Application Of Superposition Research Articles

Modeling of Turbulent Convective Heat-Transfer Characteristics in a Concentric Annular Channel

Turbulent convective heat-transfer characteristics in a concentric annular channel with both walls heated are theoretically modeled and numerically computed in this article. Generalized algebraic predictive models and equations for heating over a single wall are first reviewed by summarizing the well-known methods in the literature. These methods are then scrutinized according to the most recent investigations such that new viewpoints and corrections are introduced accordingly. Moreover, the application of superposition in temperature is used in the current work instead of the Nusselt number as seen in the literature. The numerical integration method is applied to the generalized equations to obtain the solutions, which are found to be in decent agreement with the direct numerical simulation (DNS) data in the literature. The results in this work also indicate that the wall heat flux density ratio and the annular radius ratio are two key factors that have a great influence on the heat-transfer characteristics of the case with both walls heated.

The Error in Using Superposition to Estimate Pressure During Multisite Subsurface CO2Storage

AbstractAnalytic pressure estimates for multisite CO2injection are typically performed through the superposition of single‐site injection models. This is theoretically invalid for multiphase flow because of its nonlinearity. We quantify the error associated with the application of superposition in scenarios with sites located in a rectangular grid geometry. We show that the use of superposition results in overestimates of the pressure buildup, because it neglects the presence of multiple CO2plumes, which increase the reservoir fluid mobility. The adoption of a dimensionless time scaled to the geometric average between the advective and diffusive characteristic times allows us to define a general model for the maximum error, which may be used to evaluate the validity of using superposition, or to correct the pressure estimates when errors are significant. This procedure can be applied to any analytical solution and advances the extension of single‐well models to scenarios of multiple injection sites.

Superposition of Spanwise Circulation Distributions: Accuracy Assessment and Application in Wing Design

Superposition of spanwise lift distributions is a familiar concept from lifting-line theory. However, even for linear potential flows, superposition is not rigorously applicable for aerodynamic models and wing geometries in which the shape of the wake vortex system changes with angle of attack. Nonetheless, the influence of these wake effects could generally be expected to be small, insofar as downstream vortices have a weaker influence than the vortex system in the near field of the wing. In this paper, the theoretical framework for lift distribution superposition is first examined. Next, empirical studies conducted with a panel code are presented that show that superposition remains a very good approximation for a wide range of wing geometries and operating conditions. A method for correcting the small errors in induced drag predictions that result from the application of superposition is also provided. Finally, an application for wing design in which an additional and a design distribution are superimposed to produce lift distributions at other operating conditions is presented. This formulation reveals insights into the influence of the design distribution and the planform characteristics, and it supports computationally inexpensive optimization of wing twist.

Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.

Evaluation of Time Dependent Behavior of a Wood Flour/High Density Polyethylene Composite

Short-term flexural creep and stress relaxation tests were conducted on a wood plastic composite containing 30% high density polyethylene (HDPE), 67% fir wood flour, 2% compatibilizer (MAPE), and 1% lubricant. In creep tests, applied stress levels ranged from 30 to 60% of measured flexural strength. The principle of time—stress superposition was applied to form a master curve extending for a maximum of 4 years. The horizontal shift factors conformed to an Arrhenius type equation. Stress relaxation tests were also carried out at strain levels ranging from 30 to 60% of the ultimate strain. The principle of time—strain superposition was applied to form a stress relaxation master curve that extended for 67 days. The horizontal shift factors also conformed to an Arrhenius type equation. The resulting master curves were compared with extrapolated creep and stress relaxation models. To determine whether time—stress superposition is valid for the studied composite material, creep shift factors were applied to stress relaxation data and vice versa. In both creep and stress relaxation tests, it was found that the application of superposition was verified. The results indicated that the studied composite material was rheologically simple, and a single horizontal shifting on time axis was adequate to predict the long term performance of the material.

Preloading compliant couplings and the applicability of superposition

Simple planar, multi-segmented compliant couplings are used to study the general concepts of preloading and shape changing. This study shows how stiffness or shape is a function of the effective free lengths of supporting struts embedded within the compliant coupling. The concepts of super wrench and super twist are introduced in order to facilitate study. Finally, the superposition principle is thoroughly studied, and its applicability is identified. With emphasis on internal preloading, the study departs from typical compliant mechanism assumptions of no internal preloading, e.g. [1, p. 138]. Results can be extended to the spatial case using screw theory.

Limits of sequences of stationary planar tessellations

In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.

Limits of sequences of stationary planar tessellations

In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.

Numerical Ground‐Water Flow Modeling of the Snake River Plain Aquifer Using the Superposition Technique

AbstractPredictive ground‐water flow modeling may be simplified by application of superposition when the governing equations are linear. The simplification allows evaluation of impacts of individual aquifer stresses and minimized model input, output, and interpretation. Modeling is performed by using (1) boundary conditions and aquifer properties provided by previous calibrations or analytical techniques, (2) setting the initial potentiometric surface and prescribed‐head boundaries to an arbitrary horizontal datum, and (3) simulating a specific recharge or discharge stress.Superposition was applied to an existing, calibrated model of the Snake River Plain aquifer to simplify prediction of changes in interaction with the Snake River. Simulations predict the temporal relationships between ground‐water use at multiple locations within the Snake River Plain and surface‐water depletion in four hydraulically connected reaches of the Snake River. Simulated aquifer water use at a location approximately five miles from a hydraulically connected river reach results in river depletions greater than 80% of the pumping rate after 10 years. Water use further than 50 miles from hydraulically connected river reaches results in depletions from 10 to 30% of the annual average pumping rate after 100 years. Results present spatial and temporal impacts of water uses on the Plain that are conceptually and quantitatively beneficial to water resources planners and water users.

Service, Post-Cracking, and Ultimate Response of Continuous, Post-Tensioned Voided Slab Bridges

Two quarter-scale continuous, voided slab bridge models post-tensioned longitudinally and transversely were tested to determine their service, post-cracking and ultimate responses under simulated AASHTO truck loading. The models were designed to comply with current practice and their response is indicative of bridges currently in use. Eleven tests were conducted to investigate the elastic response. The response was linear and the applicability of superposition confirmed. The applied post-cracking load was between 1.67 and 2.0 times the cracking load. Although the response was non-linear there was negligible residual deflection. The ultimate load tests indicated great ductility and reserve strength with ultimate moment capacities far in excess of designed values.

Stress-intensity factors for curved circular crack in bonded dissimilar materials

Complex potentials are used to solve the curved circular crack problem in two bonded half-planes made of dissimilar materials. The mixed boundary value problem is solved by application of superposition and the dislocation distribution for determining the unknown function. A logarithmic singular kernel is obtained for the governing integral equation. Displayed graphically are stress intensity factors for a variety of the curved crack are length and orientation and their changes due to the dissimilar properties are also exhibited.

Application of the van Everdingen-Meyer Method for Analyzing Variable-Rate Well Tests

Summary This paper discusses application of superposition to pressure-transient analysis when rate varies significantly before and during pressure measurements. To apply rigorous superposition, use of conventional pressure-transient and rate-time methods is recommended to estimate permeability, skin, and in some cases, drainage area. These properties allow calculation of the dimensionless time constant used in superposition calculations on the basis of rate change and dimensionless pressure. As van Everdingen and Meyer proposed, the time constant is varied until a linear fit of the pressure variable is made vs. superposition time. An important step is to use all available rate data, even though pressures may not be measured during periods of rate change. Our work shows the use of full superposition to check the consistency of standard well-test analysis based on the constant-rate or constant-pressure assumption. Data from two gas wells and results from a gas-well simulator provide the basis for our discussion. Problems covered are choosing the dimensionless pressure solution, estimating initial pressure by extrapolation of the superposition plot, and analyzing rate-dependent effects.

Mixed Convection Plume—Application of Superposition

By comparing with the exact similarity solution for the mixed convection plume of the point source, the limitation of the Oseen boundary layer solution is established. Superposition principles are given and applied to the cases of the vertical and the horizontal finite heated wire. Three-dimensional thermal and velocity fields are determined.

An integral equation method to solve three dimensional confined flow to drainage systems

A new special type of the boundary element method (BEM) is presented to describe three-dimensional ground water movement for arbitrarily inclined drainage systems in a horizontal, confined, aquifer. The real drain pipe will be replaced by a system of polygonal line-sinks or sources. The discharge distribution over the length of the pipe can be approximated by a linear function, p on each element. As a particular application of superposition it is possible to use the method of images to realize the Neumann condition on the impervious boundaries. The infinite array of images of the drainage system can be replaced by a finite array of N images and two semi-infinite strips with the same specific discharge distribution. A collocation method leads to a linear equation system which determines the discharge approximation p and other interesting field values.

External thermal resistance of two buried cables. Restricted application of superposition

New formulas are derived for the external thermal resistance of one of two equally loaded identical cables laid direct in the ground at the same depth. The formulas are based on a restricted application of the principle of superposition, and remain valid when the cables are close or touching. Two assumptions made are that the depth of the buried cables is much greater than the cable radius, and that the cable surfaces are isothermal at a common temperature. The former assumption is justified as the cable depth is generally equal to at least ten times the cable radius. The latter assumption is recognised to be an approximation, but the present approach may prove to be more acceptable than alternative techniques. Comparison is made with previously published formulas.

External thermal resistance of three buried cables in trefoil-touching formation. Restricted application of superposition

An approximate formula, with error bounds, is derived for the thermal resistance between three touching circular cylinders and a plane. The formula is based on a restricted application of the principle of superposition. The distance between the cylinder configuration and the plane is assumed to be much greater than the cylinder radius, which is the case for the evaluation of the external thermal resistance of three equally loaded identical cables laid direct in the ground in trefoil-touching formation. Numerical calculation indicates that formulas now in use for this application may give values that are noticeably on the high side. The method may be used to obtain approximations to the solution of other thermal resistance problems involving a plane as one of the boundaries.