4.1. Experimental procedure

the bending vibration of Si–O. And, the peak at 3449 cm<sup>1</sup> represents the stretching vibration of functional group of Si–OH. For the composite, the peaks at the wave numbers of 3500, 2935, 2860, 1500, 1090, and 750 cm<sup>1</sup> have corresponding vibration, and no significant new peaks were observed. The FTIR spectra illustrate that the composite is just a physical combination of

The DSC curves of the paraffin and the composite are shown in Figure 11. From Figure 1a, the latent heat of the paraffin is 182.22 kJ/kg (T<sup>m</sup> = 56.8C). TG curve shows that weight of paraffin hardly changes, which indicates the paraffin used as PCM has good thermal chemical stability. Figure 11b indicates that heat storage capacity of the composite happened at melting point

Figure 10. FTIR spectra of the paraffin and the silica and the paraffin/porous silica composite.

Figure 11. The DSC-TG curves of the paraffin (a) and the PCM/silica composite (b).

silica ceramics and paraffin.

166 Advances in Some Hypersonic Vehicles Technologies

3.2.5. Thermal properties

Three porous silica cylindrical disks (100 mm in diameter and 10 mm thick) with the three different solid-liquid PCMs (two kinds of paraffin and one kind of xylitol) were fabricated as the solid matrices of the silica-PCM composites according to our recent study. The thermophysical data for these samples are given in Table 3.

The composites (100 mm in diameter and 10 mm thick) were then introduced into the experimental setup (see Figure 12 left). The temperature was recorded as it varied with time. The top and bottom walls of the container were insulated by adiabatic materials. For the sake of validation of the numerical model and assumptions, the temperature of the cold face of composite X98# as a function of time was deduced by the numerical simulation.

## 4.2. Numerical model

A schematic diagram of the composite and two-dimensional grids is given in Figure 12. (Sample dimensions: 180 mm in diameter and 120 mm thick). Due to the symmetry and regularity, the samples were formulated with two-dimensional axissymmetric coordinates


Table 3. Properties of the porous silica matrix composites.

Figure 12. Experimental setup for heat transfer of phase change composite (100 mm in diameter and 10 mm thick) and modeling and grids for the composite (180 mm in diameter and 120 mm thick).

and uniformly split quadrangle grids in all 19,481 nodes by Gambit 2.2.30, and the boundary conditions were specified.

#### 4.2.1. Assumptions and governing equations

The two-dimensional governing equations have been made based on the following assumptions:

The thermophysical properties are different for the solid and liquid phases but are dependent of temperature.

Heat loss from the container to its surroundings is negligibly small.

Based on these assumptions, the enthalpy-porosity method [20] was used for the phase change region in the PCM.

Continuity:

$$\frac{\partial \rho}{\partial t} + \frac{\partial (\rho u)}{\partial x} + \frac{\partial (\rho v)}{\partial y} = 0 \tag{6}$$

v–Momentum:

Energy:

ρ ∂ν ∂t þ u ∂ν ∂x þ ν ∂ν ∂y

ρ ∂H <sup>∂</sup><sup>t</sup> <sup>þ</sup> <sup>u</sup>

where the source term is Sh <sup>¼</sup> <sup>ρ</sup>

Boundary conditions

Initial conditions

energy equation.

4.3. Experimental results and discussion

� �

∂H ∂x þ ν ∂H ∂y

where H is the enthalpy, T is the temperature, and ΔH is the specific enthalpy.

cp ∂ð Þ ΔH <sup>∂</sup><sup>t</sup> , and

� �

¼ μ

¼ k cp

H ¼ h þ ΔH <sup>h</sup> <sup>¼</sup> href <sup>þ</sup> <sup>Ð</sup> <sup>T</sup>

The density and dynamic viscosity of the liquid PCM depend on its temperature [20, 21].

Given the constant temperature of the cold face and the adiabatic top and bottom wall,

∂T

Assuming initial temperature conformity and a fixed temperature of the hot face,

T xð Þj ; <sup>y</sup>; <sup>t</sup> <sup>x</sup>¼<sup>d</sup> <sup>¼</sup> Tcold

<sup>∂</sup><sup>y</sup> <sup>y</sup>¼0,t <sup>¼</sup> <sup>0</sup> � �

T xð Þ ; y; t j ¼ <sup>t</sup>¼<sup>0</sup> T

The numerical solution was carried out using the Fluent 6.3 software package [19]. The number of computational grids was ~19,200 for the 2D model after grid-independent tests. The time step in the simulations was as small as Δt = 0.1 s. The convergence was also checked at each time step, with convergence criteria of 10�<sup>4</sup> for velocity components and 10�<sup>7</sup> for

The composites had different thermophysical data owing to the three types of organic PCMs used during the preparation of the porous silica-PCM composites (see Figure 4 and Table 3). The varying heat storage capacities of the composites have an influence on the experimental

Tref

∂<sup>2</sup>ν ∂x<sup>2</sup> þ

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle

∂<sup>2</sup>ν ∂y<sup>2</sup> � �

> ∂<sup>2</sup>H ∂x<sup>2</sup> þ

� ∂p ∂y

∂<sup>2</sup>H ∂y<sup>2</sup>

T xð Þ ; <sup>y</sup>; <sup>t</sup> <sup>x</sup>¼0,t><sup>0</sup> <sup>¼</sup> Thot <sup>j</sup> (12)

� �

þ S<sup>ν</sup> (8)

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þ Sk (9)

(11)

cpdT (10)

where ρ is the density, u is the velocity in u direction, t is the time, and v is the velocity in v direction.

u-Momentum:

$$
\rho \left( \frac{\partial u}{\partial t} + \mu \frac{\partial u}{\partial x} + \nu \frac{\partial u}{\partial y} \right) = \mu \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) - \frac{\partial p}{\partial x} + S\_u \tag{7}
$$

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle http://dx.doi.org/10.5772/intechopen.70863 169

v–Momentum:

$$
\rho \left( \frac{\partial \nu}{\partial t} + \mu \frac{\partial \nu}{\partial x} + \nu \frac{\partial \nu}{\partial y} \right) = \mu \left( \frac{\partial^2 \nu}{\partial x^2} + \frac{\partial^2 \nu}{\partial y^2} \right) - \frac{\partial p}{\partial y} + S\_{\nu} \tag{8}
$$

Energy:

$$
\rho \left( \frac{\partial H}{\partial t} + \mu \frac{\partial H}{\partial x} + \nu \frac{\partial H}{\partial y} \right) = \frac{k}{c\_p} \left( \frac{\partial^2 H}{\partial x^2} + \frac{\partial^2 H}{\partial y^2} \right) + S\_k \tag{9}
$$

where the source term is Sh <sup>¼</sup> <sup>ρ</sup> cp ∂ð Þ ΔH <sup>∂</sup><sup>t</sup> , and

$$\begin{aligned} H &= h + \Delta H\\ h &= h\_{\text{ref}} + \int\_{T\_{\text{ref}}}^{T} \mathbf{c}\_{p} dT \end{aligned} \tag{10}$$

where H is the enthalpy, T is the temperature, and ΔH is the specific enthalpy.

The density and dynamic viscosity of the liquid PCM depend on its temperature [20, 21].

#### Boundary conditions

and uniformly split quadrangle grids in all 19,481 nodes by Gambit 2.2.30, and the boundary

Figure 12. Experimental setup for heat transfer of phase change composite (100 mm in diameter and 10 mm thick) and

The two-dimensional governing equations have been made based on the following assump-

The thermophysical properties are different for the solid and liquid phases but are dependent

Based on these assumptions, the enthalpy-porosity method [20] was used for the phase change

where ρ is the density, u is the velocity in u direction, t is the time, and v is the velocity in

¼ μ

∂<sup>2</sup>u ∂x<sup>2</sup> þ

∂<sup>2</sup>u ∂y<sup>2</sup>  � ∂p ∂x

<sup>∂</sup><sup>y</sup> <sup>¼</sup> <sup>0</sup> (6)

þ Su (7)

∂ ρu ∂x þ ∂ ρν 

Heat loss from the container to its surroundings is negligibly small.

modeling and grids for the composite (180 mm in diameter and 120 mm thick).

∂ρ ∂t þ

conditions were specified.

tions:

of temperature.

region in the PCM.

Continuity:

v direction.

u-Momentum:

4.2.1. Assumptions and governing equations

168 Advances in Some Hypersonic Vehicles Technologies

ρ ∂u ∂t þ u ∂u ∂x þ ν ∂u ∂y Given the constant temperature of the cold face and the adiabatic top and bottom wall,

$$\begin{aligned} \left. T(x, y, t) \right|\_{x=d} &= T\_{\text{cold}} \\ \left. \frac{\partial T}{\partial y} \right|\_{y=0, t} &= 0 \end{aligned} \tag{11}$$

#### Initial conditions

Assuming initial temperature conformity and a fixed temperature of the hot face,

$$\begin{aligned} T(\mathbf{x}, \boldsymbol{y}, t)|\_{t=0} &= T\\ T(\mathbf{x}, \boldsymbol{y}, t)|\_{\mathbf{x}=0, t>0} &= T\_{\text{hot}} \end{aligned} \tag{12}$$

The numerical solution was carried out using the Fluent 6.3 software package [19]. The number of computational grids was ~19,200 for the 2D model after grid-independent tests. The time step in the simulations was as small as Δt = 0.1 s. The convergence was also checked at each time step, with convergence criteria of 10�<sup>4</sup> for velocity components and 10�<sup>7</sup> for energy equation.

#### 4.3. Experimental results and discussion

The composites had different thermophysical data owing to the three types of organic PCMs used during the preparation of the porous silica-PCM composites (see Figure 4 and Table 3). The varying heat storage capacities of the composites have an influence on the experimental melting process. Experiments are required to determine the suitable silica-PCM for the service conditions.

compared with the composite C58#

. For the composite X98#

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle

different time intervals (10, 30, 60, and 120 s) are shown in Figure 15 under identical conditions (a constant hot face temperature (573 K)), and liquid fraction contours of the composites X98# at 180 s are shown in Figure 16, which indicated the more stable thermal performance during

Figure 14. Contours of temperature of the composite C58# (time intervals = (a) 10s, (b) 30s, (c) 60s).

Figure 15. Contours of temperature of the composite 98# (time intervals = (a) 10s, (b) 30s, (c) 60s, (d) 120 s) (left).

, the temperature contours at

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The thermal protection properties of the three types of porous silica-PCM were experimentally studied (Figure 13). Figure 13a compares the temperature of the cold face of the composites when they are subjected to same hot face temperature; Figure 13b represents that their temperature of cold face varies with time as they are subjected to hot face temperature (600C). As can be seen in the figure, the X98# composite shows the best heat absorption properties among the three composites. On the one hand, the temperature of the cold face of the composite X98# is 45C, while one of the other two composites is 75C as the three types of composites subjected to same hot face temperature (400C) (see Figure 13a). On the other hand, the slope of the time-temperature curve of the X98# composite decreases at a temperature ~ 80–90C, which is close to the phase transition range of the X98# composite and does not vary substantially with time. This trend is obvious at the melting temperature of the X98# composite, and it did not appear for the other two composites 58# and C64# , as they are above their phase change temperature and had already melted (see Figure 13b). For the cold face of composite X98# , good agreement is obtained when comparing the temperature as a function of time to the numerical simulation results (Figure 13b).

#### 4.4. Results and discussion

Numerical studies have been carried out for the three types of composites under identical conditions. The temperature contours for the composite C58# at a constant hot face temperature (573 K), and different time intervals (10, 30, and 60s) are shown in Figure 14. The temperature rises quickly at the beginning of the heating process and propagated as time goes on, as the melting of the composites started at the hot face in direct contact with the heating surface and the solid-liquid interface moved gradually in the axial direction over time. For the composite C64# , the heat transfer numerical studies showed the same melting process

Figure 13. (a) Comparison of cold face and hot face temperature of three types of composites. (b) Cold face temperature varied with time as hot face temperature is 600C.

compared with the composite C58# . For the composite X98# , the temperature contours at different time intervals (10, 30, 60, and 120 s) are shown in Figure 15 under identical conditions (a constant hot face temperature (573 K)), and liquid fraction contours of the composites X98# at 180 s are shown in Figure 16, which indicated the more stable thermal performance during

melting process. Experiments are required to determine the suitable silica-PCM for the service

The thermal protection properties of the three types of porous silica-PCM were experimentally studied (Figure 13). Figure 13a compares the temperature of the cold face of the composites when they are subjected to same hot face temperature; Figure 13b represents that their temperature of cold face varies with time as they are subjected to hot face temperature (600C). As can be seen in the figure, the X98# composite shows the best heat absorption properties among the three composites. On the one hand, the temperature of the cold face of the composite X98# is 45C, while one of the other two composites is 75C as the three types of composites subjected to same hot face temperature (400C) (see Figure 13a). On the other hand, the slope of the time-temperature curve of the X98# composite decreases at a temperature ~ 80–90C, which is close to the phase transition range of the X98# composite and does not vary substantially with time. This trend is obvious at the melting temperature of the X98# composite, and it

temperature and had already melted (see Figure 13b). For the cold face of composite X98#

good agreement is obtained when comparing the temperature as a function of time to the

Numerical studies have been carried out for the three types of composites under identical conditions. The temperature contours for the composite C58# at a constant hot face temperature (573 K), and different time intervals (10, 30, and 60s) are shown in Figure 14. The temperature rises quickly at the beginning of the heating process and propagated as time goes on, as the melting of the composites started at the hot face in direct contact with the heating surface and the solid-liquid interface moved gradually in the axial direction over time. For

Figure 13. (a) Comparison of cold face and hot face temperature of three types of composites. (b) Cold face temperature

, the heat transfer numerical studies showed the same melting process

, as they are above their phase change

,

did not appear for the other two composites 58# and C64#

numerical simulation results (Figure 13b).

170 Advances in Some Hypersonic Vehicles Technologies

varied with time as hot face temperature is 600C.

4.4. Results and discussion

the composite C64#

conditions.

Figure 14. Contours of temperature of the composite C58# (time intervals = (a) 10s, (b) 30s, (c) 60s).

Figure 15. Contours of temperature of the composite 98# (time intervals = (a) 10s, (b) 30s, (c) 60s, (d) 120 s) (left).

Author details

Address all correspondence to: flucky-zhou@163.net

phase change materials. Polymer. 2002;43(1):117-120

Institute of Nano-Technology and New Materials, Changsha University, Hunan, China

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Figure 16. Liquid fraction of the composite 98# at 180 s (right).

the melting process due to higher heat storage capacities and phase change point as compared with the composites C58# and C64# .

The experimental results indicated that the suitable silica-PCM for the service conditions is the composite X98# . In addition, the composite X98# showed the more stable thermal performance during the melting process based on numerical results for the temperature and liquid contours of the composites. From the thermophysical data of the porous silica matrix composites (Table 3), the mass infiltration rate of PCM (xylitol) in the porous silica matrix composite X98# is more than the other two composites C58# and C64# . The X98# -type composite has both high heat storage capacity and a high phase change point. Thus, it may be concluded that controlling the surface temperature depends mainly on these two main parameters.

#### 4.5. Conclusions

The effects of the heat storage capacity and thermal properties of porous silica filled with different PCMs were studied numerically and experimentally. The results indicate that the heat storage capacity and phase change point of the composites play important roles in their thermal performance. It has been illustrated that a higher heat storage capacity leads to more stability in the thermal performance of the composite and the phase change point of the composite determined its service conditions.
