Data reduction of friction factor, permeability and inertial coefficient for a compressible gas flow through a milli-regenerator

A regenerator of a Stirling machine alternately absorbs and releases heat from and to the working fluid which allows to recycle rejected heat during theoretical isochoric processes. This work focuses on a milli-regenerator fabricated with a multiple jet molding process. The regenerator is a porous medium filled with a dense pillar matrix. The pillars have a geometrical lens shape. Two metallic layers (chromium and copper) are deposited on the polymer pillars to increase heat transfer inside the regenerator. We performed experiments on different milli-regenerators corresponding to three porosities (ε = 0.80, 0.85 and 0.90) under nitrogen steady and oscillating compressible flows (oscillating Reynolds number in the range 0 < Reω < 60 and Reynolds number based on the hydraulic diameter ReDh,max<6000) for different temperature gradients (ΔT < 100°C). Temperature, velocity and pressure experimental measurements are performed with microthermocouples (type K with 7,6 µm diameter), hotwires and miniature pressure sensors, respectively. We identified a threeterm composite correlation equation for the friction factor based on a Darcy-Forchheimer flow model that best-fit the experimental data. In steady and oscillating flows permeabilities and inertial coefficients are of the same magnitude order. Inertial coefficients decrease when the porosities increase.

Constitutive relation and mechanical mechanism analysis in granular lubrication

Purpose Granular lubrication can solve some lubrication problems under many extreme operating conditions. Meanwhile, the flow constitutive relation is one of its unsolved problems in fully understanding its rheological mechanism. Design/methodology/approach In this paper, a plane shear cell under granular lubrication is established by the discrete element method to study the flow constitutive relation and its mechanical mechanism of the hard granular lubricants. Findings Research results show that the flow regimes in granular flow lubrication strongly rely on the dimensionless parameter I, in which it is called the inertial coefficient. When the inertial coefficient I increase, the flow regimes of the granular lubricants also evolve from a quasi-static state to a collisional state accordingly. Comparing to the influence of the restitution coefficient, the friction coefficient of the hard granular lubricants has a strong influence on its constitutive relation of the granular flow lubrication. Finally, it is shows that the dimensionless parameter I has strong influence on the contacts and flow states of this granular lubrication system than the influence of the dimensionless parameter R. Originality/value These findings reveal the constitutive relation and mechanical mechanism of granular lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

Determination of Permeability and Inertial Coefficients of Sintered Metal Porous Media Using an Isothermal Chamber

Sintered metal porous media are widely used in a broad range of industrial equipment. Generally, the flow properties in porous media are represented by an incompressible Darcy‒Forchheimer regime. This study uses a modified Forchheimer equation to represent the flow rate characteristics, which are then experimentally and theoretically investigated using a few samples of sintered metal porous media. The traditional steady-state method has a long testing time and considerable air consumption. With this in mind, a discharge method based on an isothermal chamber filled with copper wires is proposed to simultaneously determine the permeability and inertial coefficient. The flow rate discharged from the isothermal chamber is calculated by differentiating the measured pressure, and a paired dataset of pressure difference and flow rate is available. The theoretical representations of pressure difference versus flow rate show good agreement with the steady-state results. Finally, the volume limit of the isothermal chamber is addressed to ensure sufficient accuracy.

Non-Darcy Flow Experiments of Water Seepage through Rough-Walled Rock Fractures

The knowledge of flow phenomena in fractured rocks is very important for groundwater-resources management in hydrogeological engineering. The most commonly used tool to approximate the non-Darcy behavior of the flow velocity is the well-known Forchheimer equation, deploying the “inertial” coefficient β that can be estimated experimentally. Unfortunately, the factor of roughness is imperfectly considered in the literature. In order to do this, we designed and manufactured a seepage apparatus that can provide different roughness and aperture in the test; the rough fracture surface is established combining JRC and 3D printing technology. A series of hydraulic tests covering various flows were performed. Experimental data suggest that Forchheimer coefficients are to some extent affected by roughness and aperture. At last, favorable semiempirical Forchheimer equation which can consider fracture aperture and roughness was firstly derived. It is believed that such studies will be quite useful in identifying the limits of applicability of the well-known “cubic law,” in further improving theoretical/numerical models associated with fluid flow through a rough fracture.

Prediction of Darcy Permeability and Forchheimer’s Coefficient of Porous Structures Relevant to Regenerator of a Stirling Cryocooler Using a Correlation Based Method

A regenerative heat exchanger is the most vital component in the design of a Stirling cryocooler. Computational Fluid Dynamics (CFD) is the best technique for the design and prediction of the performance of a regenerator. The reliability of the simulation results depend on the accuracy of the Darcy permeability [Formula: see text] and Forchheimer’s inertial coefficient [Formula: see text] used for modeling the momentum transfer in porous media. Usually these coefficients are calculated from pressure drop data obtained from experiment. Because of the requirement of sophisticated equipments for the measurement and analysis of data, experimental study becomes expensive. This paper proposes a friction factor correlation-based method for the prediction of directional permeability and Forchheimer’s inertial coefficient of wire mesh structures relevant to Stirling cryocooler. The friction factor for the flow of helium through #325, #400 and #635 SS wire matrices with porosities of 0.6969, 0.6969 and 0.6312 are calculated using standard correlations and compared with the friction factor given by Clearman et al. based on steady flow experimental study. The friction factor obtained from Blass and Tong/London correlations are in agreement with that of Clearman et al. The viscous and inertial resistances are calculated from the friction factor obtained from Blass and Tong/London correlations. Using these values, the regenerator was modeled as a porous media in Fluent. From the steady flow simulation, pressure drop at different mass flow rates (0.08–1.44[Formula: see text]g/s) is obtained. The maximum deviation of predicted pressure drop from the reported experimental data is 15.14%. The Darcy permeability [Formula: see text] and Forchheimer’s inertial coefficient [Formula: see text] obtained from correlation-based method was used for modeling the oscillatory flow of helium through a #400 regenerator. The pressure amplitude and phase at regenerator exit were obtained at different frequencies. The average deviation of predicted pressure amplitude from the experimental data is 15.83%. The model could predict the phase angle also accurately. Therefore, the proposed method can be used to calculate the hydrodynamic parameters of woven wire screen matrices applied to Stirling cryocoolers.

Pore-Scaled Analytical Modelling of Permeability and Inertial Coefficient for Pressure Drop Prediction of Open-Cell Metallic Foams

Amongst various porous media, open-cell metallic foams exhibit distinctive properties: relatively low manufacturing cost, ultra-low density, moderate stiffness and strength, and high surface area-to-volume ratio. They have been, therefore, utilized in a variety of applications such as microelectronics cooling, fuel cells, and compact heat exchangers. For such applications, the knowledge of pressure drop of fluid flowing across the foam is often a key issue, enabling control of fluid flow, heat transfer enhancement, planning and designing chemical engineering processes, optimal flow analysis as well as practical designs. We present in this paper an analytical model capable of predicting the pressure drop of a Newtonian incompressible fluid flowing unidirectionally across isotropic and fully-saturated micro open-cell cellular foams within the Darcy and Forchheimer flow regimes. Analytical exploitations are conducted to determine the foam permeability and inertial coefficient. The analytical model is based on the basis of volume-averaging approach and the assumption of piece-wise plane Poiseuille flow with the modified cubic lattice with spherical node at the junction of struts. To better mimic the foam struts shape, a concave-triangular-shaped strut consisting of two nose-to-nose cones is considered and particular attentions have been paid to both analytically and numerically examine the node shape as well as struts shape effect. Built upon a generalized tortuosity model derived from the modified cubic unit cell, an analytical model of permeability on the basis of a cubic unit cell is developed, valid within a typical engineering range of porosity (ε = 0.86 ∼ 0.98) and pore size (0.254 mm ∼ 5.08 mm). With the effect of Reynolds number considered, the pore-scaled Reynolds number dependent drag coefficient expression is introduced and through this the inertial coefficient is analytically modeled on the basis of flow over bluff bodies, which is found to agree well with experimental data from various sources. The modeling procedure for pressure drop (permeability and inertial coefficient) is based on physical principles and geometrical considerations, and the model predictions agree satisfactorily with existing experimental data. Results show that by building the analytical model on the basis of a cubic unit cell to represent the topology of metallic foams, pressure drops as well as hydrodynamic conditions within both the Darcy and Forchheimer regimes in a Newtonian fluid can be analytically predicted.

Inertial Coefficient Adopted in Pile-Pier Structure under Deep Water

In order to study the effect of hydrodynamic pressure acted on pile-pier structure in deep water, an investigation on the inertial coefficient is developed. Based on the Morison equation, the usual suggested value is analyzed, especially the noncircular slender cylinder is considered. Besides, the effect of scale of structure is studied, including accurate algorithm and approximation algorithm. Study results indicate that the Morison equation is also applied to noncircular slender cylinder, and the value of inertial coefficient is influenced by the scale of structure. Moreover, the calculated results of accurate algorithm and approximation algorithm are consistent within a certain range, so the choice of calculation method should be governed by the required precision.

Forced Convection Heat Transfer in Spray Formed Copper and Nickel Foam Heat Exchanger Tubes

A thermal spray coating process was used to deposit dense 2 mm thick metal skins on the surfaces of square cross-section channels (300 mm × 20 mm × 20 mm) of nickel and copper foams with 10 and 40 PPI (pores per inch) pore densities. A heater was wrapped around the channels to apply surface heat-fluxes varying from 427 to 6846 W/m2. Compressed air was blown through the channels at flow rates of 5–80 l/min. Foam and fluid temperature distributions along the length of the channel and the pressure drop across it were measured. The foam was modeled as a porous medium and properties such as permeability K and inertial coefficient CF were determined from the experimental data. Local and average convective heat transfer coefficients were calculated from air and foam temperature measurements. Nusselt numbers were calculated and correlated in terms of the Reynolds, Prandtl, and Darcy numbers. Heat transfer to air flowing through a 10 PPI foam channel was shown to have increased nearly seven times compared to that of hollow tube with the same dimensions.