Calculation of temperature and heat flux in quenched cylinders for different wetting processes

The cooling of pieces being quenched in evapourable fluids is mainly determined by the process of wetting, which is defined as the sequence of the three known cooling stages film boiling, nucleate boiling and convective heat transfer. All these determine the properties of the finished product. The effect of different wetting processes and heat transfer coefficients on the time-dependent distribution of temperature and heat flux in quenched cylinders was examined using numerical methods. Only transformation-free quenching was considered. When the three cooling stages simultaneouly take place on the sample's surface the radial heat fluxes are superimposed by high axial heat fluxes, which could not be pointed out experimentally before. The consequences may be great axial differences of structure and hardness, especially for steels with low hardenability, as well as residual stresses. The axial temperature gradients can be reduced by producing high wetting velocities. An optimum wetting process involves a very fast breakdown of the vapour envelope on the whole surface of the quenched piece.     

Effect of boundary conditions and workpiece geometry on residual stresses and microstructure in quenching process

In this study, the internal and residual stress states in quenched C60 steel cylinders are analyzed both numerically and experimentally in order to investigate the effects of boundary conditions (such as quench severity and temperature of quench bath) and specimen geometry. Specimen geometry has been analyzed by introducing a hole in a cylinder and varying hole diameter and its eccentricity. In the numerical analysis, the finite element method is applied and both temperature gradients and phase transformations are considered. Experiments include microstructural examination and X-ray measurements of residual stresses of the first kind. It has been found that the value of the convective heat transfer coefficient is very critical to obtain simulation results close to real ones. For instance, when a constant value obtained as the mean of a temperature dependent distribution is used for this parameter, residual stresses are seriously underestimated (up to 40%). The temperature of the quench bath affects directly the convective heat transfer coefficient. The lower the bath temperature, the higher are the resulting residual stresses. Under the same quenching conditions, if the diameter of the hole is greater than a critical value, a transition occurs from the shallow hardening case to the through hardening case, i.e., the residual stress distribution is reversed. On the other hand, for a constant hole diameter, if the eccentricity ratio reaches a critial value, a complex residual stress state results, i.e., compressive/tensile stress transition regions along the circumference are observed.     

Temperature and thermal stresses in work rolls during the hot rolling of strip

In this paper the solution of the unsteady, three-dimensional heat transfer in work rolls was derived by using Bessel functions and the δ-function and expressed by an infinite series. In this manner other problems of heat transfer in solid cylinders and hollow cylinders can also be calculated. The temperature profile of the work roll due to the distribution of the temperature in the axial direction can cause unregular pressure distribution between work roll and backup roll and can influence the quality of strip. Therefore, the thermal crowns must be considered at various moments during rolling. The thermal crown can be determined by using the FE-Method or others. The reason for the fire-cracking in the roll surface can be determined as the thermal shock load in the contact zone, in which the sharp compressive stresses lead to local plastic deformation. The local plastic deformations are followed by residual deformations. Therefore, residual tensile stresses occur in the cooling zone. On each revolution, the surface undergoes plastic strain in compression and in tension. The result is thermal fatigue. The fine network of cracks in the roll surface can result in a sharp stress concentration which is dangerous for the rolls loaded with a bending moment. The maximum tensile stresses due to the temperature distribution occur in the roll core, which usually do not lead to damages of the rolls.     

Roll cooling and its relationship to roll life

Combined experimental and numerical research has been conducted to investigate the roll cooling system used in steel rolling mills and its relationship to roll life. Roll cooling has been identified as a critical factor in the problems of excessive roll wear or spalling, which cause shortened roll life. A special laboratory apparatus resembling the cooling systems used in the steel mills has been developed to evaluate the corresponding heat transfer coefficients. These coefficients have then been utilized for numerical simulation of the rolling processes. In simulation, the thermal behavior of both the roll and the strip have been considered with emphasis on roll temperature and the induced cyclic thermal stresses. An understanding of the cyclic stress can be utilized to evaluate roll wear, and leads to reduction of the roll spalling, or to extension of the roll life by minimizing the cyclic stress or the resultant fatigue stress. As indicated by the present study, in order to minimize the cyclic or fatigue stresses, the roll should be subjected to uniform cooling, as the sharper the heat transfer coefficient distribution, the higher the thermal stress induced.     

薄板坯连铸结晶器铜板热/力行为

基于国内某钢厂CSP漏斗结晶器铜板结构,建立了考虑铜板水槽冷却水流动的薄板坯结晶器铜板三维热/力耦合计算模型,研究分析了典型连铸工艺下结晶器铜板水槽内冷却水的传热特点和铜板温度场与热应力场分布规律,并探讨了冷却水流速及铜板厚度对铜板热/力行为的影响。结果表明,铜板宽面热面与窄面热面最高温度均位于弯月面下约15 mm处,分别达436.5、379.2 ℃。宽面和窄面铜板的最大热应力均位于弯月面下方约25 mm处,分别达876.7、867.8 MPa。宽面铜板的热应力总体比窄面高且分布更为不均匀,螺栓处热面的热应力整体低于其两侧水槽处热面的热应力。增加冷却水流速、减小铜板厚度可减小铜板热面温度与热应力。将螺栓处冷却水缝延长到距结晶器下口30 mm处,可显著改善宽面铜板中下部横向温度分布的均匀性,使其热面横向最大温差减少约19.6 ℃。     

An experimental study on heat transfer process of multiple mist impinging jets

Mist jet impingement cooling is an enhanced heat transfer method widely used after the continuous galvanizing process.The key of a successful design and operation of the mist jet impingement cooling system lies in mastering heat transfer coefficients.The heat transfer coefficients of high temperature steel plates cooled with multiple mist impinging jets were experimentally investigated,and the effects of gas and water flow rates on heat transfer coefficients were studied.The test results illustrate that the gas flow rate has little effect on the mist heat transfer rate.It is also found that the water flow rate has a great impact on the heat transfer coefficient.When the water flow rate ranges from 0.96m3/h to 1.59 m3/h,an increase in the rate will produce a higher heat transfer coefficient with a maximum of 5650 W/(m2·K).Compared with the conventional gas jet cooling,the heat transfer coefficient of the mist jet cooling will be much higher,which can effectively strengthen the after-pot cooling.     

Realistic modelling and optimisation of steel section cooling process

Abstract

The cooling process in the manufacture of long steel products generates residual stresses and bending in the section. This initial state, arising from the cooling bed, influences the final residual stresses and bending at the end of the subsequent processes. Owing to the importance of the cooling process, this paper presents realistic modelling and optimisation using computational fluid dynamics (CFD) and finite element analysis. Computational fluid dynamics rendered it possible to accurately overcome two main problems common to previous cooling models: the realistic modelling of the heat transfer coefficient (especially important when modelling outdoor cooling beds because of the implications of forced convection) and the precise view factor modelling of the different section surfaces (useful when modelling a complex section). After decoupled CFD thermo‐analysis, the temperature record of each node in the section was loaded into the finite element stress displacement model. The relevant influence of steel phase transformation was considered applying a combined methodology, involving an ABAQUS user subroutine. Accordingly, accurate residual stresses and bending were obtained. After establishing the models, several strategies were analysed for reducing the residual stresses during the cooling process. Results were successfully validated with experimental data from structural section producers.     

Calculation of residual stresses in case-hardened SAE5115 steel cylinders

The development of stresses for five differently case-hardened SAE5115 steel cylinders with variable surface carbon mass contents c_S and carburization depths CD during single hardening are calculated. The carbon profiles and the retained austenite distributions in the near-surface material areas are approximated in a stepwise manner. Exemplarily, in the middle plane of cylinders with c_S = 0.5 % C (CD = 0.07 mm) and 1.1 % C (CD = 0.2 mm), the local axial stresses at the surface, at four near-surface points and in the core are described during the hardening process up to temperature balance. The influence of c_S and CD on the surface tangential residual stress values along the casing of the cylinders is outlined. Also the depths distributions of the tangential residual stresses in the middle plane are presented for differently carburized cylinders. At c_S = 1.1 % C = const. the distance of maximum compressive residual stresses beneath the surface as well as the thickness of the compressed surface and the distances with the largest tensile residual stresses increase with increasing CD.     

Dimensionless Cooling Performance Parameter for Characterization of Quench Media

The effect of varying thermal properties and boundary heat transfer coefficients on temperature profiles inside cylindrical quench probes was simulated during immersion cooling. The results of simulation indicated that, for assessment of the cooling performance of the quench media, the ratio of the quench probe diameter to its thermal conductivity should be less than 0.0005 m²K/W. A simple dimensionless cooling parameter (D ²CR/αΔT) was proposed to assess the cooling performance of quench media.     

Residual stresses in silicon carbide particulate reinforced aluminum composites

In metal matrix composites (MMCs) residual stresses are unavoidable during cooling from high temperature in fabrication or heat treatment because of the difference in the thermal expansion coefficients between the matrix and the reinforcement. In particle reinforced MMC the residual stresses have been proved to be hydrostatic in this study by both experiments and mathematical analysis. A very slight surface effect on the measured stresses was predicted in the case Cu Kα radiation was used. The residual stresses were determined to be tensile in the Al matrix and compressive in the reinforcement. A reduction in residual stress magnitudes of both the matrix and reinforcement was observed after the sample was cooled into liquid nitrogen and heated back to room temperature, which is believed to be caused by plastic deformation of the matrix in low temperature treatment.     

Heat Transfer During Quenching by Plate Roller Quenching Machine

For plate quenching on a roller quenching machine, heat transfer process is investigated. According to the practical online experiment of plate center temperature, average heat transfer coefficient under different conditions and temperature fields are analyzed by numerical simulation. The results show that, at the water temperature of 15 ℃, the instantaneous maximum quenching cooling rate is 17.6 ℃/s for the plate of 50 mm in thickness in roller quenching process. In the temperature range of 400-850 ℃, the maximum is 12.1 ℃/s. With the plate surface temperature decreasing, surface heat transfer coefficient increases at first, and reaches the maximum value of about 15 000 W/(m~2·K), and then decreases. The calculated heat transfer coefficients are applied to analyze plate temperature field of different thicknesses, and the difference between the calculated and measured temperature is less than 5%.     

小型H型钢超快冷“内并外扩”的有限元模拟

 超快速冷却对于H型钢的组织优化和性能提升具有重要的意义,冷却后的“内并外扩”是影响产品质量和生产稳定性的重要因素,也限制了超快速冷却工艺的推广和应用,在H型钢冷却过程中,换热系数是关键参数。为了研究换热系数对小型H型钢超快冷条件下“内并外扩”的影响,采用有限元模拟计算软件Abaqus建立了轧后冷却二维热力耦合模拟计算模型。考虑翼缘、腹板、R角处不同部位的冷却特点,将H型钢断面划分16个特定冷却特征区域并分别为其指定不同的换热系数,制定3个不同的冷却方案,分别进行模拟计算,得出温度场、应力场和上下翼缘宽度差,分析了温度场和应力场不均匀分布的特点。通过冷却试验模拟了小型H型钢轧后冷却过程,采用热成像仪获得冷却后的H型钢温度场。温度场与宽度差的计算结果与试验结果吻合良好。在此基础上分析了采用3种不同换热系数组合的冷却方案时上下翼缘横向、R角处纵向代表性特征截面上Mises应力与等效应变分布的规律,研究了R角处换热系数对翼缘扩并及上下翼缘宽度差的影响,发现R角处换热系数与上下翼缘宽度差具有线性关系,建立了描述其线性关系的数学模型。研究结果对于优化冷却方案以及提高小型H型钢超快速冷却的均匀性具有理论意义和参考价值。     

Influence of gases dissolved in cooling water on heat transfer during stable film boiling

Results of investigations concerning the determination of the influence of the water quality on the heat transfer of quenched hot metal surfaces are presented. With an immersion quenching device, tests have been carried out for various cooling water qualities. Apparently there was no correlation between the water quality and the cooling process (Leidenfrost temperature). High concentrations of dissolved gases yield stable vapour films (low Leidenfrost temperatures are measured). Salt displaces the dissolved gases from the water; the Leidenfrost temperature rises: the higher the salt concentration, the lower the gas concentration and, therefore, the higher the Leidenfrost temperature. If salt concentrations are high or the cooling water is degassed, the vapour film falls apart just after Immersion. An extended model considering the Influence of the gases allows the correlation of the water quality/salt concentration and the heat transfer/Leidenfrost temperature.     

Consequences of transformation plasticity on the development of residual stresses and distortions during martensitic hardening of SAE 4140 steel cylinders

Residual stresses and distortions developing during martensitic hardening of steel can be quantitatively determined by finite element calculations, if the underlying processes are adequately modelled and the materials and process data necessary are known. In this context also transformation plasticity effects have to be taken into account. Model calculations for SAE 4140 steel cylinders demonstrate the influence of these effects on the developing residual stresses. Using a special device which allows martensitic transformation under constant external loads, for SAE 4140 the transformation plasticity constant K = 4.2 · 10^?5mm²/N is determined. With this constant and assuming realistic heat transfer conditions, the development of residual stresses and distortions of SAE 4140 cylinders with a diameter of 30 mm and a length of 90 mm is modelled. The calculated results are in good agreement with experimental findings.     

Finite element simulation of quench hardening

In this study, an efficient finite element model for predicting the temperature field, volume fraction of phases and the evolution of internal stresses up to the residual stress states during quenching of axisymmetrical steel components is developed and implemented. The temperature distribution is determined by considering heat losses to the quenching medium as well as latent heat due to phase transformations. Phase transformations are modelled by discretizing the cooling cuves in a succession of isothermal steps and using the IT-diagrams. For diffusional transformations both Scheil's additivity method and Johnson-Mehl-Avrami equation are used, while Koistinen-Marburger equation is employed for martensitic transformation. Internal stresses are determined by a small strain elasto-plastic analysis using Prandtl-Reuss constitutive equations. Considering long cylinders, a generalized plane strain condition is assumed. The computational model is verified by several experimental measurements and by comparison with other known numerical results. Case studies are performed with St50, Ck45 and C60 type of solid and hollow steel components. The complete data and result sets provided for the verification examples establish a basis for benchmark problems in this field.     

A new method for evaluating cooling capacity of blast furnace cooling stave

The detailed process of the heat transfer of the cooling stave in blast furnace (BF) has been systematically analyzed and the simplified mathematical model was constructed based on heat transfer theory. Precise definitions of the cooling capacity, stable working slag thickness and safe working slag thickness were put forward so as to evaluate the cooling capacity of cooling stave systematically. The results show that 95% of heat is carried off by cooling water through convection and the heat taken away through convective heat transfer between furnace shell and atmosphere only account for 5%. The entire heat transfer process can be divided into four modules and the cooling system is divided into three parts. The cooling capacity φ is defined and function curve of temperature of cooling stave hot surface T_b with changes of brick thickness is drawn and the safe working area and stable working area are put forward.     

Water spray cooling of stainless and C-Mn steel

This paper describes laboratory cooling experiments of C-Mn and stainless steel with a water/air nozzle. Experiments included use of both the steady state and the transient experimental method. The heat transfer coefficient was calculated both analytically and by a numerical method. The heat transfer coefficient was evaluated as a function of steel surface temperature, water flux, material and water/air flow. It was found that by increasing the water flux the heat transfer coefficient also increased. The Leidenfrost point was shifted to higher temperatures. Increasing air flow was also found to increase the heat transfer coefficient. Maximum heat transfer coefficient was twice as large for the C-Mn steel as for the stainless steel. Comparison of the steady state and transient experimental method showed good agreement in the temperature range 200 – 500°C, and with a water flux of 2I/m²s. Above 500°C it was difficult to obtain stable conditions for the steady state experiments.     

Pool boiling cooling for melt spinning quench wheels

The production of rapidly quenched metal ribbons by melt spinning on a cylinder produces very high average heat fluxes through the cylinder. The problem of maintaining a low average casting surface temperature can be solved by boiling on the plain interior of the cylinder. An experimental, boiling cooled, amorphous iron alloy ribbon casting wheel was constructed to verify the concept and expand the available data on boiling heat transfer. Experiments were performed with water, near atmospheric pressure, in pools less than 0.03 m deep and at accelerations between 100 and 200 times earth gravity. Heat fluxes between 0.6 and 3.5 million W/m² were achieved. Heat transfer coefficients up to 0.1 million W/m² • K were measured. A loss of cooling occurred in a number of instances, at heat fluxes well below the predicted critical heat flux, and at heat flux conditions which were duplicated or exceeded in the remaining experiments. These conditions, possibly precipitated by local variations in the boiling heat transfer coefficient, are not considered to represent new boiling phenomena associated with high acceleration.     

On determining temperature dependent interfacial shear properties and bulk residual stresses in fibrous composites

The model of the preceding paper is applied to the analysis of interfacial sliding during thermal cycling in three titanium or titanium aluminide alloys reinforced by SiC fibers. The model is found to give an excellent account of the experimental measurements. By fitting the model to the data, values are obtained in all cases for the critical interfacial shear stress, τ₀ at room temperature. In two cases, values are also obtained for the bulk, axial residual stresses at room temperature, and the average of dτ₀/dT over the interval of temperature T between room temperature and the maximum temperature attained in the thermal cycling. The residual stresses are in good agreement with other measurements. In the third case, the residual stresses cannot be determined; but, if values for them are taken from other experiments, then the same average of dτ₀/dT can be determined. The values of τ₀ and the implied coefficient of friction are consistent in all cases with frictional sliding in graphitic layers in the carbon rich coatings on the SiC fibers.     

炉缸冷却壁对流换热系数计算及烘炉传热特性

 炉缸冷却壁冷却性能主要体现在冷却水与水管间的对流传热。因为工程上常用计算对流换热系数的经验公式不能满足不同的水流状态从而导致炉缸热应力分析误差较大，所以以某高炉炉缸结构为例，首先利用传热学准数方程推导出冷却水处于不同流动状态时对应的综合对流换热系数表达式，同时探讨了对流换热系数经验公式的适用范围；然后通过迭代计算推导出了冷却水处于层流状态下考虑衰减热阻时的综合对流换热系数表达式；最后对烘炉状态下炉缸侧壁传热模型进行瞬态传热与冷却分析，得到了微水烘炉甚至闭水烘炉的热工依据，可为初步制定高炉烘炉制度进行评估和完善。