Strength Calculation of Venturi Scrubber Elbow with Nozzle Opening

Literature Overview

The paper by He Xiaoxiang (2015), published in Petroleum and Chemical Equipment (Vol. 18, No. 5, pp. 14-16), addresses a practical design challenge encountered in the engineering of venturi scrubbers. The specific problem involves the strength verification of an elbow with a nozzle opening—a configuration that falls outside the scope of conventional pressure vessel design methodologies. The author employed finite element analysis (FEA) using ANSYS software and applied the stress linearization procedure specified in JB 4732-1995 (Steel Pressure Vessels—Design by Analysis) to evaluate the structural integrity of the component.

Core Technical Approach

The fundamental difficulty lies in the fact that standard design codes such as GB 150 or ASME VIII Division 1 do not provide direct formulas for calculating stress concentrations at the intersection of a nozzle with an elbow body. The elbow itself introduces geometric discontinuities due to curvature, and the nozzle opening adds a second discontinuity. The combined effect produces a complex three-dimensional stress state that cannot be resolved through membrane stress or bending stress formulas alone.

The author adopted the following methodology:

1. Construction of a three-dimensional solid finite element model of the elbow with nozzle, including appropriate boundary conditions representing the vessel connection, internal pressure, and thermal loading.
2. Application of the stress linearization technique as defined in JB 4732-1995, which decomposes the total stress at a reference line into membrane stress, bending stress, and peak stress components.
3. Comparison of the linearized stress components against the allowable limits specified in the standard.

Key Design Parameters and Results

Technical Interpretation of Stress Linearization

Stress linearization is a critical technique in pressure vessel design by analysis. The procedure involves extracting stress values along a straight reference line drawn from the inner surface to the outer surface of the component. The total stress distribution is then decomposed into three components:

• Membrane stress: The average stress across the reference line, which represents the overall load-carrying capacity of the section.
• Bending stress: The linearly varying component that represents the bending moment effect on the section.
• Peak stress: The remaining nonlinear component that accounts for local stress concentrations at geometric discontinuities such as welds, notches, or sharp transitions.

The allowable limits for these components differ significantly. Membrane stress is limited to 1.5 times the allowable stress (1.5S), bending stress is limited to 1.5S, and peak stress is limited to 3S. This hierarchy reflects the fact that peak stresses are local and do not contribute to gross structural failure in the same way as membrane or bending stresses.

Engineering Practice Considerations

From a practical standpoint, this paper highlights several important lessons:

1. Geometric complexity demands advanced methods: When a pressure vessel component involves multiple geometric discontinuities that interact (such as a nozzle on an elbow), conventional stress formulas become inadequate. FEA with proper stress linearization provides a reliable alternative.
2. Wall thickness optimization: The result shows that an elbow wall thickness of 28 mm and nozzle wall thickness of 40 mm satisfy the stress requirements. This demonstrates that FEA can lead to more economical designs compared to conservative rule-of-thumb approaches that might over-thicken the entire component.
3. Standard compliance: The use of JB 4732-1995 as the governing standard is appropriate for Chinese petrochemical equipment design. Engineers working internationally should note that ASME VIII Division 2 provides a similar framework for design by analysis, with slightly different stress linearization procedures and allowable stress multipliers.
4. Model validation: A critical aspect not explicitly discussed but essential in practice is the validation of the FEA model. Engineers should verify mesh convergence, ensure adequate element quality, and confirm that boundary conditions accurately represent the physical constraints.

Key Questions and Reflections

Several questions arise from studying this work:

• How does the stress concentration factor at the nozzle-elbow intersection compare with that of a nozzle on a cylindrical shell? The curvature of the elbow likely amplifies the stress concentration relative to a straight shell.
• What is the effect of thermal loading on the stress distribution? Venturi scrubbers often operate under conditions involving temperature differentials between the vessel body and the nozzle, which introduces additional thermal stresses.
• Can the results be generalized to other elbow-nozzle configurations, or is each case unique? While the methodology is generalizable, the specific stress values are geometry-dependent.

Study Insights and Implications

This paper serves as a practical demonstration that modern engineering analysis tools can solve design problems that are intractable through conventional methods. For engineers involved in pressure vessel design, the key takeaway is that FEA-based stress analysis should be considered whenever geometric configurations fall outside the scope of standard design rules. The stress linearization procedure remains the bridge between raw FEA output and code-compliant design decisions.

Furthermore, the paper reinforces the importance of understanding the underlying physics rather than relying solely on software output. The stress linearization procedure requires careful selection of reference lines, understanding of stress categories, and proper interpretation of results against code limits. Engineers who master these concepts can confidently tackle complex geometric challenges in pressure equipment design.