Effect of cooling channel geometry on re-cooled cycle performance for hydrogen fueled scramjet

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 7 0 0 2e7 0 1 1

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Effect of cooling channel geometry on re-cooled cycleperformance for hydrogen fueled scramjet

W. Bao, J. Qin*, W.X. Zhou, D.R. 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 14 March 2010

Received in revised form

5 April 2010

Accepted 7 April 2010

Available online 10 May 2010

Keywords:

Re-Cooled Cycle

Regenerative cooling

Channel geometry

Fuel

Scramjet

* Corresponding author. Fax: þ86 0451 86403E-mail address: [email protected]

0360-3199/$ e see front matter ª 2010 Profedoi:10.1016/j.ijhydene.2010.04.033

a b s t r a c t

Developing fuel with higher heat sink is widely carried out to meet the cooling requirement

for an airbreathing hypersonic vehicle. However, a Re-Cooled Cycle has been newly

proposed for a regeneratively cooled scramjet to reduce the fuel flow for cooling. Fuel heat

sink (cooling capacity) is repeatedly used to indirectly increase the fuel heat sink. Para-

metric sensitivity analysis of Re-Cooled Cycle of a hypersonic aircraft is explored. An

analytical fin-type model for incompressible flow in smooth-wall rectangular ducts in

terms of hydrodynamic, thermal, power balance and Mach number constraints is

proposed. Based on this model, the difference of the cooling channel structure design

between Re-Cooled Cycle and regenerative cooling is discussed, and a new optimization

index is introduced for Re-Cooled Cycle. The sensitivity of the cycle performance to cooling

channel geometry is investigated, and the optimal performance of a Re-Cooled Cycle is

obtained by satisfying constraints. The differences of the effect of channel design variables

between Re-Cooled Cycle and regenerative cooling are also discussed.

ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction which means that the fuel heat sink is insufficient, and so,

Hypersonic airbreathing vehicles, including Single-Stage-To-

Orbit (SSTO) vehicles or Two-Stage-To-Orbit (TSTO) aerospace

planes, fully reusable space transport vehicles and hypersonic

cruise missiles powered by scramjet, has become one of the

popular subjects in recent years [1e3].

Because of high combustion temperatures and high heat

transfer rates from the hot gases to the walls of the combustor

chamber, cooling is amajor design consideration in a scramjet

engine. Regenerative cooling with fuel used as the coolant is

generally regarded as the only feasible solution. In this way,

fuel flows through the cooling passage to cool the enginewalls

before it is used for combustion [4,5]. As a type cryogenic fuel,

hydrogen fuel can be used to provide significant cooling, and is

thus chosen as a major propellant for hypersonic vehicles [6].

However, limited fuel heat sink and fuel onboard can

barely meet the cooling requirements for the whole vehicle,

142.n (J. Qin).ssor T. Nejat Veziroglu. P

more fuel than required must be carried for the mission and

the excess fuel has to be abandoned [7]. Additional hardware

and extra fuel will increase the size, weight and complexity of

the vehicle, which, in return, will significantly degrade the

performance of the vehicle [8]. In addition, the lack of neces-

sary heat sink confines the hypersonic vehicle to a relatively

low flight speed. It is therefore very important to increase the

fuel heat sink for a high speed scramjet.

It is difficult for hydrogen to perform endothermic

conversion, though developing endothermic fuel is a very

effective method to increase fuel chemical heat sink for

hydrocarbon fuel. It was also suggested that the heat sink of

hydrogen fuel will not be increased even when excess hot

fuel re-enters the tank. But vaporized fuel will take up

a considerably larger volume than liquid. So a limit is

imposed on the amount of heat storable in this manner

without larger tankage [9]. Therefore, it is generally accepted

ublished by Elsevier Ltd. All rights reserved.

mailto:[email protected]

http://www.elsevier.com/locate/he

Nomenclature

A heat transfer surface area

a sonic speed

Cp specific heat of fuel, kJ/(kg�K)

D equivalent diameter

ff friction factor

h heat transfer coefficient, w/(m2 K)

hfc actual heat sink, kJ/kg

h1fc indirect heat sink, kJ/kg

H channel height, m

K adiabatic index

L length, m

M Mach number

m mass fuel flow rate, kg/s

Nu Nusselt number

P pressure, Pa

DP pressure drop, Pa

Pr Prandtl number

Q heat transfer rate, kw

qw heat flux, W/m2

Re Reynolds number

s heated wall thickness, mm

T temperature, K

t the fin thickness, mm

u velocity, m/s

W channel width, mm

w specific power, k/kg

r density, kg/m3

x distance from entrance of cooling panel, m

d multiplication ratio of fuel heat sink

l thermal conductivity, w m/K

h efficiency

p expansion pressure ratio

Subscripts

a property evaluated at average temperature of

coolant reference

b property evaluated at bulk temperature reference

c coolant

C cooling channel

f fin

i inlet

j segment number along the length of cooling

channel

lim limit value

net net available work

o outlet

P panel

p pump

r regenerative cooling

t turbine

wc coolant side wall

wg gas side wall

1 first cooling

2 second cooling

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 7 0 0 2e7 0 1 1 7003

that no method could be used to increase the heat sink of

hydrogen fuel until a Re-Cooled Cycle was recently advanced,

which is an indirect method to increase fuel heat sink by

multiple repeatedly utilizing fuel heat sink. Previous ther-

modynamic cycle analysis shows that Re-Cooled Cycle (RCC)

could remarkably increase fuel heat sink without introducing

new component or weight penalty [10,11].

Much of the current research on regenerative cooling is

focused on the effects of channel structure design of these

rectangular passages. Usually the goal of aircraft structure

design is to obtain a minimum weight, however, for hyper-

sonic aircraft cooled by the hydrogen fuel the most crucial

factor is the required coolant flow rate because of the limited

fuel available [12]. In this paper, parametric sensitivity model

of Re-Cooled Cycle will be established, the effects of channel

structure design of cooling passages on RCC performance will

be investigated, and a new index of channel structure design

of RCC is proposed in terms of hydrodynamic, thermal, power

balance and Mach number constraints. Furthermore, the

difference of thermal structure design between RCC and

regenerative cooling is discussed.

2. Operating principle of RCC

Re-Cooled Cycle (RCC) has been put forwarded in [13]. As

shown in Fig. 1, RCC is mainly composed of the first and

second cooling passages, a pump, and a turbine. Unlike

a traditional turbine, the primary purpose of the turbine is

designed to decrease the fuel temperature instead of doing

work. Dashed lines in Fig. 1 show the flow process of fuel.

First, the fuel coming out from the fuel tank is pumped to the

supercritical pressure, and then enters into the first cooling

passage to cool the heated surfaces, and its temperature

reaches its maximum value; second, the high temperature

and high pressure fuel expands while doing work to the

turbine, and its temperature decreases; third, fuel enters the

second cooling passage to perform the secondary cooling;

before it enters into the combustion chamber.

Compared to the traditional regenerative cooling, addi-

tional heat could be absorbed for per unit of fuel through

secondary cooling in RCC, fuel heat sink could be regarded as

an indirect improvement. And this will effectively reduce fuel

flow rate for cooling in terms of the overall cooling require-

ment of the vehicle. In addition, thework output of the turbine

can drive the fuel pump and an electric generator to provide

the power for vehicle subsystems, such as radar communi-

cation system, flight control system, electronic equipment,

and environmental control system, and so forth.

3. Performance parameters

The objective of RCC is to reduce the fuel flow for cooling,

which can be interpreted to increase the heat absorption by

per unit of fuel. This is different from the conventional power

cycle [14,15], and it is unsuitable to use thermal efficiency to

evaluate the performance of RCC [16,17]. Thus, it is necessary

Fig. 1 e Generic configuration of a scramjet engine with Re-Cooled Cycle.


to define several new performance parameters to compare the

performance of RCC with that of regenerative cooling.

The multiplication ratio of fuel heat sink can be defined

and derived as [7]

d ¼ h0fc � hfc

hfc¼ Q2

Q1(1)

4. Scramjet and cooling-channel geometrydescription

A schematic showing the location of a scramjet engine on the

lower surface of a hypersonic vehicle is given in the upper

portion of Fig. 2. A conceptual, two-dimensional scramjet

engine cross section is shown in the middle of Fig. 2. The

engine consists of a series of ramps that merge with the

vehicle lower surface, and a cowl which helps capture the air

compressed by the vehicle fuselage and the engine ramps.

Fig. 2 e Schematic of scramjet en

Themajor components of the engine are the inlet, combustor,

and nozzle.

A typical engine rampheat flux distribution is shown in the

lower portion of Fig. 2. The combustor section experiences the

highest heat flux. The nozzle and the inlet experience lower

heat fluxeswith the inlet having the lowest. Typical rampheat

fluxes of scramjet vary from 2 to 20 MW/m2.

The geometries of channel-fin cooling channels are illus-

trated in Fig. 3 [18]. For channel-fin cooling channels, the

geometry can be completely described by the channel width

(W ), the channel height (H ), the rib thickness (t), and the outer

wall (heated wall) thickness (s).

5. Analytical model and methodology

Cooling channel, turbine and pumpare the key components in

RCC, a model of RCC consisting of components performance,

flow and heat transfer in them are considered, as well as the

gine with typical heat fluxes.

Fig. 3 e Characteristic dimensions for cooling channels.


thermal, hydrodynamic, Mach number and power balance

limitations. Based on this model, the numerical computa-

tional program is used to investigate the sensitivity of the

multiplication ratio of fuel heat sink to each design variable.

Numerical optimization is often used as a cooling-jacket

design tool. It is a practical approach to the design of cooling

jacket systems since many design requirements can be

considered simultaneously [19]. The optimization goal in

conventional regenerative cooling is to design cooling jackets

which minimizes the required coolant flow rate for specified

heating rates. However, in this paper, numerical optimization

is also adopted to determine the optimal multiplication ratio

of fuel heat sink for RCC. The design must also satisfy design

requirements such as material limits on cooling-jacket

temperature, limits on coolant Mach number and pressure

drop through the coolant passages.

5.1. Channel geometry and basic assumptions

The present work considers a single cooling panel shown in

Fig. 4, which is composed by many rectangular duct geometry

cooling channels. For convenient analysis, the panel is divided

into segments along the flow length. The panel has a length

(Lp) of 1m, awidth (Wp) of 1m. And the thickness of the heated

wall (s) is 1 mm and the rib thickness (t) is 0.2 mm [20].

Fig. 4 e Cooling jacket flow and thermal models.

The heated wall is exposed to an uniform qw, the lower

surface (the inner wall) is assumed to be an adiabatic

boundary since the amount of heat transferred through the

inner wall is small compared to the heat going into the

coolant. Coolant flow and heat flux are assumed to be uniform

across the width of the panel, and thus the coolant and

structural temperatures do not vary across the panelwidth. So

the constant area, constant heat flux, rectangular duct

geometry, single cooling channel are chosen as the study

objects and shown in Fig. 5. The channel has a channel width

(W ) of 2 mm and a channel height (H ) of 2 mm, so the

equivalent diameter (D) is 2 mm and a flow area is 4 mm2. For

RCC, the cooling channel is divided into two sections with

fixed total length Lp.

The basic analysis approach employed was to assume

a steady state quasi one-dimensional energy balance across

the regenerative cooling jacket. First, an analytical model

based on fin-type assumptions and existing correlations for

heat transfer for smooth walls is introduced. To further

simplify the analysis, an analytical model will be developed

under the following assumptions:

1) All energy transferred across the coolant wall is absorbed

by the coolant.

2) There exists no temperature variation in the cross section

of the duct walls (fin assumption).

3) The channel walls are assumed to be smooth.

4) Wall-conduction in axial direction is negligible.

5) The flow is fully developed.

6) All data sets are screened to rule out buoyancy effects.

7) All the thermalphysical properties except density are

regarded as constant for different pressures, they only vary

considerably with temperature.

Property values for hydrogen are obtained from the

National Institute of Standards and Technology (NIST) Ther-

modynamic and Transport Properties of Pure Fluids database

and the NIST Chemistry WebBook [21]. The specific property

variations that must be considered are specific heat, thermal

conductivity, density and viscosity.

The coolant flow conditions, as well as each of the design

requirements, are evaluated at the exit of each segment.

A brief description of the various analytical models which

describe the actively cooled channel performance follows.

5.2. Coolant flow analysis in cooling channel

Fig. 4 illustrates the division of the cooling panel into segments

with length L for purposes of the analysis. A representative

segment with entrance temperature Tj and pressure Pj is

Fig. 5 e Single cooling channel schematic.


shown in the lower portion of Fig. 4. It is subjected to heat flux

qw. To calculate the outlet temperature of segment j with the

widthofW, the following energybalance equation is employed

along with the constant surface heat flux equation [22],

Qj ¼ mCp

�Tj;o � Tj;i

�(2)

Qj ¼ qwWL (3)

m and u meet the following relation

m ¼ ruWH (4)

From Eqs. (2) and (3), the fuel bulk outlet temperature

equation of segment j is

Tj;o ¼ qwWLmCp

þ Tj;i (5)

And the outlet temperature of segment j is the entrance

temperature of segment jþ1, as well as other flow parameters

of hydrogen. As the heat balance calculation is performed one

segment after another, the outlet temperature of two sections

of cooling passages will be eventually obtained.

The coolant pressure drop across a segment can be esti-

mated by the DarcyeWeisbach equation [23],

DPj ¼ ffrLu2

2D(6)

Where the friction factor ff is obtained from the Moody chart.

For a smooth tube Reynolds number of 10,000, the Moody

chart, ff is approximately 0.031 [24].

5.3. Determination of cooling-channel temperatures

Once the coolant conditions at the exit of a segment are

determined, the temperature distribution through the cooling

channel at the segment exit (the hottest location in a segment)

is evaluated. Newton’s Law of cooling [20] considering fin is

then used to find the surface temperature at the outlet,

Qj ¼ hj

�Tj;wc � Tj;a

�AC þ qj;fAf (7)

Where AC ¼WL is the non-finned convecting surface area and

Af is the convecting surface area of the fin or rib, as shown in

Fig. 5. And the properties are evaluated at the average

temperature of segment inlet and outlet temperature of

coolant,

Tj;a ¼ �Tj;i þ Tj;o

��2 (8)

As shown in Fig. 5 that the rib surface provides additional

wetted coolant surface area providing a fin effect for the

cooling channel. To calculate the additional heat transfer

from the finned surface area, fin efficiency is calculated as

outlined assuming an adiabatic tip as [25]

hf ¼th�eHf

�eHf

(9)

Where, Hf ¼ H þ t/2. And e as an intermediate parameter is

defined by Eq. (10):

e ¼ffiffiffiffiffiffi2hlt

r(10)

From the fin efficiency, a corresponding heat flux is calcu-

lated for the fin as

qj;f ¼ hj

�Tj;wc � Tj;a

�hf (11)

The next step is to compute the film coefficient for

convective heat transfer using published correlations.

Turbulent Nusselt number correlation developed by M. F.

Taylor [26] is chosen to determine the heat transfer coefficient

for the channel-fin cooling channel. This equation uses the

surface to bulk temperature ratio and also considers the

entrance effects. And this correlation for turbulent flows of

hydrogen in tubes is correlated over a wide range of temper-

atures, pressure and heat fluxes. The correlation is

Nu ¼ 0:023Re0:8Pr0:4ðTwc=TbÞ�ð0:57�1:59D=xÞ (12)

Where we choose Tj,i as Tb to evaluate fuel property. The

difference between gas side wall temperature Twg and coolant

side wall temperature Twc can be obtained by wall conduction

equation as

qj ¼ l

s

�Twg � Twc

�(13)

5.4. Model for turbine and pump

The expander cycle used in a liquid rocket is also adopted as

one potential scheme of fuel feeding cycle for a scramjet, so

the pump and turbine are not new components for RCC.

For the pump, the flow rate of the turbine is the samewith that

of the pump, so we are only concernedwith the specific power

of it, which can be estimated as [7]

wp ¼ Ppo � Ppi

hprpi(14)

The fuel/coolant is hydrogen stored cryogenically as a liquid

at 20 K and 240 kPa [27]. The value of fuel pressure varies

within 2e20 MPa in Ref. [7]. Under the assumptions that there

is no loss of power because of friction of the mechanical

systems, the turbine exit temperature can be calculated as [28]

Tto ¼ Tti

�1� ht

�1� pð1�KÞ=K� (15)

Specific power rate of turbine is calculated by the following

equation [7]:

wt ¼ htCPTti

�1� pð1�KÞ=K� (16)

p as the expansion pressure ratio, which can be expressed as

p ¼ Pti=Pto (17)

Efficiencies of the pump and the turbine in Eqs. (14) and (15)

are estimated on the basis of typical values for turbopumps of

rocket engines, because the operating condition of scramjet

turbopumps will be similar to that of rocket engine turbo-

pumps. Efficiency of the hydrogen pump is 70%, and the

turbine of the EC is assumed to be a reaction turbine with

efficiency of 80% [7].

5.5. Material properties and code validation

High conductivity materials are generally used in the cooling

channel construction.Nickel 201 is chosenas thematerial used

Table 1 e Constraint function in the thermal analysis.

Constraints Channel temperature Twc < Tlim

Outlet pressure Pco > PlimMach number M < Mlim

Power balance wt > wp


in the studies, which offers a range of the important material

properties such as thermal conductivity, high temperature

capability, and strength. Nickel 201 offers moderate thermal

conductivity l (60.6 W/m.K) and higher temperature capability

(1110 K) compared with other alloys. These properties along

with high ductility for fatigue resistance make nickel an

attractive choice for a cooling channel [29].

Material thermal conductivities are included as functions

of the average cooling-channel temperature in the one-

dimensional model. Detailed two- and three-dimensional

finite element models verified the accuracy of temperatures

computed from the simple models to be within ten percent

over a wide range of geometries, convective film coefficients,

and thermal conductivities. The accuracy of the simple

one-dimensional model for hydrogen convective cooling had

also been verified by many other researchers [27].

5.6. Limitation consideration

The active cooling thermal analysis of RCC must also satisfy

the requirements such as material limits on cooling-channel

temperature, limits on coolant Mach number, the outlet

pressure limit, stress, and as well as fatigue life. Also the

power balance between turbine and pump, which is a new

limit not need to be considered in conventional regenerative

cooling. In this paper, we only consider the former three

limitations and the power balance limit.

To avoid compressibility effects, a limit is needed for the

Mach number of the coolant flow. The Mach number is

calculated by

M ¼ mraWH

(18)

Where all the coolant conditions are evaluated at the channel

outlet. The estimated speed of sound for hydrogen fuel is

about 1000m/s, and aMach number limitMlim¼ 0.25 was used

by Scotti et al. [20]. This condition can be satisfied simply by

limiting u less than 250 m/s, and no constraint function is

required.

For material limits on cooling channel temperature, the

cooling channel wall temperature should be maintained

under the material limit, we set Tlim ¼ 1110 K.

The outlet pressure limit of the hydrogen should be

maintained above a limit value for proper fuel flow and

penetration into the airstream in the scramjet engine

(hydrodynamic constraint). The pressure in the combustion

chamber of scramjet is generally as low as 0.3 MPa or a little

higher [30], considering the pressure loss from the cooling

passage outlet to the combustor, we thus set Plim ¼ 0.6 MPa.

Table 1 summarizes the constraint functions needed in the

RCC thermal analysis procedure. The Mach number and

pressure constraint functions in Table 1 are evaluated at the

channel exit.

5.7. Determination of L1 and m

In order to achieve the maximum cooling capacity of

hydrogen fuel, the exit temperatures of hydrogen fuel coming

out from the first and the second cooling passage are assumed

to be even, which is the highest working temperature in the

heat transfer process, and the inlet temperature of turbine is

equal to the outlet temperature of the first cooling passage,

that is,

Tti ¼ Tco;1 ¼ Tco;2 ¼ Tclim (19)

L1 and m are the cycle variables in the calculation. Once the

heat balance in each segment for the first cooling passage is

obtained and Tco,1 satisfies the Eq. (19), L1 is determined. Then

if the heat balance in each segment for the second cooling

passage is also obtained and Tco,2 satisfies the Eq. (19), m is

determined. If not, the value of m and L1 will be adjusted, and

the new calculation cycle will begin.

5.8. Determination of d

Once L1 obtains its final value, the length distribution between

the first and the second cooling passages will be determined.

Therefore, the heat absorption of fuel in each cooling passage

is determined due to the uniform aeroheating. From Eq. (1)

d can thus be expressed as

d ¼ Q2

Q1¼ qwW

�Lp � L1

�qwWL1

¼ Lp � L1L1

(20)

So we can easily get the value of d when L1 is determined.

6. Results and discussion

Sensitivity analysis is a useful basis for system performance

analysis and optimal design in order to find the effect law of

each parameter and major factors. To examine the flow and

heat transfer down the length of the cooling channel, to see

how the cycle parameters influence themultiplication ratio of

fuel heat sink (d), as well as to illustrate potential performance

of RCC, and to find difference between cooling channel design

in RCC and that in conventional regenerative cooling, detailed

numerical examples are provided. For given fuel inlet

parameters, fixed Tclim and outlet pressure limit, cooling

passage structure are chosen here as the instance to analyze

the effect of flow and component parameters on the perfor-

mance of RCC and the flow and heat transfer down the length

of the channel.

Channelwidth (W ) and height (H ) are chosen as the design

variables for the present problem. The lower limits for duct

dimensions taken by [18] are Wmin ¼ Hmin ¼ 1 mm. In order to

have a numerical appreciation of the results, we consider the

W and H in the range 1e5 mm, with Tci ¼ 55 K, Pci ¼ 4 MPa,

Tclim ¼ 850 K, g ¼ 1.4, p ¼ 2, ht ¼ 0.85, and qw ¼ 2 MW/m2.

6.1. Effect of cooling channel height H

The effect of H on Twg is shown in Fig. 6. Twg generally

increases as H increases, due to the degraded fin efficiency,

Fig. 6 e Variation of gas side wall temperature at different

channel height down the length of the channel.


because the fin efficiency decreases as the fin length

increases. There exits a temperature spike in the entrance

region, the maximum value of Twg in the entrance region is

larger than 1100 K, which is over the temperature limit of the

wall. This phenomenon is called “heat transfer deterioration

at low temperature”, which has been reported by several

researchers [31]. And the heat transfer deterioration of

hydrogen is reported in Ref [32]. This is mainly contributed by

an extreme variation of fluid properties near the critical

temperature. It could be concluded that channel geometry H

has significant influences on heat transfer deterioration.

Furthermore, the maximum wall temperature will be higher

than 1100 K once H is larger than 2 mm, channel temperature

constrain will be activated.

The effect of H on Twg could be further illustrated by the

variation of heat transfer coefficient hc down the length of the

cooling channel in Fig. 7. The heat transfer coefficient has

a sudden reduction in the entrance region, and hc gets its

minimum value where Twg gets its maximum value. The

Fig. 7 e Variation of heat transfer coefficient at different


reason why the heat transfer deterioration occurs in the

entrance region though the coolant is at lower temperature, is

because that the viscidity of hydrogen fuel firstly decreases

and then increaseswith the increase of temperature. The heat

transfer deterioration will make the heat transfer coefficient

of cooling channel decreases, and will lead to over tempera-

ture for the wall. Therefore, the heat transfer deterioration

has to be avoided. In practical applications, fuel must be

preheated before entering the cooling channel, a possible way

is that the fuel is firstly usually used as the coolant for heat

structure with lower heat load, such as cabin environment

and the avionics, etc.

The variation of Twg down the length of cooling channel is

composed by two curves in Fig. 6 at each H, there is a sudden

decrease between the end of the first curve and the start of the

second curve, and this variation can also be seen in the later

Figures. The decrease in temperature leads to the decrease in

viscosity, and the decrease in Reynolds number, and then the

decrease in heat transfer coefficient. Such variation is caused

by the decrease of the fuel temperature at the entrance of the

second cooling passage compared with that at exit of the first

cooling passage. The property varies with the decrease in fuel

temperature, which will modify the relation between the heat

flux and the temperature difference, i.e., the convective heat

transfer coefficient. Especially, the sudden reduction of h at

the entrance of the second cooling passage in Fig. 7 dose not

lead to the sudden increase of Twg in Fig. 6, just because the

fuel temperature Tc decreases greatly, and so the heat balance

is still met. The heat transfer performance in the second

cooling passage is not worse than that in the first cooling

passage. This is the desired results for the introduction of RCC,

and can also be translated to that RCC will not bring with any

disadvantage for the heat transfer process in some extend.

As shown in Fig. 8, the velocity decreases as the increase of

H. This is because that the across area increases as the

channel height H increases. Furthermore, the velocity at the

entrance of the second cooling passage is nearly two times

that of the exit of the first cooling passage due to the severe

change in density, for the pressure at the turbine outlet is two

times that of the turbine inlet.

Fig. 8 e Variation of fuel velocity at different channel height

through RCC.

Fig. 9 e Variation of pressure drop percentage at different

channel height.

Fig. 11 e Variation of gas side wall temperature at different

channel weight down the length of the channel.


The increased velocity corresponds to an increase in

coolantMach number for the above assumptions, however, an

increase in Mach number is not allowed since the Mach

constraint is active when H is lower than 2 mm. Channel

height increases to enforce the Mach constraint. In regener-

ative cooling, u is less than 100 m/s for all cases, because the

pressure drop of fuel is relative small without the expansion

process through turbine [20]. Thus, Mach number constraint

can be put aside for regenerative cooling, but nor for RCC.

As shown in Fig. 9, fuel pressure drop through the cooling

passage decreases as H increases, but the pressure drop is less

than 1 MPa in all the cases. In terms of the pressure drop

through the turbine, the outlet pressure of RCC is higher than

Plim, which means that the DP constraint is always satisfied,

thus, the pressure drop constraint does not work. However, if

with the same outlet pressure level, RCC will consume more

pumping power to provide higher cooling passage inlet pres-

sure than regenerative cooling, because the additional pres-

sure drop through the turbine.

Fig. 10 e Variation of multiplication ratio of fuel heat sink

at different channel height.

As shown in Fig. 10, the multiplication ratio of fuel heat

sink (d) gets its maximum value when it varies from 1.5 mm to

2mm. By the above analysis, Mach constraint will be activated

when H ¼ 1 mm; and channel temperature constrain will be

activated once H is higher than 2 mm. In all, the optimal

multiplication ratio of fuel heat sink will be obtained when H

varies from 1.5 to 2 mm. So it can be concluded that H has

minor effect on d. And it is noticed that the difference between

the maximum andminimum value is only about 0.7% while H

varies five times.

6.2. Effect of cooling channel width W

In this part, the channel height design variable (H ) is at 2 mm

for the optimum design in all cases. As shown in Fig. 11, the

wall temperature increases as channel width increases, and

the maximum wall temperature correspondingly increases.

Furthermore, heat transfer deterioration can still be seen in

the entrance region in Fig. 12, channel width W has a strong

effect on heat transfer deterioration. Over temperature

Fig. 12 e Variation of heat transfer coefficient at different

channel weight down the length of the channel.

Fig. 13 e Variation of pressure drop percentage at different



phenomenon takes place when W is larger than 2 mm. The

effect ofW on heat transfer coefficient is contrary with that on

wall temperature. The total number of longitudinal fins for

a single cooling panel is a crucial factor in determining overall

performance of the panel as a heat exchanger. Since fin width

is fixed in the analysis, so the number of fins decreases as W

increases with constant panel width. Therefore, as more fins

are installed, the heat transfer efficiency increases, but more

pumping power is required.

As shown in Fig. 13, the multiplication ratio of fuel heat

sink (d) nearly dose not vary with channel width except when

W is equal to 3 mm. Thus, the optimal channel width should

be chosen to be lower than 2.5 mm. Furthermore, the power

balance constrain will not be activated for almost any condi-

tions in the analysis, because the fuel inlet temperature of the

turbine is at a high level and hydrogen has a strong expansion

ability, while the pump consumption power is low.

Furthermore, the variation law of fuel flow for cooling in

RCC with channel structure is the same with that in regen-

erative cooling. The fuel flow for cooling monotonically

decreases as W and H increase. And in regenerative cooling

optimization,Wopt and Hopt are identically equal to W, (2 mm)

and H, (2 mm) in Ref [18], respectively. By above analysis, the

optimal Wopt and Hopt are obtained with the identical value of

2 mm.

7. Conclusion

An analytical model for incompressible flow in rectangular

ducts with coupled heat conduction based on fin type

assumptions was developed for RCC. Channel width and

height are chosen to investigate the effect law of channel

geometry on RCC performance, and to find the difference of

channel design between RCC and regenerative cooling, taking

into account thermal, hydrodynamic, Mach number and

power balance constraints.

An important result was that the individual duct size

should be as small as possible, provided that the Mach

number constraint is met. The heat transfer performance in

the second cooling passage is not worse than that in the first

cooling passage. For the range of parameters considered, the

pressure drop for 1 m length of cooling channel is less than

1 MPa and, thus, is not a critical issue. But if the pressure drop

through the turbine is considered, the pressure drop in RCC is

much higher than that in regenerative cooling, and more

pumping power is consumed in RCC. The power balance

constrain will not be activated for almost any conditions in

the analysis. Thermal and Mach number constraints are

needed to be considered in RCC, however, the Mach number

constraint could be excluded in regenerative cooling.

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Effect of cooling channel geometry on re-cooled cycle performance for hydrogen fueled scramjet