Several Problems with Froude-Number Based Scale Modeling of Fires in Small Compartments

energies

Article Several Problems with Froude-Number Based Scale Modeling of Fires in Small Compartments

Mateusz Zimny 1 , Piotr Antosiewicz 2 , Grzegorz Krajewski 2, Tomasz Burdzy 3 , Adam Krasuski 1 and Wojciech W˛egrzy´nski 2,*

1 Faculty of Fire Safety Engineering, The Main School of Fire Service (SGSP), 01-629 Warsaw, Poland 2 Fire Research Department, Building Research Institute (ITB), 00-611 Warsaw, Poland 3 Faculty of Mining and Geoengineering, AGH University of Science and Technology, 30-059 Kraków, Poland * Correspondence: [email protected]; Tel.: +48-696-061-589

Received: 4 September 2019; Accepted: 19 September 2019; Published: 23 September 2019

Abstract: The Froude-number based reduced-scale modeling is a technique commonly used to investigate the flow of heat and mass in building fires. The root of the method is the thermodynamic model of a flow in a compartment and several non-dimensional flow numbers based on the proportionalities of the Navier-Stokes and heat transfer equations. The ratio of inertial forces to the buoyancy forces, known as the Froude-number, plays a pivotal role within these proportionalities. This paper is an attempt to define the range of credible scale modeling using the Froude-number. We verify the credibility of the modeling by small fire (approximately 150 kW) in a small compartment, comparing data from a physical test (scale 1:1 and 1:4) and the numerical model’s data (Fire Dynamics Simulator, scales 1:1, 1:2, 1:4, 1:10, 1:20, and 1:50). The scope of the research covers a wide range of fires, with observed change of the flow from turbulent to laminar. The results show that the applicability of Froude-number reduced-scale modeling has limitations related to the scale. Therefore, it should be applied with care following sensibility analysis. We propose a method for sensibility analysis using Computational Fluid Dynamics (CFD) modeling.

Keywords: ﬁre; Froude number; scale modeling; ﬁre modeling; CFD; FDS

1. Introduction There is continuous progress in the reflection of the fire phenomenon in computer models [1]. There is also a growing number of applications of computer software to complex fire problems [2]. Computer models are continually gaining accuracy, as is the scope of the modeled fire phenomena. However, due to limitations in representation of many fire-related phenomena, computational costs, and uncertainties related to numerical investigation, physical experimentation in reduced-scale modeling is still a popular tool. Since the first studies on the smoke control of factories performed by Thomas et al. [3], reduced-scale research allowed for the development of better techniques and solutions to prevent fires and limit their consequences to occupants, buildings, and the environment. Such studies could also be used in forensic applications [4,5] and building design. There are two governing non-dimensional numbers in low-Mach–fire-related flows, namely the Reynolds (Re) and Froude (Fr) numbers. However, the Fr scaling conflicts with the Re preservation by providing two different results for velocity in the scale models. There are analyses [6] that prove that in fire-related flows, one should preserve the Froude-number, not the Reynolds number when scaling is applied. In this case, so-called partial scaling is adopted that favors the Fr over the Re [7]. Quintiere et al. mentioned that maintaining sufficient height of the scale model compartment (>0.3 m) may be adequate to maintain flow turbulence [5].

Energies 2019, 12, 3625; doi:10.3390/en12193625 www.mdpi.com/journal/energies Energies 2019, 12, 3625 2 of 20

Energies 2019, 12, x FOR PEER REVIEW 2 of 19 The Fr scaling assumes that two fires are similar to each other, if the Froude-number characterizing The Fr scaling assumes that two fires are similar to each other, if the Froude-number both fires is equal, and there is geometrical and hydraulic similarity of the systems in which the fires characterizing both fires is equal, and there is geometrical and hydraulic similarity of the systems in take place. An illustration of the Froude-number scale fire modeling concept is shown in Figure1. which the fires take place. An illustration of the Froude-number scale fire modeling concept is shown Variable x describes dimensions of the model in full- (index “f ”) and reduced- (index “m”) scale. If the in Figure 1. Variable x describes dimensions of the model in full- (index “f”) and reduced- (index “m”) Heat Release Rate (HRR, Q) of the fire is scaled accordingly and the Fr is preserved, the temperatures scale. If the Heat Release Rate (HRR, Q) of the fire is scaled accordingly and the Fr is preserved, the (T) measured in the reduced- and full-scale fires should be equal. temperatures (T) measured in the reduced- and full-scale fires should be equal.

FigureFigure 1. 1.The The idea idea of of the the Froude-number Froude-number reduced-scale reduced-scale fire fire modeling. modeling. Illustrating Illustrating the the concept concept of of scalingscaling down down the the Heat Heat Release Release Rate Rate (HRR, (HRR,Q Q) to) to model model a a fire, fire, which which results results in in similar similar temperature temperature (T ()T) measuredmeasured in in the the scaled-down scaled-down (geometrical) (geometrical) compartment compartment [8 ].[8]. The approach of the Fr scaling must be used with care, despite its popularity. Spalding emphasized The approach of the Fr scaling must be used with care, despite its popularity. Spalding that partial scaling is “an art” and not a science, due to problems in properly relating the behavior of emphasized that partial scaling is “an art” and not a science, due to problems in properly relating the the full-scale system to the one of the model [9]. Among these problems, the most common are with behavior of the full-scale system to the one of the model [9]. Among these problems, the most the scaling the chemistry of combustion and the flow turbulence [9]. Nevertheless, Froude-number common are with the scaling the chemistry of combustion and the flow turbulence [9]. Nevertheless, scale modeling of fires has proven useful in understanding various fire phenomena, and their Froude-number scale modeling of fires has proven useful in understanding various fire phenomena, consequences [3,10–12]. and their consequences [3,10–12]. In this research, we focus on some issues identified with the practical use of the Froude-number scale In this research, we focus on some issues identified with the practical use of the Froude-number modeling of a small fire (HRR of approximately 150 kW) in a small-sized compartment (approximately scale modeling of a small fire ( HRR of approximately 150 kW) in a small-sized compartment 10 10 4 m3). We have observed a discrepancy in the measurements of the temperature between (approximately× × 10 × 10 × 4 m³). We have observed a discrepancy in the measurements of the the full- and reduced-scale experiments that match observations previously reported in the literature. temperature between the full- and reduced-scale experiments that match observations previously Furthermore, the experiment was recreated with the use of CFD modeling in larger number of scales as reported in the literature. Furthermore, the experiment was recreated with the use of CFD modeling an attempt to confirm the experimental observations, investigate the turbulent flow structure in more in larger number of scales as an attempt to confirm the experimental observations, investigate the details, and form generalised conclusions. The temperature of smoke measured in the reduced-scale turbulent flow structure in more details, and form generalised conclusions. The temperature of smoke analyses was lower than in a full-scale experiment, despite conforming to the Froude-number scaling measured in the reduced-scale analyses was lower than in a full-scale experiment, despite principles. The discrepancy was bigger when the scale used wassmaller. Moreover, in very small conforming to the Froude-number scaling principles. The discrepancy was bigger when the scale scales we have observed problems with maintaining a sufficiently high Reynolds number, and the fire used wassmaller. Moreover, in very small scales we have observed problems with maintaining a behavior has changed from turbulent to laminar, leading to significant error in the modeled smoke sufficiently high Reynolds number, and the fire behavior has changed from turbulent to laminar, temperatures and invalidating the scientific value of these experiments. leading to significant error in the modeled smoke temperatures and invalidating the scientific value 2.of Froude-Number these experiments. Based Fire Modeling

2. FroudeIn the- earlyNumber 1960s, Based mass Fire fires Model wereing considered to be an extremely complex phenomena that did present formidable scaling problems. A body of literature did exist (reviewed by Williams [9]) related to theIn scaling the early of specific, 1960s, mass simple fires types were of considered fires. It was to be in an the extremely review paper complex by Williamsphenomena [9] that where did thepresent foundation formidable for future scaling scaling problems. of fires A body was of laid, literature based did on exist the combination (reviewed by ofWilliams several [9]) diff relatederent to the scaling of specific, simple types of fires. It was in the review paper by Williams [9] where the foundation for future scaling of fires was laid, based on the combination of several different models based on the principal laws, mathematical operations, and empirical observations. The paper

Energies 2019, 12, 3625 3 of 20 models based on the principal laws, mathematical operations, and empirical observations. The paper introduced 29 dimensionless groups that describe the scaling principles for fire phenomena. In this modeling technique, some of the phenomena are simplified, and others are omitted on purpose. However, the overall image of the reduced-scale fire may be useful and provide a reasonably good picture of the characteristics of the full-scale system that is of interest. The concept of reduced-scale modeling was summarized by Quintiere in reference [13] and more recently in references [5,14]. In the technique of scale modeling using dimensionless numbers of similarity, the starting point is the Buckingham theorem, also known as the “Pi Theorem” [14]. The theorem states that: “Each function involving a certain number n of physical variables ai, and these variables are expressible in terms of k independent fundamental physical quantities, then the original expression is equivalent to an equation involving a set of p = n – k dimensionless parameters Π constructed from the original variables. If all dimensionless parameters Π are identical, the phenomenon will be identical despite the different parameters of the ai type.” The statement above (Pi Theorem) is based on the principle of dimensionless unity. Moreover, it states that if the equation expresses a proper relation between variables in physics, the process shall be dimensionally homogeneous, and its parameters will have the same dimensions [15]. Thus, a dimensionally homogeneous equation containing n mathematical variables:

Z = f (Z1, Z2 ... Zn) (1) can be recorded in the dimensionless form:

Π = Θ(Π1, Π2 ... Πn k). (2) − It was already identiﬁed by Williams [9] that creating a model that conserves all 29 dimensionless groups would be formidable. Thus, subsets were created, of which the basic subset is presented below. The geometrical scale of the model is the ratio of the characteristic dimensions of the scaled-down model (index “m”) to the corresponding dimensions in the full scale (index “f”).

x m (3) x f Froude-number similarity (4), convection and radiation groups, and gas-phase heat release were grouped together with fuel gasiﬁcation and loading groups, and ambient atmospheric condition groups [9].

u0 Fr f = Frm = p (4) gl These were foundations for future scaling principle developments. The heat release rate in small scale is determined by the scaling of Zukoski number (5), also known as dimensionless group Π9.

Q = = Π9 Q∗ 5 (5) 2 xm ρ cpT √g ∞ ∞ x f In modern ﬁre modeling, it may be assumed that two ﬁres can are similar if the following requirements are met [8]:

The Froude-numbers of both of the fires are equal; • All geometrical features related to the fire and the environment are scaled with the same scale; • The fires are occurring at well-ventilated conditions, i.e. the combustion is not significantly • influenced by the reduced-scale, and the combustion efficiency in full and reduced-scale is similar; The flow in the buoyant plume is turbulent. • Energies 2019, 12, 3625 4 of 20

If the Froude similarity criterion is met, and Reynolds criterion is satisfied, the other relevant parameters that describe the flow of mass and heat in the compartment will scale as summarized in reference [16] and listed below. The heat release rate of the fire [kW] • . !5/2 Qm xm . = (6) x f Q f

Time [s] • !1/2 t x m = m (7) t f x f

Energy [kJ] • !3 E x m = m (8) E f x f

Air velocity [m/s] • !1/2 V x m = m (9) V f x f

Mass ﬂow [kg/s] • . !3 m x m = m (10) m f x f

Temperature [K] • Tm = T f (11)

For a more thorough introduction to Fr scaling of fires, the reader is kindly referred to reference [14]. The Fr scaling approach can be potentially used in an investigation of other phenomena relevant to fire safety, where buoyancy is the dominant force in the model. An example can be flammable gas dispersion, and a recent example of full-scale research can be found in reference [17]. However, in scaling of such phenomena other set of relations may apply, as the change of density in Equation (4) will not be related to heat release, as in Equations (5) and (6). The abovementioned set of similarities was used widely in fire safety science, in a vast array of scales. Fire sizes in literature review range from 0.31 kW to 100 MW, and the scales from full scale (1:1, [18]) to 1:48 [19]. A summary of investigated research performed in reduced-scale is shown in Table1.

Table 1. Examples of ﬁres in reduced-scale used in ﬁre research.

Compartment of Number of Scale HRR (Reduced-Scale) Reference Interest Experiments 1:1 Road tunnel 5 6000–202,000 kW [18] 1:2 Railway car 10 90–1247 kW [20] 1:2 Compartment n/a n/a [21] 1:3.5 Group of houses 2 up to 100,000 kW [22] 1:4 Compartment 165 n/a [23] 1:7 Room 3 300–1500 kW [24] 1:8 Cellar 1 18.31 kW [25] 1:8 Corridor 5 50–300 kW [4] 1:10 Shopping mall 48 7,6 kW [26] 1:10 Shopping mall 25 6–10.3 kW [11] 1:12 Road tunnel 5 15.1–72.8 kW [27] Energies 2019, 12, 3625 5 of 20

Table 1. Cont.

Compartment of Number of Scale HRR (Reduced-Scale) Reference Interest Experiments 1:13 Road tunnel 61 7.81–215.1 kW [28] 1:15 Road tunnel 28 6.7–430.1 kW [29] 1:20 Road tunnel 54 n/a (5–25 MW in full scale) [30] 1:20 Subway tunnel 116 1.48–3.52 kW [31] 1:23 Road tunnel 12 102.2–320.8 kW [32] 1:48 Train tunnel 1 0.31–1.88 kW [19] undeﬁned Small scale tunnel 1 82 kW [33]

3. Materials and Methods

3.1. Experimental Setup The Froude-number based scaling technique was used in a series of full-scale (1:1) and small scale (1:4) physical experiments on the development of a hot smoke layer in a small size fire within a small, non-ventilated compartment. The n-Heptane was used as a fuel in all of the experiments, and the size of the fire was scaled through reducing the size of the pan and the amount of fuel. A secondary goal of the experiment was to verify the concept of a novel optical densitometer, which was thoroughly described in reference [8]. The physical experiments in scale 1:1 were performed in the Building Research Institute smoke detector testing chamber (Figures2a and3). The dimensions of the chamber are 9.60 9.80 4.00 m. × × The chamber was sealed, but not airtight (the leakages are not known to the authors, although no visual observation of smoke leakage to the building was observed). All doors and ventilation openings of the chamber were sealed during the experiments. Walls of the chamber are built with gypsum plasterboard (2 12 mm) over the aluminum structure. × Two experiments, each consisting of three repeats were performed. In the first series a fuel tray with dimensions of 0.33 0.33 m2 was used (further referred to as series A), and in the second series, a fuel × tray with dimensions of 0.50 0.50 m2 was used (series B). In both full-scale experiments, the fuel was × 1 l of n-Heptane. The Heat Release Rate (HRR) was determined through mass loss rate measurements of the fuel tray, with the assumed Heat of Combustion value Hc = 44,400 kJ/kg. No ventilation was used in the experiment. The reduced-scale experiment was performed in a scaled-down model of the test chamber (1:4) (Figures2b and3), with the dimensions of 2.40 2.45 1.00 m3. All physical × × features of the compartment were further scaled down accordingly in reduced-scale experiments, except the fuel tray. The size of the fuel tray was first determined through geometrical scaling and then refined based on mass-loss measurements of the combustion of n-Heptane so that the similarity of (5) and (9) is explicitly met. The correction to the size of the tray was within 10% of the geometrical size. The experiment overview is given in Table2. Each of the experiments was repeated three times, and the conclusions are formed based on the averaged values.

Table 2. Overview of the experiments.

Series Series A Series B 1:1 1:4 1:1 1:4 HRR [kW] 81.7 kW 2.55 kW 158 kW 4.94 kW volume of fuel [L] 1.015 L 0.0158 L 1.015 L 0.0158 L mass of fuel [g] 0.6943 kg 0.0108 kg 0.6943 kg 0.0108 kg duration of the ﬁre (real time) [s] 350 s 175 s 181 s 90.5 s tray size [m] 0.33 0.33 m 0.075 0.075 m 0.50 0.50 m 0.125 0.125 m × × × × Energies 2019, 12, x FOR PEER REVIEW 5 of 19

The Froude-number based scaling technique was used in a series of full-scale (1:1) and small scale (1:4) physical experiments on the development of a hot smoke layer in a small size fire within a small, non-ventilated compartment. The n-Heptane was used as a fuel in all of the experiments, and the size of the fire was scaled through reducing the size of the pan and the amount of fuel. A secondary goal of the experiment was to verify the concept of a novel optical densitometer, which was thoroughly described in reference [8]. The physical experiments in scale 1:1 were performed in the Building Research Institute smoke detector testing chamber (Figure 2a, Figure 3). The dimensions of the chamber are 9.60 × 9.80 × 4.00 m. The chamber was sealed, but not airtight (the leakages are not known to the authors, although no visual observation of smoke leakage to the building was observed). All doors and ventilation openings of the chamber were sealed during the experiments. Walls of the chamber are built with gypsum plasterboard (2 × 12 mm) over the aluminum structure. Two experiments, each consisting of three repeats were performed. In the first series a fuel tray with dimensions of 0.33 × 0.33 m² was used (further referred to as series A), and in the second series, a fuel tray with dimensions of 0.50 × 0.50 m² was used (series B). In both full-scale experiments, the fuel was 1 l of n-Heptane. The Heat Release Rate (HRR) was determined through mass loss rate measurements of the fuel tray, with the assumed Heat of Combustion value Hc = 44 400 kJ/kg. No ventilation was used in the experiment. The reduced-scale experiment was performed in a scaled- down model of the test chamber (1:4) (Figure 2b, Figure 3), with the dimensions of 2.40 × 2.45 × 1.00 m³. All physical features of the compartment were further scaled down accordingly in reduced-scale experiments, except the fuel tray. The size of the fuel tray was first determined through geometrical scaling and then refined based on mass-loss measurements of the combustion of n-Heptane so that the similarity of (5) and (9) is explicitly met. The correction to the size of the tray was within 10% of theEnergies geometrical2019, 12, 3625 size. The experiment overview is given in Table 3. Each of the experiments6 was of 20 repeated three times, and the conclusions are formed based on the averaged values.

(a) (b)

Figure 2. FullFull scale scale ( (aa)) and and reduced reduced-scale-scale (1:4, (1:4, b) b) experiments experiments on on the the free free burning burning of of n n-heptane-heptane [8] [8].. Doors visible on picture ( b) were open for the imageimage and were sealed during experiments.experiments.

Energies 2019, 12, x FOR PEER REVIEW 6 of 19 The sketch presenting both ofTable the testing3. Overview chambers, of the experiments and the location. of measurement equipment is shown in Figure3. Each of the testing chambers was equipped with: The sketchSeries presenting both of the testingSeries chambers, A and the location of measurementSeries B equipment is- shown4type in Figure K 1mm 3. Each Ni-Cr of thermocouplesthe testing1:1 chambers (T1-T4) was placed equipped1:4 in the with: corners 1:1 of the compartment,1:4 used to - 4 typemeasureHRR K 1mm [kW] the Ni average -Cr thermocouples temperature81.7 kW of(T1 the-T4) smoke placed2.55 layer, inkW the extended corners 158 uncertaintyof the kW compartment, of the4.94 measurement used kW to measurevolumewas estimated the of averagefuel at[l] 0.3 temperature◦C; 1.015 of the smoke layer,0.0158 extended l uncertainty1.015 l of the measurement0.0158 l - was1mass typeestimat of K fuel 1mmed at [g] Ni-Cr0.3 °C; thermocouple0.6943 kg placed in0.0108 the plume kg centerline,0.6943 underneath kg the0.0108 ceiling kg (T5), - 1 durationtypeused K to 1mm measureof the Ni fire-Cr the thermocouple peak temperature placed ofin the smokeplume centerline, upon entering underneath the smoke the layer,ceiling extended (T5), 350 s 175 s 181 s 90.5 s useduncertainty(real to measure time) of[s] thethe measurementpeak temperature was of estimated the smoke at 0.3upon◦C; entering the smoke layer, extended - uncertaintyloadtray cell size withof [m] the a measurement resolution0.33 of × 0.01was 0.33 gestimated m was used0.075 at to 0.3× measure 0.075 °C; m the0.50 mass-loss × 0.50 ratem of0.125 fuel in × the0.125 tray m in - loabothd cell experiments, with a resolution with extendedof 0.01 g was uncertainty used to measure of 0.02 g; the mass-loss rate of fuel in the tray in both experiments, with extended uncertainty of 0.02 g;

FigureFigure 3. 3.TheThe overview overview of the of test the chambers, test chambers, with the with localization the localization of the measuring of the measuring equipment equipment (T1- T4(T1-T4—four – four thermocouples thermocouples that were that placed were placedsymmetrically symmetrically in four corners in four of corners the compartment, of the compartment, T5 – thermocoupleT5—thermocouple that was that placed was placedabove fuel above tray) fuel. tray).

3.2.3.2. Numerical Numerical Simulations Simulations TheThe fire ﬁre experiments experiments (scale 1:1 1:1 and and 1:4) 1:4) described described in Section in Section 3.1 were 3.1 were recreated recreated with Fire with Dynamics Fire DynamicsSimulator Simulator (FDS) code (FDS) (version code (version 6.7.0). FDS 6.7.0). is a FDS Computational is a Computational Fluid Dynamics Fluid Dynamics (CFD) code(CFD) developed code developed for modeling of low Mach number fluid flows, with an emphasis on smoke and heat transport as a result of fires. The FDS software can analyse the transport of heat and combustion products of a fire, heat transfer through radiation and convection, as well as conduction (1-D Fourier’s equation). The radiative heat transfer is solved using the finite volume method (FVM). The program solves the Navier-Stokes equations using a second-order finite differences scheme. The modeling includes relatively low-velocity flows (Ma < 0,1) and non-compressible gases that are gases for which density variation at low flow velocities can be disregarded. The FDS code primarily employs the Large Eddy Simulation (LES) method for the turbulence modeling, with dynamic Smagorinsky model being the default model for the turbulent viscosity. Log-law wall functions are used to characterize the flow at the boundaries. The LES modeling assumes that only the largest flow scales (large eddies) are calculated directly from the transport equations, while below the so-called Smagorinsky filter length the turbulence is solved with a sub-scale model. The size of Smagorinsky filter is determined as the cubic root of the smallest cell in the model. The fire phenomena is introduced as a single step mixing controlled combustion reaction, for which the molar fractions of products are defined, as well as the yields of relevant products (especially CO, CO2, and soot). The space discretization is performed with a uniform Cartesian type mesh, without any wall mesh boundary layers. For more information relevant to the FDS model used in this analysis, and the

Energies 2019, 12, 3625 7 of 20 for modeling of low Mach number fluid flows, with an emphasis on smoke and heat transport as a result of fires. The FDS software can analyse the transport of heat and combustion products of a fire, heat transfer through radiation and convection, as well as conduction (1-D Fourier’s equation). The radiative heat transfer is solved using the finite volume method (FVM). The program solves the Navier-Stokes equations using a second-order finite differences scheme. The modeling includes relatively low-velocity flows (Ma < 0,1) and non-compressible gases that are gases for which density variation at low flow velocities can be disregarded. The FDS code primarily employs the Large Eddy Simulation (LES) method for the turbulence modeling, with dynamic Smagorinsky model being the default model for the turbulent viscosity. Log-law wall functions are used to characterize the flow at the boundaries. The LES modeling assumes that only the largest flow scales (large eddies) are calculated directly from the transport equations, while below the so-called Smagorinsky filter length the turbulence is solved with a sub-scale model. The size of Smagorinsky filter is determined as the cubic root of the smallest cell in the model. The fire phenomena is introduced as a single step mixing controlled combustion reaction, for which the molar fractions of products are defined, as well as the yields of relevant products (especially CO, CO2, and soot). The space discretization is performed with a Energies 2019, 12, x FOR PEER REVIEW 7 of 19 uniform Cartesian type mesh, without any wall mesh boundary layers. For more information relevant tocomplete the FDS definition model used of inthe this underlying analysis, physical and the completemodels the definition reader is of kindly the underlying referred to physical reference models [34], theand reader for information is kindly referred on the tovalidation reference of [ 34the], andmodel for is information referred to onreference the validation [35]. The of scope the model of the is referredapplication to reference of FDS makes [35]. Theit especially scope of fit the to applicationsimulate the of heat FDS and makes mass it transfer especially phenomena fit to simulate in small the heatfire and experiments, mass transfer where phenomena the buoyant in small forces fire within experiments, the smoke where plume the can buoyant be considered forces within as the the smokedominant plume forces. can be considered as the dominant forces. InIn order order to to determine determine the the scope scope of ofFr Frscaling scaling applicability applicability to smallto small fires. fires. Figure Figure4 shows 4 shows a 1:1 a scale 1:1 3-Dscale computer 3-D computer model model used inused numerical in numerical calculations. calculations. To prepare To prepare the CFD the CFD model model geometry, geometry we, used we GUIused software GUI software called called PyroSim, PyroSim developed, developed by Thunderhead by Thunderhead Engineering Engineering [36]. [36]. The The dimensions dimensions of theof model (full scale) were 9.6 m 9.6 m 4.2 m. the model (full scale) were 9.6× m × 9.6× m × 4.2 m.

FigureFigure 4. 4.3-D 3-D model model of of the the laboratorylaboratory inin full-scalefull-scale and compa comparisonrison of of the the 3 3-D-D models models in in reduced reduced scale scale..

2-D2-D slices slices were were used used to to illustrate illustrate the the temperature, temperature, velocity velocity and pressure fields.fields. Moreover, Moreover, a a matrixmatrix of of point point measurement measurement devices devices has beenhas prepared been prepared to measure to measure velocity flow velocity and the flow temperature and the distribution,temperature formingdistribution, an arrayforming in twoan array planes: in two Y planes:= 5.0 and Y = Z5.0= and4.0 Z with = 4.0 awith 0.2 ma 0.2 interval. m interval. In theIn reduced-scalethe reduced-scale simulations, simulations the, location the location and intervaland interval have ha beenve been scaled scaled following following the geometrical the geometrical scale ofscale the model.of the model. AA total total number number of of 12 12 computer computer simulations simulations were were performed, performed, i.e.i.e. si sixx simulations simulations per per series series (following(following the the same same notation notation asas full-scalefull-scale experimentsexperiments described in 3.1). Table Table 34 provides a summary summary ofof the the information information on on numerical numerical models.models. Reduction of the geometric dimensions dimensions of of the the model model caused caused thethe compression compression of of the the computing computing domaindomain andand the size of individual cells. Therefore, Therefore, in in all all different different scenariosscenarios the the number number of of gridgrid cellscells waswas constantconstant andand equalequal to 3,897,600.3,897,600. Thus, Thus, both both the the resolution resolution and and positionposition of of the the measurement measurement apparatus apparatus are consistent are cons iniste relationnt in relation to the full-scale to the model. full-scale The m comparisonodel. The ofcomparison the dimensions of the of dimensions all CFD models of all CFD is shown models in Figureis shown4. in Figure 4.

Table 4. Parameters of the Fire Dynamics Simulator (FDS) numerical models.

Scenario Scale Model Dimensions [m] Grid Size [m] Number of Grid Cells 1 A, B 1:1 9.6 × 9.6 × 4.2 0.05 3,897,600 2 A, B 1:2 4.8 × 4.8 × 2.1 0.025 3,897,600 3 A, B 1:4 2.4 × 2.4 × 1.05 0.0125 3,897,600 4 A, B 1:10 0.96 × 0.96 × 0.42 0.005 3,897,600 5 A, B 1:20 0.48 × 0.48 0.21 0.0025 3,897,600 6 A, B 1:50 0.192 × 0.192 × 0.084 0.001 3,897,600

Following the geometrical scale, the HRR of the test-fire was reduced (Equation 6), as well as the simulation time (Equation 7). Before starting the calculations, the time step of recording the results in individual simulation has been determined so that regardless of the length of calculations, 200 records are obtained. This allows us to compare the results of numerical analyses in dimensionless time, regardless of the scale of analysis. However, for clarity, all results are shown in scaled-up time, as in the scale 1:1 (Equation 7). Table 5 shows scaled-down calculation time and time step of records for each simulation.

Energies 2019, 12, 3625 8 of 20

Table 3. Parameters of the Fire Dynamics Simulator (FDS) numerical models.

Scenario Scale Model Dimensions [m] Grid Size [m] Number of Grid Cells 1 A, B 1:1 9.6 9.6 4.2 0.05 3,897,600 × × 2 A, B 1:2 4.8 4.8 2.1 0.025 3,897,600 × × 3 A, B 1:4 2.4 2.4 1.05 0.0125 3,897,600 × × 4 A, B 1:10 0.96 0.96 0.42 0.005 3,897,600 × × 5 A, B 1:20 0.48 0.48 0.21 0.0025 3,897,600 × 6 A, B 1:50 0.192 0.192 0.084 0.001 3,897,600 × ×

Following the geometrical scale, the HRR of the test-ﬁre was reduced (Equation (6)), as well as the simulation time (Equation (7)). Before starting the calculations, the time step of recording the results in individual simulation has been determined so that regardless of the length of calculations, 200 records are obtained. This allows us to compare the results of numerical analyses in dimensionless time, regardless of the scale of analysis. However, for clarity, all results are shown in scaled-up time, as in the scale 1:1 (Equation (7)). Table4 shows scaled-down calculation time and time step of records for each simulation.

Table 4. Overview of the Computational Fluid Dynamics (CFD) simulations.

Length of a Time HRR Per Unit of Calculation Scenario Scale Tray Size [m] Step for Results Area [kW/m2] Time [s] Analysis [s] 1 A 1:1 0.35 0.35 750 350 1.75 × 1 B 1:1 0.5 0.5 584 197 0.975 × 2 A 1:2 0.175 0.175 530 247 1.24 × 2 B 1:2 0.25 0.25 414 139 0.7 × 3 A 1:4 0.0875 0.0875 375 175 0.88 × 3 B 1:4 0.125 0.125 293 99 0.49 × 4 A 1:10 0.035 0.035 237 110 0.55 × 4 B 1:10 0.05 0.05 185 62 0.31 × 5 A 1:20 0.0175 0.0175 167 78 0.39 × 5 B 1:20 0.025 0.025 131 44 0.22 × 6 A 1:50 0.007 0.007 106 50 0.25 × 6 B 1:50 0.01 0.01 83 28 0.14 ×

3.3. Mesh Sensitivity Analysis for CFD Simulations The mesh size may be an important factor in the CFD analyses. In this case, a regular cubic grid was used in CFD simulations. The grid size must be small enough to model the turbulent eﬀects properly. For the used LES method, a spatial resolution of 1/4 < R < 1/16 is recommended [37]. This spatial resolution is deﬁned as R = ∆/D*, where ∆ is the element size and D* is the characteristic diameter of the plume, obtained from the Froude-number calculated as [38]: ! Q· D∗ = (12) ρ cp, T √g ∞ ∞ ∞ Figure5 presents the results of mesh sensitivity analysis in the form of measurements of (a) mean layer temperature and (b) maximum plume centerline temperature 20 cm below the ceiling in the full-scale (1:1), with subsequent values of ∆= 0.20 m, 0.10 m, and 0.05 m. It can be noted that for averaged temperatures, the difference between 0.10 m and 0.05 m mesh are below 10 ◦C, and are smaller than the differences between 0.20 m and 0.10 m. However, the differences in the maximum centerline plume temperatures between 0.10 m and 0.05 m are much lower and significantly smaller than between 0.20 m and 0.10 m. Based on these findings, the 5 cm mesh was chosen for further simulations. For simulations in reduced scale, the D* was maintained, and the mesh size was scaled accordingly. Energies 2019, 12, x FOR PEER REVIEW 8 of 19

Table 5. Overview of the Computational Fluid Dynamics (CFD) simulations.

Length of a Time HRR Per Unit of Calculation Scenario Scale Tray Size [m] Step for Results Area [kW/풎ퟐ] Time [s] Analysis [s] 1 A 1:1 0.35 × 0.35 750 350 1.75 1 B 1:1 0.5 × 0.5 584 197 0.975 2 A 1:2 0.175 × 0.175 530 247 1.24 2 B 1:2 0.25 × 0.25 414 139 0.7 3 A 1:4 0.0875 × 0.0875 375 175 0.88 3 B 1:4 0.125 × 0.125 293 99 0.49 4 A 1:10 0.035 × 0.035 237 110 0.55 4 B 1:10 0.05 × 0.05 185 62 0.31 5 A 1:20 0.0175 × 0.0175 167 78 0.39 5 B 1:20 0.025 × 0.025 131 44 0.22 6 A 1:50 0.007 × 0.007 106 50 0.25 6 B 1:50 0.01 × 0.01 83 28 0.14

3.3. Mesh Sensitivity Analysis for CFD Simulations The mesh size may be an important factor in the CFD analyses. In this case, a regular cubic grid was used in CFD simulations. The grid size must be small enough to model the turbulent effects properly. For the used LES method, a spatial resolution of 1/4 < R < 1/16 is recommended [37]. This spatial resolution is defined as R = Δ/D*, where Δ is the element size and D* is the characteristic diameter of the plume, obtained from the Froude-number calculated as [38]: 푄· 퐷∗ = ( ) (12) 휌∞ 푐푝,∞ 푇∞ √푔 Figure 5 presents the results of mesh sensitivity analysis in the form of measurements of (a) mean layer temperature and (b) maximum plume centerline temperature 20 cm below the ceiling in the full-scale (1:1), with subsequent values of Δ = 0.20 m, 0.10 m, and 0.05 m. It can be noted that for averaged temperatures, the difference between 0.10 m and 0.05 m mesh are below 10 °C, and are smaller than the differences between 0.20 m and 0.10 m. However, the differences in the maximum centerline plume temperatures between 0.10 m and 0.05 m are much lower and significantly smaller Energies 2019,than12, 3625 between 0.20 m and 0.10 m. Based on these findings, the 5 cm mesh was chosen for further 9 of 20 simulations. For simulations in reduced scale, the D* was maintained, and the mesh size was scaled accordingly.

(a) (b) Energies 2019, 12, x FOR PEER REVIEW 9 of 19 Figure 5. Comparison of results of mesh sensitivity analysis for (a) mean values of smoke layer Figure 5. Comparison of results of mesh sensitivity analysis for (a) mean values of smoke layer temperature measured 20 cm below the ceiling, and (b) maximum values of centerline plume temperature measured 20 cm below the ceiling, and (b) maximum values of centerline plume temperature 20 cm below the ceiling. temperature 20 cm below the ceiling. 4. Results 4. Results 4.1. Experimental Research 4.1. Experimental Research The HRR value for each experiment was plotted based on the moving average value (5 s averaging The HRR value for each experiment was plotted based on the moving average value (5 s time) mass loss rate measurements, and the assumed Heat of Combustion of the n-Heptane, as shown in averaging time) mass loss rate measurements, and the assumed Heat of Combustion of the n- Figure6. In the case of Series A (1:4 scale), the representation of HRR in the early part of the experiment Heptane, as shown in Figure 6. In the case of Series A (1:4 scale), the representation of HRR in the was not detailed enough, although the duration of the combustion was close to the predictions of the early part of the experiment was not detailed enough, although the duration of the combustion was analyticalclose to model. the predictions The average of the HRR analytical value model. was similar The average between HRR reduced- value was and similar full-scale between experiments reduced- (lessand than full 5%-scale diﬀerence experiments after scaling (less than up 5% the difference time). after scaling up the time).

(a) Series A, 1:1 (b) Series A, 1:1

FigureFigure 6. Heat 6. Heat Release Release Rate Rate measurements measurements in in the the performed performed experiments—moving experiments—moving averages averages (5 (5 s s averagingaveraging time) time) calculated calculated from from mass mass loss loss measurements. measurements. ValuesValues measuredmeasured in in reduced reduced-scale-scale were were scaledscaled up based up based on Equations on Equation (6)s (6) and and (7). (7).

The meanThe mean temperature temperature measured measured (mean (mean value value of of thermocouples thermocouples TC1 TC1–4)–4) show showeded a agood good fitﬁt in in termsterms of the of shape the shape of the of the temperature temperature proﬁle profile and and the the peak peak value value timingtiming (see Figure Figuress 77 andand 8).8). Average Average temperatures in reduced-scale were up to 30% lower than in the full-scale (Figure 8a,b), which can be considered significant and in line with the previous findings in the literature [4,39]. The plume centerline temperatures were in good fit (Figure 8c,d), with the exceptions of maximum temperatures during the HRR peak. The temperatures in the middle of the compartment during cooling down period were also in good agreement. It should be noted, that expected temperatures in reduced- and full-scale should be similar if conditions for Froude-number similarity are met. To identify the source of this discrepancy, the series of numerical simulations were performed (Section 3.2) and the results are shown in Section 4.2.

Energies 2019, 12, 3625 10 of 20 temperatures in reduced-scale were up to 30% lower than in the full-scale (Figure8a,b), which can be considered significant and in line with the previous findings in the literature [4,39]. The plume centerline temperatures were in good fit (Figure8c,d), with the exceptions of maximum temperatures during the HRR peak. The temperatures in the middle of the compartment during cooling down period were also in good agreement. It should be noted, that expected temperatures in reduced- and full-scale should be similar if conditions for Froude-number similarity are met. To identify the source of this discrepancy,Energies 2019, 12, thex FOR series PEER REVIEW of numerical simulations were performed (Section 3.2) and the10 results of 19 are Energies 2019, 12, x FOR PEER REVIEW 10 of 19 shown in Section 4.2.

(a) Series A, 1:1 (b) Series B, 1:1 (a) Series A, 1:1 (b) Series B, 1:1

(c) Series A, 1:4 (d) Series B, 1:4 (c) Series A, 1:4 (d) Series B, 1:4 Figure 7. Mean temperature in full- and reduced-scale experiments. Value averaged on four Figure 7.FigureMean 7. temperature Mean temperature in full- and in fullreduced-scale- and reduced experiments.-scale experiments. Value averaged Value averagedon four measurements on four measurements points underneath the ceiling. points underneathmeasurements the points ceiling. underneath the ceiling.

(a) Series A, mean layer temperature (b) Series B, mean layer temperature (a) Series A, mean layer temperature (b) Series B, mean layer temperature

(c) Series A, plume centreline temperature (d) Series B, plume centreline temperature (c) Series A, plume centreline temperature (d) Series B, plume centreline temperature Figure 8. Comparison of averaged and maximum recorded temperatures in full- and reduced-scale Figure 8. FigureComparison 8. Comparison of averaged of averaged and maximum and maximum recorded recorded temperatures temperatures in full- in full and- and reduced-scale reduced-scale research. research. research.

Additional results, related to the smoke obscuration measurements performed during the Additional results, related to the smoke obscuration measurements performed during the abovementioned experiments can be found in reference [8]. These will not be discussed here, as the abovementioned experiments can be found in reference [8]. These will not be discussed here, as the

Energies 2019, 12, 3625 11 of 20

Additional results, related to the smoke obscuration measurements performed during the Energies 2019, 12, x FOR PEER REVIEW 11 of 19 abovementioned experiments can be found in reference [8]. These will not be discussed here, as the resultresult analysis analysis of of the the experiment experiment was was performed performed primarily primarily throughthrough thethe analysis of the the smoke smoke plume plume andandEnergies smoke smoke 2019 layer ,layer 12, x temperatures. FOR temperatures. PEER REVIEW 11 of 19

4.2.result Numerical analysis Modeling of the experiment was performed primarily through the analysis of the smoke plume 4.2. Numerical Modeling and smoke layer temperatures. TheThe mean mean temperatures temperatures obtained obtained in the experimental experimental research research were were compared compared with with 1:1 and 1:1 and1:4 1:4CFD CFD4.2. Numericalmodel model predictions predictions Modeling (see (see Figure Figure 9). 9In). the In first the first150 s 150 of simulations, s of simulations, the results the resultsfor 1:1 scale for 1:1 were scale in were in a good fit between CFD and the vscale model. However, further into the experiment, some a goodThe fit mean between temperatures CFD and obtained the v inscale the experimental model. However, research further were compared into the experimentwith 1:1 and, 1:4some discrepancies occurred. The temperatures in numerical analysis were lower than in the experiment, discrepanciesCFD model predictions occurred. (seeThe Figuretemperatures 9). In the in first numerical 150 s of simulations,analysis were the lower results than for 1in:1 thescale experiment, were in with the maximum observed difference of 14 C (series B, 1:1 scale). For scale 1:4, the CFD gave higher witha good the maximumfit between observed CFD and difference the vscale of 14 ◦ model. °C (seri However,es B, 1:1 scale). further For intoscale the 1:4, experimentthe CFD gave, some higher temperaturetemperaturediscrepancies than than occurred. the the scale scale The model model temperatures in in the the initial initial in numerical part part of of the the analysis experimentexperiment were lower (which than may may in be bethe related relatedexperiment, to to lower lower initialinitialwith HRR theHRR maximum in in the the physical physical observed experiment, experiment, difference ofsee 14 Figure Figure °C (seri 7).7es). However, B, However, 1:1 scale). in in Forthe the scalelatter latter 1:4, part partthe of CFD the of thesimulationgave simulation higher the theagreement agreementtemperature was was than very very the scale good good model (less (less thanin than the 10% 10%initial difference). di partfference). of the experiment The The differences differences (which in in may measured measured be related temperatures temperatures to lower betweenbetweeninitial scale HRR scale 1:1in 1:1the and andphysical 1:4 1:4 were were experiment, slightly slightly smaller see smaller Figure than than 7). thoseHowever, those observedobserved in the latter betweenbetween part scalesof the simulation1:1 1:1 and and 1:4 1:4 thein in the the physicalphysicalagreement experiment. experiment. was very good (less than 10% difference). The differences in measured temperatures between scale 1:1 and 1:4 were slightly smaller than those observed between scales 1:1 and 1:4 in the physical experiment.

(a) Series A, mean layer temperature (b) Series B, mean layer temperature

FigureFigure 9.(a )Comparison9. Series Comparison A, mean of theoflayer the temperature tempera temperatureture measurements measurements in experimentsin(b experiments) Series B, mean and and numerical layer numerical temperature simulations simulations for full-scalefor full and-scale reduced-scale and reduced- (1:4)scale experiments.(1:4) experiments. The timeThe time value value is scaled is scaled following following Equation Equation (7). (7) Figure 9. Comparison of the temperature measurements in experiments and numerical simulations for full-scale and reduced-scale (1:4) experiments. The time value is scaled following Equation (7) FigureFigure 10 10presents present thes the mean mean smoke smoke layer layer temperature temperature (measured(measured 20 cm underneath underneath the the ceiling) ceiling) forfor all all scalesFigure scales investigated 10 investigated presents the in inmean the the CFD smoke CFD analyses. analyses. layer temperature As As observed observed (measured in in the the 20 experimental cm underneath part, part, the alsoceiling) also in in the the numericalnumericalfor all scales calculations, calculations investigated the, the mean in mean the layer CFDlayer temperature analyses. temperature As observed decreasesdecreases in withwith the experimental the scale. For For part, s scalescales also 1:1, 1:1, in 1:2 1:2 the and and 1:41:4 thenumerical the temperature temperature calculations di ffdifferenceserences, the mean are are withinlayer within temperature 10% 10% (1:1 (1:1 vs vsdecreases 1:2) 1:2) andand with 20%20% the (1:1(1:1 scale. vs 1:4) For limits. scales The1:1, The difference1:2 di ffanderence betweenbetween1:4 the 1:1 temperature 1:1 and and 1:10 1:10 scaledifferences scale is is significant, significant, are within not 10%not only (1:1only vs inin 1:2) thethe and value value 20% ofof (1:1 the vs temperature 1:4) limits. The but but difference also also in in the the temperaturetemperaturebetween 1:1 increment. increment.and 1:10 scale For For scale isscale significant, 1:1 1:1 the the temperature temperaturenot only in the increasesincreases value of in the the temperatureduration of of thebut the fire,also fire, whilein while the for for scalescaletemperature 1:10 1:10 it stabilises it stabili increment.s aroundes around For 75th scale 75 secondth 1:1 second the of temperature theof the experiment. experiment. increases Similar Similar in the di durationffdifferenceserences of were thewere alsofire, also while observed observed for for thefor maximumscale the 1:10 maximum it centerlinestabili centerlineses around plume plume 75 temperature,th second temperature, of asthe shown experiment. as shown in Figure in Similar Figure 11 .differences 11. were also observed for the maximum centerline plume temperature, as shown in Figure 11.

(a) Series A, mean layer temperature (b) Series B, mean layer temperature (a) Series A, mean layer temperature (b) Series B, mean layer temperature Figure 10. Comparison of the mean smoke layer temperature measurements in numerical Figure 10. Comparison of the mean smoke layer temperature measurements in numerical Figureexperiments 10. Comparison with different of the scales. mean smokeThe time layer value temperature is scaled following measurements Equation in numerical. (7). experiments withexperiments diﬀerent scales. with different The time scales. value The is scaledtime value following is scaled Equation following (7). Equation. (7).

EnergiesEnergies 20192019,, 1212,, x 3625 FOR PEER REVIEW 1212 of of 19 20 Energies 2019, 12, x FOR PEER REVIEW 12 of 19

(a) Series A, plume centreline temperature (a) Series A, plume centreline temperature (b) Series B, plume centreline temperature (b) Series B, plume centreline temperature Figure 11. Comparison of the centerline plume temperature measurements in numerical experiments Figure 11. Comparison of the centerline plume temperature measurements in numerical experiments withFigure different 11. Comparison scales. The of time the centerlinevalue is scaled plume following temperature Equation measurements (7). in numerical experiments withwith di differentﬀerent scales. scales. The The time time value value isis scaledscaled followingfollowing Equation (7) (7).. 5. Discussion 5.5. Discussion Discussion 5.1. Modeling the Temperature of the Smoke 5.1.5.1. Modeling Modeling the the Temperature Temperature of of the the Smoke Smoke TTheheThe data data data from from from CFD CFD CFD analyses analyses analyses was waswas post post-processedpost-processed-processed in in formform of of spatio spatio-temporal--temporaltemporal graphs. graphs. The The The x -x x-axisaxis-axis presentspresentspresents the the the position position position on onon a aaline line drawn drawn drawn through through through the the the middlemiddle middle of ofthe the room room atat aa at heightheight a height of of 4.00 4.00 of m 4.00 m above above m above the the floorthefloor floor (with (with (with middle middle middle of of the of the theline line line being being being the the the plume) plume) plume),,, Figure Figure Figure 12 12 12. The. The y y--axis y-axisaxis presents presents presents the the the time time time of of of the the the experiment,experiment,experiment, scaled scaled scaled up up up following following following Equation Equation Equation (7), (7), andand thethe colourcolour represents the the temperature temperature,temperature, ,Figure FiguresFigure 13 1313 andandand 14 14 .. 14 The The. The measurement measurement measurement resolution resolution resolution is 20 is cm.is 20 20 From cm. cm. plots, From From the plots plots differences, the differences differences in modeling in in themodelmodel temperatureinging th the e temperatureintemperature different scales in indifferent different are evident. scales scales For are are series evident. evident. A, theFor For differences seriesseries A,A, thethe between differences scales betweenbetween 1:1 and 1:2scales scales are 1:1 smaller1:1 and and 1:2 than 1:2 are10%,are smaller andsmaller for than seriesthan 10%, 10%, B, theand and results for for series series for scales B, B, the the 1:1, results results 1:2, and forfor 1:4scalesscales show 1:1, similar 1:2,, andand degree 1:41:4 showshow of agreement. similar similar degree degree In case of of of agreement.scalesagreement. 1:10, In 1:20, In case case and of of scales 1:50 scales the 1:10, 1:10, results 1:20 1:20, can,and and be1:5 1:5 considered00 the the results results to cancan be be wrong, considered and to to to have be be wrong, wrong, no scientific and and to to have value.have noItno isscientific interesting, scientific value. value. as It scales Itis isinteresting, interesting, 1:10–1:25 as are as scales scales commonly 1:10 1:10––1:251:25 used areare in commonlycommonly research (see used Equations inin researchresearch (6)–(11)). (see (see Table Table It should1). 1). It It shouldbeshould noted, be be that noted, noted, in case that that of in thisin case case study, of of this thisthe study, fire study, modeled the the fire fire can modelmodel be considereded can be “small” considered considered and “small” “small”the findings and and the maythe findingsnotfindings be relevant may may not to not modeling be be relevant relevant of tolarge to model model firesinging (such of of large as large fires fires fires of tunnel (such (such vehiclesas fires fires of ofor tunnel tunnellargecompartment vehicles vehicles or or large large fires). compartmentNevertheless,compartment observed fires). fires). Nevertheless, Nevertheless,discrepancies observed indicate observed that discrepancies discrepancies the applicability indicate of the that that Froude-number the the applicability applicability scaling of of theory the the Froude-number scaling theory should not be assumed for every research, and a scale sensitivity Froudeshould- notnumber be assumed scaling for theory every should research, not and be a assumed scale sensitivity for every analysis research, should and precede a scale such sensitivity efforts. analysis should precede such efforts. analysisAuthors should cannot precede identify such efforts. the sole reason for the observed discrepancies, although a careful Authors cannot identify the sole reason for the observed discrepancies, although a careful examinationAuthors of cannot the assumptions identify the and sole results reason of for the the modeling observed indicate discrepancies, some possible although problems a careful with examination of the assumptions and results of the modeling indicate some possible problems with examinationmaintaining of the the correct assumptions ﬂow turbulence and results (further of the discussed modeling in indicate Section 5.2some) and possible modeling probl theems thermal with maintaining the correct flow turbulence (further discussed in Section 5.2) and modeling the thermal maintaininginertia of model the correct boundaries flow (furtherturbulence discussed (further in discussed Section 5.3 in). Section 5.2) and modeling the thermal inertiainertia of ofmodel model boundaries boundaries (further (further discussed discussed in in SectionSection 5.3).5.3).

Figure 12. Location of the line along which the temperature was measured, and plo tted in a function FigureFigureof time 12. 12. on LocationLocation Figures of of13 the theand line 14. along which thethe temperaturetemperature waswas measured, measured, and and plotted plotted in in a functiona function of oftime time on on Figures Figures 13 13 and and 14 14. .

EnergiesEnergies2019 2019, 12, 12, 3625, x FOR PEER REVIEW 1313 of of 20 19

FigureFigure 13. 13.Spatio-temporal Spatio-temporal plots plots of of temperature temperature in in a a line line through through the the middle middle of of the the compartment compartment (Figure(Figure 12 12)), for, for Series Series A. A.

Energies 2019, 12, 3625 14 of 20 Energies 2019, 12, x FOR PEER REVIEW 14 of 19

FigureFigure 14. 14.Spatio-temporal Spatio-temporal plots plots of of temperature temperature in in a a line line through through the the middle middle of of the the compartment compartment (Figure(Figure 12 12),), for for Series Series B. B. 5.2. Problems with Maintaining the Reynolds Number and Laminar Flames 5.2. Problems with Maintaining the Reynolds Number and Laminar Flames In Section2, we have mentioned a rule of thumb that the flow turbulence should be maintained, In Section 2, we have mentioned a rule of thumb that the flow turbulence should be maintained, which is closely related to the Reynolds number of the modeled flow. Quintiere et al. mentioned that which is closely related to the Reynolds number of the modeled flow. Quintiere et al. mentioned that this is usually achieved in model compartments with height > 0.3 m [5]. A simplification in this aspect this is usually achieved in model compartments with height > 0.3 m [5]. A simplification in this aspect is necessary, as the conservation of Froude and Reynolds numbers in the same model may be difficult. is necessary, as the conservation of Froude and Reynolds numbers in the same model may be difficult. From the definition of the Reynolds number: From the definition of the Reynolds number: 푢 푙휌 u00lρ 푅푒Re == (13)(13) 휇µ it can be noted that scaling of the velocity or density of the fluid would invalidate the Froude similarity. Thus, if one would need to conserve the Reynolds number while following the Froude relationship, it would require scaling of the kinematic viscosity of the medium, which is not practical. However, if the flow is mainly driven by the buoyancy and is highly turbulent (we propose a rule of thumb value of Re > 10,000), the further increase of the Re number will have a limited effect on the

Energies 2019, 12, 3625 15 of 20 it can be noted that scaling of the velocity or density of the fluid would invalidate the Froude similarity. Thus, if one would need to conserve the Reynolds number while following the Froude relationship, it would require scaling of the kinematic viscosity of the medium, which is not practical. However, if the flow is mainly driven by the buoyancy and is highly turbulent (we propose a rule of thumb value of Re > 10,000), the further increase of the Re number will have a limited effect on the fluid dynamics of the smoke plume or layer. In such a case, the omission of the Reynolds similarity is justified. In practice, the flows in full fires scale are turbulent. However, once scaled down to small scale, the flow turbulence may be insufficient to justify the omission of the Reynolds scaling. In such case, the buoyant plume will not mix with the surrounding air, and the entrainment will not represent the behavior of the large scale plume. Such a problem was observed in the numerical experiments for scales 1:20 and 1:50, where laminar plumes were observed. The illustration of the plumes is shown in Figure 15. The approximated values (for velocity averaged over 30 s) of Re number for the plume flow are shown in Table5. The approximated Reynolds number for small scales (1:10, 1:20 and 1:50) indicates, that flow structure in these scenarios was laminar (significantly below Re = 2100). In case of Series A, the Re number for scale 1:4 was most likely in the transition range between laminar and turbulent flow (Re = 2982), while in Series B the flow was turbulent (Re = 5562). This observation is coherent with the temperature differences between scales, observed between the series A and B. For scale 1:2 in series B, which was in good agreement with full-scale research, the Re number was above 10,000.

Table 5. Approximation of the plume centerline Reynolds number.

Velocity [m/s] Velocity [m/s] (Calculated Reynolds Number Reynolds Number Scale (CFD) with Equation (9)) (CFD) 1 (Calculated) 1 Series A 1:1 1.50 1.50 27,531 27,531 1:2 0.95 1.06 8718 9734 1:4 0.65 0.75 2982 3441 1:10 0.40 0.47 734 871 1:20 0.05 0.34 46 308 1:50 0.08 0.21 29 78 Series B 1:1 1.50 1.50 41,713 41,713 1:2 1.00 1.06 13,904 14,748 1:4 0.80 0.75 5562 5214 1:10 0,50 0.47 1390 1319 1:20 0.07 0.34 97 466 1:50 0.09 0.21 50 118 1 For the purpose of this calculation, the kinematic viscosity of air was taken as for the air temperature of 60 ◦C and the characteristic dimension was chosen as the characteristic size of the pan (width of the plume).

A series of snapshots presenting the structure of the plume in CFD simulations (coloured by the temperature) is shown in Figure 15. The temperature scale for each picture was individually exaggerated, to highlight the plume shape (and the ﬂow structure), illustrating the visible diﬀerences in the plume shape between large and small scale simulations. Energies 2019, 12, 3625 16 of 20

Energies 2019, 12, x FOR PEER REVIEW 16 of 19

FigureFigure 15.15. Temperature sliceslice through the centerline of the the smoke smoke plume, plume, with with visible visible vortices vortices forming forming inin the the plumeplume andand laminarlaminar structuresstructures in scales 1:20 and 1:50 1:50,, for for series series A A (two (two left left columns) columns) and and B B (two (two rightright columns). columns). TheThe colourcolour scale was individually individually altered altered to to illustrate illustrate the the flow ﬂow structure structure of of the the plume plumes.s.

5.3.5.3. TheThe InfluenceInfluence ofof thethe Thermal Inertia of the B Boundariesoundaries Scaling of the thermal inertia (k ρ c) of the physical model boundaries is often disregarded in Scaling of the thermal inertia (k·ρ·c· · ) of the physical model boundaries is often disregarded in reduced-scalereduced-scale research.research. In short short-duration-duration experiments experiments (shorter (shorter than than few few minutes) minutes) such such as as the the one one shownshown inin thisthis paper,paper, thisthis maymay notnot havehave a significantsignificant impact on on the the measur measureded temperatures, temperatures, as as the the heatheat transfertransfer toto thethe boundariesboundaries will be insignificantinsignificant compared compared to to radiation. radiation. However, However, in in the the case case of of longlong experiments experiments oror very very large large fires, fires, the the di differencesfferences in in heat heat transfer transfer in in fullfull and- and reduced-scale reduced-scale may may be important.be important. It should It should be noted, be no thatted, in that many in manyresearch research available available in the literature, in the literature, the full-scale the full materials-scale suchmaterials as concrete such as or concrete masonry, or masonry, are represented are represented in the reduced-scale in the reduced with-scale steel with and steel glass. and glass. This is This due tois thedue ease to the of ease the model of the buildingmodel building process, process, and the and ability the ability to observe to observe the experiments, the experiments, at the at cost the of completelycost of completely different different heat transfer heat transfer at the model at the boundaries.model boundaries. TheThe problems problems with with thethe scaling scaling of of heat heat transfer transfer were were thoroughly thoroughly described described by Quintiere by Quintiere [14 ], where[14],where dimensionless dimensionless groups groupsΠ3, Π35, ,ΠΠ5,6 ,ΠΠ6, 7Π,7 and, andΠ Π8 8should should bebe preserved.preserved. However However,, this this leads leads to to inconsistenciesinconsistencies with with Equation Equation (11) (11) and and in in the the scaling scaling of of the the convective convective heat heat transfer transfer coe coefficientfficient (and (and the Nusseltthe Nusselt number). number). To cope To cope with with that severalthat several strategies strategies may bemay used be toused maintain to maintain partial partial scaling. scaling. One is toOne maintain is to maintain dimensionless dimensionless groups Πgroup5 ands Π58 andas constant, Π8 as constant, to preserve to preserve wall conduction wall conduction effects effects [14]. [14]. 1 1 3 ! 3 (kρc) 2 2 2 (푘휌푐)2 푥푚 xm Π5 = ∴ (kρc) (14) 훱5 = 3 ∴3 (푘휌푐)~ ( ) (14) 4 푥∼ x f ρ cp4gl 푓 휌∞푐∞푝푔푙 1 1 1 1 1 ! 1 (푘휌푐( ) )2 푔2 푥 4 4 kρ푊c W 4g 4 푚 xm (15) 훱Π8 =8 = ( ) 훿푤δ∴w 훿∴푤~δw( ) (15) 푘푤k w 푙 l ∼푥푓 x f Additional considerations must be done for radiative heat flux, especially for large fires in which Additional considerations must be done for radiative heat flux, especially for large fires in which the the radiation flux is significantly larger than convection heat flux [14]. In some cases in which radiation flux is significantly larger than convection heat flux [14]. In some cases in which radiation is radiation is believed to dominate, the Equation (14) can be ignored, while maintaining (16) instead: believed to dominate, the Equation (14) can be ignored,̇ 0 while maintaining (16) instead: 푘 푥 푞′′~ ( 푤) 푇~ ( 푚) . (16) 훿푤 . 푥푓 ! !0 In practice, the thermal parameters describingkw the wallxm (k, ρ, c) and the width of the walls (δ) can q00 T . (16) be chosen accordingly to the scale. The sensitivity∼ δw of ∼the xscalef model to these values may be verified in numerical CFD analysis, where usually these parameters can be easily defined by the user. It shouldIn practice,be noted the that thermal the convective parameters heat describing transfer will the also wall depend (k, ρ, c) on and the the Nusselt width ofnumber, the walls which (δ) canis berelated chosen to accordinglyflow velocity to and the turbulence. scale. The sensitivity This means of that the scaleconsiderations model to theserelated values to the may flow be turbulence verified in numericalfrom Section CFD 5.2 analysis, are even where more relevant. usually these Nevertheless, parameters scaling can beof easilythe thermal defined inertia by the and/or user. width It should of bethe noted model that boundaries the convective is possible, heat and transfer in research will also where depend convection on the Nusseltand conduction number, are which important is related to the modeled phenomena, a sensitivity analysis should be performed.

Energies 2019, 12, 3625 17 of 20 to flow velocity and turbulence. This means that considerations related to the flow turbulence from Section 5.2 are even more relevant. Nevertheless, scaling of the thermal inertia and/or width of the model boundaries is possible, and in research where convection and conduction are important to the modeled phenomena, a sensitivity analysis should be performed. The scaling of the thermal inertia of boundaries together with the introduction of heat sinks in the gas phase of the model tunnel can be used to increase the length of a pseudo tunnel model [40]. In this approach, the heat sinks simulate the effects of heat transfer along a significantly longer section of a tunnel, which may be useful for studying flow dynamics in long tunnels, without the need for building excessively large reduced-scale models. However, this approach was only tested in linear (close to 1D) buildings and may require further validation [40].

6. Conclusions The paper has shown observed discrepancies and problems with the application of Froude-number scaling for modeling compartment fires. The experiments were performed with a wide range of Reynolds numbers, showing the essential role that turbulent flow has on the temperatures in the plume and the compartment. The previously mentioned rule of thumb value of Re = 10,000 was confirmed, to sufficiently minimize the error of the method related to the flow turbulence. In case of small scales (1:2 and 1:4) the average temperatures measured were up to 30% lower than in the full-scale experiment, however in most of the experiment duration this difference was up to 10% (which in the opinion of the authors can be considered as an acceptable value). The temporal change in the temperature was well represented in small scale. These results indicate that the scaling method can be useful for investigation of the flow of smoke in buildings. For smaller scales (1:10 and smaller) the differences in the temperatures measured were significant, and in case of very small scales (1:20 and 1:50), the results have no scientific value due to change of the flow from turbulent to laminar. CFD modeling with FDS software did sufficiently represent the full- and reduced-scale experiments and was used to analyze a wide array of scaled fires. A similar approach can be used before future experiments, to verify the sensitivity of the experiment to the scale, and estimate the Reynolds number of the flow. Furthermore, the numerical modeling may help with investigating the effects of materials used in the reduced-scale model on the heat transfer to the model boundaries. As first discussed by Spalding, and mentioned by Williams [9] and Quintiere [14], the reduced-scale modeling is an art that requires the user to choose which dimensionless relations are conserved, and which are omitted. To maintain the high scientific value of scaled-down experiments, the user should make informed decisions, and use modern tools (such as CFD modeling) to assess the model sensibility to the changes introduced in the reduced-scale. As shown in this paper, just following the basic scaling theory is not sufficient to guarantee that the results of reduced-scale experiment are valid. Also, the temperature should not be considered as the only variable to be assessed. Other parameters such as flow velocity, mass concentration of pollutants, or heat fluxes may be useful for evaluating the validity of the model.

Author Contributions: Conceptualization, M.Z., P.A., A.K. and W.W.; Formal analysis, M.Z., G.K. and T.B.; Investigation, M.Z. and P.A.; Methodology, A.K. and W.W.; Resources, P.A.; Supervision, A.K. and W.W.; Visualization, M.Z., G.K. and T.B.; Writing—original draft, M.Z., G.K., T.B., A.K. and W.W.; Writing—review & editing, W.W. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Energies 2019, 12, 3625 18 of 20

List of Symbols cp specific heat [J/kgK] D diameter of the plume E energy [J] Fr Froude dimensionless number g gravitational pull of Earth [N/kg] Hc Heat of combustion [kJ/kg] k conductivity [W/m K] K Radiation absorption coefficient l characteristic length [m] m. mass flow [kg/s] Nu Nusselt number Re Reynolds dimensionless number T Temperature [K] t time [s] µ kinematic viscosity [m2/s] u air flow velocity [m/s] Q rate of heat release [kW] x characteristic dimension [m] ρ density [kg/m3] Π dimensionless group

Subscripts f full-scale model m reduced-scale model o ambient

References

1. McGrattan, K. Fire modeling: Where are we? Where are we going? Fire Saf. Sci. 2005, 8, 53–68. [CrossRef] 2. McGrattan, K.; Miles, S. Modeling Fires Using Computational Fluid Dynamics (CFD). In SFPE Handbook of Fire Protection Engineering; Springer: New York, NY, USA, 2016; pp. 1034–1065. 3. Thomas, P.H.; Hinkley, P.L.; Theobald, C.R.; Simms, D.L. Investigations into the Flow of Hot Gases in Roof Venting; Her Majesty’s Stationary Office: London, UK, 1963. 4. Carey, A.C. Scale Modeling of Static Fires in a Complex Geometry for Forensic Fire Applications. Ph.D. Thesis, University of Maryland, College Park, MD, USA, 2010. 5. Quintiere, J.G.; Carey, A.C.; Reeves, L.; Mccarthy, L.K. 2008-DN-BX-K178: Scale Modeling in Fire Reconstruction; Natopnal Criminal Justice Reference Service: Rockville, MD, USA, 2017. 6. Merci, B. Introduction to Fluid Mechanics. In SFPE Handbook of Fire Protection Engineering; Springer: New York, NY, USA, 2016; pp. 1–24. 7. Thomas, P.H. Dimensional analysis: A magic art in fire research? Fire Saf. J. 2000, 34, 111–141. [CrossRef] 8. W˛egrzyński,W.; Antosiewicz, P.; Burdzy, T.; Zimny, M.; Krasuski, A. Smoke Obscuration Measurements in Reduced-Scale Fire Modeling Based on Froude Number Similarity. Sensors 2019, 19, 3628. [CrossRef] [PubMed] 9. Williams, F.A. Scalling Mass Fires. In Fire Research Abstracts and Reviews, Volume 11; National Academies Press: Washington, DC, USA, 1969; pp. 1–22, ISBN 978-0-309-30950-9. 10. Prahl, J.; Emmons, H.W. Fire induced flow through an opening. Combust. Flame 1975, 25, 369–385. [CrossRef] 11. Harrison, R.; Spearpoint, M. The Balcony Spill Plume: Entrainment of Air into a Flow from a Compartment Opening to a Higher Projecting Balcony. Fire Technol. 2007, 43, 301–317. [CrossRef] 12. W˛egrzyński,W.; Konecki, M. Influence of the fire location and the size of a compartment on the heat and smoke flow out of the compartment. AIP Conf. Proc. 2018, 1922, 110007. 13. Quintiere, J.G. Scaling applications in fire research. Fire Saf. J. 1989, 15, 3–29. [CrossRef] Energies 2019, 12, 3625 19 of 20

14. Quintiere, J.G. Fundamentals of Fire Phenomena; John Wiley & Sons Ltd.: Hoboken, NJ, USA, 2006. 15. Zohuri, B. Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists; Springer: New York, NY, USA, 2015; ISBN 9783319134765. 16. Zimny, M. Physical modeling of a fire with the use of the Froude number. Bud. Archit. 2019, 18, 71–80. 17. Brzezińska,D. Ventilation System Influence on Hydrogen Explosion Hazards in Industrial Lead-Acid Battery Rooms. Energies 2018, 11, 2086. [CrossRef] 18. Li, Y.Z.; Ingason, H.; Lönnermark, A. Runehamar Tunnel Fire Tests; SP Technical Research Institute of Sweden: Borås, Sweden, 2011. 19. Kim, D.H.; Park, W.H. Experiment by using reduced scale models for the fire safety of a rescue station in very long rail tunnel in Korea. Tunn. Undergr. Space Technol. 2006, 21, 303. [CrossRef] 20. Lönnermark, A.; Lindström, J.; Li, Y.Z. Model-Scale Metro Car Fire Tests of Sweden; SP Technical Research Institute of Sweden: Borås, Sweden, 2011; ISBN 9789186622657. 21. Heskestad, G. Modeling of enclosure fires. Symp. Combust. 1973, 14, 1021–1030. [CrossRef] 22. Himoto, K.; Shinohara, M.; Sekizawa, A.; Takanashi, K.; Saiki, H. A field experiment on fire spread within a group of model houses. Fire Saf. J. 2018, 96, 105–114. [CrossRef] 23. Croce, P.A.; Xin, Y. Scale modeling of quasi-steady wood crib fires in enclosures. Fire Saf. J. 2005, 40, 245–266. [CrossRef] 24. Quintiere, J.; Mccaffrey, J.; Kashiwagi, T. A scaling study of a corridor subject to a room fire. Combust. Sci. Technol. 1978, 18, 1–19. [CrossRef] 25. Arini, D.; Pancawardani, F.; Santoso, M.A.; Sugiarto, B.; Nugroho, Y.S. Froude Modeling of Fire Phenomena: Observation of Fire-induced Smoke Movement in Basement Structure for Firefighting Purpose. Procedia Eng. 2017, 170, 182–188. [CrossRef] 26. W˛egrzyński,W. Partitions and the flow of smoke in large volume buildings. Archit. Civ. Eng. Environ. 2018, 11, 155–164. [CrossRef] 27. Tanaka, F.; Kawabata, N.; Ura, F. Smoke spreading characteristics during a fire in a shallow urban road tunnel with roof openings under a longitudinal external wind blowing. Fire Saf. J. 2017, 90, 156–168. [CrossRef] 28. Kayili, S.; Yozgatligil, A.; Eralp, O.C. Effect of Ventilation and Geometrical Parameters of the Burning Object on the Heat Release Rate in Tunnel Fires. Combust. Sci. Technol. 2012, 184, 165–177. [CrossRef] 29. Li, Y.Z.; Ingason, H. Model scale tunnel fire tests with automatic sprinkler. Fire Saf. J. 2013, 61, 298–313. [CrossRef] 30. Li, Y.Z.; Lei, B.; Ingason, H. Scale modeling and numerical simulation of smoke control for rescue stations in long railway tunnels. J. Fire Prot. Eng. 2012, 22, 101–131. [CrossRef] 31. Zhao, P.; Yuan, Z.; Yuan, Y.; Yu, N.; Yu, T. A Study on Ceiling Temperature Distribution and Critical Exhaust Volumetric Flow Rate in a Long-Distance Subway Tunnel Fire with a Two-Point Extraction Ventilation System. Energies 2019, 12, 1411. [CrossRef] 32. Ingason, H.; Li, Y.Z. Model scale tunnel fire tests with longitudinal ventilation. Fire Saf. J. 2010, 45, 371–384. [CrossRef] 33. Khattri, S.K.; Log, T.; Kraaijeveld, A. Tunnel Fire Dynamics as a Function of Longitudinal Ventilation Air Oxygen Content. Sustainability 2019, 11, 203. [CrossRef] 34. McGrattan, K.; Hostikka, S.; McDermott, R.; Floyd, J.; Weinschenk, C.; Overholt, K. Fire Dynamics Simulator User’s Guide, 6th ed.; National Insitute of Standards and Technology: Gaithersburg, MD, USA, 2017. 35. McGrattan, K.; Hostikka, S.; McDermott, R.; Floyd, J.; Weinschenk, C.; Overholt, K. Fire Dynamics Simulator Technical Reference Guide. Volume 3: Validation, 6th ed.; NIST Special Publication 1018-3; National Insitute of Standards and Technology: Gaithersburg, MD, USA, 2015; Volume 1. 36. Thunderhead Engineering. PyroSim User Manual; Thunderhead Engineering: Manhattan, KS, USA, 2017; p. 167. 37. Hill, K.; Dreisbach, J.; Joglar, F.; Najafi, B.; McGrattan, K.; Peacock, R.; Hamins, A. Verification and Validation of Selected Fire Models for Nuclear Power Plant Aplications, Volume 7; U.S. NRC: Washington, DC, USA, 2014. 38. Hurley, M.J. SFPE Handbook of Fire Protection Engineering; Hurley, M.J., Gottuk, D., Hall, J.R., Jr., Harada, K., Kuligowski, E., Puchovsky, M., Torero, J., Watts, J.M., Jr., Wieczorek, C., Eds.; Springer: New York, NY, USA, 2016; ISBN 978-1-4939-2565-0. Energies 2019, 12, 3625 20 of 20

39. Barsim, M.M.; Bassily, M.A.; El-Batsh, H.M.; Rihan, Y.A.; Sherif, M.M. Froude scaling modeling in an Atrium Fire equipped with natural and transient forced ventilation. Int. J. Vent. 2019, 1–23. [CrossRef] 40. Tanaka, F.; Fukaya, K.; Moinuddin, K.A.M. Development of a technique for establishing a pseudo tunnel length. Proc. Combust. Inst. 2019, 37, 3985–3992. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).