Non-dimensional analysis on blast wave propagation in foam concrete:Minimum thickness to avoid stress enhancement

Foam concrete is a prospective material in defense engineering to protect structures due to its high energy absorption capability resulted from the long plateau stage.However,stress enhancement rather than stress mitigation may happen when foam concrete is used as sacrificial claddings placed in the path of an incoming blast load.To investigate this interesting phenomenon,a one-dimensional difference model for blast wave propagation in foam concrete is firstly proposed and numerically solved by improving the second-order Godunov method.The difference model and numerical algorithm are validated against experimental results including both the stress mitigation and the stress enhancement.The difference model is then used to numerically analyze the blast wave propagation and deformation of material in which the effects of blast loads,stress-strain relation and length of foam concrete are considered.In particular,the concept of minimum thickness of foam concrete to avoid stress enhancement is proposed.Finally,non-dimensional analysis on the minimum thickness is conducted and an empirical formula is proposed by curve-fitting the numerical data,which can provide a reference for the application of foam concrete in defense engineering.

Non-Dimensional Analysis of Thermal Effect on Skin Exposure to an Electromagnetic Beam

We consider the problem of inducing withdrawal reflex on a test subject by exposing the subject’s skin to an electromagnetic beam. Heat-sensitive nociceptors in the skin are activated wherever the temperature is above the activation temperature. Withdrawal reflex occurs when the activated volume reaches a threshold. We non-dimensionalize the problem to write the temperature as the product of a parameter-free function of non-dimensional variables and a function of beam parameters. This formulation allows studying beam parameters without knowing skin material parameters. We examine the effects of spot size, total power and distribution type of the electromagnetic beam on 3 quantities at reflex: 1) the time to reflex, 2) the maximum temperature increase, and 3) the total energy consumption. We find that the flat-top beam is the best, with the lowest energy consumption and the smallest maximum temperature increase. The Super-Gaussian beam is only slightly inferior to the flat-top. The Gaussian beam has by far the worst performance among these three.

Local Similarity Relationships of Non-Dimensional Wind and Temperature Gradient in the Tower-Layer Atmosphere over Beijing City

Micrometeorological data for wind and temperature from a 325 m high tower in Beijing City are analyzed by use of local similarity theory. Non-dimensional wind and temperature gradients, Phi(m) and Phi(h), are determined by three techniques called, respectively, eddy-correlation, mean profiles and inertia-subrange cospectra (ISC) method for a wide range of atmospheric stratification from unstable to stable conditions. Average dissipation rate Phi(e) of turbulent kinetic energy (TKE) is evaluated from u-spectrum, as a quantity required in the last technique. Ratio of the eddy transfer coefficients, alpha(= K-h / K-m), is calculated from Phi(m) and Phi(h) estimations. The results from various techniques are compared with each other and with some available empirical results in the tower-layer, It is shown that the empirical relationships determined by mean profiles and ISC methods in the lower-layer turbulence ore in agreement with each other and with some other results.

Hydrodynamic Lubrication of Elastic Foil Gas Bearing Using Over Relaxation Iteration Method and Non-Dimensional Equation

The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental material.First,the lubrication mechanism of elastic foil gas bearing is analyzed.Then,the numerical solution process of the static bearing capacity and friction torque is analyzed,including the discretization of the governing equation of rarefied gas pressure based on the non-dimensional modified Reynolds equation and the over relaxation iteration method,the grid planning within the calculation range,the static solution of boundary parameters and static solution of the numerical process.Finally,the solution program is analyzed.The experimental data in National Aeronautics and Space Administration(NASA)public literature are compared with the simulation results of this exploration,so as to judge the accuracy of the calculation process.The results show that under the same static load,the difference between the minimum film thickness calculated and the test results is not obvious;when the rotor speed of the bearing is 60000 r/min,the influence of the boundary slip effect increases with the increase of the micro groove depth on the flat foil surface;when the eccentricity or the micro groove depth of the bearing increases,the bearing capacity will be strengthened.When the eccentricity is 6µm and 14µm,the viscous friction torque of the new foil bearing increases significantly with the increase of the depth of the foil micro groove,but when the eccentricity is 22µm,the viscous friction torque does not change with the change of the depth of the foil micro groove.It shows that the bearing capacity and performance of foil bearing are improved.

NON-DIMENSIONAL DESIGN PARAMETERS FOR FOD TOLERANT FAN BLADES

Non-dimensional design concept for FOD tolerant fan blades is introduced based on the analyses of simplified impact models. The fan blades arc idealized as either beams or plates of elastic or rigid-plastic materials. The case of constant force impact as well as that of mass impact is analyzed. The centrifugal force effects are also considered in the beam models. The critical fracture conditions arc shown in simple npn-dimensional formulae or diagrams for each case.

Simulation and Experimental Research on Liquid Spreading in a Wire-Sawn Kerf

The significance of liquids in abrasive wire sawing has been demonstrated in several studies.However,the perfor-mance of its spreading behavior is limited by the current development trend,where the wafer has a larger area and the kerf is narrower.Moreover,there are very few studies on the liquid spreading behavior in wire-sawn kerfs.Therefore,a 3D CFD(computational fluid dynamics)model is presented in this paper and used to simulate the liquid spreading behavior in a kerf based on a VOF(volume of fluid)method with a CSF(continuum surface force)model,which is used to simulate multiphase flow,and an empirical correlation for characterizing the liquid dynamic contact angle using UDF(user defined functions).Subsequently,parametric simulations are performed on the kerf area,kerf width,liquid viscosity,liquid surface tension,and liquid velocity at the inlet area of the kerf,and verification experi-ments are conducted to determine the validity of the simulation model.From the simulation and experimental results,three typical liquid spreading regimes that exhibit different effects on wire sawing in the kerfs are found,and their limiting conditions are identified using non-dimensional analysis.Subsequently,a prediction model is pro-posed for the liquid spreading regime based on a set of Weber and Capillary numbers.For wire sawing,an increase in the wafer area does not change the liquid spreading regime in the kerf;however,a reduction in the kerf width sig-nificantly hinders the liquid spreading behavior.Thereby,the spreading regime can be effectively converted to facili-tate wire sawing by adjusting the physical properties and supply conditions of the liquid.

Analysis and design of open trench barriers in screening steady-state surface vibrations

The problem of vibration isolation by rectangular open trenches in a plane strain context is numerically studied using a finite element code, PLAXIS. The soil media is assumed to be linear elastic, isotropic, and homogeneous subjected to a vertical harmonic load producing steady-state vibration. The present model is validated by comparing it with previously published works. The key geometrical features of a trench, i.e., its depth, width, and distance from the source of excitation, are normalized with respect to the Rayleigh wavelength. The attenuation of vertical and horizontal components of vibration is studied for various trench dimensions against trench locations varied from an active to a passive case. Results are depicted in non-dimensional forms and conclusions are drawn regarding the effects of geometrical parameters in attenuating vertical and horizontal vibration components. The screening efficiency is primarily governed by the normalized depth of the barrier. The effect of width has little significance except in some specific cases. Simplified regression models are developed to estimate average amplitude reduction factors. The models applicable to vertical vibration cases are found to be in excellent agreement with previously published results.

Exact solution of free vibration of adjacent buildings interconnected by visco-elastic dampers

With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.

A Concise Model and Analysis for Heat-Induced Withdrawal Reflex Caused by Millimeter Wave Radiation

In this study, we consider the heat-induced withdrawal reflex caused by exposure to an electromagnetic beam. We propose a concise dose-response relation for predicting the occurrence of withdrawal reflex from a given spatial temperature profile. Our model is distilled from sub-step components in the ADT CHEETEH-E model developed at the Institute for Defense Analyses. Our model has only two parameters: the activation temperature of nociceptors and the critical threshold on the activated volume. When the spatial temperature profile is measurable, the two parameters can be determined from test data. We connect this dose-response relation to a temperature evolution model for electromagnetic heating. The resulting composite model governs the process from the electromagnetic beam deposited on the skin to the binary outcome of subject’s reflex response. We carry out non-dimensionalization in the time evolution model. The temperature solution of the non-dimensional system is the product of the applied power density and a parameter-free function. The effects of physical parameters are contained in non-dimensional time and depth. Scaling the physical temperature distribution into a parameter-free function greatly simplifies the analytical solution, and helps to pinpoint the effects of beam spot area and applied power density. With this formulation, we study the theoretical behaviors of the system, including the time of reflex, effect of heat conduction, biological latency in observed reflex, energy consumption by the time of reflex, and the strategy of selecting test conditions in experiments for the purpose of inferring model parameters from test data.

CORRECTION METHODS FOR THERMAL OFFSET ERRORS IN TBQ-2-B PYRANOMETERS

Due to the existence of thermal offsets,global solar irradiances measured by pyranometers are smaller than actual values,and errors are larger in the daytime.Until now,there is no universally-recognized correction method for thermal offset errors.Therefore,it is imperative to identify a convenient and effective correction method.Five correction methods were evaluated based on the data measured from a field experiment from 23 January to 15 November,2011.Results have shown:1) Temporal variation characteristics of thermal offsets in the four tested pyranometers are consistent.2) Among the five methods,non-dimensional quantity method is suggested for use to correct thermal offsets,because it is convenient and no modification of instruments is required.If collocated net longwave radiation and wind speed data are available and their uncertainties are small,the historical solar radiation datasets can also be corrected.And correction effects by the method are better.

Thermal Effect of a Revolving Gaussian Beam on Activating Heat-Sensitive Nociceptors in Skin

We consider the problem of inducing withdrawal reflex on a test subject by exposing the subject’s skin to an electromagnetic beam. Heat-sensitive nociceptors in the skin are activated wherever the temperature is above the activation temperature. Withdrawal reflex occurs when the activated volume reaches a threshold. Previously we studied static beams with 3 types of power density distribution: Gaussian, super-Gaussian, and flat-top. We found that the flaptop is the best and the Gaussian is the worst in their performance with regard to 1) minimizing the time to withdrawal reflex, 2) minimizing the energy consumption and 3) minimizing the maximum temperature increase. The less-than-desirable performance of Gaussian beams is attributed to the uneven distribution of power density resulting in low energy efficiency: near the beam center the high power density does not contribute proportionally to increasing the activated volume;outside the beam effective radius the low power density fails to activate nociceptors. To overcome the drawbacks of Gaussian beams, in this study, we revolve a Gaussian beam around a fixed point to make the power density more uniformly distributed. We optimize the performance over two parameters: the spot size of static beam and the radius of beam revolution. We find that in comparison with a static Gaussian beam, a revolving Gaussian beam can reduce the energy consumption, and at the same time lower the maximum temperature.

Experimental Study on Performance of Supercritical CO_2 Heat Exchanger with Four Different Inner Tubes

The experiment was conducted to investigate the heat transfer performance of supercritical CO_2 in a casing heat exchanger by comparing their heat transfer,entropy production unit number,non-dimensional entropy production rate and field synergy factor.The results show that both heat transfer and entropy production unit number in four tubes decrease with water temperature increasing.Heat transfer and entropy production unit number in multiple tubes( i. e.,triple straight tube and double helix tube) is higher than their single counterparts; the non-dimensional entropy production rate increases with water temperature. Non-dimensional entropy production rate of triple straight tube and double helix tube is far below the single tube. Field synergy factor of double helix tube is much higher than that of the triple straight tube under the same condition. Further experiment was carried out in double helix tube,under various CO_2 pressure and inlet water temperature,the results are analyzed and reported in this paper.

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power;then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.

New Formulation for Semi-Empirical Correlations for Penetration Jets

Correlations for the extension of a water vapor jet injected in a liquid pool were historically proposed considering the mass flux (kg/m2/s) as a constant. The results were satisfactory, however adjusting the values by linear regression. Although, it presents the following drawbacks: 1) the formulation is only valid for the specific range of data for what it was created;2) it does not allow the analytical evaluation of the heat transfer coefficient from the extension equation. This paper proposes a new formulation for the calculation of the mass flux, in such a way to remove both of these drawbacks.

Minimum Energy Requirement for Inducing Withdrawal Reflex in Millimeter Wave Exposures

We consider the problem of inducing withdrawal reflex on a test subject via exposure to a millimeter wave beam. In our physical model, there are 10 physical parameters affecting the occurrence of withdrawal reflex. Our goal is to pinpoint the roles of these physical parameters in inducing withdrawal reflex. We first carry out non-dimensionalization to reduce the model to a non-dimensional system of only 3 composite parameters: non-dimensional beam power density, non-dimensional beam radius, and non-dimensional exposure time. If the beam power is kept on and steady, withdrawal reflex occurs eventually;the shortest exposure time for inducing withdrawal reflex corresponds to the smallest energy consumption at the given power density and beam radius. In the 2D space of power density and beam radius, the overall minimum energy occurs at the corner of very large power density and very small beam radius, which also produces a very large value of maximum skin temperature and a long time to withdrawal reflex. To reduce the burn injury risk, we introduce a cap on the maximum skin temperature. At each given total beam power, we carry out optimizations with respect to the beam radius, constrained by the prescribed temperature cap. The energy consumption varies negatively with the prescribed temperature cap: a lower temperature cap can be accommodated only with a higher energy consumption via the venue of a larger beam radius. The energy consumption is relatively flat with respect to the total beam power and attains a minimum at a moderately large total beam power. The time to withdrawal reflex is approximately inversely proportional to the total beam power. Our analysis demonstrates that a moderately large total beam power is a good compromise to achieve both low energy consumption and short time to withdrawal reflex.

Conduction-convection coupled heat transfer around a hollow cylinder under different buoyancy forces

In order to clarify the effect of a buoyancy force on conduction–convection coupled heat transfer in a hollow cylinder, the flow and thermal characteristics were analyzed using an RNG k-ε turbulence model. The Reynolds number was fixed at 1.014 × 10^(6), and the Rayleigh number varied from 1.122 × 10^(10)to 1.088 × 10^(11). Results have shown that, when considering the effect of an opposed buoyancy force, increasing the Rayleigh number has a positive impact on the rate of change and uniformity of the cylinder temperature. The temperature distributions along the axial and circumferential directions are similar for different Rayleigh numbers, but extreme values differ.Along the axial direction, the maximum temperature is obtained at the interface between the variable-diameter part and the constant-diameter part. The maximum dimensionless temperature value decreases to 0.12 when the Rayleigh number increases to 1.088 × 10^(11). Along the circumferential direction, the temperature distribution is affected by the buoyancy force, which results in the temperature of the upper part being higher than that of the lower part. After nondimensionalization of the temperature and time, a correlation was proposed to illustrate the transient heat transfer process quantitatively. The standard deviation of the maximum relative temperature, representing the temperature uniformity, was also calculated. It was found that the difference in the direction of the buoyancy force made a huge difference. Compared with the opposed buoyancy force, the maximum dimensionless temperature is almost two times higher with an assisted buoyancy force. Similarly, the heat transfer coefficient with an assisted buoyancy force is half of that with an opposed buoyancy force. Overall, an assisted buoyancy force plays a negative role in terms of thermal characteristics. The flow field around the hollow cylinder was also illustrated to reveal the mechanism of the buoyancy force on magnitude and direction aspects.

THE OPTIMIZATION OF CONTROL SYSTEM WITH NON-DIMENSION TIME BY LIAPUNOV'S SECOND METHOD AND THE OPTIMAL DAMPING CONTROL

In this note Liapunov’s second method with non-dimension time by Felilajam is developed from the method of parameter optimization in the second-order systemt to parameter optimization in any arbitrary order systems, and the problem of optimization in the control system becomes one of multidimensional geometric programming with constraint.

Water surface profile prediction in non-prismatic compound channel using support vector machine(SVM)

The process of estimating the level of water surface in two-stage waterways is a crucial aspect in the design of flood control and diversion structures.Human activities carried out along the course of rivers,such as agricultural and construction operation,have the potential to modify the geometry of floodplains,leading to the formation of compound channels with non-prismatic floodplains,thus possibly exhibiting convergent,divergent,or skewed characteristics.In the current investigation,the Support Vector Machine(SVM)technique is employed to approximate the water surface profile of compound channels featuring narrowing floodplains.Some models are constructed by utilizing significant experimental data obtained from both contemporary and previous investigations.Water surface profiles in these channels can be estimated through the utilization of non-dimensional geometric and flow parameters,including:converging angle,width ratio,relative depth,aspect ratio,relative distance,and bed slope.The results of this study indicate that the SVM-generated water surface profile exhibits a high degree of concordance with both the empirical data and the findings from previous research,as evidenced by its R^(2) value of 0.99,RMSE value of 0.0199,and MAPE value of 1.263.The findings of this study based on statistical analysis demonstrate that the SVM model developed is dependable and suitable for applications in this particular domain,exhibiting superior performance in forecasting water surface profiles.

Experimental Study on Heat Transfer Performance of Pulsating Heat Pipe with Refrigerants

The effects of different refrigerants on heat transfer performance of pulsating heat pipe(PHP) are investigated experimentally.The working temperature of pulsating heat pipe is kept in the range of 20℃-50℃.The startup time of the pulsating heat pipe with refrigerants can be shorter than 4 min,when heating power is in the range of 10W-100W.The startup time decreases with heating power.Thermal resistances of PHP with filling ratio 20.55% were obviously larger than those with other filling ratios.Thermal resistance of the PHP with R134a is much smaller than that with R404A and R600a.It indicates that the heat transfer ability of R134a is better.In addition,a correlation to predict thermal resistance of PHP with refrigerants was suggested.

The principle of primary spectrum pyrometry

In this paper, for the measured surface with the characteristics of continuous radiation, we put forward the general model of the spectral emissivity with non- dimensional wavelength. In the analysis process, based on the Taylor series expansion, we theoretically discuss the applicable conditions of the model. Further, introducing the concept of the non-correlative spectrum functions in colourometry, the principle of primary spectrum pyrometry is established. And the application of primary spectrum pyrometer is illustrated in a specific example.