Experimental and Modelling Studies on Thermal Insulation and Sound Absorption Properties of Cross-Laid Nonwoven Fabrics

Five high-loft nonwoven fabrics were selected to carry out this study. The thermal conductivity and sound absorption were measured via Alambeta device and Brüel & Kjær impedance tube, respectively. The nonwoven fabrics are composed of 70 wt. % staple polyester fiber and 30 wt. % hollow polyester fiber. The nonwoven fabrics were developed on a Trützschler cross-lapper thermal bonding line. To produce webs that are particularly wide, thick and virtually isotropic, the cross-lapper precisely folds the web and lays it down in 4 to 15 layers at high speed. The Trützschler cross-lapper thermal bonding line utilizes through-air drying, in which hot air is used to bond webs made of fibers with different melting points. The thermo-bonder consists of a perforated drum, heating element and radial fan. The fan generates a suction draft, this results in heated air flowing from the oven chamber through the moist web. The airflow causes fibers with a low melting point to melt and the individual fibers stick together. The hollow polyester with a low melt temperature which is 110°C for thermal bonding purpose. The specifications of staple and hollow polyester fiber are shown in Table 1. The mean fiber diameter was determined according to measurements on randomly selected 312 fibers with a value of 22.905 μm. The fiber density was measured by liquid pycnometer method [14]. Fibers randomly selected from the nonwoven were used to measure the mixed fiber density. The density has been measured five times with the value of 1171.665 kg/m³. Besides, the density of each fiber type has been measured, they are 1240.986 kg/m³ and 1032.810 kg/m³ for staple polyester and hollow polyester, respectively.

The longitudinal images of two types of polyester fibers are shown in Figure 1. The images were captured at the Technical University of Liberec (Liberec, Czech Republic) using the JENAPOL microscope (Jena, Germany) and NIS-elements software (AR 4.30.02 64-bit). The cross-sectional macroscopic images of polyester nonwoven fabric samples are illustrated in Figure 2, it can be seen that the fibers are cross-laid in the structure.

Figure 1

Figure 2

The characteristics of the nonwoven fabrics are listed in Table 2. Fabric thickness and areal density were determined according to ISO 9073-1:1989 [15]. The porosities of nonwoven fabrics were determined according to ε = 1 − ρ/ρ_f, where ε is the porosity, ρ_f is the fiber density, and ρ is the fabric bulk density [16]. The air permeability under 100 Pascal pressure drop is tested on the FX 3300 Textech Air Permeability Tester III at the Technical University of Liberec, Czech Republic. Each sample has been tested five times.

The thermal conductivities of nonwoven fabrics were tested on an Alambeta device (SENSORA, Liberec, Czech Republic) at the Technical University of Liberec, Czech Republic. The measuring head of the Alambeta contains a copper block that is electrically heated to approximately 32 °C to simulate the temperature of human skin. The lower part of the heated block is equipped with a direct heat flow sensor that measures the thermal drop between the surfaces of a very thin, non-metallic plate using a multiple differential micro-thermocouple [17].

In this study, one impedance tube was used to obtain normal incidence sound absorption coefficient according to ISO 10534-2 [18]. A Brüel & Kjær measuring instrument containing Type 4206 Impedance Tube, PULSE Analyzer Type 3560, and Type 7758 Material Test Software was used for testing within the frequency range 50Hz – 6400 kHz. A large tube (100 mm in diameter) and a small tube (29 mm in diameter) were set up for measuring the sound absorption in low-frequency range (i.e. 50-1600Hz) and mid- to high-frequency range (i.e. 500-6400Hz) respectively. A schematic of the two microphone impedance tube setup used in this work is depicted in Figure 3. A sound source is mounted at one end of the impedance tube and the material sample is placed at the other end. The loudspeaker generates broadband, stationary random sound waves. These incident sound signals propagate as plane waves in the tube and hit the sample surface. The reflected wave signals are picked up and compared to the incident sound wave.

Figure 3

Theoretically, thermal conduction always occurs if a temperature gradient exists between a material system and the environment or inner a material system. The convection can be ignored due to the significant friction that is caused by constituent fibers against natural convection [20]. Sun and Pan stated that heat transfer via radiation can be eradicated when the temperature gradient is small [21]. Thus, thermal conduction is the dominant mechanism in most situations when heat is transferred through a nonwoven fabric.

Some models used to analyze the heat transfer behavior of fibrous materials are developed based on electrical network analysis which is called thermal-electrical analogy [22,23]. Two models used to predict the thermal conductivity of fibrous materials with fibers perpendicularly oriented the heat flow will be applied in this study. Bogaty [24] proposed one model for textile fabrics in 1957. In Bogaty model, the thermal conductivity for fibrous material with fibers perpendicularly oriented the heat flow is presented as: (1)k=kfkakavf+kfvak = {{{k_f}{k_a}} \over {{k_a}{v_f} + {k_f}{v_a}}} where k is the thermal conductivity, k_a is the thermal conductivity of air, k_f is the thermal conductivity of fiber, v_f is the volume fraction of fiber, and v_a is the volume fraction of air.

Bhattacharyya [25] presented two models to predict the thermal conductivity of samples with fibers perpendicularly and randomly to the heat flow. The Bhattacharyya model for fibrous material with fibers perpendicularly oriented the heat flow is presented as: (2)k=[1-1-ka/kf1+2(ka/kf)(vf/va)(1+ka/kf)]kfk = \left[ {1 - {{1 - {k_a}/{k_f}} \over {1 + {{2\left({{k_a}/{k_f}} \right)\left({{v_f}/{v_a}} \right)} \over {\left({1 + {k_a}/{k_f}} \right)}}}}} \right]{k_f}

In these two models, the thermal conductivities and of volume fractions air and fiber should be known. All of the parameters are very easy to be obtained except thermal conductivity of fiber. The thermal conductivities of polyester are collected in one paper for thermal properties study of perpendicular-laid nonwoven fabrics [26]. The values of thermal conductivity of polyester fiber adopted in this study is 0.140 W m⁻¹ K⁻¹ [27].

In the Zwikker and Kosten theory [28], the normal-incidence sound absorption coefficient, α, is determined by the surface characteristic impedance: (3)α=1-|Zsρ0c0-1Zsρ0c0+1|2\alpha = 1 - {\left| {{{{{{Z_s}} \over {{\rho_0}{c_0}}} - 1} \over {{{{Z_s}} \over {{\rho_0}{c_0}}} + 1}}} \right|^2} where ρ₀ is the air density at room temperature, c₀ is the sound speed in air media at room temperature, and Z_s is the surface characteristic impedance: (4)Zs=Zccoth(kl){Z_s} = {Z_c}\coth (kl) where Z_c is the characteristic impedance, k is the complex wavenumber, and l is the material thickness.

The empirical and semi-phenomenological models can estimate the characteristic impedance and complex wavenumber, the surface characteristic impedance and sound absorption coefficient can be further obtained. The procedure of sound absorption coefficient prediction is illustrated in Figure 4. The main difference between Voronina model and Miki model is that the airflow resistivity is required for Miki model and the latter requires porosity. Specific device is necessary to determine the airflow resistivity of nonwoven fabric, e.g., AFD300 AcoustiFlow (The Gesellschaft für Akustikforschung Dresden mbH, Dresden, Germany). It should be noted that airflow resistivity is a key parameter to the widely used impedance (or sound absorption) models, e.g., Delany–Bazley model, Garai–Pompoli model and Komatsu model [19]. Once the airflow resistivity is known, the impedance and sound absorption coefficient can be rapidly predicted based on the empirical models. Besides, the sound absorption performance of high porous nonwoven is generally proportionally correlated with airflow resistivity which means sound absorption performance is anticorrelated with air permeability.

Figure 4

Miki [29] developed a modification on the Delany-Bazley model [30] to generate a more accurate prediction, valid for a broader frequency range. The characteristic impedance and wavenumber in Miki’s model are given by: (5)Zc=ρ0c0(1+0.0699(fσ)-0.632-j0.107(fσ)-0.632){Z_c} = {\rho_0}{c_0}\left({1 + 0.0699{{\left({{f \over \sigma}} \right)}^{- 0.632}} - j0.107{{\left({{f \over \sigma}} \right)}^{- 0.632}}} \right)(6)k=ωc0(0.160(fσ)-0.618-j(1+0.109(fσ)-0.618))k = {\omega \over {{c_0}}}\left({0.160{{\left({{f \over \sigma}} \right)}^{- 0.618}} - j\left({1 + 0.109{{\left({{f \over \sigma}} \right)}^{- 0.618}}} \right)} \right) where f is the frequency, σ is the airflow resistivity, j=-1j = \sqrt {- 1} is the complex number, and ω = 2 πf is the angular frequency. The airflow resistivity can be estimated via numerical method. Some models used to estimate airflow resistivity are presented in Ref. 31. The airflow resistivity of nonwoven fabric is estimated according to one of the Tarnow models [32]: (7)σ=16η(1-ε)d2{ln[(1-ε)-1/2]-0.5ε-0.25ε2}\sigma = {{16\eta (1 - \varepsilon)} \over {{d^2}\{\ln [{{(1 - \varepsilon)}^{- 1/2}}] - 0.5\varepsilon - 0.25{\varepsilon^2}\}}} where η is the air dynamic viscosity, d is the mean fiber diameter, and ε is the porosity.

One model depending on porosity can be alternatively used to estimate sound absorption coefficient [33]. In this model, the characteristic impedance and the complex wavenumber is given by: (8)Zc=ρ0c0(1+Q-jQ){Z_c} = {\rho_0}{c_0}(1 + Q - jQ)(9)k=ωc0(Q(2+Q)1+Q+j(1+Q))k = {\omega \over {{c_0}}}\left({{{Q(2 + Q)} \over {1 + Q}} + j(1 + Q)} \right) where Q, the structural characteristic, is: (10)Q=(1-ε)(1+q0)εd4ηπfρ0Q = {{(1 - \varepsilon)(1 + {q_0})} \over {\varepsilon d}}\sqrt {{{4\eta} \over {\pi f{\rho_0}}}} where q₀ is obtained from the following empirical expression: (11)q0=11+2×104(1-ε)2{q_0} = {1 \over {1 + 2 \times {{10}^4}{{(1 - \varepsilon)}^2}}}

It was stated that this model is valid if the following condition is met, d2πfc0104>0.5d{{2\pi f} \over {{c_0}}}{10^4} > 0.5 , which means the lower frequency limit f_low is: (12)flow=c04πd10-4{f_{low}} = {{{c_0}} \over {4\pi d}}{10^{- 4}}

The lower frequency limit for the cross-laid nonwoven fabric is ~120 Hz in current study. Hence, the comparison between predicted sound absorption and measured values will be conducted in the frequency range of 120 – 6400 Hz.

The measured and predicted thermal conductivities of nonwoven fabrics are listed in Table 2. Each sample has been measured five times on the Alambeta device. Sample B exhibits the lowest thermal conductivity, and sample E has the highest conductivity value. Except Sample E, all of the samples show acceptable standard deviation. This is due to the measurement uncertainties and large thickness of Sample E. The Alambeta device can rapidly test the thermal properties of fibrous materials by simulating the temperature of human skin. But the upper and lower heat flow sensors are open and free during test, so free convection and heat dissipation could occur at the edge of the specimen, especially for thick and high porous specimen.

From Table 3, it can be seen that predicted values have significant difference compared with the measured values. Moreover, the predicted values from two models are very close. In order to clearly compare the measured and predicted values and analyze the reason of nearly same predicted values, the thermal conductivities of nonwoven fabrics and the predicted thermal conductivities when the porosity ranges from 0 to 100% and from 90% to 100% are illustrated in Figure 5. The predicted value is based on the 0.140 W m⁻¹ K⁻¹ fiber thermal conductivity. It can be seen that the two models show very similar predictions when the sample has low porosity (i.e. < 10%) and high porosity (i.e. > 80%). Although Bhattacharyya model has higher predictions compared with Bogaty mode, the mean difference for these two models are 14.69% in the whole porosity range. The porosities of most nonwoven fabric are usually higher than 90%. Also, the predicted thermal conductivities are respectively around 0.0305 W m⁻¹ K⁻¹ and 0.0285 W m⁻¹ K⁻¹ for Bogaty model and Bhattacharyya model when the porosity is 90%, and the change of thermal conductivity is insignificant in the porosity range of 98–100%. If the porosity is between 10% and 80% the fiber volume fraction plays an important role on the thermal conductivity in these two models. But in current study, porosity of the samples ranges from 98.620% to 99.389%. Hence, the predicted values for the nonwoven fabrics are very close and lower than the measured values. It can be concluded that the Bogaty and Bhattacharyya models are not suitable for high porous nonwoven fabrics.

Figure 5

The normal incidence sound absorption coefficient of nonwoven fabric is showed in Figure 6. The sound absorption is determined as a function of frequency. The measured data in the low frequencies of 50–1600 Hz (using the Type 4206 large tube) and the high frequencies of 500–6400 Hz (using the Type 4206 small tube) were combined together to form the curves. Samples A, B, C and D have low sound absorption coefficient in low frequencies. The highest absorption coefficient of these four samples is around 0.6. Sample E exhibits a relatively good sound absorption performance. For small thickness samples, the sound absorption coefficient increases with the increase in frequency. However, sound absorption coefficient of thick samples show fluctuations with increasing frequency by reason of resonance phenomena. This can explain the behavior of the sound absorption curves in Figure 6. In addition, Sample B and Sample C have similar absorption performance at the frequency lower then approximate 3500 Hz but Sample B exhibits better performance in the high frequency range. This is due to the thickness and density differences. Sample B has higher density but smaller thickness compared with Sample C. Thickness is more significant at low frequencies and higher density usually results in higher airflow resistivity and lower air permeability.

Figure 6

The comparisons between measured sound absorption and predicted value of each sample are demonstrated in Figure 7. It is hard to conclude that which model is more suitable for nonwoven fabric by observation on each sample. The Voronina model shows a good prediction for Sample A, while the Miki model has a good agreement on Sample C. Nevertheless, both Voronina and Miki models under- or overestimate the measured values of Samples B, D and E. The overestimation on prediction of Sample E is most obvious. To numerically investigate the accuracy of Voronina and Miki models, the relative prediction error Δ was determined according to the following equation: (13)Δ=|αm¯-αp¯|αm¯×100%\Delta = {{\left| {\overline {{\alpha_m}} - \overline {{\alpha_p}}} \right|} \over {\overline {{\alpha_m}}}} \times 100\% where αm¯\overline {{\alpha_m}} and αp¯\overline {{\alpha_p}} are respectively the mean value of measured and predicted sound absorption coefficient in the frequency range of 120 – 6400 Hz. The mean relative error is the average value of five samples. Lower relative prediction error means the prediction is more accurate.

Figure 7

The relative error of Miki model is in the range of 2.971 – 24.055%. The prediction of Voronina model is more stable than Miki model. The most accurate prediction of Miki model is occurred on Sample C with the lowest relative error, while the errors for Samples B and E are over than 20%. Moreover, the mean relative error of Voronina model is smaller than the value of Miki model. It has been reported that Miki model is more suitable for multi-component polyester nonwoven fabric [16], but the Voronina model is more accurate than Miki model in this study. This can be attributed to the possible error on airflow resistivity estimation. As stated above, the airflow resistivity is critical for Miki model. One Tarnow model was adopted to estimate the airflow resistivity of nonwoven fabric. Although the Tarnow model has been proven that it is reliable for fibrous material, it is not 100% accurate for all types of nonwoven fabric. Additionally, the mean relative error of Voronina model is 13.14% which is acceptable for high porous nonwoven fabric.