Treatment of Pressure Differences in Low Reynolds Number Incompressible Flows Over Curved Boundaries

A technology with low Reynolds number and curved boundaries, which can be used in electrical digital data processing, special data processing applications, instruments, etc., and can solve problems such as pressure difference

Inactive Publication Date: 2016-08-17
WUZHOU UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] The purpose of the present invention is to provide a method for processing the pressure difference in the low Reynolds number incompressible flow on the curved boundary in view of the technical problem that the prior art cannot handle the pressure difference in the low Reynolds number incompressible flow on the curved boundary

Method used

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  • Treatment of Pressure Differences in Low Reynolds Number Incompressible Flows Over Curved Boundaries
  • Treatment of Pressure Differences in Low Reynolds Number Incompressible Flows Over Curved Boundaries
  • Treatment of Pressure Differences in Low Reynolds Number Incompressible Flows Over Curved Boundaries

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Embodiment 1

[0046] This embodiment adopts Poiseuille flow, that is, two infinite plates are respectively placed at coordinates y=-0.5YL and y=0.5YL, where YL is the distance between the two plates. Its initially stationary fluid is driven by a body force F (corresponding to the pressure difference between the inlet and outlet) parallel to the X-axis, and will eventually reach a steady state.

[0047] In this embodiment, YL=10-3 m, the flow field length is d=5×10 -4 m, the hydrostatic pressure difference is △p=10 -4 N / m 2 , the simulation results of formula (1), formula (2) and formula (3) are as follows figure 2 shown, and from figure 2 It can be seen that the method of the present invention is consistent with the simulation results using constant body force, and both agree well with the theoretical solution.

Embodiment 2

[0049] This embodiment adopts local expansion pipe flow, such as image 3 As shown, an axisymmetric blood vessel can be considered, and its pressure difference drives the fluid to flow in the pipeline, and the pressure difference is △p=p 1 -p 2 =1.939006287×10 -3 N / m 2 , the radius of the pipe is a function of the position x, which can be expressed as (4):

[0050] R R 0 = 1 | x | > X 0 1 + δ 2 R 0 ( 1 ...

Embodiment 3

[0054] The present embodiment adopts inclined plate flow, such as Figure 6 As shown, in this example, d BC =4mm,2l 1 =0.5mm, α=3.503°, and the hydrostatic pressure difference between B and C is △p=1.21665968×10 -3 N / m 2 .

[0055] Using the method of the present invention, the simulation results of the horizontal velocity of the fluid particles along the X axis are as follows: Figure 7 shown; from Figure 7 As can be seen in the figure, the simulation results using the method of the present invention are again in agreement with the theoretical solution, but not in the case of constant body force.

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Abstract

The invention discloses a method for processing the pressure difference in a low Reynolds number incompressible flow on a curved boundary. The method specifically includes the following steps, step S1, confirming whether the following formula (1) is satisfied, and if so, performing step S2, or R0< <x0，l>>R0, Re<1 (1); step S2, calculate the body force FA1 at the inlet section of the pipeline, (2); where, ρ is the fluid density; step S3, substituting the formula (2) in step S2 into the following formula (3), to obtain the body force FA2 at any section of the pipeline, (3); Among them, dA represents the area element. The invention can conveniently convert the pressure difference in the low Reynolds number incompressible flow on the curved boundary into the body force at any place.

Description

technical field [0001] The invention relates to the technical field of fluid mechanics, and more specifically relates to a method for processing pressure differences in low Reynolds number incompressible flows on curved boundaries. Background technique [0002] When applying Smoothed Particle Hydrodynamics (SPH) to simulate low Reynolds number incompressible flow, it is very important to solve the pressure gradient driving the fluid motion, because the pressure is only expressed as a gradient in the Navier-Stokes equation. In the Weakly Compressible SPH (WCSPH) algorithm, the total pressure is usually decomposed into dynamic pressure and hydrostatic pressure, so the gradient of the total pressure can be obtained through the gradient of these two pressures. [0003] For the WCSPH method, modeling the dynamic pressure gradient is simple and straightforward, while the hydrostatic pressure gradient is usually considered as a body force. Morris used WCSPH to study low Reynolds n...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
Inventor 梁朝湘张超英刘海燕黄寄洪冀肖榆时伟
Owner WUZHOU UNIV
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