Senko hanabi under various ambient conditions

Sci. Tech. Energetic Materials, Vol. 81, No. 5, 2020 121

© Copyright Japan Explosives Society. All rights reserved.

Senko-hanabi under various ambient conditions

Chihiro Inoue *†, Ryo Nishiyama**, Yasuhiro Fujisaki**, and Toshiaki Kitagawa**

* Department of Aeronautics and Astronautics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395 JAPAN † Corresponding author: [email protected] Phone: +81-92-802-3018

** Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395 JAPAN

Received: January 21, 2020　Accepted: April 7, 2020

Abstract　A traditional Japanese sparkler, senko-hanabi, is consists of paper string wrapping 0.1 g of black powder. The sparkler requires heat production by combustion of contained charcoal with ambient oxygen, showing off beautiful sparks luminous by heat radiation. In the present study, the appearance of the sparks is investigated under various ambient conditions, in which the total pressure is from vacuum to 5.0 bar and the oxygen concentration rate is set up to 40 %. The sparkler is ignited by Joule heating inside a closed vessel. Profound effects are confirmed by the ambient conditions on the sparks. As the total pressure rises, sparks spread actively, because the boundary layer surrounding the fireball, created at the bottom end of the paper string, becomes thinner, and the amount of oxygen supply increases. The oxygen concentration rate directly contributes to the amount of oxygen supply. The criterion given by molar flux of oxygen supply to the fireball is identified as 10 －1 mol · s －1 · m －2, rate-controlled by molecular diffusion through the boundary layer, for embodying fragile beauty over the centuries.

Keywords: sparkler, senko-hanabi, pressure, oxygen fraction, diffusion

1. Introduction

　There are many kinds of fireworks enjoyed over the world, whose size are from small sparklers to large aerial shells. Since the Edo period in Japan, senko-hanabi has been a popular sparkler, which simply wraps 0.1 g black powder, a mixture of charcoal, sulfur, and potassium nitrate, in one side of a paper string with no use of metal powders 1),2). After ignition to the end of the black powder holding the other side of paper string in hand, a spherical fireball with orange color is produced. Suddenly, sparks are emitted from the fireball, spreading several centimeters with successive ramifications. The beautiful spark structure similar to pine-needles are generated by so-called black body radiation following the Plank’s law, not by flame reactions, because of the low temperature of the senko-hanabi sparks in nature 3).　In the past, Hoffmann 4) and Denisse 5) in the 19 th century Europe, and Terada 6) at the beginning of the 20 th century in Japan were intensely interested in the physical and chemical phenomena occurring in the senko-hanabi. Nakaya and Sekiguchi 7) initially identified that the sparkler retains the burning reaction using the ambient oxygen, which was evidenced by extinction in nitrogen atmosphere.

Shimizu 2),8) reported that potassium sulfide is an important reactive product for the sparks. Maeda and his high school students 9) conducted chemical analyses and discovered several potassium compounds in the fireball with no potassium nitrate as oxidizer. This was because potassium nitrate quickly converted to other compounds soon after the ignition, which is consistent with Nakaya’s findings 9). Recently, Inoue et al. have first succeeded in taking the resolved high-speed images, measurement of quantitative temperature, and eventually the formulation of ramification cascade of the sparks 3),10),11).　The burning rate of black powder itself was reported to accelerate as the increment of ambient pressure. 12)-14) However, we can find all the past studies for the sparkler were conducted in atmospheric pressure condition at 1.0 bar. Some of them claim that an important exothermic reaction of senko-hanabi is C + O 2 → CO 2 rate-controlled by molecular diffusion of oxygen 7),9),10), suggesting that ambient pressure and compositions affect the spark dynamics. For more safety storage and transport of sparklers in general, it is meaningful to know the behaviors of the sparkler under various ambient conditions. In the present study, therefore, we first clarify the comprehensive effects of ambient conditions on the senko-hanabi sparks,

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122 Chihiro Inoue et al.

by visualization experiment in a combustion vessel, coupled with simple theoretical analyses. Following sections are organized as follows. In section 2, we explain the experimental apparatus. In section 3, the results and discussion are presented. Finally, in section 4, conclusions are summarized.

2. Experimental apparatus

　Figure 1 shows the experimental apparatus. The combustion vessel, 35 L in volume, can change the internal total pressure of P, ranging from 0 to 10 bar in absolute 15,16). For visualization, two cameras are set; SONY α7sII captures sparks after the ignition with 4K resolution, and a high-speed camera, Phantom v12.1, takes instantaneous enlarged images of the fireball with 10 4 fps. The circular visualization windows are 160 mm in diameter. The senko-hanabi used for the present study was produced by Tsutsui Tokimasa toy fireworks factory. When we start an experiment, a senko-hanabi is suspended from the top inside the vessel as shown in Figure 2, and the bottom end, wrapping the black powder side, is contact with the nichrome wire of 0.4 mm in diameter, bridging the two conductive rods. The vessel is closed, and the P is set in the range from 0 to 5.0 bar under the controlled oxygen concentration rate, defined by the partial pressure ratio of oxygen, P O2, to P. The mixture gas consists of oxygen and nitrogen. Then, we apply up to 5 V potential difference between the two conductive rods, heat the nichrome wire by Joule heating, and ignite the sparkler. The developed ignition procedure enables ignition without failure. The internal temperature of the vessel is room temperature. It is confirmed that the change of oxygen concentration due to the combustion of sparkler is negligible owing to the large vessel volume.

3. Results and Discussion

　The experimental conditions vary 13 cases. Table 1 shows the experimental conditions of P and P O2/P. The standard conditions are P = 1.0 bar and P O2/P = 0.21 at Case 7, same as the atmospheric condition. Three types of results regarding the spark behaviors after the Joule heating were confirmed; symbols of 〇 , △ and □ indicate the cases that sparks were emitted (Cases 6-8), fireball was not created and no sparks were visible (Cases 1-5), and burn out without sparks (Cases 9-13), respectively.　Figure 3 shows time series images after starting the Joule heating at Case 7. The heated nichrome wire glows red at time of t = 0 s, and ignites the sparkler at t = 2 s. After a while, the fireball is formed at t = 14 s (Stage 1), and the sparks pop out intermittently at t = 24 s (Stage 2), reaching

distance of 10 cm. Then, the sparks are actively released spreading several centimeters at t = 32 s (Stage 3), the sparks gradually come out weakly at t = 52 s (Stage 4), and eventually disappear. During this time, the fireball continues to rise along the paper string.

3.1 Effects of total pressure　As typical results, the dynamics of sparkler in Cases 1, 7, and 9 are shown in Figure 4, which clearly convinces the large impacts of ambient conditions on the sparklers. In Cases 1 and 9, no sparks are visible. Hence, we compare the states of visible sparks in Cases 6-8 to clarify the effects of total pressure with keeping the same oxygen concentration. Figure 5 shows the instantaneous images of sparks (left), and stacked images from Stage 1 to the end (right). The sparkler in Case 6 ends in the middle at Stage 2, while both sparklers in Cases 7 and 8 keep burning until the

Figure 1　Experimental apparatus overview.

Figure 2　Internal setup.(The two conductive rods are arranged obliquely at a gap distance of 10 mm in the vessel. The nichrome wire bridges the gap of two rods. The bottom tip of senko-hanabi is tightly folded to contact with the nichrome wire.)

Table 1　Experimental conditions and results.

Case 1 2 3 4 5 6 7 8 9 10 11 12 13

P [bar] 0 1.0 1.0 2.0 3.0 0.50 1.0 1.5 2.0 3.0 5.0 1.0 0.50

P O2/P 0 0 0.10 0.10 0.10 0.21 0.21 0.21 0.21 0.21 0.21 0.30 0.40

Result △ △ △ △ △ ○ ○ ○ □ □ □ □ □


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Figure 3　Time series of senko-hanabi in Case 7.(Visualized with room light. The oxygen concentration meter can be seen, set on the floor in the vessel.)

Figure 4　Typical image of senko-hanabi appearance.((a) No fireball created, and only the heated nichrome wire is visible. (c) The paper string burns.)


end of Stage 4 over approximately 2 minutes. At all the instantaneous images, the fireballs are confirmed. The sparks that jump out of the fireball branch, and in particular, those in Case 8 finely ramify. In the stacked images, the number of scattering sparks in Case 6 is small, and as the pressure rises in Cases 7 and 8, the number of sparks increases, resulting in a “lively” appearance. In Case 8, we can confirm that many sparks pop out even in Stage 4, as shown in Figure 6. The maximum distance from the fireball to the spark front is about 10 cm observed in Stage 2

irrespective of P.　The fireball created at the bottom end of paper string is visualized in Figure 7. The radius is approximately 3 mm at all P conditions. The fireball is suspended by the surface tension force bottom end of the paper string against the gravity force. Under the conditions that density of the fireball is ρ~10 3 kg · m －3, surface tension coefficient is σ~10 －1 N · m －1，gravity acceleration is g = 9.8 m · s －2, and the radius of the paper string is a~10 －3 m, the radius of fireball R 0 is calculated as

Figure 5　Snapshot (left) and stacked image (right) of sparks at P O2/P = 0.21.


R0 ≈σaρg

1/3

∼ O(10−3) m , (1)

which is consistent with Figure 7. Thus, the relevant physical properties of the fireball remain the same in the present conditions.　Transport coefficients of air are constant against pressure, while the density is proportional to P. Thus, the kinematic viscosity, ν, and molecular diffusion coefficient of oxygen, D, are both inversely proportional to P. Let us consider the exothermic reaction occurring on the fireball surface:

C + O2 = CO2 + q (2)

with the heat product of q = 394 kJ · mol －1. In the case of molecular diffusion control reaction, Equation (2) should proceed controlled by the molar flux of oxygen to the fireball of m [mol · s －1 · m －2] through the surrounding boundary layer with the thickness of δ [m] from ambient oxygen concentration of C (O2) [mol · m －3].

m = DC(O2)

δ. (3)

Considering the fireball of R 0 = 3 mm, the heat production on the fireball surface Q [W] is given, by using D, δ, C (O2), and surface area of A = 100 mm 2, as follows.

Q = mqA = DC(O2)

δqA . (4)

Since D is inversely proportional to P and C (O2) is proportional to P at constant P O2/P, Q is inversely proportional to δ.

Q = DC(O2)

δqA ∝ δ−1 . (5)

The value of δ can be estimated by using Nusselt number for mass transfer (or say Sherwood number) defined as Nu, a function of Reynolds number as Re, and Schmidt number as Sc 17);

Nu =2R0

δ= 2 + 0.6Re0.5S c0.3 . (6)

Inside the boundary layer surrounding the fireball, the air is heated and the density decreases with difference of Δρ a against the air density outside the boundary layer of ρ a. Ascending air velocity of u a driven by the buoyancy is calculated, considering Δρ a/ρ a of unity.

ua ≈∆ρa

ρagR0 ∼ 10−1 m · s−1 . (7)

Then, we can deduce Re = u aR 0/ν at u a = 10 －1 m · s －1, R 0

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Figure 6　Number of sparks in Stage 4 at P O2/P = 0.21.

Figure 7　Fireball at the bottom end of paper string at P O2/P = 0.21 (Stage 2).


= 3 mm, ν = 1.6×10 －5 m 2 · s －1 at P = 1.0 bar, and Sc = ν/D of unity. Considering the relationship of ν ∝ P －1, we derive Nu = 3.8, 4.6, and 5.2 at P = 0.50, 1.0, and 1.5 bar, respectively. Therefore, as the pressure increases, the boundary layer thickness of δ = 2R 0/Nu becomes thinner and the amount of Q increases. Consistently, the fireball in Cases 7 and 8 in Figure 7 look brighter than that in Case 6.　Heat conduction deliver a part of Q toward interior of the fireball, finally consumed by the nucleation and bubble growth attributed to endothermic reactions of potassium compounds 3),10). The time τ for a single bubble growing to reach the fireball surface is given as follows, using the thermal diffusivity of fireball as α~10 －6 m 2 · s －1;

τ ∼R2

0

α (8)

which is irrespective of P. Accordingly, the number of bubbles increases to consume the heat, leading to the frequent drop ejection as increasing P, consistent with Figure 5. Since the temperature of fireball is restricted by melting of potassium compounds of K 2S and K 2CO 3 3), the coloration of the sparkler is the same at Cases 7 and 8. It is interesting that the higher concentration of oxygen, proportional to P, is cancelled by decrement of D inversely proportional to P. Therefore, the effect of increasing ambient pressure on the sparkler is exactly equivalent to blowing wind for thinning the boundary layer at a constant pressure condition.

3.2 Effects of oxygen concentration　Keeping constant value of P = 1.0 bar, P O2/P changes from 0.10 to 0.30 in Cases 3, 7, and 12. Figure 8 presents the sparklers in each case. In Case 3, the black powder weakly burns. The heat production is not enough for producing the fireball. In Case 7, the standard condition, beautiful sparks are visible, while in Case 12, the paper string violently burns out.　Here, the values of D and δ can be regarded as constant values because of constant P. Hence, the heat production on the fireball surface is directly proportional to oxygen concentration.

Q = DC(O2)

δqA ∝ C(O2) . (9)

Regarding the three cases in Figure 8, not enough amount of oxygen is supplied for Case 3, appropriate amount of oxygen in Case 7, and excess oxygen supply in Case 12.

3.3 Criterion for visible sparks　Corresponding to the experimental conditions denoted in Table 1, the molar flux of oxygen supply m, and resulting heat production rate Q are calculated by Equations (3) and (4), respectively, as shown in Figure 9. The results of spark dynamics are clearly related to m. In Cases 6-8, the fireball is supplied oxygen of m ≈ 10 －1 mol · s －1 · m －2, in which we can enjoy the beautiful sparks. In contrast, m is smaller than the threshold value in Cases 1-5, sparks become invisible. In Cases 9-13, m is average, then, the paper string itself burns out. As the results, m determines the fate of senko-hanabi. At the appropriate condition, the fireball produces heat of Q ≈ 5 W. The criterion for blooming senko-hanabi is now identified.

4. Conclusions

　The present study is firstly devoted to the investigation on dynamics of a traditional sparkler, senko-hanabi, under comprehensive ambient conditions, varying the total

Figure 9　 Molar flux of oxygen and heat production on the fireball surface.

(Case numbers and the symbols correspond to Table 1.)

Figure 8　Effects of oxygen pressure ratio at P = 1.0 bar.


pressure and oxygen concentration rate inside a large closed vessel. It was clearly demonstrated that the sparkler was sustained by diffusion-controlled combustion, consistent with past studies by Nakaya and Maeda. Conclusions are summarized as follows.[1] The increment of total pressure thinned the boundary

layer thickness around the fireball suspended at the bottom end of paper string, and increased the supply of molar flux of oxygen.

[2] The increment of oxygen concentration rate directly increased molar flux of oxygen supply to the fireball.

[3] The molar flux of oxygen was identified as the essential index, determining the fate of senko-hanabi sparks. The senko-hanabi embodies beautiful sparks at the specific condition, supplied the molar flux of oxygen as 10 －1 mol · s －1 · m －2.

Acknowledgement

　This study was funded by KAKENHI (JP17H00844 and JP19K21934). The authors would like to thank them for their kind support.

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Senko hanabi under various ambient conditions