Patent Publication Number: US-11027090-B2

Title: Vapor column liquid accumulator

Description:
TECHNICAL FIELD 
     This disclosure relates to liquid accumulators and methods for reducing pulsations of the pressure of a liquid flow. 
     BACKGROUND 
     Liquid accumulators are used in various liquid delivery systems, for example, anesthesia agent delivery systems, fuel delivery systems, coolant delivery systems, etc. The liquid delivery system uses a pump (e.g., reciprocating pump) to drive the liquid into a piping to transmit the liquid flow. The pump may introduce pulsations of flow rate/pressure into the piping, which may not be desirable in many applications. For example, in an anesthesia agent delivery system, varying flow rate of the anesthesia agent in the piping can cause varying input pressure at the injector, which injects the agent into a vaporizer. Varying input pressure can lead to substantial variation of the agent vapor output rate given that the volume expansion from liquid to gas phase is huge (e.g., ˜200 times expansion). Thus, a liquid accumulator is used upstream of the injector to reduce pulsations of the flow rate/pressure. 
     A typical accumulator includes a liquid volume and a gas volume (i.e., gas spring) separated by an object (e.g., bladder, diaphragm, or piston). The liquid volume is fluidically connected to the piping of the liquid delivery system. The gas volume is pre-charged with gas, where the amount of the charged gas dictates the spring rate of the gas volume. In operation, the gas volume is compressed during the flow output phase of the pump and expanded during pump non-delivery period. The compression or expansion of the gas volume exerts force on the liquid volume through a bladder, diaphragm, or piston that separates the gas volume from the liquid volume, and thus smoothing the pulsations of the flow rate/pressure in the piping. 
     Conventional liquid accumulators may have technical problems such as gas permeation, liquid leakage, seal swelling, etc. In particular, compressed gas may permeate from the gas volume through the barrier (e.g., bladder, diaphragm, piston) to the liquid volume. Liquid may leak from the liquid volume through the barrier to the gas volume. Liquid may also cause the O-ring used for sealing around the piston to swell. Solutions to these problems are generally desired. 
     SUMMARY 
     In one embodiment, the present disclosure provides a liquid delivery system. The system comprises a pipe configured to transmit a liquid flow driven by a pump. The system further comprises a liquid accumulator fluidically connected to the pipe. The liquid accumulator comprises a chamber containing the liquid and a vapor column and a power source configured to input energy to the chamber to generate vapor from the liquid to form the vapor column. The vapor column constitutes a gas spring to reduce pulsations of the liquid flow in the pipe. 
     In another embodiment, the present disclosure provides an anesthesia agent delivery system. The system comprises a pump configured to drive an anesthesia agent liquid from a reservoir to a pipe and the pipe configured to transmit a flow of the anesthesia agent to an injector. The system further comprises a liquid accumulator fluidically connected to the pipe. The liquid accumulator comprises a chamber containing the anesthesia liquid flow and a vapor column and a power source configured to input energy to the chamber to generate vapor from the anesthesia liquid to form the vapor column. The vapor column constitutes a gas spring to reduce pulsations of the liquid flow in the pipe. 
     In yet another embodiment, the present disclosure provides a method for reducing pulsations of a liquid flow. The method comprises inputting energy to a chamber of a liquid accumulator. The chamber is fluidically connected to a pipe that transmits the liquid flow. The method further comprises generating vapor from the liquid flow to form a vapor column in the chamber, and using the vapor column as a gas spring to reduce the pulsations of the liquid flow in the pipe. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings in which: 
         FIG. 1  is a schematic diagram of a liquid delivery system, in accordance with an exemplary embodiment; 
         FIG. 2  is a graph of pulsations of flow rate/pressure output from a pump, in accordance with an exemplary embodiment; 
         FIG. 3  is a graph of relations of nominal vapor pressure and temperature, in accordance with an exemplary embodiment; 
         FIG. 4A  is a schematic perspective view of a liquid accumulator and a pipe which can be used in the system of  FIG. 1 , in accordance with an exemplary embodiment; 
         FIG. 4B  is a cross-sectional view of the liquid accumulator and pipe of  FIG. 4A  along line A-A′; 
         FIG. 5A  is a schematic perspective view of a liquid accumulator which can be used in the system of  FIG. 1 , in accordance with another exemplary embodiment; 
         FIG. 5B  is a cross-sectional view of the liquid accumulator of  FIG. 5A  along line B-B′; 
         FIG. 6  is a schematic diagram of a liquid accumulator with a heater on the outer surface of the chamber, in accordance with an exemplary embodiment; 
         FIG. 7  is a schematic diagram of a liquid accumulator with a piezoelectric actuator or an ultrasound actuator, in accordance with an exemplary embodiment; 
         FIG. 8  is a schematic diagram of a liquid accumulator with a stirrer, in accordance with another exemplary embodiment; 
         FIG. 9  is a block diagram of a controller for power source, in accordance with an exemplary embodiment; 
         FIG. 10  is a flow chart of a method for reducing pulsations in a liquid delivery system, in accordance with an exemplary embodiment; 
         FIG. 11A  is a graph of pulsations of flow rate/pressure of a liquid flow output from a pump, in accordance with an exemplary embodiment; 
         FIG. 11B  is a graph of pulsations of flow rate/pressure of the liquid flow of  FIG. 11A  after being adjusted by the liquid accumulator, in accordance with an exemplary embodiment. 
     
    
    
     The drawings illustrate specific aspects of the described liquid accumulators and methods for reducing pulsations of a liquid flow. Together with the following description, the drawings demonstrate and explain the principles of the structures, methods, and principles described herein. In the drawings, the size of components may be exaggerated or otherwise modified for clarity. Well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the described components, systems and methods. 
     DETAILED DESCRIPTION 
     One or more specific embodiments of the present disclosure are described below in order to provide a thorough understanding. These described embodiments are only examples of liquid accumulators and methods for reducing pulsations of a liquid flow. The skilled artisan will understand that specific details described in the embodiments can be modified when being placed into practice without deviating the spirit of the present disclosure. 
     When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “first,” “second,” and the like, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. As the terms “connected to,” “coupled to,” etc. are used herein, one object (e.g., a material, element, structure, member, etc.) can be connected to or coupled to another object regardless of whether the one object is directly connected or coupled to the other object or whether there are one or more intervening objects between the one object and the other object. In addition, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. 
     Referring to the figures generally, the present disclosure is to provide liquid accumulators and methods for reducing pulsations of a liquid flow. An exemplary liquid accumulator includes a chamber fluidically connected to a pipe that transmits the liquid flow driven by a pump. A power source (e.g., heater, stirrer, actuator, transducer, etc.) can input energy to the chamber to help vaporize the liquid in the chamber and thus create a vapor column in the chamber. The vapor column is compressed during the flow output phase of the pump and expanded during the pump non-delivery period. The compression or expansion of the vapor column can exert force on the liquid flow in the pipe, and thus smoothing the pulsations of the flow in the pipe. Additionally, by using small opening or orifice between the liquid flow and the chamber, damping action can be performed. The spring rate of the vapor column can be adjusted by changing the input energy level which varies the amount/height and the vapor pressure of the vapor column. Different spring rates may be used for different pump speeds in real time. 
     The liquid accumulators as disclosed herein have at least the following advantages over conventional accumulators. First, issues of gas permeation, liquid leakage, and seal swelling can be avoided because no barrier (e.g., bladder, diaphragm, piston) is used to separate the vapor from the liquid. Actually, liquid accumulators as disclosed herein require no moving part that may fatigue or wear but use a sealed container. Thus, gas sealing is simplified because the solid body of sealed container constitutes no rupture or leak points. Second, a single material can be used for the accumulator, which avoids the problem of finding combinations of liquid compatible materials. Third, conventional accumulators require pre-charged gas which puts the system under a continuous pressure. For accumulators disclosed herein, there is no need to pre-charge gas because liquid vapor functions as the gas spring. Vapor pressure can be maintained in operation and can be released when the energy input stops. Fourth, the spring rate can be adjusted by varying the energy level input to the chamber which changes the amount/height and pressure of the vapor. Thus, the spring rate can be optimized real time for different pump speeds to allow for tuned performance throughout pump operating range. Fifth, the size of the liquid accumulators as disclosed herein can be minimal and the package space can be saved. Minimal package space is desired in applications like micro fluidic designs. 
     Now referring to  FIG. 1 , a block diagram of a liquid delivery system  100  is shown, in accordance with an exemplary embodiment. In some embodiments, the system  100  is an anesthesia agent delivery system used in an anesthesia machine. In some embodiments, the system  100  is a fuel delivery system used in a vehicle. In some embodiments, the system  100  is a coolant delivery system used in a refrigerator. In some portions of the following description, examples are explained in the context of the anesthesia agent delivery system. However, it should be understood that the system  100  can be any appropriate liquid delivery system. 
     As illustrated in  FIG. 1 , in some embodiments, the liquid delivery system  100  comprises a pump  110 , a pipe  120 , a liquid accumulator  130 , and a power source  140 . The pump  110 , when activated, drives the liquid from a reservoir (not shown in the present Figure) into the pipe  120 . The liquid can be anesthesia agent, fuel, coolant, or any appropriate liquid. The pipe  120  transmits the liquid flow to, for example, an injector (not shown in the present Figure) for further processing. The liquid accumulator  130  is fluidically connected to the pipe  120  and can smooth pulsations of flow rate/pressure of the liquid flow in the pipe  120 . The power source  140  can input energy into the accumulator  130  to create vapor column functioning as a gas spring in the accumulator  130 . In some embodiments, a first flow rate (or pressure) sensor  122  is disposed upstream of the accumulator  130  for measuring the flow rate (or pressure) before being adjusted by the accumulator  130 . A second flow rate (or pressure) sensor  124  is disposed downstream of the accumulator  130  for measuring the flow rate (or pressure) after being adjusted by the accumulator. It should be understood that the liquid delivery system  100  as shown in  FIG. 1  is for illustration not for limitation. The liquid delivery system may include more, fewer, or different components than those shown in  FIG. 1 . 
     The pump  110  may be any suitable type of pump. In some embodiments, the pump  110  is a reciprocating pump, such as piston pump, plunger pump, diaphragm pump, and so on. The pump  110  may operate in a range of speed to draw the liquid from a reservoir into the pipe  120 . Intake and exhaust strokes of the pump  110  can cause pulsations of the flow rate/pressure in the pipe  120 . In some embodiments, the pump  110  is a multi-headed pump where each pump head may be out of phase thereby resulting in overlapping intake and exhaust strokes. 
     The first sensor  122  may measure the flow rate or pressure of the liquid output from the pump  110  before being adjusted by the accumulator  130 .  FIG. 2  shows pulsations of flow rate/pressure output from the pump  110 , in accordance with an exemplary embodiment. The pulsations are undesirable in many applications. For example, in an anesthesia agent delivery system, pulsations in the pipe  120  can cause fluctuations of input pressure at the injector, which in turn can lead to substantial variation of the agent vapor output rate at the vaporizer given that the volume expansion from liquid to gas phase is huge (e.g., ˜200 times expansion). 
     The liquid accumulator  130  is used to reduce the pulsations of flow rate/pressure upstream of, for example, the injector. As illustrated in  FIG. 1 , the accumulator  130  (also referred to herein as) a chamber  130  is fluidically connected to the pipe  120  through an orifice  138 . Liquid occupies a portion  132  of the chamber  130 . The power source  140  can input energy to the chamber  130  to vaporize the liquid in the chamber  130 . The power source  140  may be for example, a heater, a mechanical stirrer, a piezoelectric actuator, an ultrasound transducer, or any appropriate power source that can add energy to the chamber  130  to help vaporize the liquid. 
     Vapor of the liquid occupies the rest portion  134  (with a height h) of the chamber  130 —the portion  134  is also called the vapor column. The vapor column  134  functions as a gas spring to smooth the pulsations of the liquid flow in the pipe  120 . In particular, during the exhaustion stroke of the pump  110 , the liquid in the pipe  120  goes into the chamber  130  via the orifice  138  and the vapor column  134  is compressed (i.e., h decreases). The vapor column  134  thus exerts pressure on the liquid like a compressed spring. During the non-delivery period of the pump  100 , the liquid in the chamber  130  goes into the pipe  120  via the orifice  138  and the vapor column  134  is expanded (i.e., h increases). The vapor column  134  thus exerts pressure on the liquid like an expanded spring. As such, the compression and expansion of the vapor column  134  reduce the pulsations of the flow in the pipe  120 . Additionally, by using the orifice  138  between the pipe  120  and the chamber  130 , damping action can be performed. Structures of the accumulator  130  and the power source  140  will be discussed in further detail with reference to  FIGS. 2A through 8 . 
     The spring rate of the of vapor column  134  may change with the energy level input by the power source  140 . For example, when more energy is input to the chamber  130 , more vapor is created from the liquid and the gas spring becomes “softer.” In the following description, examples are explained in the context of the heat (i.e., thermal energy) input. However, it should be understood that the input energy can be any appropriate type such as mechanical energy, acoustic energy, etc. 
     Referring to  FIG. 3 , the graph shows the relations of nominal vapor pressure exerted by the vapor column  134  and the temperature in the chamber  130 , in accordance with an exemplary embodiment. It shows that the nominal vapor pressure increases non-linearly with temperature. The spring rate of the vapor column  134  can be expressed as: 
     
       
         
           
             
               
                 
                   
                     k 
                     = 
                     
                       - 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           F 
                         
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           h 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     wherein ΔF is the change of the force exerted by the vapor column  134 , and Δh is the change of the height h of the vapor column  134  due to compression or expansion. “-” indicates that the force F and the height h change in opposite directions. The force F exerted by the vapor column  134  can be expressed as:
 
 F=PA   (2),
 
     wherein P is the vapor pressure, and A is the cross-sectional area of the vapor column  134 . According to the ideal gas relation, the vapor pressure P can be expressed as:
 
 PV=nRT   (3),
 
     wherein V (=Ah) is the volume of the vapor column  134 , n is the amount of vapor in moles, and T is the temperature of the vapor. Based on equations (1)-(3), the spring rate of the vapor column  134  can be calculated as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         k 
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                             = 
                             
                               
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                               nRT 
                               
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                                 2 
                               
                             
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     wherein P 0  is the nominal vapor pressure of the vapor column  134  under the temperature, and h 0  is the average height of the vapor column under the temperature. The average liquid height in the chamber  130  can be maintained at a substantially constant level in the sealed space so that the average height h 0  of the vapor column can be maintained at a substantially constant level for a given temperature. As equation (4) shows, the spring rate k of the vapor column  134  changes with the nominal vapor pressure P 0  for given A and h 0 . The nominal pressure P 0  changes with the temperature as shown in  FIG. 3 , thus the spring rate k changes with the temperature accordingly. As discussed above, the pump  110  can operate in a range of speed. The spring rate can be optimized real time for different pump speeds to allow for tuned performance throughout pump operating range. Operation of a controller that controls the input energy level will be discussed in detail with reference to  FIGS. 9 and 10 . 
     Referring to  FIGS. 4A and 4B , an exemplary liquid accumulator is shown in connection with a pipe.  FIG. 4A  shows the perspective view of the liquid accumulator and pipe.  FIG. 4B  shows the cross-sectional view of the liquid accumulator and pipe along line A-A′. The liquid accumulator and pipe can be used in the liquid delivery system  100  of  FIG. 1 . As illustrated in  FIGS. 4A and 4B , in some embodiments, the liquid accumulator comprises a chamber  430 . The chamber  430  is covered by a cap  436  and hermetically sealed. The pipe  420  extends through the chamber  430  so that a portion of the pipe  420  is enclosed by the chamber  430 . The chamber  430  is fluidically connected to the pipe  420  through an orifice  438  on the pipe  420 . In some embodiments, the chamber  430 , cap  436 , and pipe  420  constitute a one-piece element constructed by, for example, casting. In some embodiments, at least one of the cap  436  and pipe  420  is a separate element and attached to the chamber  430  by, for example, glue. In some embodiments, the chamber  430 , cap  436 , and pipe  420  are made of the same material, for example, stainless steel, brass, PPSU plastics, or any appropriate material not to react with the liquid being delivered. In some embodiments, the chamber  430 , cap  436 , and pipe  420  may be made of different material. 
     A heater  440  is disposed inside the chamber  430  and configured to add thermal energy (i.e., heat) to the chamber  430 . In some embodiments, the accumulator and pipe are constructed to ensure that the heat is not transferred to the liquid flow in the pipe  420 . For example, the pipe  420  may be made of thermally insulating material to prevent the liquid flow in the pipe  420  from being heated. The heater  440  can be any appropriate type of heater made of any appropriate material, such as heating rod made of copper nickel alloy, positive temperature coefficient (PTC) thermistor made of ceramic material, etc. In some embodiments, the heater  440  is electrically to an external power supply (not shown in the present Figure) through a wire  444 . The external power supply may be a direct current (DC) power supply (e.g., battery pack) or an alternating current (AC) power supply (e.g., an AC-DC adapter that can be plugged into an AC wall outlet). In some embodiments, the wire  444  is inserted into a stick  442  before entering the chamber  430  so that the chamber  430  can remain hermetically sealed. 
     In operation, the heater  440  heats the liquid in the chamber  430  and creates the vapor column in the chamber  430 . The temperature of the chamber  430  can be controlled by controlling thermal energy level generated by the heater  440 . In some embodiments, a pulse width modulation (PWM) controller may be used to control the heat generated by adjusting the duty cycle of the power (e.g., from the external power supply) provided to the heater  440 . The greater the duty cycle, the more heat generated and the higher of the temperature in the chamber  430 . With higher temperature, more vapor is generated which makes the vapor column “softer,” as discussed above. By adjusting the heat generated, the spring rate of the accumulator can be tuned to the optimal damp pressure for different pump speed or other disturbance that causes pressure fluctuation. 
     The liquid accumulator may have various structure without departing the principle and spirit of this disclosure. Referring to  FIGS. 5A and 5B , another exemplary liquid accumulator in connection with a pipe is shown where the pipe is disposed outside of the liquid accumulator.  FIG. 5A  shows the perspective view and  FIG. 5B  shows the cross-sectional view along line B-B′. A chamber  530  includes an orifice  538  at the bottom. A pipe  520  that transmits liquid flow is disposed outside of the chamber  530  and fluidically connected to the chamber  530  via a flange  526 . The cap  536 , heater  540 , stick  542 , and wire  544 , may have similar structure as corresponding components shown in  FIGS. 4A and 4B . In some embodiments, the chamber  530 , cap  536 , flange  526 , and pipe  520  constitute a one-piece element constructed by, for example, casting. In some embodiments, at least one of the cap  536 , flange  526 , and pipe  520  is a separate element and attached to the chamber  530 . In some embodiments, the chamber  530 , cap  536 , flange  526 , and pipe  520  are made of the same material, for example, stainless steel, brass, PPSU plastics, or any appropriate material not to react with the liquid being delivered. In some embodiments, the chamber  530 , cap  536 , flange  526 , and pipe  520  may be made of different material. 
       FIGS. 6-8  show more variations of the liquid accumulation. In  FIG. 6 , a heater  640  is disposed on the outer surface of the chamber  630 . In  FIG. 7 , a piezoelectric actuator or ultrasonic transducer  740  is used to input energy to the chamber  730  to help generate vapor from liquid. In  FIG. 8 , a mechanical stirrer  840  is used to input energy to the chamber  830  to help generate vapor from liquid. In some embodiments where the liquid flow includes an anesthesia agent which may break down and release fluorine at high temperature, input energy types other than thermal energy may be desired. It should be understood that the exemplary accumulators illustrated herein are not exhaustive. A liquid accumulator can have different structure without departing the principle and spirit of this disclosure. 
     Referring to  FIG. 9 , a block diagram of a controller  900  for controlling a power source is shown, in accordance with an exemplary embodiment. The controller  900  is configured to control the energy input level to the chamber of the liquid accumulator. As discussed above, the spring rate and the sensitivity of the vapor column can be adjusted by changing the level of the energy input into the chamber. The higher the input energy level, the more vapor is generated and the greater the spring rate is. 
     As illustrated in  FIG. 9 , in some embodiments, the controller  900  is a feedback (e.g., closed-loop) controller which comprises a comparator  910 , a proportional-integral-derivative (PID) controller  920 , and a PWM controller  930 . The comparator  910  compares the measured pulsation in the pipe with a pre-set pulsation. The measured pulsation can be obtained from a flow rate/pressure sensor downstream of the accumulator (e.g., the second sensor  124  in  FIG. 1 ). The comparator  910  inputs the difference between the measured pulsation and the pre-set pulsation to the PID controller  920 , which determines a duty cycle based on the difference. The PID controller  920  inputs the determined duty cycle to the PWM controller  930 , which controls the energy input to the chamber based on the duty cycle. The greater the duty cycle, the higher the input energy level. And more vapor is generated which makes the vapor column “softer,” as discussed above. It should be understood that the controller  900  as shown in  FIG. 9  is for illustration not for limitation. An appropriate controller may include more, fewer, or different components than those shown in  FIG. 9 . 
     Referring to  FIG. 10 , a flow chart  1000  of a method for reducing pulsations in a liquid delivery system is shown, in accordance with an exemplary embodiment. The method can be executed by software, hardware, firmware, or any combination thereof to control the input energy level to the accumulator chamber. At an operation  1002 , a target spring rate of the vapor column of the accumulator is determined. In some embodiments, the target spring rate is determined using a model that describes the relation between the spring rate and the pump speed. The pump speed can be measured by a speed sensor or read from a memory that stores a pre-set pump speed. In some embodiments, a look-up table stores pump speeds and corresponding spring rates. The density and viscosity of the liquid being delivered may fluctuate due to ambient temperature changes, which introduces noise into the control scheme. In some embodiments, the gas spring rate may be adjusted to compensate the fluid density and viscosity changes. 
     At an operation  1004 , a parameter set point is determined based on the target spring rate. In some embodiments where a heater is used to add energy into the chamber, the parameter may be the temperature in the chamber. The temperature set point may be determined using the equation (4) and  FIG. 3 , for example. In some embodiments where a piezoelectric actuator or an ultrasound transducer is used to add energy into the chamber, the parameter may be the voltage applied on the actuator or transducer. The relation between the applied voltage and the spring rate may be obtained by using a model or through experiments. In some embodiments where a mechanical stirrer is used to add energy into the chamber, the parameter may be the stirrer speed. The relation between the stirrer speed and the spring rate may be obtained by using a model or through experiments. 
     In some embodiments where open-loop control is used, the input energy level is set based on the parameter (e.g., temperature, voltage, speed, etc.) set point and the process ends. In some embodiments wherein closed-loop control is used, the input energy level is further adjusted based on the feedback and operations  1006  through  1016  are performed. 
     At an operation  1006 , the measured parameter is compared with the parameter set point. If the difference between the measured parameter and the set point is within a pre-defined threshold, at operation  1008 , the energy input level (e.g., duty cycle) is maintained at the current level, at operation  1010 . If the difference between the measured parameter and the set point is beyond the pre-defined threshold, at operation  1008 , the process determines whether the measured parameter is higher than the set point, at operation  1012 . If the measured parameter is higher than the set point, at operation  1012 , the energy input level is decreased (e.g., decrease duty cycle), at operation  1014 . If the measured parameter is lower than the set point, at operation  1012 , the energy input level is increased (e.g., increase duty cycle) at operation  1016 . 
     It should be understood that the process as shown in  FIG. 10  is for illustration not for limitation. An appropriate process may include more, fewer, or different operations than those shown in  FIG. 10 . 
     Referring to  FIGS. 11A and 11B , pulsations of the flow pressure before and after being adjusted by the vapor column liquid vapor are shown, according to an exemplary embodiment. Working prototypes were built and tested, which used a PTC thermistor as a heating source for an anesthesia agent delivery system.  FIG. 11  A shows a graph of pulsations of flow rate/pressure of a liquid flow output from a pump, i.e., before being adjusted by the accumulator. The pulsations were measured by a sensor upstream of the accumulator (e.g., the first sensor  122  in  FIG. 1 ).  FIG. 11B  shows a graph of pulsations of flow rate/pressure of the liquid flow of  FIG. 11A  after being adjusted by the accumulator. The pulsations were measured by a sensor downstream of the accumulator (e.g., the second sensor  124  of  FIG. 1 .) The prototypes showed the reduction of pressure variation from up to ˜60 psi down to ˜2 psi. In the typical operating range, the prototypes showed the reduction of pressure variation from ˜30 psi to ˜1.5 psi. 
     In addition to any previously indicated modification, numerous other variations and alternative arrangements may be devised by those skilled in the art without departing from the spirit and scope of this description, and appended claims are intended to cover such modifications and arrangements. Thus, while the information has been described above with particularity and detail in connection with what is presently deemed to be the most practical and preferred aspects, it will be apparent to those of ordinary skill in the art that numerous modifications, including, but not limited to, form, function, manner of operation and use may be made without departing from the principles and concepts set forth herein. Also, as used herein, the examples and embodiments, in all respects, are meant to be illustrative only and should not be construed to be limiting in any manner.