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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mech. Eng</journal-id>
<journal-title>Frontiers in Mechanical Engineering</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mech. Eng</abbrev-journal-title>
<issn pub-type="epub">2297-3079</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">628510</article-id>
<article-id pub-id-type="doi">10.3389/fmech.2020.628510</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Mechanical Engineering</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Investigating the Effect of Structure to Structure Separation Distance on Firebrand Accumulation</article-title>
<alt-title alt-title-type="left-running-head">Suzuki and Manzello</alt-title>
<alt-title alt-title-type="right-running-head">Structure Separation on Firebrand Accumulation</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Suzuki</surname>
<given-names>Sayaka</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="http://loop.frontiersin.org/people/983505/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Manzello</surname>
<given-names>Samuel L.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="http://loop.frontiersin.org/people/983635/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<label>
<sup>1</sup>
</label>National Research Institute of Fire and Disaster, <addr-line>Tokyo</addr-line>, <country>Japan</country>
</aff>
<aff id="aff2">
<label>
<sup>2</sup>
</label>National Institute of Standards and Technology (NIST), <addr-line>Gaithersburg</addr-line>, <addr-line>MD</addr-line>, <country>United States</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/627031/overview">Myeongsub Kim</ext-link>, Florida Atlantic University, United States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/334399/overview">Xinyan Huang</ext-link>, Hong Kong Polytechnic University, Hong Kong</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/615280/overview">Gianni Pagnini</ext-link>, Basque Center for Applied Mathematics, Spain</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Samuel L. Manzello, <email>samuelm@nist.gov</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Thermal and Mass Transport, a section of the journal Frontiers in Mechanical Engineering</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>28</day>
<month>01</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2020</year>
</pub-date>
<volume>6</volume>
<elocation-id>628510</elocation-id>
<history>
<date date-type="received">
<day>12</day>
<month>11</month>
<year>2020</year>
</date>
<date date-type="accepted">
<day>15</day>
<month>12</month>
<year>2020</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Suzuki and Manzello.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Suzuki and Manzello</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Wind plays an important role in the built environment. Large outdoor fires in the built environment are no exception. Under strong wind, firebrands fly far, which leads to quick fire spread. In this study, the effect of structure to structure separation distance on firebrand accumulation was investigated by using a custom designed firebrand generator installed in a real scale wind tunnel. Firebrands accumulated at 4 and 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, but no firebrand accumulation zone was observed at 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, regardless of separation distance (SD). Experimental results were compared with a simple CFD flow simulation (no firebrands included). The size of firebrand accumulation zone as well as distance from the structure front was compared with SD in the cases of 4 and 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speeds. It was found that firebrands behave differently from SD &#x3d; 1 to 2&#xa0;m, to that of SD &#x3d; 2 to 3&#xa0;m. The results of this study are the first to explore these important interactions between firebrands and structure separation distances. The results of this work will help develop and design sustainable communities that may better resist the destruction of increasing large outdoor fire outbreaks worldwide, as well as help develop the next generation of CFD models needed to grasp the important large outdoor fire problem and associated firebrand processes.</p>
</abstract>
<kwd-group>
<kwd>large outdoor fires and the built environment</kwd>
<kwd>firebrands</kwd>
<kwd>accumulation</kwd>
<kwd>separation distance</kwd>
<kwd>firebrand generator</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Wind plays an important role in the built environment, from ventilation within buildings, wind force on buildings, effects on rain, to pollution dispersion (<xref ref-type="bibr" rid="B37">Shah and Ferziger, 1997</xref>; <xref ref-type="bibr" rid="B6">Blocken and Carmeliet, 2004</xref>; <xref ref-type="bibr" rid="B34">Quyang et al., 2006</xref>; <xref ref-type="bibr" rid="B7">Chaves et al., 2011</xref>; <xref ref-type="bibr" rid="B58">Yuan and Ng, 2012</xref>; <xref ref-type="bibr" rid="B35">Razak et al., 2013</xref>). The importance of wind applies to fire safety, where an increasing number of large outdoor fires, such as urban fires, informal settlement fires, wildland-urban interface (WUI) fires and wildland fires, are a major concern (<xref ref-type="bibr" rid="B21">Manzello et al., 2018</xref>).</p>
<p>Outdoor fires spread via three paths; direct flame contact, radiative heat, and firebrands. Wind largely influences outdoor fire spread behavior. Especially in the presence of strong wind, fires spread quickly, endangering people in vast areas. Stronger wind enhances flame spread processes; heat transfer processes are augmented (<xref ref-type="bibr" rid="B2">Albini 1985</xref>; <xref ref-type="bibr" rid="B56">Weber 1989</xref>; <xref ref-type="bibr" rid="B32">Pitts, 1991</xref>; <xref ref-type="bibr" rid="B57">Weber 1991</xref>; <xref ref-type="bibr" rid="B33">Potter, 1996</xref>; <xref ref-type="bibr" rid="B31">Morandini et al., 2001</xref>; <xref ref-type="bibr" rid="B14">Hu et al., 2009</xref>; <xref ref-type="bibr" rid="B65">Morandini and Silvani, 2010</xref>; <xref ref-type="bibr" rid="B38">Sharples et al., 2012</xref>).</p>
<p>Firebrand processes are also affected by winds (<xref ref-type="bibr" rid="B50">Tarifa et al., 1965</xref>; <xref ref-type="bibr" rid="B18">Lee and Hellman 1969</xref>; <xref ref-type="bibr" rid="B1">Albini 1983</xref>; <xref ref-type="bibr" rid="B10">Ellis 2000</xref>; <xref ref-type="bibr" rid="B3">Albini et al., 2012</xref>; <xref ref-type="bibr" rid="B16">Koo et al., 2012</xref>; <xref ref-type="bibr" rid="B45">Suzuki et al., 2013</xref>; <xref ref-type="bibr" rid="B53">Tohidi et al., 2015</xref>; <xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>; <xref ref-type="bibr" rid="B51">Tohidi and Kaye, 2017a</xref>; <xref ref-type="bibr" rid="B52">Tohidi and Kaye, 2017b</xref>; <xref ref-type="bibr" rid="B11">Fernandez-Pello, 2017</xref>; <xref ref-type="bibr" rid="B39">Song et al., 2017</xref>; <xref ref-type="bibr" rid="B46">Suzuki and Manzello, 2019</xref>; <xref ref-type="bibr" rid="B43">Suzuki and Manzello 2020a</xref>; <xref ref-type="bibr" rid="B22">Manzello et al., 2020</xref>; <xref ref-type="bibr" rid="B24">Manzello and Suzuki, 2020</xref>; <xref ref-type="bibr" rid="B48">Suzuki and Manzello 2021</xref>). Wind influences all aspects of firebrand behavior; firebrand generation from fuels (<xref ref-type="bibr" rid="B45">Suzuki et al., 2013</xref>; <xref ref-type="bibr" rid="B53">Tohidi et al., 2015</xref>; <xref ref-type="bibr" rid="B46">Suzuki and Manzello, 2019</xref>; <xref ref-type="bibr" rid="B24">Manzello and Suzuki, 2020</xref>; <xref ref-type="bibr" rid="B43">Suzuki and Manzello 2020</xref>; <xref ref-type="bibr" rid="B48">Suzuki and Manzello 2021</xref>), transport distance (<xref ref-type="bibr" rid="B50">Tarifa et al., 1965</xref>; <xref ref-type="bibr" rid="B18">Lee and Hellman 1969</xref>; <xref ref-type="bibr" rid="B1">Albini 1983</xref>; <xref ref-type="bibr" rid="B10">Ellis 2000</xref>; <xref ref-type="bibr" rid="B3">Albini et al., 2012</xref>; <xref ref-type="bibr" rid="B16">Koo et al., 2012</xref>; <xref ref-type="bibr" rid="B51">Tohidi and Kaye, 2017a</xref>; <xref ref-type="bibr" rid="B52">Tohidi and Kaye, 2017b</xref>; <xref ref-type="bibr" rid="B39">Song et al., 2017</xref>), firebrand deposition patterns (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>), and ignition behavior induced by firebrands (<xref ref-type="bibr" rid="B13">Ganteaume 2009</xref>; <xref ref-type="bibr" rid="B23">Manzello et al., 2012</xref>; <xref ref-type="bibr" rid="B25">Manzello and Suzuki 2012</xref>; <xref ref-type="bibr" rid="B19">Manzello, 2014</xref>; <xref ref-type="bibr" rid="B47">Suzuki et al., 2015</xref>; <xref ref-type="bibr" rid="B42">Suzuki and Manzello, 2017b</xref>; <xref ref-type="bibr" rid="B20">Manzello et al., 2017</xref>; <xref ref-type="bibr" rid="B55">Wang et al., 2017</xref>; <xref ref-type="bibr" rid="B44">Suzuki and Manzello, 2020b</xref>). Out of four firebrand behaviors, the firebrand deposition is the least studied to the authors&#x2019; knowledge. While many research studies that model the wildland fire behavior have been undertaken (<xref ref-type="bibr" rid="B36">Rothermel, 1972</xref>; <xref ref-type="bibr" rid="B17">Koo et al., 2005</xref>; <xref ref-type="bibr" rid="B4">Alexander and Cruz, 2006</xref>; <xref ref-type="bibr" rid="B8">Cheney and Sullivan, 2008</xref>; <xref ref-type="bibr" rid="B40">Sullivan, 2009</xref>; <xref ref-type="bibr" rid="B28">Martin and Hillen, 2016</xref>; <xref ref-type="bibr" rid="B54">Trucchia et al., 2019</xref>), including firebrands in these models is a great challenge. Modeling firebrands is complex in nature, such as change in mass, size, and combustion state during transport. More experimental studies are needed to understand the flow dynamics of firebrands near and around structures. In a past, first attempt (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>), firebrand accumulation behavior in front of a simple wall under different wind speeds was investigated and compared with simple wind flow modeling.</p>
<p>One of important measures in areas prone to large outdoor fires are home ignition zones (HIZ) (<xref ref-type="bibr" rid="B9">Cohen, 2000</xref>; <xref ref-type="bibr" rid="B49">Syphard et al., 2012</xref>; <xref ref-type="bibr" rid="B5">Biswas et al., 2013</xref>). It is important to remove all the combustibles including sheds or mulches, in case of any combustibles being ignited by firebrands, which will lead to ignition of homes. Unfortunately, it is difficult to implement in practice (<xref ref-type="bibr" rid="B30">Mell and Maranghides, 2009</xref>). More understanding on firebrand behavior around structures is needed. To this end, experiments were performed to investigate the firebrand behavior around structures, with a special emphasis on the separation distance between structures.</p>
</sec>
<sec id="s2">
<title>Experiments</title>
<sec id="s2-1">
<title>Experimental Description</title>
<p>The continuous-feed firebrand generator (NIST Dragon) was used for all the experiments. The details of this apparatus are described in (<xref ref-type="bibr" rid="B26">Manzello and Suzuki, 2014</xref>), so a brief overview is provided here. The continuous-feed NIST Dragon was made of a continuous-feed part connected to the firebrand generator (<xref ref-type="fig" rid="F1">Figure 1</xref>). The continuous-feed part has the storage of wood pieces (for firebrands) connected with a pipe to the NIST Dragon, with two gates to mitigate fire spread from the apparatus to the feeding system. The firebrand generator has a blower that was set to 3&#xa0;m&#xa0;s<sup>&#x2212;1</sup> at the exit of firebrand generator in order to loft the generated firebrands. This blower velocity is selected to be able to produce smoldering firebrands. The feeding rate was 800&#xa0;g/min, or approximately 16,000/min of wood pieces (1 piece of wood piece weighs approximately 0.5&#xa0;g before the combustion). With this feeding rate, the firebrand flux at the exit of the NIST Dragon is 17&#xa0;g/m<sup>2</sup> s (mass flux) or approximately 342/m<sup>2</sup> s (number flux). Experiments were performed in the Fire Research Wind Tunnel Facility (FRWTF) in Building Research Institute (BRI), Tsukuba, Japan as the wind is an important parameter in large outdoor fires. FRWTF has a 4&#xa0;m fan and provides a wind profile up to 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> (&#xb1;10%) in a measurement section of 5&#xa0;m width &#xd7; 15&#xa0;m length &#xd7; 20&#xa0;m height with both sides being wall.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The continuous-feed firebrand generator (the continuous-feed NIST Dragon).</p>
</caption>
<graphic xlink:href="fmech-06-628510-g001.tif"/>
</fig>
<p>Structures were symmetrically placed at 7.5&#xa0;m downwind (to the leading edge of structures) from the NIST Dragon (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>). This distance was far enough to investigate the firebrand behavior around a wall (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>). The dimensions of the structures were 1, 1.5 or 2&#xa0;m wide (shown as &#x3b1; in <xref ref-type="fig" rid="F2">Figure 2</xref>) &#xd7; 2.44&#xa0;m long &#xd7; 2.44&#xa0;m high depending on the selected separation distance (SD) &#x3d; either 3, 2, and 1&#xa0;m (shown as &#x3b2; in <xref ref-type="fig" rid="F2">Figure 2</xref>). The SD considered in this study were 1, 2, and 3&#xa0;m as the SD of approximately 2&#xa0;m is allowed in USA (<xref ref-type="bibr" rid="B27">Maranghides and Johnsson, 2008</xref>). Schematics of experimental settings are provided in <xref ref-type="fig" rid="F2">Figure 2A</xref> feeding time of 10&#xa0;min was selected for most cases as it was reported that (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>) the firebrand deposition reached a peak and remain the same after a certain time. For 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed cases with SD &#x3d; 1 and 2&#xa0;m, 5&#xa0;min feeding time was selected for safety, since it was possible to produce outside fires due to the large effluent of firebrands outside the wind facility. <xref ref-type="fig" rid="F3">Figure 3</xref> shows the images of firebrand deposition process in the experiments under 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD &#x3d; 1&#xa0;m. The firebrand accumulation zone was not completely symmetric.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Schematics of structure locations in wind tunnel.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g002.tif"/>
</fig>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Firebrand Accumulation Pattern via Time under SD &#x3d; 1&#xa0;m and 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind <bold>(A)</bold> before the experiment, <bold>(B)</bold> 4 min, <bold>(C)</bold> 5 min, <bold>(D)</bold> 7 min, <bold>(E)</bold> 9&#xa0;min and <bold>(F)</bold> after the experiment.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g003.tif"/>
</fig>
<p>Separate experiments were performed to verify the characteristics of firebrands produced under different wind speeds, specifically, 4, 6, 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>. Firebrands were produced under a desired wind and collected in water pans. After the collection, firebrands were dried at 104&#xa0;&#x00B0;C in the oven. The mass of each firebrand was measured with a scale, and a picture of each firebrand was taken. The image analysis was performed to measure the projected area. Characteristics of firebrands produced under different wind speeds is shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Characteristics of firebrands under 4, 6, 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g004.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>Experimental Results and Discussion</title>
<p>Experiments showed a clear firebrand accumulation zone in front of the separation zone (upwind side) at lower wind speeds, 4 and 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> while no accumulation zones were observed at higher wind speeds, 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> (<xref ref-type="fig" rid="F5">Figure 5</xref>). In <xref ref-type="fig" rid="F5">Figure 5</xref>, no images are provided for experiments with 8 or 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, due to the absence of accumulation zones. <xref ref-type="fig" rid="F5">Figure 5</xref> shows that the firebrand accumulation zone was not completely symmetric. In the case of SD &#x3d; 3&#xa0;m under 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, the firebrand accumulation was observed between structures, also on the downwind side (<xref ref-type="fig" rid="F5">Figure 5E</xref>). Under 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind with SD &#x3d; 1 m, firebrands accumulated into two zones (<xref ref-type="fig" rid="F5">Figure 5D</xref>). Under 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind with SD &#x3d; 1&#xa0;m, a small number of firebrands showed a tendency to accumulate, rolling on the floor together, however those accumulations were not sustained at the end. This behavior is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Firebrand Accumulation pattern under different wind speeds and SD <bold>(A)</bold> 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 1&#xa0;m <bold>(B)</bold> 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 1&#xa0;m, <bold>(C)</bold> 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 2&#xa0;m, <bold>(D)</bold> 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 2&#xa0;m, <bold>(E)</bold> 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 3&#xa0;m and <bold>(F)</bold> 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> and SD <bold>&#x3d;</bold> 3&#xa0;m. Images under 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> are not provided as accumulation was not observed.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Firebrand behavior under SD &#x3d; 1&#xa0;m and 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup>.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g006.tif"/>
</fig>
<p>The distance from the front of the structure (D<sub>f</sub>), the maximum length (L), width (W) of firebrand accumulated area, and the total area of firebrand accumulation were measured after each experiment (<xref ref-type="fig" rid="F7">Figure 7</xref>). The accumulation distance in front of a structure is plotted against SD in <xref ref-type="fig" rid="F8">Figure 8A</xref>, as well as the maximum length and width of firebrand accumulation zone in <xref ref-type="fig" rid="F8">Figures 8B and 8C</xref>, respectively. <xref ref-type="fig" rid="F8">Figure 8A</xref> showed that the D<sub>f</sub> had a peak at SD &#x3d; 2&#xa0;m for experiments at 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, while the effect of SD is less clear in experiments at 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, due to two firebrand accumulation zones observed at SD &#x3d; 1&#xa0;m. In <xref ref-type="fig" rid="F8">Figure 8B</xref>, the length of firebrand accumulation zone was longer at 4 than 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup>.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Schematic of firebrand accumulation patterns and their dimensions.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g007.tif"/>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Measurements of firebrand accumulation zone under 4 and 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind experiments <bold>(A)</bold> Distance from a structure front <italic>D</italic>
<sub>
<italic>f</italic>
</sub> and SD <bold>(B)</bold> Length of firebrand accumulation zone (L) and SD <bold>(C)</bold> Width of firebrand accumulation zone (W) and SD <bold>(D)</bold> Area of firebrand accumulation zone and SD.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g008.tif"/>
</fig>
<p>The length of the accumulation zone varies depending on SD, and that behavior for experiments at 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> was the opposite to those at 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed. The similarity between the two was a peak at 2&#xa0;m SD, which was the same as the case for D<sub>f</sub> under 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind shown in <xref ref-type="fig" rid="F8">Figure 8A</xref>.</p>
<p>
<xref ref-type="fig" rid="F8">Figure 8C</xref> shows that the width of firebrand accumulation zone was wider at 4 than 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, which is the same for length shown in <xref ref-type="fig" rid="F8">Figure 8B</xref>. The total area of the accumulation zone was plotted in <xref ref-type="fig" rid="F8">Figure 8D</xref>. It was observed that the higher wind speed led to a smaller accumulation zone. This is similar behavior to very simple wall experiments (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>). Under 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed, the size of the firebrand accumulation zone was similar, regardless of SD, yet it changed significantly under a 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind. This, in some sense, is similar to the accumulation distance, as it indicated that wind profile changes more significantly between SD 1 and 2&#xa0;m than between 2 and 3&#xa0;m. This effect needs to be more carefully investigated as the minimum SD between buildings is 2&#xa0;m. The firebrand accumulation behind the separation (downstream) under SD &#x3d; 3&#xa0;m and 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind was located (<xref ref-type="fig" rid="F7">Figure 7</xref>) between 1.4 and 2.1&#xa0;m (L &#x3d; 0.7&#xa0;m) with the width 0.25&#xa0;m and the area of 0.0829&#xa0;m<sup>2</sup>.</p>
</sec>
</sec>
<sec id="s3">
<title>Simulations</title>
<p>The Fire Dynamic Simulator (FDS) was used to simulate the wind field of these experiments (<xref ref-type="bibr" rid="B29">McGrattan et al., 2013</xref>). FDS does not contain firebrands; however, it was used to describe the firebrand accumulation behavior based on predicted wind profiles (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>). Firebrands follow the wind as they are relatively light but not completely due to their mass. FRWTF was simulated with experimental structures and the NIST Dragon as an obstacle with the dimension of 5&#xa0;m (W) &#xd7; 16&#xa0;m (L) &#xd7; 20&#xa0;m (H). The mesh size was 10&#xa0;cm &#xd7; 10&#xa0;cm &#xd7; 10&#xa0;cm. The conditions of simulation are summarized in <xref ref-type="table" rid="T1">Table 1</xref>. After 10&#xa0;s, modeling shows that the wind has stabilized. The simulation was performed up to 20&#xa0;s for all cases in order to observe the repeated wind behavior.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Conditions for FDS simulation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Mesh size</th>
<th align="center">10&#xa0;cm &#xd7; 10&#xa0;cm &#xd7; 10&#xa0;cm</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Simulation domain</td>
<td align="center">5&#xa0;m (W) &#xd7; 16&#xa0;m (L) &#xd7; 20&#xa0;m (H)</td>
</tr>
<tr>
<td align="left">Simulation time</td>
<td align="center">20&#xa0;s</td>
</tr>
<tr>
<td align="left">Wind speed</td>
<td align="center">4, 6, 8, 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>
</td>
</tr>
<tr>
<td align="left">Separation distance (SD) between structures</td>
<td align="center">1, 2, 3&#xa0;m</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Wood pieces fed from Feeding System.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>In a simple calculation performed in (<xref ref-type="bibr" rid="B41">Suzuki and Manzello, 2017a</xref>), the wind speed of 2.3&#xa0;m&#xa0;s<sup>&#x2212;1</sup> was the lowest wind speed for firebrands to move on the floor where the surface was relatively smooth considering the balance between friction force between a firebrand and the floor (gypsum board) and the wind force:<disp-formula id="e1">
<mml:math>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>w</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>And<disp-formula id="e2">
<mml:math>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3bc;</mml:mi>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>b</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math>
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>w</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>Therefore, <italic>&#x3bc;</italic> is the friction coefficient between a gypsum board and smoldering firebrands, <italic>m</italic>
<sub>
<italic>firebrand</italic>
</sub> is the average mass of a firebrand, <italic>&#x3c1;</italic>
<sub>
<italic>air</italic>
</sub> is the density of the air, <italic>g</italic> is gravitation acceleration, <italic>v</italic> is wind speed on a firebrand and <italic>A</italic> is the average projected area of a firebrand. As seen in <xref ref-type="fig" rid="F4">Figure 4</xref>, the mass and the size of firebrands under 4, 6, 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> can be considered within the range of uncertainties (&#xb1;10%), average of mass (0.05&#xa0;g) and projected area (0.78&#xa0;cm<sup>2</sup>) was used for calculation. The unknown parameter was &#x3bc;<italic>,</italic> as there is no data available for a smoldering firebrand and a gypsum board. Therefore &#x3bc; &#x3d; 0.5 was used based on data for wood on wood (<xref ref-type="bibr" rid="B15">Japanese Society of Mechanical Engineers, 2004</xref>). Applying 2.3&#xa0;m&#xa0;s<sup>&#x2212;1</sup> for the lowest wind speed for firebrands to move, we consider the stagnation zone (wind speed less than 2.3&#xa0;m&#xa0;s<sup>&#x2212;1</sup>) as the firebrand accumulation zone.</p>
<p>An FDS simulation was performed using the conditions shown in <xref ref-type="table" rid="T1">Table 1</xref>. The FWTRF was simulated. <xref ref-type="fig" rid="F9">Figures 9</xref> and <xref ref-type="fig" rid="F10">10</xref> show the FDS simulation results under 4 and 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup> in the cases of SD &#x3d; 1&#xa0;m and 3&#xa0;m. <xref ref-type="fig" rid="F9">Figures 9</xref> and <xref ref-type="fig" rid="F10">10</xref> shows the wind speed 2.3&#xa0;m&#xa0;s<sup>&#x2212;1</sup> being marked in black. As shown in <xref ref-type="fig" rid="F9">Figure 9</xref>, as the wind speed increases, the distance to the stagnation zone from the front of structures, D<sub>f</sub>, decreases, and as SD become larger, wind between structures become less turbulent. <xref ref-type="fig" rid="F11">Figure 11</xref> shows the distance to the stagnation zone from the front of structures, D<sub>f</sub>, vs. time (10&#x2013;20&#xa0;s) in the case of 1&#xa0;m SD for example. Overall, the D<sub>f</sub> increases as the wind speed increases. Data from 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> is relatively stable, while those from 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup> is changing a lot. Those from 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> are fluctuating. It is assumed the two firebrand accumulation zones observed in experiments are due to this behavior. <xref ref-type="fig" rid="F12">Figure 12</xref> shows the 10&#xa0;s average, D<sub>f,</sub> against wind speeds along with experimental results. Results from FDS shows that D<sub>f</sub> increases as the wind speed increases. D<sub>f</sub> also increases as SD increases with the exception of SD &#x3d; 1 and 2&#xa0;m under 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind. This is interesting as experiments showed the wind profile around the structures may change between SD from 1 to 2&#xa0;m, and SD from 2 to 3&#xa0;m. Experimental data with SD &#x3d; 1&#xa0;m has similar D<sub>f</sub> to FDS results while experimental results does not match well when SD &#x3d; 2 or 3&#xa0;m. For the same SD, as the wind speed increases the wind flow around structures becomes complicated, and it is expected firebrands may not follow the wind completely; the calculation deduced from simple analysis no longer works.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>FDS simulation results with different SD and wind speeds. Wind profile at centerline. Black line in the images shows wind speed of around 2.3 m&#xa0;s<sup>&#x2212;1</sup> <bold>(A)</bold> 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind, SD &#x3d; 1&#xa0;m, <bold>(B)</bold> 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed, SD &#x3d; 1&#xa0;m, <bold>(C)</bold> 4&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed, SD &#x3d; 3&#xa0;m and <bold>(D)</bold> 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed, SD &#x3d; 3&#xa0;m.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>FDS simulation results with 8&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speed and SD &#x3d; 1&#xa0;m. Wind profile at ground level.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g010.tif"/>
</fig>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Time varying distance from a stagnation zone (wind speed 2.3&#xa0;m&#xa0;s<sup>&#x2212;1</sup>) from a structure front in FDS simulation under 1&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g011.tif"/>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Comparison between average distance from a stagnation zone (wind speed 2.3 m s<sup>-1</sup>) from a structure front in FDS simulation and those in experiments.</p>
</caption>
<graphic xlink:href="fmech-06-628510-g012.tif"/>
</fig>
</sec>
<sec id="s4">
<title>Summary</title>
<p>Wind has an impact on the built environment. For large outdoor fire safety, wind plays a critical role, from enhancing flame spread processes to firebrand spotting. Firebrands fly far under high wind, which presents risks to many houses. This study focused on understanding firebrand behavior between two structures by varying the separation distances and wind speeds experimentally and by simulation. No significant accumulation was observed under 8 and 10&#xa0;m&#xa0;s<sup>&#x2212;1</sup>, regardless of structure separation distance. The size of firebrand accumulation as well as distance from structure front was compared with separation distance in the cases of 4 and 6&#xa0;m&#xa0;s<sup>&#x2212;1</sup> wind speeds. It was found that firebrands behave differently from SD &#x3d; 1&#x2013;2&#xa0;m, to that of SD &#x3d; 2&#x2013;3&#xa0;m. The results of this study are the first to explore these important interactions between firebrands and structure separation distances.</p>
</sec>
<sec id="s5">
<title>Data Availability Statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, upon request.</p>
</sec>
<sec id="s6">
<title>Author Contributions</title>
<p>SS: Conceptualization, Investigation, Formal analysis, Writing - original draft. SM: Conceptualization, Investigation, Formal analysis, Writing - original draft.</p>
</sec>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
</body>
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