Tube Bundle Heat Exchanger Stiffness Calculation
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Solution Overview
Problem
Existing methods for determining the rigidity and strength of shell and tube heat exchangers are inadequate, as they fail to accurately account for mechanical and thermal stresses, particularly the influence of spiral winding and gravitational forces, leading to unreliable calculations and potential material damage during production and operation.
Innovation Solution
A method that determines the geometric strength parameter of each winding layer by calculating the area ratio of the wound tube cross-sectional area to the cell cross-sectional area, corrected by a factor that accounts for the orientation of the winding tubes relative to gravity, and uses this to calculate the stiffness of each layer, incorporating the modulus of elasticity of the material, and applies finite element methods for stress analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If simplified models using rods or surrogate cylinders are used to calculate strength, then calculation complexity is reduced, but measurement precision and reliability of strength determination deteriorate
Solution Approach 1:
The patent transforms the simplified rod model into a more accurate representation by introducing the winding angle parameter and deriving the corrected area ratio formula (A_p/A_r) * sin(α). This parameter change accounts for the spiral geometry of wound tubes while maintaining analytical tractability, thus improving strength determination accuracy without excessive complexity
Solution Approach 2:
The patent transitions from a one-dimensional rod model to a two-dimensional spiral geometry model by incorporating the winding angle dimension. This allows the calculation to capture the actual load distribution in spiral-wound heat exchangers while remaining analytically solvable
2Ease of manufacture
If the influence of spiral winding and gravitational forces is not accounted for, then calculation simplicity is maintained, but reliability of strength and rigidity calculations deteriorates
Solution Approach 1:
The patent introduces the winding angle α as a critical parameter and derives the corrected area ratio (A_p/A_r) * sin(α) that incorporates both spiral geometry and gravitational force orientation. This single parameter modification enables reliable strength calculations that account for the actual loading conditions without requiring complex three-dimensional finite element analysis
3Measurement precision
If corrected area ratio accounting for winding angle is used, then rigidity determination accuracy is improved, but calculation complexity increases
Solution Approach 1:
The patent modifies the traditional area ratio calculation by multiplying with sin(α) to account for the winding angle. This single parameter adjustment captures the geometric influence of spiral winding on rigidity while maintaining the simplicity of analytical calculations, avoiding the need for complex numerical methods
Data Source
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AI summary
A method for determining the stiffness of a tube bundle heat exchanger (1), comprising a core tube (2) and coiled tubes (3) wound around the core tube (2) to form a tube bundle, wherein the coiled tubes (3) are wound around the core tube (2) in several winding layers (5, 6) and with a respective layer winding angle (α), has the following steps: determining a geometric strength parameter of a respective winding layer (5), wherein the geometric strength parameter comprises an area ratio of a coiled tube cross-sectional area (Ar) to a cell cross-sectional area (Ap), wherein the cell cross-sectional area (Ap) is obtained from the axial distance (T) of the coiled tubes (3) and an outer diameter (da) of the coiled tubes (3); correcting the area ratio by a correction factor to take into account the orientation of the coiled tubes (3) of the respective winding layer with respect to the gravitational force (Fg) acting on the coiled tubes;and determining the stiffness of the respective winding layer (5) as a function of the corrected area ratio and a modulus of elasticity of the winding tube material.;