Non-uniform Pressure Distribution Research Articles

Hinge and overturning moments due to unsteady heliostat pressure distributions in a turbulent atmospheric boundary layer

Non-uniform pressure distributions on the heliostat surface due to turbulence in the atmospheric boundary layer (ABL) have a significant impact on the maximum bending moments about the hinge of and pedestal base of a conventional pedestal-mounted heliostat. This paper correlates the movement of the centre of pressure due to the mean and peak pressure distributions with the hinge and overturning moment coefficients using high-frequency pressure and force measurements on a scale-model heliostat within two simulated ABLs generated in a wind tunnel. The positions of the centre of pressure were calculated for a range of heliostat elevation-azimuth configurations using a similar analogy to those in ASCE 7-02 for monoslope-roof buildings, ASCE 7-16 for rooftop solar panels, and in the literature on flat plates. It was found that the maximum hinge moment is strongly correlated to the centre of pressure movement from the heliostat central elevation axis. Application of stow and operating load coefficients to a full-scale 36 m2 heliostat showed that the maximum hinge moment remains below the stow hinge moment at maximum operating design gust wind speeds of 29 m/s in a suburban terrain and 33 m/s in a desert terrain. The operating hinge moments at elevation angles above 45° are less than 60% of the stow loads with a constant 40 m/s design wind speed. The results in the current study can be used to determine heliostat configurations and appropriate design wind speeds in different terrains leading to the maximum design wind loads on the elevation drive and foundation.

Effects of non-uniform pore pressure field on hydraulic fracture propagation behaviors

Hydraulic fracturing is one of the key technologies to stimulate oil and gas production in low-porosity and low-permeability reservoirs. Thus, understanding the hydraulic fracture (HF) propagation behaviors is of great significance for optimizing the fracturing design. It is usually assumed that HF tends to take a straight path in a symmetric stress and uniform pore pressure field. However, much more complex stress and pore pressure distribution could be encountered during the fracturing treatment as a result of long-time fluid injection and production in the reservoir. In this paper, considering the arrangement of five-spot well pattern, the effects of unsymmetric stress and non-uniform pore pressure distribution on HF growth is investigated using the cohesive zone method (CZM) and extended finite element method (XFEM). The interesting results indicate that in-situ stress and pore pressure distribution are gradually altered due to fluid injection and production, which affects subsequent HF growth. And in the reservoir developed by five-spot well pattern, HF tends to initially propagate along a straight line with fracture growth rate gradually decreasing and then prefers to extend towards the nearby injection well with fracture growth rate gradually increasing when there exists an intersection angle (0°<θ<45°) between the direction of well arrays and minimum horizontal stress orientation. When θ equals 0° or 45°, HF will extend along a straight line without curving. The results also show that a larger water injection pressure leads to a greater fracture deviation angle, but a larger fracturing fluid injection rate and a larger water injection well distance results in a smaller fracture deviation angle. Moreover, the influence of fracturing fluid viscosity on fracture deviation angle can be ignored.

Dynamic modeling of the effect of water management on polymer electrolyte fuel cells performance

Water management in Polymer Electrolyte Fuel Cell (PEFC) is a key factor in fuel cell performance, and it is an important contributor to the proton exchange membrane durability. Water droplet accumulation in the channel causes non-uniform distribution of gas pressure and spatial inhomogeneity of the local current density in potentiostatic mode. These spatial and temporal fluctuations in the operating conditions imply unequal use of the membrane surface and the catalyst layer, producing uneven degradation and aging of the Membrane Electrode Assembly (MEA). In order to study the dynamic and spatial performance of the fuel cell, a three-level model has been developed. The model is composed of a two-phase, where steam and liquid water drops movement are considered in the channel model; liquid water and gas diffusion are considered in Gas Diffusion Layers (GDLs) model; and finally, the electrochemical reactions are represented in the electrochemical model. The complete model provides a wider understanding of the effect of water on PEFCs and allows to analyze the local current density and the water distribution in response to experimental set-up parameters such as anode and cathode gas flows, total current or channel geometries. The model has been validated using neutron images and segmented cells technique to evaluate the spatial distribution of liquid water and current density in the cell. The developed model and the simulation procedure proposed in this paper allow obtaining long-term dynamic simulations with low computational effort.

Migration of a red blood cell in a permeable microvessel

One of the important features of the microvessels is with permeable vessels. The hyperpermeablility is especially prounounced due to the fast grow of the microvessel in the tumor tissues. Flow field induced by leakage often presents a different figure compared to that of the health vessel. Non-uniform velocity and pressure distribution are found in the simulation by using Lattice Boltzmann Method combined with Starling law. This non-uniform flow field has significant influence on the mass transport in permeable mocrovessel, such as the motion of red blood cell. Using 2D spring network model to express the red blood cell and immersed boundary method to implement the coupling of fluid and structure, numerical simulations were carried out to study the migration of a red blood cell in a straight permeable channel. The results show that the staying time of red blood cell in the leakage region increases with the intensity of leakage. We also found that the leakage can weaken the lateral migration of the red blood cell from the wall to the channel center, and even tune the migration towards the wall when the leakage is reasonably strong.

Towards design rules for rectangular silo filling pressures

An experimentally validated finite element model of filling pressures in rectangular silos with flexible walls is used to predict the stress regime in the stored solid in squat and intermediate aspect ratio silos. The model predicts the state of stress in the stored solid and the pressures imposed on the flexible walls of the silo. The non-uniform horizontal pressure distributions at each depth at the end of filling are explored. It is known that an empirical relation for the horizontal pressure variation on each straight wall derived from experimental observations in an earlier study closely matches the computational predictions. The coefficients of this relation are found to vary with depth below the stored solid surface, and depend on the relative stiffness of stored solid and the silo wall. Following many calculations involving different solids, an empirical relationship is derived that is suitable for practical design for a range of different stored solids for which relevant properties are known. The resulting expression is well suited to the practical determination of filling pressures in rectangular silos, and provides a silo design pressure proposal that is based on theoretical, rather than empirical findings.

Development of a One-Dimensional Model for the Prediction of Leakage Flows in Rotating Cavities Under Non-Uniform Tangential Pressure Distribution

Regenerative pumps are characterized by a low specific speed that place them between rotary positive displacement pumps and purely radial centrifugal pumps. They are interesting for many industrial applications since, for a given flow rate and a specified head, they allow for a reduced size and can operate at a lower rotational speed with respect to purely radial pumps. The complexity of the flow within regenerative machines makes the theoretical performance estimation a challenging task. The prediction of the leakage flow rate between the rotating and the static disks has the greatest impact on the prediction of global performance. All the classical approaches to the disk clearance problem assume that there is no relevant circumferential pressure gradient. In the present case, the flow develops along the tangential direction and the pressure gradient is intrinsically non-zero. The aim of the present work is to develop a reliable approach for the prediction of leakage flows in regenerative pumps. A preliminary numerical simulation on a virtual model of a regenerative pump where the disk clearance is part of the control volume has been performed for three different clearance aspect ratios. The outcome of that campaign allowed the authors to determine the behavior of the flow in the cavity and choose correctly the baseline hypotheses for a mathematical-physical method for the prediction of leakage flows. The method assumes that the flow inside of the disk clearance is two-dimensional and can be decomposed into several stream-tubes. Energy balance is performed for each tube, thus generating a system that can be solved numerically. The new methodology was tuned using data obtained from the numerical simulation. After that, the methodology was integrated into an existing one-dimensional code called DART (developed at the University of Florence in cooperation with Pierburg Pump Technology Italy S.p.A.) and the new algorithm was verified using available numerical and experimental data. It is here demonstrated that an appropriate calibration of the leakage flow model allows for an improved reliability of the one-dimensional code.

Investigation on the casing static pressure distribution and stall behaviors in a centrifugal compressor with volute

Obtaining the casing static pressure distribution of a centrifugal compressor with volute is beneficial in understanding the compressor stall mechanism and designing the corresponding asymmetric structures to improve the compressor performance and stability. The present study investigates the casing pressure evolution from the choke to stall operating conditions and focuses on the relationship between the casing pressure evolutions and stall behavior under different rotational speeds. A total of 72 steady static pressure sensors (6 sensors in circumferential direction and 12 in streamwise direction) were mounted around the compressor casing wall to measure the casing pressure. In the experiment, the steady pressure data were acquired by averaging the 50 values measured in 1 s. The results show that at the same rotational speed, from the near choke to near stall conditions, the casing pressure distribution patterns can be divided into two parts: the single-peak pressure pattern, from the choke point to maximum efficiency point (transition point), and the double-peak (peak and bulge) pressure pattern, from the transition point to near stall point. One interesting phenomenon is that the proportions of the flow rate range of the two casing pressure patterns at different rotational speeds are related to the surge line knee. The vast operating range contraction indicates that the double-peak pattern has more instability at a higher rotational speed, which is linked with the different stall behavior at different rotational speeds. Combined with unsteady full annulus simulations, the leading-edge spillage triggers the impeller long-lived stall earlier at a higher rotational speed, corresponding to the short-lived double-peak pressure pattern. However, at lower rotational speeds, short-lived diffuser stall occurs owing to the impeller outlet recirculation flow and diffuser inlet separated flow, corresponding to the long-lived double-peak pressure pattern. Furthermore, the circumferential non-uniform casing pressure distribution can indicate the circumferential position of the stall onset and provide a reason for the non-rotating stall in the impeller inlet and partly rotating stall in the diffuser, which is fundamental and beneficial to the compressor flow control system design.

Effect of Un-Balanced Water Supply and Nonuniform Pressure Distribution on the Performance of an Adsorption Cooling System

A three-dimensional numerical analysis was conducted to examine the effect on performance of un-balanced heating/cooling water supply and nonuniform pressure distribution in the beds, issues observed in an experiment by our colleague during the development of a 35[Formula: see text]kW prototype finned-tube type adsorption chiller. Case studies were conducted with reference values of [Formula: see text][Formula: see text]m/s, [Formula: see text][Formula: see text]Pa and [Formula: see text][Formula: see text]Pa, and the differences in [Formula: see text][Formula: see text]m/s, [Formula: see text][Formula: see text]Pa and [Formula: see text][Formula: see text]Pa. A remarkable increase in COP was found for the cases of un-balanced heating water supply and nonuniform pressure distribution when the bed was connected to the evaporator. However, after integration of multi-modules, the effect was smoothed out, which removed the worry about the degradation in the overall COP. The effect of un-balanced cooling water supply and nonuniform pressure distribution when the bed was connected to the condenser was not discernible. In all cases, the change in SCP was negligible.

Injection Molding of Superhydrophobic Submicrometer Surface Topography on Macroscopically Curved Objects: Experimental and Simulation Studies

Micro- and nanoscale surface topographies that give rise to superhydrophobic surfaces have been achieved mostly on 2-dimensional planar objects. Increasing interests in superhydrophobic surfaces on consumer products, optics, and biomedical devices demand topographic patterning on free-form nonplanar surfaces via a high throughput manufacturing process such as injection molding. However, successes in high-resolution (submicrometer) injection molding have been limited to flat and planar objects. A challenge associated with achieving submicrometer surface resolution on a 3-dimensional curved object lies in the control of the replication process in a multiscale mold cavity and the nonuniform temperature and pressure distribution over a macroscopically curved mold insert. Here, a two-step simulation approach is employed to investigate the replication of polymer in the macroscopic and submicrometer cavities. Both simulation and experimental data revealed the effects of holding pressure, mold temperature, and ma...

Breakdown pressure prediction with weight function method and experimental verification

Accurate estimation of fracture gradient is critical for both drilling and hydraulic fracturing. Fracture gradient by traditional methods is greatly overestimated due to the ignorance of preexisting fractures, nonlinear near wellbore stress concentration acting on fracture surfaces, or non-uniform fluid pressure distribution inside fractures. To overcome the limitations of current methodologies, a weight function method is firstly introduced to calculate breakdown pressure where there are a pair of symmetrical radial fractures collinear with borehole axis emanating from the borehole. The results are compared against both measured breakdown pressure in both field and laboratory and results of classical fracture models. Parametric studies are conducted to investigate the influence of pre-existing crack length, orientation, in-situ stress contrast, fracture toughness, and internal pressure distribution on breakdown pressure. It indicates that breakdown pressure (1) does not always decrease with increasing dimensionless crack length at different stress contrast, (2) for the fracture with non-uniform pressure is higher than the one with constant internal pressure, and (3) increases with increasing absolute value of inclination angle1It means an angle between the local maximum horizontal principal stress and the axis of the fracture.1 and fracture toughness. Comparison of breakdown pressure by traditional and weight function methods demonstrates that breakdown pressure by traditional methods is overestimated. The proven weight function method simplifies the prediction of breakdown pressure, and shows a great potential in improving the accuracy of breakdown pressure prediction because it captures more physical factors during rock fracturing 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.

Effect of Contact Geometry on the Contact Stresses in a Flat with Round Edge Contact

The blade-disc dovetail interface in an aero-engine compressor is characterized by a non-uniform pressure distribution which can be obtained by an equivalent flat with round edge-on-plate configuration. The contact tractions for a mating pair are affected by many parameters which include, contact geometry, loading conditions, and material properties; with contact geometry being one of the prominent factors. In the present work, a 2-D elastic and elasto-plastic finite element analysis has been carried out for a rounded contact geometry to study the influence of the radius of the corners ‘R’ and length of the flat region ‘2a’. It is observed that the peak tensile stress in the fretting direction was found to decrease with increasing ‘a’ (for constant ‘R’) which is likely to delay the crack initiation. Also, as compared to elasto-plastic analysis, elastic analysis overestimates peak tensile stress and possibly give a conservative estimate for the fretting fatigue life. Further, the effect of modelling elastic-plastic behaviour is significant for low a/R ratio (for constant ‘R’). However, opposite trend was observed when ‘R’ was varied keeping ‘a’ constant. Also, it is found that the effect of contact geometry cannot be characterized using a single parameter like a/R ratio or contact area.

Slip perturbation during fault reactivation by a fluid injection

Slip orientation inferred from fault striae or focal mechanism datasets is commonly used in stress inversion methods based on the Wallace-Bott hypothesis. The hypothesis postulates that slip on a fault plane is collinear with the orientation of the resolved shear stress. It is valid for a single planar fault subjected to a homogeneous far-field stress. However, the experimental displacement data from an induced fault reactivation experiment, conducted in the Mont Terri rock laboratory, Switzerland, indicated multiple triggered slip orientations, thereby preventing application of the above inversion method. We present numerical and analytical results of slip on a reactivated fracture with a non-uniform fluid pressure distribution. Using these models, we evaluate the reasons for the inconsistency of our observations and the traditional Wallace-Bott hypothesis and test the physical effects of various parameters on fault slip. In the fully coupled hydromechanical numerical model (three-dimensional distinct element method), fluid pressure at a point on the fault surface is increased stepwise (assumed planar and singular) until shear reactivation of the fault is induced. We studied two different models with high and low fault plane stiffness to represent hard and soft rock masses, respectively. The model shows that high fault stiffness preserves the planarity of the fault plane, while low fault stiffness permits dilation and morphological changes of the fracture related to fluid pressure diffusion. The highest slip perturbation was observed in the low stiffness model due to the change of the fracture shape, controlled by the non-uniform pressure distribution. The Eshelby analytical solution confirmed that the more the fracture is dilated, the more the corresponding resolved shear stress is perturbed. Additionally, when compared to dilation and fault aperture, the friction angle has the most influence on the angular difference between geomechanical slip vectors and resolved shear stress.

Wind generated equatorial Gerstner-type waves

A class of non-stationary surface gravity waves propagating in the zonal direction in the equatorial region is described in the f-plane approximation. These waves are described by exact solutions of the equations of hydrodynamics in Lagrangian formulation and are generalizations of Gerstner waves. The wave shape and non-uniform pressure distribution on a free surface depend on two arbitrary functions. The trajectories of fluid particles are circumferences. The solutions admit a variable meridional current. The dynamics of a single breather on the background of a Gerstner wave is studied as an example.

Coupled vs uncoupled analysis of one-way RC-slabs under nearby air explosions

The numerical techniques used for blast analysis of structures are categorized in “coupled” and “uncoupled” analysis methods. In a coupled analysis, the fluid–structure interaction is taken into account. Such analysis, although more accurate, is often complex and time consuming. In an “uncoupled” analysis, the blast loads are estimated by empirical equations and then applied to the structure in a separate analysis. Such an analysis is more cost effective, and of more interest for most practical design applications. The main objective of this study is to assess the efficiency of the empirical graphs prescribed by the UFC Code for uncoupled analysis of structures under the nearby air explosions of scaled distances between 0.4 and 0.7 kg/m1/3. The main characteristic of such explosions is the highly nonuniform distribution of blast-reflected pressure on the surface of structure. A method has been developed by the authors to address this nonuniform distribution in the uncoupled analysis. To examine the accuracy of analysis, the response values and the pattern of damages introduced on several reinforced concrete slabs under blast loads are compared with the results of a corresponding coupled analysis, and experimental observations. The uncoupled analysis described in this paper can be reasonably employed in the blast analysis and design of many structures.

An analytical solution for the arching effect induced by ground loss of tunneling in sand

Because the earth pressure above tunnel crown was assumed uniform and the effect of particle flow of sand and ground loss were not considered, Terzaghi method generally produces discrepancies from model tests and field observations. To overcome this deficiency, the flow of sand particles above a tunnel was investigated firstly to define the shape and size of loosening zone by following the gravity flow principles. Then, by assuming non-uniform distribution of earth pressure and incorporating the factor of ground loss, a modified Terzaghi method has been developed. It can not only determine the loosening pressure on tunnel, but also the shape and size of loosening zone corresponding to ground loss and properties of sand particles. The research results reveal that the shape of loosening zone is ellipsoidal or a part of ellipsoid affected by the eccentricity and loosening factor of sand. The height of loosening zone increases with ground loss of tunneling, resulting in the propagation of loosening zone from deep in ground to ground surface. For most shield tunnels, with ground loss ratio less than 4.0%, the loosening zone is formed only at the upper tip of the ellipse and its shape resembles to a curved arch. According to the proposed method, the height of the loosening zone for shield tunnels in sandy ground is approximately 0.1D–0.7D (D, tunnel diameter) and the earth pressure is about 35–90% of the total overburden earth pressure for typical ground loss within the range of 0.5–4.0%. Via detailed comparison with model tests and Terzaghi method, the proposed method is proved to be closer to the model tests than the Terzaghi method. For the sake of convenience in application, simplified design curves for the height of loosening zone and earth pressure were plotted against ground loss, which is of great importance for engineers to set reasonable goal of ground loss in tunneling practice.

Aeroelasticity Analysis of Unsteady Rotor Blade Forces and Displacements in LP Last Stage Steam Turbine with Various Pressure Distributions the Stage Exit

Several high vibration amplitude problems have been reported regarding the slender last stage blading of commercial LP steam turbines. This paper analyses rotor blade unsteady forces and displacements in the last stage of a low pressure steam turbine with symmetrical and non-symmetrical (exhaust hood induced) pressure distributions behind the rotor blades. The FSI partially integrated method was used for the 3D ideal gas flow. 3D unsteady non-viscous flow was analysed using the Godunov-Kolgan method. Non-symmetrical pressure distributions in the stage exit were taken from 3D viscous CFX ANSYS calculations, using a CFD mesh of all the stator blades, all the rotor blades (rotating and not vibrating) and the exhaust hood. The non-uniform and uniform pressure distributions cause rotor blades to vibrate in different bending-torsion modes. Introducing blade vibration into the flow model causes the appearance of unsteady force and blade displacement harmonics that are not multiples of the rotation frequency. The unsteady rotor blade forces and blade displacements analysis shows the importance of including an exhaust hood in the CFD mesh.

An Analytical Model for Nonhydrostatic Sheet Metal Bulging Process by Means of Polymer Melt Pressure

In this paper, a theoretical approach to model free deformation of sheet metal via polymer injection pressure is presented. It is a general methodology that can be applied for any situation where a nonuniform pressure distribution is responsible for free deformation of sheet metal within a circular cavity. This approach is composed of two iterative approximation loops. In the outer loop, the radius of curvature at the tip of dome shape was optimized based on the boundary condition at the edge of clamped area while in the inner successive loop, principal stresses determined from plasticity theories were used to satisfy the equilibrium equations. While forming sheet metal via polymer injection is a revolutionary yet complex process, its modeling is challenging. Hence, before implementing this general approach to this process, the modeling methodology as such necessitates a simplified solution for melt flow analysis to obtain a pressure distribution encompassing the entire cavity. To evaluate the proposed model, a customized experimental setup was designed and fabricated, which allows sheet metal bulging with the plastic injection. The deformation of the AA1100-O sheet was investigated during the injection of the polypropylene–olefin compound. The comparison of the theoretical and experimental results shows that the general approach formulated here can be successfully applied to predict the surface strains and thickness distributions with maximum error of 6% while the deformed geometry remains within ±0.35 mm deviation in the final deformation stage.

Numerical evaluation of an autofrettaged thick-walled cylinder under dynamically applied axially non-uniform internal service pressure distribution

Abstract A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasi-internal ballistics structural model was checked. The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared. The difference for the worse case was 20% and for the best case was 0.1%. Furthermore, the model gave better agreement for the higher charge masses. The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.

Casing wall static pressure distribution behavior in a centrifugal compressor with asymmetric inlet/outlet structures

Asymmetric structures of the bent inlet pipes and outlet volute are typically adopted in centrifugal compressors. By using asymmetric inlet/outlet structures, the uniformity of the compressor’s internal flow field in the circumferential direction will be changed. The static pressure distribution behavior around the casing wall is significantly influenced by the coupling effect of the bent inlet pipe and outlet volute. In the present work, three compressors were numerically and experimentally investigated. One compressor had a straight inlet pipe, and the other two had bent inlet pipes. Seventy-two static pressure sensors were mounted around the casing wall to obtain the static pressure distribution at different flow rates for three rotational speeds. The results show that at high rotational speeds with large flow rate conditions, when the static pressure waves induced by the bent pipe and volute act on the same circumferential position, the casing wall static pressure will be increased at the corresponding position. Furthermore, this high static pressure will further influence the static pressure values at other circumferential positions and leads to a more nonuniform circumferential static pressure distribution. Near the design flow rate, when the high static pressure strips, which are induced by both the bent pipe and volute impact different circumferential positions, the high static pressure strip induced by the volute will be weakened. As a result, the high static pressure strip induced by the volute cannot propagate upstream into the impeller. At small flow rate under designed rotational speed, the influence of the volute tongue on the casing pressure distribution will be enhanced. At small flow rate under low rotational speed, the casing pressure distributions of the three models were almost the same because the secondary flow effect of the bent pipe diminishes as the flow rate reduces.