Patent Publication Number: US-2023159185-A1

Title: Sub-coolers for refueling onboard cryogenic fuel tanks and methods for operating the same

Description:
FIELD OF THE DISCLOSURE 
     This disclosure relates generally to refueling cryogenic fuel tanks, and, more particularly, to a sub-cooling system for refueling onboard cryogenic fuel tanks. 
     BACKGROUND 
     A refueling system for cryogenic fuel tanks generally includes a supply tank and/or trailer, a flow control valve, a volumetric flowmeter, a cryogenic valve, a flexible vacuum jacketed flowline, and an onboard cryogenic fuel tank. To begin refueling, the supply tank initiates the flow of a cryogenic fuel through a series of vacuum jacketed flowlines terminating at the onboard cryogenic fuel tank. The flow control valve regulates the flowrate of the cryogenic fuel leaving the supply tank. The volumetric flowmeter measures the rate at which the cryogenic fuel flows through the flowmeter, e.g., in liters per second. The cryogenic valve generally regulates the cryogenic fuel flow with fully open or fully closed positions. The supply tank has a temperature gauge, and the cryogenic fuel has density properties dependent on the cryogenic fuel&#39;s temperature. The density of the cryogenic fuel can be determined based on the temperature of the fuel. The volume of the cryogenic fuel supplied to the onboard cryogenic fuel tank can be determined based on the volumetric flowrate and the duration of refueling. The mass of the cryogenic fuel supplied to the onboard cryogenic fuel tank can be determined based on the volume and density of the cryogenic fuel. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A full and enabling disclosure of the preferred embodiments, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended Figures, in which: 
         FIG.  1    illustrates a known system for refueling an onboard cryogenic fuel tank; 
         FIG.  2 A  illustrates a first example sub-cooling system for refueling an onboard cryogenic fuel tank in accordance with the teachings of this disclosure; 
         FIG.  2 B  illustrates a second example sub-cooling system for refueling an onboard cryogenic fuel tank in accordance with the teaching of this disclosure; 
         FIG.  2 C  illustrates a third example sub-cooling system for refueling an onboard cryogenic fuel tank in accordance with the teaching of this disclosure; 
         FIG.  3    illustrates thermodynamic properties of saturated pressure versus temperature and density versus temperature of liquid hydrogen, an example cryogenic fuel; 
         FIG.  4    is a flow diagram illustrating an operation of the sub-cooling system; 
         FIG.  5    is a flow diagram illustrating an operation of a sub-cooler in the sub-cooling system; 
         FIG.  6    is a flow diagram illustrating example machine readable instructions and/or operations that may be executed and/or instantiated by example processor circuitry to implement a sub-cooler controller that controls the sub-cooler in the sub-cooling system; and 
         FIG.  7    illustrates an example processing platform including processor circuitry structured to execute the example machine readable instructions of  FIG.  6   . 
     
    
    
     The figures are not to scale. Instead, the thickness of the layers or regions may be enlarged in the drawings. In general, the same reference numbers will be used throughout the drawing(s) and accompanying written description to refer to the same or like parts. As used in this patent, stating that any part (e.g., a layer, film, area, region, or plate) is in any way on (e.g., positioned on, located on, disposed on, or formed on, etc.) another part, indicates that the referenced part is either in contact with the other part, or that the referenced part is above the other part with one or more intermediate part(s) located therebetween. Connection references (e.g., attached, coupled, connected, joined, detached, decoupled, disconnected, separated, etc.) are to be construed broadly and may include intermediate members between a collection of elements and relative movement between elements unless otherwise indicated. As used herein, the term “decouplable” refers to the capability of two parts to be attached, connected, and/or otherwise joined and then be detached, disconnected, and/or otherwise non-destructively separated from each other (e.g., by removing one or more fasteners, removing a connecting part, etc.). As such, connection/disconnection references do not necessarily infer that two elements are directly connected and in fixed relation to each other. Stating that any part is in “contact” with another part means that there is no intermediate part between the two parts. 
     Descriptors “first,” “second,” “third,” etc., are used herein when identifying multiple elements or components which may be referred to separately. Unless otherwise specified or understood based on their context of use, such descriptors are not intended to impute any meaning of priority, physical order or arrangement in a list, or ordering in time but are merely used as labels for referring to multiple elements or components separately for ease of understanding the disclosed examples. In some examples, the descriptor “first” may be used to refer to an element in the detailed description, while the same element may be referred to in a claim with a different descriptor such as “second” or “third.” In such instances, it should be understood that such descriptors are used merely for ease of referencing multiple elements or components. 
     DETAILED DESCRIPTION 
     The operations of known refueling systems for onboard cryogenic fuel tanks refuel cryogenic fuels at temperatures similar to the temperatures at which the cryogenic fuels are stored prior to refueling. In some examples, a cryogenic fuel is stored in a supply tank at a temperature corresponding to a saturated pressure that is above atmospheric pressure. In such examples, the cryogenic fuel would also be stored at saturated pressures above atmospheric pressure in an onboard cryogenic fuel tank. The high saturated pressure can result in catastrophic damage to a vehicle powered by a liquid cryogen (e.g. a hydrogen aircraft) if the onboard cryogenic fuel tank were to malfunction or be punctured in flight. In some examples, a supply tank is driven to a take-off and/or a launch site to refuel the onboard tank with cryogenic fuel (e.g., liquid hydrogen (LH2)). In such examples, the LH2 is stored in an insulated supply tank but the temperature of the LH2 is still unregulated, in which case the mass of the onboard LH2 is neither controllable nor functionally optimized. In examples disclosed herein, a sub-cooler in refueling system for a hydrogen aircraft reduces the temperature and increases the density of LH2 during refueling such that smaller onboard cryogenic fuel tank(s) can be used to store the same mass of LH2, and the mass of LH2 supplied to the onboard cryogenic fuel tank(s) can be precisely controlled. For example, if LH2 is provided by a supply tank at 25 Kelvin (K), the density of the LH2 fuel would be about 64 kg/m 3  onboard an example hydrogen aircraft. The example sub-cooler disclosed herein can reduce the temperature of the LH2 to 20 K while refueling, thus increasing the density of LH2 to about 71 kg/m 3  and reducing the onboard tank volume by about 10%. 
     The terms “upstream” and “downstream” refer to the relative direction with respect to fluid flow in a fluid pathway. For example, “upstream” refers to the direction from which the fluid flows, and “downstream” refers to the direction to which the fluid flows. The terms “primary” and “auxiliary” refer to the endpoints of the respective flowlines. For example, “primary” refers to the flowline that directs sub-cooled cryogenic fuel to the onboard cryogenic fuel tank(s), and “auxiliary” refers to the flowline that directs unused cryogenic fuel to a storage tank. The term “saturated pressure” refers to the pressure at which a given cryogenic liquid and its vapor can co-exist in thermodynamic equilibrium within a confined container. 
     In some examples used herein, “including” and “comprising” (and all forms and tenses thereof) are used herein to be open ended terms. Thus, whenever a claim employs any form of “include” or “comprise” (e.g., comprises, includes, comprising, including, having, etc.) as a preamble or within a claim recitation of any kind, it is to be understood that additional elements, terms, etc. may be present without falling outside the scope of the corresponding claim or recitation. As used herein, when the phrase “at least” is used as the transition term in, for example, a preamble of a claim, it is open-ended in the same manner as the term “comprising” and “including” are open ended. The term “and/or” when used, for example, in a form such as A, B, and/or C refers to any combination or subset of A, B, C such as (1) A alone, (2) B alone, (3) C alone, (4) A with B, (5) A with C, (6) B with C, and (7) A with B and with C. As used herein in the context of describing structures, components, items, objects and/or things, the phrase “at least one of A and B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. Similarly, as used herein in the context of describing structures, components, items, objects and/or things, the phrase “at least one of A or B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. As used herein in the context of describing the performance or execution of processes, instructions, actions, activities and/or steps, the phrase “at least one of A and B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. Similarly, as used herein in the context of describing the performance or execution of processes, instructions, actions, activities and/or steps, the phrase “at least one of A or B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. 
     As used herein, singular references (e.g., “a”, “an”, “first”, “second”, etc.) do not exclude a plurality. The term “a” or “an” entity, as used herein, refers to one or more of that entity. The terms “a” (or “an”), “one or more”, and “at least one” can be used interchangeably herein. Furthermore, although individually listed, a plurality of means, elements or method actions may be implemented by, e.g., a single unit or processor. Additionally, although individual features may be included in different examples or claims, these may possibly be combined, and the inclusion in different examples or claims does not imply that a combination of features is not feasible and/or advantageous. 
     For the figures disclosed herein, identical numerals indicate the same elements throughout the figures. The example illustration of  FIG.  1    is a block diagram representing a prior cryogenic refueling system  100 . As shown in  FIG.  1   , the cryogenic refueling system  100  (“system  100 ”) includes components connected in series by coupled vacuum-jacketed (VJ) flowlines  110 . In general, the cryogenic refueling system  100  may include a manually operated or electronically actuated flow control valve  104  (e.g., cryogenic globe valve) to regulate flow of the cryogenic fuel being provided by a supply tank  102 . 
     The flow control valve  104  operates at working temperatures lower than 233 K and may be used for transmitting low temperature cryogenic fluid (e.g., liquefied natural gas, liquid oxygen, liquid hydrogen, etc.). In some examples, the flow control valve  104  regulates the flow of the cryogenic fluid such that a known mass of fuel can be provided to an onboard cryogenic fuel tank  112 . The example flow control valve  104  is constructed to thermally insulate the cryogenic fuel during transmission so that the fluid does not heat up, vaporize, and leak out as a gas. In some examples, the flow control valve  104  is connected to the supply tank  102  by one or more VJ flowlines  110 . 
     The example cryogenic refueling system  100  may further include a manually operated or electronically actuated cryogenic valve  108 . In some examples, the cryogenic valve is a shut-off valve to quickly terminate flow to the onboard cryogenic fuel tank  112  such that the onboard cryogenic fuel tank  112  does not overfill. The example cryogenic valve  108  is constructed to thermally insulate the cryogenic fuel during transmission so that the fluid does not heat up, vaporize, and leak out as a gas. In some examples, the cryogenic valve  108  is connected to the onboard cryogenic fuel tank  112  by one or more VJ flowlines  110 . 
     In some examples, the VJ flowlines  110  illustrated in  FIG.  1    are used to connect the components of the cryogenic refueling system  100 . The VJ flowlines  110  of the example cryogenic refueling system  100  maintain the temperatures of cryogenic fluids so the fluids do not heat up and leak out of the system  100  as gases. In some examples, the VJ flowlines  110  can include VJ pipes, flexible lines, VJ valves, vapor vents, vapor vent heaters, VJ manifolds, etc. In general, the example VJ flowlines  110  include an inner and an outer pipe or line. The inner pipe of the example VJ flowlines  110  carries the cryogenic liquid and is insulated with multiple alternating layers of a heat barrier and a non-conductive spacer. The insulating layers create a space between the inner and outer pipes in the example VJ flowlines  110  that is depressurized using a vacuum pump to create a static vacuum shield. The vacuum shield safeguards the example cryogenic fuel from heat transfer due to conduction, convection, and radiation. 
     The example cryogenic refueling system  100  illustrated in  FIG.  1    includes a flowmeter  106 . In some examples, the flowmeter  106  is a cryogenic flowmeter that measures the volumetric flowrate of the cryogenic fuel over multiple time periods. The term time period refers to the length of time over which the example cryogenic flows at a particular volumetric flowrate. The volume of the example cryogenic fuel supplied to the onboard cryogenic fuel tank  112  is determined by aggregating volumetric flowrates multiplied by the corresponding time periods for the duration of refueling. The density of the example cryogenic fuel supplied to the onboard cryogenic fuel tank  112  is a thermodynamic property dependent on the temperature of the cryogenic fuel. Since the example VJ flowlines  110  prevent the cryogenic fuel from absorbing heat during the refueling process, the temperature at which the cryogenic fuel is stored in the supply tank  102  is similar to the temperature at which the cryogenic fuel is stored on the onboard cryogenic fuel tank  112 . Therefore, the density of the example cryogenic fuel within the onboard cryogenic fuel tank  112  can be determined at multiple occurrences during the refueling process either from a temperature reading of the onboard cryogenic fuel tank  112  or the supply tank  102 . The example flowmeter  106 , thereby allows determination of cryogenic fuel mass stored in the onboard cryogenic fuel tank  112 . However, the density and mass of the example cryogenic fuel in the onboard cryogenic fuel tank  112  is dependent on the temperature of the cryogenic fuel within the supply tank  102 , which is generally not adjustable. For example, the supply tank  102  can be filled at a liquid cryogen industrial facility with LH2 at 20 Kelvin (K) prior to transporting the cryogenic fuel to the hydrogen aircraft for refueling. The example LH2 temperature of 20 K correlates to an example LH2 saturated pressure of 14 pounds per square inch (psi), which is similar to atmospheric pressure and is therefore a desired saturated pressure for example LH2 stored in the onboard cryogenic fuel tank  112 . However in transit, the example temperature of LH2 within the supply tank  102  could increase to a temperature of 24 K. The example LH2 temperature of 24 K correlates to an example LH2 saturated pressure of 40 psi, which can be an undesirable saturated pressure for stored LH2 in the onboard cryogenic fuel tank  112 . 
     As shown in  FIG.  1   , the example onboard cryogenic fuel tank  112  is located on a hydrogen aircraft to supply liquid or gaseous hydrogen to modified gas-turbine engine(s). The example hydrogen-powered turbine engine(s) combust a mixture of hydrogen fuel and compressed air to generate thrust. The example onboard cryogenic fuel tank  112  used to store cryogenic fuel (e.g., LH2) has thicker walls and made of stronger alloys than non-cryogenic fuel tanks to avoid brittle cracking. The example onboard cryogenic fuel tank  112  stores cryogenic fuel at low temperatures (e.g., 20 K) relative to non-cryogenic fuel tanks. The example onboard cryogenic fuel tank  112  thermally insulates the cryogenic fuel to prevent temperature increases (e.g., from 20 K to 24 K) which can cause boil-off and saturated pressure increases (e.g., from 14 psi to 40 psi). The onboard cryogenic fuel tank  112  of this example can be up to four times larger in volume than non-cryogenic fuel tanks due to a fundamentally different insulating architecture relative to non-cryogenic fuel tanks (e.g., a vacuum layer between an inner and outer container). In many liquid cryogen-fueled vehicles (e.g., hydrogen aircraft) reducing the volume of the onboard cryogenic fuel tank  112  (e.g., from 20 m 3  to 18 m 3 ) can increase storage capacity, passenger capacity, cargo weight limit, etc. 
       FIG.  2 A  illustrates a sub-cooling cryogenic refueling system  200  (“system  200 ”) that includes a sub-cooler  204 . The example sub-cooler  204  can be used in conjunction with the cryogenic refueling system  100  of  FIG.  1   , in place of the flow control valve  104 , and with additional and/or alternative components such as a vaporizer  222 , a compressor  224 , a storage tank  226 , etc. In the illustrated example of  FIG.  2 A , the sub-cooler  204  includes a first valve  206 , a second valve  208 , a cryogenic heat exchanger  210 , and a temperature sensor  212 . In the illustrated example of  FIG.  2   , the sub-cooling cryogenic refueling system  200  includes a supply tank  202 , a flowmeter  106 , a cryogenic valve  108 , VJ flowlines  110 , an onboard cryogenic fuel tank  214 , the vaporizer  222 , the compressor  224 , and the storage tank  226 . 
     The example sub-cooler  204  illustrated in  FIG.  2 A  includes a first valve  206  to separate the flowing cryogenic fuel into a primary flowline  228  and an auxiliary flowline  230 . The example first valve  206  can vary the volumetric flowrate into the primary flowline  228  and auxiliary flowline  230 . The example sub-cooler  204  further includes a second valve  208  to reduce the saturated pressure of the cryogenic fuel in the auxiliary flowline  230 , thereby reducing the temperature of the cryogenic fuel flowing through the auxiliary flowline  230 . The example sub-cooler  204  further includes a cryogenic heat exchanger  210  to transfer heat from the warmer cryogenic fuel in the primary flowline  228  to the cooler cryogenic fuel in the auxiliary flowline  230 . The example sub-cooler  204  further includes a temperature sensor  212  that measures the temperature of the cryogenic fuel in the primary flowline  228  and feeds the measured temperature back to a sub-cooler controller  232  to determine the actuator position in the first valve  206 . 
     The example sub-cooler  204  illustrated in  FIG.  2 A  includes the first valve  206  which can be an electronically-actuated proportional valve and/or servo valve, for example. Traditional directional control valves generally operate in fully open, fully closed, or fully switched states of flow. Changing flow direction during operation with traditional directional control valves would require separate individual valves for each direction and would involve complex hydraulic circuits. Proportional valves and/or servo valves can adjust the spool positions within the valves to control the flowrates through one or more outlets. The variable positioning allows spools to be designed with metering notches to provide directional control functions in a single valve. The example first valve  206  can be a proportional valve that inputs one flowline of cryogenic fuel and outputs two flowlines of variable and controllable volumetric flow, for example. The example first valve  206  can adjust the area of an inlet to the primary flowline  228  and the area of an inlet to the auxiliary flowline  230  by adjusting the spool position within the example first valve  206 . By adjusting the inlet areas of the primary flowline  228  and the auxiliary flowline  230 , the example first valve  206  adjusts the flowrate within the primary flowline  228  and the auxiliary flowline  230 . 
     The example sub-cooler  204  illustrated in  FIG.  2 A  includes the second valve  208 , such as a thermal expansion valve, etc. A thermal expansion valve is a metering device that can input a cryogenic fluid and, in some examples, change the state of part of the cryogenic liquid to a gas, thus reducing the saturated pressure (e.g., from 40 psi to 4 psi) and temperature (e.g., from 24 K to 16 K) within the auxiliary flowline  230 . When the saturated pressure of LH2 is decreased, the temperature of LH2 also decreases. Therefore, by thermally expanding the example LH2 in the second valve  208 , the temperature in the auxiliary flowline  230  decreases. The relationship of temperature versus saturated pressure for example LH2 is described in greater detail below in connection with  FIG.  3   . The example second valve  208  can maintain a consistent saturated pressure in the auxiliary flowline downstream of the second valve  208  by mechanically and/or electronically adjusting the flow of fluid from the upstream inlet to the downstream outlet during operation. The saturated pressure the example second valve  208  outputs can be calibrated prior to operation. 
     The example sub-cooler  204  illustrated in  FIG.  2 A  includes the cryogenic heat exchanger  210 . The example cryogenic heat exchanger  210  can transfer heat from a warmer flowline (e.g., the primary flowline  228 ) to a cooler flowline (e.g., the auxiliary flowline  230 ). The primary flowline  228  and the auxiliary flowline  230  enter the cryogenic heat exchanger  210  and flow through sets of tubes and/or plates within a casing and/or a shell. The tubes can be supported by other components, for example fans, condensers, coolants, plates, baffles, tie-rods, spacers, etc. The primary flowline  228  indirectly contacts the auxiliary flowline  230  such that the fluids do not mix, but the primary flowline  228  can freely transfer heat to the auxiliary flowline  230 . The example cryogenic heat exchanger  210  can be of single pass and/or multi pass designs with fluid flowing in a cross flow, counter flow, or parallel flow pattern. In some examples, the cryogenic heat exchanger  210  uses a cross flow method wherein the primary flowline  228  and the auxiliary flowline  230  enter the cryogenic heat exchanger  210  at two different points and cross paths perpendicularly. In some examples, the cryogenic heat exchanger  210  uses a parallel flow method wherein the primary flowline  228  and the auxiliary flowline  230  enter the cryogenic heat exchanger  210  at the same end, flow in parallel paths, and exit at the other end. In some examples, the cryogenic heat exchanger  210  uses a counter flow method wherein the primary flowline  228  and the auxiliary flowline  230  enter the cryogenic heat exchanger  210  at opposite ends, flow in parallel paths, and exit at opposite ends. The example sub-cooler  204  illustrated in  FIG.  2 A  includes a temperature sensor  212 . The example temperature sensor  212  can measure the temperature of the cryogenic fuel within the primary flowline  228  and feed back the measured temperature to the sub-cooler controller  232 . The example temperature sensor  212  can be a cryogenic silicon sensor, platinum resistance sensor, cryogenic temperature monitor, etc. 
     The example sub-cooler  204  illustrated in  FIG.  2 A  includes a sub-cooler controller  232 . The example sub-cooler controller  232  is a closed-loop control system including a first controller and a second controller. In some examples, the first controller is a temperature loop controller  234 . In some examples, the second controller is a position loop controller  236 . The temperature loop controller  234  and/or the position loop controller  236  of  FIG.  2 A  may be instantiated (e.g., creating an instance of, bring into being for any length of time, materialize, implement, etc.) by processor circuitry  238  such as a central processing unit executing instructions. In some examples, the temperature loop controller  234  and the position loop controller  236  are integrated on the processor circuitry  238  as shown in FIG.  2 A. The example temperature loop controller  234  determines a commanded first valve actuator position based on at least a source temperature and a target temperature. In some examples, the source temperature is a temperature of the cryogenic fuel in the supply tank  202 . In some examples, the target temperature is a temperature of the cryogenic fuel stored in the onboard cryogenic fuel tank  214 . The temperature in the example supply tank  202  can be read manually from a temperature gauge and entered into the temperature loop controller  234 , read and entered electronically by the temperature loop controller  234 , or any combination of those options. The example temperature loop controller  234  determines an error between a measured temperature from the temperature sensor  212  and the target temperature. The example temperature loop controller  234  determines (e.g., adjusts) the commanded first valve actuator position based on the error and a preceding commanded first valve actuator position. 
     The example position loop controller  236  determines an actual first valve actuator position based on the commanded first valve actuator position. The example position loop controller  236  generates a primary first valve effective area and an auxiliary first valve effective area based on the actual first valve actuator position. In some examples, the primary first valve effective area is at the inlet of the primary flowline  228 . In some examples, the auxiliary first valve effective area is at the inlet of the auxiliary flowline  230 . By increasing the primary first valve effective area in conjunction with decreasing the auxiliary first valve effective area, the temperature of the cryogenic fuel in the primary flowline  228  (measured by the temperature sensor  212 ) increases. By decreasing the primary first valve effective area in conjunction with increasing the auxiliary first valve effective area, the temperature of the cryogenic fuel in the primary flowline  228  (measured by the temperature sensor  212 ) decreases. 
     The example cryogenic heat exchanger  210  of the sub-cooler  204  illustrated in  FIG.  2 A  can input cryogenic fuel in the primary flowline  228  at one temperature (e.g., 24 K) and can output the cryogenic fuel in the primary flowline  228  at a lower temperature (e.g., 20 K). The temperature output in the primary flowline  228  from the example cryogenic heat exchanger  210  is dependent on the amount of cryogenic liquid and/or vapor that is input to the cryogenic heat exchanger  210  via the auxiliary flowline  230 . In some examples, the amount of cryogenic liquid and/or vapor input to the cryogenic heat exchanger  210  via the auxiliary flowline  230  is determined based on the primary first valve effective area and the auxiliary first valve effective area generated by the position loop controller  236 . Two examples disclosed below illustrate operational cases of the sub-cooler  204 , wherein the example LH2 temperature in the supply tank  202  is 24 K, the LH2 temperature in the auxiliary flowline  230  downstream of the second valve  208  is 16 K, and the target temperature in the onboard cryogenic fuel tank  112  is 20 K. In a first example, the first valve  206  is actuated by the sub-cooler controller  232  such that the primary first valve effective area is 90% of the maximum area of the inlet to the primary flowline  228  and the auxiliary first valve effective area is 10% of the maximum area of the inlet to the auxiliary flowline  230 . The first example case can result in the LH2 temperature measured by the temperature sensor  212  to be 22 K. In a second example, the sub-cooler controller  232  actuates the first valve  206  such that the primary first valve effective area is 80% of the maximum area of the inlet to the primary flowline  228  and the auxiliary first valve effective area is 20% of the maximum area of the inlet to the auxiliary flowline  230 . The second example case can result in the LH2 temperature measured by the temperature sensor  212  to be 20 K, which matches the target temperature. 
     As shown in  FIG.  2 A , the example onboard cryogenic fuel tank  214  is located on a hydrogen aircraft to supply liquid or gaseous hydrogen to modified gas-turbine engine(s). The example hydrogen-powered turbine engine(s) combust a mixture of hydrogen fuel and compressed air to generate thrust. The example onboard cryogenic fuel tank  214  used to store cryogenic fuel (e.g., LH2) has thicker walls and made of stronger alloys than non-cryogenic fuel tanks to avoid brittle cracking. The example onboard cryogenic fuel tank  214  also has a venting device, such as a vent valve, to release vapor pressure build up. The term “vapor pressure” is used herein to describe the pressure exerted on a container (e.g., supply tank  202  and/or onboard cryogenic fuel tank  214 ) and the cryogenic liquid by the evaporated or vaporized cryogenic liquid. The example onboard cryogenic fuel tank  214  stores cryogenic fuel at low temperatures (e.g., 20 K) relative to non-cryogenic fuel tanks. The example onboard cryogenic fuel tank  214  thermally insulates the cryogenic fuel to prevent temperature increases (e.g., from 20 K to 24 K) which can cause boil-off and saturated pressure increases (e.g., from 14 psi to 40 psi). The onboard cryogenic fuel tank  214  of this example can have a smaller volume than the onboard cryogenic fuel tank  112  illustrated in  FIG.  1    due to the increased density of the sub-cooled cryogenic fuel. For example, the sub-cooler  204  can reduce the temperature of example LH2 from 24 K to 20 K, thus increasing the density of the flowing LH2 from 66 kg/m 3  to 71 kg/m 3 . In some examples, the system  100  illustrated in  FIG.  1    does not include the sub-cooler  204  and thus refuels the example onboard cryogenic fuel tank  112  with LH2 at 24 K and 66 kg/m 3 . In some examples, the onboard cryogenic fuel tank  112  of the example system  100  can be 20 m 3  in volume. Since volume is inversely proportional to density, if the example system  200  refuels LH2 at a density of 71 kg/m 3 , then the volume of the onboard cryogenic fuel tank  214  can be 18.6 m 3  to contain the same mass of LH2 fuel as the onboard cryogenic fuel tank  112  of system  100 . 
     The example sub-cooling cryogenic refueling system  200  illustrated in  FIG.  2 A  includes a supply tank  202 . In some examples, the supply tank  202  is a cryogenic transport trailer and/or mobile tanker that brings cryogenic fuel to the refueling location. For example, the supply tank  202  can be driven on a tarmac to refuel a hydrogen aircraft preflight. In some examples, the supply tank  202  contains an integrated and/or separate system and/or apparatus for equalizing vapor pressure within the supply tank  202  and providing a pressure differential between the supply tank  202  and the onboard cryogenic fuel tank  214 . The term source temperature refers to the temperature of the cryogenic fuel stored in the example supply tank  202  prior to refueling of the example onboard cryogenic fuel tank  214 . Further examples of systems and/or apparatus for providing a pressure differential to the system  200  are described below. 
     The example sub-cooling cryogenic refueling system  200  illustrated in  FIG.  2 A  includes a vaporizer  222 . The example vaporizer  222  can be a cryogenic vaporizer that converts liquid cryogens into a gaseous state. The example vaporizer  222  can use fins to absorb heat from surrounding ambient air and transfer that heat to the cryogenic fuel flowing though the tube. The example cryogenic fuel can be partially or fully converted to a gaseous state by the second valve  208  and/or the cryogenic heat exchanger  210 . The example vaporizer  222  ensures that the unused cryogenic fuel in the auxiliary flowline  230  is converted to a gas for storage and reuse. The pressure setting of the example vaporizer  222  refers to the pressure of vaporized cryogenic liquid exiting the example vaporizer  222 . The pressure setting can be adjusted by the sub-cooler controller  232  or by another controller located on and/or connected to the example vaporizer  222 . Alternatively, the cryogenic fuel can be vaporized and released into ambient air. 
     The example vaporizer  222  illustrated in  FIG.  2 A  leads to a compressor  224  and a storage tank  226 . The example compressor  224  pressurizes the gas leaving the vaporizer  222  and directs the pressurized gas into the storage tank  226 . The pressure of the gas exiting the example compressor  224  divided by the pressure of the gas entering the example compressor  224  is referred to as the compression ratio of the compressor  224 . The example compression ratio can be adjusted by the sub-cooler controller  232  or another controller and/or control system located on and/or connected to the compressor  224 . The unused gas in the storage tank  226  can be converted back into a cryogenic fluid and used at a later time as a cryogenic fuel. 
       FIG.  2 B  illustrates a sub-cooling cryogenic refueling system  200  (“system  200 ”) that includes a sub-cooler  204  as previously described. The example sub-cooler  204  can be used in conjunction with the cryogenic refueling system  100  of  FIG.  1   , in place of the flow control valve  104 , and with additional components such as a pressure building coil  216 , a vaporizer  222 , a compressor  224 , and a storage tank  226 . In the illustrated example of  FIG.  2 B , the sub-cooler  204  includes a first valve  206 , a second valve  208 , a cryogenic heat exchanger  210 , and a temperature sensor  212  as previously described in reference to  FIG.  2 A . In the illustrated example of  FIG.  2 B , the system  200  includes a flowmeter  106 , a cryogenic valve  108 , VJ flowlines  110 , the onboard cryogenic fuel tank  214 , the vaporizer  222 , the compressor  224 , and the storage tank  226 . The example system  200  as illustrated in  FIG.  2 B  also includes a supply tank  202  with the example pressure building coil  216  connected to the supply tank  202 . 
     The example supply tank  202  of  FIG.  2 B  includes a flowline leading to a pressure building coil  216 . In some examples, the flowline leading to the pressure building coil  216  is separate from the flowline leading to the sub-cooler  204 . The example pressure building coil  216  includes a flowline leading back to the supply tank  202 . In some examples, the cryogenic fuel in the supply tank  202  is extracted through the flowline into the pressure building coil  216  in accordance with the flow direction illustrated in  FIG.  2 B . In some examples, the pressure building coil  216  increases the vapor pressure in the supply tank  202  prior to refueling such that the vapor pressure in the supply tank is greater than the vapor pressure in the onboard cryogenic fuel tank  214 . The example onboard cryogenic fuel tank  214  includes a vent valve that is opened to reduce the vapor pressure within the onboard cryogenic fuel tank  214 . In some examples, increasing the vapor pressure in the supply tank  202  and reducing the vapor pressure in the onboard cryogenic fuel tank  214  provides a pressure differential to the system  200 . 
     The example pressure building coil  216  of  FIG.  2 B  is used to regulate and maintain vapor pressure for consistent refueling speed in the system  200 . In some examples the pressure building coil  216  is a vaporizer with fins heated by ambient air, which cause flowing cryogenic liquid to phase change into vapor. The pressure building coil  216  of this example feeds the vapor back into the supply tank  202 , thus increasing the vapor pressure within the supply tank  202 . In some examples, the rising vapor pressure applies a distributed force to the surface of the cryogenic fuel, which drives the cryogenic fuel to flow through the pressure building coil  216 , and thus forms a pressure building loop. The example pressure building coil  216  includes a controller that actuates the input valve to the pressure building loop in response to the output vapor pressure of the pressure building coil  216 . For example, prior to refueling, the onboard cryogenic fuel tank  214  has a vapor pressure of 100 psi and the supply tank  202  has a vapor pressure of 15 psi. The example valve to the pressure building coil  216  is opened and the output pressure is set to 100 psi with the controller. At the same time, for instance, the vent valve on the onboard cryogenic fuel tank  214  is opened and the vapor pressure is reduced to 70 psi. In such examples, the refueling speed of the system  200  will be a first speed. If, for example, the vapor pressure was increased to 80 psi in the supply tank  202  by the pressure building coil  216 , and the vapor pressure was reduced to 70 psi in the onboard cryogenic fuel tank  214 , then the refueling speed would be less than the first speed. 
       FIG.  2 C  illustrates a sub-cooling cryogenic refueling system  200  (“system  200 ”) that includes a sub-cooler  204  as previously described. The example sub-cooler  204  can be used in conjunction with the cryogenic refueling system  100  of  FIG.  1   , in place of the flow control valve  104 , and with additional components such as a transfer pump  218 , a vaporizer  222 , a compressor  224 , and a storage tank  226 . In the illustrated example of  FIG.  2 C , the sub-cooler  204  includes a first valve  206 , a second valve  208 , a cryogenic heat exchanger  210 , and a temperature sensor  212  as previously described in reference to  FIG.  2 A . In the illustrated example of  FIG.  2 C , the system  200  includes a flowmeter  106 , a cryogenic valve  108 , VJ flowlines  110 , the onboard cryogenic fuel tank  214 , the vaporizer  222 , the compressor  224 , and the storage tank  226 . The example system  200  as illustrated in  FIG.  2 C  also includes a supply tank  202  with the example transfer pump  218  submerged within and/or externally connected to the supply tank  202 . 
     The example transfer pump  218  of  FIG.  2 C  can be a cryogenic centrifugal pump that is electronically and/or hydraulically driven. In some examples, the transfer pump is submerged in the cryogenic liquid with the supply tank  202  and/or externally connected to the supply tank  202 . In some examples, the transfer pump  218  is electronically actuated, controllable, and provides variable flow speeds of cryogenic fuel from the supply tank  202  to the system  200 . In some examples, the transfer pump  218  includes a gearbox that provides fixed and/or variable flow speeds of cryogenic fuel from the supply tank  202  to the system  200 . The example transfer pump  218  illustrated in  FIG.  2 C  provides a vapor pressure to the system  200  that is greater than the vapor pressure within the onboard cryogenic fuel tank  214 . In some examples, the vent valves on the onboard cryogenic fuel tank  214  can be opened to reduce the pressure within the onboard cryogenic fuel tank  214  to adjust the flowrate within the system  200  and/or to alleviate the work required by the transfer pump  218  to pump the cryogenic fuel into the system  200 . 
       FIG.  3    is a chart illustrating a thermodynamic relationship of temperature versus density  302  and temperature versus saturated pressure  304  for liquid hydrogen, an example of cryogenic fuel. The thermodynamic properties of LH2 shown in  FIG.  3    can be used to determine the mass of LH2 refueled to the onboard cryogenic fuel tank  214  and a target temperature and saturated pressure of LH2 refueled to the onboard cryogenic fuel tank  214  of  FIGS.  2 A- 2 C . For example, the temperature of LH2 measured by the temperature sensor  212  can be input to the density-temperature function  302  plotted in  FIG.  3    by the sub-cooler controller  232  or another computing system to return the density of the example LH2. In such an example, the volumetric flowrate measured by the flowmeter  106  and the density determined by the density-temperature function  302  can be used to determine the mass of LH2 supplied to the onboard cryogenic fuel tank  214 . 
       FIG.  4    is a flow diagram illustrating an example process/operation  400  to control operation of the sub-cooling cryogenic refueling system  200  as disclosed herein. While the example process/operation  400  is described with primary reference to sub-cooling LH2 with the sub-cooling cryogenic refueling system  200  of  FIGS.  2 A- 2 C , the process/operation  400  can be used to refuel an onboard cryogenic fuel tank with another sub-cooled cryogenic fuel. 
     At block  402 , the supply tank  202  increases vapor pressure within the supply tank  202  and/or increases the vapor pressure within the system  200 . The supply tank  202  has a pressure building coil  216  as illustrated in  FIG.  2 B , a transfer pump  218  as illustrated in  FIG.  2 C , and/or another pressure building system as illustrated in  FIG.  2 A  incorporated with the supply tank  202  and/or with the system  200  upstream of the sub-cooler  204 . In conjunction with increasing the vapor pressure in the supply tank  202  and/or in the system  200 , the vapor pressure in the onboard cryogenic fuel tank  214  is decreased by opening vent valves on the onboard cryogenic fuel tank  214 . This combination of pressure changes generates a pressure differential across the system  200 . 
     At block  404 , the cryogenic valve  108  is opened either manually or electronically by the sub-cooler controller  232  or another controller integrated into the system  200 . Opening the cryogenic valve  108  begins the refueling of the onboard cryogenic fuel tank  214 , allowing the cryogenic fuel to pass through the sub-cooler  204  into the onboard cryogenic fuel tank  214 . 
     At block  406 , the cryogenic fuel is sub-cooled by the sub-cooler  204 . For example, the cryogenic fuel from the supply tank  202  flows to a first valve  206  that splits the flow into a primary flowline  228  and an auxiliary flowline  230 . The auxiliary flowline  230  directs the cryogenic fuel to a second valve  208  that lowers the saturated pressure and temperature of the cryogenic fuel. Both the primary flowline  228  and the auxiliary flowline  230  flow to a cryogenic heat exchanger  210 , where heat is transferred from the primary flowline  228  to the auxiliary flowline  230 . The sub-cooled cryogenic fuel in the primary flowline  228  is then directed to a temperature sensor  212  and ultimately to an onboard cryogenic fuel tank  214 . 
     At block  408 , the temperature of the cryogenic fuel is measured by the temperature sensor  212  and stored at multiple intervals over the duration of the refueling operation. The measured temperatures can be stored in the sub-cooler controller memory  240  and/or in some other memory located in the system  200 . 
     At block  410 , the density of the cryogenic fuel is determined and stored at the same intervals over the duration of the refueling operation based on example thermodynamic properties as illustrated in  FIG.  3   . The determined densities can be stored in the sub-cooler controller memory  240  and/or in another memory located in the system  200 , for example. 
     At block  412 , the volumetric flowrate is measured by the flowmeter  106  and stored at the same intervals over the duration of the refueling operation. The measured flowrates can be stored in the sub-cooler controller memory  240  and/or in another memory located in the system  200 . 
     At block  414 , the sub-cooler controller  232  and/or another computing device located in the system  200  can determine the total mass of cryogenic fuel stored in the onboard cryogenic fuel tank  214  based on the temperatures, densities, and flowrates measured and/or determined over the duration of the refueling operation. For example, the sub-cooler  204  can refuel LH2 to the onboard cryogenic fuel tank  214  at 20 K, which corresponds to an LH2 density of 71 kg/m 3 . In such an example, the onboard cryogenic fuel tank  214  can have a maximum volume capacity for LH2 of 18 m 3 . If the flowmeter measures the volumetric flowrate to be 0.01 m 3 /s, while the example LH2 is 20 K, then the time it takes to refuel the onboard cryogenic fuel tank  214  is 30 minutes and the total mass of refueled LH2 is 1278 kg. 
     At block  416 , the sub-cooler controller  232  or another controlling device located in the system  200  can determine if the total mass of cryogenic fuel stored in the onboard cryogenic fuel tank  214  is at the target total mass (e.g., 1278 kg). If the total mass of the cryogenic fuel in the onboard cryogenic fuel tank  214  is not at the target capacity, then the sub-cooling cryogenic refueling operation continues as control reverts to block  406 . 
     At block  418 , if the total mass of the cryogenic fuel in the onboard cryogenic fuel tank  214  is at the target capacity, then the sub-cooler controller  232  or another controlling device located in the system  200  can send an electronic signal to the cryogenic valve  108  to shut off the flow and end the refueling operation. Alternatively, if the total mass of the cryogenic fuel in the onboard cryogenic fuel tank  214  is at the target capacity, then the cryogenic valve can be shut off manually. 
       FIG.  5    is a flow diagram illustrating an example process or operation  500  according to block  406  of  FIG.  4    to sub-cool the cryogenic fuel by the sub-cooler  204  (e.g., block  406  of the example of  FIG.  4   ) that may be followed by the sub-cooler  204  as disclosed herein. While the operation  500  is described with primary reference to sub-cooling LH2 with the sub-cooler  204  of  FIGS.  2 A- 2 C , the operation  500  can be used to refuel an onboard cryogenic fuel tank with another sub-cooled cryogenic fuel. 
     At block  502 , the first valve  206  of the sub-cooler  204  separates the flow of cryogenic fuel from the supply tank  202  into a primary flowline  228  and an auxiliary flowline  230 . For example, the controller can actuate the first valve  206  such that the primary first valve effective area is 90% of the maximum area of the inlet to the primary flowline  228  and the auxiliary first valve effective area is 10% of the maximum area of the inlet to the auxiliary flowline  230 . Therefore, 90% of the cryogenic fuel from the supply tank  202  flows into the primary flowline  228  and 10% of the cryogenic fuel from the supply tank  202  flows into the auxiliary flowline  230 . 
     At block  504 , the second valve  208  of the sub-cooler  204  reduces the saturated pressure of the cryogenic fuel in the auxiliary flowline  230 , thereby reducing the temperature of the cryogenic fuel in the auxiliary flowline  230 . For example, the second valve  208  can expand LH2 in the auxiliary flowline  230  such that the LH2 temperature drops from 24 K to 16 K and the LH2 saturated pressure drops from 40 psi to 14 psi. 
     At block  506 , the sub-cooler  204  directs the primary flowline  228  and the auxiliary flowline  230  to the cryogenic heat exchanger  210 . At block  508 , the cryogenic heat exchanger  210  processes the cryogenic fuel from the primary flowline  228  and the auxiliary flowline  230  to transfer heat from the primary flowline  228  to the auxiliary flowline  230 , which sub-cools the cryogenic fuel flowing through the primary flowline  228 . For example, the cryogenic fuel temperature entering the cryogenic heat exchanger  210  via the primary flowline  228  can be 24 K and the cryogenic fuel temperature entering the cryogenic heat exchanger  210  via the auxiliary flowline  230  can be 16 K. In such an example, the cryogenic fuel temperature exiting the cryogenic heat exchanger  210  via the primary flowline  228  can be 20 K, depending on how much cryogenic fuel was diverted to the auxiliary flowline  230  by the first valve  206 . 
     At block  510 , the sub-cooler  204  directs the primary flowline  228  to the temperature sensor  212  and then, to the onboard cryogenic fuel tank  214 . The sub-cooler  204  also directs the auxiliary flowline to the vaporizer  222 . 
       FIG.  6    is a flow diagram illustrating an operation  600  that may be followed by the sub-cooler controller  232  as disclosed herein. While the operation  600  is described with primary reference to the sub-cooler controller  232  of  FIGS.  2 A- 2 C , the operation  600  can be used to control any sub-cooler in a sub-cooling cryogenic refueling system. 
     At block  602 , the temperature loop controller  234  determines a commanded first valve actuator position based on the temperature of the cryogenic fuel in the supply tank  202  and the target temperature of the cryogenic fuel to be stored in the onboard cryogenic fuel tank  214 . For example, the cryogenic fuel temperature stored in the supply tank  202  can be 24 K and the target cryogenic fuel temperature to be stored in the onboard cryogenic fuel tank  214  can be 20 K. The example temperature loop controller  234  can determine that to achieve the target temperature, the first valve actuator position shall be actuated to a position in which the primary first valve effective area is 80% of the maximum area of the inlet to the primary flowline  228  and the auxiliary first valve effective area is 20% of the maximum area of the inlet to the auxiliary flowline  230 . 
     At block  604 , the position loop controller  236  determines an actual first valve actuator position based on the commanded first valve actuator position. The commanded first valve actuator position is the position to which the spool(s) inside the first valve  206  are to be actuated by a servomotor to achieve a desired primary and auxiliary first valve effective areas. The position loop controller  236  obtains the actual first valve actuator position from a servomotor sensor in the first valve  206 . The position loop controller  236  determines the error/difference between the actual first valve actuator position from the servomotor sensor and the commanded first valve actuator position from the temperature loop controller  234 . The position loop controller  236  uses a feedback loop to control the servomotor in the first valve  206  and reduce the error between the actual and commanded first valve actuator positions to near zero. 
     At block  606 , the position loop controller  236  generates a primary first valve effective area and an auxiliary first valve effective area based on the actual first valve actuator position. The primary first valve effective area and the auxiliary first valve effective area affect the volumetric flowrates in the primary flowline  228  and the auxiliary flowline  230 , respectively. 
     At block  608 , the temperature loop controller  234  determines an error between the measured temperature from the temperature sensor  212  and the target temperature. 
     At block  610 , the temperature loop controller  234  determines if the error is within an acceptable range and/or sufficiently near zero. 
     At block  612 , if the temperature loop controller  234  determines that the error is not within the acceptable range, then the temperature loop controller  234  determines an adjusted commanded first valve actuator position based on the error and the preceding commanded first valve actuator position. 
     At block  614 , if the temperature loop controller  234  determines that the error is within the acceptable range, then the position loop controller  236  maintains the current actual first valve actuator position. 
       FIG.  7    is a block diagram of an example processor platform  700  structured to execute and/or instantiate the machine readable instructions and/or operations of  FIG.  6    to implement the sub-cooler controller  232  of  FIGS.  2 A- 2 C . The processor platform  700  can be, for example, a server, a personal computer, a workstation, a self-learning machine (e.g., a neural network), a mobile device (e.g., a cell phone, a smart phone, a tablet such as an iPad™), or any other type of computing device. 
     The processor platform  700  of the illustrated example includes processor circuitry  712 . The processor circuitry  712  of the illustrated example is hardware. For example, the processor circuitry  712  can be implemented by one or more integrated circuits, logic circuits, FPGAs microprocessors, CPUs, GPUs, DSPs, and/or microcontrollers from any desired family or manufacturer. The processor circuitry  712  may be implemented by one or more semiconductor based (e.g., silicon based) devices. In this example, the processor circuitry  712  implements the example temperature loop controller  234  and the example position loop controller  236 . 
     The processor circuitry  712  of the illustrated example includes a local memory  713  (e.g., a cache, registers, etc.). The processor circuitry  712  of the illustrated example is in communication with a main memory including a volatile memory  714  and a non-volatile memory  716  by a bus  718 . The volatile memory  714  may be implemented by Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS® Dynamic Random Access Memory (RDRAM®), and/or any other type of RAM device. The non-volatile memory  716  may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory  714 ,  716  of the illustrated example is controlled by a memory controller  717 . 
     The processor platform  700  of the illustrated example also includes interface circuitry  720 . The interface circuitry  720  may be implemented by hardware in accordance with any type of interface standard, such as an Ethernet interface, a universal serial bus (USB) interface, a Bluetooth® interface, a near field communication (NFC) interface, a PCI interface, and/or a PCIe interface. 
     In the illustrated example, one or more input devices  722  are connected to the interface circuitry  720 . The input device(s)  722  permit(s) a user to enter data and/or commands into the processor circuitry  712 . The input device(s)  722  can be implemented by, for example, a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, an isopoint device, and/or a voice recognition system. 
     One or more output devices  724  are also connected to the interface circuitry  720  of the illustrated example. The output devices  724  can be implemented, for example, by display devices (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display (LCD), a cathode ray tube (CRT) display, an in-place switching (IPS) display, a touchscreen, etc.), and/or a tactile output device. The interface circuitry  720  of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip, and/or graphics processor circuitry such as a GPU. 
     The interface circuitry  720  of the illustrated example also includes a communication device such as a transmitter, a receiver, a transceiver, a modem, a residential gateway, a wireless access point, and/or a network interface to facilitate exchange of data with external machines (e.g., computing devices of any kind) by a network  726 . The communication can be by, for example, an Ethernet connection, a digital subscriber line (DSL) connection, a telephone line connection, a coaxial cable system, a satellite system, a line-of-site wireless system, a cellular telephone system, an optical connection, etc. 
     The processor platform  700  of the illustrated example also includes one or more mass storage devices  728  to store software and/or data. Examples of such mass storage devices  728  include magnetic storage devices, optical storage devices, floppy disk drives, HDDs, CDs, Blu-ray disk drives, redundant array of independent disks (RAID) systems, solid state storage devices such as flash memory devices, and DVD drives. 
     The machine executable instructions  732 , which may be implemented by the machine readable instructions of  FIG.  6   , may be stored in the mass storage device  728 , in the volatile memory  714 , in the non-volatile memory  716 , and/or on a removable non-transitory computer readable storage medium such as a CD or DVD. 
     A sub-cooler for a sub-cooling cryogenic refueling system is disclosed herein. The examples disclosed herein reduce the temperature and increase the density of cryogenic fuel supplied to onboard cryogenic fuel tank(s). The examples disclosed herein reduce the required volume of onboard tank(s) for liquid cryogen-fueled vehicles (e.g., hydrogen aircraft) and control the mass of the cryogenic fuel that is stored within the onboard tank. 
     Further aspects of the present disclosure are provided by the subject matter of the following clauses: 
     Example methods, apparatus, systems, and articles of manufacture to sub-cool cryogenic fuel during the refueling of onboard cryogenic fuel tanks are disclosed herein. Further examples and combinations thereof include the following: 
     Example 1 includes a sub-cooler comprising a first valve to separate a cryogenic fuel into a primary flowline and an auxiliary flowline, wherein the cryogenic fuel in the primary flowline has a first temperature, and wherein the cryogenic fuel in the auxiliary flowline has a second temperature, a second valve to reduce the second temperature of the cryogenic fuel in the auxiliary flowline by reducing a saturated pressure in the auxiliary flowline, a cryogenic heat exchanger to reduce the first temperature of the cryogenic fuel in the primary flowline by transferring heat from the primary flowline to the auxiliary flowline, a temperature sensor to measure a measured temperature of the cryogenic fuel in the primary flowline downstream of the cryogenic heat exchanger, and a sub-cooler controller including a temperature loop controller and a position loop controller configured to regulate the first temperature output. 
     Example 2 includes the sub-cooler of any preceding clause, wherein the first valve is a proportional valve. 
     Example 3 includes the sub-cooler of any preceding clause, wherein the second valve is an expansion valve. 
     Example 4 includes the sub-cooler of any preceding clause, wherein the primary flowline and the auxiliary flowline are vacuum jacketed flowlines. 
     Example 5 includes the sub-cooler of any preceding clause, wherein the primary flowline includes a flowmeter downstream of the cryogenic heat exchanger to measure a volumetric flowrate of the cryogenic fuel. 
     Example 6 includes the sub-cooler of any preceding clause, wherein the primary flowline includes a cryogenic valve downstream of the cryogenic heat exchanger to regulate flow of the cryogenic fuel to an onboard cryogenic fuel tank. 
     Example 7 includes the sub-cooler of any preceding clause, wherein the cryogenic heat exchanger includes a second flowline to direct the auxiliary flowline to a vaporizer, the vaporizer to convert the cryogenic fuel into a gas. 
     Example 8 includes the sub-cooler of any preceding clause, wherein the vaporizer includes a flowline to direct the gas to a compressor, the compressor to pressurize the gas in a storage tank. 
     Example 9 includes At least one non-transitory computer-readable medium comprising instructions that, when executed, cause a sub-cooler controller to at least separate a cryogenic fuel into a primary flowline and an auxiliary flowline by actuating a first valve, wherein the cryogenic fuel in the primary flowline has a first temperature, and wherein the cryogenic fuel in the auxiliary flowline has a second temperature, reduce the second temperature of the cryogenic fuel in the auxiliary flowline by reducing a saturated pressure in the auxiliary flowline using a second valve, reduce the first temperature of the cryogenic fuel in the primary flowline by transferring heat from the primary flowline to the auxiliary flowline using a cryogenic heat exchanger, measure a measured temperature of the cryogenic fuel in the primary flowline downstream of the cryogenic heat exchanger with a temperature sensor, and control a sub-cooler using a temperature loop controller and a position loop controller configured to regulate the first temperature output of the sub-cooler. 
     Example 10 includes the at least one non-transitory computer-readable medium of any preceding clause, wherein the instructions from the controller are to separate the cryogenic fuel into the primary flowline and the auxiliary flowline by actuating a proportional valve. 
     Example 11 includes the at least one non-transitory computer-readable medium of any preceding clause, wherein the instructions from the controller are to measure a volumetric flowrate of the cryogenic fuel with a flowmeter at the primary flowline downstream of the cryogenic heat exchanger. 
     Example 12 includes the at least one non-transitory computer-readable medium of any preceding clause, wherein the instructions from the controller are to regulate flow of the cryogenic fuel to an onboard cryogenic fuel tank using a cryogenic valve at the primary flowline downstream of the cryogenic heat exchanger. 
     Example 13 includes the at least one non-transitory computer-readable medium of any preceding clause, wherein the instructions from the controller adjust pressure settings of a vaporizer at the auxiliary flowline downstream of the cryogenic heat exchanger, the vaporizer to convert the cryogenic fuel into a gas. 
     Example 14 includes the at least one non-transitory computer-readable medium of any preceding clause, wherein the instructions from the controller adjust a compression ratio of a compressor at the auxiliary flowline downstream of the vaporizer, the compressor to pressurize the gas in a storage tank. 
     Example 15 includes a method to refuel an onboard cryogenic fuel tank, the method comprising controlling a sub-cooler of a cryogenic refueling system including determining, using a first controller, a commanded first valve actuator position based on at least a source temperature and a target temperature, determining, using the first controller, an error between a measured temperature from a temperature sensor and the target temperature, determining, using the first controller, the commanded first valve actuator position based on the error and a preceding commanded first valve actuator position, determining, using a second controller, an actual first valve actuator position based on the commanded first valve actuator position, and generating, using the second controller, a primary first valve effective area and an auxiliary first valve effective area based on the actual first valve actuator position. 
     Example 16 includes the method of any preceding clause, including generating a pressure differential across the cryogenic refueling system, wherein a first pressure upstream of the sub-cooler is greater than a second pressure within the onboard cryogenic fuel tank. 
     Example 17 includes the method of any preceding clause, including regulating flow, via a cryogenic valve, of a cryogenic fuel in a primary flowline to the onboard cryogenic fuel tank. 
     Example 18 includes the method of any preceding clause, further including measuring one or more volumetric flowrates, via a flowmeter, of the cryogenic fuel in the primary flowline downstream of a cryogenic heat exchanger, measuring the measured temperature, via the temperature sensor, of the cryogenic fuel in the primary flowline downstream of the cryogenic heat exchanger, determining a volume of the cryogenic fuel supplied to the onboard cryogenic fuel tank based on the one or more volumetric flowrates and one or more time periods of the one or more volumetric flowrates, determining a density of the cryogenic fuel based on at least the measured temperature of the cryogenic fuel and thermodynamic properties of the cryogenic fuel, and determining a mass of the cryogenic fuel supplied to the onboard cryogenic fuel tank based on at least the volume of the cryogenic fuel supplied to the onboard cryogenic fuel tank and the density of the cryogenic fuel. 
     Example 19 includes the method of any preceding clause, including directing, via a cryogenic heat exchanger, an auxiliary flowline to a storage tank. 
     Example 20 includes the method of any preceding clause, further including directing, via the cryogenic heat exchanger, the auxiliary flowline to a vaporizer, vaporizing, via the vaporizer, a cryogenic fuel into a gas, and pressurizing, via a compressor, the gas in the storage tank. 
     The following claims are hereby incorporated into this Detailed Description by this reference, with each claim standing on its own as a separate embodiment of the present disclosure.