Proceedings of IMECE 2007ASME 2007 International Mechanical Engineering Congress and R&D Exposition

November 11-15, 2007, Seattle, USA

IMECE2007-42580

OPEN ACCUMULATOR CONCEPT FOR COMPACT FLUID POWER ENERGYSTORAGE

Perry Y Li ∗, James D. Van de Ven and Caleb SanckenCenter for Compact and Efficient Fluid Power

Department of Mechanical EngineeringUniversity of Minnesota

Minneapolis, Minnesota 55311Email: pli@me.umn.edu

ABSTRACTEnergy storage devices for fluid power applications that are

significantly more compact than existing ones will enable energyregeneration for many applications, including fluid power hy-brid vehicles and construction equipment. The current approachto hydraulic energy storage makes use of a compressed gas en-closed in a closed chamber. As the system must contain the ex-panded gas and the hydraulic oil displaced, the optimal energydensity occurs at a modest expansion ratio resulting in a smallenergy density. By allowing intake and exhaust of compressedand expanded air from and to the atmosphere, a potential orderof magnitude increase in energy density is available in the newopen accumulator approach. Potential methods for realizing thenew configuration are described. Analysis and simulation casestudies illustrate both the advantages and challenges of the newapproach.Keyword: Energy density; accumulators; control systems; pneu-matic motor-compressor; hydraulic pump-motor; regeneration;open accumulators; closed accumulators.

1 INTRODUCTIONEnergy storage density in hydraulic systems are severely

limited relative to competing technologies. For example, volu-metric energy storage densities of electric batteries are of the or-der of 1MJ/liter, whereas those of hydraulic accumulator config-urations are less than 10kJ/liter (at 35MPa). Hydraulic systems

∗Corresponding author

however have an order of magnitude advantage in power densi-ties relative to electric systems. Dramatic improvement in energystorage densities for hydraulic systems can enable regenerationin many applications where space, weight, and power are critical.One example is the hybrid passenger vehicles where space forenergy storage is a premium (compared to larger vehicles suchas buses and trucks). As an example, to capture the 380kJ ofbraking energy of a 1000kg vehicle traveling at 100km/h wouldcurrently require about 50 liters volume.

In current practice, hydraulic energy storage is achieved byan accumulator. The most common accumulator design con-sists of an enclosed inert gas chamber connected to the hy-draulic circuit through a check valve. The basic configurationhas been unchanged for decades. The fixed volume enclosure hasa gas chamber and an oil chamber. As the oil chamber volumeincreases, the gas chamber volume decreases correspondingly.Typically, the gas chamber is a bladder enclosure or a volumeenclosed by a sliding piston, and the gas within is prechargedto a nominal pressure. Energy is stored by pumping pressurizedoil into the accumulator, thus reducing the gas volume, until thegas pressure is equal to the applied pressure. Energy is regen-erated as the compressed gas pushes the stored oil back into thehydraulic circuit. Since the gas is always contained within theaccumulator, we refer to it as a “closed” accumulator.

Previous approaches to increasing hydraulic energy storagedensity as can be found in the open literature have focused onimproving the thermodynamic process and hence the availableenergy. The system configuration remains unchanged. Otis,

1 Copyright c⃝ 2007 by ASME

Pourmovahed and other co-workers [1–4] introduced elastomericfoams in the compressed gas. The foam absorbs heat and reducesthe temperature of the gas during compression (storage); and re-stores the heat and increases the temperature of the gas duringexpansion (regeneration). This has the effect of allowing the gascompression and expansion to be closer to the isothermal processrather than an isentropic process. Reportedly, the energy den-sity can be increased by up to 40%. Sherman and Karlekar [5]showed that the use of fine metallic strands bonded to the cas-ing improves the heat transfer to the atmosphere, so that the gascompression/expansion process can also be closer to isothermal.This also has the effect of increasing performance by 15%-40%.

In pneumatic systems, compressed gas is also used as an en-ergy storage. Storage tanks with air pressurized up to 2.1 MPa(300psi) is used to power pneumatic systems. In contrast to hy-draulic systems, the compressed air is exhausted to the atmo-sphere. Carbon dioxide/dry ice has also been used as energystorage for pneumatic systems. This approach has limited usebecause the available system pressure with CO2 is limited (itstriple point pressure at 0.52MPa). Marsh et al. [6] developed ahydraulic power source for artificial limbs using liquefied gas.It is used in storing energy generated by normal walking. Thephase change of the liquefiable gas produces a constant 3.4MPa(500Psi) pressure head.

Compressed air is used in energy storage for electric plants.Such compressed air energy storage (CAES) uses large (10e6f t3) underground caverns to store compressed air up to 7.7MPa(1100psi). Regeneration is achieved by mixing the compressedair with natural gas which is then used to power a turbine for elec-tricity generation. There are currently two plants in the US thatutilize CAES for energy storage [7]. A similar idea of using com-pressed air as energy storage is being developed on smaller scalepower devices such as uninterruptible power supplies (UPS) [8].

In this paper, we describe one potential approach for dramat-ically increasing hydraulic energy storage density. The approachis based on the observation that in current hydraulic accumulatorconfigurations, the volume is determined by the volume of theexpanded gas. The system must also hold the volume and weightof the hydraulic oil displaced, which is given by the change involume by the gas expansion. While more energy can be recu-perated by increasing the decompression ratio, this is accompa-nied by large increases in the expanded gas and the displacedoil volume. Hence, the decompression ratio for optimal energydensity is limited to between 2 and 3. This is a fundamental con-straint of the current system configuration so that any increase inenergy density that can be achieved by improving the thermody-namic process (e.g. shifting from adiabatic process to isothermalprocess) will only be marginal.

In the new “Open accumulator” approach, compressed gas isexhausted to the atmosphere during expansion, and intake is alsotaken from the atmosphere. Compared to the closed accumula-tor case, significantly more energy can be obtained from the same

Hydraulic pump/motor

Oil at Pa

Accumulator and displaced oil

Gas at P_low

Accumulator only

Gas at P_highFigure 1. Conventional closed accumulator configuration: a) when ac-cumulator is empty; b) when accumulator is fully charged. Shaft work isinputed through the pump as the system transitions from a) to b). Shaftwork is extracted from the motor as the system transitions from b) to a).The total volume in defining the energy density can be considered to bejust the accumulator, or the accumulator together with the displaced hy-draulic oil.

compressed gas since the gas is allowed to expand to atmosphericpressure. Furthermore, since the expanded air is exhausted to theatmosphere, the system does not have to account for its volume,nor the volume of the displaced hydraulic oil. A potential 20 foldincrease in volumetric energy storage density for the same com-pressed gas pressure can be achieved at conventional hydraulicpressure (35MPa) [5000Psi].

In section 2, the energy densities of the current “closed”accumulator configuration is analyzed. In section 3, the new“Open accumulator” approach is described and its potential gainsand challenges analyzed. A possible design of the air compres-sor/motor, which is a critical component in the open accumula-tor approach, is described in section 4. Simulation case studiesfor the compressor/motor and for the overall “open accumula-tor” system are presented in section 5. Section 6 contains someconcluding remarks.

2 Closed AccumulatorsA conventional accumulator consists of a fixed volume en-

closure with a gas chamber and an oil chamber (Fig. 1). The gaschamber is either a bladder enclosure or a volume enclosed by asliding piston. The gas is precharged to a nominal pressure. Dur-ing storage phase, mechanical shaft work is used to pump oil intothe accumulator, thus reducing the gas volume and increasing itspressure. Energy is regenerated as the compressed gas expands,expelling oil back through the hydraulic motor. Since the gasis always contained within the accumulator, this configuration isreferred to as a closed accumulator.

2 Copyright c⃝ 2007 by ASME

Define the volumetric energy density of such a closed accu-mulator to be:

Eη =Available Energy

Total Volume(1)

where the available energy is the maximum energy that canbe extracted for a fully charged closed accumulator at pressurePcomp, the total volume is either the volume of the accumula-tor itself or the volume of the accumulator and the volume ofliquid that will have been displaced when the accumulator isempty. The volumetric energy densities of a closed accumula-tor with Pcomp = 35MPa as functions of the volumetric expan-sion ratio r :=Vexp/Vcomp whereVexp andVcomp are the expandedand compressed gas volumes are shown in Fig. 2. The gas isassumed to be ideal and undergoes either an iso-thermal or anadiabatic process, and the oil reservoir is at atmospheric pressurePatm = 0.1MPa.

Consider first when the gas undergoes an isothermal expan-sion/compression process. Let the compressed and expanded gaspressures and volumes be Pcomp and Pexp, and Vcomp and Vexp re-spectively. The available energy is computed from

WT =∫ Vcomp

Vexp(P−Pa)dV

= PcompVcompln(r)−Pa(Vexp−Vcomp) (2)

where the work on or by the atmosphere is included. The volumeof the accumulator is at least Vexp. Hence, the isothermal energydensity without accounting for the displaced oil volume is:

Egη,T = Pcompln(r)r

−Par−1r

(3)

The energy density of such a configuration is greatest whenr = 2.71, giving an energy density of 12.81 kJ/Liter at a com-pressed gas pressure of 35MPa. For energy regeneration in hy-draulic hybrid vehicles, typical energy storage requirement is380kJ. Thus, 29 liters of storage is needed.

The displaced oil volume is Vexp −Vcomp. Thus, the totalvolume of the system that includes the accumulator volume andthe displaced oil volume is at least 2Vexp −Vcomp. Hence theenergy density is at most:

Etotalη,T = Pcompln(r)

2r−1−Pa

r−12r−1

. (4)

This is maximized at r = 2.15 giving an energy density of8.08kJ/liter at a compressed gas pressure of 35MPa. 380kJ stor-age for a hydraulic hybrid vehicle would require 47 liters of totalvolume.

Similar expressions can be obtained if the gas undergoes anadiabatic process. The available energy is given by:

Ws =

[

Pcomp(1− r1−γ)

(γ−1)−Pa(r−1)

]

Vcomp (5)

The energy densities (not taking into account the volume of thehydraulic fluid displaced) is given by:

Egη,s = Pcomp(1− r1−γ)

(γ−1)r−Pa

r−1r

(6)

where γ = 1.4 is the ratio of the isobaric thermal capacity to theisovolumic thermal capacity of a diatomic gas. This is maxi-mized at r = 2.31, giving an energy density of 10.72 kJ/liter.380kJ storage requires 35 liters of accumulator volume.

When the hydraulic fluid is taken into account, the energydensity is given by:

Etotalη,s = Pcomp(1− r1−γ)

(γ−1)(2r−1)−Pa

r−12r−1

(7)

This is maximized at r = 1.91, giving an energy density of 7.04kJ/liter. A 380kJ storage would require 53 liters of total volume.

In both the isothermal and adiabatic cases, the available en-ergies in Eqs. (2) and (5), and hence the numerator in Eq.(1), in-crease with the expansion ratio r. This, however, is at the expenseof an increase in the total volume (in the denominator of Eq.(1)),which depends largely on the expanded gas volume. Hence, theenergy density of the closed accumulator is limited because thesystem must contain the volume of the expanded gas volume aswell as the displaced hydraulic oil. This makes expanding thecompressed gas beyond the optimal expansion ratio r to extractmore energy detrimental to the energy densities.

3 Open accumulator concepts3.1 Openness

Instead of keeping a fixed molarity of gas in the closed ac-cumulator and allowing it to compress and expand, in the openaccumulator system, air is drawn from the atmosphere and com-pressed into the accumulator during the storage phase, and is ex-panded to the atmosphere again during the regeneration phase(Fig. 3). Mechanical work is stored and extracted through apneumatic compressor/motor. There are three advantages to theopen system:

1. This allows for a high expansion ratio that would increasethe available energy significantly.

3 Copyright c⃝ 2007 by ASME

1 1.5 2 2.5 3 3.5 40

2

4

6

8

10

12

14Energy density accounting for accumulator size only

Volumetric expansion ratio: Vexpand/Vcomp

Ener

gy d

ensi

ty [K

J/lit

er]

IsothermalAdiabatic

1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

6

7

8

9Closed accumulator energy densities accounting for displaced oil volume

Volumetric expansion ratio: Vexpand/Vcomp

Ener

gy d

ensi

ty [k

J/lit

er]

IsothermalAdiabatic

Figure 2. Volumetric energy density of closed accumulator system forcompressed gas pressure of 35MPa. a) volume accounts for gas volumeonly; b) volume accounts for both gas and oil.

Acc. vol.

comp. gas Exp gas vol

Figure 3. The open accumulator concept. Atmospheric air is com-pressed into accumulator during storage phase. Compressed air is ex-panded to the atmosphere during motoring phase. System volume doesnot need to contain the air at atmospheric pressure.

0 1 2 3 4 5x 107

0

50

100

150

200

250

300

Pcomp [Pa]

Ener

gy d

ensi

ty [K

J/lit

er]

Open accumulator energy densities

IsothermalAdiabatic

Closed accumulator

Figure 4. Volumetric energy density of open accumulator system forcompressed gas pressure of 35MPa.

2. The accumulator volume will be decreased since it needsonly account for the compressed air volume instead of theexpanded air volume and the displaced oil as in the closedaccumulator case.

3. The displaced oil that makes up the difference between thecompressed gas volume and the expanded gas volume is nolonger needed, saving both volume and weight.

For example, assuming an isothermal process, the available en-ergy for a given volume of compressed air in an open accumula-tor will be increased by 6.5 fold compared to the optimal closedaccumulator with the same maximum pressure of 35MPa withr = 2.15. Since the closed accumulator must account for 2r− 1times the compressed air volume, the system volume will be de-creased by (2× 2.15− 1) = 3.3 times in the open accumulator,for the same volume of compressed gas. Thus, the overall in-crease in energy density in an isothermal process will be givenby 6.5×3.3 = 21.5 folds.

The energy densities of the open accumulator system underisothermal and adiabatic conditions are shown in Figure 4. Theyare computed from the available work given by Eqs.(2) and (5),and the total volume given by the compressed gas volume Vcomp.Hence, the energy density of the open accumulator system as-suming an isothermal process is given by:

Eopenη,T = Pcomp lnr−Pa(r−1) (8)

where r =PcompPa for the isothermal process. Since the volume

expansion ratio r increases with Pcomp, the energy density in-creases super-linearly with respect to Pcomp. For Pcomp = 35MPa,Eopenη,T = 170 kJ/liter so that a 380kJ storage would only require2.24 liters.

4 Copyright c⃝ 2007 by ASME

If an adiabatic process is assumed, the energy density of theopen accumulator is:

Eopenη,s = Pcomp

⎡

⎣

(r1−γγ

p −1)

(γ−1)−

(r1γp −1)

rp

⎤

⎦

where rp := Pcomp/Pa is the pressure ratio which is related to thevolume expansion ratio r by rγ = rp.

At Pcomp = 35MPa, r = 65.5, Eopenη,s = 64.62kJ/liters whichis 9.2 times that of the closed accumulator system under the adi-abatic expansion condition. A 380kJ storage would require 5.88liters.

While the open accumulator concept is simple, and theoret-ically provides an order of magnitude increase in energy density,there are several challenges to realizing its potential. Most aredue to the high compression ratio and the use of air (which con-tains O2) instead of inert gas as in closed accumulators:

1. Safety in compressing and storing high pressure air2. Excessive temperature excursions during compression and

expansion3. Accumulator pressure can become too low to be useful4. Lack of high power and efficient pneumatic compres-

sor/motor

Storing and production of compressed air at 42MPa is rou-tinely achieved in Scuba diving tanks while our desired operatingpressure is only 35MPa. Thus, high pressure compressed air isnot inherently unsafe. Safety concern stems from the risk of ig-niting hydraulic oil or oil vapor in the presence of compressedair. This can be avoided by utilizing non-flammable liquid inconjunction with the open accumulator, with proper sealing, andby using materials that properly separate oil and air if necessary.Notice that the basic open accumulator concept, as shown in Fig.3, being a completely pneumatic approach, does not even requirehydraulic fluid.

Concerns (2) and (3) and their potential solutions are dis-cussed in sections 3.2 and 3.3 respectively, and a potential designof an efficient air compressor/motor is presented in section 4.

3.2 Isothermal operationAlthough the open accumulator operating adiabatically has a

high energy density compared to the closed accumulator system,adiabatic operation at high compression/expansion ratios leadsto excessively high or low temperatures which is a challenge forreadily available materials to withstand.

The temperature change of a gas being compressed or ex-panded adiabatically can be estimated by considering the internal

energy of the air:

ncv∆T = −Work = −PcompVcomp(r1−γ−1)

(1− γ)

= nRT(r1−γ−1)

(1− γ)(9)

where n is the number of moles of air, R= 8.3144J/mol-K is theUniversal Gas constant, cv = 2.5R is the molar thermal capacityof air (with diatomic gas species). Therefore,

∆TTinit

=r1−γ−1

2.5(1− γ)= −(1− r−0.4)

where Tinit is the initial temperature, and r is the volumetric ex-pansion ratio. From this,

Tf inal = Tinit +∆T = Tinit r−0.4 (10)

Thus, air at atmospheric pressure Pa = 0.1MPa and Tinit = 278Kwhen compressed to P = 35MPa would have a temperature of1583K. Compressed air at P = 35 MPa and Tinit = 278K whenexpanded to atmospheric pressure will have a temperature of56K. These are extremely hot and cold temperatures which willbe challenging to the components.

For this reason, our aim is to design the system to operate asclose to an isothermal condition as possible. In addition to avoid-ing excessive temperatures, this also results in 2.6 fold increasein energy density over an adiabatic process.

To achieve this, it is necessary to have an environment thatcan serve as a heat sink during compression and as a heat sourceduring expansion, and whose temperature does not change sig-nificantly. The atmosphere can be such an environment if anabundance of ambient air flow is available. Another possibilityis to utilize a phase change material (PCM) as a constant tem-perature bath to the air that is being compressed or that is ex-panding. The PCM will provide a local energy source or energysink during expansion and compression so that the process oc-curs at nearly constant temperature as determined by the phasetransition temperature of the PCM. Table 1 shows several com-mon PCMs (solid-liquid) and their thermal properties ( [9]). ThePCM can be encapsulated in pellets which are then circulated ina liquid slurry to improve heat transfer.

For an ideal isothermal process, the heat exchange with thePCM or the environment equals the energy stored or regenerated.Thus, the overall energy density will be

Eopen+PCMη,T =Energy availableVcomp+VPCM

=Eopenη,T HVEopenη,T +HV

5 Copyright c⃝ 2007 by ASME

Non−flamable liquid

Optional Transient circuit

air compressor/motor

35MPa air

atm

Mechanical Load

Circulating PCM

hydraulic pump/motor 1

Figure 5. Open accumulator storage concept

PCM Trans temp. Latent heat (HV ) Latent heat (Hm) Overall energy density Eg+PCMη,T

[degC] [kJ/Liter] [kJ/Kg] @35MPa [kJ/liter]

water 0 306 333.4 109.3

CaCl2 ·6H2O 29 311 190.8 109.9

Na2SO4 ·10H2O 32.4 358 253 115.3

Na2S2O3 ·12H2O 36 426 280 121.6

Table 1. Various phase change materials (PCMs) and their thermal properties.

where Eη,T is the isothermal energy density, and HV is the vol-umetric latent heat density. The overall energy density with thevarious PCMs operating at a compressed air pressure of 35MPais given in Table 1 showing a 13 to 15 fold increase over existingclosed accumulator system.

The above calculation shows that from a thermal capacitystandpoint, it is possible to utilize a PCM to absorb and regener-ate all the heat needed to maintain an isothermal process withouta significant volume penalty. In reality, the ambient environmentcan also be a source or sink of some heat, so that even less PCMis needed.

In addition to having a heat source/sink being available,there must be adequate heat transfer to and from the air beingcompressed and expanded. Limitation in heat transfer is ex-pected to have ramifications on the power capability of the openaccumulator. Multistage compressor/motor designs with inter-cooling and enhanced heat transfer are currently being investi-gated.

The idea of using PCM as a heat source/sink has some sim-ilarity to the proposed use of thermal foam in closed accumu-lators [4]. For the open accumulator configuration, PCM andenhanced heat transfer are recommended for the air compres-sor/motor, whereas perfect insulation is recommended for theaccumulator so as to maintain, in the compressed air, the heatassociated with any un-intended increase in temperature during

compression.

3.3 Constant pressure supply and hydraulic transientoverload

In the current closed accumulator system, as energy is de-pleted, pressure decreases and an increase in flow is required toachieve the same power level. The situation would be worsein the open accumulator case if it is implemented as shown inFig. 3, since the pressure would fall as low as the atmosphericpressure. Instead, the preferred configuration would have thecompressed gas volume and molarity decrease while maintain-ing pressure constant. This simple idea can be achieved by us-ing a constant volume accumulator consisting of a liquid (non-flammable hydraulic fluid) chamber and a gas chamber separatedby a piston or a bladder just as in conventional accumulators. Asenergy is stored, compressed air is pumped into the air side ofthe accumulator and at the same time the liquid is emptied tomaintain a constant pressure. As energy is used, compressed airvolume decreases, and the voided volume is then refilled by theliquid.

Fig. 5 shows a configuration that can be controlled to achievethis. Mechanical work is put in and taken out mainly through theair compressor/motor. The air compressor/motor is connectedin tandem to a small hydraulic pump/motor and the mechanicalload or prime mover. In the storage phase, shaft work is used

6 Copyright c⃝ 2007 by ASME

to drive the air compressor to compress air from the atmosphericto a high pressure (say 35MPa). This will normally increase thepressure in the accumulator. To off-set this increase, hydraulicliquid is bled into the hydraulic motor (1) whose work is usedto offset the mechanical input needed for the compressor. Inthe regeneration phase, the air motor/compressor acts as a motorand compressed gas in the accumulator is bled into the air-motor.This would normally decrease the accumulator pressure. To off-set this decrease, a small portion of the compressor shaft workis used to drive the hydraulic pump (1) which pumps hydraulicliquid from a reservoir into the hydraulic liquid chamber of theaccumulator. The remaining shaft work is then consumed by themechanical load. To maintain the accumulator pressure, the hy-draulic pump/motor displacement must be controlled in coordi-nation with the air compressor/motor.

An added benefit with a constant volume accumulator thatconsists of a hydraulic fluid chamber and a compressed air cham-ber is that it can sustain a high momentary power overload be-yond the capability of the air compressor/motor. This is achievedby operating accumulator from both the air and the liquid sides.Specifically, when storing energy, as the air compressor is work-ing at full power compressing air into the accumulator, excesspower is accommodated by pumping hydraulic fluid (using thepump/motor (1) or the optional transient circuit) into the accu-mulator as well. Similarly, during regeneration, the air motoroperates at full power and any power deficit is accommodated bydepleting the hydraulic oil via the hydraulic motor (1) or the tran-sient power circuit. In either situation, power overload will causethe pressure not to be maintained. This causes the energy storagecapacity to decrease continuously with greater power overloadbeyond the power capability of the air compressor/motor. Theenergy storage capacity approaches that of a closed accumulatorfor very large power overload.

4 Air motor/compressorSince the open accumulator concept relies on compressing

and expanding air to store or regenerate energy, the air compres-sor/motor must be efficient and powerful.

The air motor/compressor design being investigated consistsof 2-3 stages. The motor/compressor for each stage makes use ofmultiple compression/expansion chambers connected via (non-flamable) liquid pistons to a hydraulic pump/motor (Fig. 6).The air-side of the chambers are connected to the accumula-tor and to the atmosphere. The air and liquid are separated bya bladder material (e.g. Viton). In the simplest case, the hy-draulic pump/motor is a radial piston pump/motor with each pis-ton controlling the volume of one compression/expansion cham-ber. Thus, the air chamber volume decreases as the radial pistonextends, and increases as the radial piston retracts. The controland timing of the air valves determine whether the system is instorage or motoring mode, as well as the amount of air that will

be compressed or expanded (i.e. the displacement).The motoring mode begins when the expansion chamber is

filled with liquid. The pneumatic valve is opened to the com-pressed air reservoir for a brief moment, and is then shut off.The duration that this valve is open determines the amount ofcompressed gas in the chamber and hence the energy. The com-pressed gas in the chamber expands, applying pressure throughthe liquid piston on the hydraulic motor. When the air inthe chamber has expanded sufficiently, the pneumatic valve isopened to the atmosphere. This allows the hydraulic motor topush liquid into the chamber with little resistance, returning thechamber to an oil filled position where the next motoring cyclerepeats.

The storage mode begins when the compression/expansionchamber is filled with air at atmospheric pressure and the pneu-matic valve is opened to the atmosphere. The hydraulic pumpthen pushes liquid into the chamber decreasing the air volumeby ejecting some of the air back into atmosphere. The pneumaticvalve is shut off when the desired amount of air to be compressedis reached. The air chamber volume continues to decrease untilits pressure exceeds the pressure in the open accumulator. Atthis point, the pneumatic valve is opened to the accumulator andcompressed air is pushed into the accumulator. When all the airis compressed into the accumulator, the liquid piston begins to re-tract. The pneumatic valve closes to the accumulator and opensto the atmosphere, drawing air into the compression for the nextcycle.

The advantages of this design are that:

1. The chambers can be sized and the valve timing selected sothat during motoring full expansion to atmospheric pressurecan be achieved. This maximizes the energy extracted fromair.

2. The use of liquid pistons and enclosed compressed air cham-ber minimizes air leakage through gaps.

3. Multiple chambers and pistons in different stages of expan-sion and filling allow for uniform overall torque profile.

4. The variation of the chamber volume with respect to the an-gle of rotation can be tuned by designing the cam profile ofthe radial piston pump/motor.

5. Each compression/expansion chamber and hydraulicpump/motor functions essentially the same as a regenerativecircuit with a mini conventional accumulator. Efficienttransduction of mechanical power can be expected.

One drawback of this design is that each radial piston mustaccommodate the full volume of each chamber. Since this vol-ume is determined by the expanded air volume, the radial pistonpump/motor needs to be quite large. For example with the ac-cumulator pressure at 35MPa, it must accommodate 100lpm offlow per kW power. To increase compactness, it is possible to 1)utilize an intensifier between the compression/expansion cham-ber and the radial piston pump/motor in Fig. 6; 2) use a compact

7 Copyright c⃝ 2007 by ASME

To atm

to accumumulator

liquid

air

rotating cam

Hydarulic radial piston pump/motor

Air valves

chambersCompression/expansion

Figure 6. Compressor/motor consisting of a series of expansion/compression chambers and a radial piston hydraulic pump/motor.

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

3.5x 10−5

Angle − θ [rad]

Cha

mbe

r vol

ume −

[m3 ]

Expansion Compression

Figure 7. Chamber volume as a function of rotational angle for a nearconstant power profile. Angle θ ∈ [0,π] corresponds to the expansioncycle, whereas θ ∈ (π,2π] corresponds to the compression cycle.

small displacement hydraulic pump/motor operating a higher fre-quency than the cycling frequency of the expansion/compressionchambers together with directional valves to achieve the desiredextension and retraction of the liquid pistons.

5 Simulations5.1 Air motor/compressor

To illustrate the operation of the compressor/motor, we con-sider a 1-stage design with 5 chambers and a r = 350 expansionratio. While a multi-stage design will be more practical in anactual design, the 1-stage simulation would be a more stressfulsituation with which we can evaluate the system constraints.

Each cylindrical compression and expansion chamber is as-sumed to have a diameter of 6.5cm and a maximum volume ofVmax = 33.3cc. We assume the chamber wall is made of copper,has a wall thickness of 0.5cm and is circulated with the PCMCaCl2 · 6H2O (see Table 1) which has a melting point of 29degC. The atmospheric pressure and temperature are Pa = 0.1MPa,Ta = 20degC. The accumulator pressure is assumed to be 35MPaand it is assumed to be kept at the PCM melting temperature ofT0 = 29deg C.

As mentioned earlier, the displacement of the air compres-sor/motor can be controlled by varying the amount of com-pressed air to be expanded or the volume of atmospheric air to becompressed. We define the displacement variable u ∈ [−1,umax]such that u ∈ [−1,0) corresponds to the compressor mode andu ∈ (0,umax] with umax ≥ 1 corresponds to the motoring mode.In the compressor mode, the volume of atmospheric air whenthe air valve is shut is Vmax · |u|. In the motoring mode, the vol-

8 Copyright c⃝ 2007 by ASME

0 0.5 1 1.5 2 2.5 3105

106

107

Pressure profiles various u ∈ [0.05,1.5]

Angle − θ

Pres

sure

[Pa]

increasing u

u=1

u=1.5

0 0.5 1 1.5 2 2.5 3 3.5

23

24

25

26

27

28

29

Expansion temperature profile at 10Hz

Angle − θ

Tem

pera

ture

in d

eg C

increasing u

Figure 8. Pressure and temperature profile during expansion for variousinputs u ∈ [0,1.5]: Ideal conduction case.

ume of compressed gas when the air valve is shut is (Vmax/r) ·uwhere r = 350 is the expansion ratio, u = 1 corresponds to thecase when the compressed air will be expanded to atmosphericpressure in an isothermal process when the chamber is at its max-imum volume. If u> 1, the chamber will be super-charged suchthat more energy will be produced at the expense of efficiencysince full expansion will not be achieved.

The volume profile shown in Fig. 7 was designed so that theheat generated during the expansion/compression is nearly con-stant. The design is important for reducing temperature varia-tion. In the simulations below, the compressor/motor is assumedto operate at 10Hz.

Ideally conducting case Consider first the optimisticcase in which the heat transfer between the air in the chamber

0 0.5 1 1.50

5

10

15

20

25

30

Input u

J /c

ycle

Energy per cycle at 10Hz

Actual

Isothermal

0 0.5 1 1.596.5

97

97.5

98

98.5

99

99.5

100

100.5

Input u

Effic

ienc

y %

Efficiency at freq=10Hz.

IsothermalActual

Isothermal

Actual

Figure 9. Energy per cycle and efficiency during expansion for variousinputs u ∈ [0,1.5]: Ideal conduction case. Efficiency is computed as theratio of energy extracted to the work done to produce the compressed air.The latter is assumed to be via a reversible isothermal process.

and the PCM is limited only by the copper chamber wall. Figures8-9 show the results during motoring mode for various displace-ments u > 0. Notice that the pressure profiles are very similarto the isothermal profiles indicating that the temperature effect issmall. For u< 1, full expansion is achieved. For u> 1, the pres-sure does not reduce to the atmospheric pressure as the cham-ber reaches it’s maximum volume. Hence some energy will belost. As the displacement increases, the minimum temperaturedecreases. However, the maximum temperature deviation is lessthan 7 degC from the PCM melting point. Figure 9 shows thatthe actual work extracted per cycle increases nearly linearly withu and is only slightly lower than the isothermal case at larger u’s.At u = 1, 19.12J of work is extracted per cycle per chamber so

9 Copyright c⃝ 2007 by ASME

3.5 4 4.5 5 5.5 6105

106

107

Isothermal and actual pressure for u=[−1,0]

Angle − θ

Pres

sure

[Pa]

increasing |u|

u=−1

3 3.5 4 4.5 5 5.5 620

22

24

26

28

30

32

34

Expansion temperature profile at 10Hz

Angle − θ

Tem

pera

ture

in d

eg C

increasing |u|

Figure 10. Pressure and temperature profile during storage for variousinputs u ∈ [−1,0]: Ideal conduction case. Dotted lines: the isothermalpressure profiles; Solid: actual pressure profiles.

that the motor produces 1.15KW at 10Hz and an efficiency of98.6%. Some amount of supercharging can increase the powersignificantly without affecting efficiency too much. For example,at u = 1.5, 1.69KW power is achieved at 10Hz with an overallefficiency of 96.5%.

Figures 10-11 show the results during storage mode for var-ious displacements −1 < u< 0. As the displacement magnitude|u| increases, compression begins earlier and the maximum tem-perature increases up to 5 degC above the PCM melting temper-ature (Fig.10). Note that the work done on the device per cyclein the isothermal case is more than the available energy contentby compressing the gas, which is the energy stored (Figure 11).The actual amount of energy storage per cycle is less than theisothermal case at all u. The overall storage efficiency (ratio of

−1 −0.8 −0.6 −0.4 −0.2 00

5

10

15

20

25

Input u

J /c

ycle

Energy stored per cycle at 10Hz

ActualIsothermal

Actual

Isothermal

−1 −0.8 −0.6 −0.4 −0.2 098.2

98.4

98.6

98.8

99

99.2

99.4

99.6

99.8

100

100.2

Input u

Effic

ienc

y %

Efficiency at freq=10Hz.

IsothermalActual

Isothermal

Actual

Figure 11. Energy per cycle and efficiency during storage for variousinputs u ∈ [−1,0]: Ideal conduction case. Efficiency is computed as theratio of maximum work that can be extracted from the compressed gasvia a reversible isothermal process to the actual work done to producethe compressed air.

work done to the available energy) is above 98.3% for all |u|< 1.The maximum storage power achieved is 1.15KW at 10Hz.

Poor heat transfer case In reality, the heat transfer be-tween the air in the chamber and the PCM will be limited by theheat transfer in the air inside the chamber. Since heat transfer inthe compressing/expanding air chamber is a fairly complicatedsubject [10,11], to expediently investigate the effect of poor heattransfer, we simply use a small heat transfer coefficient, namely1/40 that of copper.

Figures 12-13 show the results during motoring mode forvarious inputs u > 0. As expected, temperature decreases more

10 Copyright c⃝ 2007 by ASME

0 0.5 1 1.5 2 2.5 3105

106

107

Pressure profiles various u ∈ [0.2, 3]

Angle − θ

Pres

sure

[Pa]

increasing u

u=3

u=1

0 0.5 1 1.5 2 2.5 3

−140

−120

−100

−80

−60

−40

−20

0

20

Expansion temperature profile at 10Hz

Angle − θ

Tem

pera

ture

in d

eg C increasing u

u=3

u=1

Figure 12. Pressure and temperature profile during expansion for vari-ous inputs u ∈ [0,3]:Poor heat transfer case.

when heat transfer is poor. For u= 1, the minimum temperatureis 120 degC below the melting point of the PCM. Consequently,the pressure decreases more rapidly compared to the ideally con-ducting case. Because of this, full expansion is achieved at muchhigher us (e.g. at u= 2.8). Fig. 13 shows that a significant effectof poor heat transfer is the reduction in efficiency. At u = 1, theefficiency is 68% and at u = 1.5 the efficiency is 63%. Corre-spondingly, the motor power is reduced to 796W at u= 1 and to1.1KW at u= 1.5.

Figures 14-15 show the results during storage mode for var-ious inputs −1 < u< 0. The actual and isothermal pressure pro-files deviate from each other, especially for large u. The temper-atures are higher than the ideally conducting case and for u=−1the maximum temperature is 290degC above the PCM meltingpoint. Consequently, the pressure increases more rapidly than

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

Input u

J /c

ycle

Energy per cycle at 10Hz

FuelActualIsothermal

Actual

Isothermal

Compressed air energy

0 0.5 1 1.5 2 2.5 355

60

65

70

75

80

85

90

95

100

105

Input u

Effic

ienc

y %

Efficiency at freq=10Hz.

IsothermalActual

Isothermal

Actual

Figure 13. Energy per cycle and efficiency during expansion for variousinputs u ∈ [0,3]: Poor heat transfer case. Efficiency is computed as theratio of maximum work that can be extracted from the compressed gasvia a reversible isothermal process to the actual work done to producethe compressed air.

in the ideally conducting case. Because of the increase in tem-perature, the amount of work required for compressing the sameamount of air is higher. At u = −1, 34.3J of work is done forcycle per chamber such that 2.055KW of braking power is ab-sorbed. However, if regeneration is done at the PCM temperatureisothermally, then only 58% of the work will be recovered.

The 1-stage compressor/motor design simulation aboveshows that heat transfer within the air compressor/motor playsa significant role in efficiency and power output of the system.With good heat transfer, the compressor/motor can be efficientand powerful. When heat transfer is limited, more chambers orslower frequency can be used to improve efficiency. However,

11 Copyright c⃝ 2007 by ASME

3.5 4 4.5 5 5.5 6105

106

107

Isothermal and actual pressure for u = [−1,0.05]

Angle − θ

Pres

sure

[Pa]

increasing |u|

2.5 3 3.5 4 4.5 5 5.5 60

50

100

150

200

250

300

350

400

Expansion temperature profile at 10Hz

Angle − θ

Tem

pera

ture

in d

eg C

increasing u

Figure 14. Pressure and temperature profile during storage for variousinputs u ∈ [−1,0]: Poor conduction case. Dotted lines: the isothermalpressure profiles; Solid: actual pressure profiles.

these will be at the expense of compactness and power respec-tively. A multi-stage design in which each stage has the sameexpansion ratio, will reduce the heat transfer requirement by thenumber of stages. While the heat transfer coefficient used inthis study is for illustration only, the actual heat transfer ratedepends significantly on the detailed designs of the compres-sion/expansion chambers.

5.2 Overall system controlA control system for the open accumulator configuration in

Fig. 5 has been designed. For simplicity, it is assumed that the aircompressor/motor and the hydraulic pump/motor are connectedin tandem and have the same speed ω. The system is loaded withan additional hydraulic load that draws hydraulic flow Qload(t)

−1 −0.8 −0.6 −0.4 −0.2 00

5

10

15

20

25

30

35

Input u

J /c

ycle

Energy stored per cycle at 10Hz

ActualIsothermal

Actual

Isothermal

−1 −0.8 −0.6 −0.4 −0.2 055

60

65

70

75

80

85

90

95

100

105

Input u

Effic

ienc

y %

Efficiency at freq=10Hz.

IsothermalActual

Isothermal

Actual

Figure 15. Energy per cycle and efficiency during storage for variousinputs u ∈ [−1,0]: Poor conduction case. Efficiency is computed as theratio of maximum work that can be extracted from the compressed gasvia a reversible isothermal process to the actual work done to producethe compressed air.

w

Qload

Open accumulator

Controlleruair

uhyd

w

Pressure

Figure 16. Control System

12 Copyright c⃝ 2007 by ASME

0 1 2 3 4 5 6

−10

−8

−6

−4

−2

0

2

4

6

8

10

Time − s

Out

put f

low

− [L

pm]

0 1 2 3 4 5 6−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Control signal

Time − s

Inpu

t − [1

]

Hydraulic pump/motorAir motor/compressor

Figure 17. Alternating output flow and control signals

from the accumulator. The control system (Fig. 16) determinesthe displacements of the air compressor/motor (uair) and that ofthe hydraulic pump/motor (uhyd) based on the accumulator pres-sure P and the speed compressor/motor-pump/motor speed ω.The control is designed such that uhyd is used to maintain the ac-cumulator pressure P at 35MPa, whereas uair is used to maintainthe compressor/motor-pump/motor speed at 10Hz.

Figures 17-19 show the results in which the demand flowQload cycles between ±10lpm. This gives an alternating powerstorage and withdrawal profile. Notice that the pressure in thesystem is regulated at 35MPa and the system speed is regulatedat 10Hz. The energy content of the accumulator also cycles inthe desired manner.

0 1 2 3 4 5 63.15

3.2

3.25

3.3

3.35

3.4

3.45

3.5

3.55x 107

Time − s

Pres

sure

− [P

a]

0 1 2 3 4 5 69.5

9.6

9.7

9.8

9.9

10

10.1

10.2

10.3

10.4

10.5

Time − s

Freq

− [H

z]

Frequency

Figure 18. Pressure and frequency regulation

0 1 2 3 4 5 674

75

76

77

78

79

80

81

Time − s

Ener

gy −

[KJ]

Energy content

Figure 19. Energy content of the accumulator.

13 Copyright c⃝ 2007 by ASME

6 ConclusionsIn this paper, a new “open accumulator” configuration is

proposed for fluid power energy storage that can potentially im-prove the energy density by an order of magnitude. By not need-ing to contain the expanded gas volume, a much higher expan-sion ratio and hence energy is available, and the system volumecan be decreased. With good heat transfer and a reliable heatsink / source, temperature variation due to the large compres-sion/expansion ratio can be mitigated. The system can be op-erated in a constant pressure mode to maintain power capabilitythroughout its operation. To realize its potential, it is necessary todesign air compressor/motor that can operate nearly isothermallyto achieve good efficiency. Simulations indicate that proper heattransfer is critical for increasing the power capability and effi-ciency of the system. A prototype is current being manufacturedto experimentally verify the proposed concept.

ACKNOWLEDGMENTThis material is based upon work performed within the ERC

for Compact and Efficient Fluid Power, supported by the Na-tional Science Foundation under Grant No. EEC-0540834.

REFERENCES[1] Otis, D., 1973. “Thermal losses in gas-charged hydraulic

accumulators”. In Proceeding of the 8th Intersociety En-ergy Conversion Engineering Conference, AIAA, pp. 198–201.

[2] Otis, D., 1990. “Experimental thermal time-constantcorrelation for hdyraulic accumulators”. ASME Journalof Dynamic Systems, Measurement and Control, 112(1),pp. 116–121.

[3] Pourmovahed, A., 1988. “Durability testing of an elas-tomeric foam for use in hydraulic accumulators”. In Pro-ceedings of the AIAA Intersociety Energy Conversion En-gineering Conference, Vol. 2, pp. 31–36.

[4] Pourmovahed, A., Baum, S. A., Fronczak, F. J., andBeachley, N. H., 1988. “Experimental evaluation ofhydraulic accumulator efficiency with and without elas-tomeric foam”. Journal of Propulsion and Power, 4(2),March-April, pp. 185–192.

[5] Sherman, M. P., and Karlekar, B. V., 1973. “Improvingthe energy storage capacity of hydraulic accumulators”. InProceeding of the AIAA 8th Intersociety Energy Conver-sion Engineering Conference, pp. 202–207.

[6] David, J. F., and McLeish, R. D., 1975. “Self-containedhydraulic power source for artificial upper limbs.”. IEEETransactions on Biomedical Engineering, BME-22(4),July, pp. 322–326.

[7] Schainkler, R., and Nakhamkin, M., 1985. “Compressed airenergy storage (caes): Overview, performance and cost data

for 25mw to 220mw plants”. IEEE Transactions on PowerApparatus and Systems, PAS-104(4), April, pp. 791–795.

[8] Nakhamkin, M., Swensen, E., Schainker, R., and Pollak,R., 1991. “Compressed air energy storage: survey of ad-vanced caes development”. In American Society of Me-chanical Engineers (Paper), International Power GenerationConference, Oct 6-10 1991 San Diego, CA, USA, pp. 1–8.

[9] Clark, J. A., 1985. Thermal energy storage. McGraw-HillBook Co.

[10] Kornhasuer, A. A., 1989. “Gas-wall heat transfer duringcompression and expansion”. PhD thesis, Department ofMechanical Engineering, MIT.

[11] Faulkner, H. B., and Smith, J. L., 1983. “Instanteous heattransfer during compression and expansion in reciprocat-ing gas handling machinery”. In Proceeding of the AIAA18th Intersociety Energy Conversion Engineering Confer-ence, pp. 724–730.

14 Copyright c⃝ 2007 by ASME