Uniform Pressure Assumption Research Articles

Special-shape ring dampers for thin-walled gears subjected to traveling-wave vibration

Ring dampers are solutions to the traveling-wave vibration (TWV), a threat to high-speed thin-walled gears. But a complete design method for them is lacking, and normal dampers have contact problems, which make TWV mitigation less effective. So, a novel design method is proposed for the special-shape ring damper (SSRD), which is an improved type that aims to have good energy dissipation and contact performance. The methodology starts by estimating the optimal contact pressure, which acts on the SSRD to achieve the maximum frictional dissipation. Then its deformation is calculated based on the stress function method to get the shape that can perform the desired pressure. Furthermore, high-speed experiments are made to validate the TWV attenuation of the experimental SSRD. And its contact features are investigated by light transmission tests and finite element models. The results show that the SSRD can maintain almost complete contact with the gear, avoiding energy dissipation loss due to uncontacted parts. It also makes the contact pressure more even, which fits better with the uniform pressure assumption in the design methodology. Moreover, the SSRD effectively suppresses the TWV, and after damper installation, the strain peak reduction for the experimental gear exceeds 67.5%. The proposed methodology provides a theoretical basis for the ring damper design, and can be applied to ensure safe operation of aero-engine gears by suppressing their harmful dynamics behavior, TWV.

Thermal Behavior of Conical Friction Element Under Different Contact Pressure Boundaries

Abstract The high temperature generated on the contact interfaces of the conical friction element in clutches due to the sliding frictional heat should be responsible for the synchronization failure. In this study, an analytic model taking account of the capsizing moment and stress singularity at the end of the contact interface is established to solve the contact pressure distribution. Then, a three-dimensional finite element model has been developed to analyze the transient thermal behavior of the conical friction element. The contact pressure and temperature distribution generated along the contact interfaces are investigated and compared between the proposed new model, the combined wear assumption, and the uniform pressure assumption. Furthermore, the variations in temperature obtained from the new model and the other two assumptions are compared to the experimental results. The results show that the temperature simulated by the new model has a good agreement with reality. The maximum temperatures obtained by the new model are 95.53 °C and 71.67 °C, and the measured values are respectively 84.98 °C and 65.46 °C at the measuring position under the given two working conditions.

Quantifying the Effects of Non‐Hydrostatic Stress on Multi‐Component Minerals

AbstractMineral compositions are used to infer pressures, temperatures, and timescales of geological processes. The thermodynamic techniques underlying these inferences assume a uniform, constant pressure. Nonetheless, convergent margins generate significant non‐hydrostatic (unequal) stresses, violating the uniform pressure assumption and creating uncertainty. Materials scientists F. Larché and J. Cahn derived an equation suitable for non‐hydrostatically stressed geologic environments that links stress and equilibrium composition in elastic, multi‐component crystals. However, previous works have shown that for binary solid solutions with ideal mixing behavior, hundreds of MPa to GPa‐level stresses are required to shift mineral compositions by a few hundredths of a mole fraction, limiting the equation's applicability. Here, we apply Larché and Cahn's equation to garnet, clinopyroxene, and plagioclase solid solutions, incorporating for the first time non‐ideal mixing behavior and more than two endmembers. We show that non‐ideal mixing increases predicted stress‐induced composition changes by up to an order of magnitude. Further, incorporating additional solid solution endmembers changes the predicted stress‐induced composition shifts of the other endmembers being considered. Finally, we demonstrate that Larché and Cahn's approach yields positive entropy production, a requirement for any real process to occur. Our findings reveal that stresses between tens and a few hundred MPa can shift mineral compositions by several hundredths of a mole fraction. Consequently, mineral compositions could plausibly be used to infer stress states. We suggest that stress‐composition effects could develop via intracrystalline diffusion in any high‐grade metamorphic setting, but are most likely in hot, dry, and strong rocks such as lower crustal granulites.

A correction to the analysis of bending under tension tests

The existing analytical solutions for determining an average coefficient of friction in bending under tension tests are revisited. The most commonly used equations are based on the assumption of uniform pressure in the contact interface, which is proven to be a statically inadmissible assumption. New analytical solutions are presented based on the assumption of concentrated forces, which are shown to be statically admissible. Existing literature supports the existence of localized peaks in the pressure distribution in terms of both numerical simulations and experimental results. Due to the inhomogeneous pressure distribution, bending under tension tests are not considered appropriate for determining the coefficient of friction, but rather a qualitative test capable of relative comparison of tribo-systems.

Revisiting the flattened Brazilian disc configuration - Part I: The actual boundary conditions

In a recently presented analytic solution for the Flattened Brazilian Disc (FBD), it was shown that under the usually adopted assumption of uniform pressure on the flat edges of the FBD these edges turn to appear bent after deformation. Taking into account the high rigidity and flatness of the loading platens this bent sounds somehow unnatural. In the present study an attempt is undertaken to confront this unnatural bent by considering alternative non-uniform stress distributions on the flat edges of the FBD. In this context, the present paper, which is the first part of an ongoing research project, deals with the 1st fundamental problem for a FBD when it is compressed between two rigid flat stamps of the same length with the flat edge of the FBD. The distribution of the normal compressive stresses, and that of the respective frictional ones, imposed to the flat edge of the FBD are adopted from the approach of Muskhelishvili for the contact problem of a rigid flat stamp compressed against an elastic half plane, here the FBD in question. After obtaining the complex potentials for this 1st fundamental problem for the FBD, the stresses and the displacements are calculated in closed form everywhere on the FBD’s cross section. For the assessment of the analytic solution, a numerical model is also developed, with the aid of the Finite Element Method. The agreement between the theoretical and numerical analyses is satisfactory.

Relative importance of inter-particle mass transfer resistance in the modeling of adsorption chiller porous bed

In order to investigate the effects of various parameters on the adsorption chiller performance, the adsorbent bed must be modeled with the appropriate governing equations and assumptions. One of the assumptions, which greatly influences the modeling complexity and computational cost is the bed uniform pressure assumption, which relaxes the need for solving the momentum equations governing the motion of the refrigerant vapor through the porous bed. However, in some bed conditions the bed pressure distribution should be calculated and the inter-particle resistance cannot be neglected, which in turn requires the determination of the bed velocity field. It is of great practical importance to know in advance, whether the uniform pressure approach is appropriate for the modeling of the problem in hand. In this study, a dimensionless parameter based on the scale up analysis of the governing equations is introduced, which can be calculated based on the input data of the problem to decide about the appropriate bed pressure assumption prior to start the modeling process.

Closed-form equation for subsidence due to fluid production from a cylindrical confined aquifer

Ground surface subsidence due to groundwater production is a significant problem. Many attempts have been made to develop analytical models to forecast subsidence rates as a consequence of groundwater production. Previous analytical solutions either make limiting assumptions about the stress regime (e.g., radially symmetric with uniaxial strain or radially symmetric with zero incremental vertical total stress) or assume that the pressure distribution within the aquifer is uniform. Imposing assumptions about the stress regime lead to an overestimate of subsidence. Imposing a uniform pressure assumption often leads to an underestimate of subsidence. In this article, the principle of superposition is applied to extend a previous analytical solution, for a cylindrical uniform pressure change, to allow for a non-uniform pressure distribution resulting from constant rate production of a viscous fluid from a cylindrical confined aquifer of finite permeability. Results from the analytical solution are verified by comparison with a set of fully coupled hydro-mechanical finite element simulations. The analytical solution for subsidence directly above the production well (or uplift above an injection well) can be written in closed-form and is straightforward to evaluate. The equation also shows that, for many practical purposes, ground surface subsidence is insensitive to production fluid viscosity and aquifer permeability when the aquifer radius is less than the aquifer depth below the ground surface.

Dusty-Gas Model with Uniform Pressure: A Numerical Study on the Impact of a Frequent Inconsistent Assumption in SOFC Electrode Modeling

One of the most popular models adopted to describe the gas transport in porous electrodes is the dusty-gas model. Such a model is commonly applied in the literature under the assumption of uniform pressure. However, as we recently summarized in a short communication [A. Bertei, C. Nicolella, J. Power Sour. 279 (2015) 133-137], this assumption is incompatible with the dusty-gas model formulation and leads to serious inconsistencies, for example, fluxes that do not obey reaction stoichiometry. In such a case the model fails to predict partial pressure profiles, concentration overpotentials and limiting currents. In this study, we report the quantification of the error in the prediction of partial pressure profiles and concentration overpotential due the inconsistent assumption of uniform pressure in a broad range of conditions, focusing mainly on SOFC anodes. Simulations show that an inconsistent use of the dusty-gas model may lead to relative errors in the prediction of concentration overpotential as large as 60%. In H2/H2O/N2 mixtures, the error increases as the molar fraction of the inert species decreases and is maximum in binary H2/H2O mixtures. In addition, the error increases as porosity, pore size and water molar fraction increase while it decreases as the current density and the electrode thickness increase. These results are helpful to quantify the impact of an inconsistent use of the dusty-gas model in the literature and to promote a coherent gas transport modeling.

Dusty-Gas Model with Uniform Pressure: A Numerical Study on the Impact of a Frequent Inconsistent Assumption in SOFC Electrode Modeling

One of the most popular models adopted to describe the gas transport in porous electrodes is the dusty-gas model (DGM). However, such a model is commonly applied under the assumption of uniform pressure, which is incompatible with the DGM formulation and does not allow fluxes to obey reaction stoichiometry. In such a case, the model fails to predict partial pressure profiles. In this study, the quantification of the error in the prediction of concentration overpotential, due the inconsistent assumption of uniform pressure, is obtained by simulating the gas transport in solid oxide fuel cell anodes in a broad range of conditions. Simulations show that an inconsistent use of the dusty-gas model may lead to relative errors in the prediction of concentration overpotential as large as 60%, especially in binary H2/H2O mixtures.

ANALYSIS OF HEAT AND MASS TRANSFER IN THE ADSORBENT BED OF A THERMAL WAVE ADSORPTION COOLING CYCLE

A coupled heat and mass transfer analysis of the adsorbent bed of a thermal wave adsorption cooling cycle is performed. The adsorbent bed is modeled two dimensionally. Governing equations for energy, mass and momentum transfers are solved by Comsol Multiphysics simultaneously. Variations of temperature, pressure, adsorption capacity, equilibrium adsorption capacity and mass transfer coefficient for a finless tube adsorbent bed are presented with multicolored plots. Desorption process is simulated in the model. Results show that the adsorbent bed reaches the maximum cycle temperature uniformly after 5000s. Uniform pressure assumption can be used in the bed due to small pressure gradient during the process. Adsorption capacity decreases from 26.1% to 8.89% in 5000s. Temperature front progresses along the bed creating a thermal wave. The thermal wave length is needed to be short to enhance the bed effectiveness regenerating more heat between the beds of the thermal wave cycle. It can be concluded that a parametric study is recommended for a future work in order to investigate the effects of design and operational parameters on the dependent variables and thermal wave length.

Fluid‐driven multiple fracture growth from a permeable bedding plane intersected by an ascending hydraulic fracture

In bedded sedimentary rocks, the energy for spontaneous growth of multiple vertical fractures from a bedding plane may be provided by an overpressurized sublayer fracture that connects a fluid source to the bedding plane. In this paper, using our coupled deformation and flow model, we study the processes and mechanisms involved in the formation and interaction of closely space fractures from preexisting flaws or starter fractures located along the bedding plane. Fracture growth from multiple flaws can be convergent, parallel or divergent, depending on the factors like contrasts in moduli and far‐field stresses, flaw sizes and locations, and initial bed conductivity, fluid viscosity, and injection rate, as well as time. The results presented here have been obtained for conditions where fluid viscous dissipation is dominant, in contrast to other results available in literature based on uniform pressure assumption equivalent to use of an inviscid fluid. It is demonstrated that the earlier a hydraulic fracture starts to extend, the more likely it is to become the primary fracture in a system of closely spaced fractures. The fracture closest to the fluid source typically grows faster as a result of a higher pressure level because viscous dissipation results in a decrease in pressure with distance from the fluid source. But its development does not completely inhibit the growth of other hydraulic fractures. Simultaneous growth of closely spaced fractures is supported by the local stress and energetic analyses, and the fracture distance can be very small. Their length to spacing ratio is accordingly much larger than that predicted previously. Under certain circumstances, a longer and more permeable fracture may grow to a greater extent than a shorter fracture closer to the fluid source, which may grow toward and merge with the longer fracture to create fracture clusters adjacent to a bedding plane.

Determination of pressure-dependent friction coefficient from draw-bend test and its application to cup drawing

Friction under lubricated conditions is known to depend on pressure, and experimental determination of this dependence has typically quantified pressure as a uniform value over the contact area. However, non-uniform pressure distributions at the contact interfaces of draw-bend tests have been reported from various experiments and simulations. A previous study by the authors had evaluated the conventional methodology, which assumes uniform pressure distribution to estimate friction coefficients from draw-bend friction tests, and has concluded that the conventional methodology is only valid for measuring an average friction coefficient over the pressure range, which exists in a specific draw-bend system. In this paper, a new methodology to determine friction coefficients from draw-bend friction tests considering the pressure non-uniformity is suggested. In the methodology, contact pressure maps obtained from simulations, instead of the uniform pressure assumption, are included in the analysis of test data to measure the pressure dependency of friction coefficient. The proposed method is applied to friction measurement of aluminum sheets with anisotropic mill-finish surface and friction coefficients were obtained as functions of contact pressure, sliding velocity and sliding direction. Lastly, the obtained friction data were implemented into a finite element code, and circular cup drawing experiments and simulations were performed to validate the methodology.

Experimental and Numerical Investigation of Instructions for Hyperelastic Membrane Inflation Using Fluid Structure Coupling

During the design process of membrane structure to resist to high pressure loading, and the characterization of hyperelastic material, a structure made up of thin rubber undergoes large deformation and rotation under high pressure loading out of high pressurized gas. Until recently, to simulate the inflation of the hyperelastic membrane, a uniform pressure based on thermodynamic model or experimental tests is applied to the structure, as boundary conditions. From a computational time point of view, this approach is very fast, since no computational fluid dynamics is involved in the simulation. However, at the late stage of the membrane inflation, uniform pressure simulations lead to numerical instability due to the lack of fluid that generates damping effects and prevent numerical instability. Thus the uniform pressure assumption is unstable at the end phase of the inflation for long time duration. To simulate accurately the inflation process, computational fluid dynamics in a moving fluid domain as well as fluid structure interaction (FSI) algorithms need to be performed for accurate pressure prediction and fluid structure interface coupling. For the simulation of gas dynamic in a moving domain, Arbitrary Lagrangian Eulerian (ALE) formulation is used. Both simulations, uniform pressure and ALE simulation for computational gas dynamics, were compared to test data, indicating satisfactory results in terms of correlation for earlier stage of the inflation. However for late stage inflation, simulation using uniform pressure show numerical instability leading to the blow up of the structure. With the more recently developed procedure, ALE theory, shows the greatest accuracy, both in terms of graphical and schematic comparison, especially at the late stage of the inflation process. As a result, the new simulation procedure model can be utilised to research into the effects of changing the designs of the membrane structure to resist to highly pressure loading on soft rubber material.

CFD-based representation of non-Newtonian polymer injectivity for a horizontal well with coupled formation-wellbore hydraulics

Polymers are often injected into horizontal wells during enhanced oil recovery (EOR) processes. During injection of these high-viscosity, non-Newtonian polymers, a significant pressure drop may occur along the length of the well. Accurate models for pressure drop in the well and polymer leakage into the reservoir are necessary for simulation but presently do not exist. We developed new, approximate models for pressure in horizontal wells based on Computational Fluid Dynamics (CFD) modeling of coupled well/reservoir flow. Here, the polymer is shear-thinning in the wellbore and may exhibit viscoelastic effects (such as shear-thickening behavior) in the surrounding reservoir. The CFD results are used to improve existing analytical models for simple, Newtonian flows. The closed-form model accounts for fluid, well, and reservoir properties and can easily be implemented into conventional reservoir simulators. The CFD-based model was directly implemented into the reservoir simulator UTCHEM to evaluate the effect of pressure loss in the well on sweep efficiency. Early times (less than 100 days) yielded a significant loss in oil recovery when compared to the uniform-pressure assumption for the well. However, at later times the recovery loss was negligible, suggesting a uniform-pressure well may be a reasonable assumption at these time scales, even for highly-viscous polymer fluids.

A study of ground‐structure interaction in dynamic plate load testing

AbstractA mathematical treatment is presented for the forced vertical vibration of a padded annular footing on a layered viscoelastic half‐space. On assuming a depth‐independent stress distribution for the interfacial buffer, the set of triple integral equations stemming from the problem is reduced to a Fredholm integral equation of the second kind. The solution method, which is tailored to capture the stress concentrations beneath footing edges, is highlighted. To cater to small‐scale geophysical applications, the model is used to investigate the near‐field effects of ground‐loading system interaction in dynamic geotechnical and pavement testing. Numerical results indicate that the uniform‐pressure assumption for the contact load between the composite disc and the ground which is customary in dynamic plate load testing may lead to significant errors in the diagnosis of subsurface soil and pavement conditions. Beyond its direct application to non‐intrusive site characterization, the proposed solution can be used in the seismic analysis of a variety of structures involving annular foundation geometries. Copyright © 2002 John Wiley & Sons, Ltd.

Numerical study on coupled heat and mass transfers in an absorber with external fluid heating

This paper presents a numerical study of coupled heat and mass transfers in an adsorber with external fluid heating. A one-dimensional model incorporating both heat transfer and Ergun flow of the adsorbate inside the adsorber is developed. Numerical investigations are made for two adsorbent-adsorbate pairs: zeolite 13X-water and 13X-ammonia, whose operating pressures are considerably different. It is shown that, for the 13X-water pair which has a low operating pressure and therefore a low gas density, the dynamics of the adsorber can be significantly limited by the mass transfer inside the adsorbent bed, when its dimension is large. The poor mass transfer can lead to very large pressure variations and small adsorbed or desorbed quantities, making the heat pump process ineffective. Conversely, the zeolite-ammonia pair operates at much higher pressures (several bars) and the corresponding pressure variations in the bed are, in general, negligible. In this case, the limitation by mass transfer can be neglected and the uniform-pressure assumption is acceptable.

The thermal behaviour of oscillating gas bubbles

Several aspects of the oscillations of a gas bubble in a slightly compressible liquid are discussed by means of a simplified model based on the assumption of a spatially uniform internal pressure. The first topic considered is the linear initial-value problem for which memory effects and the approach to steady state are analysed. Large-amplitude oscillations are studied next in the limit of large and small thermal diffusion lengths obtaining, in the first case, an explicit expression for the internal pressure, and, in the second one, an integral equation of the Volterra type. The validity of the assumption of uniform pressure is then studied analytically and numerically. Finally, the single-bubble model is combined with a simple averaged-equation model of a bubbly liquid and the propagation of linear and weakly nonlinear pressure waves in such a medium is considered.

Ignition processes in hydrogenoxygen mixtures

Ignition processes in the hydrogenoxygen system were simulated by solving the corresponding conservation equations (i.e., conservation of mass, energy, momentum, and species mass) for one-dimensional geometries using a detailed reaction mechanism and a multispecies transport model. An additional source term in the energy conservation allowed the treatment of induced ignition, and a realistic model for the destruction of reactive species at the vessel surface was used to treat auto-ignitions in static reactors. Spatial discretization using finite differences and an adaptive grid point system led to a differential-algebraic equation system, which was solved numerically by extrapolation or by backward differencing codes. Comparisons with experimental works show that one common reaction mechanism is able to simulate shock-tube-induced ignitions (modeled by treating the reaction system as a homogeneous mixture heated up by the shock wave) as well as the three explosion limits of the hydrogenoxygen system. Minimum ignition energies are calculated for various mixture compositions, pressures, radii of the external energy source, and ignition times, and it is shown that for long ignition times the “uniform pressure assumption” is a quite good approximation for computing minimum ignition energies.

Infrared Laser Induced Ignition of Gas Mixtures

AbstractO2/O3 mixtures are ignited by absorption of laser pulses of a TEA CO2 laser along the axis of a cylindrical vessel. For mixtures of 0.35 bar total pressure and 20% O3 the laser excitation as well as the molecular relaxation of O3 and the flame propagation is observed by UV‐light absorption of O3 perpendicular to the cell axis. Temperatures reached in the irradiated volume by absorption of the laser pulses are deduced from the alteration of the UV intensity and from absorbed laser energy below and above the ignition limit. The results are compared with corresponding numerical simulations. Minor differences can be attributed to the simplifications of the simulations being performed in one spatial dimension with the uniform pressure assumption and a solely thermal source term.

Pressure Distribution for Patchlike Contact in Seals With Frictional Heating, Thermal Expansion, and Wear

Sliding contact in seals is known to change at high sliding speed from initially uniform pressure to a deformed state where contact is restricted to small patches of the surface. An earlier analysis of such contact was based upon the assumption of uniform pressure on the small patches. The present study draws upon a thermoelastic influence function to provide simultaneous equations for pressure on subdivisions of the patches. The final result is that at high wear rate (and, consequently, high traversal speed of the patch along the surface of the more conductive body of the contacting pair) the pressure distribution becomes roughly triangular with the maximum pressure toward the leading edge of the patch.