Nonuniform Fluid Research Articles

Nonuniform temperature boundary condition effects on data center cross flow heat exchanger dynamic performance

Abstract Cross flow heat exchangers are important components used in data center cooling systems. The thermal environment usually becomes very complex due to the cooling system design configuration, including individually operated IT equipment inside the data center. Nonuniform fluid inlet temperature conditions may become very common in the cross flow heat exchangers, and may impact the performance of these heat exchangers. In this study, cross flow heat exchanger performance is investigated accounting for the nonuniform input effect of fluid inlet temperature. Several types of nonuniform inlet temperature boundary condition model are developed, based on the several actual problems in data center thermal management. The detailed effect of these nonuniform temperature boundary conditions on both the steady state and transient responses of a crossflow heat exchanger are investigated. The combined effects of the physical model parameters with nonuniform temperature boundary conditions are also analyzed. Several specific cases related to the practical application situations of cross flow heat exchangers and thermal management in data centers are outlined and analyzed in this study.

A detailed nonuniform thermal model of a parabolic trough solar receiver with two halves and two inactive ends

In this paper a detailed one dimensional nonuniform thermal model of a parabolic trough solar collector/receiver is presented. The entire receiver is divided into two linear halves and two inactive ends for the nonuniform solar radiation, heat transfers and fluid dynamics. Different solar radiation and heat transfer modes can be taken into consideration for these four different regions respectively. This enables the study of different design parameters, material properties, operating conditions, fluid flow and heat transfer performance for the corresponding regions or the whole receiver. Then the nonuniform model and the corresponding uniform thermal model are validated with known performance of an existing parabolic trough solar collector/receiver. For applications, the uniform thermal model can be used to quickly compute the integral heat transfer performance of the whole PTC system while the nonuniform thermal model can be used to analyze the local nonuniform solar radiation and heat transfer performance characteristics and nonuniform heat transfer enhancements or optimizations. Later, it could also be effectively used with an intelligent optimization, such as the genetic algorithm or the particle swarm optimization, to quickly evaluate and optimize the characteristics and performance of PTCs under series of nonuniform conditions in detail.

Research on MRF Shear Stress Measurement Method under Non-Uniform Magnetic

Magnetorheological fluid as an important branch of the emerging intelligent material, its excellent characteristics make it widely used in electrical system and mechanical system. Common MRF system environment is limited to a uniform magnetic field, the practical application process to the vast of magneto rheological characteristics devices has shown the phenomenon, which does not match the uniform magnetic field theory, the reason is that the actual work environment is the non-uniform magnetic [1-2]. To study the characteristics of MRF shear stress in a non-uniform magnetic field, this paper established a non-uniform field magneto-rheological fluid shear stress measurement device. Comparing the experimental shear stress curves with the uniform magnetic field measured shear stress curves, we found that the non-uniform magnetic field strength of the environmental equivalent shear stress values ​​compared with the uniform magnetic field data have large deviation, this indicates that the existing uniform magnetic field theory is not well to explain non-uniform magnetic field shear properties of MRF, we need to build the introduction of non-uniform magnetic field theory.

Analysis of Flow Mal-Distribution in a Cross-Flow Heat Exchanger

Flow mal-distribution is defined as the non-uniform fluid flow distribution among the parallel channels having a common header. Flow mal-distribution is present in every header channel assembly. This mal-distribution has a significant effect on the performance of the heat exchanger by increasing the pressure drop and affecting the heat transfer characteristics. However, in designing a heat exchanger, a uniform flow distribution in each channel is assumed. The present work attempts to reduce the flow mal-distribution in a cross flow heat exchanger. A numerical analysis is done using a commercial code ANSYS FLUENT 3D and the results are validated experimentally. A parametric study is done by changing the size of the channels within the heat exchanger so as to reduce the flow mal-distribution. The effect of varying channel size on flow mal-distribution and pressure drop across the heat exchanger is studied and a geometry with reduced flow mal-distribution is found.

Pressure drop in reverse electrodialysis: Experimental and modeling studies for stacks with variable number of cell pairs

Reverse electrodialysis (RED) is a sustainable technology for salinity gradient energy harvesting. In order to make the process economically competitive, it is desirable to operate it at the highest possible net power density, which depends on the RED stack geometry and on the pressure drop along its pathways and, thus, on the energy spent for solutions pumping. The fluid flow in RED stacks generally occurs in rectangular compartment channels, equipped with spacers. The effects of spacers design and properties have been studied extensively in recent years. However, the other possible causes for a RED stack and their relative impact on the process performance have not yet been systematically studied. In this study the partial pressure drops in (1) distribution ducts, (2) branches, (3) beams, (4) due to sudden section expansion between the beam and the compartment channel and (5) in the compartment channel were taken into consideration. A model for the total pressure drop inside a RED stack, with a parallel fluid flow distribution through the compartments, is proposed and experimentally validated for lab-scale RED stacks with sheet flow spacers and compared with an open channel (spacer-free) design. The importance of each partial pressure drop was then evaluated quantitatively through model simulations for industrial-scale stacks with an increasing number of cell pairs. It was found that the net power density decreases when the cell-pair number increases, since the partial pressure drop in the branches becomes dominant. Moreover, the possible reasons for a non-uniform fluid flow distribution are discussed, thus making the proposed model useful for planning and/or optimization of RED stacks design.

Congruent Chemical Potentials and Insertion Works in Establishing Nonuniform-Fluid Structures via Uniform-Fluid Properties

We propose an effective density ρpseudo that engenders direct mapping of the free energy FU of uniform fluids to the free energy FN of nonuniform fluids by requiring FN = FU (at ρpseudo). The equality is called the congruence condition. It is made possible by considering the statistical mechanical theory: the potential distribution theorem (PDT). The PDT connects three quantities: the work Wins(z) needed for inserting a test particle into the fluid, the chemical potential μ0 of the bulk fluid, and the nonuniform singlet density ρw(1)(z). We use Monte Carlo (MC) data to obtain the insertion work Wins(z) (via the Euler–Lagrange equation) from the probability densities ρw(1)(z). The concept of the congruent effective density ρpseudo is applicable to general interaction potentials, not restricted to the hard sphere type. We examine thus two simple fluids adsorbed on a hard wall: (i) the hard spheres and (ii) the Lennard-Jones fluid for comparison. We discern the difference in behavior of the effective density...

KINETIC THEORY OF EQUILIBRIUM AXISYMMETRIC COLLISIONLESS PLASMAS IN OFF-EQUATORIAL TORI AROUND COMPACT OBJECTS

The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal MHD theory. These stationary structures can represent plausible candidates for the modelling of coronal plasmas expected to arise in association with accretion discs. However, accretion disc coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can be determined also in the case of collisionless plasmas for which treatment based on kinetic theory, rather than fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically-kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic, energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.

The dynamic reliability analysis of pipe conveying fluid based on a refined response surface method

The dynamic reliability of the pipe conveying fluid was analyzed by a refined response surface method (RSM) in this study. In the refined RSM, a new response surface expression was proposed based on functional variables with the physical characteristics of basic random variables. The sampling points were located on Gauss Hermite integration points along the coordinate axes of standard normal random variables. The response surface was constituted via an iterative strategy, in which the information of the sampling points could be utilized richly. On the other hand, Hamilton’s principle for open systems was applied to formulate the motion equations of the pipe conveying non-uniform axial fluid. The proposed RSM was used to analyze the dynamic reliability and sensitivity of the pipe conveying non-uniform axial fluid. As shown in the numerical results, the refined response surface method leads to the better approximation of the nonlinear limit state function, higher precision and better stability of the failure probability estimation, especially for the dynamic reliability analysis of the pipe conveying fluid.

Chemical potential, Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation

We present a method based on kinetic Monte Carlo (kMC) to determine the chemical potential, Helmholtz free energy and entropy of a fluid within the course of a simulation. The procedure requires no recourse to auxiliary methods to determine the chemical potential, such as the implementation of a Widom scheme in Metropolis Monte Carlo simulations, as it is determined within the course of the simulation. The equation for chemical potential is proved, for the first time in the literature, to have a direct connection with inverse Widom potential theory in using real molecules rather than ghost molecules. We illustrate this new procedure by several examples, including fluid argon and adsorption of argon as a non-uniform fluid on a graphite surface and in slit pores.

Magnetic loop generation by collisionless gravitationally bound plasmas in axisymmetric tori

Current-carrying string loops are adopted in astrophysics to model the dynamics of isolated flux tubes of magnetized plasma expected to arise in the gravitational field of compact objects, such as black holes. Recent studies suggest that they could provide a framework for the acceleration and collimation of jets of plasma observed in these systems. However, the problem remains of the search of physical mechanisms which can consistently explain the occurrence of such plasma toroidal structures characterized by nonvanishing charge currents and are able to self-generate magnetic loops. In this paper, the problem is addressed in the context of Vlasov-Maxwell theory for nonrelativistic collisionless plasmas subject to both gravitational and electromagnetic fields. A kinetic treatment of quasistationary axisymmetric configurations of charged particles exhibiting epicyclic motion is obtained. Explicit solutions for the species equilibrium phase-space distribution function are provided. These are shown to have generally a non-Maxwellian character and to be characterized by nonuniform fluid fields and temperature anisotropy. Calculation of the relevant fluid fields and analysis of the Ampere equation then show the existence of nonvanishing current densities. As a consequence, the occurrence of a kinetic dynamo is proved, which can explain the self-generation of both azimuthal and poloidal magnetic fields by the plasma itself. This mechanism can operate in the absence of instabilities, turbulence, or accretion phenomena and is intrinsically kinetic in character. In particular, several kinetic effects contribute to it, identified here with finite Larmor radius, diamagnetic and energy-correction effects together with temperature anisotropy, and non-Maxwellian features of the equilibrium distribution function.

Modelling and optimizing the gas-lift effect system for texturing silicon

Modelling and simulation techniques were used to understand the fluid flow patterns inside the silicon texturing system operating under the gas-lift effect (GLE) for solar cell applications. Experiments were performed which confirmed the validity of the simulation model and the simulated results. It was determined that due to the original non-optimal inlet, the fluid flow pattern and the non-uniform fluid velocity distribution inside the system resulted in the generation of lower velocity regions on the surface of the textured silicon. The simulation tool validated the correlation of the lower fluid velocity with the reduced surface coverage, uniformity and subsequent less optimal surface reflectivity. Various inlet designs were modelled and evaluated for optimal performance. The best-case inlet design was fabricated and tested resulting in the validation of the simulation work and significant improvement in the GLE texturing system performance. With the new inlet design, as the fluid velocity reaches and goes beyond some critical value (in this case 0.047 m s−1) in areas that had shown lower velocity in the original inlet design (mainly close to the inlet and side walls), the observed morphology and surface reflectivity improve significantly with values very similar to those of the higher velocity areas.

Relationship between local molecular field theory and density functional theory for non-uniform liquids

The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.

Heterogeneities of flow in stochastically generated porous media

Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media comprising complex networks of connected pores. Inside each pore space, the Navier-Stokes equations are numerically integrated until steady state velocity and pressure fields are attained. The intricate pore structures exert spatially variable resistance on the fluid, and resulting velocity fields have a wide range of magnitudes and directions. Spatially nonuniform fluid fluxes are observed, resulting in principal pathways of flow through the media. In some realizations, up to 25% of the flux occurs in 5% of the pore space depending on porosity. The degree of heterogeneity in the flow is quantified over a range of porosities by tracking particle trajectories and calculating their attributes including tortuosity, length, and first passage time. A representative elementary volume is first computed so the dependence of particle based attributes on the size of the domain through which they are followed is minimal. High correlations between the dimensionless quantities of porosity and tortuosity are calculated and a logarithmic relationship is proposed. As the porosity of a medium increases the flow field becomes more uniform.

Effects of non-uniform fluid saturation distribution on pressure transient analysis

Variations of fluid saturation in formation induce unusual trends in pressure transient data, which may cause ambiguities in well test interpretations. Nevertheless, uniform saturation distribution is a common assumption applied in all multiphase well test analysis methods and the effects of fluids saturation changes have not been taken into account in all these approaches. We present a theoretical model which includes non-uniform fluid saturation in pressure transient formulation. The application of the developed model is demonstrated using a simulation of a reservoir containing non-uniform oil and water saturations in the initial condition. This model provides a basis for better interpretation of unusual pressure transient behavior affected by non-uniform saturation distribution.

Comparative analysis of symmetries for the models of mechanics of nonuniform fluids

The symmetries for the main models of mechanics of binary fluids are calculated by the methods of the theory of continuous groups. The fundamental system of the differential form of the main conservation laws is characterized by the ten-parametric Galilean group. The Navier-Stokes set of equations possesses an extended set of symmetries with infinite dimensionality. Simplification of the model changes the order of the set of equations of motion, which leads to the impossibility to take into account the complete set of boundary conditions and formation of discontinuities in solutions for reduced models.

3D MODELING AND DYNAMIC CHARECTARIZATION OF STEAM TURBINE PACKET BLADE AND CYCLIC SYMMETRIC ANALYSIS

A rotating turbine blade (bucket) is the component, which converts the kinetic energy of the flowing fluid into mechanical energy. Thus the reliability of these blades is very important for the successful operation of a turbine. Turbine blades experience fluctuating forces when they pass through non-uniform fluid flow from the stationary vanes. The basic design consideration is to avoid or to minimize the dynamic stresses produced by the fluctuating forces. The aim of the project is to estimate the stresses occurring in the packet blade of steam turbine in last stage due to centrifugal forces and steam bending forces. The blade, root and disc are modeled separately in ANSYS package and they are assembled using constrained equations. After giving the constrain equations cyclic symmetric analysis conditions are applied and then static and model analysis are carried out. After that Campbell and safe diagrams are plotted.

Absolute Stability of Axisymmetric Perturbations in Strongly Magnetized Collisionless Axisymmetric Accretion Disk Plasmas

This Letter presents a kinetic description of low-frequency and long-wavelength axisymmetric electromagnetic perturbations in nonrelativistic, stronglymagnetized, and gravitationallybound axisymmetric accretion-disk plasmas in the collisionless regime. The analysis, carried out within the framework of the Vlasov-Maxwell description, relies on stationary kinetic solutions which allow for the simultaneous treatment of nonuniform fluid fields, stationary accretion flows, and temperature anisotropies. It is demonstrated that these stationary configurations are actually stable against axisymmetric kinetic instabilities of this type. As a fundamental consequence, this rules out the possibility of having the axisymmetric magnetorotational or thermal instabilities to arise in these systems.

Kinetic description of rotating Tokamak plasmas with anisotropic temperatures in the collisionless regime

A largely unsolved theoretical issue in controlled fusion research is the consistent kinetic treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchallenged to date. The goal of this paper is to address the problem within the framework of Vlasov-Maxwell description. The gyrokinetic treatment of charged particles dynamics is adopted for the construction of asymptotic solutions for the quasi-stationary species kinetic distribution functions. These are expressed in terms of the particle exact and adiabatic invariants. The theory relies on a perturbative approach, which permits to construct asymptotic analytical solutions of the Vlasov-Maxwell system. In this way, both diamagnetic and energy corrections are included consistently into the theory. In particular, by imposing suitable kinetic constraints, the existence of generalized bi-Maxwellian asymptotic kinetic equilibria is pointed out. The theory applies for toroidal rotation velocity of the order of the ion thermal speed. These solutions satisfy identically also the constraints imposed by the Maxwell equations, i.e., quasi-neutrality and Ampere’s law. As a result, it is shown that, in the presence of nonuniform fluid and EM fields, these kinetic equilibria can sustain simultaneously toroidal differential rotation, quasi-stationary finite poloidal flows and temperature anisotropy.

Adsorption of hard spheres: structure and effective density according to the potential distribution theorem

We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution theorem gives the work required to insert a test particle into the bath molecules under the action of the external (wall) potential. This insertion work W_ins can be obtained from Monte Carlo (MC) simulation (e.g. from Widom's test particle technique) or from an analytical theory. The pseudo-densities are constructed thusly so that when their values are substituted into a uniform-fluid equation of state (e.g. the Carnahan-Starling equation for the hard-sphere chemical potentials), the MC nonuniform insertion work is reproduced. We characterize the pseudo-density behavior for the hard spheres/hard wall system at moderate to high densities (from \rho^*= 0.5745 to 0.9135). We adopt the MC data of Groot et al. for this purpose. The pseudo-densities show oscillatory behavior out of phase (opposite) to that of the singlet densities. We also construct a new closure-based density functional theory (the star-function based density functional theory) that can give accurate description of the MC density profiles and insertion works. A viable theory is established for several cases in hard sphere adsorption.

Kinetic theory of heterogeneous nucleation; effect of nonuniform density in the nuclei

The heterogenous nucleation of a liquid from a vapor in contact with a planar solid surface or a solid surface with cavities is examined on the basis of the kinetic theory of nucleation developed by Nowakowski and Ruckenstein [J. Phys. Chem. 96 (1992) 2313] which is extended to nonuniform fluid density distribution (FDD) in the nucleus. The latter is determined under the assumption that at each moment the FDD in the nucleus is provided by the density functional theory (DFT) for a nanodrop. As a result of this assumption, the theory does not require to consider that the contact angle which the nucleus makes with the solid surface and the density of the nucleus are independent parameters since they are provided by the DFT. For all considered cases, the nucleation rate is higher in the cavities than on a planar surface and increases with increasing strength of the fluid-solid interactions and decreasing cavity radius. The difference is small at high supersaturations (small critical nuclei), but becomes larger at low supersaturations when the critical nucleus has a size comparable with the size of the cavity. The nonuniformity of the FDD in the nucleus decreases the nucleation rate when compared to the uniform FDD.