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1
Alexandrova, Irina V., and Dmitri V. Alexandrov. "Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2171 (April 13, 2020): 20190245. http://dx.doi.org/10.1098/rsta.2019.0245.
Анотація:
This manuscript is devoted to the nonlinear dynamics of particulate assemblages in metastable liquids, caused by various dynamical laws of crystal growth and nucleation kinetics. First of all, we compare the quasi-steady-state and unsteady-state growth rates of spherical crystals in supercooled and supersaturated liquids. It is demonstrated that the unsteady-state rates transform to the steady-state ones in a limiting case of fine particles. We show that the real crystals evolve slowly in a more actual case of unsteady-state growth laws. Various growth rates of particles are tested against experimental data in metastable liquids. It is demonstrated that the unsteady-state rates describe the nonlinear behaviour of experimental curves with increasing the growth time or supersaturation. Taking this into account, the crystal-size distribution function and metastability degree are analytically found and compared with experimental data on crystallization in inorganic and organic solutions. It is significant that the distribution function is shifted to smaller sizes of particles if we are dealing with the unsteady-state growth rates. In addition, a complete analytical solution constructed in a parametric form is simplified in the case of small fluctuations in particle growth rates. In this case, a desupercooling/desupersaturation law is derived in an explicit form. Special attention is devoted to the biomedical applications for insulin and protein crystallization. This article is part of the theme issue ‘Patterns in soft and biological matters’.
2
Sbardella, L., and M. Imregun. "Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids." Journal of Turbomachinery 123, no. 3 (February 1, 2001): 568–82. http://dx.doi.org/10.1115/1.1371777.
Анотація:
The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.
3
Duarte, A. S. R., A. I. P. Miranda, and P. J. Oliveira. "Numerical and analytical modeling of unsteady viscoelastic flows: The start-up and pulsating test case problems." Journal of Non-Newtonian Fluid Mechanics 154, no. 2-3 (October 2008): 153–69. http://dx.doi.org/10.1016/j.jnnfm.2008.04.009.
4
Boutet, Johan, and Grigorios Dimitriadis. "Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings." Aerospace 5, no. 3 (September 1, 2018): 92. http://dx.doi.org/10.3390/aerospace5030092.
Анотація:
A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta–Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge–Kutta–Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.
5
Casper, J., and F. Farassat. "A New Time Domain Formulation for Broadband Noise Predictions." International Journal of Aeroacoustics 1, no. 3 (September 2002): 207–40. http://dx.doi.org/10.1260/147547202320962574.
Анотація:
A new analytic result in acoustics called “Formulation 1B,” proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is analytically specied from a result based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B and to demonstrate its equivalence to Formulation 1A of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous, isotropic turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.
6
Bitter, Martin, Michael Hilfer, Tobias Schubert, Christian Klein, and Reinhard Niehuis. "An Ultra-Fast TSP on a CNT Heating Layer for Unsteady Temperature and Heat Flux Measurements in Subsonic Flows." Sensors 22, no. 2 (January 15, 2022): 657. http://dx.doi.org/10.3390/s22020657.
Анотація:
In this paper, the authors demonstrate the application of a modified Ru(phen)-based temperature-sensitive paint which was originally developed for the evaluation of unsteady aero-thermodynamic phenomena in high Mach number but short duration experiments. In the present work, the modified TSP with a temperature sensitivity of up to −5.6%/K was applied in a low Mach number long-duration test case in a low-pressure environment. For the demonstration of the paint’s performance, a flat plate with a mounted cylinder was set up in the High-Speed Cascade Wind Tunnel (HGK). The test case was designed to generate vortex shedding frequencies up to 4300 Hz which were sampled using a high-speed camera at 40 kHz frame rate to resolve unsteady surface temperature fields for potential heat-transfer estimations. The experiments were carried out at reduced ambient pressure of p∞ = 13.8 kPa for three inflow Mach numbers being Ma∞=[0.3;0.5;0.7]. In order to enable the resolution of very low temperature fluctuations down to the noise floor of 10−5 K with high spatial and temporal resolution, the flat plate model was equipped with a sprayable carbon nanotube (CNT) heating layer. This constellation, together with the thermal sensors incorporated in the model, allowed for the calculation of a quasi-heat-transfer coefficient from the surface temperature fields. Besides the results of the experiments, the paper highlights the properties of the modified TSP as well as the methodology.
7
ANTUONO, MATTEO, ANDREW J. HOGG, and MAURIZIO BROCCHINI. "The early stages of shallow flows in an inclined flume." Journal of Fluid Mechanics 633 (August 25, 2009): 285–309. http://dx.doi.org/10.1017/s0022112009007034.
Анотація:
The motion of an initially quiescent shallow layer of fluid within an impulsively tilted flume is modelled using the nonlinear shallow water equations. Analytical solutions for the two-dimensional flow are constructed using the method of characteristics and, in regions where neither of the characteristic variables is constant, by adopting hodograph variables and using the Riemann construction for the solution. These solutions reveal that the motion is strongly influenced by the impermeable endwalls of the flume. They show that discontinuous solutions emerge after some period following the initiation of the flow and that for sufficiently long flumes there is a moving interface between wetted and dry regions. Using the hodograph variables we are able to track the evolution of the flow analytically. After the discontinuities develop, we also calculate the velocity and height fields by using jump conditions to express conservation of mass and momentum across the shock and thus we show how the hydraulic jump moves within the domain and how its magnitude grows. In addition to providing the behaviour of the flow in this physical scenario, this unsteady solution also provides an important test case for numerical algorithms designed to integrate the shallow water equations.
8
BROOK, B. S., S. A. E. G. FALLE, and T. J. PEDLEY. "Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state." Journal of Fluid Mechanics 396 (October 10, 1999): 223–56. http://dx.doi.org/10.1017/s0022112099006084.
Анотація:
Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.
9
Joseph, Jeffrey A., and Leonard F. Koederitz. "Unsteady-State Spherical Flow With Storage and Skin." Society of Petroleum Engineers Journal 25, no. 06 (December 1, 1985): 804–22. http://dx.doi.org/10.2118/12950-pa.
Анотація:
Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804
10
Ayton, Lorna J. "Analytic solution for aerodynamic noise generated by plates with spanwise-varying trailing edges." Journal of Fluid Mechanics 849 (June 21, 2018): 448–66. http://dx.doi.org/10.1017/jfm.2018.431.
Анотація:
This paper presents an analytic solution for aerodynamic noise generated by an unsteady wall pressure gust interacting with a spanwise-variable trailing edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a tailored modal expansion in the spanwise coordinate; however, only finitely many modes are cut-on, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated trailing edges compared to those with straight edges. The two mechanisms behind the noise reduction are an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes. Five different test-case trailing-edge geometries are considered. The analytic solution identifies which geometries are most effective in different frequency ranges: geometries which promote destructive interference are best at low frequencies, whilst geometries which promote a redistribution of energy are better at high frequencies.
11
Satman, Abdurrahman. "An Analytical Study of Interference in Composite Reservoirs." Society of Petroleum Engineers Journal 25, no. 02 (April 1, 1985): 281–90. http://dx.doi.org/10.2118/10902-pa.
Анотація:
Satman, Abdurrahman; SPE; Technical U. of Istanbul Abstract This paper discusses the interference test in composite reservoirs. The composite model considers all important parameters of interest: the hydraulic diffusivity, the mobility ratio, the distance to the radial discontinuity, the distance between wells, the wellbore storage, and skin effect at the active well. Type curves expressed as a function of proper combinations of these parameters are presented. Introduction Interference tests are widely used to estimate the reservoir properties. An interference test is a multiwell test that requires at least one active well, either a producer or injector, and at least one observation well. During the test, pressure effects caused by the active well are measured at the shut-in observation wells. Basic techniques for analyzing interference tests in uniform systems are discussed in Ref. 1. Usually, type-curve matching is the preferred technique for analyzing the pressure data from the test. Early interference test studies assumed that the storage capacity of the active well and the skin region around the sandface have a negligible effect on the observation well response. Recently, investigators have focused on wellbore storage and skin effects. Tongpenyai and Raghavan presented a new solution for analyzing the pressure response at the presented a new solution for analyzing the pressure response at the observation well, which took into account the effects of wellbore storage and skin at both the active and the observation wells. They produced type curves expressed as a function of exp(2S) products, the ( / ) ratios, and ( / ) to correlate the pressure response at the observation well. Composite systems are encountered in a wide variety of reservoir situations. In a composite system, there is a circular inner region with fluid and rock properties different from those in the outer region. Such a system can occur in hydrocarbon reservoirs and geothermal reservoirs. The injection of fluids during EOR processes can cause the development of fluid banks around the injection wells. This would be true in the case of a in-situ combustion or a steamflood. In a geothermal reservoir, pressure reduction in the vicinity of the well may cause the phase boundaries. A producing well completed in the center of a circular hot zone surrounded by producing well completed in the center of a circular hot zone surrounded by a concentric cooler water region is also a composite system. During the early to late 1960's, there was great interest in the composite reservoir flow problem. Hurst discussed the "sands in series" problem. He presented the formulas to describe the pressure behavior of problem. He presented the formulas to describe the pressure behavior of the unsteady-state flow phenomenon for fluid movement through two sands in series in a radial configuration, with each sand of different permeability. Mortada studied the interference pressure drop for oil fields located in a nonuniform extensive aquifer comprising two regions of different properties. He presented an expression for the interference pressure drop properties. He presented an expression for the interference pressure drop in an oil field resulting from a constant rate of water influx in another oil field. Loucks and Guerrero presented a qualitative discussion of pressure drop characteristics in composite reservoirs. Ramey and Rowan and pressure drop characteristics in composite reservoirs. Ramey and Rowan and Clegg developed approximate solutions. Refs. 11 through 13 also discuss composite reservoir systems and present either analytical or numerical solutions. Composite system model solutions have been used to determine some critical parameters during the application of EOR processes. The formation of a fluid bank around the injection well makes the reservoir a composite system. Van Poollen and Kazemi discussed how to determine the mean distance to the radial discontinuity in an in-situ combustion project. Refs. 16 and 17 discuss the effect of radial discontinuity in interpretation of pressure falloff tests in reservoirs with fluid banks. Sosa et al. examined the effect of relative permeability and mobility ratio on falloff behavior in reservoirs with water banks. The presence of different temperature zones in nonisothermal reservoirs may resemble permeability boundaries during well testing. Mangold et al. presented a numerical study of a thermal discontinuity in well test analysis. Their results indicated that nonisothermal influence could be detected and accounted for by tests of sufficient duration with suitably placed observation wells. Horne et al. indicated the possibility of determining compressibility and permeability contrasts across the phase boundaries in geothermal reservoirs. The most recent study of well test analysis in composite reservoirs was by Eggenschwiler, Satman et al. Their studies presented a very general composite system model. The problem was solved analytically by using the Laplace transformation with numerical inversion. The solution concerned the transient flow of a slightly compressible fluid in a porous medium during injection or falloff for a single well confined in concentric regions of differing mobilities and hydraulic diffusivities. The system assumed both wellbore storage and a skin effect. Their results indicated that a pseudosteady-state pressure response exists in the transition region between the inner region and outer region semilog straight lines. This response is drawn on a Cartesian vs. plot, the slope of which is used to estimate the bulk volume of the inner region. SPEJ p. 281
12
Weiss, Felix, and Christoph Kessler. "Load prediction of hingeless helicopter rotors including drivetrain dynamics." CEAS Aeronautical Journal 12, no. 2 (February 3, 2021): 215–31. http://dx.doi.org/10.1007/s13272-020-00483-6.
Анотація:
AbstractIn contrast to analyses with constrained hub speed, the present study includes the dynamic response of coupled rotor-drivetrain modes in the aeromechanic simulation of rotor blade loads. The structural model of the flexible Bo105 rotor-drivetrain system is coupled to aerodynamics modeled by an analytical formulation of unsteady blade element loads combined with a generalized dynamic wake or a free wake, respectively. For two flight states, i. e. cruise flight and large blade loading, a time-marching autopilot trim of the rotor-drivetrain system in wind tunnel configuration is performed. The simulation results are compared to those of a baseline case with constant rotor hub speed. The comparison reveals a major change in the blade passage frequency harmonics of the lead-lag loads. Beside the full drivetrain model, reduced models are shown to accurately represent the drivetrain influence on blade loads, if the eigenfrequency of the coupled second collective lead-lag/drivetrain mode is properly predicted. In a sensitivity analysis, this eigenfrequency is varied by stiffness modification of a reduced drivetrain model. The resulting changes in blade loads are correlated to this eigenfrequency, which serves as a simple though accurate classification of the drivetrain regarding its influence on vibratory blade loads. Finally, the potential to improve lead-lag load predictions by application of a drivetrain model is demonstrated through the comparison of simulated loads with measurements from a wind tunnel test.
13
Ershaghi, I., and R. Aflaki. "Problems in Characterization of Naturally Fractured Reservoirs From Well Test Data." Society of Petroleum Engineers Journal 25, no. 03 (June 1, 1985): 445–50. http://dx.doi.org/10.2118/12014-pa.
Анотація:
Abstract This paper presents a critical analysis of some recently published papers on naturally fractured reservoirs. These published papers on naturally fractured reservoirs. These publications have pointed out that for a publications have pointed out that for a matrix-to-fracture-gradient flow regime, the transition portion of pressure test data on the semilog plot develops a portion of pressure test data on the semilog plot develops a slope one half that of the late-time data. We show that systems under pseudosteady state also may develop a 1:2 slope ratio. Examples from published case studies are included to show the significant errors associated with the characterization of a naturally fractured system by using the 1:2 slope concept for semicomplete well tests. Introduction Idealistic models of the dual-porosity type often have been recommended for interpretation of a well test in naturally fractured reservoirs. The evolutionary aspects of these models have been reviewed by several authors. Gradual availability of actual field tests and recent developments in analytical and numerical solution techniques have helped to create a better understanding of application and limitation of various proposed models. Two important observations should be made here. First, just as it is now recognized that classical work published by Warren and Root in 1963 was not the end of the line for interpretation of the behavior of naturally fractured systems, the present state of knowledge later may be considered the beginning of the technology. Second, parallel with the ongoing work by various investigators who progressively include more realistic assumptions in their progressively include more realistic assumptions in their analytical modeling, one needs to ponder the implication of these findings and point out the inappropriate impressions that such publications may precipitate in the mind of practicing engineers. practicing engineers. This paper is intended to scrutinize statements published in recent years about certain aspects of the anticipated transition period developed on the semilog plot of pressure-drawdown or pressure-buildup test data. pressure-drawdown or pressure-buildup test data. The Transition Period In the dual-porosity models published to date, a naturally fractured reservoir is assumed to follow the behavior of low-permeability and high-storage matrix blocks in communication with a network of high-permeability and low-storage fractures. The difference among the models has been the assumed geometry of the matrix blocks or the nature of flow between the matrix and the fracture. However, in all cases, it is agreed that a transition period develops that is strictly a function of the matrix period develops that is strictly a function of the matrix properties and matrix-fracture relationship. Fig. 1 shows properties and matrix-fracture relationship. Fig. 1 shows a typical semilog plot depicting the transition period and the parallel lines. Estimation of Warren and Root's proposed and to characterize a naturally fractured proposed and to characterize a naturally fractured system requires the development of the transition period. The Warren and Root model assumes a set of uniformly distributed matrix blocks. Furthermore, the flow from matrix to fracture is assumed to follow a pseudosteady-state regime. Under such conditions, in theory, this period is an S-shaped curve with a point of inflection. Uldrich and Ershaghi developed a technique to use the coordinates of this point of inflection for estimating and under conditions where either the early- or the late-time straight lines were not available. Kazemi and de Swann presented alternative approaches to represent naturally fractured reservoirs. They assumed a geometrical configuration consisting of layered matrix blocks separated by horizontal fractures. Their observation was that for such a system the transition period develops as a straight line with no inflection point. Bourdet and Gringarten identified a semilog straight line during the transition period for unsteady-state matrix-fracture flow. Recent work by Streltsova and Serra et al emphasized the transient nature of flow from matrix to fracture and pointed out the development of a unique slope ratio. These authors, later joined by Cinco-L. and Samaniego-V., stated that under a transient flow condition, the straight-line shape of the transition period develops a slope that is numerically one-half the slope of the parallel straight lines corresponding to the early- or late-time data. It was further pointed out that the transient flow model is a more realistic method of describing the matrix-fracture flow. As such, they implied that in the absence of wellbore-storage-free early-time data, or late-time data in the case of limited-duration tests, one may use the slope of the transition straight line and proceed with the estimation of the reservoir properties. Statement of the Problem The major questions that need to be addressed at this time are as follows. SPEJ P. 445
14
Fan, L., W. J. Lee, and J. P. Spivey. "Semi-Analytical Model for Thermal Effect on Gas Well Pressure-Buildup Tests." SPE Reservoir Evaluation & Engineering 3, no. 06 (December 1, 2000): 480–91. http://dx.doi.org/10.2118/68020-pa.
Анотація:
Summary This paper presents a semi-analytical wellbore/reservoir model1 that can describe general wellbore effects, especially the thermal effect, on high-temperature gas well pressure-buildup tests. A numerical simulator has been developed from the model. Using different combinations of wellbore and reservoir parameters, the simulator generated curve shapes that differed with wellbore thermal effects. Many of the curve shapes have been observed in the field.2,3 Using the results from this paper, engineers can distinguish between general wellbore effects and reservoir behavior in the pressure data, which will make the interpretation more accurate. Also, with the help of the simulator developed from the model, engineers can effectively design gas well pressure-buildup tests by running the simulator to determine the minimum time required to obtain the data not distorted by the wellbore effects.4 The governing equations of the wellbore model are based on mass, momentum, and energy balances for single-phase gas in one-dimensional space. The gas pressure/volume/temperature correlation was also used. Different flow regimes (laminar, transitional, and turbulent) inside the wellbore are modeled for calculating the friction factor. As one boundary condition, a simple analytical reservoir model was connected to the wellbore model at the bottomhole using Duhamel's principle. Heat-loss effects account for forced-convectional heat transfer inside the tubing, heat conduction between tubing and formation, natural convection and radiation heat transfer of annular fluid, and transient heat flow in the formation. Pressure, temperature, velocity, and gas properties inside the wellbore can be predicted at any depth during an entire pressure-buildup test. Variable wellbore storage, momentum, and thermal effects can be simulated. Introduction The concept of wellbore storage was introduced when pressure transient analysis was first established as a viable method for evaluating well and reservoir performance.5,6 Much effort has been spent on minimizing wellbore storage effects on well test data. Traditional type-curve matching7–9 is the first attempt to interpret the pressure data with constant wellbore storage. Semilog analysis methods10,11 are very useful when the true semilog straight line can be identified. Analyzing buildup tests with changing wellbore storage due to phase redistribution has been discussed in the literature.12,13 The results can mimic field data. However, they lack physical justification and cannot be used for forward modeling. Pseudo pressure and pseudotime functions have been used to account for variable wellbore storage for gas wells.14–17 Different approaches to modeling transient two-phase flow in the wellbore18,19 describe the phase redistribution phenomena physically by applying mass and momentum conservation equations. But no thermal effects are included. The above methods all assume that the temperature of the fluid in the wellbore is a constant. The various aspects of heat transfer between a wellbore fluid and the formation have been studied by many authors over the last few decades.20–28 Most of them are steady-state models, which assume that fluid properties and flow rate are not functions of time in the wellbore. A few wellbore models, mainly for geothermal wells with two-phase transient flow inside the wellbore, exist in the literature.29–33 Generally, these models do not work for single-phase gas wells. Hasan34 and Kabir35 presented a transient wellbore/reservoir model for estimating bottomhole pressure and temperature from measured wellhead pressure and temperature in high-pressure and high-temperature reservoirs. Gas well pressure-buildup test data do not match traditional liquid type curves mainly because the gas properties are strong functions of pressure and temperature. Most of the wellbore models available are constructed assuming isothermal conditions in both wellbore and reservoir. However, it has been noticed that gas temperature changes inside the wellbore caused by heat loss to the surrounding formation can change the curve shapes of pressure transient data at early times. This causes problems in both the interpretation and design phases of gas well pressure transient tests, especially buildup tests. To improve design and analysis of gas well pressure-buildup tests, a wellbore model that can evaluate or generalize wellbore effects during a gas well buildup test is necessary. The model can be used in the forward mode to predict pressure transient behavior, which can help in designing a gas well pressure-buildup test much more effectively and economically. Model Development We developed a one-dimensional, transient gas flow wellbore model in this study. The model was constructed using mass balance, momentum balance, and energy balance equations. Real gas pressure/volume/temperature (PVT) correlations were used to complete the model equation system. A homogeneous, radial flow, single-phase, line-source reservoir model was chosen and connected to the wellbore model at the bottomhole by applying Duhamel's principle, which combines the sandface flow rate with the bottomhole pressure to form a boundary condition. In this simple reservoir model, the dimensionless pseudo pressure function is used to allow the use of the liquid solution for the gas case. Gas flow in the pipe is quite different from gas flow in the reservoir. The wellbore-pressure transient propagation is dominated by inertial effects, as well as gravity and friction effects. During a gas well pressure-buildup test, a large disturbance to fluid motion is initiated. Therefore, an unsteady-state viscous model is required to simulate the entire buildup test. The net effect of large changes during the buildup test is a wavelike response in the wellbore, which is dampened quickly over time and is governed by Navier-Stokes-like equations. In the reservoir, however, the fluid flow is subjected to relatively moderate pressure disturbances, and is governed by diffusion-like equations. Model Equations. The general one-dimensional mass balance equation can be written as ∂ ρ ∂ t + ∂ ( ρ v ) ∂ x = 0. ( 1 ) The general one-dimensional momentum balance equation with a constant cross-sectional area can be expressed as ∂ ∂ t ( ρ v ) + ∂ ∂ x ( ρ v 2 ) + 144 g c ∂ p ∂ x + ρ g ￣ + τ = 0. ( 2 )
15
Fabian, Klausmann Sebastian, Daniel Spieker, and Heinz-Peter Schiffer. "Transonic compressor Darmstadt Open Test Case – unsteady aerodynamics and stall inception." Journal of the Global Power and Propulsion Society 8 (April 8, 2024): 52–61. http://dx.doi.org/10.33737/jgpps/183165.
Анотація:
Predicting unsteady aerodynamics and related phenomena in the vicinity of the stability limit of transonic compressors has been a challenging topic within the turbomachinery community since decades. To improve numerical tools and prediction capabilities the Transonic Compressor Darmstadt Open Test Case has been introduced to provide a reliable validation test data set for steady and unsteady compressor aerodynamics. This work investigates the unsteady aerodynamics before the occurrence of rotating stall within the TU Darmstadt OpenStage compressor rotor and introduces unsteady wall pressure data to the Darmstadt Open Test Case. Exemplary pre-stall aerodynamics and stall inception are investigated for nominal (transonic) and part speed (subsonic) operating conditions, comprising the analysis of the unsteady static pressure field at the rotor tip as well as spectral analysis of the corresponding pressure signals during transient throttling maneuvers. To capture the rotor tip flow field, the rotor casing is instrumented with axially arranged flush mounted time-resolving wall pressure transducers. To determine propagation speeds of occurring phenomena, additional circumferentially distributed sensors are considered. Vibration monitoring shows no significant flutter or non-synchronous blade vibration, prior to the occurrence of rotating stall. Thus, this work focuses on aerodynamics, such as the interaction of secondary flow and shocks.
16
Ma, Hongwei, Chao Jin, and Wei Wei. "Experimental investigation of effects of suction side squealer tip on the aeroelastic stability of a linear oscillating compressor cascade." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 11 (August 3, 2016): 2120–31. http://dx.doi.org/10.1177/0954410016662057.
Анотація:
This paper investigates the unsteady tip flow characteristics and their effects on the aeroelastic stability of a linear oscillating compressor cascade experimentally. Two test cases with different tip clearance configurations were tested, including a suction side squealer configuration and a control test. The unsteady pressure on the blade surface was measured at three blade vibration frequencies, and then was utilized to establish the aero-damping of the cascade. The results show that the impact of suction side squealer tip clearance on the tip clearance flow mainly exists at the region where it rolls up, and the unsteady flow induced by the vibration blade has no effect on the time-averaged result. In tip area of the blade, the leakage vortex plays a dominant role in determining the distribution of the first harmonic of unsteady static pressure. Compared with the baseline test case, the suction side squealer tip geometry exhibits better aerodynamic stability at high oscillating frequency. The aerodynamic response (phase angle) of the leakage flow lags behind the vibration of blade, and its streamwise variation implies strongly associated with the development of the tip leakage vortex. The spanwise three-dimensional unsteady characteristic of suction side squealer tip geometry is more obvious than that of the baseline test case.
17
Petit, Olivier, and Håkan Nilsson. "Numerical Investigations of Unsteady Flow in a Centrifugal Pump with a Vaned Diffuser." International Journal of Rotating Machinery 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/961580.
Анотація:
Computational fluid dynamics (CFD) analyses were made to study the unsteady three-dimensional turbulence in the ERCOFTAC centrifugal pump test case. The simulations were carried out using the OpenFOAM Open Source CFD software. The test case consists of an unshrouded centrifugal impeller with seven blades and a radial vaned diffuser with 12 vanes. A large number of measurements are available in the radial gap between the impeller and the diffuse, making this case ideal for validating numerical methods. Results of steady and unsteady calculations of the flow in the pump are compared with the experimental ones, and four different turbulent models are analyzed. The steady simulation uses the frozen rotor concept, while the unsteady simulation uses a fully resolved sliding grid approach. The comparisons show that the unsteady numerical results accurately predict the unsteadiness of the flow, demonstrating the validity and applicability of that methodology for unsteady incompressible turbomachinery flow computations. The steady approach is less accurate, with an unphysical advection of the impeller wakes, but accurate enough for a crude approximation. The different turbulence models predict the flow at the same level of accuracy, with slightly different results.
18
Klausmann, Fabian, Daniel Franke, Jonas Foret, and Heinz-Peter Schiffer. "Transonic compressor Darmstadt - Open test case Introduction of the TUDa open test case." Journal of the Global Power and Propulsion Society 6 (December 12, 2022): 318–29. http://dx.doi.org/10.33737/jgpps/156120.
Анотація:
Designs for future aero engines aim for increased efficiency with reduced exhaust gas and noise emissions. To achieve these goals, comprehensive physical understanding and highly innovative solutions are necessary. Even though computational capabilities are rising, the required confidence level is restrained. To understand and validate theoretical and numerical models, extensive experiments at realistic operating conditions are crucial. The modular compressor at the Transonic Compressor Darmstadt test facility at Technical University of Darmstadt enables investigations of prototype BLISK rotors in single or 1.5-stage setups, operating at high-speed conditions. Extensive steady and time-resolving instrumentation is used to determine the compressor aerodynamics and performance as well as aeroelastics. To foster improvements in numerical modelling and predictability based on high quality experimental data, the TUDa-GLR-OpenStage test case is introduced. It comprises a single stage setup, including the BLISK rotor, a 3D-optimized stator as well as the annulus contour. The data set is supplemented with comprehensive measurement data at stage inlet and outlet as well as running tip clearances. This paper describes the open test case, related geometries, measurement procedures and corresponding experimental results, including steady state performance and unsteady aerodynamics. Ultimately, it is aiming to provide a standard case for future development of numerical models and comparable validation.
19
Brandstetter, Christoph, and Sina Stapelfeldt. "Near-Stall Modelling of a Pitching Airfoil at High Incidence, Mach Number and Reduced Frequency." International Journal of Turbomachinery, Propulsion and Power 7, no. 4 (September 29, 2022): 26. http://dx.doi.org/10.3390/ijtpp7040026.
Анотація:
The prediction accuracy of aeroelastic stability in fans and compressors depends crucially on the accuracy of the underlying aerodynamic predictions. The prevalent approach in the field solves the unsteady Reynolds-averaged Navier—Stokes equations in the presence of blade vibration. Given the unsteady, three-dimensional and often separated nature of the flow in the regimes of aeroelastic interest, the confidence in URANS methods is questionable. This paper uses the simple test case of a pitching symmetric aerofoil with a sharp leading edge to illustrate the challenges of aeroelastic modelling. It compares coupled numerical simulations against time-resolved experimental measurements. The unsteady aerodynamic response of the pitching blade and its dependency on tip-clearance flow and time-averaged incidence angle are analyzed. The results indicate that differences in the unsteady aerodynamics between different numerical approaches close to stall can have a significant impact on local aerodynamic damping. Furthermore, for the chosen test case there is a strong correspondence between the local quasi-steady and unsteady behaviour which weakens, but is still present, towards stall.
20
Hunt, D. L., M. Childs, and M. Maina. "QUACC, a novel method for predicting unsteady flows — including propellers and store release." Aeronautical Journal 105, no. 1050 (August 2001): 427–34. http://dx.doi.org/10.1017/s0001924000012409.
Анотація:
AbstractAerospace designers are increasingly interested in predicting unsteady flowfields such as those associated with store release, rotating propellers etc. However, the cost of performing fully unsteady calculations is usually prohibitively expensive. In order to address this problem for unsteady flows driven by a moving surface, a novel method is presented which calculates the time derivates as an analytic function of the instantaneous flowfield. This allows an accurate solution of the unsteady flow equations to be calculated using a quasi-unsteady approach. The validity of this approach is demonstrated for a store release and a propeller test case. Possible extensions to this method for more complex unsteady flows are presented.
21
Coutier-Delgosha, O., R. Fortes-Patella, J. L. Reboud, and B. Stutz. "TEST CASE NO 30: UNSTEADY CAVITATION IN A VENTURI TYPE SECTION (PN)." Multiphase Science and Technology 16, no. 1-3 (2004): 207–18. http://dx.doi.org/10.1615/multscientechn.v16.i1-3.290.
22
DOUADY, STÉPHANE, BRUNO ANDREOTTI, PIERRE CLADÉ, and ADRIAN DAERR. "THE FOUR AVALANCHE FRONTS: A TEST CASE FOR GRANULAR SURFACE FLOW MODELING." Advances in Complex Systems 04, no. 04 (December 2001): 509–22. http://dx.doi.org/10.1142/s0219525901000449.
Анотація:
Granular surface flows have still to be fully modelled. Here, we present the four types of front that can be observed in avalanches. These strongly inhomogeneous and unsteady flows are very sensitive test cases for the different types of model. We show that, at least qualitatively for the moment, the model we propose, based on the analysis of the motion of a single grain and layers of grains, can reproduce the different characteristics of these four fronts.
23
Walters, D. Keith, and James H. Leylek. "Computational Fluid Dynamics Study of Wake-Induced Transition on a Compressor-Like Flat Plate." Journal of Turbomachinery 127, no. 1 (January 1, 2005): 52–63. http://dx.doi.org/10.1115/1.1791650.
Анотація:
Recent experimental work has documented the importance of wake passing on the behavior of transitional boundary layers on the suction surface of axial compressor blades. This paper documents computational fluid dynamics (CFD) simulations using a commercially available general-purpose CFD solver, performed on a representative case with unsteady transitional behavior. The study implements an advanced version of a three-equation eddy-viscosity model previously developed and documented by the authors, which is capable of resolving boundary layer transition. It is applied to the test cases of steady and unsteady boundary layer transition on a two-dimensional flat plate geometry with a freestream velocity distribution representative of the suction side of a compressor airfoil. The CFD results are analyzed and compared to a similar experimental test case from the open literature. Results with the model show a dramatic improvement over more typical Reynolds-averaged Navier–Stokes (RANS)-based modeling approaches, and highlight the importance of resolving transition in both steady and unsteady compressor aerosimulations.
24
LI, H., and G. BEN-DOR. "Analytical investigation of two-dimensional unsteady shock-on-shock interactions." Journal of Fluid Mechanics 340 (June 10, 1997): 101–28. http://dx.doi.org/10.1017/s0022112097005326.
Анотація:
The unsteady inviscid two-dimensional flow field and the wave configurations which result when a supersonic vehicle strikes a planar oblique shock wave were modelled and analytically predicted using some approximations and simplifying assumptions. Based on the two- and three-shock theories together with the geometric shock dynamics theory, both regular (windward) and irregular (leeward) shock-on-shock (S-O-S) interactions were investigated, and the transition criterion between them was suggested. For the case of regular S-O-S interaction, the transmitted shock wave reflects over the vehicle body surface either as a regular (RR) or a Mach reflection (MR) depending on the inclination angle and the strength of the impingement shock wave. A pronounced peak surface pressure jump was found to exist during the transition from RR to MR. A RR[harr ]MR transition criterion when the flow ahead of the shock pattern is not quiescent was proposed. Predictions based on the model developed here are superior to those of approximate theories when compared to the available experimental data and numerical simulations.
25
Korakianitis, T. "On the Prediction of Unsteady Forces on Gas Turbine Blades: Part 1—Description of the Approach." Journal of Turbomachinery 114, no. 1 (January 1, 1992): 114–22. http://dx.doi.org/10.1115/1.2927974.
Анотація:
This article investigates the generation of unsteady forces on turbine blades due to potential-flow interaction and viscous-wake interaction from upstream blade rows. A computer program is used to calculate the unsteady forces on the rotor blades. Results are obtained by modeling the effects of the stator viscous wake and the stator potential-flow field on the rotor flow field. The results for one steady and one unsteady flow case are compared with known analytical and experimental data. The amplitudes for the two types of interaction are based on an analysis of available viscous wake data, on measurements of the potential-flow disturbance downstream of typical turbine stators, and on a parametric study of the effects of the amplitudes on the results of the unsteady forces generated on a typical turbine rotor cascade.
26
Aubeny, Charles, Robert Lytton, and Dina Tang. "Simplified Analysis of Unsteady Moisture Flow Through Unsaturated Soil." Transportation Research Record: Journal of the Transportation Research Board 1821, no. 1 (January 2003): 75–82. http://dx.doi.org/10.3141/1821-09.
Анотація:
The moisture diffusion properties of unsaturated soils control the rate of infiltration of surface moisture into the soil mass and hence are critical to a wide variety of civil structures, including pavements, structures, retaining walls, and slopes. Because of the dependence of permeability on suction and the nonlinearity of the suction–moisture relationship, the analytical formulation for flow through unsaturated soils is highly nonlinear. An approximate linear analysis of this problem, which was originally proposed by Peter Mitchell, was investigated. One advantage of this approximate analysis is that it can provide the practical basis for measuring soil moisture diffusion characteristics in laboratory tests. A second advantage is that the linear formulation provides an analytical tool accessible to practitioners. Mitchell originally based his formulation on a relatively restrictive assumption on the permeability-versus-suction relationship. An approach to circumventing that restriction is proposed. The findings of a laboratory test program that uses Mitchell’s formulation to estimate a soil’s moisture diffusion characteristics are presented. Finally, some simple analytical predictions demonstrate the practical significance of the soil moisture diffusion properties.
27
Clark, Martyn P., Bart Nijssen, and Charles H. Luce. "An analytical test case for snow models." Water Resources Research 53, no. 1 (January 2017): 909–22. http://dx.doi.org/10.1002/2016wr019672.
28
Yuan, Hua, and Yan Hong. "Parameter Inversion of Field Pumping Test in Aquifer with Enclosed Impermeable Boundary." Advanced Materials Research 599 (November 2012): 720–23. http://dx.doi.org/10.4028/www.scientific.net/amr.599.720.
Анотація:
Theis formula derived under the circumstance of unsteady flow pumping in infinite aquifer without impermeable boundary is the representation of analytic method solving unsteady well flow problem, which can not be applied to the case of impermeable boundary just limited by its premise condition: “infinite permeable border”. In this paper, the well flow model of pumping in aquifer with unsealed impermeable boundary is researched based on mapping theory and superposition principle. And then this model is applied to a typical field pumping test in Pudong working shaft deep foundation of South Xizang road river-crossing tunnel. The results show that the slope of draw down and pumping duration time curve will increase while the surrounding impermeable boundary comes into play.
29
MATTHEWS, MICCAL T., and KAREN M. HASTIE. "AN ANALYTICAL AND NUMERICAL STUDY OF UNSTEADY CHANNEL FLOW WITH SLIP." ANZIAM Journal 53, no. 4 (April 2012): 321–36. http://dx.doi.org/10.1017/s1446181112000272.
Анотація:
AbstractA theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.
30
Kirrou, Ilham, Lahcen Mokni, and Mohamed Belhaq. "Quasiperiodic galloping of a wind-excited tower near secondary resonances of order 2." Journal of Vibration and Control 23, no. 4 (August 9, 2016): 574–86. http://dx.doi.org/10.1177/1077546315581757.
Анотація:
Quasiperiodic galloping of a wind-excited tower under unsteady wind is investigated analytically near secondary (sub/superharmonic) resonances of order 2 considering a single degree-of-freedom model. The case where the unsteady wind develops multiharmonic excitations consisting of the two first harmonic terms is examined. We perform two successive multiple scale methods to obtain analytical expressions of a quasiperiodic solution and its modulation envelope near the secondary resonances. The influence of unsteady wind on the quasiperiodic galloping and on the frequency of its modulation is examined for different cases of wind excitation. The results show that the quasiperiodic galloping onset and its modulation envelope can be influenced, depending on the activated resonance and the harmonic component induced by the unsteady wind. It is also shown that the frequency of the quasiperiodic galloping is higher near the 2-superharmonic resonance in all cases of wind excitation.
31
Sato, K., and L. He. "Effect of Rotor–Stator Interaction on Impeller Performance in Centrifugal Compressors." International Journal of Rotating Machinery 5, no. 2 (1999): 135–46. http://dx.doi.org/10.1155/s1023621x99000123.
Анотація:
A 3-D unsteady thin-layer Navier-Stokes code has been used to calculate the flow through a centrifugal compressor stage. The validation of the code for steady flows in centrifugal compressors was conducted for the Krain’s impeller with a vaneless diffuser as a test case and the numerical results were compared with the experimental results. The predicted flow field and performance agreed well with the experimental data. An unsteady stage solution was then conducted with this impeller followed by a generic low-solidity vaned-diffuser to examine the unsteady effects on the impeller performance. The computational results showed a stabilising effect of the blade row interaction.
32
Zhang, Zhitao, Changchuan Xie, Wei Wang, and Chao An. "An Experimental and Numerical Evaluation of the Aerodynamic Performance of a UAV Propeller Considering Pitch Motion." Drones 7, no. 7 (July 6, 2023): 447. http://dx.doi.org/10.3390/drones7070447.
Анотація:
Considering the vibration generated by a propeller-driven UAV or encountering gust, the propeller will perform a very complex follower motion. A pitch and rotating coupled motion is proposed in the present work that can take more complex unsteady performance of follower force than a regular fixed-point rotating motion. In order to evaluate the unsteady follower force and conduct parametric study, an extensive ground test bench was designed for this purpose where the whole test system was driven by a linear servo actuator and the follower force was measured by a 6-component balance. For CFD simulation, coupled motion in particular needs detailed unsteady aerodynamic model; therefore, a high-fidelity CFD-based study integrated with the overset mesh method was complemented to solve the unsteady fluid of varying conditions. The results suggest that a significant influence on unsteady follower force is observed, and the mean value of in-plane force does not equal to zero during the coupled motion process. Compared with the regular fixed-point rotation of propeller, the fluctuation frequency of follower force in present work couples the rotation and pitch motion frequencies. In addition, the oscillation amplitude of out-plane force and torque is positively related with the pitch frequency, pitch amplitude, and relative length from leading edge of wing to the rotation center. For example, the oscillation amplitude of 1-blade’s out-plane force and torque increases by 57.122% and 66.542% for the 5 Hz-5 deg case compared with the 5 Hz-3 deg case, respectively. However, the torque is not sensitive to frequency of pitch motion. The generally excellent agreement evident between the ground test and numerical simulation results is important as guidance for our future investigation on “dynamic” aerodynamic performance of a propeller-driven UAV.
33
Nath, Rupam Shankar, Rudra Kanta Deka, and Himangshu Kumar. "The Effect of Thermal Stratification on Unsteady Parabolic Flow past an Infinite Vertical Plate with Chemical Reaction." East European Journal of Physics, no. 4 (December 2, 2023): 77–86. http://dx.doi.org/10.26565/2312-4334-2023-4-08.
Анотація:
This research paper investigates the effects of thermal stratification on unsteady parabolic flow past an infinite vertical plate with chemical reaction. Using the Laplace transform method, analytical solutions are derived to simulate the physical process of the flow. The study considers the effects of thermal stratification on the flow field, as well as the effects of chemical reaction on the velocity, and temperature field. The results of the stratification case are then compared to the case of no stratification of a similar flow field. The results of this research can be used to improve understanding of the unsteady parabolic flow in thermal stratified environments and provide valuable insight into the effects of chemical reactions on the temperature field.
34
von Hoyningen-Huene, Martin, and Alexander R. Jung. "Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations." Journal of Turbomachinery 122, no. 2 (February 1, 1999): 234–46. http://dx.doi.org/10.1115/1.555440.
Анотація:
This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a nonaccelerated, fully explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain, and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier–Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The purpose of the comparison of the different numerical algorithms for explicit schemes is to facilitate the decision as to which acceleration technique should be used for calculations with regard to accuracy and computational time. The convergence acceleration methods under consideration are explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid, and implicit dual time stepping. The investigation and comparison of the different acceleration techniques apply to all explicit unsteady flow solvers. This paper also examines the influence of the stage blade count ratio on the flowfield. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is crucial from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages. [S0889-504X(00)00702-9]
35
Lopes, Gustavo, Loris Simonassi, and Sergio Lavagnoli. "Impact of Unsteady Wakes on the Secondary Flows of a High-Speed Low-Pressure Turbine Cascade." International Journal of Turbomachinery, Propulsion and Power 8, no. 4 (September 22, 2023): 36. http://dx.doi.org/10.3390/ijtpp8040036.
Анотація:
The aerodynamics of a high-speed low-pressure turbine (LPT) cascade were investigated under steady and unsteady inlet flows. The tests were performed at outlet Mach (M) and Reynolds numbers (Re) of 0.90 and 70k, respectively. Unsteady wakes were simulated by means of a wake generator equipped with bars. A bar reduced frequency (f+) of ∼0.95 was used for the unsteady case. The inlet flow field was characterized in terms of the total pressure profile and incidence. The blade aerodynamics at midspan and the secondary flow region were investigated by means of pneumatic taps and hot-film sensors. The latter provided a novel view into the impact of the secondary flows on the heat transfer topology on the blade suction side (SS). The cascade performance was quantified in terms of the outlet flow angle and losses by means of a directional multi-hole probe. The results report the phase-averaged impact of unsteady wakes on the secondary flow structures in an open test case high-speed LPT geometry.
36
Gru¨ber, B., and V. Carstens. "Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects." Journal of Turbomachinery 120, no. 1 (January 1, 1998): 104–11. http://dx.doi.org/10.1115/1.2841370.
Анотація:
This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier–Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration, and the implementation of a mixing length turbulence model. For the present investigations, two experimentally investigated test cases have been selected, in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier–Stokes code are compared with experimental data, as well as with the results of an Euler method. The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines.” Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier–Stokes code. The second test case is a highly loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier–Stokes method improves to some extent the agreement between the experiment and numerical simulation.
37
Li, Guang Ning, and Min Xu. "Numerical Investigation of Sub-Iteration Criterions for Unsteady Flow Computations with Dual-Time Method." Applied Mechanics and Materials 432 (September 2013): 189–95. http://dx.doi.org/10.4028/www.scientific.net/amm.432.189.
Анотація:
The convergence of sub-iteration with the dual-time method is very important for the prediction of unsteady flow field. The influence of sub-iteration step number, criterion of sub-iteration convergence and the choice of physical time step size on the calculation results are discussed by solving of the two-dimensional unsteady Euler equations. A new convergence criterion (named residual criterion) of sub-iteration for unsteady flows is proposed, and the unsteady flow test case AGARD-CT5 is calculated to verify the new criterion. The results show that, with the same criterion of sub-iteration, the results from different physical time step sizes are in agreement with each other. The difference between the experiment data and the numerical results are small, and if the sub-iteration criterion used is reasonable and small enough, the dependence of numerical results of unsteady flows on the physical time step will be decreased as possible. The new criterion of sub-iteration for dual-time step unsteady calculations can be used for engineering problem.
38
Nazukin, V. A., V. G. Avgustinovich, B. Thornber, P. Aguado Lopez, V. V. Tsatiashvili, and E. V. Koromyslov. "Test case of 3d unsteady swirling flows modeling using commercial and in-house codes." VESTNIK of the Samara State Aerospace University, no. 3-1(41) (April 28, 2014): 197. http://dx.doi.org/10.18287/1998-6629-2013-0-3-1(41)-197-205.
39
Al-Saif, A. S. J., and Zinah A. Hasan. "An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations." JOURNAL OF ADVANCES IN MATHEMATICS 21 (June 22, 2022): 73–88. http://dx.doi.org/10.24297/jam.v21i.9242.
Анотація:
In this paper, an analytic approximate method for solving the unsteady two-dimensional convection-diffusion equations is introduced. Also, the convergence of the approximate methods is analyzed. Three test examples are presented, two have exact and one has not exacted solutions. The results obtained show that these methods are powerful mathematical tools for solving linear and nonlinear partial differential equations, moreover, new analytic Taylor method (NATM), reduced differential transform method (RDTM), and homotopy perturbation method (HPM), are more accurate and have less CPU time than the other methods.
40
Craske, John, and Maarten van Reeuwijk. "Generalised unsteady plume theory." Journal of Fluid Mechanics 792 (March 9, 2016): 1013–52. http://dx.doi.org/10.1017/jfm.2016.72.
Анотація:
We develop a generalised unsteady plume theory and compare it with a new direct numerical simulation (DNS) dataset for an ensemble of statistically unsteady turbulent plumes. The theoretical framework described in this paper generalises previous models and exposes several fundamental aspects of the physics of unsteady plumes. The framework allows one to understand how the structure of the governing integral equations depends on the assumptions one makes about the radial dependence of the longitudinal velocity, turbulence and pressure. Consequently, the ill-posed models identified by Scase & Hewitt (J. Fluid Mech., vol. 697, 2012, pp. 455–480) are shown to be the result of a non-physical assumption regarding the velocity profile. The framework reveals that these ill-posed unsteady plume models are degenerate cases amongst a comparatively large set of well-posed models that can be derived from the generalised unsteady plume equations that we obtain. Drawing on the results of DNS of a plume subjected to an instantaneous step change in its source buoyancy flux, we use the framework in a diagnostic capacity to investigate the properties of the resulting travelling wave. In general, the governing integral equations are hyperbolic, becoming parabolic in the limiting case of a ‘top-hat’ model, and the travelling wave can be classified as lazy, pure or forced according to the particular assumptions that are invoked to close the integral equations. Guided by observations from the DNS data, we use the framework in a prognostic capacity to develop a relatively simple, accurate and well-posed model of unsteady plumes that is based on the assumption of a Gaussian velocity profile. An analytical solution is presented for a pure straight-sided plume that is consistent with the key features observed from the DNS.
41
Neely, A. J., and R. G. Morgan. "The Superorbital Expansion Tube concept, experiment and analysis." Aeronautical Journal 98, no. 973 (March 1994): 97–105. http://dx.doi.org/10.1017/s0001924000050107.
Анотація:
Abstract In response to the need for ground testing facilities for super orbital re-entry research, a small scale facility has been set up at the University of Queensland to demonstrate the Superorbital Expansion Tube concept. This unique device is a free piston driven, triple diaphragm, impulse shock facility which uses the enthalpy multiplication mechanism of the unsteady expansion process and the addition of a secondary shock driver to further heat the driver gas. The pilot facility has been operated to produce quasi-steady test flows in air with shock velocities in excess of 13 km/s and with a usable test flow duration of the order of 15 μs. An experimental condition produced in the facility with total enthalpy of 108 MJ/kg and a total pressure of 335 MPa is reported. A simple analytical flow model which accounts for non-ideal rupture of the light tertiary diaphragm and the resulting entropy increase in the test gas is discussed. It is shown that equilibrium calculations more accurately model the unsteady expansion process than calculations assuming frozen chemistry. This is because the high enthalpy flows produced in the facility can only be achieved if the chemical energy stored in the test flow during shock heating of the test gas is partially returned to the flow during the process of unsteady expansion. Measurements of heat transfer rates to a flat plate demonstrate the usability of the test flow for aerothermodynamic testing and comparison of these rates with empirical calculations confirms the usable accuracy of the flow model.
42
Gupta, Robin, Pengbo Lu, Rodney Glotzbach, and Owen Hehmeyer. "A Novel, Field-Representative Enhanced-Oil-Recovery Coreflood Method." SPE Journal 20, no. 03 (February 2, 2015): 442–52. http://dx.doi.org/10.2118/169088-pa.
Анотація:
Summary This study describes a new method that can improve laboratory determination of enhanced-oil-recovery (EOR) potential for a test fluid relative to a base fluid. The new method uses a modified steady-state fractional-flow method to measure the shift in oil saturation in a rock at an intermediate fractional flow when changing from a base brine to a test EOR brine(s). This study uses fractional-flow analysis and simulations to illustrate the new method and compare it with the conventional-unsteady-state approach. Through case studies, this work demonstrates that the conventional-unsteady-state approach can under- or overestimate EOR brine performance because of poor test design or limitations of the conventional method. The proposed method addresses these limitations. The study also discusses how to determine optimal values of fractional-flow rate and total flow rate, both of which are critical test parameters for the new method.
43
Berci, Marco. "On Aerodynamic Models for Flutter Analysis: A Systematic Overview and Comparative Assessment." Applied Mechanics 2, no. 3 (July 29, 2021): 516–41. http://dx.doi.org/10.3390/applmech2030029.
Анотація:
This work reviews different analytical formulations for the time-dependent aerodynamic load of a thin aerofoil and clarifies numerical flutter results available in the literature for the typical section of a flexible wing; inviscid, two-dimensional, incompressible, potential flow is considered in all test cases. The latter are investigated using the exact theory for small airflow perturbations, which involves both circulatory and non-circulatory effects of different nature, complemented by the p-k flutter analysis. Starting from unsteady aerodynamics and ending with steady aerodynamics, quasi-unsteady and quasi-steady aerodynamic models are systematically derived by successive simplifications within a unified approach. The influence of the aerodynamic approximations on the aeroelastic stability boundary is then rigorously assessed from both physical and mathematical perspectives. All aerodynamic models are critically discussed and compared in the light of the numerical results as well, within a comprehensive theoretical framework in practice. In all cases, results accuracy depends on the aero-structural arrangement of the flexible wing; however, simplified unsteady and simplified quasi-unsteady aerodynamic approximations are suggested for robust flutter analysis whenever the wing’s elastic axis lies ahead of the aerofoil’s control point.
44
Elniel, Fawzia Mansour, Zainal Abdul Aziz, Faisal Salah, and Shaymaa Mustafa. "Approximate analytical solution of the MHD Powell-Eyring fluid flow near accelerated plate." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4-1 (December 5, 2017): 416–20. http://dx.doi.org/10.11113/mjfas.v13n4-1.860.
Анотація:
In this article, the non-linear equation of unsteady flow of Powell-Eyring fluid is solved by using Adomian Decomposition Method (ADM). The fluid is assumed to be flowing under the effect of magnetic field. The model is developed for the case of constant accelerated plate. Sensitivity analysis is performed to show the effects of material parameters on the velocity profile and shear stress at the wall. The results confirmed the suitability of ADM in solving nonlinear equations.
45
McBean, Ivan, Kerry Hourigan, Mark Thompson, and Feng Liu. "Prediction of Flutter of Turbine Blades in a Transonic Annular Cascade." Journal of Fluids Engineering 127, no. 6 (May 29, 2005): 1053–58. http://dx.doi.org/10.1115/1.2060731.
Анотація:
A parallel multiblock Navier-Stokes solver with the k‐ω turbulence model is used to solve the unsteady flow through an annular turbine cascade, the transonic Standard Test Case 4, Test 628. Computations are performed on a two- and three-dimensional model of the blade row with either the Euler or the Navier-Stokes flow models. Results are compared to the experimental measurements. Comparisons of the unsteady surface pressure and the aerodynamic damping are made between the three-dimensional, two-dimensional, inviscid, viscous simulations, and experimental data. Differences are found between the stability predictions by the two- and three-dimensional computations, and the Euler and Navier-Stokes computations due to three-dimensionality of the cascade model and the presence of a boundary layer separation, respectively.
46
Zhang, Ming Lu, Yi Ren Yang, and Zhi Yong Lu. "Unsteady Characteristics over Dynamic Delta Wings." Applied Mechanics and Materials 128-129 (October 2011): 350–53. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.350.
Анотація:
A study of flow and frequency characteristics of the leading-edge vortices over a delta wing undergoing pitching up-stop motions is presented. The experiments with the dynamic delta wings were conducted in a water channel and a wind tunnel respectively. Among them, the test of the flow visualization was completed in the water channel with the delta wing with pitching up-stop motions. The result shows that in the case of pitching up-stop movement the vortex breakdown position is dependent on the range of incidence at which the wing is subject to pitching up-stop and the reduced frequency k (k=c/2U∞). Analysis of the pressure signal measured in the wind tunnel shows when the delta wing is subject to pitching-up the nondimensional spiral wave frequency at nominal incidence in post-breakdown is higher than that at corresponding static state and the bigger the k is, the higher the nondimensional spiral wave frequency is. The same conclusion is fitted with different sweep delta wing.
47
Dixon, Rowena, Chaoyang Jiang, Charitha de Silva, Danielle Moreau, and Con Doolan. "Tandem cylinder aeroacoustic sources." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A330. http://dx.doi.org/10.1121/10.0023703.
Анотація:
Tandem cylinders in turbulent flow are found in aircraft landing gear, chimney stacks, power lines, and bridge piers. The aim of this paper is to present detailed unsteady surface pressure measurements for tandem cylinders. These unsteady surface pressures are the major sources of noise in this important fundamental test case. A series of experiments were conducted in the UNSW anechoic wind tunnel to investigate the sound generation and flow distortion from a downstream cylinder interacting with wake from an upstream cylinder. This wake is highly anisotropic, containing large vortex shedding scales as well as energetic broadband components. The experiments were conducted using PIV (Particle Image Velocimetry) to obtain instantaneous flow fields and remote microphones to capture unsteady surface pressure measurements. Microphones were positioned outside the flow to record far-field noise. The cylinder was rotated to obtain surface pressure around the circumference. The acoustic results for the tandem cylinder case were compared with noise generation from a single cylinder in uniform flow. An increase in both surface pressure and far-field noise was observed in the tonal and broadband components. It was concluded that interaction with the wake of the upstream cylinder significantly increased the unsteady surface pressure of the downstream cylinder.
48
Vandevoorde, M., J. Vierendeels, R. Sierens, E. Dick, and R. Baert. "Comparison of Algorithms for Unsteady Flow Calculations in Inlet and Exhaust Systems of IC Engines." Journal of Engineering for Gas Turbines and Power 122, no. 4 (April 17, 2000): 541–48. http://dx.doi.org/10.1115/1.1288771.
Анотація:
A comparison of different numerical algorithms used in commercial codes for the calculation of the one-dimensional unsteady flow in the pipes of the inlet and exhaust systems of internal combustion engines is presented in this work. The comparison is made between the Method Of Characteristics (MOC), different Lax-Wendroff schemes, first order upwind schemes and the newest TVD (Total Variation Diminishing) schemes. These algorithms are representative for the complete evolution noticed in the computer codes from the beginning of their use to the present state of the art. Two models of realistic problems in engine simulation tasks are considered: the shock tube calculation (so called Sod’s problem) and the calculation in a tapered pipe. The first test case simulates the exhaust valve opening and releasing a pressure (shock)wave in the exhaust manifold while the other test case covers any gradual variation in the cross section of the manifold pipes. For both test cases computed results are compared with an exact solution and computer time and accuracy are evaluated. None of the examined schemes is completely satisfactory. They either show too much overshoots (for the first test case), or they have local discretization errors (at the section changes of the second test case). A new TVD scheme is proposed that does not introduce any of the foregoing inaccuracies. With this scheme overshoots and dips are eliminated and mass balances are fulfilled, while maintaining high accuracy. [S0742-4795(00)00304-5]
49
Pistiner, Arieh. "An Analytical Solution for Unsteady Flow in a Phreatic Aquifer in the Case of Continuous Rise." Transport in Porous Media 86, no. 3 (September 7, 2010): 815–25. http://dx.doi.org/10.1007/s11242-010-9655-z.
50
Neely, A. J., R. J. Stalker, and A. Paull. "High enthalpy, hypervelocity flows of air and argon in an expansion tube." Aeronautical Journal 95, no. 946 (July 1991): 175–86. http://dx.doi.org/10.1017/s0001924000023885.
Анотація:
AbstractAn expansion tube with a free piston driver has been used to generate quasi-steady hypersonic flows in argon and air at flow velocities in excess of 9 km/s. Irregular test flow unsteadiness has limited the performance of previous expansion tubes, and it has been found that this can be avoided by attention to the interaction between the test gas accelerating expansion and the contact surface in the primary shock tube. Test section measurements of pitot pressure, static pressure and flat plate heat transfer are reported. An approximate analytical theory has been developed for predicting the velocities achieved in the unsteady expansion of the ionising or dissociating test gas.