Study on the Transient Characteristics of the Sensor Tube of a Thermal Mass Flow Meter

2003 ◽  
Author(s):  
Dong Kwon Kim ◽  
Il Young Han ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Numerical Model ◽  
Response Time ◽  
Mass Flow ◽  
Numerical Solutions ◽  
Transient State ◽  
Experimental Results ◽  
Transient Heat Transfer ◽  
Thermal Mass ◽  
Proposed Model

Thermal mass flow meters (TMFMs) are most widely used for measuring mass flow rates in the semiconductor industry. A TMFM should have a short response time in order to measure the time-varying flow rate rapidly and accurately. Therefore, it is important to study transient heat transfer phenomena in the senor tube of a TMFM. Many models have been presented by previous investigators. But most of them focused on steady heat transfer phenomena, so it is impossible to analyze transient heat transfer phenomena in the sensor tube using previous models. Furthermore, it is impossible to predict the response time using results from previous research works. In the present work, a simple numerical model for transient heat transfer phenomena of the sensor tube of a TMFM is presented. The proposed model treats the fluid region and the tube region separately. Numerical solutions for the tube and fluid temperatures in a transient state are obtained using the proposed model and compared with experimental results to validate the proposed model. Based on numerical solutions, heat transfer mechanism in a transient state in the sensor tube is explained. A correlation for predicting the response time of a sensor tube is also presented. The functional form of the correlation is obtained using the scale analysis and coefficients appearing in the correlation are obtained by the proposed numerical model. The correlation is verified by experimental results. Using the proposed correlation, physical meaning and characteristics of the response time of the sensor tube are presented.

Modeling Transient Heat Transfer Through the Skin and Superficial Tissues—1: Surface Insulation

1986 ◽  
Vol 108 (2) ◽  
pp. 183-188 ◽  
Author(s):  
D. A. Hodson ◽  
G. Eason ◽  
J. C. Barbenel
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Heat Transfer ◽  
Transient Problem ◽  
Finite Slab ◽  
Infinite Slab ◽  
Flow Through ◽  
Superficial Tissues

Two models of transient heat transfer through the skin and superficial tissues are presented. One model comprises a finite slab and semi-infinite slab, representing the epidermis and subdermal tissues, respectively, and a heat-generating interface representing the thermal effect of blood flow through the dermis. A model is also considered where the three tissue regions are represented more conventionally by three finite slabs. A transient problem arising from surface insulation is examined and analytical solutions derived from the first model are compared with numerical solutions derived from the second.

Experimental and Numerical Impingement Heat Transfer in an Airfoil Leading-Edge Cooling Channel With Crossflow

2007 ◽  
Author(s):  
M. E. Taslim ◽  
D. Bethka
Keyword(s):  
Heat Transfer ◽  
Mass Flow ◽  
Convective Heat Transfer Coefficient ◽  
Internal Heat ◽  
Leading Edge ◽  
Impinging Jet ◽  
Suction Side ◽  
Experimental Results ◽  
Transfer Coefficients ◽  
Impingement Heat Transfer

To enhance the internal heat transfer around the airfoil leading-edge area, a combination of rib-roughened cooling channels, film cooling and impingement cooling is often employed. Experimental data for impingement on various leading-edge geometries are reported by these and other investigators. Effects of strong crossflows on the leading-edge impingement heat transfer, however, have not been studied to that extent. This investigation dealt with impingement on the leading-edge of an airfoil in the presence of crossflows beyond the crossflow created by the upstream jets (spent air). Measurements of heat transfer coefficients on the airfoil nose area as well as the pressure and suction side areas are reported. The tests were run for a range of axial to jet mass flow rates (Maxial/Mjet) ranging from 1.14 to 6.4 and and jet Reynolds numbers ranging from 8000 to 48000. Comparisons are also made between the experimental results of impingement with and without the presence of crossflow and between representative numerical and measured heat transfer results. It was concluded that the presence of the external crossflow reduces the impinging jet effectiveness both on the nose and side walls, even for an axial to jet mass flow ratio as high as 5, the convective heat transfer coefficient produced by the axial channel flow was less than that of the impinging jet without the presence of the external crossflow, and the agreement between the numerical and experimental results was reasonable with an average difference ranging from −8% to −20%.

Experimental and Numerical Impingement Heat Transfer in an Airfoil Leading-Edge Cooling Channel With Cross-Flow

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. E. Taslim ◽  
D. Bethka
Keyword(s):  
Heat Transfer ◽  
Mass Flow ◽  
Convective Heat Transfer Coefficient ◽  
Cross Flow ◽  
Internal Heat ◽  
Leading Edge ◽  
Impinging Jet ◽  
Experimental Results ◽  
Transfer Coefficients ◽  
Impingement Heat Transfer

To enhance the internal heat transfer around the airfoil leading-edge area, a combination of rib-roughened cooling channels, film cooling, and impingement cooling is often employed. Experimental data for impingement on various leading-edge geometries are reported by these and other investigators. The effects of strong cross-flows on the leading—edge impingement heat transfer, however, have not been studied to that extent. This investigation dealt with impingement on the leading edge of an airfoil in the presence of cross-flows beyond the cross-flow created by the upstream jets (spent air). Measurements of heat transfer coefficients on the airfoil nose area as well as the pressure and suction side areas are reported. The tests were run for a range of axial to jet mass flow rates (Maxial∕Mjet) ranging from 1.14 to 6.4 and jet Reynolds numbers ranging from 8000 to 48,000. Comparisons are also made between the experimental results of impingement with and without the presence of cross-flow and between representative numerical and measured heat transfer results. It was concluded that (a) the presence of the external cross-flow reduces the impinging jet effectiveness both on the nose and sidewalls; (b) even for an axial to jet mass flow ratio as high as 5, the convective heat transfer coefficient produced by the axial channel flow was less than that of the impinging jet without the presence of the external cross-flow; and (c) the agreement between the numerical and experimental results was reasonable with an average difference ranging from −8% to −20%.

PREDICTION OF CONVECTIVE HEAT TRANSFER OF NANOFLUIDS BASED ON FRACTAL-MONTE CARLO SIMULATIONS

2013 ◽  
Vol 24 (01) ◽  
pp. 1250090 ◽  
Author(s):  
BO-QI XIAO ◽  
GUO-PING JIANG ◽  
YI YANG ◽  
DONG-MEI ZHENG
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Solutions ◽  
Probability Model ◽  
Average Diameter ◽  
Physical Mechanisms ◽  
Proposed Model

With the consideration of the Brownian motion of nanoparticles in fluids, the probability model for the size of nanoparticles and the model for convective heat transfer of nanofluids are derived based on the fractal character of nanoparticles. The proposed model is expressed as a function of the size of nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of base fluids, fractal dimension of nanoparticles and the temperature, as well as the random number. It is found that the convective heat flux of nanofluids decreases with increasing of the average diameter of nanoparticles. This model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal geometry theory are performed. Every parameter of the proposed formula on convective heat transfer of nanofluids has clear physical meaning. So the proposed model can reveal the physical mechanisms of convective heat transfer of nanofluids.

scholarly journals Numerical Model of Radical Photopolymerization Based on Interdiffusion

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuhei Yoshida ◽  
Yosuke Takahata ◽  
Shuma Horiuchi ◽  
Hiroyuki Kurata ◽  
Manabu Yamamoto
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Model ◽  
Reaction Rate ◽  
Beam Propagation Method ◽  
Reaction Model ◽  
Experimental Results ◽  
Hologram Recording ◽  
Elementary Reactions ◽  
Proposed Model ◽  
And Diffusion

An accurate reaction model is required to analyze the characteristics of photopolymers. For this purpose, we propose a numerical model for radical photopolymerization. In the proposed model, elementary reactions such as initiation, propagation, and termination are considered, and we assume interdiffusion for each component in the material. We analyzed the diffraction characteristics of a radical photopolymer based on the proposed interdiffusion model with the beam propagation method. Moreover, we also performed hologram-recording experiments and evaluated the diffraction characteristics of the photopolymer medium. By comparing the numerical and experimental results, medium parameters such as reaction rate and diffusion coefficient can be estimated. We confirmed that the interdiffusion model can reproduce the experimental results and showed that the medium parameters affect the diffraction characteristics.

The Effect of Thermal Barrier Coating Surface Temperature on the Adhesion Behavior of CMAS Deposits

2020 ◽  
Author(s):  
Robert A. Clark ◽  
Nicholas Plewacki ◽  
Pritheesh Gnanaselvam ◽  
Jeffrey P. Bons ◽  
Vaishak Viswanathan
Keyword(s):  
Heat Transfer ◽  
High Pressure ◽  
Surface Temperature ◽  
Mass Flow ◽  
Experimental Results ◽  
Thermal Barrier ◽  
Back Side ◽  
Surface Temperatures ◽  
The Impact ◽  
Side Flow

Abstract The interaction of thermal barrier coating’s surface temperature with CMAS (calcium magnesium aluminosilicate) like deposits in gas turbine hot flowpath hardware is investigated. Small Hastelloy X coupons were coated in TBC using the air plasma spray (APS) method and then subjected to a thermal gradient via back-side impingement cooling and front-side impingement heating using the High Temperature Deposition Facility (HTDF) at The Ohio State University (OSU). A 1-D heat transfer model was used to estimate TBC surface temperatures and correlate them to intensity values taken from infrared (IR) images of the TBC surface. TBC frontside surface temperatures were varied by changing back-side mass flow (kept at a constant temperature), while maintaining a constant hot-side gas temperature and jet velocity representative of modern commercial turbofan high-pressure turbine (HPT) inlet conditions (approximately 1600K and 200 m/s, or Mach 0.25). In this study, Arizona Road Dust (ARD) was utilized to mimic the behavior of CMAS attack on TBCs. To identify the minimum temperature at which particles adhere, the back-side cooling mass flow was set to the maximum amount allowed by the test setup, and trace amounts of 0–10 μm ARD particles were injected into the hot-side flow to impinge on the TBC surface. The TBC surface temperature was increased through coolant reduction until noticeable deposits formed, as evaluated through an IR camera. Accelerated deposition tests were then performed where approximately 1 gram of ARD was injected into the hot side flow while the TBC surface temperature was held at various points above the minimum observed deposition temperature. Surface deposition on the TBC coupons was evaluated using an infrared camera and a backside thermocouple. Coupon cross sections were also evaluated under a scanning electron microscope for any potential CMAS ingress into the TBC. Experimental results of the impact of surface temperature on CMAS deposition and deposit evolution and morphology are presented. In addition, an Eulerian-Lagrangian solver was used to model the hot-side impinging jet with particles at four TBC surface temperatures and deposition was predicted using the OSU Deposition model. Comparisons to experimental results highlight the need for more sophisticated modeling of deposit development through conjugate heat transfer and mesh morphing of the target surface. These results can be used to improve physics-based deposition models by providing valuable data relative to CMAS deposition characteristics on TBC surfaces, which modern commercial turbofan high pressure turbines use almost exclusively.

Transient Wax Gel Formation Model for Shut-In Subsea Pipelines

2009 ◽  
Author(s):  
Chiedozie Ekweribe ◽  
Faruk Civan
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Carbon Number ◽  
Transient State ◽  
Transient Heat Transfer ◽  
Gel Formation ◽  
Unsteady State ◽  
Formation Model ◽  
Subsea Pipeline ◽  
Subsea Pipelines

Physics of wax gel formation during shut-in is analyzed and described over a cross-section of a typical subsea pipeline. Two regions are identified during this process: the liquid and gel regions. Phase transition is assumed to occur at the liquid-gel interface. Unsteady-state heat and mass transfer models are proposed for each region. Two diffusion streams are evaluated: the dissolved wax molecules moving from the pipe center towards the wall due to temperature gradient and subsequently concentration gradient and the wax molecules diffusing from the liquid-gel interface into the gel deposit. This model is essentially the modification of the model given by Bhat et al [1] which considered transient heat transfer and neglected mass transfer of wax molecules through the gel deposit and the model by Singh et al [2] which considered transient mass transfer of molecules with carbon numbers higher than the critical carbon number (CCN) necessary for wax diffusion into gel deposit but did not consider transient heat transfer effects during the cooling process. This paper presents a transient-state formulation circumventing the limitations of these previous models and better represents the true cooling and gelation process occurring in a shut-in subsea pipeline filled with waxy crude.

Numerical Investigation of Heat Transfer and Cooling Effectiveness Within a LPT-Vane Cascade and its Comparison to Experimental Results

2012 ◽  
Author(s):  
Annette Beuermann ◽  
Andreas Pahs ◽  
Stefan Rochhausen
Keyword(s):  
Heat Transfer ◽  
Mass Flow ◽  
Guide Vane ◽  
Numerical Data ◽  
Secondary Flows ◽  
Experimental Results ◽  
Cooling Effectiveness ◽  
Flow Angle ◽  
Film Cooling Effectiveness ◽  
Good Agreement

Gaps between stationary and rotating parts in turbines have to be fed with cooling air to keep metal temperatures below material limits. Reducing the coolant mass flow and analysing its impact on the flow field concerning aerodynamic and thermal data were the objectives of experiments, performed within the European research project AITEB. As part of this project, measurements of cooling effectiveness and heat transfer on the endwall of a low pressure turbine nozzle guide vane were performed at a low speed cascade wind tunnel at DLR Göttingen. Higher cooling mass flow rates increase secondary flows and subsequently heat transfer whilst metal temperatures are reduced due to larger coverage with coolant. It was also shown that heat transfer varies significantly with different flow angles. According to the experimentally investigated flow fields numerical studies were performed using the DLR code TRACE, a RANS-Solver for turbomachinery flows. TRACE simulations were done using the Wilcox k-ω turbulence modelling. The boundary conditions were taken from the experimental setup. In this paper the numerical data was analysed and compared with the experimental results regarding thermodynamics. The simulations confirmed a high influence of the flow angle. Within the flow regime affected by the injected coolant a good agreement between the numerical heat transfer results and the experimental data was observed. The qualitative and quantitative values were met after finding the optimum calculation parameters. Only in the region downstream of the throat area a different behaviour became obvious. Concerning film-cooling effectiveness quantitative differences between simulation and experiment were found whilst qualitative good agreement was observed.

scholarly journals Two-Dimensional Coupled Vortex-Induced Vibration of Circular Cylinder: Prediction and Extraction of Hydrodynamics Properties

2013 ◽  
Author(s):  
Hossein Zanganeh ◽  
Narakorn Srinil
Keyword(s):  
Circular Cylinder ◽  
Numerical Solutions ◽  
Cross Flow ◽  
Structural Equations ◽  
Experimental Results ◽  
High Mass ◽  
Two Dimensional ◽  
Fluid Structure ◽  
Vortex Induced Vibration ◽  
Proposed Model

An advanced model for predicting a two-dimensional coupled cross-flow and in-line vortex-induced vibration (VIV) of a flexibly-mounted circular cylinder in a uniform flow is proposed and investigated. Attention is placed on a systematic extraction of variable hydrodynamics properties associated with a bi-directional fluid-structure interaction system. The governing equations of motion are based on double Duffing-van der Pol (structural-wake) oscillators with the two structural equations containing cubic and quadratic nonlinear terms. The cubic nonlinearities capture the geometrical coupling of cross-flow/in-line displacements excited by hydrodynamic lift/drag forces whereas the quadratic nonlinearities allow fluid-structure interactions. The combined analytical and numerical solutions of the proposed model are established. By varying flow velocities in numerical simulations, the derived low-order model qualitatively captures several key VIV characteristics of coupled in-line/cross-flow oscillations. By making use of a newly-derived empirical formula, the predicted maximum cross-flow/in-line VIV amplitudes and associated lock-in ranges compare well with several experimental results for cylinders with low/high mass or damping ratios. Moreover, such important hydrodynamic properties as VIV-induced mean drag, added mass, excitation and damping terms can be systematically determined via the proposed model and compared well with some experimental results in the literature.

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