Steady and Unsteady Flow in Noncircular Straight Ducts

1977 ◽  
Vol 44 (1) ◽  
pp. 1-6 ◽  
Author(s):  
V. O’Brien
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Arbitrary Shape ◽  
Oscillatory Flow ◽  
Analytic Solutions ◽  
Parallel Flow ◽  
Linear Superposition ◽  
Fully Developed Flow ◽  
Forward Extension

A general numerical method to solve for the steady parallel fully developed flow in ducts of arbitrary shape is illustrated and compared to analytic solutions for simple shapes. A straight forward extension of the method is applied also to oscillatory flow solutions. By linear superposition, any pulsatile parallel flow in an arbitrary duct can be synthesized.

scholarly journals A Numerical Method of Unsteady Flow Analysis in Duct with Junction

1977 ◽  
Vol 43 (366) ◽  
pp. 596-604
Author(s):  
Takeshi ADACHI ◽  
Harutaka TSUJIMURA ◽  
Masamichi IMAIZUMI
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Flow Analysis ◽  
Unsteady Flow Analysis

Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations

1999 ◽  
Author(s):  
Martin von Hoyningen-Huene ◽  
Alexander R. Jung
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Computational Time ◽  
Test Case ◽  
The Real ◽  
Flow Simulations ◽  
Time Stepping ◽  
Acceleration Techniques ◽  
Pitch Ratio

This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a non-accelerated, 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 comparison of the different numerical algorithms for explicit schemes is intended to ease the decision about which acceleration technique to use for calculations as far as accuracy and computational time are concerned. The convergence acceleration methods under consideration are, respectively, 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 are applicable to all explicit unsteady flow solvers. As another point of interest, the influence of the stage blade count ratio on the flow field is investigated. 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 vital from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages.

Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion

1994 ◽  
Vol 277 ◽  
pp. 347-379 ◽  
Author(s):  
Eugene J. Chang ◽  
Martin R. Maxey
Keyword(s):  
Reynolds Number ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Oscillatory Flow ◽  
Reynolds Numbers ◽  
Oscillatory Motion ◽  
Rigid Sphere ◽  
Flow Conditions ◽  
Steady Streaming ◽  
Moderate Reynolds Number

A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.

scholarly journals Numerical simulation of unsteady flow of a viscous incompressible liquid in flat channels of arbitrary shape of heat exchangers

2020 ◽  
Vol 34 ◽  
pp. 41-55
Author(s):  
Y. Chоvniuk ◽  
V. Kravchuk ◽  
A. Moskvitina ◽  
I. Pefteva
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Unsteady Flow ◽  
Heat Exchangers ◽  
Arbitrary Shape ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations

Reasonable development and creation of any device in which there is an interaction between the fluid flow and the elements of the flow parts (for example, heat exchangers, transport and power machines, main pipelines), is impossible without detailed information about the characteristics of the flow, about the forces on the surfaces that are around, about vibroacoustic phenomena, etc. Among the various methods of obtaining information about the characteristics of the flow, about the forces on surfaces that are flown around, about vibroacoustic phenomena, an important role is played by theoretical methods that rely on the equation of hydrodynamics and numerous ways to solve them. In this case, the main efforts are aimed at solving the system of Navier-Stokes equations. In this paper, a general method is described for the numerical solution of the problem of unsteady flow of a viscous incompressible fluid in flat channels of an arbitrary shape of heat exchangers. An effective solution to the problem is achieved by using adaptive networks. The mathematical model of the flow is based on the two-dimensional Navier-Stokes equations in the variables "flow function - vortex" and the Poissonequation for pressure, which are solved on the basis of the finite-difference method. A numerical simulation of the fluid flow in a flat curvilinear elbow is carried out at the Reynolds number Re = 1000. This form reflects the most characteristic features of the flow paths of various hydraulic machines, heat exchangers, hydraulic and pipeline systems. The presentation of the numerical results was carried out on the basis of the VISSIM graphic processing package. One of the main problems (difficulties) in the numerical solution of problems of mathematical physics is the representation of boundary conditions for regions of arbitrary shape. The implementation of various artificial methods that are now used in the approximation of both the curvilinear boundaries themselves and the boundary conditions on them can lead to significant losses in the accuracy of the solution. This is especially evident in problems in which solutions in the boundary region have maximum gradients. An effective method for solving this problem is the use of adapted grids for the computational domain. The essence of this method lies in the fact that such a coordinate system, not necessarily orthogonal, is found in which the boundary lines (surfaces) of the region coincide with the coordinate lines (surfaces). In the flat case, the computational domain is transformed into a rectangular one, and the limit curve is displayed on the sides of the rectangle. In practice, the problem of constructing an adapted mesh is reduced to finding functions that describe the mappings of the canonical (rectangular) region onto the region for which the problem was originally formulated, that is, for the two-dimensional case, the functions x (ξ, η), y (ξ, η) are determined.

scholarly journals Semi-analytic numerical method for unsteady flow in leaky confined aquifers

2015 ◽  
Vol 1 (3) ◽  
pp. 1-5
Author(s):  
Xudong Wang ◽  
Jin Xu ◽  
Feng Zhou ◽  
Yunhang Liu
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Confined Aquifers

Numerical Investigation of Flow around a Triangle Cylinder Using a Multiscale Turbulence Model

2013 ◽  
Vol 444-445 ◽  
pp. 253-258
Author(s):  
He Dong ◽  
Ge Gao ◽  
Zhi Qiang Li ◽  
Yang Yang Tang ◽  
Huan Xu ◽  
...  
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Numerical Investigation ◽  
Strouhal Number ◽  
Turbulence Model ◽  
Vortex Shedding ◽  
Average Method ◽  
Variable Interval ◽  
Computational Results ◽  
Time Average

The unsteady flow around a triangle cylinder was simulated using the multiscale turbulence model based on the variable interval time average method. The numerical method used in this simulation is an unstructured staggered mesh scheme. The computational results show that the multiscale turbulence model can successfully simulate vortex shedding characteristics. The Strouhal number and time-averaged velocity profiles also agree better with experiments than that of the standard k-ε model.

Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations

1999 ◽  
Vol 122 (2) ◽  
pp. 234-246 ◽  
Author(s):  
Martin von Hoyningen-Huene ◽  
Alexander R. Jung
Keyword(s):  
Unsteady Flow ◽  
Numerical Method ◽  
Periodic Boundary ◽  
Computational Time ◽  
Test Case ◽  
The Real ◽  
Flow Simulations ◽  
Time Stepping ◽  
Acceleration Techniques ◽  
Pitch Ratio

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]

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