Abstract: The present disclosure relates to an afterburner structure with fuel injection nozzles. In the condition of a stable inlet flow, the present disclosure forms a sweeping oscillating jet with a certain frequency at the outlet under an alternate feedback action of a feedback channel and the fluid's Coanda effect, so that the spatial uniformity of the fuel injection is improved; Therefore, without increasing the structural complexity of current afterburner of the turbo-engine and the combustion chamber of the subsonic combustion ramjet, the atomization performance and the uniformity of the oil-gas mixture in the afterburner/combustion chamber of the ramjet can be greatly improved, the combustion efficiency and combustion instability of the engine can be improved and meanwhile the length of the afterburner and the combustion chamber of the subsonic combustion ramjet is shortened.

Abstract: An injector device for an engine device for introducing a fluidic, in particular a liquid, fuel and a fluid, in particular liquid, oxidizing agent into a combustion chamber of the engine device is provided. The injector device defines a longitudinal axis and comprises at least one first injection element, which is configured in the form of a first fluid channel for fluidically connecting a first collection space for the fluidic oxidizing agent and the combustion chamber, and at least one second injection element, which is configured in the form of a second fluid channel for fluidically connecting a second collection space for the fluidic fuel and the combustion chamber. At least one first resonator element is associated with the at least one first injection element and/or at least one second resonator element is associated with the at least one second injection element.

Abstract: A hollow plank of a combustor liner defining a combustion chamber including an inner wall having a plurality of inner openings and one or more inner holes, an outer wall having one or more outer openings and a plurality of outer holes, a plurality of lateral walls coupled to the inner wall and the outer wall to define a cavity, and a partition wall connected to the plurality of lateral walls and dividing the cavity into a first sub-cavity and a second sub-cavity. The one or more outer openings communicate with the first sub-cavity and communicate through a plurality of tubes with the second sub-cavity. The plurality of inner openings communicate with the second sub-cavity and communicate with the first sub-cavity through one or more bypass tubes. The first sub-cavity or the second sub-cavity, or both, are frequency tuned to reduce combustion dynamic frequencies.

Abstract: A modular damper plug forming a multi-volume acoustic resonator in an acoustic liner of a rocket engine is provided. In one aspect, the damper plug includes a main body including a top surface spaced from a bottom surface by a first height, a left surface spaced from a right surface by a width, and an exterior surface spaced from an interior surface by a length. A chamber within the main body extends along a part of the height, a part of the width, and a part of the length, and communicates with the top surface through an opening. The chamber also communicates with the interior surface through one or more ducts. The main body is sized and shaped to be received in any one of a plurality of cavities in the acoustic liner. The chamber includes an upstream volume of the acoustic resonator, and the one or more ducts communicate with a downstream volume of the acoustic resonator when the damper plug is received in any one of the plurality of cavities.

Abstract: Various kinds of oscillatory instabilities are seen in practical systems. We devise of way of combating these oscillatory instabilities in a thermoacoustic system. Confined combustion environments are prone to large amplitude pressure oscillations known as thermoacoustic instabilities. Although several techniques have been employed to control or mitigate such instabilities, optimization of these methods is achieved at the cost of performing multiple trial and error experiments/simulations. This invention develops a methodology to quantify the spatio-temporal dynamics using synchronization, recurrence, and fractal measures and find the coherent region in such turbulent flow field. Such an analysis provides us with a novel way to detect critical regions responsible for thermoacoustic instability, and other oscillatory instabilities in general, in the flow field and implement an optimized control strategy at these regions.

Abstract: A combustor component of a combustor for combusting fuel to produce a combustion gas includes a combustion cylinder forming a passage for the combustion gas, a first acoustic device which internally includes a first cavity communicating with the passage via a first through hole formed in the combustion cylinder, a second acoustic device which is located on a radially outer side of the first acoustic device so as to cover the first acoustic device, and internally includes a second cavity communicating with the passage via a second through hole formed in the combustion cylinder, and a first communication passage causing the first cavity and an outer space of the combustion cylinder to communicate with each other without via the first through hole and the second cavity.

Abstract: A combustion tube for a gas turbine including an outlet section having a cross-section of an annular sector-shape. The outlet section includes an outer wall forming an outer peripheral boundary of the annular sector-shape, an inner wall forming an inner peripheral boundary of the annular sector-shape, and a pair of side walls forming boundaries on both sides of the annular sector-shape in a circumferential direction, respectively. The outer wall extends obliquely with respect to the inner wall such that a height of the annular sector-shape decreases toward an outlet opening of the combustion tube. A first side wall extends obliquely with respect to a second side such that a perimeter of the annular sector-shape increases toward the outlet opening of the combustion tube. An inclination angle ?1 of the first side wall with respect to the second side wall satisfies 0<?1?56.

Abstract: A hybrid electric gas turbine engine includes a fan section having a fan, a turbine section having a turbine drivably connected to the fan through a main shaft that extends along a central longitudinal axis, a gas generating core extending along a first axis that is radially offset from the central longitudinal axis, a first electric motor drivably connected to the main shaft, wherein the electric motor is colinear with the main shaft, and an electric compressor extending along a second axis that is radially offset from the central longitudinal axis, the electric compressor in fluid communication with the second turbine section.

Abstract: An acoustic damper for a rotary machine includes at least one wall, at least one inlet, at least one outlet, at least one separating wall, and at least one neck. The wall extends from the back side of a combustor front panel and defines a damping chamber. The inlet is defined within the wall and is oriented to channel a flow of air into the damping chamber. The outlet is defined within the back side of the front panel. The separating wall is oriented to separate the damping chamber into a first volume and a second volume. The first volume of the damping chamber is configured to damp an acoustic pressure oscillation at a first frequency. The second volume of the damping chamber is configured to damp the acoustic pressure oscillation at a second frequency. The neck extends through the separating wall and is axially offset from the outlet.

Abstract: Systems and devices of the various embodiments may provide a low-drag, variable-depth acoustic liner having shared inlet volumes. Various embodiments may include a low-drag, variable-depth acoustic liner providing aircraft noise reduction. Acoustic liners according to the various embodiments may be used in engine nacelles and/or on external surfaces of an aircraft to reduce acoustic radiation. Acoustic liners according to various embodiments may provide increased broadband acoustic performance with less drag than conventional liners. Various embodiments may provide an acoustic liner with a reduced open area of the facesheet, and therefore reduced drag of the liner, when compared with conventional acoustic liners.

Abstract: The present application provides a variable frequency Helmholtz damper system for use with a combustor of a gas turbine engine. The variable frequency Helmholtz damper system may include one or more Helmholtz dampers and a purge medium temperature control unit for providing a flow of purge medium to the Helmholtz dampers. The purge medium temperature control unit may be in communication with a temperature control fluid flow such that the purge medium temperature control unit may vary the temperature of the flow of purge medium.

Abstract: Acoustic treatments for components of gas turbine engines are described. The acoustic treatments include an acoustic resonator having a backing chamber defining a respective volume and a neck arranged relative to the backing chamber and defining an opening, wherein the neck has a length and a cross-sectional area. The acoustic resonator cell satisfies the following relationships: (1) l/L=0.2-0.8, where l is a length of the neck and L is a depth of the backing chamber and (2) a/A=0.02-0.20, where a is a cross-sectional area of the neck and A is a cross-sectional area of the backing chamber.

Abstract: A rotary machine includes at least one burner including a front panel having a front side and an opposing back side. The acoustic damper includes at least one wall, at least one cooling air inlet, at least one outlet, and at least one baffle. The wall extends from the back side of the front panel and defines a dampening chamber. The cooling air inlet is defined within the back side of the front panel and is configured to channel a flow of cooling air into the dampening chamber. The outlet is defined within the back side of the front panel and is configured to channel the flow of cooling air out of the dampening chamber. The baffle extends from the back side of the front panel and is configured to reduce a velocity of the flow of cooling air within the dampening chamber.

Abstract: An annular Helmholtz damper for a gas turbine can combustor, the annular Helmholtz damper having an axis; an inner wall and an outer wall concentrically arranged with respect to the axis to define an annular damping volume arranged around a can combustor; a front and rear circumferential plates for closing the annular damping volume upstream and downstream; at least one intermediate circumferential plate arranged between the front and the rear plates for dividing the annular damping volume in a main and a secondary volume; and a plurality of intermediate drain holes passing the intermediate circumferential plate and configured for draining collected liquid from the main volume to the secondary volume.

Abstract: To provide a damping device that includes an acoustic liner that forms an acoustic-liner resonant space along an outer periphery of a combustion chamber in which a combustion gas flows, and an acoustic damper provided on an outer peripheral side of the acoustic liner, to form an acoustic-damper resonant space that communicates with the acoustic-liner resonant space. The acoustic liner is formed with a damper opening connected with the acoustic damper for causing the acoustic-liner resonant space and the acoustic-damper resonant space to communicate with each other. The acoustic liner includes a divided portion that is a portion to be divided in a circumferential direction of the combustion chamber by the damper opening, and a continuous portion that is a portion continuous over the circumferential direction of the combustion chamber.

Abstract: A combustor includes: a combustion liner having a first region in which at least one first opening is formed; a nozzle configured to inject a fuel into the combustion liner; and a first acoustic device mounted to the combustion liner. The first acoustic device includes: a first casing portion having at least one first wall disposed facing the first region on an outer side of the combustion liner and at least one second opening formed thereon. The first casing portion defining at least one first space in communication with an inside of the combustion liner through the first opening; and a second casing portion having at least one second wall disposed facing the first wall on an outer side of the first casing portion. The second casing portion defines, between the first wall and the second wall, a second space in communication with the first space through the second opening.

Abstract: A gas turbine combustor includes a combustion chamber, a liner adjacent to the combustion chamber, a liner cap capping the combustion chamber, and a swirler cup passing through the liner cap. The liner cap includes a first cavity having a first inlet receiving an air, a second cavity having a first outlet facing the combustion chamber, and an impingement plate between the first cavity and the second cavity. The air flows from the first inlet to the combustion chamber through the first cavity, the impingement plate, and the second cavity.

Abstract: A combustion system can include: a liner defining a combustion chamber; a casing covering the combustion chamber; a first tube disposed in the liner; a machined union disposed inside the casing and connected to the first tube; a second tube passing through the casing and connected to the machined union; a sensor housing disposed outside the casing and connected to the second tube; and an infinite tube connected to the sensor housing.

Abstract: A combustion liner assembly includes a combustion liner having an upstream end portion and a downstream end portion and a resonator disposed proximate to the upstream end portion of the combustion liner. The resonator includes a plurality of circumferentially spaced inlet apertures disposed along a radially outer surface of the resonator, an air chamber defined within the resonator and a plurality of outlet apertures disposed along a radially inner surface of the resonator. The plurality of inlet apertures provide for fluid flow into the air chamber and the plurality of outlet apertures provide for fluid flow out of the air chamber and into a radial flow passage defined within the combustor.

Abstract: The damper arrangement includes a plurality of interconnected volumes and a plurality of necks for connecting the damper to a combustion chamber at a plurality of contact points. The plurality of necks are connected to the plurality of volumes.

Abstract: A gas turbine and a gas turbine silencer are provided. A silencer panel has a structure that can be divided into an upstream silencer panel and a downstream silencer panel in an airflow direction, a stepped part is defined in an opening-side portion of the downstream silencer panel, and the upstream silencer panel and the downstream silencer panel are linked by the stepped part fitting into an opening in the upstream silencer panel.

Abstract: The present invention generally relates to a gas turbine and more in particular it is related to a damper assembly for a combustion chamber of a gas turbine. According to preferred embodiments, the present solution provides a damper assembly including protrusions on a wall of the neck. These protrusions result in a side wall reactance to the acoustic field that has the effect of decreasing the effective speed of sound in the neck. The decrease of the effective speed of sound in the neck is equivalent to an increase of the effective neck length.

Abstract: A method of making a combustor cap assembly uses an additive manufacturing process of consecutively adding material in layers along an upstream axial build direction starting from a base side positioned transverse to the upstream axial build direction. The base side has at least one acoustic port. A bump side extends from the base side in the upstream axial build direction and has at least one damper projecting from the bump side. The damper has at least one inclined face forming an angle with the upstream axial build direction of less than or equal to 45 degrees. The resulting cap assembly includes a hot side with an acoustic port and a cold side with at least one damper with an inclined face and a damper chamber in communication with the acoustic port.

Abstract: A bundled tube fuel nozzle assembly including a fuel plenum and an air plenum. A plurality of mixing tubes extend through the fuel plenum and the air plenum. At least one resonator is positioned in the air plenum surrounding at least one of the plurality of mixing tubes.

Abstract: A damper for a gas turbine combustion chamber as shown in FIG. 1 includes a damper volume wall and a main neck. The damper volume wall defines a damper volume inside the damper volume wall. The main neck includes a main neck wall defining a main neck volume inside the main neck wall. The main neck is associated with the damper volume for fluid communication between the damper volume and the gas turbine combustion chamber. In addition, the damper includes a gap between the main neck wall and the damper volume wall. The main neck defines a main neck axis. For example, the gap is a second neck, and in further embodiments, multiple damper volumes are provided.

Abstract: A combustor (10) including: a first premix main burner (14) comprising a first swirler airfoil section (38); a second premix main burner (15) comprising a second swirler airfoil section (40); and a supply air reversing region upstream of the premix burners (14), (15). The first swirler airfoil section (38) and the second swirler airfoil section (40) are effective to impart swirl to a first airflow and a second airflow characterized by a same swirl number as the airflows exit respective burners (14), (15). The combustor (10) is effective to generate a first airflow volume through the first premix main burner (14) that is different than a second airflow volume through the second premix main burner (15).

Abstract: An annular combustion chamber for a turbine engine is provided. The chamber includes an annular row of fuel injectors including heads engaged in fuel injection systems mounted in openings in the chamber end wall. Each injector head includes at least one fuel-passing helical channel for causing fuel to rotate about the longitudinal axis of the head. Each injection system includes at least one swirler including air-passing channels of sections with axes that are inclined relative to the plurality axis of the swirler at an angle that is substantially equal to a helix angle of the helical channel, to within ±10°, and are oriented in a same direction as the channel about the longitudinal axis of the swirler.

Abstract: A combustor cap assembly includes an impingement plate coupled to an annular shroud and a cap plate which is coupled to the impingement plate and forms an impingement air plenum therebetween. The cap assembly further includes a flow conditioning plate which is coupled to a forward end portion of the shroud. The flow conditioning plate includes an inner band portion, an outer band portion and an annular portion which extends radially therebetween. The annular portion includes upstream side, a downstream side and a plurality of flow conditioning passages which provide for fluid communication through the upstream and downstream sides. The inner band portion of the flow conditioning plate at least partially defines an exhaust channel. The exhaust channel is in fluid communication with the impingement air plenum and an exhaust outlet. The exhaust outlet is positioned to route cooling air from the impingement air plenum into an annular flow passage defined within a combustor.

Abstract: A system for utilizing cooling air within a combustor includes a fuel nozzle having an axially extending center body, a burner tube that circumferentially surrounds at least a portion of the center body and a premix passage defined between the center body and the burner tube. The system further includes a combustor cap assembly having a first cooling air plenum defined between a cap plate and a first partitioning plate, a second cooling air plenum defined upstream from the first cooling air plenum between a second partitioning plate and the first partitioning plate, and a tube that provides for fluid communication from the first cooling air plenum, through the second cooling air plenum and through the second partitioning plate. The system provides a method for utilizing the cooling air within the combustor.

Abstract: A gas turbine may include a rotatable shaft, a compressor disposed about the rotatable shaft and configured to output compressed air, and a combustor disposed about the rotatable shaft. The combustor may be configured to receive the compressed air and output high temperature compressed gas. The gas turbine may further include a power turbine disposed about the rotatable shaft and configured to receive the high temperature compressed gas, and a first liner defining a plurality of holes and disposed around the combustor. The power turbine may be configured to expand the high temperature compressed gas and rotate the rotatable shaft. The first liner may have a first end and a longitudinally opposite second end. The first end may be coupled to an inner surface of the casing at or adjacent an upstream end of the combustor and the second end may be substantially free from any connection with the casing.

Abstract: A combustor (100) for a gas turbine engine (30) has a circumferentially extending liner (109) defining at least a portion of an interior combustion chamber (107) and a hot gas path (115). The liner includes a resonator section (112) including at least one resonator (116A, 116B) having a resonator chamber (125A, 125B) formed on an exterior of the liner. A thermal barrier coating (118) is disposed along an inner surface of the liner including an inner surface (130) of the resonator section. The resonator further includes a plurality of apertures (117) and each aperture extends through the liner and the thermal barrier coating at the resonator section and there is fluid flow communication between the combustion chamber and the resonator chamber.

Abstract: A system for reducing flame holding within a combustor includes a high pressure plenum and a head end plenum defined within the combustor. A cap assembly defines an inner plenum within the combustor and a fuel nozzle passage that extends through the cap assembly. A primary fuel nozzle has an annular burner tube that at least partially defines a premix flow passage through the cap assembly. The primary fuel nozzle and the burner tube at least partially define an inlet to the premix flow passage. A high pressure flow passage and a cooling flow passage are defined within the combustor. The high pressure flow passage defines a flow path between the high pressure plenum and the inner plenum, and the cooling flow passage defines a flow path between the high pressure plenum and the head end plenum.

Abstract: A gas turbine includes a compressor and at least one combustor downstream from the compressor. The combustor includes a burner having an inner shroud extending axially along at least a portion of the burner, an outer shroud radially separated from the inner shroud and extending axially along at least a portion of the burner, and a plurality of stator vanes extending radially between the inner shroud and the outer shroud. The stator vanes have an inner end proximate the inner shroud and an outer end proximate the outer shroud. The burner further includes a vortex tip at one of either the inner end or the outer end of the stator vanes. The vortex tip provides a gap between the inner end and the inner shroud or the outer end and the outer shroud, and the vortex tip includes a plurality of fuel ports. The gas turbine further includes a turbine downstream from the combustor.

Abstract: Certain embodiments include a resonator for the head end of a turbine combustor. The resonator is partially defined by first and second plates disposed about a fuel nozzle in the head end of the turbine combustor. The resonator is further configured to receive an air flow which extends through the resonator and into the fuel nozzle.

Abstract: In a damping device according to the present invention, a damping device 63 is mounted on a bypass pipe 61 that supplies an amount of high-pressure air to a combustor transition piece 33. The damping device 63 includes a fluid introducing unit 71 that forms a fluid introduction space B by covering an outer peripheral portion of the bypass pipe 61, a plurality of acoustic boxes 73a and 73b that forms resonance spaces Da and Db with the base portions connected to the fluid introducing unit 71 and the end portions extending along the outer peripheral portion of the bypass pipe 61 in the circumferential direction, and partition plates 74a and 74b that form resonance ducts Ea and Eb of a predetermined length by partitioning the resonance spaces Da and Db.

Abstract: A combustor includes an upstream surface that extends radially across at least a portion of the combustor, a downstream surface that extends radially across at least a portion of the combustor and is axially separated from the upstream surface, and a plurality of tubes that extend through the downstream surface. A resonator is upstream from at least one of the tubes, and a fluid passage extends through the resonator and into the least one tube.

Abstract: A combustor in a gas turbine includes a liner having an interior volume defining a main combustion zone, a fuel injection system for delivering fuel into the main combustion zone, and a flow sleeve that defines, with the liner, a passageway for air to flow on its way to be mixed with fuel from the fuel injection system, wherein the mixture is burned in the main combustion zone to create hot combustion gases. The combustor further includes a flow conditioner including at least one panel having a configuration such that air is able to pass through the panel(s) on its way to the passageway, wherein at least a substantial portion of the air that enters the passageway for being burned in the main combustion zone passes through the panel(s).

Abstract: The present invention relates to a damping device for a combustor of a gas turbine for suppressing combustion instabilities. More specifically, the invention relates to a design of a broadband damping device for a low emission combustor having at least one resonator for damping pressure fluctuations in the combustion chamber. It is an object of the invention to provide a damping device with a quarter wave damper having broadband characteristics.

Abstract: A Helmholtz damper for a combustor of a gas turbine includes an enclosure defining a damping volume from which a neck portion extends and which has a flow path (F) for cooling and purging air with an inlet opening and an outlet opening to the enclosure. The outlet opening is formed in the neck portion. A seal is arranged at the neck portion adjacent to the outlet opening for cooling and purging air such that a cooling effect of the seal is provided.

Abstract: The invention relates to a damper for reducing the pulsations in a chamber of a gas turbine. The damper includes a resonator cavity and a neck in flow communication with the resonator cavity and the chamber. The neck includes a mouth to communicate with the chamber. The air flow inside the chamber flows across the mouth of the neck. The neck is so configured that the longitudinal axis of its mouth is angled 0-90° relative to the direction of the air flow inside the chamber. The damper of this invention may effectively alleviate the detrimental effect of the grazing flow and thus it enables the placement of the damper also at locations where strong grazing flows are present.

Abstract: A combustor includes a breech end, a plurality of fuel nozzles connected to the breech end and extending downstream from the breech end; and a shroud that circumferentially surrounds the plurality of fuel nozzles inside the combustor. A support extends radially inside at least a portion of the shroud, and a lip seal is between the support and at least one of the plurality of fuel nozzles.

Abstract: A gas turbine combustor is provided with a combustor basket where combustion gas flows, the combustion gas being produced by combustion of fuel injected from a nozzle, and a first resonance device and a second resonance device mounted on an outer surface of the combustor basket. The second resonance device is disposed on a downstream side from the first resonance device in a flow of the combustion gas and damps combustion oscillation of a frequency higher than the first resonance device. The first and second resonance devices are acoustic liners each having a housing mounted to the outer surface of the combustor basket. A resonance space surrounded by the housing and the outer surface of the combustor basket communicates with an interior space of the combustor basket via a plurality of acoustic holes formed in the combustor basket.

Abstract: A combustion chamber of a gas turbine includes an optimized arrangement of acoustic dampers.

Abstract: A gas turbine combustor is provided with a combustor basket where combustion gas flows, the combustion gas being produced by combustion of fuel injected from a nozzle, and a first resonance device and a second resonance device mounted on an outer surface of the combustor basket. The second resonance device is disposed on a downstream side from the first resonance device in a flow of the combustion gas and damps combustion oscillation of a frequency higher than the first resonance device. The first and second resonance devices are acoustic liners each having a housing mounted to the outer surface of the combustor basket. A resonance space surrounded by the housing and the outer surface of the combustor basket communicates with an interior space of the combustor basket via a plurality of acoustic holes formed in the combustor basket.

Abstract: A combustion device (1) for a gas turbine includes portions (12) having an inner and an outer wall (13, 14) with an interposed noise absorption plate (15) having a plurality of holes (16). The combustion device (1) further has first passages (17) connecting zones between the inner wall (13) and the plate (15) to the inside of the combustion device (1) and second passages (21) for cooling the inner wall (13). The portions (12) also have an inner layer (22) between the inner wall (13) and the plate (15) defining inner chambers (23), each connected to at least a first passage (17), and an outer layer (24) between the outer wall (14) and the plate (15) defining outer chambers (25) connected to the inner chambers (23) via the holes (16) of the plate (15).

Abstract: A strip seal arrangement for turbine components employs acoustic damping. A sealing plate having a front face adjacent a combustion chamber and a back face facing away from a combustion chamber configured to have one or more holes of a predefined cross-sectional area. Containers having predefined volumes are attached to the back face of the sealing plate such that the one or more holes are in fluidic communication with the one or more containers thereby creating at least one acoustic damper. The side edges of the sealing plate fit into a slots of burner front panels, creating a seal between the panels.

Abstract: A combustion device for a gas turbine includes an interior portion, an inner wall having a plurality of first passages and an outer wall having a plurality of second passages configured to cool the inner wall, each of the plurality of second passages having an outlet opening into a third passage. An intermediate layer is disposed between the inner wall and the outer wall and defines a plurality of chambers, each chamber forming a Helmholtz damper and being connected to the interior portion by at least one of the plurality of first passages and being connected to at least one of the plurality of second passages by at least one of the plurality of third passages.

Abstract: A combustor liner may include an annular inner liner and an annular outer liner with a plurality of air holes thereon. The outer liner may be positioned circumferentially around the inner liner such that an annular cooling space is defined between the inner and the outer liner. The combustor liner may also include at least one resonator coupled to the outer liner such that a base of the resonator is separated from the outer liner to form a gap with an external surface of the outer liner. The combustor liner may also include a throat extending from the base of the resonator penetrating the inner liner and the outer liner. The combustor liner may further include a grommet assembly that allows for relative thermal expansion between the inner liner and the outer liner proximate the throat.

Abstract: A high-bypass gas turbine engine includes a variable area fan nozzle with an acoustic system having an acoustic impedance.

Abstract: The damper arrangement includes a plurality of interconnected volumes and a plurality of necks for connecting the damper to a combustion chamber at a plurality of contact points. The plurality of necks are connected to the plurality of volumes.