Constant Fluid Properties Research Articles

Theoretical limits of vapor cooling large cylindrical structures using boil-off

The Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER) is planning to demonstrate the performance benefits of using boil-off to reduce the heat load on various upper stage structural members by using the boil-off vapor to intercept some of the heat load on the structures. A first order simplified analytical model was constructed in order to understand sensitivity of various parameters to performance as well as to understand the theoretical maximum performance of the vapor cooling of a thin-walled cylindrical structure. Constant fluid properties and a temperature dependent thermal conductivity of the structure material were assumed. The model showed that vapor cooling of an aluminum cylindrical structure with hydrogen can reduce the heat load along the cylinder by as much as 70%. Also, cooling a portion of the cylinder is quite effective in comparison with cooling it entirely.

Conservative finite-volume framework and pressure-based algorithm for flows of incompressible, ideal-gas and real-gas fluids at all speeds

A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled pressure-based algorithm. The applied conservative discretisation and implementation of the governing conservation laws as well as the definition of the fluxes using a momentum-weighted interpolation are identical for incompressible and compressible fluids, and are suitable for complex geometries represented by unstructured meshes. Incompressible fluids are described by predefined constant fluid properties, while the properties of compressible fluids are described by the Noble-Abel-stiffened-gas model, with the definitions of density and specific static enthalpy of both incompressible and compressible fluids combined in a unified thermodynamic closure model. The discretised governing conservation laws are solved in a single linear system of equations for pressure, velocity and temperature. Together, the conservative finite-volume discretisation, the unified thermodynamic closure model and the pressure-based algorithm yield a conceptually simple, but versatile, numerical framework. The proposed numerical framework is validated thoroughly using a broad variety of test-cases, with Mach numbers ranging from 0 to 239, including viscous flows of incompressible fluids as well as the propagation of acoustic waves and transiently evolving supersonic flows with shock waves in ideal-gas and real-gas fluids. These results demonstrate the accuracy, robustness and the convergence, as well as the conservation of mass and energy, of the numerical framework for flows of incompressible and compressible fluids at all speeds, on structured and unstructured meshes. In particular, the precise recovery of a divergence-free velocity field in the incompressible limit, the accurate prediction of acoustic waves, and the convergence to the correct weak solution for strong shock waves with the same finite-volume discretisation and pressure-based algorithm are important features of the proposed numerical framework.

A comprehensive review on numerical approaches to simulate heat transfer of turbulent supercritical CO2 flows

Extensive computational investigations have been performed to obtain more detailed information about the peculiar phenomena of turbulent supercritical carbon dioxide (sCO2) flow as ideal heat transfer fluids in various thermal engineering applications. This paper reviews the simulation techniques used and discusses their advantages, shortcomings and applicability. Not only is a comprehensive inspection on various computational approaches provided, but also the model refinements are suggested. Direct Numerical Simulations (DNS) provides valuable and reliable information about the thermohydraulics of turbulent sCO2 flows, in particular within the near-wall region, which well interprets the observed heat transfer enhancement and deterioration with property variations, flow acceleration and buoyancy discussed. However, DNS is not feasible when it comes to high Reynolds number flows with complex geometries encountered in practical applications because of the drastically increasing computational cost. Reynolds-Averaged Navier-Stokes (RANS) modeling is able to fill the gap with acceptable accuracy and becomes the mainstream for turbulent sCO2 heat transfer simulations. The flow and heat transfer behaviors of turbulent sCO2 can be simulated using RANS modeling leading to acceptable predictions. However, the performance variation is considerable for different models and for the same model of changing operating conditions, model generality is not reached. In addition, some treatments implemented into the RANS models for constant property fluids are not appropriate for variable-property sCO2 flows, causing inconsistency on the mixed convection predictions. Variable turbulent Prandtl number and more advanced calculation schemes for buoyancy production of turbulent kinetic energy are strongly recommended. Also, more appropriate treatments for damping functions are demanded to enable the model properly respond to the local property changes, particularly near the wall. Much simpler models with far less computational cost based upon the two-layer theory are being developed to achieve the generality. While this is promising, the examinations are still limited to the certain conditions and some model parameters need to be calibrated against the DNS data, which definitely reduces the model universality since DNS only covers a limited range of operating conditions. Developing more generic and reliable RANS models is still the main focus of simulation techniques used for turbulent sCO2 heat transfer.

Investigation on the Effect of Stirring Process Parameters on the Dispersion of SiC Particles Inside Melting Crucible

Stirring based liquid metal processing is the widely explored process by researchers for the production of metal matrix composites (MMCs). The dispersion of reinforcement particles is the major challenge in the process. The stirring process parameters govern the dispersion of reinforcement particles in MMCs. The important stirring process parameters are stirring speed, stirrer geometry, stirrer position, and stirring time. In the literature, research works are reported, where the effect of such parameters on the dispersion of particles was investigated either by analyzing flow field using computational methods (assuming constant fluid properties) or by sectioning the casted samples. In cast condition, the dispersion of particles is also influenced by the solidification phenomena. The aim of the present work is to investigate the significance and the effect of stirrer geometry, stirrer position and stirring speed on the dispersion of reinforcement particles inside melting crucible, during the stirring. Aluminium alloy LM25 was used as the matrix material and silicon carbide (SiC) particles having mean size 37.58 microns (d50 value) were used as the reinforcement phases. Samples of the composite slurry during the stirring process were dragged using a quartz tube at three levels inside crucible and microstructure analysis was carried out. Number density (ND) and inter particle distance were evaluated for parameter combinations. The uniform dispersion of SiC particles was observed at 45° stirrer blade angle, 400 rpm stirring speed and 40 mm stirrer position. And, significance order of individual parameter was observed as stirring speed < stirrer position < stirrer blade angle.

Comparative evaluation of heat transfer correlations with different fluid property considerations for fixed-bed reactor modeling

Catalytic fixed-bed reactors are well established and frequently used in the chemical industry. Full-scale catalytic fixed-bed reactors are commonly described via pseudo-homogeneous continuum models. The heat transfer is accounted for by correlations that have been predominately fitted under the assumption of constant fluid properties. As a result of chemical reactions taking place, the fluid composition and the temperature in the fixed-bed depend on the spatial position. The resulting system specific non-uniformity of the fluid properties should be taken into account during modeling. The effect of different approaches to consider the fluid properties in the bed on the predictive performance of selected heat transfer correlations is evaluated on a broad range of experimental heat transfer data obtained from the literature. Correlations from both the αw- and the λr(r)-heat transfer models were selected. Although the selected correlations have been fitted under the assumption of constant fluid properties, the predictive performance was improved for all correlations if radial and axial variations of the fluid properties were taken into account. The impact on the resulting temperature field is illustrated based on a case study. In addition, the predictive performances of the selected heat transfer correlations are compared to one another over a broad range of tube-to-particle diameter ratios and Reynolds numbers. A clear superiority of the λr(r)-correlation proposed by Winterberg et al. was identified.

The influence of heating on liquid jet spreading and hydraulic jump

The free-surface flow and thermal fields formed by an axisymmetric liquid jet impinging on a circular heated disk are examined theoretically. The disk is maintained either at a prescribed heat flux or temperature. The study explores the effect of inertia, wall heat flux and wall temperature on the momentum and thermal boundary layers as well as the film thickness and the location and height of the hydraulic jump. Only non-metallic liquids are considered, for which the kinematic viscosity is generally larger than the thermal diffusivity, causing the thermal boundary layer to remain thinner than the momentum boundary layer. The effect of surface tension resulting in the Marangoni stress at the free surface and the hoop stress at the jump is also explored. Our results corroborate well existing experimental, theoretical and numerical studies. Both the momentum and thermal boundary layers are found to decrease with increased inertia or thermal input at the disk. The thermal boundary layer is found to always reach the free surface for an imposed constant wall heat flux. The two transition locations where the boundary layers reach the free surface move downstream with inertia but move in opposite directions with increasing wall heat flux or wall temperature. Enhanced heating from the wall also tends to increase the jump radius and depress its height. More importantly, the hydraulic jump leads to a shock-type drop in the Nusselt number, confirming existing numerical findings. Finally, we show that the Nusselt number is independent of the wall temperature for a fluid of constant properties.

The impact of variable fluid properties on hydromagnetic boundary layer and heat transfer flows over an exponentially stretching sheet

This paper put forward an analysis of variable fluid properties and their impact on hydromagnetic boundary and thermal layers in a quiescent fluid which is developed due to the exponentially stretching sheet. The viscous incompressible fluid has been set into motion due to aforementioned sheet. We assume that the viscosity and the thermal conductivity of the Newtonian fluid are temperature dependent. The governing boundary layer equations containing continuity, momentum and energy equations are coupled and nonlinear in nature, thereby, cannot be solvable easily by using analytical methods. Since the general boundary layer equations admits a similarity solutions, thus a generalized Howarth-Dorodnitsyn transformations have been exploited for the set-up of a coupled nonlinear ODEs. These transformed ODEs are solved numerically by a shooting method and is verified from MATLAB built-in collocation solver bvp4c for different parameters appearing in the work. We show results graphically and in a tabulated form for a constant and a variable fluid properties. We find that the temperature dependent variable viscosity and a thermal conductivity influence a velocity and a temperature profiles. We show that the thermal boundary layer decreases for constant variable fluid properties and increases for variable fluid properties

Numerical assessment of Bödewadt flow and heat transfer over a permeable disk with variable fluid properties

Impact of variable fluid properties on heat transfer in Bödewadt flow with wall suction is the main focus of present article. Recent studies have predicted that energy equation in Bödewadt flow can have physically compatible solution only when disk is porous. We utilize the usual von-Kármán variables to transform the governing equations of fluid motion and heat transfer (with variable properties) into self-similar differential equations. The final problem comprises of a parameter θe that measures the degree of dependence of fluid viscosity on temperature. A numerical approach is pursued to determine velocity components, wall stresses, temperature and heat transfer rate from the disk. Wall suction velocity is found to have a pivotal role on the solutions. The main outcome of the study is that fluid velocity and temperature around the disk are considerably altered by varying the parameter θe. The deviations of present results from those obtained with constant fluid properties are deliberated. Present results are in perfect agreement with the available literature in a limiting sense.

Instability during transition to turbulence of supercritical pressure CO2 in a vertical heated serpentine tube

Convection heat transfer of supercritical pressure CO2 in various channels has extensive applications in many industries. In some applications, the channel may not be straight, but rather serpentine. Researchers have found that the transition to turbulence of constant-property fluid is delayed in a constant-curvature pipe, whereas it is promoted in a serpentine tube with alternating curvature. In supercritical pressure CO2 flow in a serpentine tube, the buoyancy and centrifugal forces both influence the transition process, which needs to be studied thoroughly. This study investigates the instability during transition from laminar to turbulent flow both numerically and experimentally. The wall temperature oscillations are measured by experiments. The effects of buoyancy and centrifugal force on the flow and heat transfer are analyzed through comparisons of unheated cases, to heated cases of forced flow (no buoyancy), upward flow and downward flow by simulations. The flow and heat transfer instabilities along the flow and across the cross sections and the secondary flow pattern development are studied. The location (distance from the inlet) at which the flow becomes unstable is least for downward flow, intermediate for upward flow and largest for pure forced flow. It is found that the earlier occurrence of the instability is caused by the adverse pressure gradient in downward flow, and the enhancing effect of the buoyancy on the centrifugal force in upward flow. These findings are important for understanding the flow and heat transfer during transition to turbulence of supercritical pressure CO2 flow in vertical serpentine tubes.

Three-dimensional numerical simulation of conduction, natural convection, and radiation through alveolar building walls

Numerical simulation of the coupled heat transfers by conduction, convection, and radiation through two kinds of the alveolar structures used in the construction are numerically investigated. Owing to the low-temperature differences involved, the tridimensional model is based on the Boussinesq approximation and constant thermophysical fluid properties at mean temperature. The alveolar walls are assumed grey and diffuse. The symmetric and periodic boundary conditions for flows governed by the incompressible Navier-Stokes equations are considered. Equations governing the natural convection in the alveolars, the radiative heat exchanges between their internal surfaces and the heat conduction in the surrounding walls are solved using a finite volume method. The pressure-velocity coupling is solved by SIMPLE algorithm. The objective of this study is to improve the effects of wall conduction and radiation heat exchange between surfaces on the decrease of the thermal resistance in the alveolar walls. Two kinds of concrete blocks with three and six-hole numbers are chosen and their thermal resistances are numerically predicted. The comparison between the thermal resistances, specified in terms of thermal regulations for buildings and numerical solutions, is presented.

Simulative analysis of turbulent flow through a circular conduit with uniform wall temperature and constant heat flux boundary conditions

PurposeThis study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.Design/methodology/approachThe methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.FindingsThe profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.Originality/valueThe novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

Effect of variable fluid properties on the hydrodynamic and thermal characteristics of parallel flow microchannel heat exchanger

In this paper the parallel flow microchannel heat exchanger is numerically investigate and the effect of treating the properties of fluids as variables with temperature compared with constant fluid properties assumption on its performance is studied. A numerical simulation is made to solve 3D Navier stock equations in two fluids with temperature dependent properties and 3D energy equation in two fluids and solid walls taking into account the effect of entrance region and axial conduction in the walls. The properties entered to the main program by relations as a function of temperature using subroutines written to calculate the properties at the end of each iteration. The results obtained show that, treating the properties as a temperature dependent gives higher overall performance since it leads to obtain lower pressure drop and higher effectiveness compared with constant properties assumption.

Numerical Simulation of Heat Transfer of Turbulent Flow inside a Circular Conduit at Constant Wall Temperature Boundary Condition

A numerical study was conducted by using the finite difference technique to investigate the mechanism of the fully developed turbulent flow and heat transfer in a circular tube in company of large Reynolds number with constant heat flux and at constant wall temperature condition. The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form in order to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas’ algorithm, a program in FORTRAN version 95 was developed in order to numerically solve the discretized form of the system of equations describing the problem. Finally, thanks to this elaborate program, we were able to play on some parameters involved such as the Reynolds number, the number of Peclet, and the longitudinal coordinate to obtain important results of the treated thermal model which are discussed and well detailed of this work. Comparison between the literature correlation data and the calculated simulation indicates that it is a good match of the results.

Numerical simulation of thermally developing turbulent flow through a cylindrical tube

A numerical study was conducted using the finite difference technique to examine the mechanism of energy transfer as well as turbulence in the case of fully developed turbulent flow in a circular tube with constant wall temperature and heat flow conditions. The methodology to solve this thermal problem is based on the energy equation, a fluid of constant properties in an axisymmetric and two-dimensional stationary flow. The global equations and the initial and boundary conditions acting on the problem are configured in dimensionless form in order to predict the characteristics of the turbulent fluid flow inside the tube. Using Thomas’ algorithm, a program in FORTRAN was developed to numerically solve the discretized form of the system of equations describing the problem. Finally, using this elaborate program, we were able to simulate the flow characteristics, for changing parameters such as Reynolds, Prandtl, and Peclet numbers along the pipe to obtain the important thermal model. These are discussed in detail in this work. Comparison of the results to published data shows that results are a good match to the published quantities.

A conjugate heat transfer analysis of performance for rectangular microchannel with trapezoidal cavities and ribs

A numerical investigation has been taken up to assess the efficacy of a design innovation for rectangular microchannel heat sink by applying the concepts of maximization of thermal performance (TP) and minimization of entropy generation (EG). The channel is conceived as a serial arrangement of modifying units, each with a rib symmetrically located between trapezoidal cavities (TRC) on opposite side walls. Based on SIMPLEC algorithm for the flow along with conduction through the bounding walls and the internal ribs, a three dimensional laminar-flow conjugate heat-transfer study has been carried out between Reynolds number (Re) of 140 and 600 following a validation against a representative numerical and experimental study. A comparison among the predictions of constant fluid property model and models incorporating their realistic variations with temperature has shown the cooling to be dominated by convection, of course more strongly at higher Re. Substantially higher thermal conductivity of copper than that of silicon have revealed moderate increase in bulk fluid temperature and even lower increase of substrate temperature. Four different rib structures have been considered that are rectangular (RR), backward triangular (BTR), forward triangular (FTR) and diamond (DR). The predictions against Re indicated the best TP with diamond rib combination (TRC-DR) and the highest EG with backward triangular rib combination (TRC-BTR). A notable contribution of this work is establishing the concept of minimization of EG under the constraint of given pumping power to be equivalent to the concept of maximization of TP. The effects of parametric variations of relative width and length of cavity and relative width and pitch of rib have been investigated and the highest TP has been predicted around Re of 328.

Numerical simulation of thermally developing turbulent flow through a cylindrical tube

A numerical study was conducted using the finite difference technique to examine the mechanism of energy transfer as well as turbulence in the case of fully developed turbulent flow in a circular tube with constant wall temperature and heat flow conditions. The methodology to solve this thermal problem is based on the energy equation a fluid of constant properties in an axisymmetric and two-dimensional stationary flow. From the mathematical side, a numerical technique for solving the problem of fluid–structure interaction with a fully developed turbulent incompressible Newtonian flow is described. The global equations and the initial and boundary conditions acting on the problem are configured in dimensionless form in order to predict the characteristics of the turbulent fluid flow inside the tube. Using Thomas’ algorithm, a program in FORTRAN was developed to numerically solve the discretized form of the system of equations describing the problem. Finally, using this elaborate program, we were able to simulate the flow characteristics, for changing parameters such as Reynolds, Prandtl and Peclet numbers along the pipe to obtain the important thermal model. These are discussed in detail in this work. Comparison of the results to published data shows that results are a good match to the published quantities.

Modeling wellbore heat exchangers: Fully numerical to fully analytical solutions

The successful modeling of wellbore heat exchangers requires tight coupling between the formation heat conduction and the wellbore thermal dynamics. In this paper, we developed three representative solutions: a fully numerical solution that treats both formation and wellbore numerically, a semi-numerical solution that treats formation analytically and wellbore numerically and a fully analytical solution that treats both formation and wellbore analytically. The outlet temperature, pressure, and heat flow rate predicted by the three solutions are compared. The results of this comparison indicate that the fully numerical solution is the only accurate solution for the early transient time. After the system reaches quasi-steady state, temperature and heat flow estimated from all three solutions are in very good agreement. The analysis of transient fluid properties and mass flow rates revealed that constant fluid property model cannot accurately estimate the pressure loss for the system. The newly proposed fully analytical solution is applied in an economic analysis problem for calculating the optimal insulation thickness and mass flow rate to minimize the cost of generated power.

Transient Behavior of Three-Fluid Cross-Flow Heat Exchanger Under the Influence of Temperature Nonuniformity

Abstract A typical three-fluid cross-flow heat exchanger with nonuniform inlet temperature in the central (hot) fluid is considered for the present analysis. Steady and transient state behavior of the heat exchanger is observed for four different temperature nonuniformity models along with step excitation in inlet temperature of the central fluid. Longitudinal heat conduction in the separating walls and the effect of fluid back-mixing along with axial dispersion effect are considered within the fluids with constant thermophysical fluid properties. The solution of governing equations has been obtained using implicit finite difference scheme. Temperature distribution over the separating walls has been depicted providing a clear view of the thermal stresses generated in separating walls. The performance for all the four cross-flow arrangements has been analyzed by comparing that with and without nonuniform conditions. It is found that the nonuniformity in inlet temperature has an adverse effect on the performance of heat exchanger.

The influence of low Prandtl numbers on the turbulent mixed convection in an horizontal channel flow: DNS and assessment of RANS turbulence models

In this paper, the turbulent mixed convection in a channel flow with differentially heated walls is considered for a fixed Richardson number (Rib=0.5) and three different Prandtl numbers (Pr=1,0.1and0.01). Numerical simulations are conducted assuming constant fluid properties and the effect of the buoyancy is taken into account by means of the Boussinesq approximation. Direct Numerical Simulations (DNS) are performed first and the effect of the buoyancy on the first and second order statistics of the fluid and thermal fields is highlighted. Furthermore, it is found that in mixed convection the Prandtl number has a much larger effect on the results than in the case of forced convection. The obtained DNS results are then used as a validation database for two different RANS turbulent heat flux models, i.e. the classical Reynolds analogy and a recently proposed three-equation algebraic heat flux models called AHFM-NRG+. It is observed that, as expected, the Reynolds analogy fails to predict the thermal field even for unitary Prandtl numbers fluids. On the other hand, it is shown that the AHFM-NRG+ is in a reasonable agreement with the reference DNS over the entire range of Prandtl numbers considered in the study.

Flow and heat transfer in cross-stream type T-junctions: A computational study

The present computational study is concerned with the thermal mixing of flow-crossing streams in a T-shaped junction, focussing primarily on a configuration subjected to temperature-dependent fluid property conditions. The reference experimental investigation is conducted by Hirota et al. (2010). Preliminary, a quasi two-dimensional configuration with constant fluid properties, for which the reference DNS (Direct Numerical Simulation) database is made available by Hattori et al. (2014), is simulated. The presently applied computational model is based on a VLES (Very Large Eddy Simulation) formulation of Chang et al. (2014). The residual turbulence is modeled employing the appropriately modified RANS-based (Reynolds-Averaged Navier–Stokes) elliptic-relaxation eddy-viscosity model of Hanjalić et al. (2004). In addition to the VLES, both flow configurations are computed applying the background RANS model representing the constituent of the present VLES method. Whereas the eddy viscosity model describes fully-modeled turbulence in the RANS framework, it relates to the unresolved sub-scale turbulence within the VLES methodology. Unlike the RANS method, the VLES method is capable of capturing the spectral dynamics of turbulence to an extent complying with the underlying grid resolution. The latter model feature contributes decisively to an appropriately intensified turbulence activity in the separated shear layer regions and, consequently, to an enhanced mixing process. The results obtained with the present VLES model follow closely the reference DNS data in the Hattori et al. (2014) case with respect to velocity and temperature fields as well as the fields of associated turbulent quantities in all characteristic regions of the flow domain: main and branch streams’ merging zone, flow-reversal and post-reattachment regions. In the more complex Hirota et al. (2010) configuration, the flow field is captured reasonably well, while the computationally obtained thermal fields suggest a somewhat more intensive mixing relative to the reference experiment.