A Fractal Model of Flow Resistivity for Fibrous Porous Metals

doi:10.7652/xjtuxb201506021

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A Fractal Model of Flow Resistivity for Fibrous Porous Metals

更新时间：2025-07-09

- A Fractal Model of Flow Resistivity for Fibrous Porous Metals
- Vol. 49, Issue 6, Pages: 132-137(2015)
- 作者机构：
  
  1. 西安交通大学机械工程学院,西安,710049
  2. 兰州理工大学机电工程学院,兰州,730050
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201506021
  CLC： TB535
- Online First：10 June 2015，
  
  Published：2015
- 稿件说明：
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A Fractal Model of Flow Resistivity for Fibrous Porous Metals[J]. 2015, 49(6): 132-137.
DOI：

A Fractal Model of Flow Resistivity for Fibrous Porous Metals[J]. 2015, 49(6): 132-137. DOI： 10.7652/xjtuxb201506021.

摘要

为了揭示纤维多孔金属吸声材料的流阻率与其孔隙率、孔直径以及孔的弯曲度等主要几何参数之间的变化规律

给纤维多孔金属吸声材料的结构设计提供基本的理论指导

提出了一种流阻率分形模型。通过对纤维多孔金属的孔隙结构进行分形处理

结合材料内部空气流体学分析

首先获得了流经纤维多孔金属材料截面总的空气流量Q的表达式

该表达式是最大平均孔径λ

max

、曲线分形维数D

和孔面积分形维数D

的函数

其次结合纤维多孔金属吸声材料流阻率的公式

获得了流阻率分形模型。模型理论计算值与实验测试值的最大偏差为13.9%

最小偏差为7.6%

平均偏差为10.6%

验证了该理论模型的可靠性。分析结果表明:随着孔隙率Φ的增大

纤维多孔金属吸声材料的流阻率减小; Φ和D

一定时

流阻率随着D

的增大而减小; Φ和D

一定时

流阻率随着D

的增大而增大。与通过实验确定流阻率的经验公式相比

文中所建流阻率分形模型能够反映材料的几何参数与流阻率之间的变化规律

为纤维多孔金属吸声材料的微观结构设计提供了一定的依据。

Abstract

A fractal model of flow resistivity is proposed to investigate the relations of flow resistivity with some geometric parameters of fibrous porous metals such as porosity

pore diameter and tortuosity

and to obtain a theoretical guidance for the design of sound-absorption materials. First of all

a mathematical expression of the flow Q is obtained based on the theory of fractal geometry and fluid mechanics

and the expression is a function of the maximal mean diameter of pore λ

max

the fractal dimension D

of tortuosity and the pore area fractal dimension D

. Then

the fractal model of flow

resistivity is acquired in terms of the flow resistivity formula. The maximum error

the minimum error and the mean error between experimental results and calculation results from the model are 13.9%

7.6% and 10.6%

respectively

which verifies the accuracy of the model. The calculation results show that the flow resistivity decreases as the porosity Φ increases. When the porosity Φ and the tortuosity fractal dimension D

are fixed

the flow resistivity decreases as the pore area fractal dimension D

increases. However

when the porosity Φ and the pore area fractal dimension D

are fixed

the flow resistivity increases as the tortuosity fractal dimension D

increases. The relations between the flow resistivity and the geometric parameters are revealed more clearly by the fractal flow resistivity model than by the empirical model. It can be concluded that the results provide a reliable and theoretical guidance for the design of sound-absorption materials.

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Keywords

references

卢天健, 何德坪, 陈长青, 等. 超轻多孔金属材料的多功能特性及应用 [J]. 力学进展, 2006, 36(4): 517-535.

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HAPPEL J, BRENNER H. Low Reynolds number hydrodynamics, mechanics of fluids and transport process [M]. Boston, MA, USA: Martinus Nejhoff, 1983: 23-57.

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YU Boming, CHENG Ping. A fractal permeability model for bi-dispersed porous media [J]. International Journal of Heat and Mass Transfer, 2002, 45(14): 2983-2993.

ZHANG Bo, CHEN Tianning. Calculation of sound absorption characteristics of porous sintered fiber metal [J]. Applied Acoustics, 2009, 70(2): 337-346.

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