Pump CFD Analysis

Q: What does CFD analysis of a centrifugal pump predict?

The three fundamental predictions are Head, Efficiency, and Shaft Power. The primary objective of CFD is to generate the H-Q (Head vs. Flow rate) characteristic curve.

Q: What is the equation for pump head?

The pump head is the difference in total head between the outlet and inlet. $$ H = \frac{p_2 - p_1}{\rho g} + \frac{V_2^2 - V_1^2}{2g} + (z_2 - z_1) $$ In CFD, it is simpler to calculate it directly from the total pressure difference: $H = (p_{t2} - p_{t1})/(\rho g)$. Efficiency is divided into hydraulic efficiency and overall efficiency. $$ \eta = \frac{\rho g Q H}{P_{shaft}} = \frac{\rho g Q H}{\tau \omega} $$ Here, $\tau$ is the impeller torque obtained from CFD, and $\omega$ is the angular velocity.

Q: What is the difference between hydraulic efficiency and overall efficiency?

Hydraulic efficiency accounts only for hydrodynamic losses, excluding disc friction and leakage. Overall efficiency includes all losses: disc friction, leakage flow, and mechanical losses. CFD directly yields hydraulic efficiency; disc friction and leakage are not captured unless a model for the clearance with the wear ring is included.

Category: Fluid Analysis (CFD) | Integrated 2026-04-06

CAE visualization for mixed flow pump cfd theory - technical simulation diagram

Pump CFD Analysis — Fundamental Theory of Head and Efficiency

Pump CFD: Theoretical Foundations

Overview

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What does CFD analysis of a centrifugal pump predict?

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The three basics are Head, Efficiency, and Shaft Power. Creating the H-Q characteristic curve is the main purpose of CFD.

Definition of Head and Efficiency

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Please tell me the head equation.

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The pump head is the difference in total head between the inlet and outlet.

$$ H = \frac{p_2 - p_1}{\rho g} + \frac{V_2^2 - V_1^2}{2g} + (z_2 - z_1) $$

In CFD, it's convenient to calculate directly from the total pressure difference. $H = (p_{t2} - p_{t1})/(\rho g)$.

Efficiency is divided into hydraulic efficiency and overall efficiency.

$$ \eta = \frac{\rho g Q H}{P_{shaft}} = \frac{\rho g Q H}{\tau \omega} $$

$\tau$ is the impeller torque obtained from CFD, and $\omega$ is the angular velocity.

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What's the difference between hydraulic efficiency and overall efficiency?

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Hydraulic efficiency includes only hydrodynamic losses, excluding disc friction and leakage. Overall efficiency includes all: disc friction, leakage flow, and mechanical losses. What CFD directly yields is hydraulic efficiency; disc friction and leakage won't appear unless a gap model with the wear ring is included.

Euler Head (Theoretical Head)

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The theoretical head can be derived from the Euler equation, right?

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$$ H_{Euler} = \frac{U_2 C_{\theta 2} - U_1 C_{\theta 1}}{g} $$

Assuming no swirl at the inlet for a centrifugal pump ($C_{\theta 1}=0$), it becomes $H_{Euler} = U_2 C_{\theta 2}/g$. The head considering the slip factor $\sigma_s$ is $H_{th} = \sigma_s \cdot H_{Euler}$. The CFD head corresponds to this theoretical head plus hydraulic losses.

Steady-State Analysis with MRF Method

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Is the MRF method common for pump CFD?

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For obtaining the H-Q curve, the MRF method (steady-state) is standard. For cases with a volute, Frozen Rotor or Sliding Mesh is used. For a guide vane pump without a volute, Mixing Plane can also be used.

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Specific Speed as a Compass – The Starting Point of Mixed-Flow Pump Design

The first step in turbo pump design is calculating the Specific Speed (Ns). This dimensionless number, defined by Ns = n√Q / H^(3/4) (n: rotational speed, Q: flow rate, H: head), determines the pump type (centrifugal, mixed-flow, axial). In the design domain for mixed-flow pumps (Ns = 400–1200), the standard two-step approach is theoretically to determine basic dimensions with 1D design (velocity triangles) and then verify 3D flow details with CFD. The theory of specific speed was systematized by American hydraulic engineers in the early 20th century, followed by confusion with different unit systems in Europe and Japan. Today, the IEC standard has internationalized the dimensionless specific speed in m³/s and m units.

Computational Methods for Pump CFD

Mesh Generation

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What should I be careful about with centrifugal pump meshing?

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For the impeller, generating a structured grid with TurboGrid yields the highest quality. For the volute, use an unstructured tetra/polyhedral mesh.

Region	Mesh Type	Approx. Cell Count	Tool
Impeller	Structured Grid (H/J/L+O-grid)	0.5–1.5 million/pitch	TurboGrid
Volute	Unstructured Tetra+Prism	1–3 million	Fluent Meshing, STAR-CCM+
Suction Pipe	Structured or Unstructured	0.2–0.5 million	Any
Wear Ring Gap	Structured (Hexahedral)	0.1–0.3 million	Manual

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Should the wear ring gap also be included in the model?

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It's essential if you want to evaluate the effect of leakage flow. The gap is very narrow, 0.2–0.5mm, so a minimum of 10 cells radially and 50 cells axially is recommended.

Turbulence Model Selection

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Which turbulence model is suitable for pumps?

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SST k-omega is the standard. It excels at predicting adverse pressure gradients and separation on blade surfaces. For pumps, since the number of blades is small (5–7) and blade loading is high, k-epsilon tends to underpredict separation.

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Should I use wall functions or Low-Re?

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Pump Re is on the order of $10^6$, sufficiently high, so wall functions with y+ = 30–100 generally yield reasonable results. However, for higher accuracy, the Low-Re solution with y+ < 2 is recommended. Particularly for predicting blade surface separation at partial load, wall functions have limitations.

Boundary Conditions

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What are typical pump boundary conditions?

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Inlet: Mass flow rate specified (varied from 0.2 to 1.4 times design flow rate)
Outlet: Static pressure specified (atmospheric or actual system pressure)
Blade surface, Hub, Shroud: No-slip wall
Impeller-Volute interface: Frozen Rotor or Sliding Mesh

Setting the outlet to fixed static pressure and varying the inlet flow rate is the most stable configuration.

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Between Axial and Centrifugal – Numerical Difficulties in Mixed-Flow Pump CFD

Mixed-flow pumps lie in the intermediate specific speed (Ns) range between axial and centrifugal pumps (Ns = 400–1200), and because flow mechanisms from both types coexist, numerical analysis is difficult. The axial flow component is dominated by tip vortices and secondary flows, while the centrifugal component is affected by flow curvature due to Coriolis forces. In this mixed region, turbulence model selection directly impacts pump efficiency prediction, and many comparative studies show the k-ω SST model is typically several percent more accurate than standard k-ε. In mesh design, balancing resolution in the axial, circumferential, and radial directions is important; making one direction finer is not necessarily better.

Pump CFD in Practice

H-Q Characteristic Calculation Procedure

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How do you create the H-Q characteristic curve?

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1. Converge a steady-state MRF (or Frozen Rotor) calculation at design flow rate $Q_d$

2. Set 7–10 points in the flow rate range $0.2Q_d$ to $1.4Q_d$

3. Recalculate at each point by changing the inlet mass flow rate (using the previous point's result as the restart value)

4. Calculate head H, torque τ, efficiency η at each point and plot

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Why does convergence worsen on the low flow rate side?

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At low flow rates, the incidence angle at the impeller inlet becomes large, causing large-scale separation on the blade surface. In steady-state calculations, trying to converge an unsteady separation structure into a single solution causes oscillations. Below about 0.3$Q_d$, unsteady calculations are often necessary.

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