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1.
Theoretical predictions of wall shear stresses in unsteady turbulent flows in pipes are developed for all flow conditions from fully smooth to fully rough and for Reynolds numbers from 103 to 108. A weighting function approach is used, based on a two-region viscosity distribution in the pipe cross section that is consistent with the Colebrook–White expression for steady-state wall friction. The basic model is developed in an analytical form and the resulting weighting function is then approximated as a sum of exponentials using a modified form of an approximation due to Trikha. A straightforward method is presented for the determination of appropriate values of coefficients for any particular Reynolds number and pipe roughness ratio. The end result is a method that can be used relatively easily by analysts seeking to model unsteady flows in pipes and ducts.  相似文献   

2.
The paper explores the time-wise evolution of selected turbulence parameters during gravity-driven flow establishment of incompressible fluids in rigid circular pipes. Two initial conditions are considered: flow starting from rest, passing through laminar-to-turbulent transition, and terminating in a turbulent steady state; and transient flow between two turbulent steady states. It is found that, in the second case, the properties considered, i.e., local temporal mean velocity and its transverse distribution, axial turbulence intensity, and wall shear stress, are monotonically increasing with time. However, for flow starting from rest, all properties are strongly affected by the development of turbulence. In particular, at the critical moment when laminar-to-turbulent transition is complete, the wall shear stress changes abruptly from one to the other, identifying wall shear stress as a very sensitive indicator of criticality.  相似文献   

3.
The method used in the classical paper by Zielke to estimate the unsteady component of shear stress in unsteady pipe flows is revisited. It is found that the method is undesirably sensitive to the size of the integration time step. The sensitivity is shown to be caused dominantly by the first term in the integration when inadequate allowance is made for the infinite value of the weighting function. A simple method of avoiding the error without requiring the use of small grid sizes is presented.  相似文献   

4.
Based on two-dimensional (2D) flow model simulations, the effects of the radial structure of the flow (e.g., the nonuniformity of the velocity profile) on the pipe wall shear stress, τw, are determined in terms of bulk parameters such as to allow improved 1D modeling of unsteady contribution of τw. An unsteady generalization, for both laminar and turbulent flows, of the quasi-stationary relationship between τw and the friction slope, J, decomposes the additional unsteady contribution into an instantaneous energy dissipation term and an inertial term (that is, based on the local average acceleration-deceleration effects). The relative importance of these two effects is investigated in a transient laminar flow and an analysis of the range of applicability of this kind of approach of representing unsteady friction is presented. Finally, the relation between the additional inertial term and Boussinesq momentum coefficient, is clarified. Although laminar pipe flows are a special case in engineering practice, solutions in this flow regime can provide some insight into the behavior of the transient wall shear stress, and serve as a preliminary step to the solutions of unsteady turbulent pipe flows.  相似文献   

5.
Conventionally, wall shear stress in an unsteady turbulent pipe flow is decomposed into a quasi-steady component and an “unsteady wall shear stress” component. Whereas the former is evaluated by using “standard” steady flow correlations, extensive research has been carried out to develop methods to predict the latter leading to various unsteady friction models. A different approach of decomposition is used in the present paper whereby the wall shear in an unsteady flow is split into the initial steady value and perturbations from it. It is shown that in the early stages of an unsteady turbulent pipe flow, these perturbations are well described by a laminar-flow formulation. This allows simple expressions to be derived for unsteady friction predictions, which are in good agreement with experimental and computational results.  相似文献   

6.
The accurate simulation of pressure transients in pipelines and pipe networks is becoming increasingly important in water engineering. Applications such as inverse transient analysis for condition assessment, leak detection, and pipe roughness calibration require accurate modeling of transients for longer simulation periods that, in many situations, requires improved modeling of unsteady frictional behavior. In addition, the numerical algorithm used for unsteady friction should be highly efficient, as inverse analysis requires the transient model to be run many times. A popular model of unsteady friction that is applicable to a short-duration transient event type is the weighting function-based type, as first derived by Zielke in 1968. Approximation of the weighting function with a sum of exponential terms allows for a considerable increase in computation speed using recursive algorithms. A neglected topic in the application of such models is evaluation of numerical error. This paper presents a discussion and quantification of the numerical errors that occur when using weighting function-based models for the simulation of unsteady friction in pipe transients. Comparisons of numerical error arising from approximations are made in the Fourier domain where exact solutions can be determined. Additionally, the relative importance of error in unsteady friction modeling and unsteady friction itself in the context of general simulation is discussed.  相似文献   

7.
This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse’s experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows.  相似文献   

8.
A new approach to numerical modeling of water hammer is proposed. An unsteady pipe flow model incorporating Brunone’s unsteady friction model is used, but in contrast to the standard treatment of the unsteady friction term as a source term, the writers propose a nonconservative formulation of source term. Second-order flux limited and high order weighted essentially nonoscillating numerical schemes were applied to the proposed formulation, and results are in better agreement with measurements when compared with results obtained with standard form.  相似文献   

9.
The paper addresses the problem of unsteady flow in an elastic pipe, starting from rest and tending towards a turbulent steady state. Careful experiments, involving uncommonly long, smooth-walled conduits, indicate that the hydraulic performance of an elastic pipe is controlled by its finite speed of response to a change in boundary conditions. The actually occurring, pulsatile flow is well described by a water-hammer analysis of the establishment process, but disagrees significantly with theoretical predictions based on assumed conduit rigidity. Flow accelerations, both temporal and convective, are shown to cause a significant increase in the values of the lower-critical Reynolds number of laminar-to-turbulent transition.  相似文献   

10.
An accurate, simple, and efficient approximation to the Vardy–Brown unsteady friction equation is derived and shown to be easily implemented within a one-dimensional characteristics solution for unsteady pipe flow. For comparison, the exact Vardy–Brown unsteady friction equation is used to model shear stresses in transient turbulent pipe flows and the resulting waterhammer equations are solved by the method of characteristics. The approximate Vardy–Brown model is more computationally efficient (i.e., requires one-sixth the execution time and much less memory storage) than the exact Vardy–Brown model. Both models are compared with measured data from different research groups and with numerical data produced by a two-dimensional turbulence waterhammer model. The results show that the exact Vardy–Brown model and the approximate Vardy–Brown model are in good agreement with both laboratory and numerical experiments over a wide range of Reynolds number and wave frequencies. The proposed approximate model only requires the storage of flow variables from a single time step while the exact Vardy–Brown model requires the storage of flow variables at all previous time steps and the two-dimensional model requires the storage of flow variables at all radial nodes.  相似文献   

11.
Expressions for the Reynolds stress and bed shear stress are developed for nonuniform unsteady flow in open channels with streamwise sloping beds, assuming universal (logarithmic) velocity distribution law and using the Reynolds and continuity equations of two-dimensional open-channel flow. The computed Reynolds stress distributions are in agreement with experimental data.  相似文献   

12.
A cell vertex finite volume algorithm and an artificial compressibility approach are employed to enable simulation of three-dimensional incompressible unsteady turbulent flow using unstructured tetrahedral meshes. Unsteady flow modeling is accomplished through the use of an implicit dual time stepping scheme, and stabilization of the procedure is achieved by the explicit addition of artificial viscosity in the Jameson–Schmidt–Turkel manner. The Spalart–Allmaras detached eddy simulation model is adopted for turbulent flow simulations. The computational performance is enhanced by the incorporation of multigrid acceleration and by parallelization of the solution algorithm. A number of examples are presented to demonstrate the capabilities of the resulting procedure.  相似文献   

13.
The effects of unsteadiness in the turbulent flow through a staggered array of circular cylinders, modeling an ultraviolet disinfection system, are studied by means of solutions of the two-dimensional Reynolds-averaged Navier–Stokes equations incorporating the standard k–? turbulence model. Time averaging is applied to the unsteady solution, and the time-averaged characteristics are compared with a solution where a steady flow is a priori assumed, as well as with time-averaged measurements. Differences between the predictions of time-averaged and the steady-flow models are found to be largest in the entrance region of the array, and to decline in importance in the downstream direction. Comparison with measurements indicate that, while the time-averaged unsteady model predictions exhibited better agreement in some respects, the turbulent kinetic energy remained substantially underpredicted. Predictions of head losses through the array are also discussed.  相似文献   

14.
In this paper, basic unsteady flow types and transient event types are categorized, and then unsteady friction models are tested for each type of transient event. One important feature of any unsteady friction model is its ability to correctly model frictional dissipation in unsteady flow conditions under a wide a range of possible transient event types. This is of importance to the simulation of transients in pipe networks or pipelines with various devices in which a complex series of unsteady flow types are common. Two common one-dimensional unsteady friction models are considered, namely, the constant coefficient instantaneous acceleration-based model and the convolution-based model. The modified instantaneous acceleration-based model, although an improvement, is shown to fail for certain transient event types. Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model. The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.  相似文献   

15.
This paper investigates the importance of unsteady friction effects when performing water hammer analyses for pipe systems with external fluxes due to demands, leaks, and other system elements. The transient energy equation for a system containing an orifice-type external flow is derived from the two-dimensional, axial momentum equation. A quasi-two-dimensional flow model is used to evaluate the relative energy contribution of total friction, unsteady friction, and the external flow, in a 1,500?m pipeline, with orifice flows ranging from steady-state flows of 2–70% of the mean pipe flow, and a Reynolds number of 600,000. It is found that for initial lateral flows larger than around 30% of the mean flow, unsteady friction effects can probably be neglected, whereas for external flows smaller than this, unsteady friction should generally be considered. Overall, the relative role of unsteady friction is found to diminish as the external flux increases, implying that unsteady friction is not critical for systems with large external flows. These results imply that unsteady friction may have a significant impact on the validity of transient leak detection techniques that have been derived assuming quasi-steady friction. To demonstrate this point, an existing transient leak detection method, originally derived under quasi-steady conditions, is tested with unsteady friction included.  相似文献   

16.
To date, the majority of studies on stability of axisymmetric jets have been completed under the assumption of steady mean flow. Yet, many of the natural and man-made flows that are modeled by these jets can have an inherent unsteadiness; the effects of which on the stability and transition have not been determined. Moreover, controlled unsteadiness can be used to control stability and possibly the transition to turbulence. In this note, the effects of periodic variations of the mean flow on the stability of axisymmetric jets are examined. The problem is treated analytically. The results show that the governing equations and dispersion relation for the unsteady jet can be reduced to those governing the steady jet with a time transformation. It is shown that the periodic variations in the mean flow cause amplitude and phase modulations of the unstable modes. The implications of the modulations on the subsequent transition stages are discussed.  相似文献   

17.
An experimental pipeline system with a multistage centrifugal pump was used to study the effect of transient operations on the hydrodynamic performance of a centrifugal pump. Several transient flow operations were considered, ranging from very mild to severe transients. The dynamic relationship of total pressure rise across the pump to the flow rate was compared with that of the steady state. Deviation between the dynamic pump head and the value given by the steady-state curve at the same instantaneous discharge was established and found to be a function of the severity of the transient. It was found that severe flow conditions could cause this deviation to exceed 30% of the steady-state value. The use of the steady-state pump head-discharge relationship in the solution of transient pipe flow by the method of characteristics (MOC) is discussed. It was found that the steady-state pump head-discharge curve was not accurate enough to support the solution of unsteady pipe flow application by the MOC.  相似文献   

18.
Estimating rheological parameters of a non-Newtonian fluid is performed with rheometers, but experiments are limited to fine sediments, in the absence of appreciable sedimentation. An approach based on pipe flow measurements may be more flexible and convenient. The aim of this paper is to experimentally verify the latter approach in order to assess the rheology of natural mixtures of heavy materials with high tendency toward sedimentation.  相似文献   

19.
介绍不同雷诺数下海水绕流深海扬矿管的流动情况,分析管面形成层流及湍流边界层的分离过程,比较二者分离点的位置及压差阻力情况,分析绕流阻力和举力的形成过程、计算方法、影响因素及相应的减阻措施。  相似文献   

20.
Nonuniform-unsteady flow in open channels with streamwise sloping beds having uniform upward seepage is theoretically analyzed. Expressions for the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic law of velocity profile due to upward seepage, and using the Reynolds and continuity equations of two-dimensional open channel flow. The computed Reynolds stress profiles are in agreement with the experimental data.  相似文献   

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