlets  320 , respectively, relative to the area A B  of the bulging region  322 , may increase the amount of heat absorbed by flame holder  302 . The increased about of heat absorbed by the flame holder  302  may increase the temperature of at least one surface of the flame holder  302  (e.g., at least one inner surface  326  defining the opening  304 ) above an autoignition temperature of the fuel/oxidant which may, in turn, increase the amount of the fuel/oxidant that combusts in the opening  304 . 
     The location within the opening  304  where the fuel/oxidant combusts may be controlled depending on the velocity of the fuel/oxidant. Similar to the openings  204   a ,  204   b , and  204   c  ( FIGS. 2A-2C ), the fuel/oxidant may combust at a location within the opening  304  that is more proximate the outlet  320  when the velocity of the fuel/oxidant is increased and may combust at a location within the opening  304  that is more proximate the inlet  318  when the velocity of the fuel/oxidant is decreased. 
       FIGS. 4A-4F  are partial cross-sectional views of flame holders, according to different embodiments. Except as otherwise described herein, the flame holders shown in  FIGS. 4A-4F  and their respective elements and components may be similar to or the same as any of the flame holders  102 ,  202   a - e ,  302  ( FIGS. 1A-3 ) and their respective elements and components. Any of the openings illustrated in  FIGS. 4A-4F  may be used in any of the flame holder embodiments disclosed herein. It is noted that while  FIGS. 4A-4F  illustrate only a single opening, the illustrated flame holders may include a plurality of openings formed therein arranged according to any suitable pattern including any of the patterns disclosed herein. 
       FIG. 4A  is a partial cross-sectional view of a flame holder  402   a  that includes a first portion  428   a , a second portion  429   a  upstream from the first portion  428   a , and at least one opening  404   a . The first portion  428   a  may be thicker than the second portion  429   a . For instance, a bulging region  422   a  may be offset from a centerline of the flame holder  402   a  between the proximal side  414   a  and the distal side  416   a  (e.g. the bulging region  422   a  may be closer to the distal side  414   a  than proximal side). In an embodiment, the opening  404   a  may include an inlet  418   a  that has a smaller area than an outlet  420   a.    
     The flame holder  402   a  may improve flame stability and robustness in substantially the same manner as the flame holder  302  of  FIG. 3 . For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   a  that is greater than the flame propagation rate thereby substantially preventing flashback. In another example, combustion of the fuel/oxidant may move closer to the outlet  420   a  when the velocity of the fuel/oxidant increases and may move closer to the inlet  418   a  when the velocity of the fuel/oxidant decreases. 
     In some embodiments, the bulging region may have a largest area at a point or that may lie along a line or a plane. Alternatively, the largest area of the bulging region may extend along the length of the opening.  FIG. 4B  is a partial cross-sectional view of a flame holder  402   b  includes at least one opening  404   b , which has a bulging region  422   b  that extends along a length of the opening  404   b . For instance, along the length of the opening  404   b , the bulging region  422   b  may have a constant area in plan view. For example, the bulging region  422  may have a constant diameter or other lateral dimension. Additionally or alternatively, as mentioned above, in an embodiment, the flame holder  402   b  may be formed from a single piece of material. 
     The flame holder  402   b  may improve flame stability and robustness in substantially the same manner as the flame holder  302 ,  402   a  of  FIGS. 3-4A . For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   a  that is greater than the flame propagation rate, thereby substantially preventing flashback. The velocity of the fuel/oxidant may generally decrease from the inlet  418   b  to the bulging region  422   b  and generally increase from bulging region  422   b  to the outlet  420   b . However, the velocity of the fuel/oxidant may be relatively constant in the bulging region  422   b  due to the relatively constant area of the bulging region  422   b  along a length of the opening  404   b . The relatively constant velocity of the fuel/oxidant may improve mixing of the fuel/oxidant, increase the percentage of the fuel/oxidant that combusts in the opening  404   b , improve absorption of the heat into the flame holder  402   b , etc. 
     Furthermore, as described above, the cross-sectional shape of the openings (e.g., at cross-section taken along the length of the opening) may vary from one embodiment to the next.  FIG. 4C  is a partial cross-sectional view of a flame holder  402   c  that includes at least one opening  404   c , which may have at least one curved inner surface  426   c . For example, the opening  404   c  may have a concave curvature extending between inlet  418   c  and outlet  420   c  of the opening  404   c . In an embodiment, a bulging region  422   c  may be formed at location where a slope of the curved inner surface  426   c  is substantially vertical. It should be appreciated that the openings in the flame holder may have any number of suitable configurations that may include a bulging region between inlets and outlets thereof. 
     The flame holder  402   c  may improve flame stability and robustness in substantially the same manner as the flame holder  302 ,  402   a - b  ( FIGS. 3-4B ). For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   a  that is greater than the flame propagation rate, thereby substantially preventing flashback. 
     Furthermore, the opening may exhibit a sudden and/or discontinuous transition, increase, and/or decrease along the length of the opening.  FIG. 4D  is a partial cross-sectional view of a flame holder  402   d  that includes a plurality of portions that collectively form the flame holder  402   d . Each of the plurality of portions may define a perforation and the perforations may collectively define an opening  404   d . The opening  404   d  may extend from an inlet  418   d  to an outlet  420   d  and include a bulging region  422   d  therebetween. In the illustrated embodiment, the opening  404   d  may exhibit a stepped shaped. For example, at least some of the perforations exhibit an area that is different than the area of another perforation. The plurality of portions may be stacked such that the areas of the perforations generally increases from the inlet  418   d  to the bulging region  422   d  and decrease from the bulging region  422   d  to the outlet  420   d.    
     The flame holder  402   d  may improve flame stability and robustness in substantially the same manner as the flame holder  302 ,  402   a - c  ( FIGS. 3-4C ). For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   d  that is greater than the flame propagation rate, thereby substantially preventing flashback. Additionally, the fuel/oxidant may form eddies or vortices at and/or near where the area of the opening  404   d  suddenly increases, similar to the openings  104 ,  204   c ,  204   e  ( FIGS. 1B, 2C, and 2D ). 
       FIG. 4E  illustrates a flame holder  402   e  that is formed from a plurality of portions. In the illustrated embodiment, the flame holder  402   e  includes a first portion  428   e , a second portion  429   e , and a third portion  450   e . The first portion  428   e  may include an entrance  436   e , and exit  438   e  downstream from the entrance  436   e , and a perforation  440   e  extending therebetween that at least partially forms an opening  404   e . The entrance  436   e  exhibits a maximum width W EN  and the exit  438   e  exhibits a maximum width W EX . In the illustrated embodiment, the maximum width W EN  and the maximum width W EX  are substantially the same. However, in other embodiments, the maximum width W EN  and W EX  may be different. The second and third portions  429   e ,  450   e  comprise a plank-like shape having a length in a longitudinal direction thereof and a width W S  and W T , respectively, measured substantially parallel to the widths W EN  and W EX . The widths W S  and W T  may be less than the maximum widths W EN  and W EX , respectively. The width W S  and W T  may be substantially the same or different. 
     Similar to the flame holder  202   e  ( FIG. 2D ), the second and third portions  429   e ,  450   e  may partially obstruct the entrance  436   e  and the exit  438   e , respectively, when the second and third portions  429   e ,  450   e  are stacked relative to the first portion  428   e . In the illustrated embodiment, the second and third portions  429   e ,  450   e  may obstruct a middle section of the entrance  436   e  and exit  438   e , respectively. As such, the entrance  436   e  may include a first section  460  and a second section  462  located on either side of the second portion  429   e  that are unobstructed by the second portion  429   e . Similarly, the exit  438   e  may include a first section  466  and a second section  468  on either side of the third portion  450   e  that are unobstructed by the third portion  450   e . The first and second sections  460 ,  462  of the entrance  436   e  may collectively form an inlet  418   e  and the first and second sections  466 ,  468  of the exit  438   e  may collectively form an outlet  420   e . In another embodiment, the second and/or the third portion  429   e ,  450   e  may only obstructs a side section of the entrance  436   e  and/or the exit  438   e , respectively, when the second and/or third portion  429   e ,  450   e  are stacked relative to the first portion  428   e . In another embodiment, the entrance  436   e  and/or the exit  438   e  may be at least partially obstructed by a plurality of second portions  429   e  and/or a plurality of third portions  450   e , respectively. 
     The flame holder  402   e  may improve flame stability in substantially the same manner as the flame holder  302 ,  402   a - d  ( FIGS. 3-4D ). For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   e  that is greater than the flame propagation rate, thereby substantially preventing flashback. Additionally, the fuel/oxidant may form eddies at and/or near where the area of the opening  404   e  suddenly increases, similar to the openings  104 ,  204   c .  204   e ,  404   d  ( FIGS. 1A-1B, 2C, 2D, and 4D ). 
       FIG. 4F  illustrates a flame holder  402   f  that is collectively formed from a plurality of portions. In the illustrated embodiment, the flame holder  402   f  may be collectively formed from a first portion  428   f , a second portion  429   f  upstream from the first portion  428   f , and a third portion  450   f  downstream from the first portion  428   f . Each of the first, second, and third portions  428   f ,  429   f , and  450   f  may define a first entrance  436   f , a second entrance  446 , and a third entrance  470 , respectively; a first exit  438   f , second exit  448 , and a third exit  472 , respectively; and a first perforation  440   f , a second perforation  449 , and a third perforation  474 , respectively. Each of the first, second, and third perforations  440   f ,  449 ,  474  collectively form an opening  404   f . Additionally, the second entrance  446  may form an inlet  418   f  of the opening  404   f  and the third exit  472  may form an outlet  420   f  of the opening  404   f.    
     In the illustrated embodiment, an area of the opening  404   f  may suddenly and discontinuously increase from the inlet  418   f  to an intermediate location (e.g., the first perforation  440   f , a bulging region  422   f , etc.) and may suddenly and discontinuously decrease from the intermediate location to the outlet  420   f . For example, the second exit  448  may exhibit an area and/or shape that is different (e.g., less than) the area and/or shape of the first entrance  436   f . Similarly, the first exit  438   f  may exhibit an area and/or shape that is different (e.g., greater than) the area and/or shape of the third entrance  470 . In another embodiment, the first, second, and third portions  428   f ,  429   f ,  450   f  may be configured to form an opening exhibiting an area that smoothly and continuously increases from the inlet  418   f  to the intermediate location and/or may smoothly and continuously decreases from the intermediate location to the outlet  420   f.    
     The flame holder  402   e  may improve flame stability in substantially the same manner as the flame holder  302 ,  402   a - e  ( FIGS. 3-4E ). For example, a fuel/oxidant may have a velocity at and/or near the inlet  418   d  that is greater than the flame propagation rate, thereby substantially preventing flashback. Additionally, the fuel/oxidant may form eddies at and/or near where the area of the opening  404   f  suddenly increases, similar to the openings  104 ,  204   c .  204   e ,  404   d ,  404   e  ( FIGS. 1A-1B, 2C, 2D , and  4 D- 4 E). 
       FIG. 5  is a partial cross-sectional view of a flame holder  502  defining an opening  504 , according to an embodiment. Except as otherwise described herein, the flame holder  502  shown in  FIG. 5  and its respective elements and components may be similar to or the same as any of the flame holders  102 ,  202   a - e .  302 ,  402   a - f  ( FIGS. 1A-4F ) and their respective elements and components. It is noted that while  FIG. 5  illustrate only a single opening, the illustrated flame holder may include a plurality of openings formed therein arranged according to any suitable pattern including any of the patterns disclosed herein. 
     In the illustrated embodiment, the opening  504  extends from an inlet  518  to an outlet  520 . The opening  504  exhibits an area that generally decreases from the inlet  518  to a narrowed region  576 . The area of the opening  504  then increases from the narrowed region  576  to another location of the opening  504  (e.g., an intermediate location, a bulging region  522 , and/or the outlet  520 ). The area of the opening  504  may increase and/or decrease in a smooth and continuous manner or in a sudden and discontinuous manner. 
     In an embodiment, decreasing the area of the opening  504  from the inlet  518  to the narrowed region  576  may improve the aerodynamics of the flame holder  502 . For example, referring to  FIGS. 1A-1B , the velocity of a fuel/oxidant may decrease between nozzles  106  and the flame holder  102 . The decrease in the velocity of the fuel/oxidant may be at least partially caused by the non-aerodynamic shape of the flame holder  102  (e.g., relatively small areas A I  relative to the surface area of the proximal side  114 ). As such, referring to  FIG. 5 , increasing the size of the inlet  518  may improve the aerodynamics of the flame holder  502  and may increase the velocity of the fuel/oxidant flowing into the opening  504 . 
     In operation, the velocity of the fuel/oxidant may increase from the inlet  518  to the narrowed region  576 . The velocity of the fuel/oxidant at the narrowed region  576  may be greater than the flame propagation rate of the fuel/oxidant thereby substantially preventing flashback. Additionally, the velocity of the fuel/oxidant flowing through the narrowed region  576  may be greater than the velocity of a fuel/oxidant flowing through an opening having the same area as the narrowed region  576  (e.g., all other conditions the same) because of the improved aerodynamics of the flame holder  502 . The velocity of the fuel/oxidant than then decrease from the narrowed region  576  to another region of the opening (e.g., the bulging region  522  and/or the outlet  520 ). 
     The flame holder  502  may be used in any of the flame holder embodiments disclosed herein. For example, any of the flame holders  102 ,  202   a - e ,  302 ,  402   a - f  ( FIGS. 1A-4F ) may include an opening exhibiting an area that generally decreases from the inlet to a narrowed region thereof and generally increase from the narrowed region to another region of the opening (e.g., an intermediate location, a bulging region, and/or an outlet). 
       FIGS. 6A and 6B  are partially cross-sectional views of flame holders that include one or more mechanisms disposed in an opening thereof that increase mixing of the fuel/oxidant, according to one or more embodiments. Increasing the mixing of the fuel/oxidant may also improve flame stability and robustness by improving combustion of leaner fuels and/or poorly mixed fuel/oxidant. Except as otherwise described herein, the flame holders shown in  FIGS. 6A-6B  and their respective elements and components may be similar to or the same as any of the flame holders  102 ,  202   a - e ,  302 ,  402   a - g ,  502  ( FIGS. 1A-5 ) and their respective elements and components. The flame holders shown in  FIGS. 6A-6B  may be used in any of the flame holders disclosed herein. It is noted that while  FIGS. 6A-6B  illustrate only a single opening, the illustrated flame holders may include a plurality of openings formed therein arranged according to any suitable pattern including any of the patterns disclosed herein. 
       FIG. 6A  illustrates a flame holder  602   a  including an opening  604   a  therein. The opening  604   a  is defined by at least one inner surface  626   a  of the flame holder  602   a . At least a portion of the inner surface  626   a  may include one or more textured features  678  formed (e.g., machined) therein. The textured features  678  may include one or more protrusions, recesses, notches, channels, fins, divots, or other suitable textured feature. The textured features  678  may form a corkscrew-like pattern, a checkered pattern, or any other suitable pattern configured to cause at least some of the fuel/oxidant flowing within the opening  604  to swirl and/or exhibit turbulent flow and generate eddies or vortices, which may increase mixing of the fuel/oxidant. 
       FIG. 6B  illustrates a flame holder  602   b  including an opening  604   b  therein. The opening  604   b  is defined by at least one inner  626   b  of the flame holder  602   b . The opening  604   b  may include one or more turbulators  680  positioned therein that are attached to the at least one inner surface  626   b  or otherwise secured within the opening  604   b . The turbulators  680  may be configured to increase the turbulence of a fuel/oxidant flowing through the opening  604   b . The turbulators  680  may be formed from any of the high-temperature resistant materials disclosed herein. 
     In the illustrated embodiment, the turbulators  680  includes an elongated member  682  attached to the inner surface  626   b  at a first end thereof. The turbulators  680  may further include a plate  684  attached to a second end of the elongated member  682 . The plate  684  may exhibit an oblique angle or perpendicular angle relative to a length L of the opening  604 . The plate  684  and/or the elongated member  682  may increase turbulent flow of the fuel/oxidant. The turbulent flow may increase the mixing of the fuel/oxidant, form eddies, combinations thereof, etc. In another embodiment, the turbulators  680  may include a coiled rod, a wire mesh, or any other suitable turbulator. 
       FIG. 7  is a partial cross-sectional view of a flame holder  702  including sleeve  786  that is attachable to a refractory plate  715  or other type of refractory body, according to an embodiment. Except as otherwise described herein, the flame holder  702  shown in  FIG. 7  and its respective elements and components may be similar to or the same as any of the flame holders  102 ,  202   a - e ,  302 ,  402   a - g ,  502 ,  602   a - b  ( FIGS. 1A-6B ) and their respective elements and components. For example, the sleeve  786  may be formed from any of the high-temperature resistant materials disclosed herein. The sleeve  786  and the refractory plate  715  shown in  FIG. 7  may be used in any of the flame holders disclosed herein. It is noted that while  FIG. 7  illustrates only a single opening  704  (e.g., sleeve  786 ), the illustrated flame holder may include a plurality of openings formed therein arranged according to any suitable pattern including any of the patterns disclosed herein. 
     In the illustrated embodiment, the sleeve  786  includes at least one side wall  788  having at least one inner surface  726  and at least one outer surface  790  spaced from the inner surface  726 . The inner surface  726  defines an inlet  718 , an outlet  720  downstream from the inlet  718 , and an opening  704  extending therebetween. The opening  704  may be substantially the same as or similar to any of the openings disclosed herein. The inner surface  726  may also include one or more textures surfaces  778  formed therein and/or turbulators extending therefrom. 
     The refractory plate  715  may define a conduit  792 . The conduit  792  may exhibit a size and shape configured to receive the sleeve  786 . For example, the conduit  792  may exhibit a shape that substantially corresponds to a shape of the outer surface  790 . For instance, the conduit  792  may exhibit a width We that is substantially the same as or slightly greater than a maximum width W O  of the outer surface  790 . 
     In an embodiment, the sleeve  786  may be attached to the refractory plate  715 . For example, the sleeve  786  may be attached to the flame holder  702  by welding, press-fitting, using a high-temperature resistant adhesive, a mechanical fastener, or any other suitable technique. In another embodiment, the sleeve  786  may reversibly attached to the refractory plate  715  thereby allowing the flame holder  702  to be adapted for different applications. 
       FIGS. 8A-8D  illustrate top plan views of a distal side of flame holders  802   a ,  802   b ,  802   c ,  802   d , according to one or more embodiments. Except as otherwise described herein, any of the flame holders  802   a .  802   b ,  802   c ,  802   d  as well as elements and components thereof may be similar to or the same as the flame holders  102 ,  202   a - e ,  302 ,  402   a - g ,  502 ,  602   a - b ,  702  ( FIGS. 1A-7 ) and its corresponding elements and components. For example, as shown in  FIG. 8A , the flame holder  802   a  may include openings  804   a ,  804   a ′,  804   a ″, which may be similar to or the same as one or more of the openings  104 ,  204   a - e ,  304 ,  404   a - g ,  504 ,  604   a - b ,  704  ( FIGS. 1A-7 ). Additionally or alternatively, the openings  804   a ,  804   a ′,  804   a ″ may include corresponding bulging regions  822   a .  822   a ′,  822   a ″ (shown as phantom lines) at intermediate locations between the inlets and outlets thereof. 
     Referring to  FIG. 8A , in some embodiments, the opening  804   a  may be positioned approximately in the center of the flame holder  802   a  and the openings  804   a ′ and  804   a ″ may be arranged circularly or concentrically about the opening  804   a . For example, openings  804   a ′ may be arranged in two circular arrangements, where some of the openings  804   a ′ form a first circular arrangement (e.g., centered about the opening  804   a ) and other openings  804   a ′ form a second circular arrangement that encloses or encircles the first circular arrangement. Additionally or alternatively, openings  804   a ″ may be arranged circularly (e.g., the openings  804   a ′″ may encircle at least some of the openings  804   a ′). 
     In one or more embodiments, the openings  804   a ′ and  804   a ″ may have a similar or the same radial distance therebetween. The openings  804   a ,  804   a ′,  804   a ″ have generally circular cross-sections. In an embodiment, the opening  804   a  may be larger than the openings  804   a ′ and/or openings  804   a ″. In some embodiments, the openings  804   a ′ may be larger than the openings  804   a ″. In other words, in some embodiments, the flame holder  802   a  may have openings of three different sizes. It should be appreciated, however, the flame holder  802   a  may include any number of openings of any number of suitable sizes, which may vary from one embodiment to another (e.g., the flame holder  802   a  may have openings of two, three, four, five, etc., different sizes). 
     Furthermore, the openings of the flame holder may have any number of suitable arrangements.  FIG. 8B  illustrates a top view of the flame holder  802   b  with openings  804   b  having a generally spiral arrangement, according to an embodiment. The openings  804   b  may be arranged in a helical pattern having substantially same helical spacing between the openings  804   b . For example, the flame holder  802   b  may include an opening  804   b  at or near the center thereof, while additional openings  804   b  that may be arranged along a substantially helical pattern that spirals outward from the opening  804   b  at or near the center of the flame holder  802   b . In some embodiments, radial and/or lateral spacing between the openings  804   b  may be approximately constant along the helical pattern thereof. In the illustrated embodiment, the openings  804   b  may exhibit a generally circular cross-sectional shape or any other suitable shape. 
     As described above, the openings  804   a .  804   a ′,  804   a ″.  804   b  may have generally circular cross-sectional shapes. It should be appreciated, however, that cross-sectional shapes of the openings may vary from one embodiment to the next. For example,  FIG. 8C  is a top view of the flame holder  802   c  with openings  804   c  that have approximately triangular shapes in plan view, according to an embodiment. In some embodiments, the openings  804   c  may be arranged along equally spaced linear paths. For instance, the openings  804   c  positioned along a first path may be offset from the openings  804   c  arranged along another path. 
     Furthermore, in some embodiments, the openings  804   c  may be arranged along paths that are approximately parallel one to another. For example, one or more sides of the openings  804   c  positioned along the first path may be approximately parallel to one or more sides of the openings  804   c  positioned along another path that is approximately parallel to the first path. In an embodiment, the one, some, or all of the openings  804   c  may lie along two or more paths. For instance, one, some, or all of the openings  804   c  may lie along at least two paths that have non-perpendicular orientation relative to each other. 
     In some embodiments, the openings  804   c  may have approximately the same cross-sectional shape along the entire lengths thereof (e.g., along the thickness of the flame holder  802   c ). For example, bulging regions  822   c , which may be positioned between the inlets and outlets of the openings  804   c , may have a generally triangular shape. Additionally or alternatively, in at least one embodiment, the cross-sectional shape of one, some, or all of the openings  804   c  may vary along respective lengths thereof (e.g., the opening  804   c  may have different cross-sectional shapes at the inlet and outlet, at the outlet and bulging region  822   c , at the inlet and bulging region  822   c , etc.). 
       FIG. 8D  is a top view of the flame holder  802   d  with openings  804   d  that have inlets and/or outlets with different shapes from bulging regions  822   d  thereof, according to an embodiment (e.g. in cross-sections take transversely to the lengths of the openings  804   d  or to the thickness of the flame holder  802   d ). In an embodiment, the inlets and outlets of the openings  804   d  may have approximate rectangular or square cross-sectional shapes and the bulging regions  822   d  may have approximately circular cross-sectional shapes. Also, in some embodiments, the inlets and outlets of the openings  804   d  may have different cross-sectional shapes one from another. In any event, the area at the bulging regions  822   d  may be larger than corresponding areas at the inlets and/or outlets of the openings  804   d.    
     Moreover, in some embodiments, the openings  804   d  may be arranged in a grid-like or periodic pattern. For instance, the flame holder  802   d  may have the same lateral spacing between the openings  804   d . In an embodiment, the openings  804   d  may be arranged along approximately linear paths. For example, one, some, or all of the openings  804   d  may lie on two approximately perpendicular paths. 
       FIG. 9  is a top plan view of a flame holder assembly  900  that includes a plurality of flame holders  902 , according to an embodiment. Generally, the flame holders  902  may include any of the flame holders described herein, which may be arranged in any number of patterns. For example, the flame holders  902  may be similar to or the same as the flame holder  102  ( FIGS. 1A and 1B ) and may be arranged in a circular pattern around an opening  904  in a main plate  906 . In particular, the main plate  906  may define one or more holes  908  therein that may accept flame holders  902 , which may be secured to the main plate  906  therein. 
     While various aspects and embodiments have been disclosed, other aspects and embodiments may be contemplated. The various aspects and embodiments disclosed here are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.