Variable Property Model Research Articles

Similarity solutions of a Blasius flow with variable fluid properties and viscous dissipation

AbstractAn analytical model of the Blasius flow is studied including temperature-dependent fluid properties and viscous dissipation. The friction coefficient and Nusselt number at the wall are calculated from the resulting dimensionless velocity and temperature fields. The variable properties model is compared to a constant properties model to verify if and under which conditions this simplification is valid. Air, water and oil are analyzed as fluids over a representative operating regime, respectively. For air, the variable properties do not influence the friction coefficient and the Nusselt number. For water, the influence of the variable properties is present for both parameters but limited since no large temperature difference can occur in water without a phase change. New correlations for the friction coefficient and Nusselt number were derived for water and oil over a large range of operating conditions. Viscous dissipation does not significantly affect these parameters for air and water because of their relatively low Prandtl numbers. The high Prandtl number of oil in combination with a viscosity that is strongly decreasing with increasing temperature, leads to a more complex behavior. The friction coefficient as well as the Nusselt number are strongly dependent on the fluid properties. Dissipation effects cannot be neglected above an Eckert number of around 0.01. The superposition principle to evaluate wall heat flux in experiments is based on the assumption of constant fluid properties. It can be used without restrictions for air but should be thoroughly checked for all other fluids, especially liquids, using the presented methodology.

Numerical investigation of transient phase-change transpiration cooling based on variable properties of coolant

Aimed at promoting the practical application of transpiration cooling technology in the field of active thermal protective system of hypersonic vehicles, this study presents a comprehensive numerical approach combining two-phase mixture model (TPMM), local thermal non-equilibrium (LTNE) assumption and variable properties of coolant to investigate the transient transpiration cooling problems with phase change. The real variable physical properties of coolant as functions of temperature and pressure are taken into consideration based on the data from the National Institute of Standards and Technology (NIST). The model is verified by comparing with the numerical and experimental data in previous researches. Results suggest that a new phenomenon of “reverse temperature distribution” in two-phase region is observed in the transient simulation considering variable properties. Comparison between the constant-property model and variable-property model indicates the necessity of the real variable physical properties, especially at low-pressure conditions with large differential pressure gradient. Meanwhile, the simulation with a non-uniform heat flux boundary condition reveals the mechanism of heat transfer deterioration. A gap of liquid outflow is formed after vapor generation, next moves along the outlet, then disappears and finally regenerates. The non-uniform heat flux will certainly lead to an uneven pressure distribution, resulting in the deterioration of local heat transfer in the porous matrix.

Transient air natural convection in asymmetrically heated vertical channels

A numerical analysis of natural convection in air in a vertical channel asymmetrically heated at uniform heat flux is carried out in this work. One channel wall is heated whereas the other one is adiabatic, and the problem is transient, two-dimensional and laminar. Constant and variable property models are considered. For both models, numerical solution is obtained by means the commercial CFD code Fluent. An extended computational domain is considered in order to simulate the far field conditions and it consists of the channel geometry with an upstream reservoir and a downstream reservoir. Simulations are achieved for Rayleigh number, Ra, values in the range 102–106 and results are showed as temperature profiles along the heated wall as a function of time, stream function and temperature fields. The present analysis allows to improve the knowledge of the effects related to the variable properties on the inlet and outlet zone and consequently inside the channel by numerical investigation during the development of fluid dynamic and thermal fields which are strongly linked. The results give quantitative information on the errors due to the use of constant properties model with respect to the variable properties model in natural convection in asymmetrical heated vertical channels.

Brownian models effect on turbulent fluid flow and heat transfer and entropy generation of water/boehmite alumina nanofluid inside enclosure

PurposeThe purpose of this paper is to study the effects of using different Brownian models on natural and mixed convection fluid flow and heat transfer inside the square enclosure filled with the AlOOH–water nanofluid.Design/methodology/approachDue to fulfill of this demand, five different models for the effective thermal conductivity and viscosity of the nanofluid are considered. The following results are presented for the Ra=107 to 1010 and Ri=0.01 to 100, whereas the volume fraction of the nanoparticles is varied from φ = 0.01 to 0.04.FindingsAccording to the obtained results, increasing of Rayleigh number and reduction of Richardson number leads to the higher values of the average Nusselt number and entropy generation. Also, it is realized that, variation trend of the average Nusselt number and entropy generation in all cases is increasing by growing the volume fraction. It is found that the obtained average Nusselt numbers and entropy generations with Koo and Kleinstreuer are the highest among all the studied cases, and it is followed by Patel, Vajjha and Das, Corcione and Maxwell–Brinkman models, respectively.Originality/valueBased on the results of present investigation, the Nusselt number difference predicted between the Maxwell–Brinkman model (as constant-property model) and Koo and Kleinstreuer model is about 7.84 per cent at 0.01 per cent volume fraction and 5.47 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. The entropy generation difference predicted between the two above studied model is about 8.05 per cent at 0.01 per cent volume fraction and 5.86 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. It is observed that using constant-property model has a significant difference in the obtained results with the results of other variable-property models.

Numerical study of laminar-forced convection of Al2O3-water nanofluids between two parallel plates

Laminar-forced convection of Al2O3-water nanofluid between two parallel plates was studied numerically. The channel walls were assumed to be isothermal. The effective viscosity and thermal conductivity of nanofluid were considered as variables, and the effects of applying a variable properties model were investigatedby using two relatively new models. The numerical results were compared to the results obtained from a previous non-variable properties model. Also, the effects of nanoparticle size on the flow and heat transfer within the channel were investigated. The study was carried out using Reynolds numbers between 100-1000, nanoparticle diameters in the 15-75 nm range, and nanoparticle volume fractions in the range 0.01-0.05 nm. The numerical results show that using nanofluid could enhance heat transfer by up to 35 %, compared to the base fluid. In addition, reducing the nanoparticle diameter can enhance heat transfer by up to 15.9 %.

Laminar convective heat transfer characteristic of Al2O3/water nanofluid in a circular microchannel

In this study, laminar convective heat transfer characteristics Al2O3/water nanofluid in a circular microchannel is investigated using a two-phase (discrete phase) model. The computational fluid dynamic code FLUENT (ANSYS) is employed to solve the coupled momentum and energy equations with the boundary conditions of uniform wall heat flux and velocity at channel inlet. Detail analysis is done showing variation of wall temperature, fluid bulk mean temperature, heat transfer coefficient, Nusselt number, shear stress, friction, pressure drop, entropy generation etc. along the microchannel at two particle volume concentrations (1% and 4%) of the nanofluid. Comparison of results is provided between base and nanofluid and also for two cases, one with constant property and the other with variable temperature thermal conductivity and viscosity. Results show that heat transfer is enhanced in case of the nanofluid with low entropy generation and the heat transfer parameters increase with increase in nanoparticle volume concentration and Reynolds number. However, use of nanofluid also causes increase in pressure drop and shear stress. A comparison of the constant and variable property model showed that heat transfer is further enhanced; entropy, shear stress and pressure drop further decrease when temperature dependent properties of the nanofluid are considered instead of constant properties.

Numerical simulation of mixed convection heat transfer of nanofluid in a double lid-driven cavity using lattice Boltzmann method

In this study, mixed convection heat transfer of water-Cu nanofluid in a double lid-driven cavity has been analyzed by lattice Boltzmann method. The double lid-driven are insulated and the side walls have sinusoidal temperature distribution. Simulations have been carried out at constant Grashof number 100, the Richardson numbers of 0.01, 0.1,1,10 and 100, temperature phase deviation of 0, π/4, π/2, 3π/4 and π, the solid volume fraction from zero to 0.06 and the Prandtl number of 6.57. The thermal modeling of passive scalar is applied and two separate distribution functions for the flow and temperature fields are considered. In order to calculate the thermal conductivity coefficient of nanofluid, constant and variable properties models are used. The results showed that in high Richardson numbers, the effect of the thermal phase deviation changes on the flow pattern is evident and in low Richardson numbers, the phase deviation changes do not affect the flow pattern. In all thermal phase deviations by reducing the Richardson number, the Nusselt number increases and thus the heat transfer increases. Also the average Nusselt number obtained for the constant properties model is higher compared with that of variable properties model.

Prediction of the in-service performance of a railway hydraulic damper

In this study, an improved physical parametric model with key in-service parameters was established and experimentally validated for a high-speed railway hydraulic damper. A subtle variable oil property model was built and coupled into the full model to address the dynamic flow losses and the relief-valve system dynamics. Experiments were conducted to evaluate the accuracy and robustness of the full damper model and simulation, which determined the damping characteristics over an extremely wide range of excitation speeds. Further simulations with in-service conditions and excitations were performed using the validated model, and the results revealed that improper key in-service parameters, such as improper rubber attachment stiffness, entrained air ratios and small mounting clearances, can greatly degrade the damping capability of a hydraulic damper. The obtained physical model includes all the influential factors that have an impact on the damping characteristics, so it will serve as a useful basic theory in the prediction of in-service performance, optimal specification and product design optimization of hydraulic dampers for modern high-speed rail vehicles.

Mixed convection heat transfer in a CuO–water filled trapezoidal enclosure, effects of various constant and variable properties of the nanofluid

Different models for the thermophysical properties of the CuO–water nanofluid have been proposed in recent years. In the more sophisticated variable-property models, the thermophysical properties of the nanofluid are considered to be functions of the temperature and the volume fraction of the nanoparticles; while, in the constant-property models, they depend on the nanoparticles volume-fraction only. In this study, a new variable-property model is proposed for the thermophysical properties of the CuO–water nanofluid based on the experimental and the theoretical results available in the literature. The impacts of using the newly generated as well as the existing models on the flow and temperature fields during numerical simulation of mixed convection heat transfer in a trapezoidal enclosure filled with the CuO–water nanofluid are investigated. The simulation results are presented in terms of the average Nusselt number and the entropy generation within the enclosure for a wide range of Richardson numbers and volume fractions of the nanoparticles. In general, more heat transfer enhancements and higher entropy generations are observed employing the variable-property models which consider the effect of the Brownian motion as compared to using the constant-property Maxwell–Brinkman model. Furthermore, the results indicate that the effective thermal conductivity of the nanofluid for a variable-property model plays a pre-eminent role in the heat transfer and the entropy generation inside the enclosure. However, the differences between the average Nusselt number and the entropy generation obtained using the different considered variable-property models decrease with increasing the nanoparticles volume fraction.

Multivariate characterization, modeling, and design of ionic liquid molecules

Ionic liquids that have tailored structures with an array of unique functional properties can have important applications in areas such as CO2 capture and sequestration, sulfur removal from fuels, energy storage, biomass pretreatment, and chemical separations. Within a computer-aided molecular design (CAMD) framework, a characterization based method was combined with chemometric techniques in a reverse problem formulation to design ionic liquid (IL) structures corresponding to particular physical properties. Infrared spectra generated from density functional theory (DFT) simulations were used for capturing information on molecular architecture and calibration of latent variable property models to synthesize ILs in a logical and systematic methodology.

In-service parametric modelling a rail vehicle׳s axle-box hydraulic damper for high-speed transit problems

Due to the high-speed operation of modern rail vehicles and severe in-service environment of their hydraulic dampers, it has become important to establish more practical and accurate damper models and apply those models in high-speed transit problem studies. An improved full parametric model with actual in-service parameters, such as variable viscous damping, comprehensive stiffness and small mounting clearance was established for a rail vehicle׳s axle-box hydraulic damper. A subtle variable oil property model was built and coupled to the modelling process, which included modelling of the dynamic flow losses and the relief-valve system dynamics. The experiments validated the accuracy and robustness of the established full in-service parametric model and simulation which captured the damping characteristics over an extremely wide range of excitation speeds. Further simulations were performed using the model to uncover the effects of key in-service parameter variations on the nominal damping characteristics of the damper. The obtained in-service parametric model coupled all of the main factors that had significant impacts on the damping characteristics, so that the model could be useful in more extensive parameter effects analysis, optimal specification and product design optimisation of hydraulic dampers for track-friendliness, ride comfort and other high-speed transit problems.

Modelling of a rotary desiccant wheel: Numerical validation of a Variable Properties Model

Desiccant cooling systems have been used since the early '30s, mainly for industrial applications in which significant economic benefits could be achieved from an accurate humidity control. The core unit of a desiccant cooling system is the desiccant wheel device, the performances of which determine size and cost of the whole system. As a result, having a good desiccant wheel mathematical model can be an useful tool to optimize the operation of the device, as well as a valuable aid in the design phase.In this paper a one-dimensional coupled heat and mass transfer desiccant wheel model was developed, taking into account the dependence of thermodynamic and transport properties of humid air with temperature (Variable Properties Model, VPM). The model has been validated using both literature and experimental data in terms of temperature and humidity profiles at the exit of the wheel, dehumidification effectiveness, dehumidification coefficient of performance and sensible energy ratio.Compared to the traditional models, significant improvements in the agreement between numerical predictions and experimental data have been observed. It was found that mean relative error between measured and VPM calculated data were always significantly lower than those between the same experimental data and values calculated according to widespread literature models which consider moist air properties constant with temperature; as a consequence, it can be inferred that neglecting variations of moist air properties with temperature leads to unacceptably low accuracy variables estimation.

Transient modeling and dynamic characteristics of thermoelectric cooler

Dynamic characteristics are extremely important for design and operation of thermoelectric coolers (TECs). This paper develops a three-dimensional transient TEC model based on the coupling of heat transfer and electric conduction within semiconductors. The model takes into account all thermoelectric effects, including Joule heating, Thomson effect, Peltier effect and Fourier’s heat conduction. For most of semiconductor materials, Seebeck coefficient, electric conductivity and thermal conductivity are strongly temperature-dependent. Therefore, the present transient model is used to compare dynamic temperature variations at the cold and hot ends with constant and variable material properties. Small, medium, and large applied currents with various cooling loads are adopted as operating conditions. The results show that, at small currents, constant property model developed by this work can predict accurately the dynamic characteristics, however, with the increase in current, the temperature-dependence of properties have more and more remarkable effect on the dynamic temperature variations, especially for high cooling loads. When the current is larger than a specific value, the heat transferred from the hot end to the cold end by Fourier’s heat conduction will exceed the heat adsorbed at the cold end by Peltier effect, thus, the temperatures at the cold and hot ends increase continuously, the TEC cannot reach the steady-state. This phenomena is predicted exactly by the variable property model, oppositely, the constant property model predicts that the TEC still supply refrigeration.

A Simulative Study on the Impact of Physical Property Parametersupon Flow and Heat Transfer in Annular Space

Through finite volume method, this study establishes a steady state flow and heat transfer model of a single phase flow flowing vertically upward in annular space. The model sets the inner cylinder of the annular space as a heating body with fixed heat generation rate. Flow and heat transfer boundary layers are set between the flow and the inner cylinder wall, in order to give more accurate description of momentum and heat coupling and transfer processes between the fluid and the solid near the wall. Compared with the constant physical property model, the variable physical property model, in which the fluid density, heat transfer coefficient, and viscosity change along with the temperature, has relatively lower heat transfer capacity and a little bit lower interface shear stress between the fluid and the solid heat transfer surfaces. Through the comparison between Re and Ri of the constant physical property model and the variable physical properties model, it can be concluded that the physical property changes of the fluid have gradually lower impact on flow and heat transfer processes along with the acceleration of the forced circulation of the fluid.

Improved mathematical modeling for the sheet reheat phase during thermoforming

AbstractIn any thermoforming process, plastic sheet heating is the most important phase as it is responsible for final part quality as well as overall process efficiency and productivity. The goal of the study reported here was to improve existing mathematical models to accurately predict the temperature profile inside a heated sheet, where the model could be used to better control the overall thermoforming process. A mathematical model with temperature dependent, variable sheet material properties including density, thermal diffusivity, specific heat, and thermal conductivity was developed and validated against experimental data. Models with constant and variable plastic sheet properties were created, simulated, and compared in Matlab. The models were validated by experiments which obtained temperature profiles at different depths within a plastic sheet by inserting thermocouples and recording temperatures. Further, the effect of sheet color on heating was investigated by considering two extreme cases: white (transparent) and black (opaque) colored sheets, and the effect of oven air temperature and velocity on sheet heating was also investigated. Results indicated that a variable properties model was needed to control sheet reheating especially with narrow forming windows, and that the heating profiles required for colored and noncolored sheets were very different. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers

Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannel

This paper is directed at the numerical simulation of pressure-driven nitrogen slip flow in long microchannels, focusing on conjugate heat transfer under uniform heat flux wall boundary condition. This problem has not been studied in detail despite its importance in many practical circumstances such as those related to the cooling of electronic devices and localized heat input in materials processing systems. For the gas phase, the two-dimensional momentum and energy equations are solved, considering variable properties, rarefaction, which involves velocity slip, thermal creep and temperature jump, compressibility, and viscous dissipation. For the solid, the energy equation is solved with variable properties. Four different substrate materials are studied, including commercial bronze, silicon nitride, pyroceram, and fused silica. The effects of substrate axial conduction, material thermal conductivity and substrate thickness are investigated in detail. It is found that substrate axial conduction leads to a flatter bulk temperature profile along the channel, lower maximum temperature, and lower Nusselt number. The effect of substrate thickness on the conjugate heat transfer is very similar to that of the substrate thermal conductivity. That is, in terms of axial thermal resistance, the increase in substrate thickness has the same impact as that caused by an increase in its thermal conductivity. By comparing the results from constant and variable property models, it is found that the effects of variation in substrate material properties are negligible.

Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels

A model based on the augmented Young–Laplace equation and the Clausius–Clapeyron equation was developed to describe the extended evaporating meniscus in a microchannel. The effects of the adsorbed film thickness, channel height and temperature-dependent thermophysical properties of the fluid are included in the model at wall superheats up to 50K. The liquid flow is coupled with the vapor flow to obtain the mass transport across the liquid–vapor interface. The results show that the constant thermophysical property model greatly overestimates the liquid pressure difference and the total thin film heat transfer rate at higher superheats compared with the variable thermophysical property model. The adsorbed film thickness, which is controlled by the disjoining pressure limit, reaches a minimum near about 20K superheat for water. The maximum film curvature and liquid pressure difference then decrease at superheats larger than 20K. The effects of the capillary pressure limit produced by the channel height can be reduced by increasing the superheat.

The effect of variable gas property on axial turbine performance

Industrial gas turbine flow has been evaluated by using computational fluid dynamics with a variable gas property model. The study of a three-stage turbine model has revealed some considerable variable gas property effects on the engine performance. When the gas properties are made constant with respect to the first blade row conditions, the exit total temperature has been over-predicted by about 15 Kelvin. There is also an over-prediction of turbine power output of 0.6%. Simulations using a constant averaged gas property or the fixed value at the last blade row both over-predict the mass flow rate by 0.5% and 1% respectively. The predicted efficiency from the various simulations is found to be less influenced than the parameters discussed above, with a difference of merely 0.25%. The findings suggest that it is necessary to include the variable gas property effect in 3D calculations of practical industrial gas turbine flow.

排気ノズルを有するパルスデトネーションエンジンの数値解析による推力性能評価

The propulsive performance was estimated for the H2/Air PDE with a convergingdiverging exhaust nozzle using multi-cycle two-dimensional limit cycle simulations with the detailed chemical reaction model. The present simulation also compared with a variable property model reported in the literature. The overall features such as the effects of filling fraction, nozzle configuration, and flight condition in the present results are in agreement. The present results show that optimum rth/rtube for Ispf are 0.6 and 0.5 for M=2.1 and 3.5, respectively.

Investigation of variable-property microchannel flows with electro-thermo-hydrodynamic interactions at constant pressure gradient or constant flow rate

In the present paper, a systematic investigation on numerical modeling of variable-property microchannel flows with electro-thermo-hydrodynamic interactions is presented. General variable-property electro-thermal flow model consisting of mass, momentum, energy, electric potential and ions transport equations in dimensionless form is formulated and employed to study transport phenomena in microchannel flows. The major concerns are: (1) evaluation of the model approximations such as equilibrium ion distribution, constant-property and/or small zeta potential for non-overlap electric double layer (EDL); (2) the electro-thermo-hydrodynamic interactions under conditions of strong EDL effects, and (3) differences in microchannel flow characteristics at driving conditions of constant pressure gradient (CPG) and constant flow rate (CFR). Variations of fluid, transport and electric properties with local temperature and/or ion concentration are considered. The present results demonstrate that the variable-property model with Poisson–Boltzmann potential is an appropriate approximation for transport phenomena in microchannel flows. The results also disclose that, compared to those in CPG flows based on the same Reynolds number, effects of temperature non-uniformity and variable-property are relatively more pronounced in the CFR flows. At either CPG or CFR condition, heat transfer performance changes little with the variations of electric and flow parameters in this low Reynolds number ( Re = 0.1) flow; while electric and flow fields can be significantly affected by variation of the governing parameters.