Hole Diameter Estimation from Gas Flow Across Mixed Flow Regimes
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Solution Overview
Problem
Existing leakage tests in pharmaceutical packaging and similar fields suffer from dispersion in measurement conditions and unclear scientific validity, necessitating a quantitative method to determine gas flow rate from hole diameter and vice versa, without requiring determination of the gas flow state.
Innovation Solution
A relational expression is used to estimate gas flow rate and hole diameter by combining calculation expressions for different flow states, incorporating parameters like molecular weight, viscosity, specific heat ratio, temperature, and pressures, applicable across various flow regions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If qualitative leakage tests (submersion tests, liquid leakage tests, microbial ingress tests) are used, then leakage detection is possible, but measurement dispersion occurs and scientific validity is unclear
Solution Approach 1:
The invention changes the measurement approach from qualitative binary detection to quantitative continuous measurement by introducing flow rate as a measurable parameter. The relational expression establishes a quantitative relationship between hole diameter and gas flow rate, enabling precise measurement of leakage amount rather than just detection, thereby eliminating measurement dispersion and establishing scientific validity through mathematical modeling.
Solution Approach 2:
The invention replaces mechanical/physical leakage detection methods (submersion tests, liquid leakage tests, microbial ingress tests) with a gas flow-based measurement system. By using gas flow rate measurement and a relational expression to calculate hole diameter, the system substitutes mechanical detection with a more precise quantitative measurement approach that provides both leakage detection and measurement.
2Measurement precision
If gas flow rate is calculated using different flow region formulas, then accurate calculation is possible for each flow state, but flow state determination is required which complicates the process
Solution Approach 1:
The invention creates a universal relational expression that can calculate gas flow rate for all flow regions (molecular flow, laminar flow, turbulent flow, critical flow, subcritical flow) without requiring separate calculations for each flow state. This multi-functional formula eliminates the need for flow state determination while maintaining calculation accuracy across different flow conditions, thereby reducing process complexity while preserving measurement precision.
3Measurement precision
If iterative calculation is used to obtain flow rate for continuous flow, then accurate flow rate can be obtained, but calculation process becomes complicated
Solution Approach 1:
The invention extracts the essential relationship between hole diameter and gas flow rate into a direct relational expression that eliminates the need for iterative calculation. By formulating the relationship as a direct mathematical expression rather than an iterative process, the invention maintains flow rate accuracy while removing the complexity of iteration, allowing for straightforward calculation without repeated computations.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate estimation of gas flow rate and hole diameter without determining the flow state, simplifying calculations and ensuring consistent results across different flow conditions.
Implementation Method 1
the flow rate of the gas flowing through the hole, regardless of a state of flow of the gas, from a molecular weight, a viscosity coefficient, and a specific heat ratio of the gas, a diameter and a length of the hole, and the upstream and downstream pressures of the gas flowing through the hole
Data Source
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AI summary
In this gas flow rate estimation method, regardless of the flow state of a gas, the flow rate of the gas is determined from the molecular weight, viscosity coefficient, and specific heat ratio of the gas, the diameter and length of a hole, and the pressures upstream and downstream from the hole, based on a predetermined relational expression including, as parameters: the flow rate of the gas; the diameter and length of the hole; the upstream and downstream pressures; and the temperature, molecular weight, viscosity coefficient, and specific heat ratio of the gas. Additionally, in this invention, setting conditions for the type and temperature of the gas, the length of the hole, and the pressures upstream and downstream from the hole are set; the relational expression is used to obtain the correspondence relationship between the diameter of the hole and the flow rate of the gas flowing through the hole; an approximation function approximating the obtained correspondence relationship is determined; the flow rate of a gas passing through a test piece having a hole of an unknown diameter is measured; and the diameter of the hole is estimated, based on the basis of the measured flow rate and the approximation function.