Transverse Temperature Distribution Research Articles

A field study of temperature field distribution characteristics of flat steel box girder and its influential environmental factors

As one of the mainstream girder types of long-span bridges, the flat steel box girder (FSBG) under thermal action has been one primary concern for bridge engineers and researchers. This research presents a field study of the temperature field distribution characteristics of FSBG and its influential environmental factors. To achieve this, an acquisition equipment that comprises of thermometers and environmental sensors is applied to a prototype cable-stayed bridge under construction, in which the structural temperature field of FSBG and the surrounding environmental data are collected and analyzed thoroughly. The results indicate that the vertical temperature distribution (VTD) in certain time instants exhibits significant variations and the maximum vertical temperature gradient can reach up to 27.9 °C. Despite of this, it is found that the VTD of FSBG can be covered by several current standards such as AASHTO standard and New Zealand standard. As for the transverse temperature distribution (TTD), it is found that both the variation and temperature difference of TTD in certain time instants are considerable, especially at the deck surface, which far exceed those of the TTD prescribed in current standards. This indicates that the TTD of FSBG should be seriously considered during the bridge design phase. Furthermore, the field study reveals that the wind speed has negative effect on the structural temperature of FSBG (when the air temperature is less than that of FSBG), while the solar radiation exerts positive effect on the structural temperature of FSBG. The outcome of this study can provide valuable references for thermal design, monitoring and control of long-span bridges employing FSBGs as bridge main girder.

Analytical Thermal Analysis of Radially Functionally Graded Circular Plates with Coating or Undercoating under Transverse and Radial Temperature Distributions

This study aims to provide analytical solutions for circular plates coated or undercoated with functionally graded materials (FGMs) having Young’s modulus functionality through the radius. The circular plates are subjected to thermal loads in radial and thickness directions. Because of the uncoupled stretching–bending problem of the radially FGM circular plate, the bending equilibrium equations in terms of displacements of the FGM-coated or -undercoated circular plates with Young’s modulus based on the power–law function were established individually. General solutions for the homogeneous portion or FGM ring of the radially FGM-coated or -undercoated circular plate were developed separately. Subsequently, analytical thermal solutions for the radially FGM-coated or -undercoated circular plate were evaluated by solving the simultaneous boundary and continuity conditions equations. The analytical results were validated by comparing them with finite element solutions. When degenerated, they coincided with those of the homogeneous circular plate in the literature, enhancing the obtained solutions’ reliability. These analytical solutions provide valuable insights into the plates’ responses and expand the understanding of their mechanical behaviors under thermal loads. Furthermore, the effects of the FGM thickness, the material index, and the thermal loading conditions on the mechanical behaviors were under investigation. This parameter study offers valuable perspectives into the influence of these factors on the plate’s structural response and aids in the optimization and design of FGM-coated or -undercoated circular plates.

Transverse Thermal Behavior of a Hot‐Rolled Strip During the Edge‐Induction‐Heating Process

To obtain the transverse temperature distribution of running strips under C‐type edge induction heaters during the hot‐rolling process, a coupled electromagnetic–thermal finite‐element model is established using COMSOL, in which the electromagnetic and temperature distributions regularity with various process parameters are systematically obtained. It is shown in the results that the temperature increase is directly proportional to the frequency and current and inversely proportional to the thickness. Meanwhile, the edge temperature drop can be rapidly compensated for using an edge heater, but it also leads to the appearance of a “cat‐ear” high‐temperature zone at the edge; thus, the transverse temperature uniformity cannot be guaranteed. To improve the temperature uniformity of the running strip, a magnetic shield plate is designed to weaken the effect of the cat ear, and the effects of the size and installation position of the shielding plate on the temperature distribution are analyzed. The standard deviation and uniformity of the temperature are used to determine the uniformity of the transverse temperature, and the optimal parameter combination mode of the magnetic shielding amounts is obtained, which can provide a reference for optimizing the heating process at the edge of the strip under moving conditions.

Experimental study on temperature distribution beneath tunnel ceiling under the condition of transverse double fire sources

The maximum ceiling temperature and transverse temperature distribution under the condition of transverse double fire sources are experimentally and theoretically studied. A series of experiments were carried out in a scaling tunnel (1:20) to investigate the effects of heat release rates (HRR) and distance of the two fire sources (S) on the maximum temperature and the transverse temperature distribution beneath tunnel ceiling. Results shown that when the fire sources were set close to each side of the wall, the location of the maximum temperature was found at the middle ceiling of the tunnel. A inverted “N” shape ceiling temperature distribution, with the ceiling temperature firstly decreased and increased and then decreased, was found along the half-cross section of the tunnel. New maximum and transverse ceiling temperature models were developed with considering the distance and heat release rate of the two fire sources, and considering the air entrainment restrictions by the sidewall. New findings of this work can provide a significant reference for the risk assessment of tunnel fires with two transverse fire sources.

Natural Convection Modeling in a Solar Tower

Objectives: We present in this study a modeling of thermal laminar convection airflow in a solar tower. Methods: To formulate with precision, the boundary conditions of the solar chimney model chosen, the Cartesian equations are transformed into hyperbolic coordinates. An orthogonal grid is elaborated. It then makes it possible to draw up the diagrams of physique and calculation fields. The computer code uses the heat equation, the vorticity, and the stream function formalism as the boundary conditions for pressure are difficult to set. We use the Boussinesq approximation, which consists in considering that the density (r) of the fluid varies only in the term of the gravity forces, whose variations with temperature, assumed to be linear, generate natural convection. These variations are then translated into an equation of state which relates density to temperature. The system of dimensionless equations is solved by using an intégro-interpolation method referring to finite differences scheme. Findings: The solutions obtained from the dimensionless equations enabled us to determine the space evolution parameters (temperatures and velocities) in the tower according to the Rayleigh number. The fluid temperature and velocity evolution in the collector increase when one moves in the direction of radius decrease. The fluid temperature evolution in the chimney showed that the highest temperature is located at the chimney base while we obtained a parabolic profile of the transverse temperature distribution within the chimney. Finally, the evolution of the fluid velocity in the chimney showed that there was a preferred zone for turbine installation. Novelty : The use of dimensionless geometric parameters is unique and in general, the approach adopted in this paper differs from that encountered in the literature.

Experimental study on wall fire behavior produced by n-heptane pools with different aspect ratios and orientations in arched tunnel

A series of experiments were carried out in an arched tunnel (50 m long, 2 m wide, 2.3 m high). Under the influence of aspect ratios (1, 2 and 3) of oil pool and pool orientation relative to sidewall, the flame length and temperature distribution under the arched ceiling was studied. Oil pools with 3 aspect ratios were placed in the center as a control group. Results show that the pool orientation relative to sidewall is a decisive factor affecting the fire behavior. The heat release rate decreases with the aspect ratio increases. According to the physical meaning of flame extending along arched ceiling, the heat release rate is modified and prediction formula of transverse flame length under arched ceiling is obtained. The transverse temperature decay rate of different sections is different because of buoyant force. By modifying the transverse travelling distance, the prediction formula of the transverse temperature distribution is obtained, and the prediction error is within ±15%.

Experimental study on combustion parameters and temperature distribution of linear fire under different oxygen concentration in tunnel

Many cables are placed in the underground utility tunnel, which are with greater fire hazards. Once fire occurs in an enclosed tunnel, thermal radiation may ignite the adjacent cables, which will cause cable fire and further expanding of fire scale, and oxygen will be consumed over time. Thus, it's important to investigate cable fire under low oxygen concentration. In this paper, a fire experiment has carried out in a reduced-scale enclosed tunnel with different heights of linear fire near the side wall. The combustion parameters, as well as transverse temperature distribution and maximum ceiling temperature rise under different oxygen concentration are investigated. Based on oxygen consumption calorimetry, the combustion efficiency and heat release rate of each fire source can be obtained. And two formulas to predict transverse temperature distribution and temperature rise under ceiling are proposed based on dimensionless analysis. Results show that different combustion parameters changing under varies oxygen concentrations, two temperature peaks exist in the cross section and the highest temperature is directly above the fire source. Conclusions are given to provide references in fire protection work in utility tunnel.

Effect of lateral smoke extraction on transverse temperature distribution and smoke maximum temperature under ceiling in tunnel fires

This paper studied the effect of lateral smoke extraction on the transverse temperature distribution and maximum smoke temperature beneath the ceiling. The experiments were conducted in a reduced model tunnel (1:8). In the experimental study of optimal aspect ratio of the smoke extraction vent, a series of experimental conditions were considered. Keeping the same area of vents, four kind aspect ratios were set (n = 1, 2, 3, and 4). In experiment investigation of ceiling maximum smoke temperature, under the best vent aspect ratio n = 3, four fire heat release (50 kW, 60 kW, 70 kW, and 80 kW) rates were considered. The experimental results showed that the lateral smoke extraction system will affect the transverse temperature distribution, the transverse temperature distribution curve shows good stratification phenomenon, and the maximum temperature point will offset to the direction of the lateral extraction vent. The data of the maximum temperature under different test conditions were analyzed, and the influence factors of lateral smoke extraction were considered. Finally, the correlation of the maximum smoke temperature under the influence of lateral smoke extraction was proposed.

Pennes\u2019 bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation

The objective of this study was to compare three different heat transfer models for radiofrequency ablation of in vivo liver tissue using a cooled electrode and three different voltage levels. The comparison was between the simplest but less realistic Pennes’ equation and two porous media-based models, i.e. the Local Thermal Non-Equilibrium (LTNE) equations and Local Thermal Equilibrium (LTE) equation, both modified to take into account two-phase water vaporization (tissue and blood). Different blood volume fractions in liver were considered and the blood velocity was modeled to simulate a vascular network. Governing equations with the appropriate boundary conditions were solved with Comsol Multiphysics finite-element code. The results in terms of coagulation transverse diameters and temperature distributions at the end of the application showed significant differences, especially between Pennes and the modified LTNE and LTE models. The new modified porous media-based models covered the ranges found in the few in vivo experimental studies in the literature and they were closer to the published results with similar in vivo protocol. The outcomes highlight the importance of considering the three models in the future in order to improve thermal ablation protocols and devices and adapt the model to different organs and patient profiles.

Numerical study on temperature distribution of tunnel structure in fires

A series of simulations with different heat release rates (HRRs) are conducted in a full-scale horseshoe-shaped tunnel model. Thermocouples are arranged in 21 cross-sections of the tunnel to obtain entire temperature field. The prediction formulas of the ceiling maximum temperature and the longitudinal temperature attenuation beneath the ceiling are obtained, which are consistent with the model of Albert and Gong. It is found that the dimensionless transverse temperature rise distribution under the semicircular ceiling conforms to the Boltzmann curve, but the coefficients of the fitting formula are different for the near field zone and the far field zone. Transverse temperature distribution in the sidewall part can be regarded as constant, which is equal to the temperature at the bottom of semicircular ceiling in most engineering applications. A prediction model is established to estimate the temperature of each position of tunnel structure. It provides a more accurate and detailed temperature field prediction method for tunnel fire prevention and structural damage research.

Transient 3D conjugate heat transfer simulation of a rectangular GOX–GCH4 rocket combustion chamber and validation

This paper aims to predict the transient temperature fields of rocket combustion chambers. This is important for design and lifetime estimation. A thermally coupled simulation (conjugate heat transfer) model was developed and validated using a combustion chamber experiment with rectangular cross-section and the propellant combination gaseous oxygen–methane. The simulation is based on a thermal finite element model of the structure, Reynolds-averaged Navier–Stokes simulations of nine cooling channel flows and a Reynolds-averaged Navier–Stokes simulation with flamelet extension of the hot-gas flow. A pseudo-transient, implicit Dirichlet–Neumann scheme is used for calculating the equilibrium of structure and fluids. A comparison with experiment shows good agreement with the axial, vertical and transverse temperature distribution in the structure, the transient behavior and the wall heat flux through the cooling channels. It is shown that wall functions in the coolant domains can efficiently decrease the computational effort.

Experimental Study of the Temperature Distribution in CRTS-II Ballastless Tracks on a High-Speed Railway Bridge

To study the temperature distribution in the China Railway Track System Type II ballastless slab track on a high-speed railway (HSR) bridge, a 1:4 scaled specimen of a simply-supported concrete box girder bridge with a ballastless track was constructed in laboratory. Through a rapid, extreme high temperature test in winter and a conventional high temperature test in summer, the temperature distribution laws in the track on the HSR bridge were studied, and the vertical and transverse temperature distribution trend was suggested for the track. Firstly, the extreme high temperature test results showed that the vertical temperature and the vertical temperature difference distribution in the track on HSR bridge were all nonlinear with three stages. Secondly, the extreme high temperature test showed that the transverse temperature distribution in the track was of quadratic parabolic nonlinear form, and the transverse temperature gradient in the bottom base was significantly higher than that of the other layers of the track. Thirdly, the three-dimensional temperature distribution in the track on HSR bridge was a nonlinear, three-stage surface. Furthermore, similar regularities were also obtained in the conventional high temperature test, in which the temperature span ranges were different from those of the extreme high temperature test. In addition, the conventional high temperature test also showed that under the natural environment conditions, the internal temperature gradient in the track layers changed periodically (over a period of 24 h).

Experimental study on ceiling smoke temperature distributions in near field of pool fires in the subway train

Several existing studies have been performed on the fire characteristics of traditional tunnel and enclosure models; however, these findings may not be applicable to a subway train with a special confined structure. Therefore, to investigate the smoke temperature distributions under conditions involving different fire locations and door statuses, a set of experiments were conducted by using a reduced-scale subway train model. The results indicated that the longitudinal and transverse temperature distributions correspond to the exponential decay law, although the transverse temperature does not exhibit a regular distribution under certain conditions. Furthermore, the previously developed empirical models were not applicable to the subway train considered in this work. Consequently, empirical models similar to those involving the exponential function were developed to predict both the longitudinal and transverse smoke temperature distributions. The corresponding results exhibited a reasonable fit with the experimental data. The powers of the exponential functions were noted to be proportional to the dimensionless heat release rate, with values of 0.4 and 0.3 for the longitudinal and transverse smoke temperature distributions, respectively. The research findings and empirical models provide a reference for the fire risk assessment of subway train or other similar frameworks.

Experimental study on temperature distribution beneath an arced tunnel ceiling with various fire locations

This paper attempts to study experimentally the impact of fire location on the temperature distribution of thermal plume induced by fire under an arced ceiling. A series of experiments considering different pool sizes and fire locations were carried out in an arced tunnel-like structure. Two fuels (n-heptane and ethanol) were used to generate pool fires with various fire sizes. Results demonstrated that the flame was deviated from the vertical direction when the fire was close to the sidewall, meanwhile, the heat release rate (HRR) increased significantly. Consequently, the flame propagation length was enhanced due to the constraint effect, while its variation was not significant when the HRR was not large enough. The transverse ceiling temperature distribution was predicted using correlating the HRR and the vertical height above the pool for a classical model. Also, a correlation was given to calculate the maximum excess temperature beneath the centerline of the arced ceiling, and it gave a relatively good prediction for the maximum temperatures of the weak plume. Note that this correlation is only available for the ethanol fires. Nonetheless, it is necessary to further study the temperature distribution of strong plumes beneath arced ceilings with constraint effect.

Experimental study on the effect of ceiling mechanical smoke extraction system on transverse temperature decay induced by ceiling jet in the tunnel

This paper focused on studying the transverse temperature distributions induced by ceiling jet under the effect of ceiling mechanical smoke extraction system. Many test conditions were investigated by conducted reduced tunnel model experiments. These changes in fire heat release rates (HRRs) and ceiling mechanical smoke extraction velocities were all taken into consideration. The longitudinal and transverse temperature distributions beneath the ceiling were also compared in this paper, it was found that the transverse temperature decays more slowly than the longitudinal temperature without ceiling extraction. In order to reveal the effect of ceiling mechanical smoke extraction system on the transverse temperature distributions induced by ceiling jet in a tunnel, the attenuation rate of transverse temperature increases as the increasing ceiling mechanical smoke extraction velocities. The modified model for transverse temperature attenuation under the ceiling induced by tunnel fire with different ceiling mechanical smoke extraction velocities was developed by modified the characteristic radius. And the dimensionless transverse temperature decay mainly shows a piecewise function.

Experimental investigation on longitudinal and transverse temperature distribution in a horseshoe shaped tunnel fire

The longitudinal temperature distribution in a tunnel fire has been investigated wildly as the classical problem, while the transverse temperature distribution, especially sidewall temperature, has not received adequate attention. In this article, a 1:3.7 reduced scale horseshoe shaped model tunnel constructed by concrete was established, in which a series of comparative burning experiments were carried out to investigate the longitudinal and transverse temperature distributions. The quantitative trends of smoke longitudinal and transverse temperature including sidewall temperature were observed and analyzed. The major conclusions are summarized as follows: The temperature rise under the ceiling first decreases sharply with longitudinal distance from fire source, followed by a slight decrease, which can be well predicted by Gong’s model of a sum function of two exponential equations. The transverse temperature rise in fire zone is dominated by two different heat transfer regions: convection region (angle below 45° or dimensionless angle below 0.8) and radiation region (angle beyond 45° or dimensionless angle beyond 0.8). The inclination angle is the angle between center line of tunnel and connection line of thermocouple with fire source. The transverse temperature drops with angle in convection region and rises in radiation region, which can be well described by proposed empirical exponential functions. The non-monotonic variation trend of transverse temperature distribution in fire zone is a result of competition between convection of hot smoke and radiation of fire source. All these results are significantly important for fire safety design of tunnel and fire hazard evaluation of tunnel fire.

Experimental study on liquid fire behavior at different effective ceiling heights in a full-size simulated cargo compartment

When a fire occurs in an aircraft cargo compartment, the fire plume will rise from a different location, intermittently or continuously impact the ceiling, and form a ceiling jet flame at varying heights. Meanwhile, the low-pressure environment within the cargo compartment has a great influence on flame height and high-temperature zone, which could lead to the violent development of ceiling jet fire. Based on this discussion, a series of square oil pan fires were conducted in a full-size cargo compartment located in Kangding airport (altitude 4250 m, atmospheric pressure 61 kPa). Fire behaviors, such as burning rate, flame temperature, flame heights, and smoke gas temperature distribution beneath the ceiling, were measured and analyzed. The experimental results show that as the effective ceiling height decreases, the burning rate of 30 cm square pan fires grows, with a sharp change in the low-pressure environment (50 kPa), where flames impinges on the ceiling. For 20-cm square pan fires, the burning rate at 50 kPa has the same trend with 30 cm, at 75 kPa looks like a parabolic plot, and at 101 kPa shows a continuous dropping. The centerline flame temperature decreases slowly along the axis when the fire occurs at higher height above the floor. Considering the influence of ambient pressure, effective ceiling height, and oil pan size, an empirical correlation for the ceiling transverse smoke temperature distribution is proposed by modifying the current models.

Experimental investigation on transverse ceiling flame length and temperature distribution of sidewall confined tunnel fire

This paper presents an experimental investigation on the transverse ceiling flame length and the temperature distribution of a sidewall confined tunnel fire. The experiments were conducted in a 1/6th scale model tunnel with the fire source placed against the sidewall, 0m, 0.17m and 0.35m above the floor, respectively. Experiments of fire against a wall without a ceiling, 0.35m above the floor in a large space, were also conducted as a control group. Results shows that for small heat release rate (HRR), the flame is lower than the ceiling and extends along the sidewall. With the increase of HRR and elevation of burner height, the flame gradually impinges on the ceiling and spreads out radially along it. The flame impingement condition and the flame shapes of the wall fire with and without ceiling are presented. From the viewpoint of the physical meaning of flame impinging on the ceiling, the horizontal flame length should be a function of the unburned part of the fuel at the impinging point. Based on the proportional relation between the flame volume and HRR, the effective HRR (Qef) at the ceiling is determined and the effective dimensionless HRR, Q*ef is defined to correlate the horizontal ceiling flame length. Additionally, predictive correlations of transverse ceiling temperature distribution are proposed for the continuous flame region, the intermittent flame region and the buoyant plume region under the ceiling, respectively.

Temperature profile of fire-induced smoke in node area of a full-scale mine shaft tunnel under natural ventilation

This paper investigated ceiling temperature profile of fire-induce smoke in the common node area of tunnels. The experiments were conducted in a full-scale mine shaft tunnel under natural ventilation with the node area consisted of a straight tunnel and two curved tunnels. Maximum ceiling temperature above the fire, transverse ceiling temperature along the elliptic ceiling and longitudinal ceiling temperature along the main and branch tunnels were measured by K-type thermocouples or thermometric cable. Dimensionless expression for predicting transverse and longitudinal ceiling temperature distribution was proposed based on previous models. Normalized expression of longitudinal temperature decay coefficients were correlated as well by taking the heat release rate and transverse fire locations under the elliptic ceiling into account. Then the results calculated by the proposed formula were compared with the experimental measured maximum ceiling temperature along the main tunnel and shows good agreement. Finally, effects of vertical wall and ceiling height on temperature decay trend in branch tunnels were investigated by analyzing the accumulation and descendant of smoke in front of the portals based on measured temperature data.

Experimental study on longitudinal and transverse temperature distribution of sidewall confined ceiling jet plume

This paper investigates the longitudinal and transverse temperature profiles of a strong plume impinging flow, induced by a turbulent porous gas burner impinging on the sidewall confined ceiling of a long-narrow tunnel-like structure. A series of model scale experiments were conducted for fires against a tunnel sidewall with increasing vertical burner heights (0, 0.17 and 0.35m), 8 different HRRs (heat release rate) from 15.94 to 106.28kW were used. Measurements of the vertical temperature profiles against the sidewall and radial horizontal temperature profiles under the ceiling are presented. Results show that for the strong impingement plume, the temperatures at the impingement point can be well correlated by the three-regime of buoyant plume, intermittent flame and continuous flame. The horizontal temperature profiles under the ceiling show obviously asymmetric. It is confirmed that the characteristic length scale of plume radius at ceiling level is sufficiently applicable for predicting the ceiling excess temperatures of strong plume impingement flow, and the correlations of the ceiling excess temperature in both transverse and longitudinal directions are proposed and validated by comparing them with previous research.