Increase Of Gap Distance Research Articles

Scaled experiment and observation of the lightning discharge process of rotating wind turbines under different shapes of high-voltage electrodes in the laboratory

In this study, a discharge test for scaled wind turbine is performed to examine the lightning discharge characteristics of rotating wind turbines, and an observation platform is designed. Moreover, the wind turbines are subjected to discharge simulation with rod and arc electrodes, and high-speed and single-lens reflex cameras are used to observe the physical discharge process. Under the rod electrode, the downward leader is initiated first, and its length occupies a larger proportion of the discharge gap. The discharge contains multiple stepped leaders. When the gap distance is less than 4 m, the probability of occurrence of negative stepped leaders may be smaller. As the gap distance increases, the number of stepped leaders increases significantly. Under the arc electrode, the upward leader is initiated first, and its length accounts for a larger proportion of the discharge gap. With the rotation of the wind turbine, the upward leader is initiated earlier and the length is longer. Furthermore, the speed of its development does not differ significantly. The discharge simulation process under the arc electrode is similar to natural lightning strikes on wind turbines.

Impact of Electrode Distance in a Quasi-Uniform Model Electrode System on Lightning Impulse Breakdown Voltage in Various Insulating Liquids

This study presents findings on the influence of gap length distance on the lightning impulse breakdown voltage of three dielectric liquids of different chemical origins. The liquids were tested in a model electrode system with a quasi-uniform electric field distribution and a pressboard plate placed on the grounded electrode. The experimental studies were supported using calculations and simulations to show the individual relationships between the lightning impulse breakdown voltage and gap distance, which represent the so-called volume effect of the most stressed liquid. The results of the experiment, which involved four considered gap distances of 2, 4, 6, and 8 mm, show that a dynamic increase in lightning impulse breakdown voltage with an increase in gap distance is associated with mineral oil and bio-based hydrocarbons. However, similar trends were not observed for synthetic ester. Calculations that allowed us to assess the impact of gap length distance on lightning impulse breakdown voltage support the observations from the experimental studies. The curves obtained in this field can be considered in the process of designing insulating systems for transformers.

Dynamic gap crossing in Dendrelaphis, the sister taxon of flying snakes.

Arboreal animals commonly use dynamic gap-crossing behaviors such as jumping. In snakes, however, most species studied to date only employ the quasi-static cantilever crawl, which involves a whole-body reach. One exception is the paradise tree snake (Chrysopelea paradisi), which exhibits kinematic changes as gap distance increases, culminating in dynamic behaviors that are kinematically indistinguishable from those used to launch glides. Because Chrysopelea uses dynamic behaviors when bridging gaps without gliding, we hypothesized that such dynamic behaviors evolved ancestrally to Chrysopelea. To test this predicted occurrence of dynamic behaviors in closely related taxa, we studied gap bridging locomotion in the genus Dendrelaphis, which is the sister lineage of Chysopelea. We recorded 20 snakes from two species (D. punctulatus and D. calligastra) crossing gaps of increasing size, and analyzed their 3D kinematics. We found that, like C. paradisi, both species of Dendrelaphis modulate their use of dynamic behaviors in response to gap distance, but Dendrelaphis exhibit greater inter-individual variation. Although all three species displayed the use of looped movements, the highly stereotyped J-loop movement of Chrysopelea was not observed in Dendrelaphis. These results support the hypothesis that Chrysopelea may have co-opted and refined an ancestral behavior for crossing gaps for the novel function of launching a glide. Overall, these data demonstrate the importance of gap distance in governing behavior and kinematics during arboreal gap crossing.

Study on long front time wave switching impulse of rod-plane air gap

In long-distance transmission lines, the switching overvoltage waveform differs from that of ordinary lines. The wave front time is primarily distributed above 1000 μs. And the switching overvoltage waveform has an important influence on the design of external insulation. This paper aims to deeply study the effect of various factors on the discharge of air gaps under the long front switching impulse voltage. This paper selects three kinds of rod-plane air gaps, and the switching impulse discharge experiments with different front lengths and absolute humidity under positive polarity are carried out. The effects of front time Tf, absolute humidity h, and gap distance d on the discharge characteristics of the air gap are analyzed. The results show that the U50% of an air gap is positively correlated with absolute humidity, front time, and gap distance. When considering the additional influence of humidity, the humidity additional influence factor c and the atmospheric parameter influence index n at different front times are almost unchanged. With the increase in gap distance, the influence of front time on U50% is more obvious. With the growth of the operating wave front time, the rising rate of U50% tends to slow down. The discharge time of the air gap under different conditions is mainly determined by the front time. The research results can provide a theoretical and experimental reference for the influence of front time Tf and atmospheric parameters on the discharge characteristics of air gaps under long front switching impulse.

Dynamic response of a circular cylinder in the presence of a detached splitter plate: On the gap distance sensitivity

Flow-induced vibration of a circular cylinder fitted with a detached rear splitter plate in a laminar flow with Re = 120 is studied numerically. Effects of the gap distance (G/D= 0–2) and reduced velocity (Ur= 2–18) on the vibration response, flow pattern, and hydrodynamic coefficient are investigated in detail. As the gap distance increases, three vibration responses are identified: IB-resonance-galloping at G/D=0, VIV with a wide lock-in region but low frequencies at G/D=0.5 and 1, and typical VIV at G/D=1.5 and 2. The associated phase difference angles and the added mass coefficients for the VIV responses at G/D= 0.5–2 show a jump from 0° to 180° and a transition from positive to negative, respectively, while they always keep being zero and positive for the IB-resonance-galloping response at G/D=0. At G/D= 0–1, the shear layers from the cylinder surface cannot roll up to form complete vortices in the cylinder wake but reattach to the splitter plate’s surface or rear tip, leading to the overshoot (OS) and shear-layer reattachment (SR) flow pattern, and meanwhile the elongated vortex formation length and delayed vortex shedding. As a consequence, the optimal drag- and lift-reductions are achieved at G/D=1. In contrast, complete vortices can be found both behind the cylinder and plate for the cases of G/D= 1.5–2, resulting in the co-shedding (CS) flow pattern, including CS-I and CS-II pattern based on whether the vortices from the cylinder and plate are merged or not. The 2S vortex shedding modes are generally observed at present Reynolds number, while the 2P modes are identified in the galloping and lock-in region. The splitter plate positively contributes to the total lift forces when the cylinder-plate body gallops, while it presents a negative effect by counteracting the forces on the plate itself or on the circular cylinder in the VIV region.

Research on the trigger process of surface flashover triggered vacuum switch

The key to promoting the development of triggered vacuum switch is an in-depth research on the physical process of its trigger phase. This paper mainly divides the trigger process into metal electrode melt evaporation, neutral metal vapor layer expansion, electron collision ionization multiplication, and charged particle migration. An approximate analytical formulation of the trigger delay time theory is presented based on a one-dimensional heat conduction model and an electron collision ionization multiplication process. The trigger delay time experimental platform is built with a removable vacuum chamber. The influence factors involved in the mathematical description proposed are studied experimentally. Theoretical analysis and experimental results show that both trigger current rise rate and main electrode operating voltage have an approximate inverse relationship with trigger delay time. The main electrode gap distance is directly proportional to the trigger delay time, but the effect will be weaker as the main electrode gap distance increases. Overall, the consistency of the experimental results and theoretical analysis on influence trends well support the theoretical model.

Experimental investigations into the effusion plate wall temperature of impingement/effusion cooling systems for gas turbine combustors

Cooling technologies are playing critical roles in the development of advanced gas turbine combustors. The present experimental investigation has studied the effects of geometric factors such as gap distance, impingement hole diameter, and effusion hole arrangement on the wall temperature of a novel impingement-effusion cooling system. The wall temperature of the effusion plate was directly measured by high-precision thermocouples. The wall temperature distribution of the cooling unit was obtained by biharmonic spline interpolation based on the measured temperature data. The cooling performance of cooling systems with different structures under different working conditions was compared. The experimental results indicate that the increase of gap distance weakens the strength of impinging jet, and the overall cooling performance decreases, accordingly. The smaller the diameter of the impingement hole is, the weaker the cooling film is, leading to a poor overall cooling performance at the same cooling airflow. However, better overall cooling performance can be obtained at the same blowing ratio at the cost of much more cooling airflow. Dense and uniform effusion hole arrangement has a very favorable impact on improving the cooling film quality and cooling performance.

Impact of Coulomb scattering on argon plasma based thermionic converter performance

Particle-in-cell (PIC) simulations were performed to study the impact of Coulomb scattering on the performance of argon plasma based thermionic converters. Using a simplified model, studies from the 1970’s concluded that plasma resistance resulting from Coulomb collisions shifts the IV-curves of thermionic converters that use plasmas to mitigate space charge, thereby strongly limiting their electricity generation capability. In this work the impact of Coulomb collisions in such devices were studied as a function of the relative electrical potential between the electrodes, with higher fidelity than earlier models, using a fully kinetic approach (PIC-MCC with grid based electron–ion scattering). This approach overcomes the incorrect assumption in earlier models that the electron temperature is equal to the cathode temperature in all operating conditions. The fully self-consistent results presented here showed an increase in electron temperature with an increase in gap distance or electrode bias, which decreases the plasma resistivity. It was consequently found that earlier reports overestimated the negative impact of Coulomb collisions at the maximum power point, suggesting the practical usefulness of such devices is higher than previously believed. Electronic conversion efficiency higher than 15% was shown to be feasible at 1200 °C cathode temperature with reasonable electrode work-functions.

A nonequal gap distance dielectric barrier discharge: Between spiral‐shaped and cylinder‐shaped electrodes

AbstractIn this paper, a nonequal gap distance dielectric barrier discharge (DBD) between a spiral‐shaped electrode and a cylinder‐shaped electrode is reported. A spiral‐shaped plasma is generated when a nanosecond pulse voltage is applied to the two electrodes. The smaller the pitch of the spiral‐shaped electrode is, the more diffuse the plasma appears. The discharge current has a pulse width of more than 400 ns, which is much longer than that of ordinary DBDs in air. According to the high‐speed photographs of the plasma captured by an intensified charge‐coupled camera detector camera, the discharge first ignites at the position where the gap distance is smallest, then it propagates continuously along the spiral electrode with the increase of gap distance at a speed of about 106 m/s. Both the optical emission spectrum method and the electric field‐induced second harmonic method are employed for the measurement of the electric field at different locations. The obtained electric field from both methods have a good agreement and are in the range of 60–110 kV/cm depending on the gap distance of the locations, which is much higher than the breakdown voltage of air under direct current voltage. This structure can obtain diffuse plasma in a larger gap, which makes the application of DBD more extensive. And it also has a deeper understanding of DBD with nonequal gap distance.

Discharge characteristics of ground potential live-line work air gaps in cup towers and double circuit towers

Ground potential live-line work (GPLW) is an irreplaceable means for the maintenance and elimination of overhead transmission lines. In order to put forward safety protection suggestions for GPLW, the dielectric strength of the GPLW gaps in cup towers and double circuit towers were studied based on a prediction method. The results showed that in both cup towers and double circuit towers, as the gap distance increases, the dielectric strength will also increase. In cup towers, when the lineman is on the side of the window, standing inside the window will increase the dielectric strength of GPLW gaps. When the lineman is at the bottom of the tower window, raising hands will reduce the dielectric strength of GPLW gaps, but this will not happen on the side or top of the tower window. In double circuit towers, the position and posture of the lineman have little effect on the dielectric strength of GPLW air gaps. The results of the study could provide guidance for the live-line work engineering.

Electrical properties of palm oil and rice bran oil under AC stress for transformer application

This paper presents the investigation on the dielectric properties (dissipation factor, relative permittivity, and resistivity) and AC breakdown voltage behaviour of Palm Oil (PO) and Rice Bran Oil (RBO). The dielectric properties experiment was carried out according to the IEC 60247 standard using an automatic ADTR-2K Plus instrument. The AC breakdown test was carried using two different setups (automatic oil tester and BHT AC Generator) using similar VDE electrodes with 23 mm in diameter and comply with IEC 60156 standard. The data of AC breakdown voltage were statistically analysed to predict the withstand voltage (1%) of oil samples by using Weibull distribution. The results show that RBO has lower DDF than PO in which will give better insulating oil capability than PO. For relative permittivity, PO has the highest value among the oil samples which gives advantages in terms of stress distribution between solid and liquid inside the transformer. The relative permittivity of PO is 2.176 closer to that of solid insulation (4.0) which leads to an evener stress distribution between solid and liquid materials. On the other hand, for resistivity, RBO has the highest value among the oils, and it is correlated well with the results in AC breakdown. In the AC breakdown voltage study, two different equipment which having da differences in the volume of oil, electrodes arrangement and as well stirrer were investigated. In the AC breakdown study, RBO has the highest breakdown voltage for both test setups. PO is the second-best in AC breakdown voltage while MO shows the lowest breakdown voltage among oil samples. The percentage difference between using BAUR oil tester and BHT AC generator setup is between 4% and 10% at a 2.5 mm gap distance which is comparable for both types of equipment. For various gap distances studies, the breakdown voltage is increased with the increase of gap distance between the electrodes, for all oil samples. The Weibull distribution of MO, PO and RBO has well fitted with the fitting line of AC breakdown data. From the Weibull distribution, the empirical withstand voltages equations with gap distances of PO and RBO are derived.

Ultrafast optical-field-induced photoelectron emission in a vacuum nanoscale gap: An exact analytical formulation

By exactly solving the one-dimensional time-dependent Schrödinger equation, we construct an analytical solution for nonlinear photoelectron emission in a nanoscale metal–vacuum–metal junction driven by a single-frequency laser field, where the impact of image and space charges is neglected. Based on the analytical formulation, we examine the photoelectron energy spectra and emission current under various laser fields and vacuum gap distances. Our calculation shows the transition from direct tunneling to multiphoton induced electron emission as gap distance increases. In the multiphoton regime, the photoemission current density oscillatorily varies with the gap distance, due to the interference of electron waves inside the gap. Our model reveals the energy redistribution of photoelectrons across the two interfaces between the gap and the metals. Additionally, we find that decreasing the gap distance (before entering the direct tunneling regime) tends to extend the multiphoton regime to higher laser intensity. This work provides clear insights into the underlying photoemission mechanisms and spatiotemporal electron dynamics of ultrafast electron transport in nanogaps and may guide the future design of advanced ultrafast nanodevices, such as photoelectron emitters, photodetectors, and quantum plasmonic nanoantennas.

Plasmonic gap resonances of electrically excited MIS-AgNR hybrid system

In this paper, a kind of light-emitting tunnel junction composed of three layers of metal–insulator–semiconductor (MIS, Au-Al2O3-Si) is introduced and this structure mainly relies on electron tunneling to excite SPPs. The finite element method is used to calculate the electric field distribution and extinction spectrum of the silver nanorod (AgNR) placed on the metal–insulator–semiconductor tunnel junction (MIS-AgNR). In the simulation, the influence of tunneling current on the strength of SPPs propagating along the metal surface is quantitatively studied by changing the thickness of the insulator layer of the MIS tunnel junction and the bias voltage across it. The AgNR is placed on the tunnel junction, and the gap distance between the gold surface of the MIS structure and the AgNR is changed to qualitatively study the relationship between the extinction characteristics of the AgNR and the gap distance. The study found that the amount of the tunneling current is proportional to the intensity of the SPPs on the metal surface. In the range of 4 nm–20 nm gap distance, the adjustment of the resonance peak position in the 500 nm–700 nm range of the extinction spectrum is realized. As the gap distance increases, the position of the resonant peak in the AgNR extinction spectrum will undergo blue-shift, and at the same time the intensity of the extinction peak will decrease. It is worth noting that the change of the blue-shift displacement is exponentially related to the change of the gap distance.

Statistical analysis of pulsed discharges in dielectric liquid: effects of voltage amplitude, pulse width, electrode configuration, and liquid composition

Discharge in dielectric liquid is an active field of research involved in many technological applications. Such multiple discharges are often applied during an experiment and that the electrode and liquid are altered by these stochastically behaving discharges. Therefore, it is important to address the variation of discharge characteristics as a function of discharge occurrence. In this study we analyze the electrical characteristics of multiple discharges run at low repetition rate (5 Hz) in a liquid of known initial composition using an electrode with a specific geometry. The discharges are run continuously until they fail to occur due to the increase in gap distance, and the recorded voltage and current waveforms are processed using an algorithm in order to determine the probability of discharge occurrence, breakdown voltage, discharge current, and discharge delay. The injected charge and energy of each discharge are also calculated. Furthermore, the effects of applied voltage, pulse width, electrode configuration, and liquid composition on the characteristics of the discharge are investigated. The obtained results demonstrate that the highest and lowest numbers of occurred discharges are achieved using the plate-to-plate and pin-to-pin configurations, respectively. Moreover, the composition of the liquid has an appreciable effect on the discharge current, as well as on electrode erosion. For discharges in water and cyclohexane, we measured the lowest and highest current, respectively. As for the erosion rate, it was comparable for the three liquid hydrocarbons but relatively smaller than that in water. The plot of breakdown voltage as a function of discharge current varies depending on the discharge parameters and displays regions that may be linked to the ignition mechanisms. The original data reported herein is of great significance for various applications that utilize repetitive discharges in liquid.

Aero-acoustic response of flat plates at sub-sonic flow

Natural aero-acoustic resonance of single and double flat plates was experimentally investigated. Ten single plates of six different chord-to-thickness ratios were tested for flow around single plate, and four different gap-to-thickness ratios were tested for flow around two plates in tandem. For the case of single plates, a tool for the prediction of resonant flow velocities was established using reduced velocity. For tandem plates, the acoustic response was characterized by the presence of double resonance response that is the excitation of first acoustic mode in two different ranges of flow velocities. Reduced velocity range of low-frequency resonance fits to the range of Mode1 in single plates, this is because both resonances are natural. For high-velocity resonance, a common range could hardly be identified although the increase of gap distance showed an increase in the onset reduced velocity at resonance. It is hypothesized that the first resonance of the double response is caused by normal shedding of vortices in the gap between the plates, whereas the latter resonance is due to vortices caused by the interaction of shear layers with the downstream plate. This mechanism is different than that present in case of tandem cylinders due to the difference in separation points. It was also shown that the downstream plate can serve as a duct modification that leads to the excitation of new acoustic modes that were not excited in the case of single plates.

Electric field dependence of SF6 nonlinear discharge characteristics: N-curve estimations

The N-curve of SF6 describes the relationship between the AC breakdown voltage in an extremely inhomogeneous electric field and pressurized SF6 gas. It is directly dependent on the electric field distribution, which is determined by the gas gap, curvature radius, and background electric field. An increase in gap distance, a decrease in curvature radius, and relatively weak background electric field are all conducive to corona stabilization. The electrode curvature radius is the determining factor in the positive glow corona (PGC) discharge quenching pressure. The breakdown voltage dominated by the streamer mechanism can be estimated accurately by calculating the electric field based on the Deutsch assumption and combining it with the SF6 static field breakdown criterion. The proposed method is applicable to the estimation of N-curves in gaps with varying field distributions. The work presented in this paper may support further quantitative research on the discharge mechanism of strongly electronegative gas dielectrics.

Gap length effect on discharge mode and etching profiles in asymmetric dual frequency capacitive CF<sub>4</sub>/Ar discharges

The capacitive CF<sub>4</sub>/Ar discharges driven by a dual frequency source based on the electrical asymmetry effect (EAE) are studied by using a one-dimensional fluid coupled with Monte-Carlo (MC) model and a two-dimensional trench model. The effects, induced by varying the relative gap distance, on self-bias voltage, electronegativity, ion flux, neutral flux and other plasma characteristics are systematically discussed. In this asymmetric discharge, as the gap distance increases, the absolute value of the self-bias voltage and electronegativity decrease. Meanwhile, the plasma density and absorption power increase accordingly because the effective discharge area expands but the boundary loss is still limited. In addition, both <inline-formula><tex-math id="M72">\begin{document}$ \mathrm{\alpha } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20210546_M72.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20210546_M72.png"/></alternatives></inline-formula> mode and drift-ambipolar (DA) mode can play their important roles in the discharges with different gap distances, though DA mode is weakened in large gap discharge. Owing to the fact that the self-bias is larger and electronegativity is stronger for the case of smaller gap distance, the sheath expansion electric field at the powered electrode and the bulk electric field heat the electrons, leading the ionization rate to greatly increase near the collapse of the sheath at the grounded electrode. Besides, at the larger gap distance, the maximum value of the ionization rate decreases due to the reduction of electrons with relatively high-energy, and the ionization rate near the grounded electrode is reduced evidently. Moreover, with the increase of the gap distance, the maximum ion energy decreases and the ion energy distribution width becomes smaller due to the reduction of the self-bias voltage. Meanwhile, the etching rate increases a lot since the neutral flux increases significantly near the powered electrode. However, as the gap distance increases to 5 cm, the etching rate stops increasing and the trench width at the bottom becomes narrow because the neutral flux increases greatly compared with ion flux, forming a thick layer of polymer. So, besides separately controlling the ion energy and flux, optimizing the synergistic effect of ion flux and neutral group flux to adjust the etching rate and improve the etching morphology is also an interesting topic in the asymmetric CF<sub>4</sub>/Ar discharges.

Truck Platooning to Minimize Load-Induced Fatigue in Steel Girder Bridges

Truck platooning has been demonstrated to possess several advantages in relation to energy savings. To implement this technology in the future, a better understanding of the effects of truck platooning on bridges is needed in relation to safety, serviceability, and remaining service life. This research aims at investigating the effects of truck platooning on the fatigue of steel girder bridges. Different types of platoons are simulated in line girder analysis for simple spans and two-equal continuous spans bridges. Then the rainflow counting method is applied to obtain the stress ranges and cycles. Miner’s rule is used to quantify the fatigue damage. The fatigue damage of different platoons is normalized by American Association of State Highway Transportation Officials Load and Resistance Factor Design Fatigue Load for comparison. The effects of the number of trucks and gap distances of truck platoons are further investigated. In some cases, truck platooning helps decrease the fatigue damage since, although truck platooning brings higher load effects, it also decreases the number of cycles. For platoons with different truck wheelbases, there are specific span to wheelbase ratios, beyond which fatigue damage decreases as gap distance increases. In addition, depending on the platoon configurations, there are ranges of span lengths where it is more beneficial to travel as truck platoons rather than traveling individually in relation to fatigue damage.

The localized surface plasmon resonance on noble metal-semiconductor: Au nanosphere-ZnO nanorod

In this work, we have investigated the localized surface plasmon resonance of metal-semiconductor model. The raw materials are gold nanosphere (Au-NP) and ZnO nanorod (ZnO-NR). The nanoparticles were surrounded by air with refractive index constant (1.0+0i). Moreover, the diameter and aspect ratio of Au-NP and ZnO-NR were 40 nm and 4, respectively. Then, we designed the nanoparticle in two different configurations. First, Au-NP was placed at the sides of ZnO-NR and second, Au-NP was placed at the tip of nanorod. Next, we varied the gap-distance among them from 0 nm to 40 nm with 10 nm increment. The photon wavelength used were from 300 nm to 1200 nm within two different excitations (transverse and longitudinal excitation). Furthermore, our result suggests that on the longitudinal excitation, when the gap-distance increases, the resonance peak of second configuration remains at constant value and the intensity significantly decreases compared to the first configuration. However, on the transverse excitation, the first configuration has a high intensity and the resonance peaks is slightly red-shifted. In addition, based on the near-field mapping which reflects the energy density of electromagnetic field by LSPR, the LSPR of Au-NP stands to aid the exciton production to enhance the photocatalytic activity.

Effects of impingement gap and hole arrangement on overall cooling effectiveness for impingement/effusion cooling

The effects of geometrical parameters on overall cooling effectiveness were experimentally investigated on the flat plate with impingement/effusion cooling. Geometrical parameters investigated included two relative positions of impingement and effusion holes (staggered arrangement and overlapped arrangement) and three impingement gap distances (H/D = 2.5, 5 and 7.5). In addition, numerical simulation was employed to predict the effect of gap distance in a wider range. The results indicate that overall cooling effectiveness is significantly improved by adding impingement, while distribution of cooling effectiveness is mainly determined by film cooling and bore cooling. The comparison of cooling effectiveness between staggered and overlapped hole arrangement indicates that the former produces higher value at each blowing ratio and gap distance. At the same blowing ratio, the overall cooling effectiveness decreases as the increase of gap distance for staggered arrangement. For overlapped arrangement, the cooling effectiveness peaks at H/D = 10. Specific scaling principles of overall cooling effectiveness are experimentally validated by three cases with different temperature ratios. After matching mainstream side Reynolds number, Biot number, and the momentum flux ratio, the cooling effectiveness of case with lower temperature ratio agrees well with that of case with higher temperature ratio at each gap distance and hole arrangement.