The Effects of Insulation thickness on Heat Transfer for Thermal Protection System

Shuang Liu, Boming Zhang, Weihua Xie

Abstract-The effects of insulation thickness are investigated

with potential application in thermal protection system of

hypersonic and re-entry vehicles. The traditional thermal

protection system is modeled by the finite difference approach.

Four different thicknesses of insulations' TPS are studied. The

numerical calculation results show that structure temperature

decreases as the insulation thickness increases as well as

temperature difference increases, however, this effect weakens

as the insulation thickness increased.

I. INTRODUCTION

THERMAL management is one of the priority issues of

hypersonic aircrafis[I,2], which are subjected to the severe aerodynamic heating caused by flight altitudes, flight time and Mach numbers[3-5].Insulation is the critical part of thermal protection system to protect inner structure within the maximum operational temperature limit. The advantages of insulation are lightweight, non-load-bearing. Increasing the thickness of thermal protection system's thickness is an alternative method to improve the heat capability of thermal protection system.

The insulation has been studied recent years. The main researched are focus on the heat transfer of inner structure[6-7]. Kamran Daryabeigi[8] analyzed and tested the high temperature fibrous insulation utilizing the optically thick approximation to research radiation in insulation. Xie experimented the effective thermal conductivity of high temperature insulation[9].

But few researches have been done on the thickness affection of heat transfer in the whole thermal protection structure.

The objective of the current work is to evaluate the effects of insulation thickness on the thermal protection structure and to numerically model it using the finite difference approach. The traditional TPS is modeled using the approach of Bolender and Doman [10], which is discreted into a one-dimension finite difference model along its axial dimension. Four different insulation thicknesses of TPS are studied using the same approach. The temperature

Manuscript received December 27, 2009. Shuang Liu. Center for Composite material and structure, Harbin Institute

of Technology, Harbin, I 50080, China (phone: 86-0451-86418172; fax: 86-0451-86418172; e-mail: shuangliu07@ gmail.com).

Boming Zhang. Center for Composite material and structure, Harbin Institute of Technology, Harbin, I 50080, China (e-mail: zbm@hit.edu.cn).

Weihua Xie. Center for Composite material and structure, Harbin Institute of Technology, Harbin,150080, China (e-mail: Michael@hit.edu.cn).

978-1-4244-6044-1/10/$26.00 ©2010 IEEE 392

distribution and temperature difference are profiled according to the numerical calculation results.

II. NUMERICAL MODEL

A. A Traditional Thermal Protection System Model A traditional thermal protection system is required to

prevent the underlying structure from reaching the maximum operational temperature limit. Thermal protection system configuration varies depending on the location where TPS is fixing on and aerodynamic heating that location encounters. However, the primary metal TPS is more likely to be as shown in figure I.

outer skin ... ----------1111111� insulation structure

Figure 1. Simplified sketch of typical metal TPS

Typically, the components of metal TPS are outer skin layer which is exposed to the aerodynamic heating, insulation layer and underlying structure layer. Hence, the model that is taken here will consider the typical thermal protection system and serve as the acreage outer skin of a generic hypersonic configuration. The prediction of the temperature of TPS which is due to the high flight March number will be performed. The traditional metal TPS model is a I-dimention fmite difference beam model. The model will lead to the discretization of a continuous structure and the insulation porous material part will be considered as effective homogeneous solid.

Consider the typical TPS construction, the tradition TPS is modeled and shown in figure 2[11,12].The TPS is specified into I-dimention finite difference model along its axial dimension and consists of three different layers which are outer skin layer, insulation and underlying structure respectively. The thickness of each layer can be varied according to the special structure. Each layer is discretized into separate nodes along the axial dimension. The number of nodes of each layer was determined by the thickness of each layer, or in other words, the grid sizes in each layer can be different, but the nodes have the equal space within same layer. In addition, the nodes are classified into four types base on the location: exterior surface node, interior nodes, material interface nodes and structure node. Material properties in each layer are assumed to be isotropic and independent of temperature.

aerodynamic heat flux

\ outer skin j = 1

material interface

insulation j = 2

material interface

structure j = 3

4� 0

4�

radiation

ldei=l

<">y, p,c""k,

4� <">Y2 P2Cp,2k2 4�

4� <">Y3 P3Cp,3k3

Node i = n

Figure 2. Finite difference model of tradition TPS

For the exterior node, this is node 1, the governing equation base on load boundary condition is,

qgen + qcond = qaero - qrad (1)

where q is the heat flux, subscript gen, cond, aero, rad denote

internal generation heat flux, conduction heat flux which transfer to interior nodes, aerodynamic heating heat flux and radiation heat flux respectively. In which

(2)

where PI is the density of the first layer, Cp,l is the specific

heat of the first material layer, T is the temperature, kl is the

thermal conductivity of the first layer material, t denotes the temporal coordinate, y denotes the spatial coordinate and

dy denotes step size in the spatial coordinate.

Using forward finite difference of the temperature in time,

the following is obtained,

aT TP+I -TP aT TP -TP -dy::::; I I �y , _ ::::;

2 I �y (3)

at At I cy y+<ly At I

In which superscript p denotes the time step and At is the

step size in the temporal coordinate. In order to have a simpler solution of temperature, substituting Eq.(3) into Eq.(1) and

T;P+I can be expressed as,

(4)

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For interior nodes, heat transfer in the same layer which has the equal space between the nodes and same material properties. The governing equation base on the conservation of energy

law for the node i in the /h layer is,

In which,

. aT . aT

I E = Apjc p,j -a

dy, qin = -kjA-a t t y-<ly

q. =-kA aT

I out J at y+<ly

(5)

(6)

Note kj is the thermal conductivity of the /h layer material,

but for insulation layer, which is generally consist of porous

material, therefore[18], kj is the effective thermal

conductivity for the porous material, which consider about the coupling affection of conduction, convection and radiation. Using forward difference equations and following can be carried out,

aT

I = 7;+I,j - 7;,j ,

aT I ::::; 7;P - 7;�1

(7) a t ij hx cy y-<ly �Yj

Substituting Eq.(3), (6) and (7) into Eq.(5) and T;P+I can

be solve out as following,

k.At [ ] [ 2k.At ] TP+I = J TP + TP + 1- J TP I ()2 HI I-I ( )2 I

PjCp,j �Yj PjCp,j �Yj (8)

For the material interface node, the thermal analysis control volume is show as figure 3, the node space is different as well as the material properties.

The governing equation base on the law of conversation energy is as following,

Where,

. = _ Ak aT . = _ Ak

aT qm J cy , qoUI j+ 1 cy

y-.aYj y+.aYj+l

(9)

. aT E = Apc -dy (10) p

at ·th I In Eq.(10) kj is the thermal conductivity of the} ayer

material, kj+ 1 is the thermal conductivity of the material in

(j + lyh layer. Note parameter Llyand pCp are the average

value of value in /h and (j + 1 yh layer, which are defmed

as,

.'1Y = .'1Y} + .'1Y}+1 , pCp = PjCp,j.'1Yj + Pj+lCp,j+l.'1Yj+l

2 AYJ + AyJ+! (11)

Substituting Eq.(10),(II),(3) and (7) into Eq.(9), solving

TP+1 i as

Node i-I --

qin

.'1y

- - - - -t - - - - p,c,.A

Node i -

Material 111 rface

Node i + 1 -

Figure 3 Control volume of material interface node

For the structure node, that is the innerface note, two kind of boundary condition can be employed, one is constant temperature and the other one is insulate heat. Insulate heat is applied here for the operation temperature of metal is low, As a result, the energy balance equation of the last note is,

This is,

E = q', In

C AY3 =-k aT

P3 p,3 2 3 ay 3 Y-�Y3

(13)

(14)

Substituting forward difference equations(3) into above

equation, r;p+l is solved out as,

r;p+l = T"P

+l = (1 2k3M 2 JT"P + 2k3M 2 T:'-l P3Cp,3(AY3) P3cp/AY3)

(15)

B, Numerical Implementation of finite difference model In the implementation of the fmite difference model

developed above, outer skin layer of traditional TPS are constructed of 10mm-thick PM2000, which is discreted into 2 elements by 3 nodes in the finite difference code where the

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first node is the exterior surface node and the third node is the material interface node shared with the insulation layer. This material has a predicted maximum operational temperature of 1570K, the density is 7116kglm3, thermal conductivity is 19.2W/mK and the specific heat is O.534kJ/kgK. The insulation layer is assumed to be manufactured by Saffil alumina fibrous which is 50mm thickness and is discreted into 5 elements by 6 nodes, The material has a predicted maximum operational temperature of IS70K, the density is 96kglm3, thermal conductivity is O.2W/mK and the specific heat is lkJ/kgK.Note that the first node and the last node in the insulation layer are shared with the upper outer skin layer and bottom structure layer. The last part is the titanium structure layer, which is assumed to be 5mm and is discreted into 1 element by only two nodes. This material has a

predicted maximum operational temperature of 450·C, the

density is 450Skg/m3, thermal conductivity is 23W/mK and the specific heat is O.515kJ/kgK. The first node is the material interface node shared with the upper insulation layer and the other is structure node. It is important to note that the element number of each layer is determined based on the porosity and length.

The set of traditional TPS models used four different thicknesses of insulation to study the effect of insulation thickness on the temperature distribution and insulation efficiency. The four space thicknesses of each insulation are kept constant as 100mm, 150mm, 160mm and IS0mm. In addition, these four different thicknesses of insulation are discreted into 10, 15, S and 9 elements respectively. Moreover, the other layers are a constant dimension and are discreted into the same elements as a traditional TPS model.

Constant heat flux which is applied on the outer skin is employed to study the performance of the TPS. 240kw/m'is assumed to be the constant heat flux. To calculation of the temperature of the insulated side, the second boundary condition is used, that is the last node is perfectly insulated. Specifically, the initial temperature of the structure and TPS is assumed to be 300K uniformly.

It is important to note that the properties of insulation used here is the effective properties which assumes porous insulation material to be homogeneous material.

III. RESULTS AND DISCUSSION

Figure 4 shows the temperature history for all nodes of the tradition TPS model. The positive ordinate is oriented

from inner structure node to the outer skin node. It can be seen that the out skin reach steady-state rapidly, all inner layer do not reach steady-state for 2 hours yet. Note that the material temperature of the out skin layer has already reached 1492K which is near to the maximum operational temperature limit, meanwhile the structure layer temperature has already reached 1340K. So, the traditional TPS is hard to prevent the inner structure and it must be improved by increasing the thicknesses of the insulation layer or applied the active cooling methods.

� � :J

� Q) a. E Q) f-

1600

1400

1200

1000

800

600

400

200 -1000 1000 2000 3000 4000 5000 6000 7000 8C

Time/ s

Figure 4 Temperature histories for all traditional TPS model nodes. The insulation's thickness is 50mm and the applied heat flux is 240kw/m2

1400

1200

� � 1000 .3 � Q) 800 Q. E Q) f-

600

400

200 ·1000

-- insulation=50mm - - - insulation=1 OOmm . - - .. insulation=150mm - - - - insulation=160mm

1000 2000 3000 4000 5000 6000 7000 8000 Time / s

Figure 5 Effect of insulation's thicknesses on the temperature history for node n-l, which is the first node of the structure layer.

The applied heat flux is 240kw/m2

1500 • • • • • 1400 -e- exterior surface node 1300 -e- interior node of first layer

1200 -.... - first material interface node

1100 -"'- interior node of second layer

� -+- second material interface node 1000 ---<11- interior structure node

� 900 .3

/

'" '" '" '" '" ill 800 Q. E 700 ill f- 600

500

.� 400 300 *----- • • •

2 4 5

case study

Figure 6 Temperature histories of the typical nodes in different thickness of insulation TPS models. Casel: insulation's thickness=50mm, case2:

insulation's thickness= I 00mm,case3: insulation's thickness=150mm, case4: insulation's thickness=160mm, case5: insulation's

thickness= 180mm. Time= 1 OOOs

Figure 5 shows the temperature history of the fIrst node of the structure layer in fIve different TPS models whose the thicknesses of the insulation layer is 50mm, 100mm, 150mm, 160mm and 180mm respectively. Clearly, the structure temperature decreases as the thickness of insulation's

395

thicknesses increases and the extension of the temperature different decreases.

1400

1200

� � 1000 :J

T§ ill 800 Q. E �

600

400

.-------.-------,.------�.-------.

-'" '" '" '" '" -e- exterior surface node -e- interior node of first layer

-.... - first material interface node

-"'- interior node of second layer

• second material interface node

---<11 - interior structure node � �

2 3 case study

4 5

Figure 7 Temperature histories of the typical nodes in different thickness of insulation TPS models. Casel: insulation's thickness=50mm, case2:

insulation's thickness=100mm,case3: insulation's thickness=150mm, case4: insulation's thickness=160mm, case5: insulation's

thickness= 180mm. Time=3600s 1500 • • • • • 1450 1400 1350 .,� 1300 1250 '" '" '" 1200

� 1150 -e- exterior surface node

� 1100 -e- Interior node of first layer

.3 1050 -.... - first material Interface node

� 1000 ill 950 • second material Interface nodE a. E 900

---<II-Interior structure node � 850 800 750 700

---------. 650 600 550

4 case study

Figure 8 Temperature histories of the typical nodes in different thickness of insulation TPS models. Casel: insulation's thickness=50mm, case2:

insulation's thickness=100mm,case3: insulation's thickness=150mm, case4: insulation's thickness=160mm, case5: insulation's

thickness=180mm. Time=7200s

This trend indicates that the thicknesses of the insulation effect weaken as the insulation's thickness increases. It is important to mention that the temperature profIles which insulation layer's thickness are 50mm and 100 mm increases non-linearly and the left three temperature profIles increases linearly.

Figures 6-8 show, respectively, the temperature of the special nodes in all fIve TPS model cases whose insulation is 50mm, 100mm, 150mm, 160mm and 180mm at discreted times. The temperatures of all three nodes in the fIrst layer have already reach steady-state at 1000s and this state will not change while the insulation's thicknesses increase. As indicate in the figures, increasing the thicknesses of the insulation can decrease the structure temperature and the temperature differences between the out skin and the structure will increase at the same time.

1600

1400

\ 1200

\ �

� 1000 " :::l T!i 800 Q) c. E • Q) \ I- 600

••

400

-.- Thickness=65mm

-e- Thickness= 115mm

-.011.- Thickness=165mm

-.... - Thickness=175mm

-+- Thickness=195mm

this tread weakens as insulation's thickness reach a certain lever, after that, increasing insulation's thickness effect little on the structure temperature.

1600

1400

1200 �

!!! .3 1000 � Q) c. E 800 Q) -.- time=1 OOOs

I- -e- time=3600s

-.011.- time=7200s -20 0 20 40 60 80 100 120 140 160 180 200 22( 600

thickness / mm

Figure 9 Temperature distributions of all nodes through the finite difference TPS structure thickness' direction. Time is at 1000s

�

!!! .3 � Q) c. E Q) I-

�

!!! :::l T!i Q) c. E Q) I-

1600 1500 -.- Thickness=65mm 1400 -e- Thickness=115mm

-.011.- Thickness=165mm 1300 -.... - Thickness=175mm 1200 -+- Thickness=195mm 1100 1000 e�

900 � � 800 � 700 '-.

600 "'" 500

400 .. 300

-20 0 20 40 60 80 100 120 140 160 180 200 220 Thickness / mm

Figure 10 Temperature distributions of all nodes through the finite difference TPS structure thickness' direction. Time is at 3600s

1600

1500 -.- Thickness=65mm

-e- Thickness=115mm 1400 -.011.- Thickness=165mm

1300 -.... - Thickness=175mm

-+- Thickness=195mm 1200

1100 "-"e 1000 �e

900

�� 800 .u. 700

600 .. 500

-20 0 20 40 60 80 100 120 140 160 180 200 Thickness / mm

220

Figure 11 Temperature distributions of all nodes through the finite difference TPS structure thickness' direction. Time is at 7200s

Figures 9-11 show the temperature distribution of all nodes through the direction of the TPS structure thickness in five different TPS model at 1000s, 3600s and 7200s, respectively. These figures show that structure temperature can decreases as insulation's thickness increase, however,

396

-10 o 10 20 30 40 Thickness / mm

50

-.

60 70

Figure 12 Temperature distributions of all nodes through TPS structure at three discrete times. Structure's thickness= 65mrn, insulation's

thickness=50mrn 1600

... -.-time=1000s

1400 .oil. -e-time=3600s

e -.011.-time=7200s .oil.

1200 • e .oil. � .oil. e !!! 1000

.oil. ::J • e T!i .oil. Q) 800 e .oil. c. E • .oil. Q) e I- 600 .u. • e

e 400 • .. • • • •• 200

0 50 100 150 200 Thickness / mm

Figure 13 Temperature distributions of all nodes through TPS structure at three discrete times. Structure's thickness= 195mrn, insulation's

thickness= 180mrn

Figures 12-13 show the temperature distribution of all nodes through the direction of the TPS structure thickness in five different TPS model at 1000s, 3600s and 7200s, respectively. These figures show that structure temperature can decreases as insulation's thickness increase, however, this tread weakens as insulation's thickness reach a certain lever, after that, increasing insulation's thickness effect little on the structure temperature.

IV. CONCLUSION

The effect of insulation thickness on TPS has been modeled using a fmite difference approach. A heat transfer model of the traditional TPS has been studied. It has been determined that the traditional TPS can not keep the temperature of the inner titanium structure bellow its

operational temperature limit due to the severe aerodynamic heat caused by flight altitude, flight time and flight Mach number. So, four different thickness insulation TPS have been studied in order to solve previous issue, it is observed that increasing the thicknesses of the insulation decreases the temperature lever of inner structure, at the same time increases the weight of the TPS and temperature difference between the two surface. Moreover, It is observed that this insulation effect weakens as the thickness of the insulation thickness increases.

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