Sonic Limit Research Articles

Theoretical analysis of the vapor-liquid slug-train dynamic formation in an ultra-maximum hydraulic diameter oscillating heat pipe in horizontal orientation

The formation of liquid slug is critical to the pulsating flow of vapor-liquid slug-train (VLST) in an ultra-maximum hydraulic diameter oscillating heat pipe (UHDOHP) in horizontal orientation. The high-speed vapor causes the fluctuations in the vapor-liquid interface and forms local low pressure at the wave peak, which promotes the wave peak growth to create a liquid slug. Therefore, how to obtain a sufficient vapor velocity is important. The results show that the required heat to obtain sufficient vapor velocity cannot exceed the maximum load-bearing heat that maintains the effective evaporation of liquid and the unobstructed flow of vapor. And the effects of liquid reflux limit (RL), sonic limit (SL) and critical heat flux (CHF) appear sequentially as the diameter increases. In the effective range of RL, the optimal filling ratio decreases with diameter. And reducing the effective length can weaken the RL limitation and increase the effective range of SL. Moreover, increasing the diameter and filling ratio can weaken the limiting effect of CHF. This study reveals the start-up of UHDOHP in a horizontal orientation and provides a guideline for promoting the VLST formation.

Numerical study on the characteristics of sodium heat pipes for space application at operation limits

Sodium heat pipes are important thermal conductive components in space nuclear power sources. They efficiently transfer heat within the range of 500–1000 °C by utilizing the latent heat of phase change. However, their maximum heat transfer capacity is limited by various factors. In this study, numerical simulations were conducted to investigate the operating conditions of sodium heat pipes when encountering different heat transfer limits, with a focus on analyzing the vapor–liquid distribution and axial temperature distribution in evaporator section. It is revealed that as reaching the heat transfer limits, sodium heat pipes exhibit wall temperature fluctuations in evaporator section. When encountering the viscous limit, liquid aggregation occurs within the wick, causing discontinuous flow. As reaching the sonic limit, a vapor blockage zone forms at the outlet of evaporator section, disrupting the flow circulation within heat pipe. For the entrainment limit, the liquid inside wick is carried away by vapor flow, reducing the amount of liquid involved in phase change cycle. As in the capillary limit, inadequate liquid reflux leads to thinner liquid layer, weakening the flow circulation. During the transition from the viscous limit to the sonic limit, no significant phenomena of phase distribution occur in the evaporator section. As the sonic limit and the entrainment limit act together, both vapor blockage and liquid entrainment occur, accompanied by liquid accumulation. The phenomena when the entrainment limit and the capillary limit act together differ from those occurring individually. The simulation results provide references for a deeper understanding of heat transfer limit mechanism and other operating characteristics.

Density jump as a function of magnetic field strength for perpendicular collisionless shocks with anisotropic upstream pressure

ABSTRACT Shock waves are common in astrophysical environments. On many occasions, they are collisionless, which means they occur in settings where the mean free path is much larger than the dimensions of the system. For this very reason, magnetohydrodynamic (MHD) is not equipped to deal with such shocks, be it because it assumes binary collisions, hence temperature isotropy, when such isotropy is not guaranteed in the absence of collisions. Here, we solve a model capable of dealing with perpendicular shocks with anisotropic upstream pressure. The system of MHD conservation equations is closed assuming the temperature normal to the flow is conserved at the crossing of the shock front. In the strong shock sonic limit, the behaviour of a perpendicular shock with isotropic upstream is retrieved, regardless of the upstream anisotropy. Generally speaking, a rich variety of behaviours is found, inaccessible to MHD, depending on the upstream parameters. This work can be viewed as the companion paper of MNRAS 520, 6083-6090 (2023), where the case of a parallel shock was treated. Differences and similarities with the present case are discussed.

Experimental study of non-condensable gas effects on sonic limit of sodium heat pipe

Due to unexpected gas leakage and long-term operation, the non-condensable gas (NCG) inevitably exists in high-temperature alkali metal heat pipe. Previous studies have mainly focused on its influences on startup and steady state operation characteristics of heat pipes. However, few of them conducted experiments to study the effects of NCG on sonic limit, which usually occurs during heat pipe startup or during steady state operation when the heat transfer coefficient at condenser section is high. In present work, experimental and analytical studies are conducted to the explore the effects of NCG on sonic limit of sodium heat pipes. With the heating power ranging from 500 to 1400 W, the sonic limit of 1 m-long sodium heat pipes with artery wick and axial groove wick are obtained based on oil-cooling system, which can widely adjust the cooling capacity at condenser section. The amount of NCG in heat pipe is estimated by Heat Pipe Transient Analysis Code (HPTRAN) and verified by experimental data. It is found that the existence of NCG in heat pipe leads to the decrease of maximum heat transfer rate under sonic limit. The mechanism of NCG effects on sonic limit is discussed based on phenomenological analysis. By introducing the added back pressure, a modified model to predict sonic limit considering NCG effect is proposed and the comparison with experimental data shows good agreements.

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number ε ranging from 0 to O(1). High-order accuracy in time is obtained by SI implicit-explicit Runge–Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.

Design and Thermal Performance Research of Airfoil Alkali Metal High-Temperature Heat Pipe

Abstract An integrated airfoil alkali metal high-temperature heat pipe structure is proposed for the air rudder. The heat transfer properties of lithium and sodium are analyzed, and the equal-thickness test pieces are designed and prepared. The sonic limit, condensation limit, viscosity limit, entrainment limit, capillary limit and boiling limit are calculated theoretically, and the corresponding feasible working areas are drawn according to each limit curve. It is found that the optimal working temperature range of the test piece is 800∼1500 K. The effects of heating power and placement angle on the start-up time, isothermal performance, and heat transfer performance of the test piece are studied by experiments. The increase in heating power is helpful to shorten the start-up time and improve the isothermal performance and heat transfer performance of the test piece. The placement angle has little effect on the start-up time, but it has an effect on the isothermal performance and heat transfer performance.

Thermal performance of a medium temperature cesium heat pipe at different inclination angles

The cesium heat pipe has great potential in the medium temperature heat transfer fields for its large heat transfer capacity and high isothermality. To present the thermal performance of a cesium heat pipe, especially under different inclination angles, a cesium heat pipe is fabricated and tested in this work. As a result, the applicability of the theoretical calculation of the transition temperature to the cesium heat pipe is verified by the maximum temperature variation rate. Then, the frozen startup process with a sonic limit is described in detail which obeys the same rule as other alkali metal heat pipes. Furthermore, the effects of the heating powers (317.2 W ∼ 1416.2 W) and the inclination angles (0°, 30°, 60°, 68°, and 80°) on the thermal performance of the cesium heat pipe are experimentally analyzed. To precisely evaluate the temperature uniformity, the standard deviation of axial temperature in the condenser is calculated. The results indicate that the cesium heat pipe shows excellent temperature uniformity at 68°. The end of the condenser presents a non-negligible temperature gradient at 80° which can be reduced by adding a heat shield in the adiabatic section.

Virtual impaction in compressible flows with pressure recovery

Virtual impactors have been utilized towards classifying and increasing aerosol concentrations in sampling and measurement systems for half a century; in an ideal virtual impactor, sampled particles larger than a critical diameter (known as the cutsize) are directed inertially into a small fraction of the sample flow, known as the minor flow. Concentrating submicrometer particles with virtual impactors while maintaining near-atmospheric pressure downstream in the minor flow remains a challenge, due the low mass-to-drag ratios of these particles. Increased inertial behavior for small mass-to-drag ratio particles can be overcome by increasing flow velocities; however, in most prior work with virtual impaction of submicrometer particles, pressure recovery (keeping the aerosol outlet pressure similar to the inlet pressure) in the receiving tube at high sample flow rates was not investigated. Here, we describe the development and testing of virtual impactors functioning with flow velocities near the sonic limit, capable of submicrometer particle concentration, and with near-complete pressure recovery in the minor flow. We specifically designed, built, and tested two round-nozzle virtual impactors (denoted as VI-1 and VI-2) and evaluated their performances using fluorescent polystyrene latex particles and uranine-doped oleic acid particles with varying particle diameter. The results show that both virtual impactors, operating with 12 L per minute sample flow and a 10:1 sample flow-to-minor flow ratio, have submicrometer cutsizes (∼700 nm and 200 nm for VI-1 and VI-2, respectively) and near-complete pressure recovery. However, significant particle losses were observed in VI-2 with larger particle diameters. To understand such losses and particle trajectories in compressible flow virtual impactors, we also carried out computational fluid dynamics (CFD) simulations coupled with particle trajectory simulations. Importantly, trajectory calculations incorporated a recently developed drag model capable of predicting particle drag coefficients in a wide Mach number and Knudsen number (and hence Reynolds number) range. Trajectory calculations yielded cutsizes and large particle penetration curves in good agreement with experiments, indicating that large particle losses are due to overfocusing (radial inertial motion leading to deposition) within the nozzle and major flow chamber. Overfocusing always leads to an upper size limit in any virtual impactor system, but it is of greater concern in higher velocity systems. In addition to comparing simulations to measurements sampling at atmospheric pressure, we used trajectory calculations to examine compressible flow virtual impactor performance with variable sampling flow pressure and varying the driving pressure in the major flow. Such simulations reveal that sub-atmospheric pressure sampling leads to a reduced penetration “window” for virtual impaction, such that although it is possible for virtual impactor operation in reduced pressure environments, virtual impactors are applicable to a decreasing range of sizes at low pressure.

Experimental evaluation on heat transfer limits of sodium heat pipe with screen mesh for nuclear reactor system

• Wall and vapor temperature of heat pipes are measured. • Capillary limits are characterized experimentally and are predicted by the model of Chi under horizontal condition. • Sonic limits are characterized and occur during the frozen startup process. • A model of entrainment limit is proposed and verified by the experiments. • Transition temperature of vapor is measured experimentally and is affected by the inclination angle. Heat pipe cooled reactor (HPR) is an ideal technology and a potential future niche where reliability and simplicity are key requirements. The heat transfer capacity of heat pipes determines the application range of HPR. Heat transfer limits (HTLs) of heat pipes are investigated, and the models of HTLs are evaluated in this study. Various HTLs of heat pipes with different filling ratios are tested. For the capillary limit, there is a sudden dryout in the evaporator section, in which the model of Chi is applicable for the horizontal conditions with a deviation of 19.0% but not for the inclined conditions. There is a possibility of sonic limit for a temperature rise in the adiabatic and condenser sections. The sonic limit predicted by Levy model is always higher than the experimental results. The entrainment limit is accompanied by a sudden rise in temperature of the evaporator section and temperature fluctuation in the condenser section, which can be estimated by using the wave-induced model with a relative error of 45.3% and is affected by the wick and inclination angle. The Knudsen number is used to determine the vapor state and the recommended critical Knudsen number of 0.01 is less than experimental data, which neglects the effect of inclination angle. The experimental results provide references for the heat pipe design and the accuracy of the present models are estimated.

Nondispersive One-Way Signal Amplification in Sonic Metamaterials

Parametric amplification---injecting energy into waves via periodic modulation of system parameters---is typically restricted to specific multiples of the modulation frequency. However, broadband parametric amplification can be achieved in active metamaterials which allow local parameters to be modulated both in space and in time. Inspired by the concept of luminal metamaterials in optics, we describe a mechanism for one-way amplification of sound waves across an entire frequency band using spacetime-periodic modulation of local stiffnesses in the form of a traveling wave. When the speed of the modulation wave approaches that of the speed of sound in the metamaterial---a regime called the sonic limit---nearly all modes in the forward-propagating acoustic band are amplified, whereas no amplification occurs in the reverse-propagating band. To eliminate divergences that are inherent to the sonic limit in continuum materials, we use an exact Floquet-Bloch approach to compute the dynamic excitation bands of discrete periodic systems. We find wide ranges of parameters for which the amplification is nearly uniform across the lowest-frequency band, enabling amplification of wave packets while preserving their speed, shape, and spectral content. Our mechanism provides a route to designing acoustic metamaterials which can propagate wave pulses without losses or distortion across a wide range of frequencies.

Design Calculations of the Limiting Characteristics of Heat Pipes for Cooling Active Phased Antenna Arrays

The article provides an algorithm for calculating the limiting characteristics of heat pipes for cooling active phased antenna arrays at a given saturation temperature. The maximum transmitted power is determined taking into account the limitations of the heat pipes operation by the capillary limit, by boiling (transition to film boiling, boiling limit), by the sonic limit at which the speed of steam reaches the speed of sound (sonic limit), by the entrainment of droplets liquid coolant from the surface of the wick with a counter flow of steam (entertainment limit) and viscous limit, which is realized at low temperatures (viscous limit). It is shown that an increase in the thickness of the wick and its porosity may be necessary to increase the capillary limit of heat pipes, while an increase in the thickness of the wick increases the thermal resistance of the tube and, accordingly, can lead to overheating of the cooled elements. Based on the above algorithm, design calculations for two types of heat pipes have been carried out. The dependences of various limits of the heat pipe on the operating temperature are plotted. Based on the above algorithm, calculations were performed for two types of heat pipes.

Design and operational assessment of a low-boom low-drag supersonic business jet

There has been a worldwide interest to develop a supersonic business jet (SSBJ) for a minimum range of 4000 nm with low sonic boom intensity and high fuel efficiency. An SSBJ design model is developed in the GENUS aircraft conceptual design environment. With the design model, a low-boom low-drag SSBJ concept is designed and optimized. This article studies the design concept for its operational performances. The sustained supersonic cruise flight is studied to find out the fuel-efficient Mach number and altitude combinations. The combined supersonic and subsonic cruise flight scenarios are studied to evaluate the feasibility of boom-free flight routes. The one-stop supersonic cruise flight scenario is studied to compare the fuel consumption and time advantage over subsonic airliners. The off-design sonic boom intensity is studied to explore the operational space assuming there would be a sonic boom intensity limit in the future. Through the studies, it is revealed that there is a corresponding most fuel-efficient operating altitude for a specific cruise Mach number. To operate the aircraft near the cutoff Mach number leads to both increases in the fuel consumption (6.3%–8.1%) and the mission time (11.7%–13.1%). The business-class supersonic transport (231 g/PAX/km) consumes nearly three times fuel as the economic-class supersonic transport (77 g/PAX/km), which is still far more than the economic-class subsonic transport (20 g/PAX/km). Off-design sonic boom intensity studies reveal different trends against the common understanding: the sonic boom intensity does not necessarily decrease as the altitude increases; the sonic boom intensity does not necessarily decrease as the Mach number decreases.

Operational Limitations of Heat Pipes with MgO-Water Nanofluid: An Experimental Investigation

This paper presents the study of functional limits of heat pipes with MgO deionized (DI) water nano fluid as working fluid. The nano fluid is made with the help of two step method and it is surfactant free. The output has been analyzed with the increase in concentrations of MgO / DI water nano fluid (0.005%, 0.025% and 0.05 %) and at power input of (10 W, 30 W & 60 W), for covering operational range temperature of the electronic instruments. (<600C). On the basis of the thermo physical properties of the MgO/DI water nano fluid, the functional limits of heat pipe are determined. The changed of working fluids shows an improvement in boiling, pick up(entrainment), viscous and sonic limit except the capillary limit of heat pipe. The surfactant free nano fluids give good safety margin to the boiling limit of the heat pipe, with elimination of chances of locking due to vapor. The capillary limit reduces by the application of nano fluids due to increase in the vapor and liquid flow path resistance rather than capillary pressure in the evaporator section of heatpipe.

Experimental investigation on the heat transfer performance of high-temperature potassium heat pipe for nuclear reactor

Heat pipe cooled reactor (HPR) is considered as an excellent candidate for space power systems. As a core cooling method, the operational characteristics of high-temperature heat pipes need to be researched. In this paper, the heat transfer performance of potassium heat pipes (Φ30mm × 800 mm) is studied experimentally. The thermal behavior of heat pipe is tested under various conditions, including heating power (0.2–4 kW), air/water cooling method, inclination angle (0–90°), and filling ratio (20% and 100% of void in wick). And the characteristics of heat transfer limits are analyzed, consisting of dryout, entrainment, and sonic limit. The results show heating power is beneficial to heat transfer within the capillary limit. However, overheating occurs when heating power exceeds the capillary limit. The inclination angle has a strong effect on the thermal efficiency of heat pipe for the competition between gravity and entrainment, and the angle of 30° corresponds to the best thermal performance. Sonic limit and entrainment limit are estimated with a relative error of 38.7% and 17.9%. Dryout is divided into local dryout (<200 °C/m) and integral dryout (>200 °C/m). It is concluded that the high filling ratio (100%) and the small inclination angle (30°) are helpful to realize the optimal thermal performance. This work makes it possible to validate the operation of a high-temperature heat pipe and provides a reference for the design and application of HPR.

Rarefactive lattice solitary waves with high-energy sonic limit.

We compute rarefactive solitary wave solutions in a nonlinear lattice with nearest-neighbor interaction forces that are sublinear near the undeformed state. This setting includes bistable bonds governed by a double-well potential. In contrast to the prototypical Korteweg-de Vries-type delocalization, the obtained solutions feature a nontrivial sonic limit (Chapman-Jouguet regime) with nonzero energy and algebraic decay at infinity. In the bistable case the waves are strongly localized and have high energy over the entire velocity range. Direct numerical simulations suggest stability of the computed solitary waves. We consider several quasicontinuum models that mimic some features of the obtained solutions, including the nontrivial nature of the sonic limit, but fail to accurately approximate their core structure for all velocities in the bistable regime.

Experimental study on heat transfer limit of high temperature potassium heat pipe for advanced reactors

Heat pipe cooled reactor (HPR) is widely applied in various environment due to its remarkable advantages compared with other nuclear power systems, such as high reliability, low noise level and compact structure. As one of the essential components in HPR, the high temperature heat pipe has an important effect on HPR operation performance. In this paper, an experimental study was carried to investigate the thermal–hydraulic characteristics and heat transfer limit of potassium heat pipe. Under the steady-state conditions, heating power and inclination angle of heat pipe were taken as sensitivity parameters. By increasing heating power, the heat transfer capacity was enhanced. For inclination angle, an increase in inclination angle would enhance heat transfer for low filling ratio heat pipe, while it does not make obvious effect on high filling ratio heat pipe. As for heat transfer limit, by analyzing the axial wall temperature distribution and predicting the vapor flow pressure drop, the particular phenomena is classified to four heat transfer limits including viscosity, sonic, entrainment and condensation limit. When heat pipe is cooled by natural air convection, the accurate prediction of condensation limit under effect of inclination is performed by air convection heat transfer relationship. Because of the friction force influence on viscosity limit when operating at low temperature state, the temperature at inlet of condenser section is 11℃ lower than adjacent position. The same reason for sonic limit when operating at low temperature state, the temperature at outlet of evaporator section is 17 ℃ higher than adjacent position. The occurrence of local dryout which lead evaporator temperature increasing sharply to 632 ℃ is entrainment limit. The experimental results provide guidance for the engineering application of high temperature heat pipe.

Axial rotating heat-pipe grinding wheel for eco–benign machining: A novel method for dry profile-grinding of Ti–6Al–4V alloy

Sustainable grinding is one of the development directions of modern processing. When profile grinding titanium alloys, since the grinding burn-out is easy to happen, a large amount of cooling fluid is commonly used for cooling the grinding zone. However, the cooling fluid is harmful to human health and is neither economical nor efficient. Given that, a method of dry profile-grinding Ti–6Al–4V alloy to achieve environmentally-friendly machining was proposed in this article. An axial rotating heat-pipe profile grinding wheel (HPGW) was designed and manufactured, not only to eliminate the harmful cooling fluid; but also to augment heat transfer in the grinding zone and control the grinding temperatures. By developing this HPGW, a sustainable grinding process will be achieved with less resource utilization, less environmental and health issues, less energy consumption, and carbon emission. The design methods of HPGW were put forward through comprehensive consideration of the sonic limit, heat transfer and structural strength requirements. Then, the design was checked by FEM simulation. Moreover, experiments were conducted to investigate the influences of the filling ratio, rotational speed, and material removal rate on the heat transport performance of HPGW. The Ti–6Al–4V alloy profile structure was successfully dry ground by this HPGW. Results reveal that the temperature of the ground surface was controlled below 80 °C and temperature difference on the profile surface was within 10 °C. The novel HPGW with desirable heat transfer performance can be applied in the metal processing industries, and it is a promising candidate for sustainable grinding of titanium alloys.

A New Perspective on Heat Transfer Mechanisms and Sonic Limit in Pool Boiling

Pool boiling is postulated as a single-phase heat transfer process with nucleating bubbles providing a liquid pumping mechanism over the heater surface. This results in three fluid streams at the heater surface—outgoing vapor and liquid streams, and an incoming liquid stream. Heat transfer during periodic replacement of the liquid in the influence region around a nucleating bubble is well described by transient conduction (TC) and microconvection (MiC) mechanisms. Beyond this region, free convection (FC) or macroconvection (MaC) contributes to heating of the liquid. A bubble growing on the heater surface derives its latent heat from the surrounding superheated liquid and from the microlayer providing a direct heat conduction path. Secondary evaporation occurs in the bubbles rising in the bulk after departure, and at the free surface. This secondary evaporation does not directly contribute to the heat transfer at the heater surface but provides a means of dissipating liquid superheat. A sonic limit-based model is then presented for estimating the theoretical upper limit for pool boiling heat transfer by considering the three fluid streams to approach their respective sonic velocities. Maximum heat transfer rates are also estimated using this model with two realistic velocities of 1 and 5 m/s for the individual streams and are found to be in general agreement with available experimental results. It is postulated that small bubbles departing at high velocity along with high liquid stream velocities are beneficial for heat transfer. Based on these concepts, future research directions for enhancing pool boiling heat transfer are presented.

Ultrafast photonic micro-systems to manipulate hard X-rays at 300 picoseconds

Time-resolved and ultrafast hard X-ray imaging, scattering and spectroscopy are powerful tools for elucidating the temporal and spatial evolution of complexity in materials. However, their temporal resolution has been limited by the storage-ring timing patterns and X-ray pulse width at synchrotron sources. Here we demonstrate that dynamic X-ray optics based on micro-electro-mechanical-system resonators can manipulate hard X-ray pulses on time scales down to 300 ps, comparable to the X-ray pulse width from typical synchrotron sources. This is achieved by timing the resonators with the storage ring to diffract X-ray pulses through the narrow Bragg peak of the single-crystalline material. Angular velocities exceeding 107 degrees s−1 are reached while maintaining the maximum linear velocity well below the sonic speed and material breakdown limit. As the time scale of the devices shortens, the devices promise to spatially disperse the temporal width of X-rays, thus generating a temporal resolution below the pulse-width limit.

Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic–sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.