scholarly journals Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
James B. Polly ◽  
J. M. McDonough
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Real Time ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Nonlinear Partial Differential Equations ◽  
Navier Stokes ◽  
Control Force ◽  
Machining Processes ◽  
The Poor

Control of fluid flow is an important, underutilized process possessing potential benefits ranging from avoidance of separation and stall on aircraft wings to reduction of friction in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier-Stokes (N.-S.) equations, whose solutions describe such flows, consist of a system of time-dependent, multidimensional, nonlinear partial differential equations (PDEs) which cannot be solved in real time using current computing hardware. The poor man's Navier-Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the PDE N.-S. system at specific spatial locations. Herein, we outline derivation of these equations and discuss their basic properties. We consider application of these equations to the control problem by adding a control force. We examine the range of behaviors that can be achieved by changing this control force and, in particular, consider controllability of this (nonlinear) systemvianumerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general and may be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.

scholarly journals Application of the Poor Man’s Navier–Stokes Equations to Real-Time Control of Fluid Flow

2011 ◽  
Author(s):  
James B. Polly ◽  
J. M. McDonough
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Real Time ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Navier Stokes ◽  
Control Force ◽  
The Poor ◽  
Non Linear ◽  
Non Linear System

Control of fluid flow is an important, and quite underutilized process possessing significant potential benefits ranging from avoidance of separation and stall on aircraft wings and reduction of friction factors in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier–Stokes (N.–S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man’s Navier–Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.–S. system at specific spatial locations. In this paper we outline derivation of these equations and present a short discussion of their basic properties. We then consider application of these equations to the problem of control by adding a control force. We examine the range of PMNS equation behaviors that can be achieved by changing values of this control force, and, in particular, consider controllability of this (non-linear) system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general, and, at least in principle, it can be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.

Real-Time Particle Simulation for Virtual Environments

1997 ◽  
Author(s):  
Armand D. Assadi ◽  
James H. Oliver
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Real Time ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Particle Simulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Interactive Environment ◽  
Primary Contribution

Abstract A real-time interactive environment for particle simulation is presented with specific attention given to fluid flow from a fountain system. The complex Navier-Stokes equations from fluid dynamics theory give way to simple dynamic equations of motion for systems of independent particles from particle theory. Due to the ease of integration of the dynamic linear first order differential equations, compared to the nonlinear second order partial differential equations of Navier-Stokes, a real-time rate was achieved for a visually aesthetic model of fluid flow. The primary contribution is that interactive changes made by the user are perceived to occur simultaneously in the environment. There is no need to resolve a predetermined set of equations when making the changes.

Exact Solutions of the Unsteady Navier-Stokes Equations

1989 ◽  
Vol 42 (11S) ◽  
pp. S269-S282 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Nonlinear Partial Differential Equations ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Partial Differential ◽  
Navier Stokes Equations

The unsteady Navier-Stokes equations are a set of nonlinear partial differential equations with very few exact solutions. This paper attempts to classify and review the existing unsteady exact solutions. There are three main categories: parallel, concentric and related solutions, Beltrami and related solutions, and similarity solutions. Physically significant examples are emphasized.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Fast Fluid Thermodynamics Simulation by Solving Heat Diffusion Equation

2021 ◽  
Vol 11 (04) ◽  
pp. 1-11
Author(s):  
Wanwan Li
Keyword(s):  
Diffusion Equation ◽  
Real Time ◽  
Stokes Equations ◽  
Fluid Simulation ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Heat Diffusion Equation ◽  
Acceleration Techniques ◽  
Speed Up

In mechanical engineering educations, simulating fluid thermodynamics is rather helpful for students to understand the fluid’s natural behaviors. However, rendering both high-quality and realtime simulations for fluid dynamics are rather challenging tasks due to their intensive computations. So, in order to speed up the simulations, we have taken advantage of GPU acceleration techniques to simulate interactive fluid thermodynamics in real-time. In this paper, we present an elegant, basic, but practical OpenGL/SL framework for fluid simulation with a heat map rendering. By solving Navier-Stokes equations coupled with the heat diffusion equation, we validate our framework through some real-case studies of the smoke-like fluid rendering such as their interactions with moving obstacles and their heat diffusion effects. As shown in Fig. 1, a group of experimental results demonstrates that our GPU-accelerated solver of Navier-Stokes equations with heat transfer could give the observers impressive real-time and realistic rendering results.

Coriolis effects on MHD newtonian flow over a rotating non-uniform surface

2020 ◽  
pp. 095440622096973
Author(s):  
Abayomi S Oke ◽  
Winifred N Mutuku ◽  
Mark Kimathi ◽  
Isaac Lare Animasaun
Keyword(s):  
Differential Equations ◽  
Lorentz Force ◽  
Coriolis Force ◽  
Stokes Equations ◽  
Physical Phenomenon ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Simultaneous Increase ◽  
Convection Flow ◽  
The Impact

The roles of the simultaneous effect of Coriolis force and Lorentz force (resulting from MHD flow) in Sunspots, solar wind, and many other natural and physical phenomenon is undoubtedly significant. The impact of fluids heated by the Sun is influenced by the rotation of the earth’s surface and this necessitates the study of fluid flow over such surface as the Earth. For this reason, the significance of Coriolis force on MHD free-convection flow of Newtonian fluid over the rotating upper horizontal surface of paraboloid of revolution is explored. The relevant body forces are derived and included in the Navier-Stokes equations to obtain appropriate equations governing the flow. By nondimensionalizing the governing equations using similarity variables, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is solved using Runge-Kutta-Gills method along with Shooting technique and the results are depicted graphically. It is observed that simultaneous increase in both Coriolis force and Lorentz force causes an increase in the temperature profile of the flow. It is also observed that the effect of increasing Coriolis force on the Skin Friction and heat transfer rate is counter-balanced by increasing Lorentz force.

Numerical Simulation of Gas Flow Pattern in Cyclone Spray Scrubber

2011 ◽  
Vol 233-235 ◽  
pp. 701-706
Author(s):  
Bing Tao Zhao ◽  
Yi Xin Zhang ◽  
Kai Bin Xiong
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Flow Pattern ◽  
Gas Flow ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Computational Domain ◽  
Spray Scrubber ◽  
Cfd Method

The numerical simulation of the fluid flow is presented by CFD technique to characterize the flow pattern of cyclone spray scrubber. In this process, the Reynolds-averaged Navier-Stokes equations with the Reynolds stress turbulence model (RSM) for fluid flow are solved by use of the finite volume method based on the SIMPLE pressure correction algorithm in the fluid computational domain. According to the computational results, the tangential velocity, axial velocity and turbulence intensity of the gas flow are addressed in the different flowrate. The results indicate that the CFD method can effectively reveal the mechanism of gas flow in the cyclone spray scrubber.

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