1

Proceedings of IWHT2013 2nd International Workshop on Heat Transfer Advances for

Energy Conservation and Pollution Control October 18-21, 2013, Xi’an, China

IWHT2013-001

Thermal Analysis of a Compressor for Application to Compressed Air Energy Storage

C. Zhang1, B. Yan

1, J. Wieberdink

1, P. Y. Li

1, J. D. Van de Ven

1, E Loth

2, T. W. Simon*

1

1Mechanical Engineering Department, University of Minnesota,

111 Church St. S.E. Minneapolis, MN, 55455, USA

2Mechanical and Aerospace Engineering Department, University of Virginia,

122 Engineer’s Way P.O. Box 400746, Charlottesville, VA 22904, USA

(*Corresponding Author: tsimon@me.umn.edu)

Abstract In this paper, the topic of Compressed Air Energy Storage

(CAES) is discussed and a program in which it is being applied

to a wind turbine system for leveling power supplied to the grid

is described. Noted is the importance of heat transfer in the

design of the compressor and its effect on performance.

Presented is a design for minimizing the temperature rise in the

compressor during compression. The design requires modeling

regenerative heat transfer from the compressed air to solid

material inserted in the compression space. Modeling requires

characterizing pressure drop through the porous insert,

interfacial heat transfer between solid and fluid in the matrix,

and thermal dispersion within the porous regions. Computation

and experimentation are applied for developing correlations for

such terms. Two types of porous media are applied, interrupted

plates and open-cell metal foams. Cases with foam inserts are

computed and the results are discussed. Discovered in the

results are some complex secondary flow features in spaces

above the porous inserts.

Keywords: Energy storage, Compressor, Wind turbine, Heat

transfer, Porous media

1. Introduction

1.1. Motivation

This paper presents thermal analyses on a liquid piston

driven compressor used for Compressed Air Energy Storage

(CAES). The CAES system stores energy as high-pressure air,

to retrieve it later in a liquid piston expander. Compression leads

to a tendency for temperature rise in a compressible gas. This

paper discusses techniques for minimizing that temperature rise.

Absorbing heat from air during compression to reduce its

temperature rise is important for improving compression

efficiency. As the air temperature rises, part of the input work is

being converted into internal energy rise that is wasted during

the storage period as the compressed air cools toward the

ambient temperature. Referring to the P-V diagram in Fig.1, one

sees that the work input is represented by the integral of the area

under the P-V curve. For the same pressure compression ratio,

an isothermal process always requires smaller work input

because the cooling process and the work required to maintain

reservoir pressure during cooling are missing. Therefore, near-

isothermal compression is important for reducing work input

and enhancing efficiency for CAES systems.

1.2. Background on wind turbines and energy storage

Our desire is that the CAES system is integrated into a

wind power field. The benefit of integrating energy storage into

a wind power array is that fluctuations in wind power input can

be smoothed over time and electric power generation equipment

can be sized commensurate with a supply power that is nearer

the average wind power of the day. The alternative is sizing for

peak power or “throttling back” the wind turbine when the wind

is strong.

Use of storage techniques for wind power is discussed in

reference [1]. Various scenarios with and without storage were

considered. In one, wind generation capacity in 2050 was

302GW without storage and 351GW with storage. Further, they

concluded that CAES is more economical than hydroelectric

pump storage (HPS) or batteries.

2

Fig. 1. Schematic of isothermal compression vs. non-isothermal

compression

From a report written by the US Offshore Wind

Collaborative [2], we read that the total amount of US offshore

wind energy capacity is almost equal to the current total

installed capacity. Noting that most electricity-demanding

regions are on the coasts, the report highlights the significant

potential for offshore wind generation. It urges establishment of

“opportunities to coordinate technological, economic, and

environmental advances, along with the chance to build public

trust and investor confidence in the potential that offshore wind

energy holds for the nation.” Toward that goal, implementing

CAES allows efficient use of offshore equipment and reduction

of transmission line capacity.

Traditional CAES systems store the compressed air in

underground caverns and often marry this with combustion

plants by using the compressed air as oxidant for burning in

combustion turbines [3]. More recent advancements include

using multi-stage compressors with inter-cooling between stages

and multi-stage expansion turbines, with reheat [4]. The

advantages of using near-isothermal compression and expansion

to improve efficiency in the CAES systems were demonstrated

in reference [3]. Herein, near-isothermal compression and

expansion is by using regenerative heat exchange with elements

within the compressor/expander volumes.

A traditional reservoir for CAES, an accumulator, is a

volume into which air is compressed. Energy is released by

expanding that air to derive work until the accumulator-to-

ambient pressure difference has decreased to the point at which

further expansion is not practical. Then, power and energy

density of the expanding air are small. If used in a hydraulic

system, the air is compressed by displacing it with a pumped

liquid and work derived from that compressed air drives the

liquid through a hydraulic motor, as shown in Fig. 2(a). In the

present system, we employ the “open accumulator” concept

proposed in [5] and shown in Fig. 2(b). In this system, gas is

exhausted to the atmosphere during expansion, reversing during

compression. Compression is with pumped liquid and air and

expansion is with a liquid motor and an air expander. It is

operated at a constant accumulator pressure; the maximum

design pressure. Thus, with the open accumulator, the energy

storage density per unit volume of air is always high since the

low-power, low-accumulator-pressure situation in the closed

accumulator is avoided. An added benefit is a dramatic

reduction in accumulator pressure oscillation cycles and

improved fatigue performance.

(a) Conventional closed accumulator configuration [5]

(b) The open accumulator concept [5]

Fig. 2. Closed and open accumulators

Though not necessary for the open accumulator CAES to

be successful, our design is proposed to be used in a fluid power

wind turbine system. In such as system, we use hydraulic

equipment for power conversion and transmission, as shown in

Fig. 3. It employs hydraulic circuits, a hydraulic drive pump,

hydraulic pumps and motors, open accumulators, and liquid-

piston air compressors. Advantages include having a hydraulic

pump in the nacelle at the top of the tower, rather than a heavy

transmission and generator assembly and having much of the

equipment, including the generator, at ground (or sea) level,

allowing easier access for assembly and maintenance. When

electricity demand is small, the system operates in storage mode

in which the excess shaft power from the wind turbine is

transferred to hydraulic power in the drive pump and the

hydraulic power is transmitted through the hydraulic circuit to

the hydraulic transformers, which are a series of specialized

hydraulic pumps and valves to pump the liquid into the liquid-

piston chamber to compress air. During this mode, compressed

air is stored in the open accumulator. When the electricity

demand is larger than the direct supply from the wind turbine,

the unit switches to the generation mode in which air is

withdrawn from the open accumulator and expanded in the

liquid piston chamber to derive shaft power for the generator.

Key to success of the system is efficient compression and

expansion of air in the compressor/expander. As noted, this

must be done under near isothermal conditions. Thus, the

present paper will concentrate on the thermal design of the

compressor/expander and the analysis on which it is based. This

paper focuses on compression and expansion with a liquid

3

piston. The term “liquid piston” is applied because the gas

compression is done with a liquid-gas interface rather than a

solid piston. It will be shown that having a liquid piston design

for the compressor is a major step in having an efficient

compressor/expander.

In the liquid-piston compressor, liquid (water in the present

study) is pumped into the compression chamber from below. It

is found in [6] that liquid-piston compressors have an advantage

over solid pistons in terms of efficiency and reduced power

consumption [6]. Further, for the purpose of cooling, insertion

of solid material into the chamber is possible with liquid-piston

compressors as liquid can flow through the open portions of the

matrix.

Cooling of the compressed air could also be effected by

spraying drops into the air space and allowing them to be heated

by the compressed air. Having a liquid piston is beneficial to

spray cooling for the residue of the spray falls to join the piston

liquid. Though spray cooling is effective and is being pursued

by our group, this paper will focus on the method of inserting

heat-absorbing solids into the compression chamber.

Since thermal storage to the porous material in the

compressor volume is so important to success, the remainder of

the paper will be dedicated to modeling that process in

preparation for design of the compressor.

Fig. 3. Schematic of CAES system for offshore wind energy

storage and generation [7]

Nomenclature

Area per unit volume of porous medium (

Cross-sectional area ( )

Half plate distance ( )

Coefficient for the Forchheimer term ( )

Constant-pressure specific heat (J/kgK)

Specific heat for solid (J/kgK)

Constant-volume specific heat (J/kgK)

Hydraulic diameter ( )

Characteristic diameter ( )

Characteristic length based on filament dia. ( )

Filament diameter ( )

Mean pore diameter ( )

Storage energy (J)

Gravitational acceleration (m/s2)

Surface heat transfer coefficient (W/m2K)

Volumetric heat transfer coefficient (W/m3K)

Permeability (m2)

Thermal conductivity (W/mK)

Dispersion conductivity (W/mK)

Chamber length ( )

Length of the upper region without insert ( )

Length of the insert region ( )

Plate length ( )

Total mass of air (kg)

Polytropic exponent

Nusselt number

Bulk pressure (Pa)

Supplied hydraulic pressure (Pa)

Peclet number

Area averaged wall heat flux

Local pressure (Pa)

Final air pressure (Pa)

Prandtl number

Radius of chamber ( )

Reynolds number based on Radial coordinate

Ideal gas constant (J/kgK)

Reynolds number based on characteristic length

Momentum source term (Pa/m)

Local air temperature (K)

Initial temperature; wall temperature (K)

Average air temperature in the chamber (K)

Local solid temperature (K)

Average temperature of solid in the chamber (K)

Final averaged air temperature (K)

Plate thickness ( )

Time (s)

Liquid piston velocity (m/s)

Instantaneous volume of chamber (m3)

Work input (J)

Axial coordinate

Greek Symbols

Volume fraction

Porosity

Compression efficiency

Dynamic viscosity (Ns/m2)

Density (kg/m3)

Final pressure compression ratio

Subscripts

Initial value of variable

Air phase

4

Water phase

Based on filament diameter

Darcian

Fluid phase

Averaged on the REV

Solid

Local streamwise direction

Local cross-stream direction

Superscripts

Dimensionless variable

1.3. Analysis on heat transfer and compression efficiency

The effect of heat transfer on compression efficiency will

be shown quantitatively through a simple thermodynamic

analysis. The compression efficiency CAES is defined as the

ratio of storage energy to work input [9, 10]. The storage energy

is defined as the amount of work extraction from compressed air

as it is isothermally expanded to atmospheric pressure.

(1)

Compression of air is completed in two steps: compress the air

from atmospheric pressure to a high pressure, typically resulting

in temperature increase, and allow the air to cool while

compressing at the storage pressure so that the work potential

(storage energy) is maintained as volume decreases. Work of the

latter stage is identified as “cooling work.” The total work input

is the sum of the work done in the two steps. It is given by,

∫

(2)

The compression efficiency is given by the ratio of the storage

energy to the total work input,

∫

(3)

It is shown that the compression process can be

characterized as a polytropic process [10],

(4)

where the polytropic exponent, , shows the effect of heat

transfer; represents isothermal compression and

for air represents adiabatic compression, with no heat

transfer. Substituting Eq. (4) into Eq. (3), and writing in terms of

dimensionless pressure and volume based on their initial values,

(5)

Equation (5) shows that the compression efficiency is dependent

on the pressure compression ratio, *p and heat transfer, given

by n . Figure 4 shows that for the same pressure compression

ratio, decreasing , which means enhancing heat transfer from

the compressed air, significantly improves efficiency.

Fig. 4. Effects of heat transfer on compression efficiency with

different pressure compression ratios.

2. Heat transfer to the porous inserts

2.1. Introduction

Porous media can be inserted into the liquid-piston

compression chamber so that the solid can absorb thermal

energy from the air as it heats during compression. Because

solid has much higher thermal capacity than air, the solid can

absorb thermal energy from the air, while its temperature rises

only a small fraction of the temperature drop of the air.

The present study will introduce two kinds of porous

inserts, an interrupted-plate insert and an open-cell metal foam

(Fig. 5). The interrupted-plate insert consists of an array of

plates oriented in a staggered fashion so that a new thermal

boundary layer develops on each successive plate in the

streamwise direction. The metal foam has very thin filament

features that enhance mixing of the flow. Both have large heat

transfer surface area to volume ratios.

A zero-dimensional (Zero-D) numerical model has been

developed [11] that can give quick solutions for the transient

change of the gas bulk temperature and pressure during

compression of air in a chamber having porous inserts.

Applying the first law of thermodynamics to the air,

(6)

Since air follows the ideal gas law and, in this case, the liquid

piston volume flow rate is constant, Eq. (6) can be written,

(

)

(7)

Energy conservation for the solid gives,

(8)

Equations (7) and (8) are the governing equations of the Zero-D

model.

5

(a) A sketch of the interrupted

plate insert [11]

(b) Metal foam inserts [12]

Fig. 5. Porous inserts used in the liquid piston compressor

Important fluid and thermal characteristics of the porous

inserts that must be included are the flow resistance and

resulting pressure drop, the heat transfer coefficient between the

solid material and surrounding air, and thermal dispersion. Next,

these terms will be presented for the two types of porous inserts

discussed in this paper.

2.2. Interrupted plate

2.2.1. Shape analysis

Because details of the shape of the interrupted-plate insert

are known, CFD simulations on a Representative Elementary

Volume (REV) of the interrupted-plate can be done. These CFD

analyses are used to obtain the pressure drop and interfacial heat

transfer relationships for flow with various velocities through

the matrix. The REV is the minimum representative, repeating

geometric feature of the porous medium. Its geometry for the

interrupted plate insert is shown in Fig. 6. Three geometric

dimensions are important: the plate length, , the plate distance,

, and the plate thickness, .

A study was conducted to quantify the effects of the shape

parameters on heat transfer and compression efficiency [11].

Twenty-seven different shapes were analyzed. For each shape,

two flow conditions were studied: and ,

where is defined as,

(9)

The flow is presumed to be in the same direction as the axis

(Fig. 6). Periodic momentum and thermal boundary conditions

are used on the entry and exit surfaces of the REV model such

that the flow being simulated is representative of a fully-

developed flow through a central region of the porous matrix.

The solid surfaces are maintained at a uniform and constant

temperature in the REV simulations. Pressure drop and

interfacial heat transfer correlations for use in the compressor

analysis are extracted from the results of these simulations.

Fig. 6. Schematic of an REV of the exchanger [11]

The CFD results show that smaller dimensional features are

beneficial for effecting higher surface heat transfer rates. The

fluid temperature distribution and the wall heat flux of the case

with the smallest geometry features among all the cases studied

are shown in Fig. 7. The maximum local heat flux is found at

the edges of the frontal areas. The figure shows that the flow is

effectively cooled by the solid surfaces. The hottest spot of the

flow is in the fluid region at the core of the REV.

Fig. 7.Temperature and wall heat flux [11]

( )

A heat transfer correlation based on the hydraulic diameter

is developed [11]. The Reynolds number and Nusselt number

based on hydraulic diameters are:

(10)

(11)

where,

(12)

(13)

The heat transfer correlation is given by [11]:

(14)

It is plotted with the data from the various CFD runs in Fig. 8.

6

Fig. 8. Dimensionless numbers based on hydraulic diameter,

, computed from CFD runs on the REV with various values

of the three dimensions and various flow velocities [11]

Equation (14), developed based on different geometries

given in terms of plate length, , plate distance, , plate

thickness, , but generalized in terms of hydraulic diameter is

used in the compressor analysis to assess the compression

efficiency for different interrupted-plate inserts. The

compression efficiency is defined by Eq. (3). In order to

calculate the efficiency, the pressure vs. volume trajectory

during compression in a compressor volume containing the

interrupted-plate insert must be obtained. This can be evaluated

using the Zero-D compression model given by Eqns. (7) and (8).

The interfacial heat transfer coefficient that couples Eqns. (7)

and (8) can be obtained from the Nusselt number correlation:

(15)

In addition, since the interrupted-plate has a flow resistance, this

must be included in the calculation of compression efficiency.

Thus, a pressure drop term must be added to the work in Eq. (3)

to account for pressure drop work to the liquid of the piston. At

any time, this pressure drop is computed in terms of the length

of the porous section through which liquid passes, :

(16)

where, and are obtained from CFD simulations. The

results of this analysis show that, in general, decreasing the

separation distance between plates in the interrupted plate insert

leads to improved efficiency. For a given plate separation

distance, decreasing the plate length improves efficiency, as

shown from a simple boundary layer development analysis. The

results are given in Fig. 9 (from [11]).

2.2.2. Heat transfer and pressure drop for a fixed shape

Analyses in this section are focused on an interrupted-plate

insert with the following shape parameters: ,

, . Simulations are done at eleven

different Reynolds numbers, , ranging from 0.67 to 5333.

Three different runs are computed at while

varying the density of the air flow and the mass flow rate. Each

is a single CFD run. Commercial CFD Software ANSYS

FLUENT is used and the model is used for turbulence

closure. The REV models have periodic momentum and thermal

boundary conditions. The formulation and boundary conditions

are the same as those discussed in [11]. The number of

computational cells varies with Reynolds number; specifically:

169,632 for , 588,816 for ,

1,357,056 for , and 2,024,352 for

. These grid cells have been verified by grid-

independence studies. From the CFD simulations, heat transfer

coefficients and pressure drop terms are obtained.

The area-averaged surface heat transfer coefficient depends

on both flow velocity and density, as shown in Fig. 10. The

Reynolds numbers and Nusselt numbers given by Eqns. (10)

and (11) are calculated and plotted in Fig. 11. The data are fit

using a least-square method to yield the following correlation:

(17)

The pressure drop terms also can be determined from CFD

simulations. The pressure drop, written as a momentum source

term, is given by the following governing equation:

(18)

From the CFD results, the permeability, K , as well as the

Forchheimer coefficient, , are computed:

, ⁄

2.2.3. Thermal dispersion analysis for a fixed shape

When volume averaging is applied to the energy equation,

a thermal dispersion term appears. It is associated with spatial

variations of velocity and temperature within the pores of the

matrix. It is anisotropic in that a value found for streamwise

dispersion is different than a value found for cross-stream

dispersion. In this section, the streamwise thermal dispersion

term for x-direction flow (see Fig. 6) is calculated based on

CFD runs on the REV model for the interrupted plate insert and

, and . The term is:

∫

(19)

The streamwise thermal dispersion term is modeled using the

dispersion conductivity, ,

(20)

Cross-stream dispersion is computed similarly, but the velocity

component for transport is normal to the streamline. The

dispersion conductivity is normalized based on the air

conductivity and plotted against the Peclet number. The results

are shown in Fig. 12. The Peclet number dependency is

expected since dispersion transport is by mechanisms that are

velocity dependent. One of the dispersion mechanisms is, by

nature, similar to eddy transport in turbulent flow. For porous

media, the “eddies” are within the pores and scale on pore size.

7

(a)

(b)

(c)

Fig.9. Compression efficiency of different interrupted-plate

insert shapes; pressure compression ratio=10, [11]

Fig. 10. Area-averaged surface heat transfer coefficient

2.3. Porous metal foam

The fine-scale geometry of the metal foam is randomly

variable (over a feature size range) and essentially unknown to

the numerical modeler. Computing the pressure drop, heat

transfer and dispersion terms for representative, repeated

geometries and combining them statistically would be

approximate and tedious. Thus, we have chosen to determine the

pressure drop and interfacial heat transfer terms through

experiments and simulation. The dispersion term for the foam

matrix is discussed later.

Fig. 11. Heat transfer correlation for the interrupted-plate:

, ,

Fig.12. Streamwise dispersion conductivity for x-direction flow

Pressure drop values for the metal foams have been

measured in [12]. The setup is shown in Fig. 13 (a). Air flow is

driven by a fan, as shown. The flow rate of air is adjusted by a

manual valve. A Sierra TopTrack 822S flowmeter is used to

measure the volumetric flow rate. The pressure drop, due to the

metal foam insert, is measured using a micro-manometer and

the pressure tap shown. The micro-manometer has an

uncertainty of 0.125Pa. The uncertainty of the measured Darcian

velocity is 1.5%. The results are shown in Fig. 13 (b). The

pressure drop is a momentum sink term in the momentum

equation. It can be modeled using the form of Eq. (18). The

results from the measurements lead to the coefficients:

10PPI metal foam: , ⁄

40PPI metal foam: , ⁄

The indicator PPI refers to the nominal number of pores per

inch, a frequently-used descriptor of these foams. We used two

foams in this study, as noted above and in Fig. 5(b).

The following discusses how the porous foam interfacial

heat transfer Nusselt was determined from compression

experiments. First, the experiment is described. A schematic of

the experimental setup is shown in Fig. 14. Water is circulated

in the clockwise direction of the figure. A relief valve is

installed between the pump and the remainder of the system to

limit pressure to a maximum of 11 atm. (165 psia). The volume

of water that enters the compression chamber is measured

continuously using an Omega FTB-1412 turbine flow meter.

8

The upstream pressure is maintained approximately constant by

the control valve. Downstream of the control valve is the

compression chamber, a polycarbonate cylinder with length 353

mm and internal diameter 50.8 mm. A 16-bit analog input board

is used to communicate with the lab controller using

MATLAB/Simulink. The sampling frequency is 4kHz. Two

experimental runs each are conducted with 10PPI and 40PPI

metal foam inserts. Instantaneous values of volume and pressure

are computed from the data and instantaneous gas-volume-

average temperatures are calculated using the ideal gas law.

(a) Schematic of the experimental setup

(b) Results of pressure drop measurements

Fig. 13. Pressure drop from the experiments [12]

The experimental runs were simulated using the Zero-D

model (Eqns. (7) and (8)) by substituting different heat transfer

correlations found from the literature. The experimental data are

shown in Fig. 15 (taken from [12]). By comparison to these

data, a modified version of the Kamiuto heat transfer correlation

was selected as the most suitable heat transfer model for these

metal foams, as discussed in [12]:

(21)

where is the Darcian velocity, the velocity that the fluid

would have in the absence of the solid.

2.4. Simulations of a compressor filled with metal foam

Simulations of liquid piston compression with inserted

metal foam matrices were conducted [12]. Numerical modeling

of the problem combines Volume of Fluid (VOF) and two-

energy equations, one for the fluid and a second for the solid.

Thus, we solve for energy transport in the fluid and solid phases

and couple the two through the interfacial heat transfer

correlation. The VOF method tracks the instantaneous location

of the water/air interface in the compression chamber. Let

subscripts 1 and 2 represent air and water, respectively. The

continuity equations for air and water are:

Fig.14. Schematic of the experimental setup used to select the

optimum open-cell metal foam heat transfer correlation [12]

(a) 10PPI metal foam insert

(b) 40PPI metal foam insert

Fig. 15. Comparison of experimental results to the Zero-D

model solutions obtained by using different heat transfer

correlations (Variables are non-dimensionalized by their initial

values). [12]. Correlations: Fu et al. [14], Kamiuto and Yee,

[13], Kuwahara et al. [15], Nakayama et al. [15], Wakao and

Kaguei [16], and Zukauskas [17].

(22)

and

(23)

Momentum and energy equations are solved for the immiscible

fluid mixture,

(24)

where

(25)

9

The stress tensor, , is based on viscosity of the mixture of air

and water in nodes that contain the liquid-gas interface,

(26)

The momentum sink term, is given by Eq. (18). The energy

equation for the fluid is,

( )

(

)

(27)

where

(28)

and

(29)

The energy equation for the solid is

(30)

Next, CFD simulations are conducted using the commercial

software ANSYS FLUENT and its VOF solver using user-

defined-function scripts to include changes in the governing

equations for two-energy equation (solid and fluid) modeling of

the porous medium.

Results (taken from [12]) show that when the entire length

of the chamber is occupied by metal foam insert, the velocity

streamlines are smooth (see Fig. 16). But, when only a portion

of the chamber is occupied by the porous insert, flow is stable in

the porous insert region but vortices develop in regions outside

the porous insert. A study of the computed flow field indicates

that optimization of the distribution of porous inserts in the

chamber may be done to achieve minimal temperature rise of air

during compression and best compression efficiency. This

optimization study is ongoing.

(a) 10PPI metal foamfulllyinserted in the chamber, ,

(b) 10PPI metal foampartiallyinserted in the chamber, ,

Fig. 16. CFD simulations on the chamber with metal foam insert (note that up is to the right in this figure)

2.5. Adding thermal dispersion

In this section, a CFD simulation of one of the faster

compression cases in [12] is conducted, but thermal dispersion

is added. The chamber is fully occupied by the 10 PPI foam.

The chamber length and radius are, respectively: 0.294 m and

0.0254 m. The foam characteristic diameter, . The

compression speed and total compression time are: 0.206 m/s

and 1.3 s. The continuity, momentum, and energy equations for

the solid phase are given by Eqns. (22) through (24) and (30).

The energy equation for the fluid mixture is given by:

( )

(

)

(31)

The thermal dispersion term is modeled as,

(32)

10

Kuwahara and Nakayama [18] proposed a thermal dispersion

model for 2-D cross flow over small square rods:

(33)

(34)

⁄ (35)

⁄ (36)

where is the local streamwise direction and is the local

cross-streamwise direction. In this example, this model is

implemented in Eqns. (31) and (32) for the CFD simulation.

The bulk temperature rise of the air is computed and

compared to a simulation of the same case but without thermal

dispersion (Fig. 17). Results of both cases show that, though the

compression time is very short and isentropic compression

would lead to a temperature of 575K, the insert is effective in

suppressing the temperature rise. Further, they show that during

the latter period of compression, the calculated temperature of

the case with dispersion is less. This is due to larger thermal

gradients in the flow for that case and the resulting higher heat

transfer. Thermal dispersion has an influence on the bulk

temperature when temperatures and temperature gradients rise

to the point where dispersion becomes significant. The flow

fields at two times during compression are shown in Fig. 18.

The warmer region is in the upper portion of the chamber in

which the velocities, heat transfer coefficients and thermal

dispersion coefficients are low.

Fig. 17. Bulk temperature of air

Fig. 18. Temperature field and velocity streamline (note that up is to the right in this figure)

3. Conclusions

A compressed air energy storage system designed for use in

wind turbine plants was introduced and the importance of

thermal control during compression and expansion was

emphasized. A compressor design was proposed and models for

its analysis were presented. Noted in modeling was a need for

sub-models to characterize pressure drop in the porous insert,

heat transfer from fluid to solid phases of the insert and thermal

dispersion within the insert. Such models were presented for

two candidate inserts, one based on interrupted plates and

another based upon metal foams. The models came from

detailed computation of a representative elementary volume, in

the case of the interrupted plate, and from experiments, in the

case of the foam. Computational results using these models for

the foam insert case were presented. The inserts are very

effective in suppressing temperature rise. Computed results that

compare a case with a completely-filled chamber and a case

having the insert partially filling the chamber show that the

insert stabilizes the flow where present; but, beyond the insert,

there is a tendency for development of secondary flows. A study

in which dispersion was added to the analysis showed that its

effect is small and in the direction of reducing the maximum

average temperature reached during compression. Dispersion

weakens temperature gradients in the fluid, increasing near-wall

gradients, and heat transfer to the walls.

Acknowledgments

This work is supported by the National Science Foundation

under grant NSF-EFRI #1038294 and University of Minnesota,

Institute for Renewable Energy and Environment (IREE) under

grant: RS-0027-11. The authors thank also the Minnesota

SuperComputing Institute for the computational resources used

in this work.

11

References

1. P. Sullivan, W. Short, and N. Blari, “Modeling the Benefits

of Storage Technologies to Wind Power,” American Wind

Energy Association (AWEA) WindPower 2008 Conference,

Houston, Texas, June, 2008

2. US. Offshore Wind Collaborative, “U. S. Offshore Wind

Energy: A Path Forward,” A Working Paper of the U. S.

Offshore Wind Collaborative, October, 2009

3. C. Bullough, C. Gatzen, C. Jakiel, M. Koller, A. Nowi, and

S. Zunft, “Advanced Adiabatic Compressed Air Energy

Storage for the Integration of Wind Energy,” Proceedings of

the European Wind Energy Conference, EWEC 2004, Nov.

22-25, London, UK, 2004

4. M. Nakhamkin, M. Chiruvolu, M. Patel, S. Byrd, R.

Schainker, “Second Generation of CAES Technology –

Performance, Operations, Economics, Renewable Load

Management, Green Energy,” POWER_GEN International

Conference, Las Vegas, NV, Dec. 2009

5. P. Y Li, J. Van de Ven, and C. Shancken, “Open

Accumulator Concept for Compact Fluid Power Energy

Storage,” Proceedings of ASME 2007 International

Mechanical Engineering Congress and Exposition, IMECE

2007

6. J. Van de Ven and P. Y. Li, “Liquid Piston Gas

Compression,” Applied Energy, v. 86, n. 10, p. 2183-2191,

2009

7. P. Y. Li, E. Loth, T. W. Simon, J. D. Van de Ven, and S. E.

Crane, “Compressed Air Energy Storage for Offshore Wind

Turbines,” 2011 International Fluid Power Exhibition

(IFPE), Las Vegas, NV, March, 2011

8. C. J. Sancken, and P. Y. Li, “Optimal Efficiency-Power

Relationship for an Air Moto-compressor in an Energy

storage and Regeneration System,” Proceedings of the

ASME 2009 Dynamic Systems and Control Conference,

DSCC2009

9. M. Saadat, and P. Y. Li, “Modeling and Control of a Novel

Compressed Air Energy Storage System for Offshore Wind

Turbine,” 2012 American Control Conference, Montreal,

Canada, Jun. 2012

10. C. Zhang, T. W. Simon, P. Y. Li, “Storage Power and

Efficiency Analysis Based on CFD for Air Compressors

Used for Compressed Air Energy Storage,” Proceedings of

the ASME 2012 International Mechanical Engineering

Congress and Exposition, Houston, TX, Nov. 2012.

11. C. Zhang, F. A. Shirazi, B. Yan, T. W. Simon, P. Y. Li, and J.

Van de Ven, “Design of an Interrupted-Plate Heat

Exchanger Used in a Liquid-Piston Compression Chamber

for Compressed Air Energy Storage,” Proceedings of

ASME 2013 Summer Heat Transfer Conference,

Minneapolis, MN, July 2013

12. C. Zhang, J. H. Wieberdink, F. A. Shirazi, B. Yan, T. W.

Simon, and P. Y. Li, “Numerical Investigation of Metal-

Foam Filled Liquid Piston Compressor Using a Two-

Energy Equation Formulation Based on Experimentally

Validated Models,” Proceedings of the ASME 2013

International Mechanical Engineering Congress and

Exposition, San Diego, CA, Nov. 2013,

13. K. Kamiuto, and S. S. Yee, “Heat Transfer Correlations for

Open-Cellular Porous Materials,” Int. Comm. Heat Mass

Transfer, Vol. 32, pp. 947-953, 2005

14. F. Kuwahara, M. Shirota, and A. Nakayama, “A Numerical

Study of Interfacial Convective Heat Transfer Coefficient in

Two-Energy Equation Model for Convection in Porous

Media,” In.t J. Heat Mass Transfer, Vol. 44, pp. 1153-1159,

2001

15. A. Nakayama, K. Ando, C. Yang, Y. Sano, F. Kuwahara,

and J. Liu, “A Study on Interstitial Heat Transfer in

Consolidated and Unconsolidated Porous Media,” Heat and

Mass Transfer, Vol. 45, No. 11, pp. 1365-1372, 2009

16. N. Wakao, and S. Kaguei, “Heat and Mass Transfer in

Packed Beds,” Gorden and Breach, pp. 243-295, New York,

1982

17. A. A. Zukauskas, “Convective Heat Transfer in Cross-Flow,”

in: S. Kakac, R. K. Shah, and W. Aung (Editors), Handbook

of Single-Phase Convective Heat Transfer, Wiley, New

York, 1987

18. X. F. Kuwahara and A. Nakayama, “Numerical

Determination of Thermal Dispersion Coefficients Using

a Periodic Porous Structure,” Journal of Heat Transfer,

Technical Notes, Vol. 121,pp. 160- 163, Feb. 1999