Patent Publication Number: US-11643995-B1

Title: Liquid rocket engine injector with variable flow area

Description:
BACKGROUND 
     Field 
     This development relates to rocket engines, in particular to liquid rocket engine injectors. 
     Description of the Related Art 
     Liquid rocket engines allow for throttled thrust. However, deep-throttling of the engine can create challenges for propellant injectors. One challenge of deep throttling a rocket engine is minimizing the pressure drop across the injector, while avoiding coupling between the feed system and the thrust chamber. There is a need for improved injectors that address these and other challenges with liquid rocket injectors. 
     SUMMARY 
     The embodiments disclosed herein each have several aspects no single one of which is solely responsible for the disclosure&#39;s desirable attributes. Without limiting the scope of this disclosure, its more prominent features will now be briefly discussed. After considering this discussion, and particularly after reading the section entitled “Detailed Description” one will understand how the features of the embodiments described herein provide advantages over existing approaches to injectors for rocket engines. 
     A rocket combustion chamber injector having a passively varying flow area is described. The injector comprises a housing, a poppet, a spring and a bellows. The housing comprises a sidewall extending along a longitudinal axis between a proximal end and a distal end, where the sidewall is comprising a variable inner width portion and a plurality of ports arranged radially about the longitudinal axis near the variable inner width portion, and the plurality of ports are configured to receive a propellant along a propellant flow path that extends from the plurality of ports towards the distal end of the housing. The poppet extends axially between a proximal end and a distal end, the poppet is moveable within the housing along the longitudinal axis, the distal end of the poppet has a variable outer width portion located radially inwardly of the variable inner width portion of the housing to define therebetween an annular flow area of the propellant flow path, and the variable outer width portion is configured such that propellant flowing along the propellant flow path around the variable outer width portion applies a first axial force on the distal end of the poppet. The spring is coupled to the proximal end of the poppet within the housing and is configured to apply a second axial force on the proximal end of the poppet. The bellows is located within a cavity at the proximal end of the housing, the cavity is configured to receive propellant therein, the bellows is coupled to the proximal end of the poppet and located outside of the propellant flow path, and the bellows comprises a plurality of openings through which propellant is configured to be transmitted to dampen movement of the poppet along the longitudinal axis. The poppet is configured to move toward the distal end of the housing in response to the first axial force exceeding the second axial force and thereby increase the annular flow area, and the poppet is configured to move toward the proximal end of the housing in response to the second axial force exceeding the first axial force and thereby decrease the annular flow area. 
     There may be a variety of embodiments of the above and other aspects. The injector may further comprise an orifice holder supporting an orifice that is in fluid communication with the cavity at the proximal end of the housing. The injector may further comprise a first hard stop and a second hard stop configured to limit axial travel of the poppet within the housing to thereby limit a maximum area and a minimum area of the annular flow area. The injector may further comprise a guide within the housing configured to radially support the poppet during axial movement of the poppet through the guide. A ratio of A) a pressure drop across the injector to B) a pressure within a combustion chamber in fluid communication with the injector, may be maintained within a target range across a range of flow rates. The ratio may be controlled within a target range of 15% to 25% across the range of flow rates. 
     In another aspect, a rocket combustion chamber injector having a passively varying flow area is described. The injector comprises an elongated housing, an elongated poppet, a spring and a bellows. The elongated housing extends from a proximal end to a distal end to define a longitudinal axis, and the housing comprises a variable inner width portion and a plurality of ports arranged proximally of and adjacent to the variable inner width portion and partially defining a propellant flow path that exits out the distal end of the housing. The elongated poppet is supported within the housing and moveable axially, and the poppet comprises a variable outer width portion located radially inwardly of the variable inner width portion of the housing to define therebetween an annular flow area of the propellant flow path. The spring is located within the housing and is configured to bias the poppet in a proximal direction. The bellows is located within a cavity at the proximal end of the housing and located outside of the propellant flow path, and the cavity is configured to be filled with propellant. The poppet is configured to move in a distal direction in response to an increased propellant flow along the propellant flow path to thereby increase the annular flow area and to move in the proximal direction in response to a decreased propellant flow along the propellant flow path to thereby decrease the annular flow area. 
     There may be a variety of embodiments of the above and other aspects. The variable inner width portion may increase in inner width in the distal direction. The plurality of ports may be arranged radially about the longitudinal axis. The propellant flow path may bend from the plurality of ports toward the distal end of the housing. The variable outer width portion of the poppet may increase in outer width in the distal direction. The variable outer width portion of the poppet may be configured such that propellant flowing along the propellant flow path around the variable outer width portion applies a first axial force in the distal direction on the variable outer width portion of the poppet. The spring may be configured to apply a second axial force in the proximal direction on the poppet. The increased propellant flow along the propellant flow path may cause the first axial force to exceed the second axial force to thereby move the poppet in the distal direction. The decreased propellant flow along the propellant flow path may cause the second axial force to exceed the first axial force to thereby move the poppet in the proximal direction. The bellows may comprise a plurality of openings through which propellant is configured to be transmitted to dampen movement of the poppet along the longitudinal axis. The bellows may be located proximally of the poppet and provide a damping force to a proximal end of the poppet. A ratio of A) a pressure drop across the injector to B) a pressure within a combustion chamber in fluid communication with the injector, may be maintained within a target range across a range of flow rates. The ratio may be controlled within a target range of 15% to 25% across the range of flow rates. 
     In another aspect, a rocket combustion chamber is described. The rocket combustion chamber comprises an injector plate and a plurality of variable flow area injectors. The plurality of variable flow area injectors are configured to inject propellant through the injector plate. Each variable flow area injector comprises an elongated housing, an elongated poppet, a spring, and a bellows. The elongated housing extends from a proximal end to a distal end to define a longitudinal axis, and the housing comprises a variable inner width portion and a plurality of ports arranged proximally of and adjacent to the variable inner width portion and partially defining a propellant flow path that exits out the distal end of the housing. The elongated poppet is supported within the housing and is moveable axially, and the poppet comprises a variable outer width portion located radially inwardly of the variable inner width portion of the housing to define therebetween an annular flow area of the propellant flow path. The spring is located within the housing and is configured to bias the poppet in a proximal direction. The bellows is located within a cavity at the proximal end of the housing and is located outside of the propellant flow path, and the cavity is configured to be filled with propellant. The poppet is configured to move in a distal direction in response to an increased propellant flow along the propellant flow path to thereby increase the annular flow area and to move in the proximal direction in response to a decreased propellant flow along the propellant flow path to thereby decrease the annular flow area. 
     In another aspect, a method of injecting propellant into a rocket combustion chamber is described. The method comprises increasing a propellant flow through a plurality of ports of a housing of an injector along a propellant flow path that at least partially extends in a distal direction, impinging the propellant flow on a variable outer width portion of an axially moveable poppet, moving the poppet distally such that the variable outer width portion of the poppet moves distally within a variable inner width portion of the housing to increase an annular flow area therethrough, decreasing the propellant flow through the plurality of ports, biasing the poppet in a proximal direction using a compression spring, dampening movement of the poppet with a bellows in a propellant-filled cavity that is separate from the propellant flow path, and moving the poppet proximally such that the variable outer width portion of the poppet moves proximally within the variable inner width portion of the housing to decrease the annular flow area therethrough. In some embodiments, the further comprises flowing the propellant radially through the plurality of ports and axially out of a distal end of the injector. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other features of the present disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several embodiments in accordance with the disclosure and are not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings. In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented here. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are explicitly contemplated and make part of this disclosure. 
       Described herein are embodiments of injectors for a liquid rocket propulsion system. The injector passively varies the cross-sectional area of fluid flow across the injector as the throttle is increased and decreased. The area changes based in part on the velocity of the fluid flow—the higher the velocity, the larger the area, and vice versa. The area is larger in part because a poppet or bluff body moves more in the higher velocity flow, thus increasing the flow area. The injector may include hard stops for the poppet that provide minimum and maximum flow areas. In some embodiments, the poppet does not rest on the hard stops, so that flow area is continuously varied. 
         FIG.  1 A  is a side view of an embodiment of rocket combustion chamber. 
         FIG.  1 B  is an end of view of an embodiment of a rocket injector plate of the chamber of  FIG.  1 A  and having a plurality of variable flow area injectors. 
         FIG.  2 A  is a cross-sectional view of the variable flow area injectors of  FIG.  1 B . 
         FIGS.  2 B and  2 C  are cross-section views of the injector as taken along the line  2 B- 2 B as indicated in  FIG.  2 A  showing the variable annular flow area, respectively, with smaller and larger flow areas. 
         FIGS.  3 A- 3 C  are various data plots showing the pressure drop across the injector versus a range of throttling levels, as well as predictive data from an analytical model, for various embodiments of the injector of  FIG.  2 A . 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description is directed to certain specific embodiments of the development. Reference in this specification to “one embodiment,” “an embodiment,” or “in some embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. The appearances of the phrases “one embodiment,” “an embodiment,” or “in some embodiments” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. Moreover, various features are described which may be exhibited by some embodiments and not by others. 
     Various embodiments will now be described with reference to the accompanying figures, wherein like numerals refer to like elements throughout. The terminology used in the description presented herein is not intended to be interpreted in any limited or restrictive manner, simply because it is being utilized in conjunction with a detailed description of certain specific embodiments of the development. Furthermore, embodiments of the development may include several novel features, no single one of which is solely responsible for its desirable attributes or which is essential to practicing the present disclosure. 
       FIG.  1 A  is a side view of an embodiment of rocket combustion chamber  100 . The chamber extends from a proximal end  102  to a distal end  104 . The chamber  100  includes a barrel portion  106  and a nozzle portion  108  located at a distal end of the barrel portion  106 . The chamber  100  defines a longitudinal chamber axis  110  as shown. 
       FIG.  1 B  is an end of view of an embodiment of a rocket injector plate  112 . The plate  112  may be implemented in the chamber  100  of  FIG.  1 A . The plate  112  may be located at or near the distal end  102  of the chamber  100  when assembled with the chamber  100 . The plate  112  has a top surface  114  and an outer edge  116 . The top surface  114  may be substantially planar and perpendicular to the chamber axis  110  when assembled. The edge  116  may be circular. 
     The plate  112  includes a plurality of variable flow area injectors  200 . For clarity, only some of the injectors  200  are labelled in  FIG.  1 B . Some or all of the injectors  200  may be longitudinally oriented at an angle to the chamber axis  110 . In some embodiments, the injectors  200  may be oriented axially, radially, angled, other orientations, or combinations thereof. 
     The injectors  200  may form a number of small diameter flow paths arranged in patterns through which the fuel and oxidizer travel. For example, the flow paths can be arranged in carefully constructed patterns that optimize the flow of fuel and oxidizer through the flow paths. The speed of the flow may be determined by the square root of the pressure drop across the injectors  200 , the shape of the flow paths and/or openings in the injector plate  112 , and other factors such as the density of the propellant. 
     The injectors  200  and/or injector plate  112  may include a number of holes. The holes may range in width or diameter from about 0.125 inches (in.) to about 1 in, from about 0.25 in. to about 0.75 in., from about 0.375 in. to about 0.5 in., or other larger or smaller sizes. The holes may be oriented to aim jets of fuel and oxidizer to collide. The jets may collide at a point in space a distance away from the injector plate  112 . The jets may collide at a distance of no more than 0.5 in, 1 in., 2 in., 3 in., 4 in., 5 in., 10 in., 20 in., or other distances, from the plate  112 . This helps to break the flow up into small droplets that burn more easily. The injectors  112  may be arranged to form a variety of different injector layouts, such as shower head, self-impinging doublet, cross-impinging triplet, centripetal or swirling, pintle, other suitable arrangements, or combinations thereof. 
       FIG.  2    is a cross-sectional view of an example variable flow area injector  200  according to the present disclosure. The injector  200  is elongated and extends along a longitudinal axis  210 . The injector  200  includes a housing  212 . The housing  212  provides a structural cover and support to the injector  200 . The housing  212  extends from a proximal end  214  to a distal end  216 . The distal end  216  may be positioned at a chamber of a rocket engine to expel propellant through an outlet  222  and into the chamber for combustion therein. The housing  212  includes a proximal portion  218  and a distal portion  220 . The proximal and distal portions  218 ,  220  may be separate parts that attach together, or the housing  212  may be unibody. “Proximal” and “distal” refer to the directions as shown in  FIG.  2   . 
     The housing  212  includes a plurality of ports  224  through which propellant flows into the injector  200 . There may be one, two, three, four, five, six, seven, eight, nine, ten or more ports  224 . The ports  224  may be openings in a sidewall of the housing  212 , such as in the distal portion  220 . The ports  224  may be located annularly on all sides of the housing  212 . The ports  224  as shown define openings through which propellant flows radially or substantially radially. “Radial” refers to a direction perpendicular to the axis  210 . The housing  212  includes an upstream chamber  226 . The chamber  226  may receive the propellant and be located upstream of a variable flow area  280  described in detail below. The ports  224  may open into the chamber  226 . 
     The housing  212  may include a variable inner width portion  228 . The portion  228  may be located distally of the chamber  226 . The portion  228  may increase in width, e.g. diameter, along the distal direction. The portion  228  may include a proximal lip as shown such that the cross-sectional area decreases slightly before increasing in the distal direction. The cross-sectional area of the housing  212  may thus increase in a section that is distal to the proximal lip. In some embodiments, there may not be a lip, and so the cross-sectional area of the housing  212  may increase in the distal direction from the chamber  226 . The portion  228  may have a nozzle-opening type shape with a minimum width throat portion, which may be located closer to the proximal end of the portion  228  than to the distal end. The portion  228  may be conical or funnel-shaped. The portion  228  opens into the downstream chamber portion  230 . The portion  230  may be cylindrical as shown. The portion  230  may have a constant cross-sectional area. The portion  230  ends in the circular outlet  222 . 
     The injector  200  includes a poppet  240 . The poppet  240  extends distally from a flange  242  at a proximal end thereof. The flange  242  is at the proximal end of an elongated first portion  246 . The first portion  246  includes a flange  248  located along the length of the first portion  246 . At a distal end of the first portion  246  is a relatively wider second portion  250 . The second portion  250  extends into the chamber  226 . The second portion  250  narrows in width to a neck  252 . 
     The poppet  240  includes a variable outer width portion  244 . The portion  244  may be located at a distal end of the poppet  240  as shown. The portion  24  may connect to the neck  252 . The portion  244  increases in outer width in a distal direction. The portion  244  may have a conical or funnel shape. The portion  244  may include a constant-width or constant-diameter cylindrical portion located distally of the increasing-width portion. The portion  244  may be hollow or have a bore therein, for example to reduce weight and improve moving response time of the poppet  240 . 
     The injector  200  includes a variable flow area  280 . The area  280  may be an annular area. The area  280  may be formed between the variable inner width portion  228  of the housing  212  and the variable outer width portion  244  of the poppet  240 . As described in further detail herein, for example with respect to  FIGS.  2 B and  2 C , movement of the poppet  240  in an axial direction may vary the size of the area  280  and thus control the propellant flow mass rate through, and pressure drop across, the injector  200 . 
     The injector  200  includes a guide  260 . The guide  260  may be an elongated, cylindrical structure with an opening therethrough configured to receive the poppet  240  and radially guide the poppet  240  as it moves axially. The guide  260  may be formed of TEFLON® material, other suitable materials, or combinations thereof. The guide  260  may be located proximally of the ports  224 . Inner surfaces of the guide  260  may slide against outer surfaces of and axially direct the wider second portion  250  of the poppet  240 . The guide  260  may center the poppet  240 . In some embodiments, flexural bearings may be used to center the poppet  240 , either alternatively or in addition to the guide  260 . 
     The injector  200  may include first and second stops  262 ,  264 . The stops  262 ,  264  are inwardly protruding structures, e.g. discs or other suitable projections, that limit axial travel of the poppet  240 . The first stop  262  limits proximal movement of the poppet  240 , and the second stop  264  located distally of the first stop  262  limits distal movement. The stops  262 ,  264  may limit axial travel of the flange  248  on the poppet  240 . The stops  262 ,  264  are located within the longitudinal proximal channel  219  of the housing  212 . The stops  262 ,  264  may be adjustable to finely control the range of motion of the poppet  240 . One or more first shims  266  may be strategically used to control the axial distance between the stops  262 ,  264 . One or more second shims  268  may be used to control the axial placement of the distal portion  220  within the proximal portion  218  of the housing  212 . Additional shims may be used in suitable locations, for example distal of the first stop  262 , to locate the stops  262 ,  264  in desirable positions. Positioning of the stops  262 ,  264  may affect the performance of the injector  200  as further described herein. In some embodiments, the injector  200  may not need shims  266  and/or  268 . For example, the stops  262 ,  264  may be mechanically adjustable within the housing  212 . In some embodiments, the injector  200  may include contact sensors at the stops  262 ,  264  to identify when the poppet  240  contacts the stops  262 ,  264  and thus when the flow area is at a maximum or minimum, in order to control the throttle. 
     The injector  200  includes a spring  270 . The spring  270  biases the poppet  240 . The spring  270  biases the poppet  240  in the proximal direction. The spring  270  may be a compression spring. The spring  270  may be located distally of the proximal flange  242  of the poppet  240  within the channel  219 . The spring  270  may be located proximally of the distal portion  220  of the housing  212 . The spring  270  may be located proximally of the first and/or second stop  262 ,  264 . The spring  270  may apply a force in the proximal direction against the moveable poppet  240  to restore the position of the poppet  240 , as further described herein. The spring  270  may be located separately from the main flow path  278  as shown. The spring  270  may be located within the injector  200  but not in fluid communication with the chamber  226 . 
     The injector  200  includes a bellows  272 . The bellows  272  may be a flexible structure configured to compress and elongate. The bellows  272  may have a resilient, zig-zag sidewall. The bellows  272  defines an annular structure as shown. The bellows  272  by alternate expansion and contraction may draw in fluid into a series of openings and expel the fluid out through the openings. The openings may be in the sidewall of the bellows  272 . The bellows  272  may be located in a proximal channel portion  271  of the channel  219  of the housing  212 , which may be in the proximal portion  218  of the housing  212 . The bellows  272  may contact a proximal side of the poppet  240 . The bellows  272  extend from a distal end to a proximal end. The distal end of the bellows  272  contacts the proximal side of the flange  242 . The proximal end of the bellows  272  contacts a holder  276 . The bellows  272  may partially surround a distal end of the holder  276 . The holder  276  and flange  242  axially limit movement of the bellows  272 . The proximal end of the bellows  272  may be fixed while the distal end of the bellows  272  may move as the poppet  240  moves. 
     The injector  200  includes an orifice  274 . The orifice  274  defines an opening therethrough. Propellant may flow through the opening of the orifice  274  and into the proximal channel portion  271  to be drawn into and expelled out of the bellows  272  through the series of openings in the bellows  272 . The orifice  274  is located proximally of the bellows  272 . In some embodiments, the orifice  274  may be located directly in the bellows  272 . The propellant flow path within the proximal channel portion  271  may be separate from a main propellant flow path that leads to the combustion chamber of the rocket engine, as further described. The same fluid flowing across the injector is used in the bellows  272 , such as liquid oxygen (LOX) or liquid natural gas (LNG). In some embodiments, the bellows  272  and the spring  270  may be combined. As shown the bellows  272  is a separate component from the spring  270 . 
     One challenge when incorporating the spring  270  into the injector  200  is that there may be a coupling between the injector  200  and the combustion dynamics. In order to avoid this, high damping may be employed. Fluidic damping using the orifice  274  and the series of openings in the bellows  272  results in high damping. In some embodiments, a transition time from a maximum to a minimum throttle, or vice versa, is about 0.3 seconds. The damping can be varied by changing the orifice size. 
     The variable volume in the bellows  272  may create impedance for damping out the effects of pressure oscillations in the combustion process. This can be tuned by adjusting the flow area into or out of the volume. Two ways to create that flow are to use an inlet orifice and/or openings in the bellows  272 . Forming small holes directly in the baffles can be an economical, low cost approach to creating flow into or out of the volume. Another approach is to use a single precision drilled orifice  274 . In some embodiments, a single precision drilled orifice  272  may be used. In some embodiments, single or multiple holes drilled directly into the bellows  272  may be used. The sizing of direct drilled holes in the bellows  272  may provide an equivalent effective flow area as a single orifice. 
     The injector  200  defines a main propellant flow path  278 . The propellant may be any fuel or oxidizer, such as LOX, hydrogen, LNG, kerosene or hypergols. The path  278  extends through the ports  224 , but only one flow path  278  extending through one port  224  is shown for clarity. The path  278  extends through the ports  224 , into the upstream chamber  226 , through the variable inner width portion  228 , and into the downstream chamber portion  230  through the outlet  222 . The portion of the flow path  278  extending between the variable inner width portion  228  of the housing  212  and the variable outer width portion  244  of the poppet  240  defines an annular-shaped flow area  280 .  FIGS.  2 B and  2 C  illustrate how a cross-section of the flow area  280  as taken along the line  2 B- 2 B in  FIG.  2 A  changes as the poppet moves in the distal direction from a first position shown in  FIG.  2 A  to a second position. 
       FIGS.  2 B and  2 C  are cross-section views of the injector  200  showing the variable annular flow area  280 , respectively, with smaller and larger flow areas. The housing  212 , such as the distal portion  220  as shown, includes an inner surface  221  defining the variable inner width portion  228 . The variable outer width portion  244  of the poppet  240  is defined by an outer surface  245  that is opposing the inner surface  221 . The annular flow area  280  is defined between the surfaces  221 ,  245 . 
     The size of the flow area  280  may be varied by moving the poppet  240  axially. Movement of the poppet  240  in the proximal direction will cause the outer surface  245  of the poppet  245  to be closer to the opposing inner surface  221  of the housing  212 , thus decreasing the size of the flow area  280  as shown in  FIG.  2 B . In contrast, as shown in  FIG.  2 C , movement of the poppet  240  in the distal direction will cause the outer surface  245  of the poppet  245  to be farther from the opposing inner surface  221  of the housing  212 , thus increasing the size of the flow area  280 . 
     The poppet  240  may be moved in the distal direction due to an increased propellant mass flow rate along the main flow path  278 . The spring  270  biases the poppet  240  in the proximal direction. In some embodiments, the bellows  272  may also bias the poppet  240  in the proximal direction. The propellant applies a force on the poppet  240  in the distal direction. The propellant may apply a drag force on the poppet  240 . The propellant  240  may also apply normal forces on the poppet  240  with force vector components in the distal direction that cause it to move distally. As the mass flow rate of the propellant along the flow path  278  increases, an increasing axial force is exerted on the variable outer width portion  244  of the poppet  240  in the distal direction. When the force in the distal direction to the propellant flow is greater than the force in the proximal direction due to the spring  270  (and possibly also due to the bellows  272 ), then the poppet  240  will move in the distal direction. The mass flow rate through the element at a given pressure drop across the orifice  274  may be increased by increasing the supply pressure to the element. 
     The poppet  240  may be moved proximally due to a decreased propellant flow along the main flow path  278 . As the propellant mass flow rate decreases, at some point the proximal forces from the spring  270  (and possibly the bellows  272 ) are greater than the distal forces due to the propellant flow, and thus the poppet  240  will move proximally. 
     As the poppet  240  moves distally due to increased propellant flow, the flow area  280  increases due to increased separation between the opposing surfaces of the poppet  240  and the housing  212 , as described. This in turn increases the mass flow rate through the injector  200  and thereby controls (e.g., decreases) the pressure drop across the injector  200 , as further described herein. Conversely, as the poppet  240  moves proximally due to decreased propellant flow, the flow area  280  decreases due to decreased separation between the opposing surfaces of the poppet  240  and the housing  212 , as described. This in turn decreases the mass flow rate through the injector  200  and thereby controls (e.g., increases) the pressure drop across the injector  200 , as further described herein. 
     Thus, during sufficiently low enough flow velocities, the poppet  240  is forced proximally. The proximal travel of the poppet  240  may be limited by the upper stop  262 . Likewise, the poppet  240  moves distally during sufficiently high enough fluid drag forces acting on it. The downward travel of the poppet  240  is limited by the lower stop  264 . 
     One of the significant challenges in producing a deep-throttling engine is managing the pressure drop across the injector  200 . Advantageously, the variable flow area  280  of injectors according to the present disclosure may minimize the pressure drop across the injector  200  at maximum flow rates while avoiding coupling between the fluid injector system and the thrust chamber of the rocket engine. Optimization of this pressure drop while avoiding coupling in this manner is an important design requirement for deep throttling rocket engines. In some embodiments, the injector  200  according to the present disclosure may be used as co-axial injectors in a 1.5 Mlbf engine using LOX/LNG and deep throttling to 7%. This represents a significant improvement to injectors for deep-throttling engines. 
     Advantageously, the injectors  200  of the present disclosure are highly configurable by adjusting various parameters. In some embodiments, the preload force due to the spring  272 , the spring rate or elasticity of the spring  272 , the diameter of the orifice  274 , the minimum flow area  280  and/or the maximum flow area  280  may be configured for optimal performance in particular engines. The preload force in the compression spring  272  may be from about 0.5 pound-force (lbf) to about 10 lbf, from about 1 lbf to about 5 lbf, from about 1.25 lbf to about 4.5 lbf, from about 1.5 lbf to about 4 lbf. The spring rate may be from about 5 pound-force per inch (lbf/in) to about 150 lbf/in, from about 7.5 lbf/in to about 125 lbf/in, from about 10 lbf/in to about 110 lbf/in, from about 25 lbf/in to about 75 lbf/in. The annular flow area  280  may have a minimum flow area from about 0.008 square inches (in 2 ) to about 0.100 in 2 , from about 0.010 in 2  to about 0.050 in 2 , or from about 0.016 square inches (in 2 ) to about 0.025 in 2 . The annular flow area  280  may have a maximum flow area from about 0.017 square inches (in 2 ) to about 0.250 in 2 , from about 0.025 in 2  to about 0.200 in 2 , from about 0.030 square inches (in 2 ) to about 0.150 in 2 , or from about 0.035 square inches (in 2 ) to about 0.125 in 2 . It will be understood that these ranges are example implementations and that other preload forces, spring rates, and annular flow areas can be suitably implemented in accordance with the present disclosure. 
     Over the entire throttle range, the pressure drop across the injector (ΔP) needs to be high enough to avoid coupling between the thrust chamber and the feed system. This minimum value is engine dependent and needs to be determined through testing, but a rule of thumb is that the dimensionless pressure drop, ΔP/P C , is above 15%, preferably above 20%, where P C  is the pressure in the rocket engine combustion chamber. The ΔP/P c  versus throttle profile is highly tuneable in embodiments of the present disclosure. Various modes of operation may be demonstrated by adjusting the spring rate, preload force, and stop positions. For example, the injector  200  can be adjusted to have the lowest allowable ΔP/P c  at high throttle, with providing near constant ΔP/P c  at lower throttles, decreasing susceptibility to combustion instabilities without penalizing performance of the engine with high injector pressure drop at full power. As a further example, in the event that the combustor does not run stably when the poppet  240  is not resting on a stop, the injector  200  can be configured to run with a keep-out zone, where the poppet  240  is resting on a stop for most of the throttle range. 
       FIG.  3 A  is a data plot  300  showing the pressure ratio ΔP/P c  as a percentage (%) versus throttle percentage (%) for an embodiment of the injector  200  and having stops  262 ,  264 . The data plot  300  has a first portion  302  corresponding to the poppet  240 , for example the flange  248 , bottomed out on the proximal hard stop  262  and thus having a minimum flow area  280 . A second portion  304  of the data plot  300  corresponds to the poppet  240 , for example the flange  248 , floating between and not contacting either of the hard stops  262 ,  264 , and thus having a variable flow area  280  that increases as the throttle % increases. A third portion  304  of the data plot  300  corresponds to the poppet  240 , for example the flange  248 , bottomed out on the distal hard stop  264  and thus having a maximum flow area  280 . As shown, the ΔP/P c  is greater than about 15% over substantially the entire range of throttling, and over the entire range of high throttling. The ΔP/P c  may be kept between about 15% and about 25% over substantially the entire range of throttling. The ΔP/P c  may be greater than 15% for throttle percentages greater than about 20%. The ΔP/P c  may be greater than 15% for throttle percentages greater than about 50%, greater than about 60%, greater than about 70%, greater than about 80%, or greater than 90%. At full throttle or 100%, the ΔP/P c  may be greater than 15% or greater than 20%. 
       FIG.  3 B  is a data plot  310  showing the pressure ratio ΔP/P c  as a percentage (%) versus throttle percentage (%) for an embodiment of the injector  200  at low throttle and having stops  262 ,  264 . The ΔP/P c  increases to about 15% throttle and then decreases after the poppet  240  begins to move due to the increased propellant flow. Then, the ΔP/P c  decreases to a lower limit at about 30% throttle, due to the hard stop not allowing the flow area to increase any more. With the flow area  280  at a maximum, the ΔP/P c  then continually increases as the throttle continues to increase. 
       FIG.  3 C  is a data plot  320  showing ΔP/P c  as a percentage (%) versus throttle percentage (%) for an embodiment of the injector  200  with continuously varying flow area  280 . A first set of data  322  is shown corresponding to a manifold pressure of about 600 pounds per square inch absolute (psia), and a second set of data  324  is shown corresponding to a manifold pressure of about 680 psia. The injector  200  was able to flow well above 150% throttle level while maintaining a ΔP/P c  of just over the desired 15% level. Due to the large pressure drop across the injector  200  at these high throttle levels, cavitation began to occur, and at the vertical lines the flow becomes choked due to cavitation. In addition, ΔP/P c  was increased at lower throttle levels, which would yield increased resistance to combustion instability. The ΔP/P c  increases to about 20% throttle and then gradually and continually decreases after the poppet  240  begins to move due to the increased propellant flow. The ΔP/P c  decreases continually since there is no hard stop to limit the flow area, and thus the flow area continues to increase as the throttle % and propellant flow increases. The ΔP/P c  continually approaches a horizontal asymptote located between 15% and 20%, e.g. at about 17%. 
       FIG.  3 C  further shows a third set of data  326  showing predicted results from an analytical model of the injector  200 . In some embodiments, the injector  200  may be designed to have a desired pressure drop profile. The design may be based on an equation (1) of motion for the poppet  240 . The equation (1) may be the following: 
     
       
         
           
             
               
                 
                   
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     In equation (1), m is the mass of the poppet  240 , {umlaut over (x)} is the acceleration of the poppet  240 , B P  is the base area of the poppet  240 , ρ is the density of the injected propellant, μ p  is the maximum propellant velocity at the minimum area location of the poppet  240 , k is the restoring force due to the combination of the spring  270  and bellows  272 , x is the location of the poppet  240  as measured from a no-flow preloaded position of the poppet  240 , F P  is the preload force on the poppet  240 , {dot over (x)} is the velocity of the poppet  240 , sign({dot over (x)}) is the mathematical positive (+) or negative (−) sign of the value of {dot over (x)}, B b  is the base area of the bellows  272  and  B   b  is the mean base area of the bellows  272 , where the mean base area multiplied by the height of the bellows  272  gives the volume, to take into account the convolutions or corrugations in the wall of the bellows  272 , A b  is the area of the bellows orifice, and C d,b  is the discharge coefficient of the bellows orifice which can be calibrated using test data. 
     Using equation (1), the behavior of the injector  200  can be estimated. A model based on equation (1) can estimate the forces on the poppet  240  and determine its position and the pressure drop across the injector  200 . 
     The third set of data  326  in  FIG.  3 C  shows the pre-test prediction using a calibrated model, which shows close correlation with the test sets of data  322 ,  324 . The model based on equation (1) of motion for the poppet can be used to tune the pressure drop versus throttle to any desired profile. 
     While the above detailed description has shown, described, and pointed out novel features of the present disclosure as applied to various embodiments, it will be understood that various omissions, substitutions, and changes in the form and details of the device or process illustrated may be made by those skilled in the art without departing from the spirit of the present disclosure. As will be recognized, the present disclosure may be embodied within a form that does not provide all of the features and benefits set forth herein, as some features may be used or practiced separately from others. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope. 
     The term “comprising” as used herein is synonymous with “including,” “containing,” or “characterized by,” and is inclusive or open-ended and does not exclude additional, unrecited elements or method steps. With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art may translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity. 
     It will be understood by those within the art that, in general, terms used herein are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should typically be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. 
     In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, typically means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.” 
     All numbers expressing quantities of ingredients, reaction conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the present invention. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should be construed in light of the number of significant digits and ordinary rounding approaches. For example, terms such as about, approximately, substantially, and the like may represent a percentage relative deviation, in various embodiments, of ±1%, ±5%, ±10%, or ±20%. 
     The above description discloses several methods and materials of the present disclosure. The present disclosure is susceptible to modifications in the methods and materials, as well as alterations in the fabrication methods and equipment. Such modifications will become apparent to those skilled in the art from a consideration of this disclosure. Consequently, it is not intended that the present disclosure be limited to the specific embodiments disclosed herein, but that it covers all modifications and alternatives coming within the true scope and spirit of the present disclosure.