Strong Property Variations Research Articles

Momentum boundary layers in transcritical channel flows

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. We apply a physically consistent subgrid-scale turbulence model, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. In total seven cases are computed covering different Reynolds numbers, pseudo-boiling positions and pressure values. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum layer thicknesses. All cases feature a turbulent mass flux which is essential in turbulence modelling. Furthermore, we analyse the turbulent kinetic energy budgets, perform a quadrant and octant analysis of the Reynolds shear stress and employ an invariant map to study the anisotropy in transcritical turbulent channel flows.

Linear stability of real-fluid mixing layers at supercritical pressures

Linear stability analysis is a useful tool for the exploration of the initial evolution of flow motions in mixing layers. A real fluid mixing layer exhibits strong property variations and, thus, may present stability behaviors distinct from its ideal gas counterpart. The present study carries out spatial and temporal stability analyses of nitrogen mixing layers at supercritical conditions, with special attention to the density stratification induced by the temperature and velocity gradients across the mixing layer. The differences between the ideal gas and real fluid approaches are discussed. The maximum spatial growth rate and the most unstable frequency evaluated based on the real fluid density profile are found to be substantially lower than their ideal gas counterparts near the critical point, where an inflection of the density distribution occurs in the mixing layer. Across the inflection point, the strong density stratification arising from the real fluid effect tends to stabilize the mixing layer. The maximum growth rate and the most unstable frequency do not show a monotonic trend with the ratios of temperature and density. In the absence of the inflection point, however, the mixing layer is destabilized and features a substantially higher maximum spatial growth rate at lower ratios of density and temperature. The most unstable frequency and the maximum spatial growth rate increase with increasing pressure. The real fluid effect diminishes when the pressure is away from the critical value or when there is no inflection point in the density profile. The temporal stability analysis also indicates that a detailed density distribution plays a key role in dictating the stability characteristics of mixing layers at supercritical pressures.

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.

On the sensitivity to convective heat transfer correlation uncertainties in supercritical fluids

Most industrial heat transfer applications involve the utilization of heat transfer correlations to estimate heat flow. Due to their simplicity, these equations often carry significant uncertainty in their utilization. This study theoretically investigates the effect of the uncertainty of convective heat transfer correlations on measurable bulk flow properties such as the temperature and enthalpy using a steady state, dimensionless, one-dimensional internal flow model of a supercritical fluid heat exchanger. The sensitivity of bulk quantities to uncertainties in a correlation is shown to be a function of various parameters, including flow geometry, and, more importantly, thermophysical properties, through the Stanton number. The analysis shows that the fluid’s bulk temperature and enthalpy exhibit varying sensitivity to a correlation uncertainty, depending on local thermophysical properties. In fact, the uncertainty in temperature is attenuated near the critical temperature, whereas the uncertainty in enthalpy peaks as the flow crosses the pseudo-critical line. This behavior is further demonstrated to be a consequence of the strong property variations near the critical point, almost independently of the correlation used to estimate heat transfer. The thermodynamic location where the minimal temperature and maximal enthalpy sensitivity occur agree well with the pseudo-critical line, particularly close the critical point, for many fluids, confirming the thermodynamic nature of the phenomenon. Finally, the analysis is applied to data reported in the literature indicating the practical impact of propagated sensitivity.

Numerical simulation of upward flowing supercritical fluids using buoyancy-influence-reflected turbulence model

The mechanism behind heat transfer deterioration, occurring in fluids at supercritical pressures under particular conditions accompanying strong property variations, is not fully understood. The numerical simulations employing RANS type turbulence modelings have never succeeded in reproducing the thermal field of fluids under such conditions, although some success in particular cases has been reported, since the widely-used turbulence models do not account for the property variations and consequential boundary layer deformation. The authors recently reported that an introduction of varying dimensionless damping length (A+) as a function of the shear stress ratio between the wall and boundary layer edge into a turbulence model greatly improved the RANS type numerical simulation of highly buoyant flows. In this paper, the authors attempted to directly integrate the momentum equation under appropriate assumptions and approximations, and to establish a functional relation between A+ and shear stress in the buffer layer (τδt). The introduction of A+ as a function of τδt in the eddy viscosity formula in addition to the property-dependent turbulent Prandtl number, which was proposed earlier by the first author, resulted in numerical simulations of supercritical fluid with strong buoyancy agreeing excellently with the experimental data.

Conservative and nondispersive schemes for diffusion terms with strong property variations

ABSTRACTThe spatial discretization of diffusion terms leads to a theoretical order loss, specially in the presence of strong property and variable gradients. New conservative and nondispersive numerical schemes are proposed to circumvent this issue. Their spectral resolution, numerical order, and cost are evaluated and compared to traditional finite volume and difference schemes. Cost is measured through the computer time and memory it takes these schemes to reach a user-prescribed error tolerance. A manufactured test case is constructed to evaluate these characteristics. Its analysis shows that the new schemes are more cost-effective than traditional schemes under the conditions analyzed.

Numerical simulation of supercritical pressure fluids with property-dependent turbulent Prandtl number and variable damping function

When fluids at supercritical pressure enter into a region close to the pseudo-critical temperature, their numerical simulations with constant turbulent Prandtl number, Prt, and conventional damping function in turbulence modeling are never successful in reproducing the fluid–thermal behaviors, since fluids experience strong physical property variations across the turbulent boundary layer, and their influence has not been properly incorporated into a turbulence model. Several experimental data and numerical studies have indicated that Prt can be very smaller or larger than unity in a region of strong property variation. Recent research, both numerical and experimental, has also indicated that Prt is very likely a function of fluid–thermal variables, when the gradients of the physical properties of the fluid are significant. In this regard, the property-dependent turbulent Prt as a function of physical properties, which has recently been published by the first author, was introduced. Another point deserving attention is that turbulent boundary layer (TBL) deforms so severely, and so does the effective viscous sublayer thickness, A+, such that A+ is no longer a constant, but a function of the degree of TBL deformation due to buoyancy. A+ is expressed as a function of buoyancy and acceleration parameters when using already-known information. With this introduction of the functional form for A+ it is believed that the velocity overshoot and consequential TBL deformation are taken into account. The numerical simulations with property-dependent Prt and buoyancy-dependent A+ of flows under strong buoyancy agreed very well with the experimental data.

Vaporization of two liquid oxygen (LOX) droplets in tandem in convective hydrogen streams at supercritical pressures

Vaporization of two liquid oxygen (LOX) droplets in tandem in supercritical convective hydrogen environments has been numerically investigated. The theoretical formulation consists of a complete set of conservation equations of mass, momentum, energy, and species concentrations. The solution technique is based on a unified treatment of general fluid thermodynamics incorporated into a dual time-stepping preconditioning approach. In addition, a self-consistent property evaluation method is implemented to calculate strong property variations in the transcritical and supercritical fluid regimes. The flow conditions cover a range of pressures between 100 and 400atm and freestream velocities from 2.5 to 20m/s. Special attention is given to the effect of droplet interaction on the droplet dynamics and vaporization characteristics. Results indicate that the vaporization behaviors of the two interacting droplets are different from those of an isolated droplet. The presence of the trailing droplet has a minor effect on the lifetime and trajectory of the leading droplet. In contrast, the lifetime of the trailing droplet is substantially prolonged and its moving trajectory is strongly altered. At an ambient pressure of 100atm, a forward bag-type break-up of the leading droplet is observed when the two droplets are placed closely, with the H/R (the initial droplet spacing to the droplet radius) ratio less than 4. Under the same operating conditions, forward movement takes place for the trailing droplet. Increasing ambient pressure weakens droplet interaction.

Numerical investigation of stably stratified turbulent channel flow under non-Boussinesq conditions

The low Mach number flow between two isothermal infinite parallel horizontal walls at different temperatures under the influence of gravity is studied using Large-Eddy Simulation (LES). As a result of high temperature difference between two walls and strong property variations, the Boussinesq approximation is not valid and is not used. Various test cases with different wall temperature ratios, ranging from 1.01 to 6, and different Richardson numbers, Ri = gL ref/u 2 ref, ranging from 0 to 60, are considered. In the range of temperature ratio and Richardson number considered, the flow stayed turbulent. The study reports on a systematic investigation of the flow regimes. The mean flow properties, the fluctuating values, as well as the energy budgets are presented. The results are in good agreement with the available data in the literature.

A numerical and experimental study of three-dimensional transport in the channel of an extruder for polymeric materials

A numerical study of the three-dimensional flow and heat transfer in a single-screw extruder for polymeric materials such as plastics is carried out. The mathematical model is considerably simplified by conceptually unwrapping the channel and fixing the coordinate system to the rotating screw. Despite this simplification, strong property variations, particularly in the viscosity, complicated cross-sections employed in practical systems, large viscous dissipation effects and non-Newtonian nature of typical extruded materials make the problem a very difficult one to model numerically. Therefore, the transport processes in the extruder channel are simulated by means of a finite-element scheme which employs marching in the down-channel direction. The cross-section of the channel is taken as the commonly used rectangular or self-wiping profiles. An experimental study is also carried out using Newtonian and non-Newtonian fluids in order to provide data for the validation of the numerical model and also to quantify possible recirculation in the channel. Numerical results are presented on the temperature and velocity fields, resulting shear effects, pressure rise, heat transfer rates and viscous heating. The comparisons with experimental results indicate good agreement. A strong recirculating flow is found to arise over the cross-section of the channel. It is shown that a three-dimensional modeling of the process is necessary to capture the effects of recirculation in the channel. However, the marching procedure considerably simplifies the model as well as the inclusion of property changes and chemical reactions.