Pump CFD Analysis
Pump CFD: Theoretical Foundations
Overview
What does CFD analysis of a centrifugal pump predict?
There are three basics: Head, Efficiency, and Shaft Power. The main purpose of CFD is to create the H-Q characteristic curve.
Head and Efficiency Definitions
Please tell me the head equation.
The pump head is the difference in total head between the inlet and outlet.
In CFD, it's simpler to calculate directly from the total pressure difference. $H = (p_{t2} - p_{t1})/(\rho g)$.
Efficiency is divided into hydraulic efficiency and overall efficiency.
$\tau$ is the impeller torque obtained from CFD, and $\omega$ is the angular velocity.
What's the difference between hydraulic efficiency and overall efficiency?
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)
The theoretical head can be derived from the Euler equation, right?
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 head from CFD corresponds to this theoretical head plus hydraulic losses.
Steady-State Analysis with MRF Method
Is the MRF method common for pump CFD?
For obtaining the H-Q curve, the MRF method (steady-state) is standard. For cases with a volute, use Frozen Rotor or Sliding Mesh. For pumps with guide vanes but no volute, Mixing Plane can also be used.
The Foundation of Centrifugal Pump TheoryโEuler's Pump Equation (1754) and Its Connection to the Modern Era
The fundamental theory of centrifugal pumps, Euler's "Turbo Machine Equation" (U1*Vtheta1 - U2*Vtheta2 = g*H), was derived by Leonard Euler in 1754. The principle that the energy imparted to a fluid by a rotating body is proportional to the difference between the circumferential and swirl velocity components at the inlet and outlet remains an immutable truth that appears in the first chapter of textbooks on pumps, turbines, and compressors even 270 years later. Euler was the greatest mathematician of the 18th century, leaving monumental achievements not only in fluid machinery but also in rigid body mechanics, mathematics, and optics. Remarkably, the origin of the modern CFD Navier-Stokes equations, the "Euler Equations (inviscid)," also bears his nameโthe fact that Euler's name is engraved in both the fundamental theory of turbomachinery and the numerical methods of CFD is proof of how much fluid mechanics is built upon his work.
Computational Methods for Pump CFD
Mesh Generation
What should I be careful about with centrifugal pump meshing?
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
Should the wear ring gap also be included in the model?
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
Which turbulence model is suitable for pumps?
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.
Should I use wall functions or Low-Re?
Since pump Re is on the order of $10^6$ and sufficiently high, wall functions with y+ = 30~100 generally yield reasonable results. However, for higher accuracy, the Low-Re approach with y+ < 2 is recommended. Particularly for predicting blade surface separation at partial load, the limitations of wall functions become apparent.
Boundary Conditions
What are typical boundary conditions for a pump?
- 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
The most stable setup is to fix the outlet static pressure and vary the inlet flow rate.
Coffee Break Yomoyama Talk
Practical Settings for Pump CFDโChoosing Between Rotating Reference Frames and MRF, and Mesh Requirements
The first setting to decide in centrifugal pump CFD analysis is "MRF (Moving Reference Frame) vs. Sliding Mesh (SM)." For confirming basic characteristics like total head and efficiency near the design point, MRF (steady-state) is overwhelmingly advantageous in terms of computation time, providing comparable accuracy at 1/10 to 1/50 the cost of sliding mesh. For pumps where blade passing frequency (BPF) vibration, noise, or fatigue are issues, unsteady SM is necessary. Mesh requirements are a practical guideline of at least 20-30 prism layers normal to the blade surface in the impeller passage (when using low-Re wall treatment with y+<1) and a minimum of 0.5 million cells per blade passage. For full model analysis including the volute and scroll, a total cell count of 3-5 million is typical.
What should I be careful about with centrifugal pump meshing?
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 |
Should the wear ring gap also be included in the model?
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.
Which turbulence model is suitable for pumps?
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.
Should I use wall functions or Low-Re?
Since pump Re is on the order of $10^6$ and sufficiently high, wall functions with y+ = 30~100 generally yield reasonable results. However, for higher accuracy, the Low-Re approach with y+ < 2 is recommended. Particularly for predicting blade surface separation at partial load, the limitations of wall functions become apparent.
What are typical boundary conditions for a pump?
- 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
The most stable setup is to fix the outlet static pressure and vary the inlet flow rate.
Practical Settings for Pump CFDโChoosing Between Rotating Reference Frames and MRF, and Mesh Requirements
The first setting to decide in centrifugal pump CFD analysis is "MRF (Moving Reference Frame) vs. Sliding Mesh (SM)." For confirming basic characteristics like total head and efficiency near the design point, MRF (steady-state) is overwhelmingly advantageous in terms of computation time, providing comparable accuracy at 1/10 to 1/50 the cost of sliding mesh. For pumps where blade passing frequency (BPF) vibration, noise, or fatigue are issues, unsteady SM is necessary. Mesh requirements are a practical guideline of at least 20-30 prism layers normal to the blade surface in the impeller passage (when using low-Re wall treatment with y+<1) and a minimum of 0.5 million cells per blade passage. For full model analysis including the volute and scroll, a total cell count of 3-5 million is typical.
Pump CFD in Practice
H-Q Characteristic Calculation Procedure
How do you create the H-Q characteristic curve?
1. Converge a steady-state MRF (or Frozen Rotor) calculation at the design flow rate $Q_d$
2. Set 7~10 points in the 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 ฯ, and efficiency ฮท at each point and plot
Why does convergence worsen on the low flow rate side?
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators