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Related Concept Videos

Navier–Stokes Equations01:28

Navier–Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
Euler's Equations of Motion01:28

Euler's Equations of Motion

In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Continuity Equation01:28

Continuity Equation

The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:

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Scale matters.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2018
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Finite-scale equations for compressible fluid flow.

L G Margolin1

  • 1Los Alamos National Laboratory, Los Alamos, NM 87545, USA. len@lanl.gov

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 18, 2009
PubMed
Summary

Finite-scale equations (FSE) model fluid dynamics evolution. New transport terms in FSE offer insights for computational fluid dynamics and highlight the need for careful velocity averaging in simulations.

Area of Science:

  • Fluid Dynamics
  • Computational Science

Background:

  • The Navier-Stokes equations govern fluid motion.
  • Existing numerical methods for fluid dynamics often incorporate artificial terms.

Purpose of the Study:

  • To analyze finite-scale equations (FSE) for a one-dimensional compressible fluid.
  • To interpret new transport terms within the FSE and their implications for computational fluid dynamics (CFD).

Main Methods:

  • Derivation and analysis of FSE for a compressible fluid.
  • Comparison of FSE transport terms with existing numerical simulation techniques.

Main Results:

  • Introduction of novel momentum and internal energy transport terms in FSE.
  • Physical interpretation of these new terms through analysis of the FS continuity equation.

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  • Identification of the necessity to differentiate between volume-averaged and mass-averaged velocities in numerical simulations.

    • Conclusions:

    • FSE present a potential new foundation for computational fluid dynamics.
    • The new transport terms in FSE share similarities with artificial viscosity and subgrid-scale models.
    • Understanding FSE may refine numerical approaches to fluid flow simulation.