Design and thermal test of high-vacuum insulator for heat delivery pipes

Thermal piping insulation of implants is crucial for heat delivery, production, collection, or storage at high temperature values. It is currently obtained by enveloping low thermal conductivity materials such as rockwool, fiberglass, polyurethane, polystyrene, and aerogel. However, better performances can be reached by adopting vacuum technology. In this case, conductive losses are annihilated, and the radiative heat transfer mechanism represents the only loss mechanism. Here, we compare a high vacuum-based novel solution and the traditional insulation for heat delivery applications. We propose a high vacuum- based solution consisting of an evacuated gap that surrounds the hot pipe coated by a thin aluminium foil. Experimental results using this novel solution show a fivefold reduction of the thermal radiation losses compared to the traditional solutions when in the temperature range between 100 °C and 250 °C.


Introduction
Thermal insulation is crucial in various applications and systems where a temperature sensibly above or below ambient is required, together with low energy consumption.In the building sector, proper wall insulation can represent a satisfying trade-off to find a compromise between people's comfort and energetic efficiency [1,2].Indeed, sanitary hot water requires well-insulated pipes to avoid thermal losses along the network [3] and storage of cryogenic or hot fluids demands high-performance insulators to limit the heat exchange over time [4].
Depending on the application and temperature ranges, different technological solutions have been investigated by changing materials and/or geometries [5].Usually, to quantitatively define the performance of an insulator, two parameters are considered: thermal conductivity λ (W/m‧K) and thermal transmittance U (W/m 2 ‧K).The first parameter derives from the linear Fourier's equation of conduction as an intrinsic parameter of the insulating material, whereas the second quantifies the performance of the insulator based on its geometry, materials, and total exchanged heat.The most used materials for insulators are fiberglass, polyurethane, polystyrene, rockwool [6], aerogel [7], with the last reaching the lowest value of 17 (mW/m‧K).Better performances, with an equivalent thermal conductivity of 4 (mW/m‧K), can be achieved by adopting composite insulation and vacuum technology, as demonstrated by Vacuum Insulation Panel (VIP) [8,9,10], where thermal radiation represents the main thermal exchange mechanism, minimizing the role of conduction of residual gases.
Between 100 °C and 250 °C, rockwool is the most used insulation material for heat delivery piping, as it achieves thermal conductivity values of 0.040 (W/m‧K).However, the thermal insulation efficiency of rockwool is influenced by environmental conditions: in the presence of 5% moisture level, the thermal conductivity of the material can reach a maximum value of 0.065 (W/m‧K) [11].Different technologies have been applied to get rid of the dependence on atmospheric conditions.Among these, the best results have been obtained with pipes wrapped in VIP, which have reached lower thermal conductivity than traditional rockwool [12,13].
In this work, we present a comparison between a high vacuum-based novel solution and traditional insulators for heat delivery applications.The adopted solution involves isolating the hot pipe with high-vacuum technologies and a low-emissivity material coating to minimize radiative heat transfer.The work also proposes a new measurement technique for axial losses compensation inspired by the guarded plate method [14,15,16].Experimental results show that this novel solution reduces the thermal losses by a factor of 5 compared to the traditional solutions, ensuring a primary energy saving [17] in the temperature between 100 °C and 250 °C and considering the same geometry and boundary conditions.

Design of the vacuum insulator
The designed prototype consists of two coaxial pipes (figure 1), both made of stainless steel AISI 304.The choice of using steel as the preferred material is based on several factors.First, compared to aluminium and copper pipes, steel has a lower thermal conductivity without compromising the insulation performance.Additionally, steel has excellent mechanical strength properties.The inner pipe has a diameter of 54 mm and a length of 1.7 m, while the outer pipe is 1.4 m long with a diameter of 100 mm.At this stage, we assumed the thickness of pipes equal to zero. Figure 2 shows the gas thermal conductivity trend as a function of the pressure.At decreasing pressure, the gas thermal conductivity decreases until reaching a threshold that depends on the characteristic dimensions δ of the vacuum container.For the designed prototype, we generate a vacuum gap between the inner and outer pipes.
The characteristic dimension δ, in this case, is equal to 23 mm.For pressure lower than 10 -4 mbar, gas thermal conductivity is less than 1% compared to the value at atmospheric pressure, thus the conduction is negligible, and radiation is the predominant heat exchange mechanism [18], resulting in a vacuum thermal insulation condition.Considering a cylindrical geometry and the one-dimension hypothesis of the temperature field, we can express the radiative thermal power ܳ ̇ in equation ( 1) [19]: where A1 is the lateral area of the inner pipe (m 2 ), T1 and T2 are the temperatures (K) of the internal and external surfaces, ߪ is the Stefan-Boltzmann constant equal to 5.67‧10 -8 (W/m 2 ‧K 4 ), and ε eq is the equivalent thermal emissivity between the internal and external surface, expressed as reported in equation ( 2).The factor ε eq depends on both internal and external thermal emissivity and a shape factor, i.e., the diameter ratio D1/D2 that represents the view factor.
The combination of equations 1 and 2 marks the relevance of low thermal emissivity to reduce the thermal exchange in high vacuum conditions.
The convective heat exchange between the outer pipe surface and the environment, as defined by equation (3), completes the analytical model: where A2 is the lateral area (m 2 ), ℎ݈݅݉i is the liminar coefficient which considers both convective and radiative heat exchange, and Tenv is the environmental temperature of the laboratory, equal to 24 °C.
The thermal insulation performance of the adopted solution is evaluated in terms of equivalent thermal conductivity (W/m‧K) expressed in equation ( 4): where ܳ ̇ (W) is the total thermal power exchanged between internal and external pipe, L (m) is the axial length, and T1 (K) and T2 (K) are the temperatures of the inner and the outer surface, respectively.
Figure 3 shows theoretical curves of the equivalent thermal conductivity as a function of inner temperature, obtained for different power supply ܳ ̇.
We choose a Vacuum Insulation Panel (VIP) wrapped around a stainless-steel pipe, with a thermal conductivity λ = 0.012 (W/m‧K) as reference: it represents the lowest value found in the literature for heat delivery systems in the temperature range between 50 °C and 100 °C [12].The literature suggests the use of conventional thermal insulating materials above a temperature of 100 °C; among these, rockwool is one of the most used materials with a thermal conductivity of 0.040 (W/m‧K).All the other curves are referred to the λeq trend of the designed prototype for different internal emissivity ε1 values: 0.15 for stainless steel [20], 0.045 for aluminium coating [21], and 0.02 for copper coating [22].The simulations show no advantage at high vacuum thermal insulation between two stainless steel surfaces, as the emissivity of stainless steel is too high.Therefore, the use of a thin sheet coating on the inner pipe is found to be necessary to reduce emissivity while enhancing the performance of the system, as highlighted in equation ( 2).We have chosen aluminium as a coating to test the prototype experimentally, as it is more economically advantageous than copper.

Experimental setup
Figure 4 shows the setup used for the experimental analysis.In particular, the internal pipe section, where thermal-insulation performance is measured, is hidden within the vacuum gap.The prototype design has provided significant improvements in thermal insulation performance achieved by using an internal emissivity value equivalent to that of aluminium.The adopted solution involves a 15 ߤ݉ thickness aluminium foil around the inner pipe, as shown in Figure 5, attempting to achieve complete adhesion to the surface and simulate the behavior of a thick coating.The vacuum gap between the two pipes is created by removing the interstitial gas using a pumping system connected to a copper pipe called "pumping port" (see Figure 4).A Cold Cathode All Metal Gauge is installed on the outer pipe monitoring in real time the pressure during thermal tests, ensuring that it is always below the threshold that defines the high vacuum regime, thereby retaining the advantages of minimal gas thermal conductivity (Figure 2).

Cold Cathode All Metal Gauge
To ensure the vacuum seal of the prototype, two flat washers are welded to the ends of the two pipes, as shown in Figure 6, defining a length of the sample to be tested for vacuum thermal insulation of 1.4 m.Once the prototype was built up, it was necessary to verify the experimental measuring conditions to evaluate λeq in accordance with equation ( 3).The predictive model assumes the onedimensionality of the temperature field in the radial direction for pipes of infinite length.
Preliminary tests have shown that conduction losses at the ends of the pipe have led to measurement errors in the evaluation of the equivalent conductivity λeq.Moreover, the errors increase with decreasing value of equivalent thermal conductivity because the two contributions, radiative and conductive, cannot be distinguished.Therefore, to avoid conductive losses, it has been necessary to apply a temperature compensation technique: the lateral elements of the test specimen are supplied with additional energy to unify the temperature field in the axial direction, with a temperature difference of less than 1 °C.
In particular, a schematic view of the custom-made heating cartridge designed by the authors to realize the compensation is shown in Figure 7.The object is divided into three sections: the central heater (1 m long), whose length represents the effective tested one, the side heaters (15 cm long), and two Teflon spacers that provide thermal isolation between them.Power is supplied by a DC generator  The power of the three heating elements is controlled individually.Figure 8, on the left, shows the electrical resistance that crosses each element inside a copper pipe that provides uniform heat transfer thanks to its high thermal conductivity.Each section of the cartridge is made of a steel housing that serves as a temperature gauge for the inner pipe.The thermocouples are placed in grooves as close as possible to the inner surface of the hot pipe, as shown in Figure 8 on the right.Three different temperatures are monitored along the axis by means of three type K thermocouples: one placed in the center used as reference value for calculating λeq, and two placed at the ends of the central zone, which allow to assess the effects of compensation.Similarly, thermocouples are placed on the outer surface of the vacuum chamber pipe.

Results and discussion
In this work, an experimental analysis was performed to characterize the insulation performance of piping for thermal collectors operating at mid temperatures.The high vacuum technology combined with a low emissivity layer was studied to find an alternative solution for the insulation of piping in the medium temperature range with lower thermal conductivity than the solutions known in the literature.Tests were conducted by heating the prototype with electrical power for three different temperature values: 100 °C, 160 °C, and 220 °C.The experimental points, shown in Figure 9, were recorded in steady-state conditions.We considered only measurements with an axial temperature gradient ΔT lower than 1 °C, resulting in good compensation.
The system operates in high vacuum with a maximum pressure of 3.87•10 -6 mbar at 220 °C; in this condition, the gas thermal conductivity can be neglected, and radiation is the only heat transfer mechanism during all thermal tests.
Figure 9 shows a comparison of the thermal test results for three temperature conditions using three different solutions: x analytic model based on the hypothesis of full contact (dashed line) between Al layer and pipe; x an analytic model based on the hypothesis of no contact (dotted line) between Al layer and pipe, where a net internal emissivity εIN =0.020 between the inner pipe and the aluminium foil is assumed and evaluated as in equation ( 2) with a view factor equal to 1; x a reference solution based on VIP until 100 °C (λeq = 0.012 (W/m .K)) and on rockwool (λeq = 0.04 (W/m .K)) for higher temperatures.Experimental equivalent conductivity values (red squares) are in good agreement with the model based on the hypothesis of no contact between Al layer and pipe (see figure 9).

Conclusions
In the temperature range 100 °C -250 °C, commercially available solutions to contain thermal losses along heat pipelines are rockwool, fiberglass, and polyurethane with respectively 0.04 W/mK, 0.052 W/mK, 0.02 W/mK as thermal conductivity.In this study, the authors conducted thermal tests to evaluate the thermal insulation (i.e.thermal conductivity) of a high vacuum enclosure (pressure < 10 -6 mbar) with an aluminium layer covering the stainless steel pipe under test.This solution takes advantage of the high reflectivity of the aluminium layer, which contains the emitted radiation from the pipe, acting as a radiation barrier.Experimental results showed a fivefold reduction of the thermal radiation losses compared to the traditional solutions when in the temperature range between 100 °C and 250 °C.In the following are summarized the results obtained: x The measured equivalent thermal conductivity of the aluminium coating solution is lower than that of common commercial solution rockwool and developing technologies described in the literature for the temperatures between 100 °C and 250 °C temperature range, reducing the equivalent thermal conductivity from 0.04 (W/m•K) to 0.003 (W/m•K) at 150 °C.x The reduction of the equivalent thermal conductivity obtained by using the proposed technology allows primary energy savings due to the lower required heat input.For the same thickness of insulation of 23 mm, the thermal losses were reduced from 56 W to 4 W per unit of pipe length with the use of the proposed technology.x A robust high-vacuum tight enclosure solves the issue of degradation of thermal insulation performance due to atmospheric conditions, returning a stable lifetime performance.In a few years, thermal losses with rockwool insulation could become 50% higher than nominal.x The use of vacuum insulation allows to save space that might be critical in some applications.This is because thermal radiation depends utterly on the thermal emittance of surfaces, whereas traditional insulating materials use their low thermal conductivity, such as rockwool, where the thicker, the better.
Further investigation is needed to optimize the geometry of the tested prototype and find a solution that also reduces its size.The analytical curves suggest that copper coating can improve thermal insulation under high vacuum conditions.In the future, the economic compromise between low thermal conductivity and cost-saving should be evaluated to find the proper coating material.

Figure 2 .
Figure 2. Gas thermal conductivity vs pressure trend depending on vacuum vessel size.

Figure 3 .
Figure 3. Theoretical curves of equivalent thermal conductivity vs inner temperature.

Figure 8 .
Figure 8.On the left, the copper pipe inserted into a stainless steel one, and the Teflon spacer.On the right, thermocouples groove on stainless steel casing.

7 Figure 9 .
Figure 9. Experimental results carry out an equivalent thermal conductivity about three times lower than VIP reference (between 50 °C and 100 °C) and about two times lower than theoretical value for full contact hypothesis.