Flow Divider Superellipse Geometry for Lower Pressure Loss
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Solution Overview
Problem
Conventional flow dividers in fluid line systems cause significant pressure loss and measurement inaccuracies due to their geometric shape, which is influenced by Reynolds number, turbulence, and temperature fluctuations, leading to non-linear measurement errors and variance.
Innovation Solution
A flow divider design with specific cross-sectional areas and radii defined by mathematical formulas, featuring a superellipse shape for the fourth cross-sectional area, reduces pressure loss and stabilizes it across varying Reynolds numbers, improving measurement accuracy and reproducibility by minimizing pressure loss and enhancing flow stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If conventional flow dividers are used with standard geometric shapes, then manufacturing is simpler, but pressure loss increases and measurement accuracy deteriorates
Solution Approach 1:
The patent applies parameter changes by defining the cross-sectional areas and radii of the flow divider lumens through specific mathematical formulas (superellipse equations) rather than using standard geometric shapes. This allows optimization of flow characteristics to minimize pressure loss while maintaining manufacturability through precise dimensional control.
Solution Approach 2:
The patent utilizes curvature principles by employing superellipse shapes for the cross-sectional areas of the lumens. The superellipse geometry provides smooth curved transitions that reduce flow separation and turbulence, thereby decreasing pressure loss compared to sharp-cornered or simple circular sections.
2Measurement precision
If conventional flow divider geometries are used, then design is simpler, but measurement precision deteriorates due to non-linear errors and variance
Solution Approach 1:
The patent improves measurement precision by changing the geometric parameters of the flow divider according to specific mathematical relationships. The superellipse formulas with optimized coefficients create more stable flow patterns that reduce non-linear measurement errors and variance, enabling higher accuracy in flow measurement applications.
3Stability of the object's composition
If standard cross-sectional shapes are used, then manufacturing is easier, but flow stability worsens under varying Reynolds numbers and temperature fluctuations
Solution Approach 1:
The patent enhances flow stability by changing the cross-sectional geometry parameters according to superellipse equations with specifically optimized coefficients. This geometry maintains more consistent flow characteristics across varying Reynolds numbers and temperature conditions compared to standard shapes, while the parameters can be implemented through modern manufacturing processes.
Solution Approach 2:
The patent applies curvature principles through the use of superellipse shapes that provide smooth, continuous curves without sharp corners. This geometry promotes stable laminar flow patterns and reduces turbulence under varying operating conditions, improving overall flow stability while remaining manufacturable.
Data Source
AI summary
A flow divider comprises a lumen having perpendicular, symmetry planes intersecting in an axis of inertia connecting the ends. Cross sectional area have radii extending from a geometric center of gravity to the wall and lying at an angle φ (−180°≤φ≤180°) to a reference axis and being perpendicular to its axis of inertia, wherein each radius lying at an angle φ=0° to the relevant reference axis points away from the symmetry plane, and fulfills a formula fi(φ, Pi) associated with its cross sectional area and defined by a coefficients set Pi (Pi=[ai bi m1i m2i n1i n2i n3i]) corresponding to the flow divider opening:Ri(φ)=R0·ri(φ)=fi(φ,Pi)=fi(φ,[ai bi m1i m2i n1i n2i n3i])=R0·<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[LeftBracketingBar]"</annotation></semantics>1aicos(m1i4φ)<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[RightBracketingBar]"</annotation></semantics>n2i+<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[LeftBracketingBar]"</annotation></semantics>1bisin(m2i4φ)<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[RightBracketingBar]"</annotation></semantics>n3i-n1i,in such a manner that the radii R4(φ) of a cross sectional area of the lumen fulfills a formula f4(φ, P4) defined by a coefficients set P4=[a4 b4 m14 m24 n14 n24 n34], with a4=(0.95 . . . 1), b4=(0.45 . . . 0.7), m14=4, m24=4, n14=3.0, n24=n14 and n34=(3 . . . 4).