Energy Conversion and Management 50 (2009) 1908–1914

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Energy Conversion and Management

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Performance limit analysis of Recooled Cycle for regenerative cooling systems

Wen Bao, Jiang Qin, Weixing Zhou, Daren Yu *

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China

a r t i c l e i n f o

Article history:Received 17 September 2008Accepted 20 April 2009Available online 23 May 2009

Keywords:ScramjetRecooled CycleRegenerative coolingHeat sink

0196-8904/$ - see front matter Crown Copyright � 2doi:10.1016/j.enconman.2009.04.023

* Corresponding author. Tel./fax: +86 0451 864031E-mail address: yudaren@hit.edu.cn (D. Yu).

a b s t r a c t

This paper presents a new cooling cycle called Recooled Cycle (RC) for systems with active cooling anddemonstrates how coolant could be utilized for secondary cooling through the transfer of enthalpy fromcoolant to work with an indirect increase in the coolant cooling capacity (heat sink), without any prop-erty change in the coolant. The basic concept and working principle are introduced; a thermodynamiccycle analysis is performed to demonstrate the system performance gains with RC over the conventionalsystem with regenerative cooling. Using the principle of thermodynamics, performance potential analysisof RC is performed; expression of performance limit is obtained by deduction. Numerical analysis resultsfurther reveal the potential performance of RC taking scramjet engine with RC as the example. Resultsshow that RC is with great potential performance and scientific feasibility. It can increase coolant heatsink and correspondingly reduce the coolant flow for cooling. In addition, the power output of RC couldprovide energy supply for subsystems.

Crown Copyright � 2009 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Active cooling has been playing a great role in the developmentof systems with high flux. These systems such as aerospace vehi-cles, satellites and chips will operate in severe and harsh environ-ment due to the effect of intense external heating, inner heatgeneration and uncertainties. Higher performance (higher speed,higher operating temperature, more powerful) is expected forthese systems vis-a-vis more heat generating devices, smaller vol-ume and sustained longer working time [1–4]. All of these makethe requirement of cooling or thermal control utmost importantthat requires urgent attention [5]. Such system performance isbeing limited by cooling problems [6–8].

State-of-the-art of material used for passive thermal protectionis gradually making progress [9], but active cooling technology isconsidered more important, especially in the areas where the usualpassive systems are not adequate for the application [10–13]. It isnoticed that regenerative cooling (convective cooling) is alreadyused as the primary cooling method for systems such as aerospacevehicles, because these systems generally work in extremely high-temperature and high-flux thermal environments and also due totheir operating characteristics or environmental limitation [14–16]. In regenerative cooling, thermal protection is ensured by theforced convection of coolants at the critical areas of the systems.Heat is carried away by the coolant from the hot spots to otherareas of the systems where it may be dumped, radiated away orabsorbed [17].

009 Published by Elsevier Ltd. All r

42.

However, available coolant flow for active cooling is very finite,limited by volume and weight, and cannot meet the coolingrequirement sometimes. In the operation of the airbreathinghypersonic vehicle for example, the external air is too hot to beused for cooling and fuel is considered as the only available cool-ant. Coolant flow rate exceeds stoichiometric flow rate in the highflight Mach number region; beyond certain Mach number, the fuelheat sink is insufficient. This means that more fuel must be carriedthan that is required for the mission, and the excess fuel has to beabandoned [15,18]. The additional hardware and extra liquid cool-ants will increase the size, weight and complexity of the vehicle,which, in turn, can significantly degrade vehicle performance [19].

The available coolant is limited and could not meet the totalcooling requirement, which also confines the design freedom whilesystem performance degrades [20]. In order to improve the totalcooling effect without seeking to take extra coolant, a coolant withhigher cooling capacity is the answer. Many methods are success-fully developed: cryogenic coolant is one method to improve thesensible heat of coolant, the second method is to utilize latent heatby adopting phase change coolant [21], and the third one is to useendothermic coolant with the introduction of chemical heat sink toincrease the total heat sink [22,23].

Although these methods are very effective, they are restricted tocertain application fields with comparatively high cost, becausethere are many new technical issues needed to be solved or otherlimitations. At the same time, the potential of these methods to in-crease the coolant capacity is still very limited, and the case thatthe dissatisfaction of cooling requirement also exists. In airbrea-thing hypersonic vehicle with cryogenic hydrogen as the coolant,the vehicle cooling requirement above Ma10 flight condition could

ights reserved.

Nomenclature

Cp specific heat of coolant, kJ/(kg K)hfc actual heat sink, kJ/kgh0fc indirect heat sink, kJ/kgK adiabatic indexM cooling timesm coolant flow rate, kg/sP pressure, MPaPb operating pressure in combustor, MPaQ rate of heat exchange for each section of cooling pas-

sage, kJ/sq specific heat absorbing capacity of each section of cool-

ing passage, kJ/(kg s)Dst process entropy of expansion for per unit of coolant, kJ/

(kg K)

T temperature, KTH average temperature of heat source, KW specific power output, kW/kggt turbine adiabatic efficiency for each stagep expansion ratio for each staged multiplication ratio of coolant heat sinkRg universal gas constant, kJ/(kg K)Dsh process entropy of each section of cooling passage, kJ/

(kg K)

Subscriptsi number of expansion stage or section of cooling passagee exit

Fig. 1. RC and the M–RC.

Fig. 2. Simplified schematic of Recooled Cycle based on principle of workconversion of heat.

W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914 1909

not be met and endothermic hydrocarbon fuel could only meet thecooling requirement below Ma8 [24].

This paper proposed a new thermo cycle – Recooled Cycle (RC)without any change in the coolant property. Performance gain ofRC has more heat absorption per unit of coolant. This property in-creases the coolant cooling capacity and solves the problem ofinsufficient cooling capacity of the available coolant. Further, theworking principle of RC is introduced, performance index is de-fined and performance analysis is carried out to illustrate the sci-entific feasibility and potential performance.

2. The working principle of Recooled Cycle

The improvement in a coolant’s cooling capacity is often limitedby heat-resistant temperature of material and thermal stability ofthe coolant, etc. So, the highest working temperature of heat trans-fer is fixed. If some heat of the coolant could be converted to otherkind of energy, the coolant temperature would decrease; whilethere exists the utilization space between the coolant temperatureand the highest working temperature, the coolant could be used astwice or multiple cooling, and coolant cooling capacity is repeat-edly utilized. Thus, each unit of coolant will absorb more heat,which is equivalent to indirectly improving the cooling capacity.

It is worth noting that coolant out of the regenerative coolingpassage is at least with high temperature level and probably withcertain pressure energy or kinetic energy. Such character of coolantprovides the energy conversion probability from heat to other kindof energy; only one energy conversion process is needed to beadded. At the same time, the energy conversion process shouldnot be seen as the burden or penalty, just because energy obtainedfrom heat recovery is also the product of energy regeneration andwaste heat utilization. This part of energy could be used as thedriving power for power generation subsystem and coolant feedingsubsystem.

This paper advanced the concept of RC based on the principle ofwork conversion of heat to increase the cooling capacity of coolantwith limited resource. The basic idea of RC is that the coolant tem-perature would decrease if thermal energy of high-temperaturecoolant was converted to other kind of energy. Thus, the coolantcould be used as secondary cooling, and if the cooling capacity ofcoolant is repeatedly utilized, more heat will be absorbed by eachunit of coolant, which is equivalent to indirectly increasing thecooling capacity of coolant.

Fig. 1 shows T–S diagrams of RC and multiple-RC. Fig. 1a showsthe basic working process, in which 1–2 presents the compressionprocess through pump, 2–3 is the first cooling, 3–4 presents theenergy conversion from heat to other kind of energy, and 4–5 is

the secondary cooling; 5–1 contains the entire or part of processafter cooling of original regenerative cooling system (such as com-bustion or condensation); some process is assumed to be existing,so the RC may be closed or open.

We may have one, two or more such RCs as shown in Fig. 1b–d.We denote such cycles as M–R cycles with M being the number ofcooling times. Obviously, as M goes to infinity the M–R cycle ap-proaches the continuous RC, which is the C–R cycle, and the coolingprocess is completed at constant temperature.

This paper puts forward one possible realization form based onthe principle of work conversion of heat; notional schematic ofone-staged RC is shown in Fig. 2. First, coolant from coolant tankis pumped to high pressure, and then it enters the first section ofregenerative cooling passage to complete the first cooling, and itstemperature reaches the highest temperature. Secondly, thehigh-temperature and high-pressure coolant expands through

1910 W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914

the turbine doing work, and the temperature of coolant decreases.Thirdly, fuel enters into the second section of regenerative coolingpassage to perform secondary cooling. Lastly, heat is carried awayby the coolant from the hot spots to other areas of the systemswhere it may be dumped, radiated away or soaked in, i.e., heatsink. For this method, 3–4 is the work conversion of heat, whichis realized by the turbine between these two sections of coolingpassages.

The RC proposed above can bring the gain of heat absorbingfor certain coolant flow rate, which is equivalent to indirectlyincreasing the coolant cooling capacity. For the whole heatload requirement, this will effectively reduce the coolant flowfor cooling. At the same time, the output work of turbinecould provide power for subsystems, such as coolant supplysystem, power generating system, and environmental controlsystem. Using turbine to realize the energy conversion fromheat to work is a relatively simple method, and RC systemhas a good match of components and function with other sub-systems this method is in accordance with the design thoughtsof integrated thermal management system. Obviously, there arestill many other realization methods, yet this paper only takesthis method as the example to illustrate the potential perfor-mance of RC.

3. Basic definition of performance parameters

The objective of RC is to increase the amount of heat absorbedper unit of coolant. RC is different from conventional power cycle,and it is unsuitable to use thermal efficiency or power output toevaluate the performance of RC. Thus, it is instructive to comparethe performance of RC with regenerative cooling. For this purpose,multiplication ratio of coolant heat sink is defined as the perfor-mance parameter in the following analysis to illustrate the perfor-mance potential of RC.

For the same outlet condition of pump and the same coolantflow rate, heat rate absorption of once cooling is Q0 for regenerativecooling, as shown in Fig. 2. However, excess heat rate absorption Q1

of secondary cooling will be obtained in RC. So, we define multipli-cation ratio of coolant heat sink to evaluate the degree of indirectimprovement of coolant heat sink.

For regenerative cooling, cooling capacity relation of coolantcan be expressed as

mhfc ¼ Q 0 ð1Þ

For RC, cooling capacity relation of coolant for the same massflow rate can be written as

mh0fc ¼ Q 0 þ Q 1 ð2Þ

Multiplication ratio of coolant heat sink is defined and deducedas

d ¼h0fc � hfc

hfc¼ Q 1

Q 0ð3Þ

Fig. 3. Sketch configuration of M–RC only con

Eq. (3) shows that d will be greater than zero so long as Q1 – 0 andRecooled process exists. This is the expected result once the RC wasbuilt. If the coolant only completes the work conversion from heat,shown in Fig. 2, without performing the secondary cooling,although some amount of available work will be generated, therewill be no gain for multiplication ratio of coolant heat sink just be-cause Q1 is zero at this time.

4. Performance limit analysis model of multi-Recooled Cycle

4.1. Scheme and basic assumptions of multi-Recooled Cycle

Working principle and performance indexes are introduced inthe above analysis. Similar to multi-reheated stream power cycleand multi-reheated gas turbine cycle [25–27], heat absorption willincrease constantly as the recooled times for certain coolant flowrate, and RC performance will be further improved. Performanceanalysis of multi-RC will be carried out to illustrate the potentialperformance of RC.

Fig. 3 shows the sketch configuration of multi-RC consideringonly cooling and expansion process. The coolant out of each sectionof cooling passage will do work to turbine through expansion, andthen enters next section of cooling passage to continue cooling. Thenumber of cooling times M is determined by total expansion ratioand pressure ratio distribution for each stage; this will be specifi-cally discussed in the following analysis.

Generally, coolant is stored in coolant tank as liquid, and it will beheated to vaporize at the exit of cooling passage. Thus, no liquid orgas coolant will exist in gaseous state after completing the cooling.

For simplified analysis, we assume (1) constant specific heat, (2)perfect gas after first cooling, (3) no pressure loss in cooling pas-sages, and (4) no heat transfer loss from the turbine. The precedingassumptions are not accurate enough for real design purposes;however, they are important for the purpose of proof of concept.The following steps are used in the cycle calculations.

4.2. Performance model of multi-Recooled Cycle

Heat rate absorbing relation of coolant for each cooling in cool-ing passage can be expressed as

Qi ¼ mCpðTe � TiÞ i ¼ 0;1;2; . . . ;M ð4Þ

In order to fully make use of the maximum cooling capacity ofcoolant, the exit temperature of coolant at each section of coolingpassage is assumed to be even.

Under the assumption that there is no loss of power because offriction of the mechanical systems, the turbine exit temperature ofeach stage can be calculated as

Ti ¼ Te½1� gtð1� p�ni Þ� i ¼ 1;2; . . . ;M ð5Þ

We set n ¼ ðK � 1Þ=K.Specific power output of each stage of the turbine can be ex-

pressed as

Wi ¼ Q i ¼ mCpðTe � TiÞ i ¼ 1;2; . . . ;M ð6Þ

sidering cooling and expansion process.

W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914 1911

Working pressure for each section of cooling passage meets thefollowing relation

P0 ¼ P1 � p1 ¼ P2 � p2 � p1 ¼ P3 � p3 � p2 � p1 ¼ � � �¼ PM � pM � pM�1 � � � � � p2 � p1 ð7Þ

So expansion ratio of each stage satisfies

p1 � p2 � p3 � � � � � pM ¼ P0=PM ð8Þ

By Eq. (3), multiplication ratio of coolant heat sink d for multi-RC can be easily extended and written as

d ¼ Q1 þ Q2 þ Q 3 þ � � � þ QM

Q 0¼XM

i¼1

Q i=Q 0 ð9Þ

By Eqs. (4) and (5), d can be further expressed as

d ¼XM

i¼1

ðTe � TiÞ" #,

ðTe � T0Þ¼ gtTe M �XM

i¼1

p�ni

!" #,ðTe � T0Þ

ð10Þ

At fixed total pressure ratio P0/PM, the following analysis will fo-cus on getting optimal distribution ratio of each stage of the tur-bine when maximum d is obtained.

4.3. Optimal distribution ratio of each stage of the turbine

By Eq. (10), solution procedure of maximum d could be con-verted to solve the minimum value of the following relation.

XM

i¼1

p�ni M P 1; M 2 N ð11Þ

When cooling times M is relatively small, it would be easilyobtained

When M = 1, there is

p�n1 ¼ p�n

1 ¼ ðP0=PMÞ�n ð12Þ

When M = 2, there is

p�n1 þ p�n

2 P 2ffiffiffiffiffiffiffiffip�n

1

p ffiffiffiffiffiffiffiffip�n

2

pð13Þ

where equality can be obtained only when p2 = p1; so, there is

p�n1 þ p�n

2 ¼ 2p�n1 ¼ 2ðP0=PMÞ�n=2 ð14Þ

When M = 3, there is

p�n1 þ p�n

2 þ p�n3 P 3

ffiffiffiffiffiffiffiffip�n

113p ffiffiffiffiffiffiffiffi

p�n2

13p ffiffiffiffiffiffiffiffi

p�n3

13p

ð15Þ

where equality can be obtained only when p3 = p2 = p1; so, there is

p�n1 þ p�n

2 þ p�n3 ¼ 3p�n

1 ¼ 3ðP0=PMÞ�n=3 ð16Þ

Above analysis for M = 1, 2 and 3 are well-known conclusion.We will further discuss whether the same conclusion could be ex-tended when M > 3, that is

XM

i¼1

p�ni ¼ ðp�n

1 þ p�n2 þ � � � þ p�n

M ÞP MðP0=PMÞ�n=M ð17Þ

where equality can be obtained only when p1 = p2 = . . . = pM.Mathematical deduction will be used to illustrate the justifica-

tion of above conclusion.M = 1, 2 and 3, the conclusion has been justified.When M = k, proposition is assumed to be correct; so, there is

Xk

i¼1

p�ni P kðP0=PMÞ�n=k k P 2 ð18Þ

where equality can be obtained only when p1 = p2 = . . . = pk-1 = pk.When M = k � 1, proposition is naturally correct; so, there is

Xk�1

i¼1

p�ni P ðk� 1ÞðP0=PMÞ�n=ðk�1Þ k P 2 ð19Þ

When M = k + 1, there is the following relation

Xkþ1

i¼1

p�ni ¼

Xk�1

i¼1

p�ni þ p�n

k þ p�nkþ1

P ðk� 1Þp�n1 þ 2

ffiffiffiffiffiffiffiffip�n

k

q ffiffiffiffiffiffiffiffiffiffip�n

kþ1

qð20Þ

Obviously, equality can be obtained only whenpk+1 = pk = . . . = p1; so, there is the following conclusion

Xkþ1

i¼1

p�ni P ðkþ 1ÞðP0=PMÞ�n=ðkþ1Þ ð21Þ

Thus, the proposition is justified to be correct. So, there is

minXM

i¼1

p�ni ¼ MðP0=PMÞ�n=M M P 1 ð22Þ

where expansion ratio of each stage of the turbine satisfies the fol-lowing relation

p1 ¼ p2 ¼ � � � ¼ pM ¼ p ¼ ðP0=PMÞ1=M ð23Þ

Above analysis illustrates that d will get the maximum valuewhen expansion ratio of each stage of the turbine is even.

So, Eq. (10) could be further expressed as

d ¼ ngtTeð1� p�nÞðTe � T0Þ

¼ gtTe

ðTe � T0ÞM � ½1� ðP0=PMÞ�n=M� ð24Þ

In Eq. (24), besides cooling times M, the effect of other param-eters on d could be directly reflected. Thus, following analysis willfocus on the effect of M on d.

4.4. Limit expression of d when M ?1

Derivation of Eq. (24) by M could be expressed as

dddM¼ gtTe

ðTe � T0Þ½1� ðP0=PMÞ�n=M þmðP0=PMÞ�ð

nMþ1Þ� ð25Þ

By Eq. (8), there is P0/PM P 1, so here is

1� ðP0=PMÞ�n=M P 0 ð26Þ

Combined with Eqs. (25) and (26), we can get

dddM

> 0 ð27Þ

By Eq. (27), we conclude that d increases as M increases. Next, wewill consider whether the limit value of d exists when M ?1.

For convenience sake, we assume that M is a continuous realnumber and bigger than 1, so the conclusion obtained is necessar-ily correct for real integers.

We set t = (P0/PM)�n/M, so when M ?1, here is t ? 1. M couldbe further expressed as

M ¼ �nlnðP0=PMÞ

ln tð28Þ

Combined with Eqs. (24) and (28), there is

d ¼ ngtTe

ðTe � T0ÞlnðP0=PMÞ

ðt � 1Þln t

ð29Þ

1912 W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914

So when M ?1, limit expression of d could be expressed as

limM!1

d ¼ ngtTe

ðTe � T0ÞlnðP0=PMÞ lim

t!1

ðt � 1Þln t

¼ ngtTe

ðTe � T0ÞlnðP0=PMÞ ð30Þ

Eq. (30) shows that limit expression of d exits when M ?1.

4.5. Other conclusion when M ?1

By Eq. (23), when M ?1, there is

limM!1

p ¼ 1 ð31Þ

So, inlet and exit pressures of each stage of the turbine satisfy

limM!1

Pi

Piþ1¼ 1 i ¼ 1;2; . . . ;M ð32Þ

Combined with Eqs. (5) and (23), exit temperature of each stageof the turbine could be further expressed as

Ti ¼ Te½1� gtð1� p�nÞ� i ¼ 1;2; . . . ;M ð33Þ

By Eqs. (31) and (33), drop in coolant temperature through theexpansion of each stage of the turbine namely temperature rise ineach stage of the recooled process could be written as

limM!1

DT ¼ limM!1ðTe � TiÞ ¼ 0 ð34Þ

Similarly, by Eqs. (4) and (34), rate of heat exchange for eachsection of cooling passage satisfies

limM!1

Q i ¼ 0 ð35Þ

By Eqs. (6) and (34), there is the similar conclusion for specificpower output of each stage of the turbine

limM!1

Wi ¼ 0 ð36Þ

Above analysis shows that there are infinite expansion cells andrecooled cells, each expansion cell can realize infinitesimal tem-perature drop, and each recooled cell can realize infinitesimal heataddition when M ?1. Furthermore, temperature change in eachexpansion cell and recooled cell are approaching to zero. In otherwords, both energy conversion from heat to mechanical energyand heat addition are performed at high temperature Te, and inter-nal energy (temperature) of coolant does not change; this can beseen in Fig. 1d.

For adiabatic expansion of each stage of the turbine, entropy in-crease of coolant is just that of the process. Combined with compu-tational formula of process entropy for ideal gas, process entropy ofexpansion for each unit of coolant could be expressed as

Dsti ¼ Cp lnTe

Ti� Rg ln

Piþ1

Pii ¼ 1;2; . . . ;M ð37Þ

Combined with Eqs. (32) and (34), when M ?1, there is

limM!1

Dsti ¼ 0 ð38Þ

For the heat absorption process of each section of cooling pas-sage, process entropy could be written as

Dshi ¼ Cp lnTe

Ti� Rg ln

Piþ1

Pi� qi

THi ¼ 1;2; . . . ;M ð39Þ

While the operating pressure in each section of cooling passagedoes not change, combining Eqs. (34) and (35), when M ?1, thereis

limM!1

Dshi ¼ 0 ð40Þ

Eqs. (38) and (40) show that the irreversible loss of each expan-sion cell and recooled cell is equal to zero, which could be appre-ciatively seen as the reversible process. At this condition, heatcould be completely converted to mechanical power output; heataddition for each recooled cell is performed at isothermal condi-tion. This is just the thermodynamic explanation why d reach thelimit value when M ?1.

5. Analysis and calculation

Problem encountered by scramjet as the propulsion system ofairbreathing hypersonic vehicle has shown that limited coolant(fuel) available could not meet the total cooling requirement. Manymethods such as changing the fuel property have been developedand tried in an attempt to increase fuel heat sink. This work takeshydrogen-fueled scramjet as the instance to discuss the potentialperformance of RC. Notional schematic of Open RC for scramjet isshown in Fig. 4.

First, fuel from fuel tank is pumped to supercritical pressureand then enters the first section of regenerative cooling passageto cool the heat structure with its sensible heat; fuel is heatedfrom liquid to gas. Secondly, the high-temperature and high-pressure fuel expands through the turbine; the temperature offuel decreases greatly. Thirdly, fuel enters the second section ofregenerative cooling passage to continue to cool the other heatstructure. Lastly, the fuel enters into the ramburner, so this isone kind of Open Recooled Cycle (ORC). In order to fully makeuse of the maximum heat sink of fuel, the exit temperature offuel at the two sections of cooling passage are assumed to beeven.

Hydrogen fuel in cooling passage operates at high-pressurestate; its pressure is higher than the critical pressure (Pc = 1.3 MPa).At the same time, as the critical temperature of hydrogen is verylow, hydrogen fuel is quickly heated to gas from liquid, the temper-ature also quickly reaches the critical temperature, and its temper-ature will be extremely higher than its critical temperature as theheat transfer continues [28]. Furthermore, working temperatureregion of hydrogen fuel is very large, about 1000 K. Its workingcharacteristics have a good match with above assumptions for gen-eral RC.

For scramjet with ORC, we will combine specific calculation tofurther illustrate potential performance of RC in the following anal-ysis. A simple Matlab language program was written to performthe preceding calculations.

5.1. The effect of M on d

As the fuel at the exit of the last section of cooling passage willcontinue entering the combustor, the exit pressure of cooling pas-sage (back pressure) PM of ORC should not be lower than the oper-ating pressure in the combustor Pb. Thus, there is PM P Pb; here, weset Pb = 0.2 MPa. By Eq. (24), d will increase with the reduction ofPb, so, we set PM = Pb to greatly reflect the potential performanceof ORC. For hydrogen fuel, we set T0 = 25 K, Te = 1100 K (consider-ing the use of nickel alloy for the wall material), P0 = 3 MPa,Pb = 0.2 MPa, and gt = 0.85. So, we will get variation relation of dwith M.

Fig. 5 shows that multiplication ratio of fuel heat sink d in-creases as recooled times M increases. Furthermore, d variesgreatly with M when M 6 5 and varies little with M when M > 5.This illustrates that the ORC will get great performance gain whenM is relatively small, which will further be explained in Table 1 andcalculations are explained in Section 5.2.

As shown in Table 1, d is relatively high compared with d1when M = 2, which illustrate that relative high performance could

Fig. 4. Generic configuration of a scramjet engine with Open Recooled Cycle.

Fig. 5. Variation of d with M.Fig. 6. Variation of d with M at different P0.

Table 1Comparison of d between different M and d1.

M = 1 M = 2 M = 3 M = 4 M = 5 M = 10 M ?1

d (%) 44.1 52.52 55.83 57.59 58.68 60.95 63.34d/d1 (%) 69.62 82.92 88.14 90.92 92.64 96.23 100

W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914 1913

be obtained with smaller M. This is very advantageous for the prac-tical application for ORC.

Table 2d at different P0 when M = 1 and M = 2.

3 MPa 8 MPa 12 MPa 20 MPa

M 1 2 1 2 1 2 1 2

d (%) 55.12 65.66 66.66 83.83 70.56 90.63 74.87 98.65

5.2. Representative performance calculations

The results discussed in the previous sections have shown thatORC has some degree of potential performance, in order to reflectthe potential performance as greatly as possible, cycle parameterswill be chosen with the maximum value within reasonable range.It is obvious that there exists great difference between T0 and Te, sothere is Te � Te � T0. The influence of T0 and Te on d could be ig-nored by Eq. (24). Simultaneously, we fixed Pb = 0.2 MPa andgt = 0.95.

(1) Value of d at different P0.

Following analysis will focus on the variation of P0 on d; the va-lue of P0 is selected from Ref. [20].

Fig. 6 reveals the maximum potential performance of Open Re-cooled Cycle to certain extents, and the maximum value of which

can reach 100%. Such results are very attractive for developinghypersonic vehicle with much higher speed.

(2) Value of d when M = 1 and M = 2.

When we fixed M = 1 and M = 2, following results will beobtained.

As shown in Table 2, the maximum value of d can reach 74.87%when M = 1, and the maximum value of d can reach 98.65% whenM = 2. It is obvious that d will reach a higher value when M isrelatively small, namely, ORC will obtain greater potentialperformance.

The increase of d is an indication that the requirement of fuelflow for cooling is decreased. These advantages can translate toreductions in engine and fuel tank volume and weight. ORC tech-niques hold significant promise for extending the flight Mach num-ber envelope of conventional hypersonic airbreathing engines.

1914 W. Bao et al. / Energy Conversion and Management 50 (2009) 1908–1914

6. Conclusion

A new RC to indirectly increase the coolant cooling capacity forsystems with regenerative cooling and with limited coolantavailable has been developed. Derivation and justification of perfor-mance limit expression of RC are performed, scramjet with ORC ischosen as the analysis example to illustrate the potential perfor-mance. Results of the analysis show that d could be reach higherthan 100%, and single-staged ORC will realize good effect. Althoughmore refined calculations must be done for detailed performanceanalysis and real design, the relatively simple analysis in this sec-tion is fundamental and is suitable as an indicator of potential per-formance gains. The analysis does reveal the essential operationalbenefits of RC and demonstrates fundamental scientific feasibility.

The work shows that there is no need to change the property ofcoolant. Coolant cooling capacity is indirectly increased because ofmultiple recooled processes, and the requirement of coolant flowfor cooling is decreased. These advantages can translate to reduc-tions in system and coolant tank volume and weight. So, the diffi-culty in cooling or thermal control system is mitigated, andperformance of the system will be improved. Again, available workoutput can provide energy for coolant supply system, electric gen-eration system and other subsystems, and so on. It is useful to real-ize comprehensive utilization of energy for the entire system. Thispaper discussed only one kind of RC and the result gives us an in-sight into an in-depth study and development of other realizationmethods of RC.

Acknowledgments

This paper is supported by the National Natural Science Foun-dation of China (Grant No. 50676024) and the Programme forNew Century Excellent Talents in the Universities of China (ProjectNo. NCET-06-0331).

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