Whole-surface emission concentric shells for large light bulb using total internal reflection

Surface emission concentric shells that can emit both light rays and a large amount of heat from the whole outer surface are proposed here for a large globe light-emitting diode (LED) bulb. The concentric shells are composed of an outer total internal reflection (TIR) shell and an inner metallic shell adjacent to the outer shell. The TIR shell can guide light rays emitted from LEDs owing to the TIR and emits illuminating light from the outer surface. Assuming that the thickness of the TIR shell is sufficiently small, the TIR shell can also emit heat of the inner shell to the outside. It is theoretically predicted based on the heat transfer theory that the larger the concentric shells are, the larger the amount of heat that can be emitted to the outside. A large globe LED bulb prototype having the concentric shells with an outermost diameter of about 95 mm is therefore designed and fabricated, with which it is shown that an illuminating light flux of about 1064 lumens and heat of about 12.2 W can both be emitted to the outside. The prototype also shows to have a large hollow structure in which several kinds of devices can be accommodated. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.OE.60.8.085108]


Introduction
The replacement of traditional incandescent light bulbs with light-emitting diodes (LEDs) has been progressing rapidly owing to the high efficiency and long life of LEDs. The traditional incandescent light bulb, however, had some positive features such as a wide-angle light distribution with a half-intensity angle of more than 270 deg and a simple appearance since it is covered by a transparent glass globe and has no metal heat sinks. Although the wide-angle light distribution is one of the most important features for lighting applications, the light distribution angle of the LED itself is not wide enough. Thus, additional optical elements are necessary to widen the light distribution angle. Several solutions have then been developed to produce wideangle light distributions.  A total internal reflection (TIR) shell with LED light sources has also been developed, which can emit illuminating light from its surface. 29 Concentric shells composed of the TIR shell that encloses a metallic inner shell are applicable to LED bulbs, enabling heat generated by the LED to be released through both the inner shell and the TIR shell to the outside. In Ref. 29, a standard pear-shape light bulb having the concentric shells with the outermost diameter of about 60 mm is fabricated, which is shown to emit an illuminating light flux of about 600 lumens.
Heat release rate from the concentric shells can be theoretically predicted to increase with respect to the outermost surface area of the concentric shells. The larger the TIR shell is, the larger the amount of heat that can be released to the outside. A large globe LED bulb composed of the concentric shells is therefore proposed with an outermost diameter of about 95 mm, which can emit both light rays and a large amount of heat from the whole outer surface. The concentric shells are also advantageous in that several kinds of devices can be accommodated inside them. The remainder of this paper is organized as follows. First, the heat release rate with respect to the outermost diameter of the concentric shells is estimated based on the heat transfer theory.
Second, a design of the concentric shells for a large globe LED bulb prototype is described based on the geometrical optics. Third, the large globe LED bulb prototype is fabricated, which shows that an illuminating light flux of about 1064 lumens and heat of about 12.2 W can both be emitted to the outside. Lastly, discussions and conclusions are presented.
2 Heat Release Rate of Concentric Shells Figure 1 shows a schematic cross-sectional view of concentric shells composed of an outer TIR shell and an inner metallic shell. The outer TIR shell is assumed to have a uniform thickness of δ with an outermost radius of R TIR . Light rays emitted from LEDs will travel inside the TIR shell owing to the TIR. The inner metallic shell with an outermost radius of R TIR − δ is assumed to have sufficient thermal conductivity, which makes the temperature distribution uniform. Heat generated from the LEDs is thermally connected to the inner metallic shell. The heat will then be conducted through the TIR shell from the inner metallic shell and will be released to the outside by convection and thermal radiation.
The heat release rate, Q total [W], from the concentric shells to the outside can be described based on the heat transfer equation. The temperature of the outermost TIR shell is set to T TIR whereas that of the atmosphere (i.e., air) is set to T air . Using a thermal convection resistivity Γ conv caused by the convection from the TIR shell with an emissivity ε of the thermal radiation, the heat transfer equation can be written as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 4 8 9 where the σ denotes the Stefan-Boltzmann constant. The thermal convection resistivity Γ conv can be written with a heat transfer coefficient of natural convection, α ½W∕m 2 ∕K, as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 4 2 0 (2) Figure 2 shows the heat release rate of Q total [W] calculated using Eq. (1) with respect to the outermost diameter of 2R TIR of the concentric shells. Outermost diameters of standard-size and large-size bulbs are 60 and 95 mm, respectively. The heat transfer coefficient of the natural convection, α, is set to 10 W∕m 2 ∕K. 30 The ε and σ are set to 0.9 and 5.67 × 10 −8 W∕m 2 ∕K 4 , respectively. The outer surface temperature T TIR of the TIR shell is set to 60°C, which is less than the acrylic endurance temperature of 80°C. The atmosphere temperature T air is set to 25°C. It can be found that the heat release rate becomes more than 16 W if the outermost diameter is more than O

Outer TIR shell
Hollow structure Heat Heat Fig. 1 Schematic cross-sectional view of concentric shells composed of outer TIR shell and inner metallic shell. The outer TIR shell is assumed to have a uniform thickness of δ with an outermost radius of R TIR . The inner metallic shell with an outermost radius of R TIR − δ is assumed to have sufficient thermal conductivity, which makes its temperature distribution uniform.
that of the large-size bulb, namely, 95 mm. On the other hand, the heat release rate becomes <7 W if the outermost diameter is less than that of the standard-size bulb, namely, 60 mm.
A temperature rise, ΔT TIR , of the innermost TIR shell with respect to the outermost TIR shell can be written with the Q total represented by Eq. (1) and a thermal conductive resistivity Γ cond of the TIR shell as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 4 7 9 where the Γ cond can be written with a thermal conductivity of the TIR shell, β [W/m/K], as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 4 3 6 Assuming that the TIR shell is made of acrylic, the thermal conductivity β is set to 0.17 W∕m∕K. The temperature rise ΔT TIR is about 12°C for the thickness δ of 3 mm with the Q total of 16 W and the 2R TIR of 95 mm. It can be found from Eqs. (3) and (4) that the thickness δ of the TIR shell should be as thin as possible to decrease the temperature rise of the ΔT TIR through reducing the thermal resistivity of the TIR shell.
In this work, the outermost diameter of the concentric shells is set to 95 mm with the TIR shell thickness δ of between 0.5 and 5.0 mm, which enables a heat release rate about twice that of the standard-size bulb.  Light rays emitted from the LEDs are guided by the TIR shell owing to the TIR toward the top of the LED light bulb in the positive Z direction. In other words, the TIR shell can guide the light rays emitted from the LEDs in the negative Z direction and gradually change the directions of the light rays toward the positive Z direction. The inner surface of the TIR shell is coated with white light-scattering particles, which make the light rays traveling inside the TIR shell diffuse gradually to the outside. This allows the light rays to be emitted from the whole surface of the TIR shell to produce a wide-angle light distribution. The concentric shells also make it possible to release heat generated from LEDs to the outside from the whole outer surface. Furthermore, the concentric shells construct a hollow structure capable of accommodating several devices. Figure 4 shows a schematic cross-sectional view close to an LED in x-z plane of a local Cartesian coordinate system ðx; y; zÞ with its origin O 0 corresponding to an edge of the LED emitting surface. The z axis is parallel to the Z axis. A two-dimensional (2D) polar coordinate system ðρ; θÞ is also taken with its origin corresponding to the O 0 . The origin O 0 is located at distance of ρ 0 from the global coordinate origin O in the direction of the X axis.

Design of TIR Shell
A TIR curve that corresponds to the outer surface of the TIR shell reflects light rays coming from the edge of the LED (i.e., the origin O 0 ) owing to the TIR. A position vector P of the TIR curve is set to ðρ; θÞ. An infinitesimal displacement of the position vector, namely, ðΔρ; ΔθÞ, satisfies the following equation based on the geometrical optics 29 as where Θ 0 represents an angle between the position vector P and an outward normal vector at the position. When the angle Θ 0 is set to more than the critical angle θ c of the TIR shell, a light ray emitted from the LED will always be reflected by the TIR at the position P. The critical angle θ c can be written with the refractive index n of the TIR shell as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 6 5 3 θ c ¼ arcsin 1 n : (6) In this work, the angle Θ 0 is set to a constant value that is a little larger than the critical angle of the acrylic. Equation (5) can thus be analytically solved as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 1 1 6 ; 5 8 3 where ρ 1 denotes a radius of the local coordinate for θ ¼ 0. When the ρ 1 is set to larger than a side length of the LED emitting surface, any light rays emitted from the LED can always be reflected by the TIR curve owing to the TIR because internal incident angles of the light rays on the TIR curve become larger than the critical angle of Θ 0 . This can be well described by the edge ray principle. [31][32][33][34] Moreover, once a light ray is reflected by the TIR curve, the light ray consecutively continues to be reflected by the TIR curve because the internal incident angles of the consecutive reflections automatically become larger than the critical angle of Θ 0 . Any light rays emitted from the LED can therefore be guided along the TIR curve.

Prototype of Large Globe LED Bulb
A prototype of a light LED bulb having the large globe with diameter of 95 mm is designed using the concentric shells composed of the TIR shell and the metallic shell as shown in Fig. 5. In this work, the parameters of the TIR shell, namely, ρ 0 , ρ 1 , and Θ 0 are set to 20.0 mm, 0.8 mm, and 43 deg, respectively. The thickness δ of the TIR shell is set in a range of from 0.5 to 5.0 mm. An axisymmetric LED array is composed of multiple LEDs with each emitting surface of 1.4 mm × 2.8 mm. The luminous efficiency of the LED is 85 lm∕W at operating temperature of about 80°C. A supplemental mirror is introduced to reflect some of the light rays emitted from the LEDs into the TIR shell. A transparent flange is attached to protect the LEDs from dust. A hollow structure can be constructed by the concentric shells, which can accommodate several devices.

Experimental Results of Prototype of Large Globe LED Bulb
The prototype of the large globe LED bulb composed of the concentric shells with outermost diameter of 95 mm is fabricated as shown in Fig. 6. The LED bulb turned off is shown in Fig. 6(a) and that turned on is shown in Fig. 6(b). A luminous flux is measured to be 1064 lumens at an input power of 16.0 W with an operating temperature of the LED of about 80°C. The inner surface temperature of the TIR shell becomes about 65°C with atmosphere temperature of 25°C in the steady state. The heat release rate of the prototype to the outside is estimated to be 12.2 W where the rest of the power, 3.8 W, is used for light ray generation. The heat release rate is larger than that of the standard-size LED bulb of about 7 W that is estimated in Sec. 2. Luminaire efficiency that is the ratio of light output emitted by the concentric shells to the light output emitted by the LED array is measured to be about 78%.  Note that experimental data are measured in steady state with the operating temperature of the LED of about 80°C.

Discussions
As shown in Fig. 5, the hollow structure constructed by the concentric shells could accommodate several devices, such as a brightness control circuit, a color control circuit, and an auxiliary battery. These devices would enhance the value of the LED bulb.
As shown in Fig. 6, a stripe illumination pattern is found on the LED bulb surface. The stripe pattern can be erased by sandblasting on the outermost surface of the LED bulb as shown in Fig. 8. The sandblasted LED bulb that is turned off is shown in Fig. 8(a) and that turned on is shown in Fig. 8(b).
The arrangement of the LED array is axisymmetric, and therefore the light angle distribution of the whole bulb should be axisymmetric as well. Although the light angle distribution shown in Fig. 7 is plotted only for one azimuth angle, the axisymmetric distribution is confirmed by both the experiment and the ray-tracing simulation. 35

Conclusions
Surface emission concentric shells that can emit both light rays and a large amount of heat from the whole outer surface are proposed here for a large globe LED bulb with an outermost diameter of 95 mm. The concentric shells are composed of an outer TIR shell and an inner metallic shell adjacent to the outer shell. The TIR shell can guide light rays emitted from LEDs owing to the TIR and emit illuminating light from the outer surface. Assuming that the thickness of the TIR shell is sufficiently small, the TIR shell can also emit heat of the inner shell to the outside. It is theoretically predicted using Eq. (1) that the larger the concentric shells are, the larger the amount of heat that can be emitted to the outside. A large globe LED bulb prototype having concentric shells with the outermost diameter of about 95 mm is therefore designed and fabricated, with which it is shown that an illuminating light flux of about 1064 lumens and heat of about 12.2 W can both be emitted to the outside through the whole outer surface. The heat release rate of the prototype of 12.2 W is larger than that of the standard-size LED bulb of about 7 W. The measured light angle distribution of the prototype is wide enough where a half-intensity angle is 310 deg as shown in Fig. 7. Furthermore, the prototype can have a large hollow structure in which several kinds of devices can be accommodated as shown in Fig. 5.