Full-scale experimental study on the critical Rayleigh number for the onset of internal natural convection inside a horizontal insulation layer of blown glass wool

Abstract

Glass wool is a common high-performance insulation material employed in buildings. The effective thermal conductivity of such materials with large open-pore structures can drastically increase if internal natural convection takes place inside the latter. This can occur in the case of a thick insulation layer with high porosity (low density) and subjected to a large temperature gradient. Such conditions can be met for blown glass wool insulation during winter in cold-climate regions. Consequently, the accurate assessment of the criteria determining the onset of internal natural convection in porous insulation is fundamental to optimizing the thermal performance of the latter. However, the numerical simulation of such phenomena is very complex and does not yield reliable results. Experimental investigations in realistic conditions are thus necessary. This article reports the findings of a full-scale experimental replication study on the onset of internal natural convection inside a horizontal insulation layer of blown glass wool with joists. The insulation layer is heated from below with a closed boundary enclosure at the bottom and an open boundary at the top. The thickness of the insulation layer is set to 30 cm or 60 cm, with a glass wool density ranging from 11.9 to 19.7 kg/m³, a temperature difference spanning from 5.2 to 59.5 K, and an average temperature ranging from −5.3°C to 26.5°C. The onset of the internal natural convection is identified by the critical Rayleigh number above which the modified Nusselt number (Nu + 1) increases with increasing Rayleigh number. For this configuration, the critical Rayleigh number is found to be situated between 13 and 15. These results are in good agreement with the recommendations from standards and other similar experimental studies on this topic. This study provides additional guidance for insulation design in cold-climate buildings.

Graphical abstract

Keywords

full-scale experimental investigations critical Rayleigh number internal natural convection heat transfer effective thermal conductivity porous insulation material blown glass wool

Highlights

Large-scale experimental investigations in a controlled laboratory environment.

Horizontal porous insulation layer of blown glass wool: 30-60 cm; with joists; heated from the bottom.

Insulation density: 11.9-19.7 kg/m³; temperature difference: 5.2-59.5 K.

Critical Rayleigh number for the onset of internal natural convection: 13-15.

Introduction

Motivations

Improvement of the energy efficiency of the building stock has been clearly identified as one of the key solutions to address the pressing sustainability challenges concerning the reduction of CO₂ emissions and energy demand, together with improving indoor environmental quality and occupants’ well-being (Muddu et al., 2021; The European Commission, 2011; The North American Insulation Manufacturers Association (NAIMA), 1996). To achieve that, minimizing heat losses through the building envelope by properly insulating the latter is crucial, especially in regions with a large temperature difference between the indoor and outdoor environments. To that matter, the correct understanding of the effective thermal conductivity of insulation materials is thus essential.

A large share of the building insulation products employed today are porous media made of fibrous material. Although designed to have the largest thermal resistance possible (i.e. the smallest thermal conductivity possible), a key parameter at play in their heat transfer characteristics is often overlooked: the internal natural convection (INC) within those porous materials. Indeed, it is often assumed that porous media made of fibers are not permeable enough (to the air) for INC to occur. If this supposition holds for normal conditions of buildings located in temperate climate zones, this is not the case for winter conditions in cold-climate regions like Scandinavia, Northern Europe, Eastern Europe, Canada, the USA, and the Northern part of Asia, where the temperature differences across the insulation layer can be greater than 60 K. In addition, such large temperature differences between indoor and outdoor environments are typically associated with thick insulation layers. These two elements put together are very favorable for INC to occur.

Glass wool is one of the most common high-performance insulation materials employed in the construction industry. The effective¹ thermal conductivity of such porous materials with large open-pore structures can drastically increase (e.g. double) if internal natural convection takes place inside the latter. This can occur in the case of a thick insulation layer with high porosity (low density) and subjected to a large temperature gradient. Such conditions can be met with blown glass wool insulation during winter in cold climates.² Consequently, the accurate assessment of the criteria determining the onset of INC in porous insulation is fundamental to optimizing the thermal performance of the latter.

Theoretical background

To determine the share of INC in the heat transfer mechanism occurring in porous media, it is necessary to decouple the former from other thermal transfer processes. Inside porous thermal insulations, INC is often considered negligible, and thermal transfer occurs through conductive and radiative transfers. To determine if INC is present, the heat flow without convection is measured and compared to the total heat flow measured in the conditions for which INC occurrence is unknown. If the total heat flow is larger than the heat flow without convection, INC is present. If the total heat flow is the same, there is no INC.

To investigate INC presence and its intensity, two non-dimensional numbers are typically used: the Rayleigh number (Ra) and the Nusselt number (Nu). The Rayleigh number³ is the ratio between convection-driving forces over dissipative forces. In a porous medium filled with air (here, a porous insulation material), the Rayleigh number is written as follows (International Organization for Standardization (ISO), 2007; Nield and Bejan, 2017; Silberstein et al., 1990; Wahlgren, 2007):

Ra = g \frac{β_{a} ρ_{a} c_{a}}{ν_{a}} \frac{δ_{i} K_{i} Δ θ_{i}}{λ_{i}}

With $g [m s^{- 2}]$ the acceleration due to the Earth’s gravity near its surface, $β_{a} [K^{- 1}]$ the thermal expansion coefficient of air, $ρ_{a} [kg m^{- 3}]$ the density of air, $c_{p} a [J k g^{- 1} K^{- 1}]$ the isobaric specific heat capacity of air, and $ν_{a} [m^{2} s^{- 1}]$ the kinematic viscosity of air, $δ_{i} [m]$ the thickness of the insulation layer, $K_{i} [m^{2}]$ the effective air permeability of the insulation layer, $λ_{i} [W m^{- 2} K^{- 1}]$ the thermal conductivity of the insulation layer, and $Δ θ_{i} [K]$ the temperature difference across the insulation layer.

A key focus point when discussing natural convection is the critical Rayleigh number ${Ra}_{c}$ : The value of the Rayleigh number for which INC appears. In other words, there is no INC for $Ra < {Ra}_{c}$ , and there is an INC for $Ra > {Ra}_{c}$ . In the context of porous insulation, the question about whether the thermal performance of the latter is optimal boils down to knowing if the Rayleigh number is below ${Ra}_{c}$ , indicating that no INC occurs.

Computing the Rayleigh number for an attic’s horizontal porous insulation layer is rather straightforward. However, determining the presence of INC in this insulation layer requires estimating ${Ra}_{c}$ . The latter can be computed theoretically for ideal porous medium conditions (Chandrasekhar, 1961; Nield and Bejan, 2017). Unfortunately, real-world attic configurations deviate significantly from ideal theoretical scenarios, as there are typically wood joists placed inside the insulation layer, wind-driven forced convection can occur at the top open insulation surface, and the porous insulation layer is neither isotropic nor homogeneous. Therefore, the theoretical ${Ra}_{c}$ cannot be considered a realistic threshold to determine the presence of INC in the porous insulation layer of an attic.

The second key non-dimensional number, the Nusselt number, represents the ratio between the convective heat flux and conductive heat flux:

Nu = \frac{ϕ_{convective}}{ϕ_{conductive}}

A modified notation of the Nusselt number is also commonly used in scientific literature (Silberstein et al., 1990):

Nu + 1 = \frac{ϕ_{total}}{ϕ_{conductive}}

A common approximation in fibrous material is to consider that the “conductive” thermal conductivity (associated with $ϕ_{conductive}$ ) is the sum of a purely conductive part (solid-solid conduction from fibers plus conduction from the air) and a radiative part. This approximation is used in the present study. Therefore, the radiative heat transfer is not neglected; it is linearized and included in the conductive part. Consequently, $ϕ_{total} = ϕ_{conductive} + ϕ_{convective}$ . This notation is very convenient because the modified Nusselt number $Nu + 1 = 1$ when there is no INC and $ϕ_{total} = ϕ_{conductive}$ , and increases continuously ( $Nu + 1 > 1$ ) when INC begins, that is, when $Ra > {Ra}_{c}$ (see Figure 1).

Figure 1.

Theoretical correlation between Rayleigh number and modified Nusselt number characterizing the onset of internal natural convection in a porous medium with connected and open pore structures.

It should be noted that Figure 1 is only illustrative: the critical Rayleigh number depends on numerous parameters, and the evolution of the modified Nusselt number is not necessarily linear above the critical Rayleigh number, especially for very large Rayleigh numbers. Although the overall relationship between the Nusselt number and the Rayleigh number generally follows this characteristic trend for all porous media subjected to internal natural convection, the slope and shape of the Nusselt number increase beyond the critical Rayleigh number can vary significantly depending on the system configuration and the properties of the porous medium.

State of the art

A few scientific studies have investigated the phenomenon of natural convection in horizontal porous insulation layers for typical northern European attic geometries. Wahlgren (2007) reviewed the work on this topic that was published up to 2007. For small-scale experimental setups (horizontal insulation cross-section smaller than 3 × 3 m²), Langlais et al. (1990) found that convection occurs as soon as the thermal gradient appears, but it only becomes significant when the Rayleigh number is close to the critical value of 27. Serkitjis (1995) estimated that the critical Rayleigh is at 20 when the top surface of an insulation layer of polystyrene pellets is permeable and 40 when it is impermeable. In another study, Serkitjis et al. (2001) observed that the critical Rayleigh drops to 10 for a mineral wool insulation layer, and 8 in the presence of joists. Silberstein et al. (1990) found a critical Rayleigh value of 15, and a negligible influence of airflow above the top insulation surface, as long as the air velocity is below 0.5 m/s. As expected, it was also found that the thermal resistance of the insulation layer decreases with increasing air velocity.

In the case of large-scale experimental setups, several studies from Wahlgren show that INC arises for $Ra$ above 22 (Wahlgren, 2001, 2002, 2004). Wilkes et al. (1991) suggested that the critical $Ra$ is between 13 and 20. Gullbrekken et al. (2017) investigated the influence of the insulation layer’s angle of inclination on the onset of INC. They reported that no INC was observed in the investigated horizontal configuration cases for $Ra$ below 8.3, whereas INC can occur for inclined configurations with similar low-Rayleigh conditions. On the other hand, Kivioja and Vinha (2020) observed that INC appears for $Ra$ lower than 5 in a horizontal setup. However, these results also indicate that the Nusselt number does not increase with increasing Rayleigh number above the ${Ra}_{c}$ , which is unexpected as it is in total opposition with both theory and observations on the convection phenomenon for both homogeneous and porous media (Chandrasekhar, 1961; Nield and Bejan, 2017). Overall, experimental investigations indicate that the critical Rayleigh number may be sensitive to insulation-related characteristics (e.g. density, air permeability, thermal conductivity) and system configuration (e.g. geometry, orientation, joists’ properties), despite the use of a non-dimensional formulation that is theoretically expected to reduce or eliminate dependence on those parameters. This suggests that standard non-dimensional scaling may not fully capture all relevant physical effects, potentially due to differences in porous structure, boundary conditions, or system configuration, which can influence heat and mass flow. To the best of the authors’ knowledge, this discrepancy has not been explicitly discussed in the literature.

On the numerical investigation side, 2D simulations from Wahlgren (2004) and Ciucasu et al. (2005) suggest a ${Ra}_{c}$ between 24–27 and 28. These results were corroborated by large-scale experiments. Wahlgren (2005) used 3D Computational Fluid Dynamics (CFD) simulations to study the influence of attic geometry and insulation materials on the variation of the INC onset. Results indicate that the critical $Ra$ varies greatly and ranges from 9 to 25. Delmas and Arquis (1995) and Delmas and Wilkes (1992) studied the influence of joist presence in the insulation layer. They found that the ${Ra}_{c}$ is lowered when joists are present. Conversely, for high- $Ra$ conditions, the joist can become an obstacle to fluid motion and thus decrease the intensity of INC.

In general, the aforementioned experimental and numerical investigations that try to assess the critical $Ra$ indicate a wide range of possible values. Nevertheless, most studies point toward a critical $Ra$ above 10, and often larger than 15. Accordingly, the European standard ISO 140456:2007 regulating the design of insulation in attics using loose-fill product recommends that the $Ra$ of the attic configuration should not be greater than 15.

Novelty and contributions of the current study

The study of the critical Rayleigh number for the onset of internal natural convection in a large layer of porous insulation is a complex endeavor that cannot be tackled with numerical simulations only. Several experimental and numerical investigations have been previously conducted on this topic, and many point in a certain direction, which is followed by standards. Nonetheless, there is no strong scientific consensus yet: the range of possible values for ${Ra}_{c}$ is quite broad, and the influence of certain material properties is not clear. There is thus a need for replication studies and laboratory tests on full-scale systems with dimensions and boundary conditions that are closer to those of the building application.

In that context, this article reports and discusses the findings of a full-scale experimental study on the onset of internal natural convection inside a horizontal insulation layer of blown glass wool with joists, heated from below. To this day, this experimental test is the largest of its kind, with dimensions, configurations, insulation characteristics, and boundary conditions that are representative of real-world situations for which blown glass wool is employed to insulate attics in cold winter climates.

The present study aims to provide a well-documented and in-depth replication large-scale investigation of the ${Ra}_{c}$ for the onset of INC in blown glass wool with an extensive variation of key parameters (i.e. blown glass wool product type, insulation thickness, insulation density, temperature gradient, and average temperature of the insulation layer). The systematic calculation of the Nusselt number for a large range of Rayleigh number (0–37) with an uncertainty estimate is based on the analysis of more than 2000 hours of curated large-scale experimental data. For the sake of transparency and reproducibility, all measurement data collected during this study is published in open access.

The main research questions of the present study are as follows:

What is the critical Rayleigh number for the onset of internal natural convection in a thick horizontal blown glass wool insulation layer with joists?

Is there evidence for the presence of internal natural convection at low Rayleigh numbers (below 10)?

Is there a difference between different blown glass wool insulations regarding the critical Rayleigh number?

Following the Introduction section, the tested insulation materials are presented. The methodology for the measurement and uncertainty analysis of all needed parameters to compute the Nusselt number as a function of the Rayleigh number is then explained in detail. The resulting profiles of $Nu + 1$ as a function of $Ra$ for the different insulation products are then presented and discussed. Finally, the article closes with key conclusions and suggestions for future investigations on this topic of investigations.

Methodology and materials

This methodology section provides a concise overview of the approach used to determine the critical Rayleigh number at which internal natural convection occurs within porous insulation layers of blown glass wool. A schematic overview of the full methodology is presented in Figure 2. The different procedures, setups, and methods are presented in brief in the following subsections, while a detailed description of the former is provided in the Appendices 1 –10 for clarity and reproducibility. The analysis relies on experimentally assessing the Nusselt and Rayleigh numbers for six different blown glass wool insulation products with varying density and thermal conductivity, and subjected to a large range of temperature boundary conditions.

Figure 2.

Schematic overview of the full methodology used in this study to determine the critical Rayleigh number at which internal natural convection occurs within porous insulation layers of blown glass wool.

Description of the tested insulation materials

The main investigations of this article concern blown glass wool insulation products that are commercially available in Europe and typically used in the Nordic countries to insulate building attics with a glass wool blowing injection method (see Appendix 1).

Three different blown glass wool insulation products are tested: here denominated “Blown Glass Wool A, B, and C,” respectively. The Blown Glass Wool A is tested at four different blowing densities. There are thus a total of six distinct insulation cases covering a material density ranging from 11.9 to 19.7 kg/m³, and a thermal conductivity ranging from 0.038 to 0.046 W/m.K (at 10°C for standard tests in a guarded hot plate apparatus), which encompasses all typical applications for blown glass wool in the building industry. These glass wool products come from different manufacturing plants and countries. Therefore, minor variations in the glass wool flakes’ shape and structure are expected when blown. Moreover, changing the operator (technician blowing the wool), the blowing equipment, or the equipment’s settings can also alter the micro-structure of the glass wool insulation layer. To ensure replicability and comparability, all six glass wool insulation cases were blown by the same operator with the same blowing equipment, using the same operational settings (except for the blowing density).

In addition, this experimental study includes the testing of two reference insulation products (“Expanded Polystyrene” and “Glass Wool Mat,” respectively) with negligible effective air permeability and, therefore, not experiencing any INC phenomena. These reference insulation products are crucial to assess the accuracy of the experimental setup and serve as reference points for conditions without any risks of INC.

Methodology for the determination of the critical Rayleigh number

As mentioned above, the main goal of the present study is to identify the critical Ra corresponding to the onset of INC inside a thick layer of blown glass wool insulation. As illustrated in Figure 1, the critical Ra can be identified by observing the correlation between the modified Nusselt number $Nu + 1$ and $Ra$ .

Since $Nu + 1$ is the ratio between the total heat transfer by conduction with potential INC and the reference heat transfer by conduction only (without INC), one has to estimate these two components independently. The total heat transfer by conduction with potential INC is directly measured within a large guarded hot box (LGHB) setup described below. The heat transfer by conduction only without INC is estimated from the thermal conductivity without INC and the boundary conditions of the LGHB experiments. The former is directly estimated from small-scale guarded hot plate (GHP) measurements with conditions ensuring that there is no INC (no joists, limited insulation layer thickness, downward heat flow, and limited temperature gradient). These GHP measurements are then corrected for deviation in insulation density and temperature between the full-scale (LGHB) and the small-scale (GHP) measurements with calibrated numerical models. All experiments and measurements are conducted with a steady-state thermodynamic regime and boundary conditions.

The estimation of $Ra$ for the different tests in the LGHB is determined from air properties (thermal expansion coefficient, density, isobaric specific heat capacity, and kinematic viscosity for air at atmospheric pressure and with 50% relative humidity⁴) that are linearly interpolated from tabulated data (Boukhriss et al., 2013) to account for temperature dependence (see Appendix 2), and insulation layer properties (thickness, effective air permeability, thermal conductivity, and temperature difference) that are directly measured in this study with state-of-the-art methods. These methods are presented in the following sub-sections.

In some cases, the initial plateau of $Nu + 1$ at low Ra is not equal to 1 (Silberstein et al., 1990). This is because the estimate of the heat transfer by conduction without INC might not be estimated in the exact same conditions as the total heat transfer by conduction with INC, as those are performed in two different setups, and because the blowing process has significant intrinsic variabilities (further discussion on that matter can be found at the end of this article). However, this bias is not problematic as it is applied equally to all reference heat transfer by conduction without INC estimates. For the sake of clarity in the comparison of the different test cases, the results of $Nu + 1$ are normalized by the plateau value of $Nu + 1$ at low Ra (see Figure 3 for an illustrative example).

Figure 3.

Normalization of experimental results: from modified Nusselt number ( $Nu + 1$ ) to the normalized modified Nusselt number ( $Nu + 1^{*}$ ). This is for illustrative purposes only. This figure does not contain real measurement data.

Large-scale measurement of the total heat transfer by conduction with internal natural convection

The total heat transfer by conduction with (potentially) INC is directly measured in a full-scale blown glass wool insulation layer installed inside a large guarded hot box. As shown in Figure 4, a standard LGHB setup is modified to accommodate a large horizontal wooden floor (3.60 × 4.53 m of surface area) with a metering zone underneath, the insulation above (up to 60 cm in thickness), the cold zone above the insulation layer, and a guarded zone all around the metering zone and the insulation layer.

Figure 4.

Overview schematic (side view) of the large guarded hot box setup for the measurement of the total heat transfer in the full-scale insulation layer. The placement of the different elements is only indicative.

The temperature in the metering room is maintained stable at 22°C or 30°C by regulating the heating power of an electric heating element (0–100%) with a tuned PI controller, and a mixing fan (20%–100%). A dedicated air handling unit maintains the guarded zone at the same temperature as the metering zone. Therefore, all heat losses from the metering zone go through the wooden floor and the insulation layer above, and the heating power dissipated inside the metering zone corresponds to the heat flux through the insulation layer. The cold zone is cooled down at a temperature ranging from −31 °C to 23°C by a large compressor cooling unit and mixing fans. The cooling unit is controlled by an ON/OFF controller with a dead band of 1°C. A fabric baffle is placed in front of the main mixing fan on the evaporator of the cooling system to avoid high air velocities above the insulation layer’s top surface. An additional mixing fan connected to a ventilation sleeve distributes the cold air from the cooling unit chamber to the cold zone part above the insulation layer with low air velocities. Calibrated hot-sphere anemometers are placed above the insulation layer to measure the air velocities during the tests. The recorded average air velocity above the insulation layer is 0.012 m/s with a standard deviation of 0.017 m/s. The relative humidity in the cold zone above the insulation layer (cold side) is stable for all tests and ranges from 55% to 80%. The relative humidity at the bottom of the insulation layer (warm side) is stable for all tests and ranges from 30% to 50%. There is no active humidity control system in the experimental setup: the relative humidity is only monitored but not adjusted. The variation of the relative humidity is due to the change of temperature, but the absolute humidity content in the insulation layer and the cold zone remains constant. Moreover, the influence of moisture on thermal transfer is negligible as glass properties do not vary with ambient air relative humidity and air properties variations are negligible below 30°C (Boukhriss et al., 2013). This range of temperature, air speed, and relative humidity boundary conditions is commonly observed in attics of residential buildings across Nordic countries, which are the focus of this study.

The LGHB configuration of the insulation layer on the wooden floor is meant to be as close as possible to a realistic configuration of an attic in Nordic residential buildings (typically a single-family house) that would be renovated (upgrade of the insulation class to improve thermal performance of the building envelope) with the blown glass wool injection method. The wooden floor is made of large interlocking wooden slabs (2 cm thick oriented strand board with interlocking slits; thermal conductivity of 0.23 W/m.K). All junctions, holes, cracks, and screw fixations are sealed with acrylic seal and durable duct tape to ensure maximum airtightness between the insulation layer and the metering zone through the wooden floor. Five wooden beams (rectangular section of 43 × 95 mm, length of 4.53 m) are placed horizontally on the wooden floor to emulate the presence of joists (typically placed in attics to ensure structural stability). The side-to-side distance between the joists ranges between 835 and 855 mm. The top surface of the insulation layer is open to the cold zone (no cover). A more detailed description of the LGHB setup can be found in Appendix 3.

Because the total heat transfer to be measured can be very small in the case of a large insulation layer and a small temperature difference between the cold and metering zones, it is very important to eliminate all parasitic and residual heat losses between the metering zone and the guarded zone or the surrounding laboratory environment in which the LGHB is located. The residual heat losses between the metering zone and the guarded zone are estimated from the temperature difference measured between the surface of each wall in the metering zone and the corresponding surface on the other side of the 23 cm insulation inside the ventilated guarded zone (for all five surfaces facing the guarded zone: four walls and the floor). Moreover, parasitic heat losses between the metering zone and the surrounding laboratory environment (direct heat transfer through the wire-connection hatch) are estimated during the calibration phase. The latter consists in maintaining the metering zone, the guarded zone, and the cold zone at the same temperature above that of the laboratory. The residual heat losses are thus estimated as a function of the temperature difference between the metering zone and the laboratory and the heating power demand of the metering zone (the guarded zone and the cold zone are heated by independent heating systems).

In addition, parasitic heat losses due to the presence of joists in the insulation layer (part of the insulation layer is occupied by joist wooden beams with a thermal conductivity that is much larger than that of the surrounding insulation) are estimated with 3D numerical simulations. These simulations are carried out with COMSOL Multiphysics stationary models. Temperature boundary conditions are imposed at the top surface of the insulation layer, at the top surface of the metering zone, and at the inner-facing internal walls of the guarded zones, to replicate the temperature measurements of the corresponding LGHB experiments. The insulation layer is modeled as a homogeneous and isotropic medium with a thermal conductivity corresponding to the one estimated from the LGHB experiments without the simulation-based parasitic heat loss corrections. For each case, a simulation with joists and one without joists is run. Heat fluxes through the different sides of the insulation layer are then compared to estimate the impact of the joists on the overall heat flow through the insulation layer.

Besides the joist effect estimation, the COMSOL simulations are used to assess supplementary heat losses or gains on the lateral sides of the insulation layer (toward the guarded zone). Indeed, the temperature gradient within the thickness of the insulation layer can be different from that of the adjacent walls of the guarded zone, which are slightly heated up by the ventilated cavity of the guarded zone that is maintained at the same temperature as the metering zone.

One should note that the COMSOL simulation-based estimate of parasitic heat losses does not account for potential local temperature anomalies in the boundary conditions, or small-scale blown wool structure disruptions at the LGHB’s corners and joists’ junctions. The latter could induce residual small-scale and localized internal convection cells, even at a very low Ra. The overall parasitic and residual heat losses compensation (metering zone heating power measurement adjustments) accounts for around 5% of the measured gross heat injection in the metering zone, and typically range from 1% to 10%, but can reach more than 50% in the case of a very low temperature gradient within a large insulation layer, and a large temperature difference with the surrounding laboratory.

A blower-door test was performed to verify the airtightness of the metering zone and ensure that no major air leakage could occur between the metering zone and the guarded zone, or to the insulation layer through the wooden floor. The blower-door test indicated that the metering zone was very air-tight. Moreover, no significant pressure difference was measured between the metering zone and the cold zone or the metering zone and the guarded zone.

The temperature measurements within the experimental setup are performed with resistance temperature detectors (Pt100 with 4-wire configuration) connected to National Instruments NI-9216 8-channel Pt100 C Series temperature input modules. The 4-wire Pt100 temperature sensors are preferred to thermocouples due to their durability, accuracy, long-term stability, and lower sensitivity to electrical noise and static charges. However, the cable of the Pt100 sensors is significantly larger than that of thermocouples, which increases the risk of disturbance of the blown glass wool when set in place. A compromise has to be found between the number of temperature sensors within the insulation layer and the level of detail for monitoring the temperature gradient. Moreover, great care is taken in distributing the different sensors within the insulation and optimizing cable management to limit the disruption of the blown glass wool layer. All temperature sensors are calibrated against a reference thermometer ASL F200 (Johra, 2019a). In addition to the temperature sensors placed on each side of the guarded zone walls, two sensors measure the dry-bulb temperature in the metering zone, four sensors measure the bottom surface temperature of the wooden floor, four sensors measure the temperature at the bottom of the insulation layer, four sensors measure the temperature at the top of the insulation layer, and two sensors measure the dry-bulb temperature in the cold zone. In addition, temperature sensors are placed every 5 cm within the thickness of the insulation layer to verify the linearity of the temperature profile during the experiments. The four temperature sensors at the top of the insulation layer and the four temperature sensors at the bottom of the insulation layer are used to calculate the temperature difference across the entire insulation layer. The temperature sensors embedded in the insulation layers are firmly fixed using thin support wires to ensure a stable and well-defined position. Their vertical location is determined by using a rigid ruler during installation. Sensors located near the top of the insulation layer are placed slightly below the upper surface and are, therefore, covered by a layer of glass wool. Consequently, all temperature sensors within the insulation are shielded from direct long-wave radiative heat exchange with the cold-zone walls. To assess the sensitivity of the results to sensor placement, all calculations were also repeated with sensors located 5 cm below the top surface of the insulation layer; these calculations yielded similar results. The detailed placement of the temperature sensors can be found in Appendix 4.

The relative humidity in the insulation layer and in the cold zone is measured with Sensirion SHT75 – Digital Humidity & Temperature Sensors. The humidity sensors are calibrated with reference vials of set relative humidity.

The heating power dissipated by the heating element and the mixing fan in the metering zone is measured with two independent power meters: a NORMA AC Power Analyzer D 5255 S, and a power quality measurement setup composed of a National Instruments NI 9225 AI 300 Vrms C Series module and a NI 9227 AI 5 Arms C Series module mounted on a NI CompactDAQ cDAQ-9174. The two power meters are calibrated against a reference voltmeter, ampere meters, and a power-factor meter for the entire range of electrical power measurement in the LGHB setup. The discrepancy between the electrical power measured by the NORMA AC Power Analyzer and the NI CompactDAQ setup is always below 0.1%.

The total heat transfer through the insulation layer in the LGHB setup is measured in steady-state conditions. After changing the temperature boundary conditions in the cold zone, metering zone, and guarded zone, the steady state is reached after 48 hours. After the stabilization period (when the steady state is reached), the measurement of the total heat transfer is typically carried out for 15–30 hours. Some measurement recordings are shorter or longer due to technical limitations.

The temperature in the metering zone and within the insulation layer is very stable over time in most cases, and marginally stable in a few cases with a very high temperature gradient. During the LGHB tests, the temperature profile within the insulation layer is relatively linear, indicating that the whole system is at steady state. It should be acknowledged that, if the temperature sensors’ placement is adequate (aligned along a narrow vertical section within the ascending or descending convection cell air flow), it is possible to directly observe INC as it disrupts the linearity of the vertical temperature profile. However, in the present study, the placement of temperature sensors is made to minimize disturbances in the blown wool structure (spreading them horizontally). It is thus not possible to perform detailed temperature gradient measurements within a convection cell associated with INC. The non-linearities in the temperature profiles are thus attributable to a combination of sensors’ placement, local blown wool structural inhomogeneities, and convection cells (if any). One can find the temperature profiles within the insulation layer, as well as the stability of the temperature and electrical power measurements for the different tests, in Appendix 5.

Prior to testing the blown glass wool products, five reference tests have been conducted on expanded polystyrene and glass wool mat insulation, for which no INC is possible. After applying the different parasitic heat losses and joist effect compensations described above, the measured thermal conductivity in the LGHB for these cases only deviates by 1%–7% from that of the GHP measurements (for identical average temperature and bulk density). These minor deviations are within the uncertainty margin of the respective measurement methods. These preliminary tests on reference insulation cases demonstrate the validity of the LGHB measurement method described in this sub-section and the correctness of the parasitic and residual heat losses adjustment.

One can find in the summary Table 1 an overview of the different experimental tests conducted in the LGHB setup to measure the total heat transfer in full-scale insulation layers. For each case, a large range of Rayleigh numbers is explored by maximizing the temperature difference in the LGHB experiments. However, the maximum temperature difference of 60 K could not always be reached, due to technical limitations. Supplementary overview tables with key characteristics of the different tests can be found in Appendix 6.

Table 1.

Overview of the experimental tests conducted in the LGHB setup to measure the total heat transfer in full-scale insulation layers.

Case denomination	Insulation thickness (cm)	Bulk density (kg/m³)	Number of tests	Range of temperature difference (K)	Range of Rayleigh number (-)	Heat flow through insulation (W)
Expanded Polystyrene–Reference	20 ; 30	14.9	4	26.8–34.9	0	60.7–115.0
Glass Wool Mat–Reference	26.5	20.2	1	22.5	0.6	50.9
Blown Glass Wool A–Case 1	31.31	13.4	5	7.9–32.4	1.9–10.0	25.3–108.2
Blown Glass Wool A–Case 2	60.17	15.5	12	7.9–59.5	2.7–30.7	39.2–140.8
Blown Glass Wool A–Case 3	30.77	19.7	16	5.2–51.0	0.5–7.1	19.7–134.5
Blown Glass Wool A–Case 4	60.80	12.9	14	6.9–47.6	3.3–31.7	11.3–88.2
Blown Glass Wool B–Case 5	31.21	11.9	16	6.6–47.6	1.6–17.9	23.9–170.2
Blown Glass Wool C–Case 6	60.78	12.0	16	6.2–46.0	3.0–37.4	9.0–114.0

Measurement of the insulation density and thickness in the large guarded hot box

The density of the blown glass wool layer in the LGHB setup is calculated from the total volume of the insulation layer and its mass. The volume of the joists and the effective thickness of the insulation layer are accounted for in the evaluation of the total volume of the insulation layer. At the end of each measurement round (specific case), the thickness of the insulation layer is measured with a rigid metallic ruler in 100 points (regular grid measurements, as shown in Appendix 7).

The mass of the insulation layer is measured by weighing all the blown glass wool when removed from the LGHB setup at the end of a measurement case.

Determination of the reference insulation thermal conductivity without internal natural convection

For the calculation of the $Nu + 1$ number, the reference heat transfer by conduction only (without INC) is computed from the thermal conductivity without INC in the insulation layer. The latter is determined from GHP measurements on the same insulation products as those tested in the LGHB setup. The GHP measurements are performed at steady-state conditions on top-heated (downward heat flow) cubical samples (50 × 50 × 12 cm) at 10°C, 25°C, and 40°C, with a temperature difference of 15 K, using a Guarded Hot Plate apparatus EP500 (Johra, 2019b). In these conditions, this state-of-the-art measurement method on meso-scale insulation sample ensures very low Rayleigh numbers ( $0.5 < Ra < 1.3$ ) that are largely below theoretical and experimental estimates of the critical Ra for the onset of INC. One can thus confidently assume that the GHP effective thermal conductivity measurements of the blown glass wool are without any INC component.

The results of the GHP measurements are presented in Figure 5, together with Heat Flow Meter (HFM) measurement results obtained from external sources of information. One can observe that the results of the current study for the different blown glass wool insulation products are in very good agreement with those of the other independent data sources.

Figure 5.

Thermal conductivity measurements (no internal natural convection) of tested materials: Standard test at meso scale with a guarded hot plate apparatus; Average temperature 10°C; $0.5 < Ra < 1.3$ (very low $Ra$ , way below the theoretical estimates of ${Ra}_{c}$ ). The figure includes heat flow meter measurement results obtained from external sources of information. The error bars represent the 3σ (99.7% confidence interval) uncertainty range.

Since there are some differences in the characteristics of the insulation products between the GHP tests and the corresponding cases of the LGHB experiments (different insulation temperature and bulk density), the thermal conductivity measurements of the GHP are adjusted to the corresponding LGHB cases’ densities and temperatures with a numerical model. One can see in Appendix 8 that, given the uncertainty of the measurements, the numerical models used for adjusting the reference thermal conductivity (without INC) to different temperatures are in good agreement with the GHP results.

Measurement of insulation effective air permeability

The effective air permeability of the blown glass wool products is measured in a meso-scale horizontal air permeameter (insulation layer of dimensions 50 × 50 × 11–23 cm) that has been designed and calibrated to study porous insulation materials (Johra, 2023). These measurements are performed at 21°C and 50% relative humidity (the laboratory environment in which the LGHB is located). The results of the effective air permeability measurements are presented in Figure 6, together with standard air permeability test results obtained from external sources of information. One can observe that the results of the current study for the different blown glass wool insulation products are in very good agreement with those of the other independent data sources. These effective air permeability measurement results are in line with tabulated data from various sources on mineral and glass fiber insulation materials (see Appendix 9; Johra, 2021).

Figure 6.

Effective air permeability measurements of tested blown glass wool products as a function of density. The figure includes standard effective air permeability test results obtained from external sources of information. The error bars represent the 3σ (99.7% confidence interval) uncertainty range.

In addition, one can observe in Figure 6 that there is no significant difference in the correlation between the effective air permeability and the density for the different blown glass wool products. It is thus chosen to build a single numerical model (fitted exponential function with density as an input) from all effective air permeability measurement points of the different tested blown glass wool products. This exponential model is used to estimate the density-adjusted effective air permeability for the computation of $Ra$ in the different LGHB test cases.

Uncertainty analysis

All results presented in this study include an uncertainty estimate for a 3σ (99.7%) confidence interval. The uncertainty components of the different input variables are estimated from the technical documentation of employed instruments and the standard deviation of repeated measurements. The uncertainty budget (combination of the different uncertainty components) is then performed with the Kragten method (Johra, 2024). Examples of the uncertainty budgets with the Kragten method can be found in Appendix 10. Table 2 gives a summary of the uncertainty for the different parameters and results of the current study.

Table 2.

Overview of the uncertainty for the different parameters and results of the current study.

Parameter	Measurement/estimation method	Uncertainty (99.73% confidence interval; 3σ confidence interval; coverage factor k = 3)	Relative uncertainty (99.73% confidence interval; 3σ confidence interval; coverage factor k = 3)
Ra	Calculation	0.05–3	3.5–31
Nu + 1	Calculation	0.07–0.6	5.4–60
Metering zone heat power input measurements	Electrical power meter	1.5–10 W	2–10
Insulation temperature measurements	4-wire Pt100 resistance temperature detector	0.12°C–1°C	-
Insulation temperature sensor placement	4-wire Pt100 resistance temperature detector attached to wires: position measured with a rigid ruler	0.01 m	-
Insulation mass	Precision scale	0.2 kg	0.15–0.3
Insulation thickness	Repeated manual measurement with a rigid ruler	0.02–0.08 m	6–13
Insulation length	Ruler	0.015 m	0.3
Insulation width	Ruler	0.015 m	0.4
Insulation density	Calculation from mass and volume measurements	0.3–1.2 kg/m³	2–6.2
Insulation effective air permeability	Air permeameter	3.6 × 10⁻¹¹–4.1 × 10⁻⁹ m²	2.5–39
Insulation thermal conductivity	Guarded Hot Plate + adjustment numerical model	1.7 × 10⁻⁴–9.8 × 10⁻⁴ W/m.K	0.4–2.5
Density of air	External source	0.01 kg/m³	3
Isobaric specific heat capacity of air	External source	6 J/kg.K	0.6
kinematic viscosity of air	External source	8.6 × 10⁻⁸ m²/s	0.6
Thermal expansion coefficient of air	External source	1.8 × 10⁻⁶ K⁻¹	0.05
Acceleration due to the Earth’s gravity near its surface	External source	0.01 m/s²	0.1

Upon examining the primary sources of uncertainty in more detail, one can see in Figure 7 that the predominant contributor to the combined uncertainty of the $Nu + 1$ is the uncertainty in measuring the thickness of the insulation layer, followed by the temperature measurement on the cold side of the insulation layer, and the estimate of the parasitic heat flow on the lateral sides of the insulation layer. Similarly, one can observe in Figure 8 that the main contributors to the combined uncertainty of the $Ra$ are the uncertainties in measuring the insulation layer thickness, followed by the effective air permeability of the insulation, and the temperature difference across both sides of the insulation layer.

Figure 7.

Contribution of the different uncertainty components to the combined uncertainty of $Nu + 1$ . The uncertainty contribution of each component is calculated as the average of all 79 large-scale experimental tests in the LGHB. The error bars represent 1σ standard deviation of all 79 large-scale experimental tests in the LGHB.

Figure 8.

Contribution of the different uncertainty components to the combined uncertainty of $Ra$ . The uncertainty contribution of each component is calculated as the average of all 79 large-scale experimental tests in the LGHB. The error bars represent 1σ standard deviation of all 79 large-scale experimental tests in the LGHB.

Results

All raw data of the experimental tests and computed results (compiled into a summary table) can be found in open access on a dedicated zenodo.org repository: https://doi.org/10.5281/zenodo.15092703 (Johra, 2025a, 2025b). All following results are based on temperature measurements at the top surface and bottom surface of the insulation layer in the LGHB setup, but very similar results are found when taking the temperature measurements 5 cm below the insulation top surface and the temperature at the bottom surface of the insulation layer.

All experimental results obtained from the LGHB setup measurements are shown in Figure 9. The modified Nusselt number ( $Nu + 1$ ) is represented as a function of the Rayleigh number ( $Ra$ ) for all investigated cases: six blown glass wool test cases, a glass wool mat reference case, and an expanded polystyrene reference case. One can observe that, as expected, the reference cases with negligible or very limited effective air permeability and a micro-structure that does not allow for any INC, have a $Ra$ of 0 or very close to 0, and a $Nu + 1$ that is very close to 1. The different blown glass wool products have various bulk densities (ranging from 11.9 to 19.7 kg/m³) and effective air permeability (ranging from 4.96 × 10⁻⁹ to 1.65 × 10⁻⁸ m²). Consequently, even if the range of temperature boundary conditions is similar for the different blown glass wool test cases, the result data points cover different $Ra$ intervales.

Figure 9.

Modified Nusselt number ( $Nu + 1$ ) as a function of the Rayleigh number ( $Ra$ ) for all six blown glass wool test cases, the glass wool mat reference case, and the expanded polystyrene reference case. The error bars represent the 3σ (99.7% confidence interval) uncertainty range.

If looking at the different blown glass wool products individually, one can observe that the evolution of $Nu + 1$ as a function of $Ra$ is always very similar: $Nu + 1$ plateaus at low $Ra$ numbers and then ramps up for $Ra$ above 13–15. However, this plateau value differs from one product to another: for example, the plateau for the Blown Glass Wool C–Case 6 (red circles) is $Nu + 1 = 1$ , whereas it is $Nu + 1 ~ 1.3$ for the Blown Glass Wool A–Case 1, 2, and 3 (darker blue circles). Even so, regardless of the $Nu + 1$ plateau value, pasted a $Ra$ of 13–15, the $Nu + 1$ increases quasi-linearly for all investigated cases, to reach values as large as $Nu + 1 = 2.24$ .

The different values of the $Nu + 1$ plateau are surprising (especially since some of these values are larger than 1), however, similar experimental results have already been observed for horizontal configuration, such as in Silberstein et al. (1990), where the low- $Ra$ plateau was at $Nu + 1 = 1.14$ . No explanation for a plateau value larger than 1 was given in Silberstein et al. (1990). In theory, if there is no convection, the heat flux through the porous insulation is purely conductive. By construction, the Nusselt number should thus be $Nu + 1 = 1$ . Therefore, one may deduce that these $Nu + 1$ values above 1 indicate that there is INC at very low $Ra$ for certain insulation products. However, once INC has taken place, it is expected that the $Nu + 1$ continuously increases with increasing $Ra$ , because the convective heat flux should increase with increasing $Ra$ . Consequently, observing constant $Nu + 1$ with increasing $Ra$ clearly indicates that INC is not occurring on those plateaus (Bories, 1987; Nield and Bejan, 2017; Silberstein et al., 1990). To resolve that apparent contradiction, one can argue that some of the $Nu + 1$ plateaus are not equal to 1 because the reference conductive flux without INC measured with the GHP (meso-scale with regular top-heated configuration) is not representative of the conductive flux without INC in the LGHB setup (large-scale with possible complex 3D heat transfer paths and more complex configuration with joists, and intrinsic variability of the wool blowing process). Moreover, the combined uncertainty of the low-Ra plateau data points is significant. As a result of a biased reference conductive heat flux, the computation of the $Nu + 1$ is biased. This matter is further discussed in the Discussions section.

To remedy this bias, it is assumed that, as long as $Nu + 1$ is not increasing with increasing $Ra$ , INC is not taking place and, therefore, the heat flux is only conductive. For each insulation product, the respective $Nu + 1$ data points of the LGHB tests are thus normalized by the corresponding $Nu + 1$ plateau value to obtain a new set of normalized modified Nusselt numbers $Nu + 1^{*}$ . The normalized modified Nusselt number as a function of the Rayleigh number for all six blown glass wool test cases, the glass wool mat reference case, and the expanded polystyrene reference case is presented in Figure 10. By construction, every Nusselt number plateau is now set to $Nu + 1^{*} = 1$ . This normalization eases the identification of the value of $Ra$ for which $Nu + 1^{*}$ starts increasing. One can clearly observe that this critical value of $Ra$ ranges between 13 and 15, depending on the insulation product. Finally, one can also notice that the quasi-linear ramp correlation between $Nu + 1^{*}$ and $Ra$ differs slightly from one product to another but conserves a rather similar slope (the different ramps appear to be parallel to each other).

Figure 10.

Normalized modified Nusselt number ( $Nu + 1^{*}$ ) as a function of the Rayleigh number ( $Ra$ ) for all six blown glass wool test cases, the glass wool mat reference case, and the expanded polystyrene reference case. The error bars represent the 3σ (99.7% confidence interval) uncertainty range.

Discussions

Convection is characterized by an increasing Nusselt number with an increasing Rayleigh number. By construction, when there is no internal natural convection, the Nusselt number cannot increase. Contrary to the conclusions of some previous studies (Kivioja and Vinha, 2020), the fact that the value of the initial $Nu + 1$ plateau is not equal to 1 (as illustrated in Figure 9) is not an indisputable proof that INC is present. Instead, $Nu + 1 > 1$ plateau at low- $Ra$ could be due to a bias or a mistake in the measurement of the reference conductive heat transfer without INC, which is then used as normalization to compute the Nusselt number. In light of this, the evidence for INC does not come from the value of the Nusselt number, but rather from the slope change on the Nusselt number/Rayleigh number graph (Bories, 1987; Nield and Bejan, 2017; Silberstein et al., 1990). On the non-normalized $Nu + 1 = f (Ra)$ graph, each profile presents a plateau at low Rayleigh numbers, and then a quasi-linear increase above a threshold $Ra$ value. This threshold value can be better identified when normalizing the data by the value of low- $Ra$ Nusselt plateau, thus collapsing all initial Nusselt plateaus to 1. The critical value of the Rayleigh number for which the Nusselt number starts to increase is in the range of ${Ra}_{c} \in [13; 15]$ .

As mentioned above, the different porous insulation products have slightly different slopes for the increasing $Nu + 1^{*}$ ramp once passed ${Ra}_{c}$ . This is rather unexpected when using non-dimensional numbers, assuming, of course, that the physics is correctly captured in the model of those non-dimensional numbers. In addition, one can observe that the increasing $Nu + 1^{*}$ ramp is not always perfectly linear and presents some flattening at ${Ra}_{c} \in [20; 27]$ for two of the cases. Those two points might indicate that some physics or influential parameters are not well considered in the current analysis, or in the non-dimensional numbers used here. Nonetheless, this is of minor relevance for the main goal of this study, which focuses on the critical Rayleigh number ${Ra}_{c}$ marking the onset of internal natural convection in porous insulation materials, but not on the Nusselt/Rayleigh scaling law.

Although considerable care and effort have been put into identifying and addressing all possible biases and errors in the different experimental tests, numerical simulations, and data analyses of the present study, the authors are conscious of certain possible limitations and uncertainties that might explain some of the aforementioned unexpected observations. The differences between the slopes of the ramps and the $Nu + 1 > 1$ value of the low-Rayleigh initial plateaus for the different insulation products could be explained by discrepancies between the measured effective air permeability in the meso-scale permeameter setup and the full-scale insulation layer of the LGHB experiments. Moreover, the micro-structure differences between meso-scale tests in the GHP and the permeameter, and the tests in the LGHB setup are overlooked, whereas the blowing process of loose-filled glass wool products is known to have significant intrinsic variabilities. In addition to the impact of the presence of joists inside the insulation layer, blowing glass wool over frames of different scales can introduce micro-structure and density variations, which could partly explain the observed differences. Yet, despite the uncertainty around the representativity of properties determined with small- and meso-scale experiments, some parameters are directly measured or inferred from the latter to compute the Nusselt and Rayleigh numbers of the full-scale LGHB cases. Furthermore, complex local 3D effects around the joists and the sides of the large-scale insulation layer, thickness heterogeneities, vertical insulation density gradient, horizontal insulation density heterogeneities, and boundary condition instabilities might introduce additional non-linear heat and air transport in the LGHB experiments that are not accounted for in the analyses. Moreover, some inevitable approximations were made to estimate the correction factors of parasitic and residual heat losses to the guarded zone and the surrounding laboratory environment, and the joist effect. These correction factors are assumed to be constant (i.e. independent of temperature): for example, the residual heat transfer between the metering zone and the surrounding guarded zone is linearly dependent on the residual temperature difference between the metering wall surface and its corresponding guarded zone wall surface. However, some of those correction factors might not be constant, but rather temperature-dependent, which would introduce non-linearities in the parasitic heat losses that are not accounted for in the current analysis. Finally, the numerical model used to adjust the thermal conductivity of the insulation without any INC from the GHP measurements to the LGHB cases’ conditions (temperature and bulk density) also holds a certain level of inaccuracy.

Despite all the above-mentioned limitations, the authors of the current study are confident that all necessary simplification assumptions are adequate. It is reasonable to consider that the uncertainties and possible biases introduced by these simplifications will not significantly change the key findings and conclusions of this experimental investigation. A particular effort has been made to compute and indicate the error bars (uncertainty range) in all result figures. In the case of the Nusselt-Rayleigh figures, the uncertainty bars are significantly large for the data points at low Ra, corresponding to small heat flux through the insulation layer. Nonetheless, this does not impact the clarity of the critical Rayleigh number location at the connection between the low-Ra plateaus and the increasing $Nu + 1^{*}$ ramps.

Conclusions and suggestions for future work

This article reports the findings of a large-scale experimental study on the onset of internal natural convection inside a horizontal insulation layer of blown glass wool with joists, heated from below with a closed boundary enclosure at the bottom and an open boundary at the top. The thickness of the insulation layer is set to 30 or 60 cm, with a glass wool density ranging from 11.9 to 19.7 kg/m³, an effective air permeability ranging from 4.96 × 10⁻⁹ to 1.65 × 10⁻⁸ m², a temperature difference spanning from 5.2 to 59.5 K, and an average temperature ranging from −5.3°C to 26.5°C. To ensure transparency and reproducibility, all measurement data collected in this study is made publicly available as open access, accompanied by comprehensive methodological documentation. This facilitates re-analysis of the raw data and enables comparisons with other studies.

The onset of the internal natural convection is identified by the critical Rayleigh number ( ${Ra}_{c}$ ): below ${Ra}_{c}$ , the modified Nusselt number ( $Nu + 1$ ) is stable with increasing Rayleigh number; above ${Ra}_{c}$ , the modified Nusselt number increases continuously with increasing Rayleigh number. For this configuration, the critical Rayleigh number is found to be situated between 13 and 15. For a Rayleigh number below 12, the modified Nusselt number is stable. However, it is possible sometimes to observe low- $Ra$ plateaus with a constant modified Nusselt number above 1. Nonetheless, one should not conclude that the latter is evidence that internal natural convection occurs at $Ra$ below 13, because the modified Nusselt number remains constant with increasing $Ra$ . Instead, the $Nu + 1 > 1$ low- $Ra$ plateaus are most likely due to measurement uncertainties and biases in estimating the reference conductive heat flux without internal natural convection for the computation of the modified Nusselt number. Indeed, the blowing process of loose-filled glass wool products presents significant intrinsic variabilities. This can lead to some differences in the insulation micro-structure and, consequently, different thermal performance, which could explain some of the observed discrepancies between the meso-scale reference (GHP) and the large-scale test (LGHB) measurements. Consequently, the transition from a low- $Ra$ constant $Nu + 1$ plateau to a continuously increasing $Nu + 1$ ramp should be used to identify ${Ra}_{c}$ , instead of isolated high $Nu + 1$ values, or low- $Ra Nu + 1 > 1$ plateaus alone. Nonetheless, this does not affect the conclusions made on the onset of the internal natural convection inside loose-filled glass wool insulation. It is thus reasonable to conclude that, in this configuration, there is no internal natural convection for Rayleigh numbers below 13. Finally, the observed ${Ra}_{c}$ differs slightly for some of the different blown glass wool products, but not significantly enough compared to the measurement uncertainties to conclude that those actually are different.

Overall, these new experimental results are in good agreement with the standard ISO 10456:2007 and most of the previous studies on the onset of internal natural convection in porous insulation. To this day, this experimental investigation is the largest of its kind and contributes to the existing body of knowledge by providing solid estimates of the critical Rayleigh number for blown glass wool products set in a thick horizontal insulation layer with joists.

Further investigations on the onset of internal natural convection in porous insulation should focus on the possible biases and discrepancies in the assessment of the reference conductive heat flux without internal natural convection for the computation of the modified Nusselt number. In particular, one should further study the differences of micro-structure and heat and air transport characteristics between small-, meso-, and full-scale layers of blown wool and other similar fibrous insulation materials. Furthermore, detailed full-scale experimental tests like the present ones should be replicated with different classes of insulation products, such as blown wood wool. New full-scale laboratory investigations are also needed to refine the understanding of the impact of joists and 3D effects in blown wool insulation configurations. This specific topic could also be further investigated using 3D direct numerical simulations in order to get insight into flow dynamics in the porous matrix and the shape of the macroscopic convection cells. In addition, new experimental setups could be developed to identify the presence of internal natural convection in a more direct manner, for instance, by deploying a tracer gas system inside the insulation layer to detect the internal flow of air within the porous medium. Detailed temperature profile measurements within narrow vertical sections of the insulation layer using less intrusive sensors (e.g. thin thermocouples) could reveal temperature distribution anomalies associated with the presence of macroscopic convection cells and help identify the shape of the latter. Finally, one could explore the suitability of non-dimensional Nusselt and Rayleigh numbers to analyze heat and air transfer in blown wool-based porous media, independently of their material properties and boundary conditions. New normalization factors related to insulation and joist properties (e.g. geometry, thermal conductivity, effective air permeability) could be introduced to modify the currently used non-dimensional numbers and reconcile discrepancies in ${Ra}_{c}$ and $Nu + 1$ ramp slope across the different cases.

Footnotes

Appendix

Appendix 1

Appendix 2

Appendix 3

Appendix 4

Appendix 5

Appendix 6

Appendix 7

Appendix 8

Appendix 9

Appendix 10 Acknowledgements

The authors of this study would like to acknowledge the generous contributions of Lars Isbach Poulsen, Assistant Engineer at Aalborg University (Denmark), Department of the Built Environment, Henrik Pape Vestergaard, Mikkel Frostholm, Harri Kemppainen, Clothilde Charmantray, Rita Tozy, David Luis, and Sanna Lindholm.

ORCID iD

Hicham Johra

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This experimental study has been financed by Saint-Gobain.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availablity statement

All raw data of the experimental tests and summary tables of all result points can be found in open access on a dedicated zenodo.org repository: https://doi.org/10.5281/zenodo.15092703 (Johra, 2025a, ).

Notes

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