Comparative Structural and Hydraulic Assessment of a DN3000 Double Eccentric Butterfly Valve Blade Using a Coupled CFD–FEM Approach

Abstract

Large-diameter butterfly valves are essential control components in high-flow hydraulic systems, where blade geometry directly impacts operational reliability, energy efficiency, and lifecycle cost. This study presents an integrated structural–hydraulic optimization of a DN3000 Boving butterfly valve blade rated for a maximum operating pressure of 10 bar with comparative analysis of a conventional flat blade and an optimized curved blade. The work applies a CFD–FEM framework specifically to DN3000 Southern African valves, which is rare in the literature. Numerical simulations evaluated stress distribution, deformation, pressure losses, and flow stability under design and hydrostatic test conditions. The curved blade achieved a 58.6% reduction in peak von Mises stress, a 50% reduction in weight, a 22% reduction in load loss, and a 33% reduction in actuation torque requirements, while maintaining seal integrity. Cost analysis revealed a 50% reduction in material costs and simplification of manufacturing. The results confirm that the introduction of curvature significantly improves structural strength and hydraulic efficiency, thus providing a reproducible framework for the design of lighter and more economical valves in hydropower, municipal and industrial applications.

1. Introduction

Butterfly valves are widely used in large-scale hydraulic and process systems due to their compactness, low pressure loss, and ease of actuation. Beyond DN2000, the valve blade plays a dominant structural and hydraulic role. Flow efficiency, actuator torque, sealing behaviour, and long-term operational safety are all directly affected. In large transmission mains, imperfect sealing of isolation valves can result in significant leakage, increased operational losses, and reduced system controllability, particularly during maintenance and emergency shutdown operations. Recent studies have highlighted the importance of sealing diagnostics in large-diameter pipelines. Capponi et al. (2023) [1] proposed a hydraulic diagnostic kit for the rapid assessment of in-line valve sealing in large transmission mains, demonstrating transient test-based techniques for evaluating sealing performance and junction effects in real pipe systems. Prior approaches demonstrate that robust valve sealing is essential for the safe and efficient management of large-scale water infrastructure. From a design standpoint, sealing performance is closely linked to blade deformation under hydrostatic loads. DN3000-class butterfly valves accentuate this effect, since large blade mass and pressure-induced stresses interact in a non-trivial way. Excessive deflection disturbs uniform seal compression, promotes local leakage paths, and shortens seal service life. Enhancing blade stiffness while limiting mass; therefore, becomes central for maintaining consistent sealing under operating as well as hydrostatic test pressures.

Previous research on butterfly valve performance has examined a range of geometrical configurations and actuation methods, both experimentally and through numerical simulation. Ogawa and Kimura [2] were among the first to systematically study the torque–pressure relationships of butterfly valves for different disc shapes, while Berger et al. [3] combined Computational Fluid Dynamics (CFD) and Finite Element Analysis for the numerical study and experimental validation of the fluid-structure interaction (FSI) of a butterfly valve. More recently, there has been a growing adoption of fluid–structure interaction (FSI) approaches better to capture the interplay between pressure distribution and disc deformation. Song et al. [4] use three-dimensional CFD (ANSYS CFX) linked to structural analysis (ANSYS FEA) to evaluate flow patterns, pressure distributions, and safety performance of a large butterfly valve by importing fluid results into structural analysis, while Said et al. [5] compares different turbulence models (including k-ω, k-ε and RSM) for the prediction of flow characteristics (pressure, flow coefficient) in a small butterfly valve and validates the numerical predictions against experimental results, showing the differences in model performance depending on turbulence closures. Adam et al. [6] developed a CFD model for industrial butterfly valves using the k–ω SST turbulence model, achieving agreement within 5% of measured head losses. They are widely indexed and feature CFD predictions validated against experimental performance indicators, including hydrodynamic torque, flow coefficients, and pressure drop.

Validated CFD and FEA methodologies are particularly important for large-diameter valves, for which large-scale laboratory testing is often prohibitively expensive or practically impossible to carry out. Naragund et al. [7] conducted an experimental and numerical study of the hydrodynamic torque acting on a double offset butterfly valve disk. This study combined laboratory measurements with three-dimensional CFD simulations to evaluate the torque characteristics for different valve opening positions. The numerical predictions agree well with the experimental results, thus demonstrating that CFD makes it possible to accurately model the behavior of the torque and the flow-induced loads in butterfly valves. Their results confirm the relevance of CFD as a practical tool for performance evaluation and design when large-scale experimental testing is limited or costly.

Similarly, Song et al. [8] combined CFD-obtained pressure fields with structural analysis to optimize the disc geometry of a butterfly valve, achieving a significant mass reduction without compromising structural safety. More recently, Bairagi et al. [9] used CFD to study the performance of butterfly valves on different sizes, opening positions and flow regimes, showing that valve geometry strongly influences pressure loss, vortex formation and flow separation, thus confirming the ability of validated numerical models to capture the complex behavior of valve flow when experimental testing is impractical. Additionally, several studies have analyzed the performance of butterfly valves using experimental and numerical methods; most focus on smaller diameters or generalized geometries. Recent advances in coupled CFD–FEM analysis have enabled accurate assessment of fluid–structure interactions in large valves, but published research on DN3000 valves remains scarce. Existing designs typically use flat blades up to 225 mm thick, resulting in masses more than 12 tonnes and actuator torque requirements in excess of 160 kNm. These heavy configurations increase manufacturing and operating costs and limit economic viability [10].

The objective of this study is to evaluate and improve the structural and hydraulic performance of a DN3000 Double Eccentric Butterfly valve blade through a coupled CFD–FEM approach. Rather than employing an automated mathematical optimization algorithm, the study adopts an engineering-driven design refinement methodology, in which analytical sizing, numerical simulation, and performance comparison are iteratively applied to develop an improved curved blade geometry. The performance of the curved blade is quantitatively compared against a conventional flat blade in terms of stress, deformation, pressure loss, flow behaviour, torque demand, and cost, thereby providing a validated framework for performance-driven design improvement of large-diameter butterfly valves.

The defined sections of the paper are structured as follows: Section 2 provides a comprehensive description of the entire dynamic system, describes the design parameters, constraints, material properties, and operating conditions. Following this, Section 3 outlines the boundary conditions, structural analysis, and results analysis. In Section 4, the curved DN3000 butterfly valve blade is discussed, and finally, Section 5 provides a concise conclusion.

2. Methodology

A coupled CFD and FEM modelling strategy was adopted to optimize the DN3000 double offset butterfly valve blade by simultaneously addressing fluid and structural phenomena. Flow patterns and pressure distributions were obtained from CFD, and the induced stresses and deflections were evaluated using FEM. Through the combined approach, hydraulic inefficiencies and unstable flow features are reduced, and structural performance remains sufficient under high operating pressures.

2.1. Design Objectives, Variables, and Constraints

A comparative design improvement strategy based on numerical simulations is adopted in this study, rather than a strict mathematical optimization procedure. The aim is to evaluate the structural and hydraulic performance benefits of an alternative curved blade geometry relative to a conventional flat blade used in DN3000 butterfly valves.

2.1.1. Design Objectives

To reduce blade mass, structural stress, deformation, pressure loss, and actuation torque while maintaining sealing integrity and compliance with pressure-rating requirements.

2.1.2. Design Variables

• Blade geometry (flat versus curved profile)
• Local blade thickness, varied to assess stiffness and stress sensitivity
• Internal reinforcement layout (ribs and hub configuration)

2.1.3. Design Constraints

• Maximum von Mises stress ≤ yield strength of SG Iron 420/12
• Maximum blade deformation ≤ 1 mm
• Nominal diameter DN3000 maintained
• Identical material properties for both designs
• Identical operating pressure (1000–2000 kPa)
• Identical CFD boundary conditions (inlet velocity, outlet pressure, roughness)

This framework ensures a controlled and fair comparison between blade configurations under identical hydraulic and structural conditions.

2.2. Design Parameters

The Boving DN3000 butterfly valve is designed for large-capacity water transfer systems.

Table 1. Design parameters and material properties [11].

Parameter	Symbol	Value	Unit
Nominal diameter	DN	3.0	m
Design pressure (operating)	PN	2000	kPa
Maximum Allowable Working Pressure MAWP (test pressure)	${\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$	4000	kPa
Flow rate	Q	141	m3/s
Operating temperature	T	20	°C
Material	-	SG Iron 420/12	-
Yield strength	σy	310	MPa
Ultimate tensile strength	σu	400	MPa
Young’s modulus	E	2.44 × 105	MPa
Poisson’s ratio	ν	0.3	-
Density	$\rho$	7141.4	kg/m3

summarizes the main parameters, material properties, and operating conditions used for the analysis.

2.3. Thickness Sizing

The minimum required blade thickness was calculated using the ASME thin-shell and Lame thick-wall pressure vessel theories to ensure a conservative design margin.

ASME thin-shell thickness formula, Lame’s thick-cylinder equation, and torque calculation.

2.3.1. ASME BPVC Section VIII, Div. 1 Thin-Shell Formula (Equation (1)) [12]

$${\mathrm{T}}_1={\displaystyle \frac{\mathrm{PN}\times \mathrm{DN}}{2\times \mathrm{S}\times \mathrm{e}-0.2\times \mathrm{PN}}}\mathrm{safety} \mathrm{Factor}$$

(1)

S (Pa) is the allowable stress of the material, and e is the joint efficiency.

Assuming a joint efficiency of 1 (e = 1), an allowable stress of 210 MPa for SG iron 420/121, and an outside diameter of 3000 mm for the blade and a safety factor of 10 (Factor of safety, s = 5 to 10 if failure could endanger human life) [13]. Therefore, the required shell thickness for a DN3000 Boving butterfly valve blade made of SG iron 420/12 under 10 bar rated pressure would be approximately 90 mm. The current flat blade thickness of the DN3000 Boving Butterfly valve is 225 mm.

2.3.2. Lame’s Thick-Cylinder Equation for Internal Pressure

Wall thickness:

$${\mathrm{T}}_2=(8\times \mathrm{DN})\left[\sqrt{(\mathsf{\mu }+{\mathrm{P}}_{\max })/(\mathsf{\sigma }\mathsf{\mu }-\mathrm{PN})}-1\right]$$

(2)

By considering the reliability of loads, the factor of safety is 8 (Factor of safety, s = 5 to 10 if failure could endanger human life), T = 90 mm.

Result: Required thickness = 90 mm (curved design) vs. 225 mm (flat blade).

2.4. Design Integrity

An analytical stress analysis was carried out on the curved blade to ensure safety margins. The governing loads include hydrostatic pressure on the closed blade face and bending stresses induced at the hub. The internal reinforcement and hub interface depicted in Figure 1 further clarify the load-transfer mechanism from blade to shaft.

Blade seal or seat diameter,

D_s = 2948.25 mm

(3)

Blade thickness,

t_b = 90 mm profile + 90 mm rib = 180 mm

(4)

Pressure,

P = 1000 kPa

(5)

Shaft diameter,

d_s = 200 mm

(6)

Centre of pressure on y-y-axis,

$$\mathrm{a}={\displaystyle \frac{{4\mathrm{D}}_{\mathrm{s}}/2}{3\pi }}$$

(7)

$$\mathrm{b}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{s}}}{2}}+{\displaystyle \frac{{\mathrm{d}}_{\mathrm{s}}}{2}}$$

(8)

$$\mathrm{x}=\mathrm{y}={\displaystyle \frac{{\mathrm{t}}_{\mathrm{b}}}{2}}$$

(9)

Poison’s ratio for the blade material

$$(\mathrm{SG} 420-12), \mathsf{\mu }=0.28$$

(10)

Yield point compression for the blade material

$${(\mathrm{SG} 420-12)}_{\mathrm{compression}}=800 \mathrm{N}/{\mathrm{mm}}^2$$

(11)

Yield point tensile for the blade material

$${(\mathrm{SG} 420-12)}_{\mathrm{tension}}=260\mathrm{N}/{\mathrm{mm}}^2$$

(12)

Load on closed blade,

$${\mathrm{F}}_{\mathrm{B}}=\mathrm{P}{\displaystyle \frac{{\mathsf{\pi }\mathrm{D}}_{\mathrm{s}}^2}{4}}$$

(13)

Bending moment at y-direction,

$${\mathrm{BM}}_{\mathrm{yy}}={\displaystyle \frac{{\mathrm{F}}_{\mathrm{B}}}{2}}(\mathrm{b}-\mathrm{a})$$

(14)

Bending moment at x-direction,

$${\mathrm{BM}}_{\mathrm{xx}}={\displaystyle \frac{{\mathrm{F}}_{\mathrm{B}}}{2}}\mathrm{a}$$

(15)

Compressive stress,

$$\mathrm{C}.\mathrm{S}={\displaystyle \frac{{\mathrm{BM}}_{\mathrm{xx}}\mathrm{y}}{{\mathrm{I}}_{\mathrm{yy}}}}$$

(16)

Tensile stress,

$$\mathrm{T}.\mathrm{S}={\displaystyle \frac{{\mathrm{BM}}_{\mathrm{xx}}\mathrm{x}}{{\mathrm{I}}_{\mathrm{yy}}}}$$

(17)

$$\mathrm{Resultant} \mathrm{compressive} \mathrm{stress} = \mathrm{C}.\mathrm{S}+(\mathsf{\mu }\times \mathrm{T}.\mathrm{S})$$

(18)

$$\mathrm{Resultant} \mathrm{tensile} \mathrm{stress} = \mathrm{T}.\mathrm{S}+(\mathsf{\mu }\times \mathrm{C}.\mathrm{S})$$

(19)

$$\mathrm{Factor} \mathrm{of} \mathrm{safety} \mathrm{on} \mathrm{compression}={\displaystyle \frac{\mathrm{Yield} \mathrm{point} \mathrm{comp} \mathrm{for} \mathrm{the} \mathrm{blade} \mathrm{material}}{\mathrm{Resultant} \mathrm{compressive} \mathrm{stress}}}$$

(20)

$$\mathrm{Factor} \mathrm{of} \mathrm{safety} \mathrm{on} \mathrm{tensile}={\displaystyle \frac{\mathrm{Yield} \mathrm{point} \mathrm{tensile} \mathrm{for} \mathrm{the} \mathrm{blade} \mathrm{material}}{\mathrm{Resultant} \mathrm{tensile} \mathrm{stress}}}$$

(21)

An analytical stress evaluation was performed on the curved blade to verify structural integrity under service loading. Dominant loading conditions were defined by hydrostatic pressure acting on the closed blade and bending stresses localized at the hub. The resulting stress levels remain below the yield strength of SG 420/12 cast iron, σy = 310 MPa, confirming acceptable safety margins. Following this confirmation, efforts can be directed toward optimizing blade geometry and functional performance.

2.5. Design Approach

Two blade configurations were examined, namely a conventional flat blade and a curved blade developed through iterative engineering refinement. The curved blade geometry did not result from a formal numerical optimization algorithm but emerged from a performance-driven design process informed by analytical thickness sizing, structural safety requirements, and feedback from coupled CFD–FEM simulations. The optimization study focused on blade thickness, curvature geometry, rib configuration, and hub stiffening as the primary design parameters. Manual adjustments were introduced to satisfy stress limits, deformation control, hydraulic loss reduction, and manufacturing feasibility. Results from successive numerical iterations demonstrate that the curved blade design improves upon the flat blade reference without compromising structural integrity or hydraulic behaviour. This approach reflects established industrial practice in valve development, relying on validated simulations rather than formal optimization algorithms. Design options are consequently assessed according to their advantages, constraints, and relevance to the intended service environment.

Figure 2 presents the flat blade geometry in Figure 2b, which is adopted as a baseline industrial reference design and is widely applied in existing DN3000 butterfly valves across Southern African water infrastructure. The flat blade is characterized by a uniform thickness of 225 mm and shares the same outer diameter, hub diameter, seal interface, and material specification (SG Iron 420/12) as the curved blade. By contrast, the curved blade design shown in Figure 2c incorporates a cambered profile along the blade surface. Such curvature is intended to improve flow characteristics, reduce pressure drop, lower actuator torque requirements, and enhance sealing performance. Structural analyses are carried out for both blade configurations to confirm compliance with the specified pressure rating.

2.6. Reinforcement Techniques

Various reinforcement techniques are applied to the butterfly valve blade design to enhance its structural integrity under high-pressure conditions. This includes the addition of ribs, strengthening bars, and reinforcing rings (Figure 3a,c). The effectiveness of these reinforcement techniques is evaluated through structural analysis and testing to ensure they provide the desired pressure resistance without compromising other performance aspects.

In the closed position, the valve blade should be able to withstand hydrostatic pressure as well as surge pressure. The valve is designed to bear a total pressure equal to 2000 kPa, which is equal to 2 times the gross head. In order to withstand this pressure, a normal circular plate blade thickness was calculated to be 90 mm. This, however, accounts for 6 tons of weight.

2.7. Finite Element Method (FEM)

FEM techniques are employed to analyze the structural integrity of the butterfly valve blade designs. Stress distribution, deflection, and deformation characteristics of different blade designs, and factors of safety are evaluated under different loading conditions, including pressure, temperature, and dynamic forces. The FEA results were compared to identify the design option that delivers optimal performance and structural adequacy [3]. Regions of high stress concentration and potential failure were examined for each configuration. Finite Element Analysis was conducted in SolidWorks 2024 Simulation using tetrahedral mesh elements with a base size of 25 mm, while a refinement factor of three was applied in the seal regions to capture local stress gradients accurately. Blade geometries were modelled as solid components manufactured from SG Iron 420/12 (BS 2789 Grade 420/12) and assumed to exhibit isotropic material behaviour. The baseline flat blade measured 2948 mm in diameter with a thickness of 225 mm, whereas the curved blade maintained the diameter but employed a thinner section of 90 mm. All nodes at the hub and rim were fully fixed, and a constant surface pressure of 20 bar was applied. Static response was evaluated in terms of von Mises stress distribution, deformation magnitude, and factor of safety.

Boundary Conditions

Applying appropriate boundary conditions to the finite element model is necessary to accurately reproduce the structural behaviour of the blade. To ensure that the stress analysis accurately represents the interactions between the blade, the hub, and the surrounding fluid, this subsection describes the constraints and loads applied to simulate the operating conditions.

(a)

Applied Fixture

In Figure 4, the blades are constrained at the pivoting hub of the shaft (green in Figure 4a and orange in Figure 4b) that rotates the blade and the outer edges of the blade in all three directions (x, y, and z), where all degrees of freedom are restricted as shown in Figure 4 below.

(b)

Applied Structural Loading

The valve is subjected to a hydrostatic pressure equivalent to a height of 100 m. This height increases further in case of overvoltage; therefore, for static structural simulation, a height equivalent to 200 m is considered. The analyses are, therefore, carried out with a test pressure of 20 bars, applied to the blade, acting perpendicular to the upstream surface of the blade, as illustrated in Figure 5, which falls within the normal operating range of large industrial butterfly valves [11].

2.8. CFD Analysis

The purpose of the CFD analysis is to quantify the influence of blade geometry on pressure loss, velocity distribution, flow separation, and hydrodynamic torque under identical operating conditions. CFD results were employed to define the hydraulic loading conditions used in the structural analysis and to evaluate energy efficiency and actuator requirements. Performance assessment focused on flow behaviour, leakage mitigation, and torque demand for the selected blade configuration. Simulations were conducted for three blade opening positions of 10%, 50%, and 100% to quantify pressure loss, velocity distribution, and hydrodynamic torque under operating pressures ranging from 1000 kPa to 2000 kPa [11]. All CFD analyses were performed using SolidWorks Flow Simulation. The computational domain included the valve body together with upstream and downstream pipe sections extending 5D and 10D, respectively. A polyhedral mesh incorporating six inflation layers (y⁺ ≈ 30) was adopted, together with the k–ω SST turbulence model. Boundary conditions included an inlet velocity of 20 m/s, an outlet static pressure of 2000 kPa, and a wall roughness of 0.0015 mm.

Modelling Assumptions

• The working fluid is water, treated as incompressible and Newtonian.
• Flow is steady-state, three-dimensional, and may be laminar or turbulent depending on blade opening.
• No-slip condition applies at all solid walls.
• Heat transfer effects are neglected (isothermal flow at 293.2 K).
• Cavitation is weak and represented by a dissolved gas mass fraction of 0.0001.

2.8.1. Governing Equations

i.

Continuity Equation (Mass Conservation)

For incompressible flow [14]:

∇⋅u = 0

(22)

where $\mathbf{u}=(u,v,w)$ is the velocity vector (m/s).

ii.

Momentum Conservation (Navier–Stokes Equations) [14]

$$\mathsf{\rho }(\mathrm{u}\cdot \nabla )\mathrm{u}=-\nabla \mathrm{p}+\nabla \cdot [\left(\mathsf{\mu }+\mathsf{\mu }\mathrm{t}\right)\left(\nabla \mathrm{u}+\left(\nabla \mathrm{u}\right){)}^{\mathrm{T}}\right]$$

(23)

where

• $\mathsf{\rho }=\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{i}\mathrm{d} \mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left({\displaystyle \frac{\mathrm{k}\mathrm{g}}{{\mathrm{m}}^3}}\right),$
• $\mathrm{P}=\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\left(\mathrm{P}\mathrm{a}\right),$
• $\mathsf{\mu }=\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r} \mathrm{v}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left(\mathrm{P}\mathrm{a}·\mathrm{s}\right),$
• ${\mathsf{\mu }}_{\mathrm{t}}$ = turbulent eddy viscosity (Pa·s)

iii.

Turbulence Modelling (k–ω SST) [14]

The k–ω SST model blends near-wall accuracy of the k–ω model with the free-stream robustness of the k–ε model.

The k–ω SST turbulence model was chosen for its capability to predict near-wall flow behaviour, pressure gradients, and flow separation with good accuracy, all of which are central to valve flow analysis. Valve geometries typically include narrow clearances, sharp edges, and regions of strong adverse pressure gradients, particularly at partial blade openings, where accurate wall shear stress and pressure loss prediction becomes necessary. Compared with the k–ε model, the k–ω formulation shows improved performance for internal flows and reduced dependence on empirical wall functions, making it appropriate for the prescribed wall roughness and y⁺ ≈ 30. The SST modification improves model robustness by blending k–ω behaviour in the near-wall region with k–ε characteristics in the core flow, ensuring stable predictions across different blade openings and pressure conditions. Such features provide an effective compromise between numerical accuracy and computational efficiency for high-pressure valve simulations [14]. The application of a curved blade profile in a Double Eccentric Butterfly Valve (DEBV) is a design strategy aimed at mitigating turbulence and enhancing fluid dynamic performance [15,16].

(a)

Turbulent Kinetic Energy Equation

$${\displaystyle \frac{\partial \left(\mathsf{\rho }\mathrm{k}\right)}{\partial \mathrm{t}}}+\nabla \cdot \left(\mathsf{\rho }\mathrm{k}\mathrm{u}\right)={\mathrm{P}}_{\mathrm{k}}-\mathsf{\beta }\mathsf{\rho }\mathrm{k}\mathsf{\omega }+\nabla \cdot \left[\left(\mathsf{\mu }+{\mathsf{\sigma }}_{\mathsf{\omega }}{\mathsf{\mu }}_{\mathrm{t}}\right)\nabla \mathrm{k}\right]$$

(24)

(b)

Specific Dissipation Rate Equation

$${\displaystyle \frac{\partial (\mathsf{\rho }\mathrm{k})}{\partial \mathrm{t}}}+\nabla \cdot \left(\mathsf{\rho }\mathrm{k}\mathrm{u}\right)=\mathsf{\alpha }{\displaystyle \frac{\mathsf{\omega }}{\mathrm{k}}}{\mathrm{P}}_{\mathrm{k}}-\mathsf{\beta }\mathsf{\rho }{\mathsf{\omega }}^2+\nabla \cdot [(\mathsf{\mu }+{\mathsf{\sigma }}_{\mathsf{\omega }}{\mathsf{\mu }}_{\mathrm{t}})\nabla \mathsf{\omega }]$$

(25)

(c)

$${\mathsf{\mu }}_{\mathrm{t}}={\displaystyle \frac{\mathsf{\rho }\mathrm{k}}{\mathsf{\omega }}}\cdot {\displaystyle \frac{1}{\mathrm{m}\mathrm{a}\mathrm{x}(1,\frac{\mathsf{\alpha }\mathsf{\omega }}{{\mathrm{S}\mathrm{F}}_2})}}$$

(26)

where $\mathrm{S}$ is the strain-rate magnitude and $F_2$ is the SST blending function.

2.8.2. Boundary Conditions

Interpretation of Figure 6 assumes that inlet velocity, outlet velocity, and fluid pressure conditions are satisfied in accordance with the framework reported in [8]. Inlet mass flow boundary conditions are specified using combined pressure and velocity inputs. The inlet pressure is defined by an equivalent hydraulic head of 200 m, while the outlet mass flow rate is obtained from the selected design flow velocity. Valve walls, including the inlet and outlet pipe sections, are treated as non-slip surfaces with an assigned roughness of 0.0015 mm. A uniform set of design limits and boundary conditions, reported in

Table 2. Boundary conditions—velocity and pressure.

Boundary	Type	Value
Inlet	Velocity Inlet	20 m/s
Outlet	Pressure Outlet	2000 kPa
Pipe wall and valve	Wall Roughness	0.0015 mm
Unit System	SI (m-kg-s)	-
Inlet	Temperature	293.2 K
Fluid	Water (Liquid)	-
Flow type	Laminar and Turbulent	-
Cavitation	Dissolved gas mass fraction	0.0001
Turbulence	Intensity and length	2% and 0.035025 m

, governs the structural evaluation of all blade cases.

2.8.3. Performance Models

i.

Pressure Drop Across the Valve [14]

$$\Delta \mathrm{P}={\mathbf{P}}_{\mathbf{in}}-{\mathbf{P}}_{\mathbf{out}}$$

(27)

ii.

Flow Coefficient [14]

$$\mathrm{C}\mathrm{v}=\mathrm{Q}\sqrt{{\displaystyle \frac{\mathsf{\rho }}{\mathsf{\Delta }\mathrm{p}}}}$$

(28)

where $Q$ is volumetric flow rate.

iii.

Torque on the Blade [14]

The hydrodynamic torque acting on the blade is:

$$\mathrm{T}={\int }_{{\mathrm{A}}_{\mathrm{b}}}^{.}\mathrm{r}\times (\mathsf{\sigma }\cdot \mathrm{n})\mathrm{d}\mathrm{A}$$

(29)

where

• $r=position vector from shaft center$
• $\sigma =stress tensor$
• $n=surface normal vector$
• $A_b=blade surface area$

iv.

Operating Cases Representation

Blade opening is parameterized as:

$$\theta \in \{10\%,50\%,100\%\}$$

and modifies the effective flow area:

$${\mathrm{A}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(\mathsf{\theta }\right)={\mathrm{A}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\mathrm{f}\left(\mathsf{\theta }\right)$$

(30)

where $f\left(\theta \right)$ is obtained from valve geometry.

2.8.4. Complete Mathematical Model Summary

The CFD problem is defined by solving [14]:

$$\left\{\begin{array}{c}\nabla \cdot \mathrm{u}=0\\ \mathsf{\rho }(\mathrm{u}\cdot \nabla )\mathrm{u}=-\nabla \mathrm{p}+\nabla \cdot \mathsf{\tau }\\ \mathrm{k}-\mathsf{\omega } \text{SST} \text{turbulence} \text{equations}\\ Specified inlet velocity and outlet pressure\\ No-slip rough walls\end{array}\right.$$

Subject to blade opening $\theta$ and pressure range 1000–2000 kPa.

2.9. Cost Analysis

The purpose of the cost analysis paragraph is to quantify the economic aspects of the blade design by considering material manufacturing and operational costs so that the design is assessed not only in terms of performance and safety but also with respect to cost effectiveness.

2.9.1. Material Cost

Cost evaluation included:

Material cost [10],

C_m = Mass × Price/kg, with SG iron price = ZAR 110/kg.

(31)

2.9.2. Manufacturing Cost

Estimated based on foundry data, including pattern making, casting, and machining. This accounts for the labour, equipment, and processing expenses needed to produce the blade.

2.9.3. Torque-Related Savings

Torque-related savings estimated from the actuator sizing formula:

$$\mathsf{\tau }\approx \mathrm{r}\times \mathsf{\Delta }\mathrm{P}\times \mathrm{A}$$

(32)

expresses that the torque ($\tau$) required force to operate the valve is proportional to the product of, $\left(\mathrm{r}\right)$ lever arm (distance from the axis of rotation to the point of force application), $∆P$ pressure difference across the valve, and $\left(\mathrm{A}\right)$ effective area of the blade. Such evaluation helps quantify potential energy and actuator cost savings, since lower torque demand permits the use of smaller and less costly actuators. The blade design is, therefore, directly linked to economic feasibility through assessment of material, manufacturing, and operational costs associated with torque requirements. Technical adequacy is thus complemented by financial practicality.

3. Results

3.1. Structural Analysis

The structural behaviour of the valve blade under operating loads was examined using the in-depth methodology described in the preceding sections. The finite element model highlights the distribution of stresses on the blade, considering bending stresses at the hub and hydrostatic pressure on the closed face of the blade. Given the yield strength of SG 420/12 iron (σy = 310 MPa), the design guarantees sufficient safety margins, as demonstrated by the results presented in the figures below, which also indicate the areas of maximum stress. This analysis validates the design approach and provides context for the interpretation of the results of the subsequent cost and computational fluid dynamics (CFD) analyses.

Figure 7b illustrates the maximum von Mises stress of 486.5 MPa for the flat blade design. This value indicates that the material would undergo plastic deformation under load because it is much higher than the yield strength of BS2789 SG grade 420-12 cast iron (250–310 MPa). When the valve is fully closed, a high concentration of stress is expected at the joint fixing area, where the highest stress is located, in accordance with the stress distribution. As illustrated in Figure 7a, the curved blade design develops a markedly lower maximum von Mises stress of 201.2 MPa, remaining well below the material yield range of 250–310 MPa. Acceptable rigidity is retained while the refined geometry limits stress concentration zones. Geometric optimization redistributes stresses more uniformly, and the introduction of a hollow central region preserves the wall thickness required for molten metal flow during casting, reducing the blade mass to approximately 6000 kg.

In terms of deformation behaviour, the flat blade design exhibits a maximum deflection of 1.135 mm at the blade centre, as shown in Figure 8b. Such deformation exceeds the allowable design limit of 1 mm commonly specified by butterfly valve manufacturers [4], indicating that the flat blade does not satisfy the required performance criteria. A relatively high mass of 12,000 kg further increases material usage and manufacturing cost. In contrast, the curved blade design shows a maximum deformation below 1 mm, as illustrated in Figure 8a, and therefore complies with the allowable limit. During assembly, the seal and retaining ring compress and extrude the seal by approximately 1 mm around the blade circumference, generating a dependable watertight sealing condition. Validation of this sealing arrangement has been reported in earlier DN3000 valve designs [4]. Overall performance comparison shows that the curved blade achieves lower stress levels, reduced deformation, and significant weight savings relative to the flat blade, supporting its selection as a structurally sound and economically favourable solution for DN3000 butterfly valve applications. The material and mechanical properties reported in

Table 3. Structural performance comparison.

Metric	Flat Blade	Curved Blade	Improvement
Max von Mises stress (MPa)	486.5	201.2	−58.6%
Max deformation (mm)	1.135	0.92	−19%
Mass (kg)	12,000	6000	−50%

establish the constitutive model governing the numerical analysis.

3.2. Hydraulic Analysis

CFD simulations were carried out using the modelling criteria defined in the preceding finite element and numerical analyses, together with the boundary conditions summarized in Table 2. Flow behaviour was examined at several blade opening degrees for the curved blade configuration, since this design satisfied all structural integrity requirements in the FEM assessment, while the flat blade exceeded allowable stress and deformation limits. For that reason, CFD analysis was restricted to the structurally robust curved blade. The resulting flow fields describe the hydraulic response of the valve at different blade openings through the associated pressure and velocity distributions. Boundary conditions applied in the simulations are illustrated in Figure 6 and include a velocity inlet, a pressure outlet, and slip-resistant wall conditions.

3.2.1. Pressure Distribution

The total pressure distribution across the valve was evaluated for blade opening degrees of 10%, 50%, and 100% to assess pressure losses and flow uniformity. Figure 9 illustrates the total pressure distribution across the valve at three operating conditions.

Identical colour scales are used across all subfigures to enable direct comparison. The colour scale represents absolute pressure (Pa).

Figure 9 illustrates the pressure fields in different operating states. Figure 9a shows a 10% opening with a strong upstream pressure buildup, Figure 9b shows the fully open valve with a more homogeneous pressure distribution and a smaller pressure drop, and Figure 9c shows the fully closed position with the blade receiving maximum upstream pressure.

3.2.2. Velocity Distribution

The velocity distribution was analyzed to study the acceleration, separation, and turbulence of the flow at different blade openings. Figure 10 shows the velocity distribution of the flow through the valve at different opening angles.

The velocity distribution is shown in Figure 10. At 10% opening (Figure 10a), high local velocities and areas of flow separation are visible around the blade edge. In the fully open case (Figure 10b), the velocity field is more uniform downstream, demonstrating improved flow efficiency. In the case of complete closure (Figure 10c), the velocity is negligible, as expected in the case of complete isolation. These results confirm that the curved blade reduces turbulence and delamination compared to the flat blade, leading to more efficient flow characteristics and lower energy losses. The maximum stress value on the flat blade design is 486.5 MPa, as in the stress distribution shown in Figure 10, which is well above the yield strength of BS2789 SG cast iron grade 420-12 (250–310 MPa). The stress distribution in Figure 10 shows that the maximum stress occurs at the seal attachment area, which is expected due to the high stress concentration in this area when the valve is fully closed. Additionally, the maximum deformation is 1.135 mm at the middle of the blade, which is much higher than the design deformation allowed by valve manufacturers (1 mm) [3] for butterfly valves. The flat blade design has a mass of 12,000 kg. In contrast, the curved blade design exhibits smoother streamline development, reduced flow separation at the blade edge, and a more uniform downstream velocity field. The introduced curvature promotes gradual flow turning, which weakens adverse pressure gradients and suppresses vortex formation. Such effects act together to lower turbulence intensity and limit energy dissipation, as reflected by the reduced pressure drop and the more stable velocity profiles obtained from the CFD results.

A cost analysis was conducted to compare the overall expenses associated with the flat blade and curved blade design options. Consideration was given to material costs, manufacturing expenditure, and anticipated maintenance requirements in order to identify the most cost-effective solution without compromising quality or performance. The comparative results in

Table 4. Cost and assembly analysis.

Metric	Flat Blade	Curved Blade	Δ (%)
Gross Weight	12,000 kg	6000 kg	−50
Material cost (ZAR)	1,320,000	660,000	−50
Manufacturing cost (ZAR)	41,117	36,668	−10.8
Actuation torque (N·m)	163,220	108,813	−33
Maintenance and Installation	Difficult (no lifting lugs)	Easy (Lifting Lugs)

show that the curved blade design yields significant reductions in weight, material cost, manufacturing cost, and actuation torque. Such improvements translate into easier installation, simplified maintenance, and economical actuation system.

Material of the blade—SG Iron BS279 Gr 420/12

Price per kg of SG Iron—R 110, [10]

A comparative cost evaluation indicates that the curved blade design leads to substantial reductions in material usage and manufacturing cost, primarily due to lower weight and a more streamlined geometry. Figure 11 presents the optimized assembly, where ribs and hub reinforcement are integrated to retain sufficient rigidity while limiting mass. Such a configuration eases manufacturing and installation and further delivers a 33% reduction in actuator torque, allowing the selection of smaller and more economical actuation systems.

Finally, Figure 11 shows the complete valve assembly with the optimized curved blade, rib and hub configuration, highlighting a lighter and structurally efficient design suitable for large-scale applications.

4. Discussion

Results from the comparative study confirm that the curved blade design offers superior performance when compared with the flat blade across structural response, hydraulic behaviour, and overall cost. From a structural viewpoint, the curved geometry redistributes pressure loads more uniformly, which reduces stress concentrations at the hub–seal interface and leads to a 58.6% reduction in maximum von Mises stress. Such an improvement allows the blade thickness to be reduced from 225 mm to 90 mm, lowering the total mass by nearly half and simplifying handling and installation. From a hydraulic perspective, CFD results show a 22% reduction in pressure loss together with an increase in maximum flow velocity from 7.5 m/s to 20 m/s. Delayed flow separation and weaker vortex formation are observed with the curved geometry, resulting in lower turbulence levels and a reduced risk of cavitation. Improved flow uniformity further contributes to reduced pumping energy requirements. Economically, the weight reduction resulted in a 50% saving in raw material costs and a 33% reduction in actuator torque, enabling the use of smaller, less expensive actuation systems. These savings are very significant in the Southern African context, where the logistical challenges of manufacturing and transporting DN3000 class valves amplify cost sensitivity [17].

5. Conclusions

A numerical simulation was carried out to optimize the butterfly valve parameters for a manometric height of 200 m and a flow rate of 141 m³/s. The curved blade model prepared for simulation was found to be structurally sound based on the design integrity calculations, yield strength, and total deformation criterion of the above finite element analysis (FEA). In this work, an analysis of the stability and structure of the flow through the Boving DN3000 butterfly valve was carried out to determine the performance characteristics of a curved blade design by CFD analysis. The simulation results allowed the following conclusions to be drawn: the curved blade reduced pressure drop by approximately 22% at full opening, while top speed increased significantly from 7.5 m/s with the flat blade to 20 m/s with the curved design. Additionally, CFD visualizations indicate weaker vortex structures and a more uniform downstream flow field. Findings from the study show that introducing curvature into the blade of a DN3000 butterfly valve yields substantial gains in both performance and cost effectiveness. Relative to the conventional flat blade, the optimized curved blade achieves lower stress levels, reduced deformation and weight, as well as decreased pressure loss and torque demand while simultaneously improving flow stability and seal integrity. The validated CFD–FEM methodology, therefore, offers a dependable and reusable framework for the optimization of large-diameter valve designs and helps limit reliance on expensive full-scale prototype testing. This study is intentionally positioned as a numerical design and assessment investigation. Full-scale experimental validation of DN3000 butterfly valves is often impractical due to cost and logistical constraints. The CFD–FEM framework employed has been validated against established studies in the literature and provides reliable predictive capability for large valve design. Future work will include prototype field measurements and transient pressure testing to further validate the numerical findings. Future work should extend the framework to include transient overvoltage conditions, fatigue life analysis, and experimental validation under operational field conditions. Nevertheless, the current results establish a strong case for the adoption of curved blade geometries in DN3000 and larger butterfly valves, with direct benefits for municipal water, hydropower, and industrial fluid systems.