Maximizing Performance from Loudspeaker Ports* 最大限度地提高扬声器端口的性能*。
ALEX SALVATTI, AES Member, ALLAN DEVANTIER, AES Member, AND DOUG J. BUTTON, AES Member ALEX SALVATTI， AES 会员；ALLAN DEVANTIER， AES 会员；DOUG J. BUTTON， AES 会员 JBL Professional, Northridge, CA 91329, USA JBL Professional，Northridge，CA 91329，USA Infinity Systems, Northridge, CA 91329, USA
Abstract 摘要
There is a current trend in the marketplace for loudspeaker ports to have a more aerodynamic appearance. 目前市场上的趋势是扬声器端口的外观更符合空气动力学原理。 While this may be as much for appearance as for performance reasons, the sharp discontinuity at the end of a traditional port does create turbulence which negatively affects most performance parameters. 虽然这可能是出于外观和性能方面的考虑，但传统端口末端的尖锐不连续性确实会产生湍流，从而对大多数性能参数产生负面影响。 Ports altered to provide a more aerodynamic shape to minimize turbulence for both the inlet and the exit air streams show performance improvements in efficiency, acoustic compression, maximum output, and distortion reduction. 为尽量减少进气和出气气流中的湍流而改变端口形状，使其更符合空气动力学原理，从而在效率、声学压缩、最大输出和减少失真等方面实现了性能改进。 The ideal port shapes for high-velocity inlet and exit air streams are different, and the best solution is one that balances both. In addition turbulence is actually preferred in matters of cooling the box through heat exchange via the air in the port. 高速入口气流和出口气流的理想端口形状是不同的，最佳解决方案是两者兼顾。此外，湍流实际上更有利于通过端口中的空气进行热交换来冷却箱体。
0 INTRODUCTION 0 引言
Loudspeaker ports are generally used to augment the low-frequency acoustic output by supplying a Helmholtz resonator. 扬声器端口通常通过提供亥姆霍兹谐振器来增强低频声输出。 At resonance, the inertance of the vent resonates with the compliance of the air in the cabinet, and the system acts as an acoustic impedance transformer presenting a high impedance to the rear of the loudspeaker cone and a low impedance to the air [1]. 在共振时，通气孔的惰性与箱体内空气的顺应性发生共振，系统就像一个声阻抗变压器，扬声器音盆后部阻抗高，空气阻抗低[1]。 This increases the acoustic output over a limited low-frequency range compared to a sealed-box design. Several complications occur in vented designs as the output is increased beyond the point where the air in the port is able to respond in a linear fashion. 与密封箱式设计相比，这增加了有限低频范围内的声输出。在通风设计中，当输出增加到端口中的空气能够以线性方式响应的范围之外时，就会出现一些复杂问题。 They include undesirable extraneous noises generated within the port as well as acoustic compression and distortion. 它们包括端口内产生的不良外来噪音以及声压缩和失真。 These generally broad-band "chuffing" noises due to fast moving air have been dealt with (since the late 1970s; see [2]) by rounding the port ends with various radii, which led to the now common flared port. 自 20 世纪 70 年代末以来，这些由快速流动的空气引起的宽带 "嗤嗤 "声一直是通过在端口两端设置不同半径的圆角来解决的（见 [2]），这就形成了现在常见的喇叭形端口。
Recent studies by Vanderkooy [3], [4], Backman [5], and Roozen et al. [6] suggest that performance advantages can be achieved by providing a more aerodynamic profile throughout the length of the port. Vanderkooy [3]、[4]、Backman [5] 和 Roozen 等人[6] 最近的研究表明，通过在整个端口长度上提供更符合空气动力学的轮廓，可以实现性能优势。 In addition, it is important that this aerodynamic profile be on both the entrance and the exit of the port. 此外，重要的是，这种气动外形必须同时出现在端口的入口和出口处。
Due to a longer "end correction," as discussed in Section 3.3, the tapered port also behaves as if it were longer than a straight ducted port. This is very useful for 如第 3.3 节所述，由于 "端部校正 "较长，锥形端口也比直管道端口长。这对于
use in compact systems, where the port length is often restricted. Our investigational method for measuring port performance utilizes a microphone for pressure measurements and a hot-wire anemometer for velocity. 在紧凑型系统中，端口长度往往受到限制。我们研究的测量端口性能的方法是利用麦克风测量压力，利用热线风速计测量速度。 Extensive benchmarking of current designs reveals that current attempts at high-output ports suffer from compression effects at high drive, showing that at very high levels all ports eventually "lock up," limiting the maximum output. 对当前设计进行的广泛基准测试表明，当前尝试的高输出端口在高驱动力时受到压缩效应的影响，显示在非常高的电平下，所有端口最终都会 "锁定"，从而限制了最大输出。 At very high drive levels the air in the port becomes turbulent. Measurements show the velocity and pressure moving from a reactive relationship to a resistive one at high levels. At these levels the output from the port is out of phase with the output of the cone, creating a nearly complete cancellation of low-frequency energy. 在非常高的驱动水平下，端口中的空气会变得湍流。测量结果显示，在高电平时，速度和压力从反应关系转变为电阻关系。在这种情况下，端口输出与音盆输出的 相位失调，几乎完全抵消了低频能量。
This paper includes a preliminary discussion on the history of loudspeaker port performance in Section 1 and on theoretical issues in Section 2. Section 3 presents 10 studies as follows: 本文第 1 部分初步讨论了扬声器端口性能的历史，第 2 部分讨论了理论问题。第 3 部分介绍了以下 10 项研究：
Section 3.1 examines acoustic port compression in straight versus radiused ports, showing that the former compresses to a much greater degree. 第 3.1 节研究了直孔和辐射孔的声学孔压缩情况，结果表明前者的压缩程度要大得多。
Section 3.2 expands on the preceding by developing the utility of the Reynolds number as a general description of flow dynamics. 第 3.2 节在前文的基础上，进一步阐述了雷诺数作为流动动力学一般描述的实用性。
Section 3.3 introduces a novel method to model a generalized flared port and presents an empirical formula to predict the tuning of a flared port accurately. 第 3.3 节介绍了建立广义喇叭口模型的新方法，并提出了准确预测喇叭口调谐的经验公式。
Section 3.4 explores port compression among various flare rates, showing that there is a tradeoff between greater output at low levels and output at high levels. 第 3.4 节探讨了不同燃烧率下的端口压缩问题，结果表明，在低水平输出和高水平输出之间存在权衡。
Section 3.5 examines how port profiles affect distortion, 第 3.5 节探讨了端口剖面如何影响失真、
finding that once again there exists a tradeoff between performance at low SPL and at high SPL. We discuss the effect of port profile on odd-order distortion and the implications of port symmetry on even harmonic distortion. 我们发现，在低声压级和高声压级性能之间再次存在权衡。我们讨论了端口轮廓对奇次失真的影响，以及端口对称性对偶次谐波失真的影响。
Section 3.6 discusses velocity profile measurements made across different ports and how the results point to one profile as a preferred condition. 第 3.6 节讨论了在不同港口进行的速度剖面测量，以及测量结果如何将一种剖面作为首选条件。
Section 3.7 tests the hypothesis that port wall roughness imparts some performance improvements, finding that in fact roughness is detrimental to distortion and compression. 第 3.7 节检验了端口壁粗糙度能改善性能的假设，发现事实上粗糙度不利于变形和压缩。
Section 3.8 presents the same type of data as Sections 3.4 and 3.5 using a different mathematical port profile, but shows that the same conclusions and tradeoffs apply. 第 3.8 节介绍了与第 3.4 节和第 3.5 节相同类型的数据，使用了不同的数学端口剖面图，但 显示了相同的结论和权衡。
Section 3.9 expands on the importance of port symmetry for lowest even-order distortion. 第 3.9 节进一步阐述了端口对称对于实现最低偶阶失真的重要性。
Section 3.10 concludes the work by discussing the thermal implications of port design and placement, introducing the concept of port turbulence as a benefit to cooling. 第 3.10 节最后讨论了端口设计和布置对散热的影响，并引入了端口湍流对冷却有利的概念。
Some general conclusions about designing ports of maximum performance are presented in Section 4. 第 4 节介绍了有关设计性能最高的端口的一些一般性结论。
1 HISTORY 1 历史
As early as 1980 (Laupman [2]) patents started to surface, suggesting that flaring the end of ports was beneficial (Fig. 1). There exist also many good studies on turbulent effects in pipes dating back much further. 早在 1980 年（Laupman [2]），就开始有专利表明，在端口末端翻边是有益的（图 1）。此外，还有许多关于管道湍流效应的优秀研究，其历史可以追溯到更早的年代。 In 1968 Ingard and Ising [7] studied the nature of compression and distortion in orifices. Fig. 2 [7] shows the effects of compression on the SPL with increasing level, and Fig. 1968 年，Ingard 和 Ising [7] 研究了孔口压缩和失真的性质。图 2 [7] 显示了压缩对声压级随电平升高而产生的影响，而图 3 [8] 则显示了压缩对声压级随电平升高而产生的影响。 3 illustrates the nonlinear behavior of high SPL and the resulting harmonic content from a symmetrical orifice driven at high level. Note that the odd harmonics are much stronger, 3 展示了高声压级的非线性行为，以及在高电平下驱动对称孔板所产生的谐波内容。请注意，奇次谐波要强得多、
Fig. 1. Early loudspeaker design with radii on both ends of a port. (From Laupman [2].) a point we will discuss in Section 3.5. Fig. 图 1.早期的扬声器设计，端口两端都有半径。(摘自劳普曼[2]）这一点我们将在第 3.5 节中讨论。图 2. 4 also shows how at very high velocities the quadrature (reactive) relationship between velocity and pressure in the orifice disappears and the two are nearly in phase at high levels. 4 还显示了在非常高的速度下，孔口内的速度和压力之间的正交（反作用）关系如何消失，两者在高水平时几乎是同相位的。 This is particularly interesting because if the port pressure is in phase with velocity, the output of the port (which is now in phase with the back side of the cone) will be out of phase with the front of the cone. In this condition the output in the far field could be reduced significantly in a bass reflex loudspeaker. 这一点尤为有趣，因为如果端口压力与速度同相，则端口输出（现在与音盆背面同相）将与音盆前端 不相。在这种情况下，低音反射式扬声器的远场输出可能会大大降低。
Extensive studies by Young [8] in 1975 and by Harwood [1] in 1972 outline expected performance limitations of traditional straight ports. Young points to a maximum velocity of about before serious sonic detriment occurs to the signal. In Fig. 5 Harwood shows the maximum allowable SPL for various pipe diameters Young [8] 和 Harwood [1] 分别于 1975 年和 1972 年进行了大量研究，概述了传统直端口的预期性能限制。Young 指出，在对信号造成严重声损之前，最大速度约为 。在图 5 中，Harwood 显示了不同管道直径的最大允许声压级
Fig. 2. SPL transmitted through an orifice in a plate as a function of driving sound pressure . Shaded portion shows difference in level (compression) of and . (From Ingard and Ising [7].) 图 2.作为驱动声压 的函数，通过板中孔口传输的声压级。阴影部分表示 和 的电平（压缩）差异。(摘自 Ingard 和 Ising [7]）。
Fig. 3. Harmonic content of a pressure wave transmitted through an orifice in a plate of driving SPL. Note dominance of odd-order harmonics. (From Ingard and Ising [7].) 图 3.通过 驱动声压级板上的孔口传输的压力波的谐波含量。注意奇阶谐波占主导地位。(摘自 Ingard 和 Ising [7]）。
Fig. 4. Traces of pressure and velocity at low and high SPL in an orifice. At low SPL and are in quadrature; at high SPL they are in phase. represents pressure from backside of cone; is radiated sound from port. (From Ingard and Ising [7].) 图 4.孔口内低、高声压级时的压力 和速度 曲线。在低声压级时， 和 是正交的；在高声压级时，它们是相交的。 代表来自锥体背面的压力； 是来自孔口的辐射声。(摘自 Ingard 和 Ising [7]）。
before appreciable distortion due to turbulence ensues. Both authors point to a need for ports to be large in order that they produce greater SPL before losses and distortion 在湍流造成明显失真之前。两位作者都指出，端口需要较大，以便在损失和失真之前产生更大的声压级。
Fig. 5. Minimum SPL in a room of for various-diameter long pipes and vent resonant frequencies before distortion is appreciable. Note that the larger the pipe, the better, and doubling the area improves performance by 10 dB . Also lower tuning requires a larger pipe. 图 5.不同直径的长管道和通风口共振频率在 房间内的最小声压级，失真明显。请注意，管道越大越好，面积增加一倍，性能提高 10 dB。此外，较低的调谐需要较大的管道。 (From Harwood [1].) become intolerable, the bottom line being to limit the velocity to below about . Both allude to turbulence being generated as the Reynolds number becomes too high, this being the cause of performance degradation. The degradation takes the form of broad-band noise, harmonic distortion, and compression. (摘自 Harwood [1]）变得难以忍受，底线是将速度限制在 以下。两者都提到雷诺数过高会产生湍流，这是性能下降的原因。性能下降的形式包括宽带噪声、谐波失真和压缩。
More recently, in 1995, Backman [5] showed the effects of adding very small radii to the ends of ports. The study shows a reduction in the distortion when adding even such a small change. Fig. 最近，Backman [5] 在 1995 年展示了在端口两端增加极小半径的效果。研究结果表明，即使是很小的变化，也能减少变形。图 6 shows the difference in distortion and compression measured by Backman after radiusing the ends of the ports. Recent patents by Roozen et al. [6] showed a rather slow taper as being optimum. Roozen et al. display some very informative finite element analysis plots in Figs. 6 显示了 Backman 在对端口两端进行辐射处理后测得的失真和压缩差异。Roozen 等人最近的专利[6]显示，最佳锥度为相当缓慢的锥度。Roozen 等人在图中展示了一些非常有用的有限元分析图。 7 and 8, showing the vortex shedding as the air exits on a highly radiused port and on a slow taper port. The more flared port shows the vortices being generated inside the port, whereas the straighter port shows the vortex shedding occurring nearer the port ends. 7 和 8 显示了空气从高弧度端口和慢锥度端口流出时的涡流脱落情况。弧度较大的端口显示涡流在端口内部产生，而较直的端口显示涡流脱落发生在靠近端口的两端。 Also, the magnitude of the vortices is less in the slow taper port. 此外，慢锥形端口的涡流幅度也较小。
\footnotetext{ \脚注文本{ For more information on vortex shedding see [6]. 有关涡流脱落的更多信息，请参阅 [6]。
Input level 输入电平
Compression 压缩
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Fig. 6. Changes in distortion and compression. Lighter trace —straight port; heavier trace — port with small radii at both ends. (From Backman [5].) 图 6.变形和压缩的变化。较轻的轨迹 - 直端口；较重的轨迹 - 两端半径较小的端口。(摘自 Backman [5]）。
This study shows that for high exit velocities a slower taper may be required, but it neglects to take into account that as an inlet a more extreme flare might actually be preferred. Granowski and Caron’s 1998 patent [9] (Fig. 9) claims that an ellipsoidal flare is preferred. 这项研究表明，在出口速度较高的情况下，可能需要较慢的锥度，但它没有考虑到作为入口，实际上可能更倾向于更极端的扩口。Granowski 和 Caron 1998 年的专利[9]（图 9）声称，椭圆形扩口是首选。 A further invention, outlined in patents by Polk and Campbell [10] (Fig. 10) and Goto [11] (Fig. 11), describes radiused ports with a plunger on the exit that smoothly directs the port velocity in all directions to the outer periphery of the port. The previous study by Backman [5] showed that forcing the air to make any kind of turn will cause turbulence to occur at lower levels and is to be avoided if possible. Polk 和 Campbell [10]（图 10）以及 Goto [11]（图 11）的专利中概述了另一项发明，该发明描述了在出口处带有柱塞的半径端口，该柱塞可将端口速度 从各个方向平稳地引导到端口外围。Backman [5] 以前的研究表明，强迫空气进行任何形式的转弯都会导致湍流发生在较低的位置，因此应尽可能避免。 However, these designs may have the great benefit of making the port effectively longer and useful in redirecting the airflow, which otherwise might exist straight into a wall or floor. 不过，这些设计可能有一个很大的好处，那就是可以有效地延长端口的长度，并有助于改变气流的方向，否则气流可能会直接进入墙壁或地板。
Figs. 12 and 13 are from a patent by Gahm [12]. The basic invention is a modular kit for making port tubes with radiused ends. Fig. 13 is particularly interesting as it shows a method for using the port velocity to cool the loudspeaker driver directly. 图 12 和 13 来自 Gahm [12] 的专利。其基本发明是一种模块化套件，用于制造末端呈半径状的端口管。图 13 特别有趣，因为它显示了一种利用端口速度直接冷却扬声器驱动器的方法。
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Fig. 7. Simulation of vortex shedding in highly radiused port on exit stroke. Note how early in the throat shedding begins. (From Roozen et al. [6].) (a) . (b) . (c) . (d) . 图 7.模拟出口冲程中高弧度端口的涡流脱落。请注意涡流在喉部开始脱落的时间。(摘自 Roozen 等人[6]） (a) 。(b) 。(c) 。(d) 。
Fig. 8. Simulation of vortex shedding from very slow taper port. (From Roozen et al. [6].) (a) . (b) . (c) . (d) . 图 8.模拟极慢锥度端口产生的涡流脱落。(摘自 Roozen 等人[6]） (a) 。(b) 。(c) 。(d) 。
Fig. 9. Port 3 is shown with an elliptical cross section, which is said to be optimum. (From Gawronski and Caron [9].) 图 9.图中 3 号端口的横截面为椭圆形，据说是最佳横截面。(摘自 Gawronski 和 Caron [9]）。
The most extensive and recent work on the topic comes from Vanderkooy [3], [4], [13]. This work is showing detailed measurements of port velocities and pressure waveforms, presents waveform analysis, and outlines a detailed methodology for taking the data. In Figs. Vanderkooy [3]、[4]、[13] 在这方面的最新研究成果最为丰富。这项工作展示了端口速度和压力波形的详细测量结果，进行了波形分析，并概述了获取数据的详细方法。图 14 and 15 we see the waveform distortions at progressively higher levels o a straight and a radiused port. Note that the straight port develops a rather asymmetrical waveform with high levels of both odd and even harmonics. 从图 14 和图 15 中，我们可以看到直端口和辐射端口在电平逐渐升高时的波形失真。请注意，直端口产生的波形相当不对称，奇次谐波和偶次谐波都很高。 The radiused (at both ends) port, however, generates a more symmetrical wave, resembling a square wave with largely odd harmonics only. In Fig. 16 Vanderkooy reports on compression effects on several ports with a variety of interesting mathematical descriptions. 然而，辐射状（两端）端口产生的波形更加对称，类似于方波，只有大部分奇次谐波。在图 16 中，Vanderkooy 报告了几个端口的压缩效应，并给出了各种有趣的数学描述。 While no one profile stands out as superior, an interesting observation of the data (also shown by Backman) shows that at medium to higher levels, a small amount of gain takes place before compression sets in. 虽然没有哪种配置文件具有突出优势，但一个有趣的数据观察结果（Backman 也展示了这些数据）显示，在中高电平时，压缩开始之前会出现少量增益。 This might suggest that boundarylayer separation is beginning but is very small and provides a more aerodynamic flow of the air in the center of the port, which is still laminar. 这可能表明边界层分离已经开始，但非常小，而且端口中心的气流更符合空气动力学，仍然是层流。 Vanderkooy was also able to develop a model and present the supporting measurements that show that at high SPL the in-box pressure and the port throat velocity are in phase, supporting Ingard. Vanderkooy 还开发了一个模型，并提供了辅助测量结果，表明在高声压级时，箱内压力和端口喉管速度是相位的，从而支持了 Ingard 的观点。 This clearly supports the earlier contention that at high levels the output from the port will be out of phase with the front of the driver in a bass reflex enclosure and will 这清楚地证明了之前的论点，即在高电平时，端口的输出将与低音反射箱体中驱动器的前端不同相位，并将
Fig. 10. Center fixture is said to improve aerodynamics and reduce air noise. (From Polk and Campbell [10].) 图 10.据说中心固定装置可以改善空气动力学性能，降低空气噪音。(摘自 Polk 和 Campbell [10]）。
Fig. 11. Similar but earlier version of the Polk idea. (From Goto [11].) add additional compression, possibly completely canceling the fundamental. The port is now simply a leak in the box. 图 11.与波尔克理念相似但更早的版本（摘自后藤[11]）。(摘自后藤[11]）增加了额外的压缩，可能会完全消除基波。现在，端口只是盒子中的一个漏孔。 As the cone moves inward, air exits the port in the opposite direction, and the resulting volume of displaced air is reduced. Vanderkooy shows detailed measurements and analyses of the exit jet formation at high levels, which support much of the analysis of Roozen et al. 随着锥体向内移动，空气从相反的方向流出端口，由此产生的置换空气体积减少。Vanderkooy 展示了对高空出口喷流形成的详细测量和分析，这支持了 Roozen 等人的大部分分析。 It is also important to examine closely the dynamics of the air during the inlet stroke. 仔细研究进气冲程中空气的动态也很重要。
2 FLUID-FLOW THEORY 2 流体理论
Fluid flow is a very complex field, and rigorous solutions to some problems, such as the fine-scale random fluctuations in turbulent flow, defy closed-form solutions. In fact, there are no analyses, not even computer solutions, that exist to describe turbulent flow completely. 流体流动是一个非常复杂的领域，某些问题（如湍流中的细尺度随机波动）的严格解法无法以封闭形式求解。事实上，没有任何分析，甚至没有计算机解决方案，能够完全描述湍流。 Luckily there are some simplifications that can be made for the flow in loudspeaker ports. The most important is the assumption of incompressible flow, that is, density fluctuations are negligible. This simplifies the general continuity equation: 幸运的是，扬声器端口内的流动可以做一些简化。最重要的是假设流动不可压缩，即密度波动可以忽略不计。这简化了一般连续性方程：
Fig. 12. Modular design for adding radii to a straight port. (From Gahm [12].) 图 12.为直端口增加半径的模块化设计。(摘自 Gahm [12].
Fig. 13. Further refinement of modular port concept which uses port for cooling transducer. (From Gahm [12].) 图 13.模块化端口概念的进一步完善，将端口用于冷却传感器。(摘自 Gahm [12].
Fig. 14. Waveform data and FFT analysis at increasing levels from a straight flanged port. Note: Waveform is triangular and asymmetrical. (From Vanderkooy [3].) 图 14.直法兰端口在电平增加时的波形数据和 FFT 分析。注：波形呈三角形且不对称。(摘自 Vanderkooy [3]）。
Fig. 15. Waveform data and FFT analysis at increasing levels from a radiused (at both ends) flanged port. Note: Waveform approaches a square wave. (From Vanderkooy [3].) 图 15.辐射（两端）法兰端口在电平增加时的波形数据和 FFT 分析。注：波形接近方波。(摘自 Vanderkooy [3]）。
where is the density of air and is the velocity, to 其中， 是空气密度， 是速度，即
For air at standard temperature and pressure, this is a valid assumption when the velocity is less than the commonly accepted limit of the Mach number, , or a velocity of less than about . This is the case for all loudspeaker applications. 对于标准温度和压力下的空气，当速度小于通常公认的马赫数极限 或速度小于约 时，这一假设是有效的。所有扬声器应用都属于这种情况。
The definition of a Newtonian fluid is that forces due to viscosity are proportional to the rate of deformation. Air and water are Newtonian. Toothpaste is non-Newtonian because one must apply a large amount of force to get the flow started, but then it flows easily. 牛顿流体的定义是，由于粘度而产生的力与变形率成正比。空气和水都是牛顿流体。牙膏是非牛顿流体，因为必须施加很大的力才能开始流动，但随后就很容易流动了。 The primary parameter used to describe the behavior of all Newtonian fluids is the dimensionless Reynolds number Re. For flow in a circular pipe, the pipe Reynolds number is 用于描述所有牛顿流体行为的主要参数是无量纲雷诺数 Re。对于圆形管道中的流动，管道雷诺数为
where is the pipe diameter, is the viscosity of air, and is the velocity of flow. 其中， 是管道直径， 是空气粘度， 是流速。
In oscillating flows the dimensionless Strouhal number St is also important and is defined as 在振荡流动中，无量纲斯特劳哈尔数 St 也很重要，其定义为
where is angular frequency and is the characteristic length (that is, the port radius). According to Peters et al. [14], the values of St lead to flow separation, vortices, and jets. 其中 是角频率， 是特征长度（即端口半径）。根据 Peters 等人的研究 [14]，St 的值会导致气流分离、涡流和喷流。
Flow can be laminar or turbulent, with the commonly accepted transition between the two occurring near 2300 for pipes. This value is accurate for commercial pipes, but the critical Reynolds number can be much higher if the pipe has flared ends or smooth walls. 流动可以是层流也可以是湍流，对于管道而言，通常认为两者之间的转变发生在 2300 附近。对于商用管道来说，这一数值是准确的，但如果管道两端呈喇叭状或管壁光滑，临界雷诺数可能要高得多。 For example, even for a rather large 4-in (102-mm) port tube this would predict that turbulence would commence at velocities above , a very low velocity indeed. A practical upper limit for the Reynolds number obtainable in loudspeaker ports is on the order of 100000. 例如，即使是相当大的 4 英寸（102 毫米）端口管，也会在速度超过 时开始出现湍流，这确实是一个非常低的速度。扬声器端口中可获得的雷诺数的实际上限约为 100000。
Turbulence can be defined as an eddy-like state of fluid motion where the inertial vortex forces of eddies are larger than other forces, such as viscous or buoyant forces, which arise to damp out the eddies. 湍流可定义为流体运动中的一种类似涡流的状态，在这种状态下，涡流的惯性旋涡力大于其他力（如粘性力或浮力），而其他力的产生是为了抑制涡流。 It leads to random fluctuations in the flow velocity, with amplitude variations of up to of nominal and with a wide frequency band- width of "noise" components up to 10 kHz . Physically, turbulence occurs when viscous forces are unable to damp out the nonlinear inertial vortex forces that arise in the pipe. Fig. 17 illustrates viscous pipe flow. The flow is to the right, and the vortex rings appear clockwise, facing downstream. Note that the direction of the vortex forces is inward, and these are balanced by the viscous forces, which are directed outward. 它导致流速的随机波动，振幅变化可达 额定值，"噪声 "成分的频带宽度可达 10 kHz。从物理上讲，当粘性力无法抑制管道中产生的非线性惯性涡流力 时，就会产生湍流。图 17 展示了粘性管道流动。气流向右流动，涡环顺时针方向出现，面向下游。请注意，旋涡力的方向是向内的，这些旋涡力被向外的粘性力所平衡。 This equilibrium is delicate and can be upset as the velocity increases. Beyond a critical value of any small perturbation will cause the formation of eddies that are too large to be damped. These tiny eddies will cause other eddies to form in the opposite direction, which will then pair up. 这种平衡是微妙的，会随着速度的增加而被打破。超过 的临界值后，任何微小的扰动都会导致形成太大而无法阻尼的涡流。这些微小的涡流会导致其他方向相反的涡流形成，然后这些涡流会结成对。 The swirling eddy pair will similarly lead to other eddy pairs, two of which will pair, and so on, from small scale to large, growing larger until the entire pipe is full of eddies of all sizes and the flow is fully turbulent. 漩涡对同样会导致其他漩涡对，其中两个漩涡对又会导致其他漩涡对，依此类推，由小到大，不断扩大，直到整个管道充满各种大小的漩涡，水流完全湍急。
At high Reynolds numbers viscosity can generally be neglected except in the thin layer of fluid that forms along solid boundaries which is aptly called the boundary layer. Here viscous effects are significant. 在高雷诺数条件下，粘度一般可以忽略不计，但沿固体边界形成的流体薄层除外，这种薄层被恰当地称为边界层。在这里，粘滞效应非常明显。 The velocity profile across the boundary layer varies from zero (there is no slip between the boundary and the layer of fluid immediately adjacent) to of the free stream velocity at the edge (see Fig. 18). The typical width of a boundary layer in 边界层上的速度分布从零（边界和紧邻的流体层之间没有滑移）到边缘处自由流速度的 之间变化（见图 18）。图 18 中边界层的典型宽度
Fig. 16. Output versus input of several flared ports. Note gain before compression. (From Vanderkooy [3].) 图 16.几个扩口的输出与输入对比。注意压缩前的增益。(摘自 Vanderkooy [3]）。
Fig. 17. Balance between viscous forces and internal vortex forces. 图 17.粘性力和内部涡流力之间的平衡。
ports is on the order of 1 mm . 端口大约为 1 毫米。
When the fluid boundaries converge, such as through a nozzle, the flow is essentially squeezed down into a smaller area. The velocity increases and the pressure decreases. This is called a favorable pressure gradient, which occurs at the inlet of a flared port. 当流体边界汇聚时，例如通过喷嘴，流体基本上被挤压到一个较小的区域内。流速增加，压力降低。这就是所谓的有利压力梯度，发生在扩口的入口处。 When the boundaries diverge, such as the exit of a gently flared port, a socalled unfavorable or adverse pressure gradient is generated where the fluid is forced to lose velocity and gain pressure as the boundary layer hugs the wall. 当边界发散时，例如平缓扩口的出口，就会产生所谓的不利或逆向压力梯度，流体在边界层拥抱壁面时被迫失去速度并获得压力。 If the flare is too extreme, however, the deceleration of the flow is too great and causes the shear stress at the wall to approach zero. If this happens, the flow runs out of momentum at the boundary and local flow reversal occurs. 然而，如果扩口过于剧烈，气流的减速就会过大，导致壁面的剪应力趋近于零。如果出现这种情况，气流就会在边界处耗尽动量，出现局部气流逆转。
As shown in Fig. 19, when the momentum goes to zero, the pressure gradient becomes so large that undesirable flow separation occurs along with the localized reversal. 如图 19 所示，当动量变为零时，压力梯度会变得非常大，以至于在发生局部逆转的同时会出现不理想的流动分离。 Theoretically this separation of the acoustic flow leads to output-robbing vortices, which sink the acoustical energy into the kinetic energy of the vortex. This energy is then uselessly dissipated by friction instead of acoustic propagation [14]. 从理论上讲，声流的这种分离会导致输出吸收涡旋，从而将声能转化为涡旋的动能。这些能量会通过摩擦而不是声波传播无用地耗散掉 [14]。 Note that this situation cannot occur in the other half of the period, when the flow is going in the opposite direction, because flow separation cannot occur when there is a favorable pressure gradient. 需要注意的是，这种情况不可能发生在另一半时间段，即水流方向相反的时候，因为当存在有利的压力梯度时，不可能发生水流分离。
Boundary layers may be laminar or turbulent. Turbulent boundary layers have the desirable quality of being able to withstand higher pressure gradients without becoming separated. This is because the turbulent layer has larger wall shear stress and higher momentum near the wall. 边界层可以是层流的，也可以是湍流的。湍流边界层的理想特性是能够承受较大的压力梯度而不会发生分离。这是因为湍流层具有较大的壁面剪应力和较高的壁面动量。 This extra momentum near the wall allows a turbulent layer to withstand the unfavorable pressure gradient without separation. How does one cause the boundary layer to become turbulent? 这种靠近壁面的额外动量使湍流层能够承受不利的压力梯度而不发生分离。如何使边界层变成湍流层？ Some of the factors that would tend to cause transition to turbulence include free stream disturbances, boundary roughness, pressure gradients, or vibration. Obstructions in the boundary layer also hasten the onset of transition to turbulence. 容易导致向湍流过渡的一些因素包括自由流扰动、边界粗糙度、压力梯度或振动。边界层中的障碍物也会加速向湍流的过渡。
Some experiments performed by Merkli and Thomann [15] found that for oscillating flow, turbulence does not occur over an entire cycle. Rather it occurs in the form of periodic bursts followed by "relaminarization" during the Merkli 和 Thomann [15] 进行的一些实验发现，对于振荡流，湍流不会在整个周期内发生。相反，湍流是以周期性爆发的形式出现的，在周期性爆发之后的一段时间内，湍流会 "再层流化"。
Fig. 18. Velocity profile near a stationary wall. same cycle. They plot that the factor 图 18.静止墙壁附近的速度曲线。他们绘制了系数
and found a critical value above which transition into turbulence occurs. Their study was limited to the frequency range away from the resonance of the pipe , whereas we are mainly interested in the frequency near resonance, where the acoustic port output is greatest. 并发现了一个临界值 ，超过该值就会过渡到湍流。他们的研究仅限于远离管道共振 的频率范围，而我们主要关注的是共振附近的频率，即声学端口输出最大的频率。
The vorticity is defined as the curl of the velocity vector. Physically it is equivalent to the rate of angular deformation. If , then there is no angular deformation in any plane at any point. The circulation is defined as . Physically, circulation is the flux of vorticity. If , then the flow is irrotational. This is the case outside the boundary layer if we neglect the Coriolis force and gravity. The boundary layer is definitely not irrotational. These assumptions simplify the momentum equation to the unsteady Bernoulli equation. 涡度 被定义为速度矢量的卷曲。在物理学上，它等同于角变形率。如果 ，则任何平面上的任何点都不存在角变形。环流 定义为 。从物理学角度看，环流就是涡度的通量。如果 ，则流动是不旋转的。如果我们忽略科里奥利力和重力，边界层外就是这种情况。边界层肯定不是非旋转的。这些假设将动量方程简化为非稳态伯努利方程。
To make a detailed analysis of the airflow in a port and develop a design approach it is important to understand the fluid flow dynamics in both directions. 要对端口中的气流进行详细分析并制定设计方法，就必须了解两个方向的流体流动动力学。 The preferred geometry for each may be in conflict as the intake stroke would be well served with a large radius providing a slow head loss and a favorable pressure gradient, and the exit would be well served with a more gradual flare to avoid an excessive adverse pressure gradient. 两者的优选几何形状可能会有冲突，因为进水冲程的半径大，水头损失慢，压力梯度大，而出水冲程的半径小，水头损失大，压力梯度大，而出水冲程的半径大，水头损失慢，压力梯度大。
3 TEN STUDIES 3 十项研究
3.1 Power Compression on Straight versus Radiused Ports 3.1 直端口与半径端口的功率压缩对比
The first study undertaken by the authors several years ago was simply to make a side-by-side comparison of the power compression of a straight versus a radiused port. 作者在几年前进行的第一项研究只是对直端口和弧形端口的功率压缩进行了并排比较。 Previous work by Gander [16], Harwood [1], and Young [8] clearly pointed out that all ports do power compress at high levels. Gander [16]、Harwood [1] 和 Young [8] 以前的研究明确指出，所有端口在高水平时都会进行功率压缩。 As mentioned before, radiused ports have become something of a fashion, and the authors intuitively concluded that they should also have superior fluid flow properties, at least on the inlet air stream, and subsequently less compression. Figs. 如前所述，弧形喷口已成为一种时尚，作者凭直觉认为，至少在进气流中，弧形喷口也应具有出色的流体流动特性，从而减少压缩。图 20, 21, and 22 show the compression versus the level for a straight 6-in (152-mm)long, 3-in ( )-diameter port and for the same port with large radii on the inside and outside. The different plots are at different frequencies of 25,30 , and 35 Hz . The port was driven by two 12 -in ( )-high excursion 20、21 和 22 显示的是 6 英寸（152 毫米）长、3 英寸（ ）直径的直端口以及内侧和外侧具有大半径的相同端口的压缩与电平关系。不同的图表显示的频率分别为 25、30 和 35 Hz。该端口由两个 12 英寸 ( )- 高偏移驱动。
Fig. 19. Adverse pressure gradients can lead to flow separation. 图 19.不利的压力梯度会导致气流分离。
Fig. 20. Compression of 3 -in ( )-diameter 6-in ( )-long straight port versus highly radiused port at 25 Hz . Note gain before compression. 图 20.3 英寸 ( )- 直径 6 英寸 ( )- 长直端口与高辐射端口在 25 Hz 时的压缩情况。注意压缩前的增益。
Fig. 21. Compression of 3-in (76-mm)-diameter 6-in (150-mm)-long straight port versus highly radiused port at 30 Hz . 图 21.30 Hz 时直径 3 英寸（76 毫米）、长 6 英寸（150 毫米）的直端口与高辐射端口的压缩率对比。
Fig. 22. Compression of 3-in (76-mm)-diameter 6-in (150-mm)-long straight port versus highly radiused port at 35 Hz . Note: Velocity is too low to compress radiused port at 35 Hz . 图 22.35 Hz 时直径 3 英寸（76 毫米）、长 6 英寸（150 毫米）的直口与高辐射口的压缩情况。注：速度太低，无法在 35 Hz 时压缩辐射端口 .
woofers in a (57-l) box. The tuning frequency was about 30 Hz . The input voltage and current were monitored to account for thermal compression effects, and the output was plotted versus the actual input drive power. The microphone was a small -in ( ) B&K microphone spaced about 4 in from the port on axis. This was determined not to interfere with the airflow yet give a high enough port-to-driver output ratio that good results could be seen. A number of observations can be made from this simple experiment. （57 升）箱体中的低音扬声器。调谐频率约为 30 赫兹。对输入电压和电流进行了监测，以考虑热压效应，并绘制了输出与实际输入驱动功率的对比图。麦克风是一个小型的 -in ( ) B&K 麦克风，距离轴上的端口约 4 英寸 。这样既不会干扰气流，又能提供足够高的端口与驱动器输出比，从而获得良好的效果。从这个简单的实验中可以得出一些结论。
The first and most obvious observation is that the radiused port compresses substantially less at moderate levels of operation than the straight port. Also at lower frequencies (higher velocities) the effect is much more pronounced. 第一个也是最明显的观察结果是，在中等运行水平下，半径端口的压缩率大大低于直端口。此外，在较低频率（较高速度）下，效果也更为明显。 There appears to be a "wall" beyond which neither port is able to go. The conclusion is that this wall exists at the point where the air in the port becomes completely turbulent. 似乎有一堵 "墙"，两个端口都无法越过。结论是，这堵墙存在于端口中的空气变得完全湍流的地方。 Another observation is that about 8-dB more output can be obtained before significant compression sets in. A close examination of the curves suggests an increase or expansion in the medium area of operation of 0.5 dB or so. 另一个观察结果是，在出现明显压缩之前，输出功率可增加约 8 分贝。仔细观察这些曲线可以发现，在中等工作范围内，输出功率增加或扩大了 0.5 分贝左右。 This implies that at moderate levels the radiused port might have a small boundary-layer separation, which acts as "air bearing" and actually reduces losses in the port. 这意味着，在中等水平下，辐射端口可能会有少量的边界层分离，起到 "空气轴承 "的作用，实际上减少了端口的损耗。
Most of these conclusions are basically correct but need some adjustment. Previous work by Strahm [17], following Young [8], show that the minimum impedance at port resonance rises as a port compresses. 这些结论大多基本正确，但需要做一些调整。Strahm [17] 继 Young [8] 之后的研究表明，端口共振时的最小阻抗会随着端口的压缩而上升。 This means that the power delivered to the loudspeaker will go down even if the drivers do not thermally power compress. 这意味着，即使驱动器不进行热功率压缩，输送到扬声器的功率也会下降。 Since the plot is based on the real power to the drivers, and the straight port begins to compress very early on, the impedance will rise and the compression will appear to be worse. 由于曲线图是根据驱动器的实际功率绘制的，而直通端口很早就开始压缩，因此阻抗会升高，压缩效果也会变差。 The rise in output in the middle range was also witnessed by Vanderkooy [3], confirming these data. The bottom line is that the difference between the two may not be as great as this experiment suggests, but the radiused port is still much better. Vanderkooy [3] 也见证了中间范围输出的上升，证实了这些数据。总之，两者之间的差别可能并不像实验显示的那么大，但辐射端口还是要好得多。 Nevertheless, the issue is clearly velocity related, and boundary-layer separation is quite possibly involved at lower levels. 不过，这个问题显然与速度有关，在较低的水平上很可能涉及到边界层分离。
3.2 Port Compression versus Reynolds Number 3.2 油口压缩与雷诺数的关系
The previous study and the historical work suggest that port performance and maximum output capability are related to the velocity in the port. 之前的研究和历史工作表明，港口性能和最大输出能力与港口速度有关。 In the process of working toward developing ports with optimum performance, the next step is to confirm that turbulence is in fact the culprit and to develop a simple measurement of when that turbulence is too great for desirable acoustical performance. 在努力开发具有最佳性能的端口的过程中，下一步是确认湍流实际上是罪魁祸首，并开发出一种简单的测量方法，用于测量湍流何时过大，从而达到理想的声学性能。
This study involved the measurement of the velocity of the airflow in three large subwoofers with two 18-in (457mm ) drivers in each. A hot-wire anemometer was placed in the center of the port of three very different port designs. The SPL was again measured with a small -in (6-mm) microphone a few inches from the port. Of the enclosures tested, one had a large single rectangular port, one had three circular ports, and one had four rectangular ports. None had any radii. 这项研究涉及测量三个大型超低音中的气流速度，每个超低音中都有两个 18 英寸（457 毫米）的驱动器。在三种截然不同的端口设计的端口中心放置了一个热线风速计。在距离端口几英寸的地方，再次用一个 英寸（6 毫米）的小型麦克风测量声压级。在测试的箱体中，一个有一个大的单矩形端口，一个有三个圆形端口，一个有四个矩形端口。它们都没有任何半径。 The area of each port was dif- ferent in each case, the boxes were tuned differently, and each had different volumes. 每种情况下，每个端口的面积不同，盒子的调谐方式不同，体积也不同。 The question was, what figure of merit could be applied to all subwoofers that would clearly show a relationship to power compression, which would be independent of design? 问题是，怎样才能对所有超重低音扬声器都适用功勋值，从而清楚地显示出与功率压缩之间的关系，而这种关系又与设计无关？
The conclusion was to take data on the velocity in the middle of the port. The velocity measurements would then be converted to a Reynolds number using Eq. (3) for each of the designs and then plotted versus compression. Figs. 结论是测量端口中间的速度数据。然后使用公式 (3) 将速度测量值转换为每种设计的雷诺数，并绘制出速度与压缩率的关系图。图 23, 24, and 25 plot compression versus Reynolds number for each of the designs. What stands out is that, for the most part, all three designs show very similar compression curves at all frequencies tested. All designs seem to hit a wall near a Reynolds number of about . This number was also confirmed by Vanderkooy [3]. The Moody chart, a standard reference chart used in fluid mechanics, shows the relationship between the Reynolds number and the turbulence in pipes (Fig. 26). 23、24 和 25 图示了每种设计的压缩率与雷诺数的关系。值得注意的是，在大多数情况下，所有三种设计在测试的所有频率下都显示出非常相似的压缩曲线。所有设计似乎都在雷诺数 附近碰壁。Vanderkooy [3] 也证实了这一数值。流体力学中使用的标准参考图表 Moody 图表显示了雷诺数与管道中湍流之间的关系（图 26）。 It can be considered to have three regions: laminar, turbulent, and a region of transition between the two, shown shaded in the figure. The range of Reynolds numbers given here falls in the transition zone. 可以认为有三个区域：层流区、湍流区和两者之间的过渡区，如图中阴影所示。这里给出的雷诺数范围属于过渡区域。 The conclusion is that compression is clearly related to turbulence and that a Reynolds number of about 50000 is a good indicator of when the system begins to degrade. 结论是压缩明显与湍流有关，约 50000 的雷诺数是系统开始退化的良好指标。
3.3 Modeling Flared Ports and Prediction of Tuning 3.3 扩口建模和调谐预测
Everyone, from piping system engineers to carburetor designers, knows that pipe entrance losses are highly dependent on the geometry. Interestingly, exit losses are independent of geometry. 从管道系统工程师到化油器设计师，每个人都知道管道入口损失与几何形状密切相关。有趣的是，出口损失与几何形状无关。 However, audio signals by definition are oscillating, and therefore both sides of a loudspeaker port are "entrances" and would benefit from rounding of the edges. A well-rounded entrance with a radius of of the pipe diameter yields a very low loss, whereas a sharp entrance asymptotically reaches a loss (Fig. 27). 然而，音频信号顾名思义是振荡的，因此扬声器端口的两侧都是 "入口"，边缘圆滑会使其受益。半径为管道直径 的圆润入口可产生极低的 损耗，而尖锐的入口则会逐渐达到 损耗（图 27）。
The main difficulty in modeling flared loudspeaker ports is the infinite variety of profiles that will yield the same port tuning. 扬声器喇叭口建模的主要困难在于，有无数种外形会产生相同的喇叭口调谐。 Many loudspeaker designers choose not to experiment with flared ports because without a welldefined diameter to plug into the standard port tuning formula, they are left to design by trial and error. 许多扬声器设计者选择不尝试使用喇叭口，因为没有明确定义的直径来输入标准的喇叭口调整公式，他们只能通过试验和错误来进行设计。 There are no CAD programs that incorporate the ability to design flared ports as of yet. However, there is a growing demand to take advantage of flared ports and a need for predicting their performance. 目前还没有任何 CAD 程序具备设计扩口的能力。但是，利用扩口的需求越来越大，而且需要对扩口的性能进行预测。
The tuning of a port, flared or otherwise, is a function of the ratio of the port cross-sectional area to the port length. For a standard straight cylindrical port, and neglecting end corrections, there are several equivalent embodiments of the port tuning equation: 端口（无论是否扩口）的调谐是端口横截面积与端口长度之比的函数。对于标准的直圆柱形端口，忽略端部修正，端口调谐方程有几个等效的实施例：
where for air, is the ambient atmospheric pressure (101 000 Pa ), the density of air ( ), the port cross-sectional area, the box volume, the port length, 式中： 为空气； 为环境大气压力（101 000 Pa）； 为空气密度（ ）； 为端口横截面积； 为箱体容积； 为端口长度、
Fig. 23. Port compression versus Reynolds number in double 18-in (457-mm) subwoofer, , tuned to 45 Hz with a single rectangular port. 图 23.双 18 英寸（457 毫米）超低音扬声器 的端口压缩与雷诺数的关系，使用单矩形端口调谐到 45 Hz。
Fig. 24. Port compression versus Reynolds number in double 18-in (457-mm) subwoofer, , tuned to 35 Hz with three straight round ports. 图 24.双 18 英寸（457 毫米）超低音扬声器 的端口压缩与雷诺数的关系，调谐到 35 Hz，有三个直圆形端口。
Fig. 25. Port compression versus Reynolds number in double 18 -in (457-mm) subwoofer, , tuned to 39 Hz with four straight square ports. 图 25.双 18 英寸（457 毫米）超低音扬声器 的端口压缩与雷诺数的关系，调谐到 39 Hz，有四个直方形端口。
and the acoustic mass of air in the port. Notice that the ratio enters directly with other nonport parameters. 和 端口的空气声质量。 注意， 比值与其他非端口参数直接相关。
The acoustic mass reactance in the port in units of , is given by 端口 中的声质量电抗（单位： ）由以下公式给出
For the generalized cause of ports with arbitrary cross sections, one only needs to find the effective ratio to 对于具有任意横截面的端口的广义原因，我们只需要找到有效的 比值，就可以得出
which simplifies to 简化为
for a standard cylindrical port. 为标准圆柱形端口。
Fig. 26. Moody chart showing relationship between Reynolds number, turbulence, and roughness. (Adapted from White [18].) 图 26.显示雷诺数、湍流和粗糙度之间关系的 Moody 图。(改编自 White [18]）。
Fig. 27. Entrance loss coefficients for rounded and beveled inlets. Lower curve applies to rounded geometry. loss coefficient related to ratio of pressure drop to velocity. Note: yields a nearly lossless inlet. (From White [18].) 图 27.圆形和斜面入口的入口损失系数。下曲线适用于圆形几何体。 损失系数与压降和速度的比率有关。注： 表示几乎无损耗的入口。(摘自 White [18].
find the actual tuning frequency. Vanderkooy has shown the formula for this to be 找出实际的调谐频率。范德高伊给出的计算公式为
where is the area function and any end correction. The difficulty for flared ports arises in finding the correction . End corrections are needed because the radiation impedance of a port is not zero, the free ends of which act as a vibrating diaphragm. However, since the radiation impedance is small, the effect is merely to increase the effective length of the tube by an amount . For traditional straight ports, is a well-known quantity, equal to for a free end and for a flanged end, where is the port radius [19, p. 131]. For straight ports is relatively constant over a wide range of driving amplitudes. 其中 是面积函数， 是任何端部修正。扩口端口的困难在于找到 修正。需要进行端部修正是因为端口的辐射阻抗不为零，其自由端就像一个振动膜片。然而，由于辐射阻抗很小，因此其效果仅仅是增加了管道的有效长度 。对于传统的直端口， 是一个众所周知的量，自由端等于 ，法兰端等于 ，其中 是端口半径 [19, 第 131 页]。对于直端口， 在很宽的驱动振幅范围内相对恒定。
Flared ports, however, do not have a well-defined diameter, and so is not so simple. In effect, the end correction is a measure of the inertia of the flow at the exit. Given that each port shape has a different correction, is there any hope of developing a generalized port tuning equation? 然而，扩口没有明确的直径，因此 就不那么简单了。实际上，末端修正是对出口处流动惯性的测量。鉴于每种端口形状都有不同的修正量，是否有希望建立一个通用的端口调整方程？ Some method of approximating a general port flare would need to be devised so that the effect of the "amount of flare" could be studied. For simplicity, we chose to investigate flare profiles described by a simple radius. 为了研究 "耀斑量 "的影响，需要设计一些近似一般端口耀斑的方法。为了简单起见，我们选择研究用简单半径描述的耀斑剖面。 Using this simplification we can define a normalized flare rate (NFR) as the ratio of overall port length to flare radius, 利用这一简化，我们可以将归一化扩口率 (NFR) 定义为端口总长度与扩口半径之比、
Thus a straight port would have an NFR of 0.0 , and a very extreme port with a full radius would have an NFR of 1.0 (Fig. 28). Most port profiles can be approximated with an NFR in this range. This normalization of scale allows the results to be generalized to any port size. 因此，一个直端口的 NFR 为 0.0，而一个全半径的极端端口的 NFR 为 1.0（图 28）。大多数端口剖面的近似 NFR 都在这个范围内。这种尺度的归一化可使结果适用于任何尺寸的端口。
An initial sample of six port tubes, all of length and a minimum diameter of 60 mm , were made with NFRs of , and 1.0. In addition, all profiles had a small 12-mm blend radius on both ends to avoid sharp edges, as well as a 140 -mm outsidediameter inner baffle for symmetry (Fig. 29). 最初制作了六个端口管样本，长度均为 ，最小直径为 60 毫米，NFR 分别为 和 1.0。此外，所有型材的两端都有一个 12 毫米的小混合半径，以避免尖锐的边缘，以及一个外径为 140 毫米的内挡板，以保持对称（图 29）。
Unexpectedly the port tuning frequency was only weakly dependent on the amount of flare. Clearly, the port length and minimum throat diameter appear to be the main determinates of tuning. 出乎意料的是，端口调谐频率与喇叭口的大小只有微弱的关系。显然，端口长度和最小喉管直径似乎是调谐的主要决定因素。 As the port flare becomes more pronounced, the end correction, as typically calculated based on the radius at the mouth, overestimates the reactive air mass present. 随着端口扩口越来越明显，通常根据端口半径计算的末端修正会高估存在的反应气团。 A better way to predict tuning appears to be basing the length correction on the minimum throat diameter instead of the maximum diameter. 预测调整的更好方法似乎是根据最小喉管直径而不是最大直径进行长度修正。 Following this path, fitting the experimentally determined tuning frequencies to a function of the flare radius leads to a striking linear relationship ( ) between NFR and the effective port area (Fig. 30). The data fit yields port tuning predictions within for all six ports, and within for all other port profiles tested subsequently, including elliptical and exponential profiles. Of course, the accuracy of prediction is better the closer a given profile can be approximated by a simple radius. The formula is 按照这一思路，将实验确定的调谐频率与喇叭口半径的函数进行拟合，可以在 NFR 和有效端口面积之间找到显著的线性关系 ( )（图 30）。通过数据拟合，所有六个端口的端口调谐预测值都在 范围内，而随后测试的所有其他端口剖面（包括椭圆和指数剖面）的端口调谐预测值都在 范围内。当然，预测的准确度越高，给定的剖面就越接近于简单的半径。计算公式为
where 其中
Here is the speed of sound, the actual port length, the best fit flare radius, the minimum throat area, the minimum throat diameter, and the net box volume. 此处 为声速， 为实际端口长度， 为最佳拟合扩口半径， 为最小喉管面积， 为最小喉管直径， 为净箱容积。
The only difficulty in using this formula is finding the best fit flare radius to a given profile. But even this is relatively easy using the built-in optimizers in most spreadsheet software. 使用该公式的唯一困难是找到与给定轮廓最匹配的扩口半径。但即使是这样，使用大多数电子表格软件的内置优化器也相对容易。
3.4 Acoustic Compression 3.4 声学压缩
As the SPL of a port is increased, there is no escaping some degree of port compression. The question becomes, how the port flare affects this compression, if at all. As described previously, turbulence is most likely the culprit. 随着音箱声压级的提高，音箱在一定程度上会受到压缩。问题是，如果有的话，端口扩口如何影响这种压缩。如前所述，湍流很可能是罪魁祸首。 One effect of turbulence in a port is a reduction of the of the resonance. This causes a drop in the acoustical output at resonance. 端口湍流的影响之一是降低共振的 。这会导致共振时的声学输出下降。
In order to explore this phenomenon, another test enclosure was constructed using a 1 -in ( ) MDF with a single high-throw 18 -in ( ) woofer. The bandpass box had a ported chamber volume of 201 l and a sealed chamber volume of 111 l. Testing conducted with this 为了探索这一现象，我们使用 1 英寸（ ）中密度纤维板和单个 18 英寸（ ）高掷低音扬声器构建了另一个测试箱体。该带通箱体的端口腔容积为 201 升，密封腔容积为 111 升。
NFR
Fig. 28. Simple radiused port nomenclature. 图 28.简单辐射状端口命名法。
box would effectively remove acoustic contributions from the transducer (as it is buried within the box), leaving only the port output. The box loss was measured by the Thiele method at over 14, indicating a very rigid, low-loss box. 箱体将有效消除换能器的声波贡献（因为它被埋在箱体内），只留下端口输出。通过 Thiele 方法测得的箱体损耗 超过 14，表明箱体非常坚固，损耗很低。
Initial trials were made to find the best microphone placement for measuring compression (see Pedersen and Vanderkooy [13] for an extensive investigation). 为了找到测量压缩的最佳传声器位置，我们进行了初步试验（详见 Pedersen 和 Vanderkooy [13]）。 The pretrials were conducted with the microphone at the port mouth, inside the box, and at 2 m measured on a ground plane (Fig. 31). 预试时，麦克风位于端口口、箱内和 2 米处的地平面上（图 31）。 The data showed that the compression measurements are very similar in all cases, yet the cleanest data came from the in-box measurement, so this method was chosen for subsequent experiments. In-box acoustic measurements were performed using a B&K -in microphone, which has a distortion limit of greater than SPL. To prevent transducer power compression from contaminating the results, a very highpower driver with minimum power compression in the test range was employed. The transducer was driven using a large power amplifier in the bridged mode, which can provide 2 kW of output into . Most measurements were made over a frequency range of using a 15-s sweep from low frequency to high. Each port was driven 数据显示，所有情况下的压缩测量结果都非常相似，但箱内测量得到的数据最清晰，因此后续实验选择了这种方法。箱内声学测量使用 B&K -in 麦克风进行，其 失真极限大于 SPL。为了防止换能器的功率压缩对结果造成污染，我们采用了在测试范围内功率压缩最小的超大功率驱动器。在桥接模式下，使用大型功率放大器驱动换能器，该放大器可为 提供 2 kW 的输出功率。大多数测量都是在 的频率范围内进行的，从低频到高频扫描 15 秒。每个端口都被驱动
Fig. 31. Bandpass loudspeaker setup for compression testing. Before selecting the "in-box" position for all compression measurements, the three microphone locations shown were tried. 图 31.用于压缩测试的带通扬声器设置。在为所有压缩测量选择 "箱内 "位置之前，尝试了所示的三个传声器位置。
Fig. 29. Port profiles for study. 图 29.供研究的港口剖面图。
Fig. 30. Curve fit of flare rate to port tuning data. 图 30.耀斑率与端口调整数据的曲线拟合。
at successively higher voltages in 6-dB increments beginning at 1.25 V and ending at 40 V . The curves were then mathematically lowered by the amount the input power was increased so that they would overlap, except for the compression effects. 从 1.25 V 开始到 40 V，电压以 6 分贝的增量依次升高。然后，根据输入功率的增加量，用数学方法降低曲线，这样，除了压缩效应外，它们就会重叠。 The results from some representative ports are shown in Figs. 32-35. They indicate that there is no compression at the end of the sweep, so we can be sure that all compression shown is solely due to the port. 图 32-35 显示了一些代表性端口的结果。这些结果表明，在扫描结束时没有任何压缩，因此我们可以确定所有显示的压缩都是由端口造成的。 Despite the fact that all ports compress, the ways they compress appears to differ. The largely radiused ports not 尽管所有端口都在压缩，但压缩的方式似乎有所不同。弧度较大的端口不会
Fig. 32. Port compression measured in box for port with NFR voltage increments from 1.25 to 40 V rms. Each progressive curve was lowered 6 dB . Since all curves overlap at higher frequencies, no thermal compression is evident, and all curve differences are due to acoustic compression. 图 32.NFR 电压增量从 1.25 到 40 V rms 时，在盒中测量的端口压缩情况。每条渐进曲线都降低了 6 dB。由于所有曲线都在较高频率处重叠，因此没有明显的热压缩，所有曲线差异都是由于声压缩造成的。
Fig. 33. Port compression measured in box for port with . 图 33.带 的端口在盒内测得的端口压缩率。
Fig. 34. Port compression measured in box for port with . 图 34.带有 的端口在箱体内测量的端口压缩率。
Fig. 35. Port compression measured in box for port with NFR . 图 35.NFR 的端口在箱内测得的端口压缩率。
only compress in level, but the frequency of the resonance shifts also. It is suspected that this happens because the port becomes effectively shorter as it starts to become turbulent, confirming Vanderkooy's contention that the end correction changes with the level. 这证实了 Vanderkooy 的论点，即末端校正随水平面的变化而变化。人们怀疑出现这种情况的原因是，当端口开始变得湍流时，端口实际上变短了，这证实了范德高伊的论点，即末端修正会随着水平面的变化而变化。 The section of the port area near the end has severe boundary separation due to the adverse pressure gradient, as predicted by Roozen et al. The air in this section is largely turbulent and is not part of the acoustic mass of the port. 根据 Roozen 等人的预测，靠近末端的端口区域由于不利的压力梯度而出现严重的边界分离。 The port is thus effectively shorter and tunes higher. Of additional interest is that the largely radiused ports have a higher output at low levels. The of the port is clearly higher and losses are less. The straighter ports show less frequency shift, but in the straight ports the compression and losses are relatively high, especially at low levels. 因此，端口实际上更短，音调更高。另外一个值得关注的现象是，大部分呈半径状的端口在低电平时具有更高的输出。端口的 显然更高，损耗也更小。较直的端口显示的频率偏移较小，但直端口的压缩和损耗相对较高，尤其是在低电平时。 An optimum solution strikes a balance between minimizing frequency shift and compression. The port with NFR appears to find this balance. 最佳解决方案是在尽量减少频率偏移和压缩之间取得平衡。带有 NFR 的端口似乎找到了这种平衡。
Fig. 36 shows the same data as Figs. 32-35, but "sliced" vertically at 20 Hz and plotted relative to the straight port, whereas Fig. 37 is taking the maximum value of each curve instead. 图 36 显示与图 32-35 相同的数据，但在 20 赫兹处垂直 "切片"，并绘制出相对于直口的曲线，而图 37 则取每条曲线的最大值。 Either way, all ports measured showed severe compression, on the order of 10 dB at port tuning at the highest power levels. Despite the close grouping of the data, suggesting that any moderate 无论如何，所测量的所有端口都显示出严重的压缩，在最高功率水平下，端口调整时的压缩量约为 10 分贝。尽管数据分组很接近，表明任何适度的
Fig. 36. Port compression versus level at 20 Hz for simple radius ports. Note: NFR is best. 图 36.简单半径端口在 20 Hz 时端口压缩与电平的关系。注：NFR 最佳。
Fig. 37. Port compression at port tuning versus level for simple radius ports. Note: NFR is best. amount of flaring is good and that there is no clear winner, there were some differences noted. The most obvious conclusion is that a large radius is clearly better at lower levels. 图 37.简单半径端口调整时的端口压缩率与水平。注：NFR 最佳。最明显的结论是，在低电平时，大半径显然更好。 Also, it appears that the more extreme the port flare, the worse the compression at high levels. In addition, the straight port starts out with about 2 dB less output than any flared port, but it compresses less dramatically than would be expected. 此外，端口外扩的程度越大，高电平时的压缩效果就越差。此外，直端口开始时的输出比任何喇叭口都要低约 2 分贝，但其压缩效果却没有预期的那么明显。 A close examination points to a "sweet spot," where a moderate amount of flare (NFR ) works better than all others. 仔细观察会发现一个 "甜蜜点"，在这个点上，适度的耀斑（NFR ）比其他所有耀斑都更有效。
3.5 Distortion Measurements 3.5 失真测量
Probably the single most remarkable characteristic of flared ports as compared to straight ones is the marked reduction in distortion that can be achieved. 与直端口相比，扩口端口最显著的特点可能就是可以明显减少变形。 It is clear that aerodynamic profiles are much quieter than their straight counterparts, but once again we can question whether a particular profile has advantages over any other. 显然，空气动力型材比直线型材要安静得多，但我们可以再次质疑，某种特定的型材是否比其他型材更有优势。
To answer the question, another enclosure was built as a bandpass box, which could be mounted in a anechoic chamber to maximize the signal-to-noise ratio, as shown in Fig. 38. A very long throw 15 -in (381-mm) woofer was used to excite the ports. Harmonic distortion was measured using a sine source set to the tuning frequency of each port in the vented test enclosure. 为了回答这个问题，我们制作了另一个带通箱，可以安装在 消声室中，以最大限度地提高信噪比，如图 38 所示。使用一个 15 英寸（381 毫米）的超长低音扬声器来激励端口。谐波失真使用正弦源进行测量，正弦源设置为通风测试箱中每个端口的调谐频率。 MLSSA was used as a digital storage scope to capture several cycles of the acoustic output at a distance of 1 m from the port. The microphone was placed off axis to avoid contamination from jets. A fast Fourier transform was applied to the captured waveform, and the amount of energy at the desired frequency multiples was calculated. The test was MLSSA 用作数字存储范围，用于捕捉距离端口 1 米处的几个声输出周期。麦克风放置在 轴外，以避免喷流污染。对捕捉到的波形进行快速傅立叶变换，计算所需频率倍数的能量。测试
Fig. 38. Distortion measurement setup. A bandpass loudspeaker mounted in a anechoic chamber was used to measure distortion. Note off-axis position of microphone to avoid contaminating data with subsonic noise due to exit jets. 图 38.失真测量装置。使用安装在 消声室中的带通扬声器测量失真。注意麦克风的离轴位置，以避免出口喷流产生的亚音速噪音污染数据。
repeated at an increasing input voltage in 1-dB increments until the limit of the amplifier was reached at 40 V . Results were examined for odd harmonics, even harmonics, and total harmonic distortion (THD) (all harmonics). 在输入电压以 1 分贝递增的情况下重复进行，直到放大器的极限电压达到 40 V。检查结果包括奇次谐波、偶次谐波和总谐波失真 (THD)（所有谐波）。 Although noise is the most obvious artifact, nonharmonic noise was not considered for this experiment because early testing showed that port differences are captured well with harmonic analysis (Fig. 39). 虽然噪音是最明显的伪影，但由于早期测试表明谐波分析可以很好地捕捉端口差异，因此本实验没有考虑非谐波噪音（图 39）。 In all cases, most harmonic distortion occurs in the odd harmonics, with most ports examined having generally low amounts of even harmonics (Fig. 40). 在所有情况下，大部分谐波失真都发生在奇次谐波中，而大多数端口的偶次谐波量普遍较低（图 40）。 Examination of these results shows that port symmetry (that is, adding a flange on the inside port end) is important for minimizing this type of distortion. As expected, a low even harmonic content is found in symmetrical ports. 对这些结果的研究表明，端口对称性（即在端口内端增加一个凸缘）对于最大限度地减少此类失真非常重要。不出所料，对称端口的偶次谐波含量较低。 Odd harmonic content, however, is strongly affected by port flare geometry (Fig. 41). Fig. 42 combines both odd and even harmonics into a THD measurement. In these experiments, straight ports are clearly inferior to ports with even the gentlest flare. 然而，奇次谐波含量受端口扩口几何形状的影响很大（图 41）。图 42 将奇次谐波和偶次谐波合并到 THD 测量中。在这些实验中，直端口明显不如具有最轻微喇叭口的端口。 As to flared ports, the results generally show that at lower acoustic levels, greater port flares yield lower distortion, with the NFR port performing best as it is the least lossy, as shown in Section 3.4. 至于喇叭口，结果普遍显示，在较低的声级下，较大的喇叭口喇叭口会产生较低的失真，其中 NFR 端口的表现最好，因为它的损耗最小，如第 3.4 节所示。
At higher levels, near 100 dB at 1 m , ports with moderate flare lead the pack, with NFR being optimum. 在较高水平（1 米处接近 100 分贝）时，具有中等耀斑的端口处于领先地位，NFR 为最佳。
At very high levels (over 100 dB at 30 Hz from a 2.5-in (63.5-mm) port), however, it is apparent that too much flare causes more distortion than gentler flares. Surprisingly, standard straight ports do not fare as poorly at high levels as would be expected. In fact, very gentle 然而，在极高的音量下（2.5 英寸（63.5 毫米）的端口在 30 Hz 时超过 100 dB），太强的喇叭口显然比柔和的喇叭口造成更大的失真。出乎意料的是，标准直端口在高电平下的表现并没有想象中那么差。事实上，非常柔和的
Fig. 39. Spectra of worst port ( ) and one of the best ports ( - ) at SPL fundamental of 33 Hz , showing that a THD measurement captures the differences. Noise is well below harmonics; therefore the level of harmonics represents a good measure of the performance. 图 39.最差端口 ( ) 和最佳端口之一 ( - ) 在 声压级基本为 33 Hz 时的频谱，显示 THD 测量可捕捉到差异。噪声远低于谐波，因此谐波水平是衡量性能的良好指标。
Fig. 40. Even harmonics of some representative ports versus fundamental at increasing SPL. 图 40.在声压级增大时，一些代表性端口的偶次谐波与基波的对比。
flares are worse than no flare at all. 耀斑比没有耀斑更糟糕。
There appears to be an optimum. A moderate amount of flare for best overall distortion performance is required. This profile is a compromise for best performance over the entire amplitude range. Once again, the optimum normalized flare rate is near 0.5 . 似乎有一个最佳值。为了获得最佳的整体失真性能，需要适度的耀斑。该曲线是在整个振幅范围内实现最佳性能的折衷方案。最佳归一化耀斑率再次接近 0.5。
3.6 Velocity Measurements and Jet Formation 3.6 速度测量和喷流形成
As discussed in earlier sections, the air velocity in the ports is intimately related to performance. 如前几节所述，端口中的气流速度与性能密切相关。 In order to explore the velocity magnitude and distribution across the face of flared ports and to gain a better insight into jet for- mation, a hot-wire anemometer (TSI model 8360) was used to measure the air velocity across the six ports studied in Section 3.5. Measurements were mainly performed at the mouth in the baffle plane. 为了探究扩口表面的速度大小和分布情况，并更好地了解喷流状态，我们使用了热丝风速计（TSI 8360 型）来测量第 3.5 节中研究的六个扩口的气流速度。测量主要在挡板平面的口部进行。 The velocity profile across each port mouth was measured for increasing input power into a test enclosure, which was a 24-in (243-mm) cube made of 1-in (25-mm) MDF with four 18-in (457-mm)high power woofers. One side was fitted with a cutout to accept interchangeable baffles. 测试箱是一个 24 英寸（243 毫米）的立方体，由 1 英寸（25 毫米）的中密度纤维板制成，配有四个 18 英寸（457 毫米）的大功率低音扬声器。箱体的一侧有一个开口，用于安装可互换的障板。 Based on the 2 -3-in ( ) minimum port throat diameter selected, four woofers undoubtedly would be sufficient to create the required volume displacement needed to fully characterize 根据所选的 2 -3 英寸（ ）最小端口喉管直径，四个低音扬声器无疑足以产生所需的体积位移，从而充分表征以下特性
Fig. 41. Odd harmonics of some representative ports versus fundamental at increasing SPL. 图 41.在声压级不断升高的情况下，一些代表性端口的奇次谐波与基波的对比。
Fig. 42. THD for some representative ports versus fundamental at increasing SPL. 图 42.一些代表性端口在声压级增加时的总谐波失真（THD）与基波的关系。
each port for air velocity measurements. The transducers were driven using a large power amplifier in bridged mode, which can provide 2 kW of output into . Measurements were made near port tuning, where the velocity would be greatest. As can be seen in Fig. 每个端口用于气速测量。传感器使用桥接模式的大型功率放大器驱动，该放大器可为 提供 2 千瓦的输出功率。测量在端口调谐附近进行，那里的速度最大。如图所示 43, the measurements tend to confirm previous work, indicating that at low to medium levels the air velocity is greatest near the port walls, and a ring of high velocity is forming lower velocity on the port axis. 43. 测量结果趋向于证实以前的工作，表明在中低水平时，端口壁附近的气流速度最大，而端口轴线上的高速环正在形成较低的气流速度。 At high levels, when jets form, however, this behavior is not present, and the velocity magnitude is greatest at the port center. It is interesting to note in Fig. 然而，在高水位时，当喷流形成时，这种行为就不存在了，端口中心的速度幅度最大。值得注意的是，图 44 that the straight port and the most gently flared ports have the highest velocities across an area that maps to the center hole diameter; it then rapidly drops off, suggesting a clear jet has formed. 44 直端口和最平缓外扩的端口在映射到中心孔直径的区域内速度最高，然后迅速下降，表明已形成清晰的射流。 They seem to exhibit very similar maximum velocities, and this transition occurs at about , as predicted by Young. On the other hand the most radiused ports have a much more evenly distributed velocity profile, with a lower maximum velocity possible, suggesting more compression as the total area under the curve appears similar. 它们似乎表现出非常相似的最大速度，这种转变发生在大约 处，正如杨所预测的那样。另一方面，辐射最大的端口的速度分布更均匀，最大速度可能更低，这表明压缩程度更高，因为曲线下的总面积看起来相似。 The one port profile that stands out as having the best of both worlds is the port with the radius ( ). The "area under the curve" approaches a maximum, suggesting the least amount of total compression and the greatest output. This study also points to a balance of conditions for inlet and outlet airflow preferences in geometry. 其中，具有 半径（ ）的端口曲线最为突出。曲线下面积 "接近最大值，表明总压缩量最小，输出功率最大。这项研究还指出了进气口和出气口气流几何偏好的平衡条件。
3.7 Roughness Experiment 3.7 粗糙度实验
One might think that smoother surface textures in ports would directly result in higher performance. However, since Coulomb's experiments in the 1800s it has been known that the surface roughness has an effect on friction resistance. 人们可能会认为，端口表面纹理更光滑会直接带来更高的性能。然而，自 19 世纪库仑的实验以来，人们已经知道表面粗糙度对摩擦阻力有影响。 Interestingly, the effect is negligible in laminar flow, but not if the flow is turbulent, that is, surface roughness effects would be evident only at the higher port velocities. 有趣的是，在层流情况下，表面粗糙度的影响可以忽略不计，但如果是湍流则不然，也就是说，表面粗糙度的影响只有在端口速度较高时才会明显。 If reduced drag is desired, a rough surface will actually perform better due to boundary-layer effects. This 如果希望减少阻力，由于边界层效应，粗糙表面的性能实际上会更好。这
Fig. 44. Velocity profiles at 20 Hz at very high levels for all ports in study. 图 44.研究中所有港口在 20 赫兹极高频率下的速度曲线。
Fig. 43. Port velocity profiles at 20 Hz . (a) NFR . Note higher velocity at port edges for measurement. (b) NFR measurement shows rise in velocity at edges. (c) . Ports with NFR or higher do not show higher velocity at port edges. (d) 图 43.20 Hz 时的端口速度曲线 (a) NFR 。注意 测量结果中端口边缘的速度较高。(b) NFR 测量显示端口边缘速度上升。(c) 。NFR 或更高的端口在端口边缘没有显示更高的速度。(d)
is the reason why golf balls have dimples - the surface roughness is intended to "trip" the boundary layer so that it will go turbulent at a lower Reynolds number (in flight the Re of gold balls is about 100000 ). 这就是高尔夫球有凹痕的原因--表面粗糙度的目的是 "绊住 "边界层，使其在较低的雷诺数（飞行中金球的雷诺数约为 100000）下发生湍流。 The turbulence causes the separation point to move from the front to the back of the golf ball, thereby reducing drag and allowing a farther flight. There are now even commercially available subwoofer loudspeakers that use a flared port with dimples, similar to a golf ball. Fig. 湍流会使分离点从高尔夫球的前部移到后部，从而减少阻力，使飞行距离更远。现在甚至有商业化的低音炮扬声器，使用与高尔夫球类似的带有凹陷的喇叭口。图 45 shows a bowling ball entering the water at , demonstrating how much larger the wake is on the smooth ball [Fig. 45(a)] versus that of the surface-roughened ball [Fig. 45(b)]. Notice also that the separation point has moved farther back. 45 显示了一个保龄球在 处入水的情况，可以看出光滑球 [图 45(a)]的尾流与表面粗糙球 [图 45(b)]的尾流相比要大得多。还请注意，分离点向后移动了很远。
Another example of intentionally induced turbulence is often seen on the top surface of airplane wings near the leading edge. These "vortex generators" are used to prevent boundary-layer separation, which could cause the wing to stall under high lift conditions such as during 另一个有意诱导湍流的例子是在飞机机翼靠近前缘的顶面上经常看到的。这些 "涡流发生器 "用于防止边界层分离，因为边界层分离会导致机翼在高升力条件下失速，例如在下列情况下
(a)
(b)
Fig. 45. Strong differences in laminar and turbulent boundarylayer separation of ) bowling ball entering water at . (a) Smooth ball, laminar boundary layer. (b) Same entry; turbulent flow induced by patch of roughness on leading surface. (From [18].) landing. 图 45. ）保龄球在 处进入水中的层流和湍流边界层分离的强烈差异。(a) 光滑的球，层流边界层。(b) 相同的入水位置；前表面的粗糙斑块诱发湍流。(摘自 [18]）着陆。
In fluid mechanics, surface roughness is characterized by the dimensionless roughness ratio: 在流体力学中，表面粗糙度的特征是无量纲粗糙度比：
Small changes in the roughness ratio can lead to very large effects in the turbulent flow region. To test the hypothesis, we constructed five copies of the best performing port (NFR ) and then affixed precision glass beads of various sizes, ranging from 1 to 2.5 mm , to the inside port walls using a spray adhesive. This corresponds to a roughness ratio range of approximately . These ports were manufactured such that the volume occupied by the beads was accounted for. The ports were then subjected to the same distortion and compression tests described earlier. 粗糙度比的微小变化会对湍流区域产生非常大的影响。为了验证这一假设，我们复制了五个性能最好的端口（NFR ），然后使用喷涂粘合剂在端口内壁粘贴不同尺寸的精密玻璃珠，尺寸从 1 毫米到 2.5 毫米不等。这相当于大约 的粗糙度比范围。在制造这些端口时，要考虑到珠子所占的体积。然后，对这些端口进行与前面所述相同的变形和压缩测试。 Contrary to expectation, over the range of roughness examined, rough ports were generally inferior to the smooth-walled port. Rough ports had more harmonic distortion above 95 dB at 1 m . 与预期相反，在所检查的粗糙度范围内，粗糙端口通常不如光滑壁端口。粗糙端口在 1 米处 95 分贝以上的谐波失真更大。 Only in a very narrow range, between 90 and 95 dB , did the wall roughness produce a marginal improvement in odd harmonic distortion. At all other levels the smooth-walled port performed better (Fig. 46). 只有在很窄的范围内，即 90 到 95 dB 之间，壁面粗糙度才会对奇次谐波失真产生微弱的改善。在所有其他级别中，光滑壁端口的表现更好（图 46）。
Based on the fluid mechanics literature [18], we expected to see a benefit in rough walls in the acoustic compression measurement. Unfortunately, roughened port walls failed to show any advantages here as well. In fact, Fig. 根据流体力学文献[18]，我们期望在声学压缩测量中看到粗糙壁的优势。遗憾的是，粗糙的端口壁在这里也没有显示出任何优势。事实上，图 47 shows that all rough ports were consistently compressing about more than the smooth port. 47 显示，所有粗糙端口的压缩率始终高于光滑端口。 These negative results may be explained by noting that even at the highest Reynolds numbers near 100000 , the Moody chart predicts that we are only just entering the transition region and have not reached the fully turbulent region where roughness would be expected to make a large impact. 即使在最高雷诺数接近 100000 时，Moody 图表也预测我们只是刚刚进入过渡区域，还没有到达粗糙度会产生巨大影响的完全湍流区域，这就可以解释这些负面结果。 Based on these results, it does not appear that dimpling the walls guarantees any extra performance. 根据这些结果，凹陷的墙壁似乎并不能保证任何额外的性能。
Fig. 46. THD of ports in roughness study. Textured ports performed poorly over most of the testing amplitude range. Differences are mainly due to odd-order distortion (not shown). 图 46.粗糙度研究中端口的总谐波失真。在大部分测试振幅范围内，纹理端口的表现较差。差异主要是由于奇阶失真造成的（未显示）。
3.8 Polynomial Flare Profile 3.8 多项式扩口轮廓
Taking a slightly different approach to defining the flare rate, we chose to use a polynomial expression to define the port profile instead of a simple radius. The idea was to see whether an optimum solution might exist by approaching the problem from a different angle. 在定义耀斑率时，我们采用了一种稍有不同的方法，即使用多项式表达式来定义端口轮廓，而不是简单的半径。这样做的目的是想看看从不同的角度来处理问题是否能找到最佳解决方案。 It was further desired 还希望
Fig. 47. Port compression of ports in roughness study. All textured ports performed worse than smooth port. that all ports tune to the same frequency so that this would be a tightly controlled, legitimate comparison. 图 47.粗糙度研究中的端口压缩情况。所有纹理端口的表现都比光滑端口差。 This tuning requirement dictated that the ports have different minimum throat diameters in order to achieve identical values. Recall that all ports from the previous studies had identical minima and therefore tuned differently. A series of seven ports was designed with ratios of maximum to minimum diameter ranging from 1:1 to 2:1. All ports had the same physical length, and a radius was added to both ends of each port. For reference a straight port (port s) and an elliptical port (port el), similar to the one cited by Gawronski and Caron [9], were also included in the experiment. Fig. 为了达到相同的 值，这种调整要求决定了端口具有不同的最小喉管直径。回想一下，之前研究中的所有端口都具有相同的最小直径，因此调谐方式也不同。我们设计了一系列七个端口，其最大直径与最小直径的比例从 1:1 到 2:1。所有端口的物理长度相同，每个端口的两端都增加了 半径。作为参考，实验中还包括一个直端口（端口 s）和一个椭圆端口（端口 el），与 Gawronski 和 Caron [9] 引用的端口相似。图 48 depicts the profile of the ports, and Table 1 completes the description of the ports. 48 描述了各港口的概况，表 1 则完成了对港口的描述。
The ports were mounted in the bandpass enclosure described in Section 3.5. The experimental setup follows that of Section 3.5, except that all ports were driven by a sine wave with drive levels ranging from 1.12 to 50.79 V rms. 这些端口安装在第 3.5 节所述的带通外壳中。实验设置与第 3.5 节相同，但所有端口均由 正弦波驱动，驱动电平范围为 1.12 至 50.79 V rms。
Fig. 49 is a plot of THD versus SPL for ports, s, sr, a, b, and c, and Fig. 50 shows the same data for ports el, c, d, e, and f. At low sound pressure levels any flare works significantly better than a traditional straight port, and the more flare, the better. 图 49 是端口 s、sr、a、b 和 c 的总谐波失真与声压级的关系图，图 50 显示了端口 el、c、d、e 和 f 的相同数据。 At medium SPL there is a clear trend that is revealed in the data for the ports examined in 在中等声压级情况下，以下所研究的端口的数据显示出一种明显的趋势
Fig. 48. Port profiles for polynomial study. 图 48.多项式研究的端口剖面图。
Table 1. Port characteristics. 表 1.端口特征。
Port 港口
物理 .
长度 .
.
Physical
Length
Minimum .
直径 .
.
Minimum
Diameter
最大值 .
直径 .
.
Maximum
Diameter
Max/Min .
直径 .
Max/Min
Diameter
Max/Min .
Area .
Max/Min
Area
Tuning in .
59-L 测试箱 .
.
Tuning in
59-L Test Box
s
120
68.7
68.7
1.00
1.00
33.0
sr
120
66.1
66.1
1.00
1.00
32.9
a
120
64.4
72.3
1.12
1.26
33.0
b
120
62.9
79.2
1.26
1.59
33.1
c
120
61.8
87.4
1.41
2.00
33.2
d
120
60.9
96.7
1.59
2.52
33.4
e
120
60.1
107.0
1.78
3.17
33.5
f
120
59.5
119.0
2.00
4.00
33.6
el
120
58.0
120.0
2.07
4.28
33.4
Fig. 49. Here performance is strongly related to the flare rate; the ports with more flare have lower distortion. For the ports with significant flare (Fig. 50) the differences are more subtle. 图 49.在这里，性能与耀斑率密切相关；耀斑较多的端口失真较低。对于有明显耀斑的端口（图 50），差异则更为微妙。 At high SPL the performance gap becomes even tighter with no clear winners, only losers, that is, here the straight port actually outperforms ports sr and a. At high levels, however, ports c and d with a best fit NFR near 0.5 appear to have an edge. 在高声压级下，性能差距变得更小，没有明显的赢家，只有输家，也就是说，直端口实际上优于 sr 和 a 端口。
These data lead us to the same conclusions found in Section 3.5, namely, that a generous flare, to a point, enhances port performance. There is some indication that too much flare is not necessarily a good thing. 这些数据使我们得出了与第 3.5 节相同的结论，即在一定程度上，大 幅度的扩口可以提高港口性能。有迹象表明，过多的扩口并不一定是好事。 At medium SPL ports c and d perform nearly as well as the ports with more generous flares, and they appear to have an edge at higher levels. These differences, however, are extremely subtle when one compares the performance to ports sr, s, and a. 在中等声压级下，端口 c 和端口 d 的表现几乎与喇叭口更宽的端口一样好，而且在更高的声压级下，它们似乎更胜一筹。但是，与 sr、s 和 a 端口的性能相比，这些差异非常微妙。 Like the experiment with simple radii, the flare rates that are in the middle range are the best, and an optimum solution was achievable. The ellipse also performed quite well, suggesting that a different approach could be used to find a near optimum solution. 与简单半径的实验一样，处于中间范围的耀斑率是最好的，可以达到最优解。椭圆的表现也相当不错，这表明可以采用不同的方法找到接近最佳的解决方案。 The suggestion here is that there are probably an infinite number of profiles (all moderate in nature) that will perform well. 这里的意思是，可能有无数种配置文件（性质都比较温和）都会有很好的表现。
3.9 Port Asymmetry 3.9 端口不对称
In the previous experiment we noted that at high SPL ports c and d had the lowest odd harmonic distortion. In contrast, at high SPL ports c and d had a more even harmonic distortion than the others. 在之前的实验中，我们注意到在高声压级下，端口 c 和端口 d 的奇次谐波失真最小。相反，在高声压级下，端口 c 和端口 d 的谐波失真比其他端口更均匀。
From our experience with transducers and amplifiers we tend to associate even harmonic distortion with asymmetry and odd harmonic distortion with symmetrical 根据我们对传感器和放大器的经验，我们倾向于将偶次谐波失真与不对称联系起来，而将奇次谐波失真与对称联系起来。
Fig. 49. THD versus fundamental for ports s (straight), sr (straight with radius), a, b, and c. 图 49.端口 s（直端口）、sr（带半径的直端口）、a、b 和 c 的总谐波失真与基波。
Fig. 50. THD versus fundamental for ports el (elliptical), c, d, e, and f. 图 50.端口 el（椭圆形）、c、d、e 和 f 的总谐波失真与基波。
"clipping." Could ports c and d have hidden asymmetry? All the ports were surface mounted in the enclosure. This means that one end of the port has a baffle and the other end does not. Thus all the ports were asymmetric. "削波"。端口 c 和 d 是否有隐藏的不对称？所有端口都是表面安装在箱体内的。这意味着端口的一端有挡板，而另一端没有。因此，所有端口都是不对称的。 This suggests a preferential airflow in one direction over another, analogous to a fluid flow diode effect, and it can be thought of as "port rectification." Interestingly, the ports with the most generous flares, ports f and el, still have low even harmonic distortion at high SPL. 这表明一个方向的气流优先于另一个方向，类似于流体流动二极管效应，可以认为是 "端口整流"。有趣的是，在高声压级下，喇叭口 f 和 el 的外扩幅度最大，但偶次谐波失真仍然很低。 It appears that the maximum diameter of these ports is enough to simulate a mounting baffle on the inside edge of the port. If this is true, then adding a simple flange to the inside of ports c and d should reduce even harmonic distortion. Fig. 这些端口的最大直径似乎足以模拟端口内缘的安装挡板。如果情况属实，那么在 c 端口和 d 端口内侧添加一个简单的挡板就可以减少谐波畸变。图 51 shows even harmonic distortion for ports c and d and for the same ports with a small 15-mm-wide flange added to the inside (cf and df). A dramatic improvement is clearly seen in the even-order harmonic distortion, approaching 12 dB at the highest levels. 51 显示了端口 c 和 d 的偶次谐波失真，以及在端口内侧添加了 15 毫米宽的小凸缘（cf 和 df）的相同端口的偶次谐波失真。偶次谐波失真明显改善，最高时接近 12 dB。 It is clear that when choosing a port flare of moderate rate an additional design feature that should be incorporated is a flange on the inside of the port. 显然，在选择中等流量的端口扩口时，还应该在端口内侧加装一个法兰。
3.10 Thermal Implication of Port Design and Placement 3.10 端口设计和布置的热影响
In matters of the acoustical performance of a port, turbulence is the enemy. However, in matters of heat exchange, turbulence is a friend. 就港口的声学性能而言，湍流是敌人。然而，在热交换方面，湍流却是朋友。 If the acoustic port mass acts as a slug of air during laminar flow, it could be argued that the same slug of air moves in and out of the box and that no effective exchange of air from inside to outside occurs. 如果在层流过程中声学端口质量就像一个空气弹头，那么可以说进出箱体的是同一个空气弹头，箱内和箱外的空气没有发生有效交换。 The inside of a loudspeaker enclosure heats up as the components radiate heat into the box. In fact, it is not unusual for the air temperature in high-power designs to reach inside the enclosure. Temperatures this high limit the life of all components significantly, and it would therefore be desirable to keep the box as close to room temperature as possible. 扬声器箱体内部会因元件向箱内辐射热量而发热。事实上，在大功率设计中，箱体内部的空气温度达到 的情况并不罕见。如此高的温度大大限制了所有组件的使用寿命，因此最好尽可能保持箱体接近室温。 The ports in a vented box provide an ideal path for replacing the hot air in the box with cool ambient air, but if we have designed the port such that there is no net exchange, then the box will heat up and heat dissipation must occur through the walls. 通风箱中的端口为箱内热空气与周围冷空气的置换提供了理想的途径，但如果我们设计的端口没有净交换，那么箱体就会发热，热量必须通过箱壁散失。 Turbulent air is extremely effective at dissipating heat as it rapidly mixes cool and warm air. 湍流空气能迅速混合冷空气和暖空气，因此散热效果极佳。
This line of thinking led the authors to speculate that smaller straight turbulent ports would have an advantage over well-designed larger tapered ports. To prove this hypothesis, an experiment was devised to test the heat dissipation of several port configurations. Fig. 作者根据这一思路推测，较小的直湍流口将比设计良好的较大锥形口更具优势。为了证明这一假设，作者设计了一个实验来测试几种端口配置的散热情况。图 52 shows the six configurations tested. Besides trying flared versus straight ports, we made the straight ports substantially smaller. We designed all ports to tune to about 25 Hz in a box with a single 18 -in driver. Experiments were run with one port and two ports. 52 显示了测试的六种配置。除了测试喇叭口与直喇叭口的对比，我们还将直喇叭口做得更小。我们将所有端口都设计成在一个带有单个 18 英寸 驱动器的 箱中调谐到约 25 Hz。我们用一个端口和两个端口进行了实验。 The condition with two ports placed one near the top and one near the bottom of the box, the idea being that with two ports in this configuration a convective "chimney effect" might provide additional cooling as cool air would come in at the bottom and warm air would exit the top. 在这种情况下，有两个端口，一个靠近箱体顶部，另一个靠近箱体底部。我们的想法是，在这种配置下，两个端口的对流 "烟囱效应 "可以提供额外的冷却效果，因为冷空气会从底部进入，而热空气会从顶部排出。 To take further advantage of this idea, a configuration was devised that had asymmetrical ports at the top and bottom, with the bottom port oriented to cause preferential airflow in the inward direction and the upper port oriented to provide preferential flow in the outward direction. 为了进一步利用这一想法，我们设计了一种在顶部和底部具有非对称端口的结构，底部端口的方向是使气流优先向内流动，而上部端口的方向是使气流优先向外流动。
The measurement setup is also pictured in Fig. 52. A pink-noise signal of was presented to the woofer. A broad-band signal was used so that a large amount of heat would be generated, but the port velocity in the case of the tapered ports would be low enough that they remain laminar, as only a small portion of the signal has energy near port tuning. 测量设置也如图 52 所示。向低音扬声器提供 的粉红噪声信号。使用宽带信号是为了产生大量热量，但在锥形端口的情况下，端口速度将足够低，使其保持层流状态，因为只有一小部分信号在端口调谐附近具有能量。 The size of the smaller ports was chosen to ensure that they were in fact turbulent. The diameter of the tapered port was about 3.5 in ( 89 mm ) and the smaller ports were about 1.75 in ( 44 mm ). The tapered ports were also much longer (to ensure the same tuning). 选择较小端口的大小是为了确保它们实际上是湍流。锥形端口的直径约为 3.5 英寸（89 毫米），较小的端口约为 1.75 英寸（44 毫米）。锥形端口也更长（以确保相同的调整）。 The amount of power to the system was monitored with a special device that also tracks voice-coil temperatures. A 系统的功率大小由一个特殊装置进行监控，该装置还能跟踪音圈温度。A
Fig. 51. Even harmonic distortion versus fundamental for ports cf (c with inside flange), df (d with inside flange), c , and d . 图 51.端口 cf（带内法兰的 c）、df（带内法兰的 d）、c 和 d 的偶次谐波畸变与基波的关系。
level of 250 W (true electrical power based on voltage and current, not dc resistance) was placed on the driver, and the voice-coil temperature and the in-box air temperature were monitored versus time. 在驱动器上放置 250 W 的电平（基于电压和电流的真实电功率，而不是直流电阻），并监测音圈温度和箱内空气温度随时间的变化。
Fig. 53 shows the results of all six trials. One trial was done with the box completely sealed. The air temperature results clearly show that all ported conditions cool the box significantly over the sealed box. 图 53 显示了所有六次试验的结果。其中一次试验是在箱体完全密封的情况下进行的。空气温度结果清楚地表明，所有端口条件下的箱体冷却效果都明显优于密封箱体。 The rise in the voice-coil temperature tracks the rise in the box temperature, except in the sealed box condition (which appeared not to have reached equilibrium and was still heating up after 3 hours). This would be expected. 音圈温度的升高与箱体温度的升高同步，但密封箱体除外（密封箱体似乎尚未达到平衡，3 小时后仍在升温）。这在意料之中。 Interestingly the conditions that cooled the box the most were the two iterations with the small turbulent ports. The trial with two small ports outperformed all other configurations tested. 有趣的是，在两个迭代试验中，使用小湍流口的箱体冷却效果最好。带有两个小端口的试验结果优于其他所有测试配置。 Clearly, the turbulent flow and the arrangement of the ports at the top and bottom both contributed to an excellent heat exchange in the box. Is this tradeoff of lower temperature versus reduced port output worthwhile? Most likely not. 显然，湍流以及顶部和底部端口的布置都有助于在箱体内进行良好的热交换。降低温度与减少端口输出之间的权衡是否值得？很可能不值得。 The gains in maximum output of the system obtained by using well-designed ports should outweigh any thermal compression benefits gained through lowered box temperatures. 通过使用精心设计的端口所获得的系统最大输出功率收益，应超过通过降低箱体温度所获得的热压效益。
While the tapered ports performed poorly, it is a little surprising that the two asymmetrical tapered ports did not improve things as much as expected. 虽然锥形端口的性能很差，但两个不对称锥形端口的性能改善程度却不如预期，这有点令人惊讶。 Clearly the amount of dc flow due to the asymmetry was not substantial enough to create a significant heat exchange through the box. Turbulence exchanges heat far more effectively from the inside to the outside of the box than even large laminar ports. 显然，由于不对称而产生的直流流量不足以在箱体中产生显著的热交换。湍流能更有效地将热量从箱体内部交换到箱体外部，甚至比大型层流孔还要有效。 There may be a happy medium in running two asymmetrical ports slightly into turbulence, which would find a balance of compression, distortion, and heat dissipation. 两个不对称的端口在运行时可能会略微产生湍流，这样就能在压缩、失真和散热之间找到一个平衡点。
Fig. 52. Setup for thermal experiments. 图 52.热实验装置。
4 GENERAL CONCLUSIONS 4 一般性结论
Based on the studies discussed, the following design rules should be applied to the design of loudspeaker ports: 根据所讨论的研究，扬声器端口的设计应遵循以下设计规则：
Vast historical data and the results presented in this paper suggest that the largest port area allowable by a given design should be employed to keep the air velocity down if low port compression and low distortion are desired. 大量的历史数据和本文介绍的结果表明，如果希望获得较低的气口压缩率和较低的失真度，则应采用特定设计所允许的最大气口面积，以保持较低的气流速度。
When designing a port for maximum acoustical output, both the inlet and the exit fluid dynamics should be balanced. The geometry for best exit flow is different from that for inlet flow. 在设计端口以获得最大声学输出时，入口和出口的流体动力学应保持平衡。最佳出口流体的几何形状与入口流体的几何形状不同。 Inlet flow is best with a very large taper (NFR close to 1.0). For exit flow a very slow taper is best (NFR closer to 0). This points to an NFR of 0.5 as the optimum. 入口流量最好采用非常大的锥度（NFR 接近 1.0）。对于出口流量来说，锥度越小越好（NFR 接近 0）。由此可见，最佳的 NFR 值为 0.5。
Inlet head loss should be minimized. Use port profiles that do not have any sharp discontinuities. This requires all port edges to have a blend radius of at least of the minimum diameter. 应尽量减少进口水头损失。使用没有任何尖锐不连续性的端口轮廓。这就要求所有端口边缘的混合半径至少为最小直径的 。
For flared ports, choose an NFR to match the design application and intent. 对于扩口，应选择与设计应用和意图相匹配的 NFR。 For lowest harmonic distortion at low levels, use NFRs near 1.0. At moderate levels, NFRs near 0.5 work best. At high levels, NFRs near 0 are desirable (though the blend radius in rule 3 should still be used). For the best compromise at all levels, NFR 在低电平时，若谐波失真最低，则使用接近 1.0 的 NFR。在中等电平时，NFR 接近 0.5 效果最佳。在高电平时，NFR 最好接近 0（尽管仍应使用规则 3 中的混合半径）。为了在所有音量下达到最佳的折衷效果，NFR
(a)
(b)
Fig. 53. Thermal repercussions for various port configurations versus time. (a) Box air temperature. (b) Voice-coil temperature. 图 53.不同端口配置的热影响与时间的关系。(a) 箱内空气温度。(b) 音圈温度。
appears to be optimum. 似乎是最佳的。
For best distortion performance at higher levels, make sure both sides of the port are symmetrical. Adding a small flange to the inside of a flush-mounted port makes a dramatic improvement in distortion. 为了在较高音量下获得最佳失真性能，请确保端口两侧对称。在齐平安装的端口内侧添加一个小凸缘可显著改善失真。
Roughening the port walls generally does not appear to be beneficial in the normal operating range of acoustic ports. 在声学端口的正常工作范围内，对端口壁进行粗化处理一般不会带来好处。
In designing a flared port, the closer the radius used for the flare is to a simple radius, the simpler and more accurate the end correction can be, and the port tuning will be easy to calculate. 在设计扩口时，用于扩口的半径越接近简单半径，端部修正就越简单和准确，端口调整也就越容易计算。
Maximally radiused ports have the best low-level performance, but they have poor high-level performance due to excessive turbulence within the port, near the ends. This will lead to compression and tuning shift due to the shortening of the apparent length of the port. 最大辐射端口具有最佳的低电平性能，但由于端口内靠近两端的湍流过多，其高电平性能较差。由于端口的视长度缩短，这会导致压缩和调谐偏移。
Large ports with a taper designed to minimize turbulence will act poorly to exchange the air (and heat) in the box. Ports that are in fact overdriven under maximum use and located at the top and bottom of the box would be preferred thermally. 为尽量减少湍流而设计的锥形大端口对箱内空气（和热量）的交换效果很差。在最大使用情况下，位于箱体顶部和底部的端口实际上会被过度驱动，这在热学上是更可取的。
There are many approaches to finding a port profile that will provide excellent performance. It is mainly the macroscopic shape and not the specific profile that influences performance. 有许多方法可以找到提供卓越性能的端口轮廓。影响性能的主要是宏观形状，而不是具体的轮廓。
5 ACKNOWLEDGMENT 5 致谢
The authors wish to thank Harman International, Mark Gander, and John Vanderkooy. 作者感谢哈曼国际公司、Mark Gander 和 John Vanderkooy。
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7 BIBLIOGRAPHY 7 参考文献
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THE AUTHORS 作者
A. Salvatti A.萨尔瓦多
A. Devantier A.德万蒂埃
D. Button D.按钮
Alex Salvatti was born in 1973 and was raised in Southern California where he received an extensive musical education. He earned a B.S. degree in engineering physics with an acoustics specialization from the University of California at San Diego in 1996. 亚历克斯-萨尔瓦蒂出生于 1973 年，在南加州长大，并在那里接受了广泛的音乐教育。1996 年，他获得加州大学圣地亚哥分校工程物理学学士学位，主修声学。 After internships at IBM Storage Systems Division and TC Sounds, Inc, he joined JBL Professional as a transducer engineer where he has had design responsibilities for transducers including the LSR series of studio monitors and MPro line of sound reinforcement products. 在 IBM 存储系统部门和 TC Sounds 公司实习后，他加入了 JBL Professional，担任传感器工程师，负责设计包括 LSR 系列录音室监听器和 MPro 系列扩声产品在内的传感器。 Mr. Salvatti is currently a senior research and development engineer with a professional focus on high-performance LF and HF transducer design. He has three patents in transducer design pending and is a member of the AES. Salvatti 先生目前是一名高级研发工程师，专业领域是高性能低频和高频换能器设计。他在换能器设计方面有三项专利正在申请中，并且是 AES 的成员。
Allan Devantier was born 1964 June 6 in Newmarket, Ontario, Canada. He received a bachelor's degree in electrical engineering technology with honors in 1987 from Ryerson Polytechnical University in Toronto. Allan Devantier 于 1964 年 6 月 6 日出生于加拿大安大略省纽马克特市。1987 年，他以优异成绩获得多伦多瑞尔森理工大学电气工程技术学士学位。 He has been chief engineer for Infinity Systems, a division of Harman International located in Northbridge, California, since 1998 May. Prior to that, he spent three years as the director of systems engineering and three years as a systems engineer for JBL Consumer. 自 1998 年 5 月以来，他一直担任位于加利福尼亚州北桥市的哈曼国际公司 Infinity Systems 分部的总工程师。在此之前，他曾在 JBL Consumer 担任过三年的系统工程总监和三年的系统工程师。 He was systems engineer on Infinity's Prelude MTS loudspeaker system and is the inventor of Infinity's Room Adaptive Bass Optimization System and coinventor of the Ceramic Metal Matrix Diagram cone material (patent pending). 他是 Infinity Prelude MTS 扬声器系统的系统工程师，也是 Infinity 室内自适应低音优化系统的发明者和陶瓷金属矩阵图音盆材料的共同发明者（专利申请中）。 Before joining Harman, he worked as a loudspeaker systems engineer for Plateau Camber and Belbois Ltee., both located in 在加入哈曼之前，他曾在 Plateau Camber 和 Belbois Ltee 担任扬声器系统工程师。
Montreal, Quebec. More recently, Mr. Devantier cochaired the loudspeaker student design competition that was held at the 140th meeting of the Acoustical Society of America. 魁北克省蒙特利尔市。最近，Devantier 先生还担任了美国声学学会第 140 届会议扬声器学生设计竞赛的共同主席。 He is keenly interested in improving the correlation between the objective and subjective loudspeaker performance. He is married and has three children. 他对提高扬声器的客观和主观性能之间的相关性非常感兴趣。他已婚，有三个孩子。
Douglas Button was born in 1959 in Fort Knox, Kentucky. He was educated at Iowa State University where he received a B.S.E.E. in 1982. He is currently vice president of research and development for JBL Professional in Northridge, California. He has been with JBL since 1988. 道格拉斯-巴顿 1959 年出生于肯塔基州诺克斯堡。他曾就读于爱荷华州立大学，并于 1982 年获得电子工程学士学位。他现任加利福尼亚州北岭市 JBL Professional 研发副总裁。他自 1988 年以来一直在 JBL 工作。 Before that he worked for Harris Broadcast products from 1983 to 1985 and Electro-Voice from 1985 to 1987. He holds six patents with five pending. The focus of his work has been maximizing performance through innovative designs. 在此之前，他于 1983 年至 1985 年在 Harris 广播产品公司工作，1985 年至 1987 年在 Electro-Voice 公司工作。他拥有六项专利，其中五项正在申请中。他的工作重点是通过创新设计最大限度地提高性能。 JBL products of his invention include the high-power Vented Gap Cooling transducers, Neodymium Dual Coil Drivers and the EON Thermal Management System along with recent ultralight compression driver designs utilizing beryllium diaphragms. 他发明的 JBL 产品包括大功率通风间隙冷却换能器、钕双线圈驱动器和 EON 热管理系统，以及最近采用铍振膜的超轻压缩驱动器设计。
Mr. Button has participated in several AES workshops on loudspeaker design and has delivered six papers on transducer design to AES conventions of which three have been published in the Journal. Button 先生曾多次参加 AES 的扬声器设计研讨会，并在 AES 大会上发表了六篇关于换能器设计的论文，其中三篇已在杂志上发表。 He has been a regular contributor to the AES Technical Committee on Transducers and previously served as a member of the executive committee of the AES Los Angeles Section. In 1997 Mr. Button was made a fellow of the AES. 他经常为美国电子工程师协会传感器技术委员会做出贡献，并曾担任美国电子工程师协会洛杉矶分会执行委员会成员。1997 年，巴顿先生被授予 AES 研究员称号。
Presented at the 105th Convention of the Audio Engineering Society, San Francisco, CA, 1998 September 26-29; revised 2001 October 16. 于 1998 年 9 月 26-29 日在加利福尼亚州旧金山举行的第 105 届音频工程学会大会上发表；2001 年 10 月 16 日修订。
