Specific Speed and Design Guidelines for Turbomachinery

Category: Fluid Analysis (CFD) | Integrated 2026-04-06
CAE visualization for turbo specific speed theory - technical simulation diagram
Specific Speed and Design Guidelines — Cordier Diagram and Type Selection

Specific Speed and Design Guidelines for: Theoretical Foundations

Overview

🧑‍🎓

Specific speed is a parameter used for selecting the type of turbomachinery, right?


🎓

Yes. Specific speed is a dimensionless parameter calculated from flow rate, head (pressure difference), and rotational speed. It is the most fundamental indicator for determining the optimal machine type.


Definition of Specific Speed

🧑‍🎓

Please show me the formula.


🎓

This form is widely used in Japan.


$$ N_s = \frac{N \sqrt{Q}}{H^{3/4}} $$

$N$: Rotational speed [rpm], $Q$: Flow rate [$m^3/min$], $H$: Head [m]. Although not dimensionless, this dimensional form is the most commonly used in practice.


Internationally, the dimensionless specific speed ($\Omega_s$ or $\omega_s$) is also used.


$$ \omega_s = \frac{\omega \sqrt{Q}}{(gH)^{3/4}} $$

🧑‍🎓

How does the specific speed value determine the type?


🎓
Specific Speed $N_s$ (Dimensional)TypeCharacteristics
100~300Centrifugal (Radial)High head, low flow rate
300~600Mixed FlowMedium head, medium flow rate
600~1500Axial FlowLow head, high flow rate

Cordier Diagram

🧑‍🎓

What is the Cordier diagram?


🎓

It's a diagram showing the optimum line for dimensionless specific speed $\omega_s$ and dimensionless specific diameter $\delta_s$.


$$ \delta_s = \frac{D (gH)^{1/4}}{\sqrt{Q}} $$

The relationship between $\omega_s$ and $\delta_s$ that achieves optimum efficiency is drawn as the Cordier line, which holds true for both pumps and turbines. As a starting point for design, you first check if your point lies on the Cordier line.


🧑‍🎓

So you check with the Cordier diagram before starting CFD, right?


🎓

Yes. Determining initial values for basic dimensions (diameter, blade width) from the specific speed and Cordier line before proceeding to CFD is an efficient workflow.

Coffee Break Trivia

History of the Specific Speed Concept – A Design Similarity Rule Born from 19th-Century Hydraulic Engineers

The concept of Specific Speed (Ns) was empirically developed by hydraulic machinery engineers in the late 19th century to compare similar water turbines. Italian hydraulic engineers and Germany's Vogel independently proposed similar parameters, and a unified definition was established in Europe and America in the 1910s-20s. Initially used as "hydraulic specific speed" for turbine design, it was later extended to centrifugal pumps and compressors. The dimensionless form (Shape Number Omega = omega*sqrt(Q)/(g*H)^(3/4)) was established in the 1940s and later to clarify its physical meaning. In Japanese hydraulic machinery engineering, the domestic calculation formula for Ns (Ns = N*sqrt(Q)/H^(3/4)) is still used today. Since its coefficient differs from the ISO dimensionless formula, confusion can easily arise when comparing with international papers—it is a basic practice to clearly state which definition is being used.

Computational Methods for Specific Speed and Design Guidelines for

1D Design and CFD Integration

🧑‍🎓

After deciding the type with specific speed, what is the design flow to CFD?


🎓

Let me show a typical design flow.


1. Specification Determination: Flow rate Q, Head H (or pressure ratio), Rotational speed N

2. Specific Speed Calculation: Calculate $N_s$ and select the type

3. Mean-Line Design: Determine velocity triangles, blade angles, meridional dimensions

4. Throughflow Analysis: Calculate 2D meridional flow field

5. 3D Blade Shape Definition: Generate 3D blade surfaces using BladeGen, etc.

6. 3D CFD: Detailed analysis with TurboGrid + CFX

7. Optimization: Parametric study or automatic optimization


🧑‍🎓

What do you do in Mean-Line design?


🎓

Design the velocity triangle at the mid-span. Determine blade angles from inlet/outlet absolute velocity, relative velocity, and blade speed, and check load validity using the de Haller number or diffusion factor.


Throughflow Analysis

🧑‍🎓

What is Throughflow analysis?


🎓

It's a 2D analysis that solves the flow on the meridional plane (r-z plane) assuming axisymmetry. The influence of the blade row is simulated as a body force representing blade force. Since you obtain the spanwise velocity and pressure distribution, it forms the basis for determining the blade angle distribution from hub to tip.


ToolMethodDeveloper
Concepts NREC COMPAL/AXIALStreamline Curvature MethodConcepts NREC
AxSTREAM (SoftInWay)Streamline Curvature MethodSoftInWay
NUMECA AutoBladeAutomatic Blade DefinitionNUMECA
Vista CCD (Ansys)1D Centrifugal DesignAnsys
🧑‍🎓

What is the Streamline Curvature Method?


🎓

It's a method that calculates the spanwise pressure gradient based on the curvature of streamlines on the meridional plane. It's the standard method for Throughflow analysis of turbomachinery. Since results are obtained in seconds, it's optimal for parametric design.

Coffee Break Trivia

Cross-checking Specific Speed and CFD Results – Relationship between Analytical Verification of η-Ns Curves and Numerical Calculation Accuracy

Specific Speed Ns is a design similarity parameter that non-dimensionalizes turbomachinery by flow rate, head, and rotational speed. The optimal blade type is determined from the Ns value. After CFD analysis, before comparing efficiency with experimental values, it's important to first cross-check with known Ns-η (specific speed-efficiency) charts. If the result deviates from the maximum efficiency Ns-η curve compiled from experimental collections like Lomakin(1958) or Kaplan(1935), there is either a design problem or a CFD model problem. Especially if "CFD efficiency exceeds the upper limit of the Ns-η curve (physically impossible high efficiency)," it's almost certainly due to missing loss modeling (volute loss, bearing loss, etc.) or erroneous boundary condition settings.

Specific Speed and Design Guidelines for in Practice

CFD Considerations by Specific Speed

🧑‍🎓

Does the CFD approach change depending on specific speed?


🎓

It changes significantly. Let's summarize the characteristics for each type.


Specific Speed RangeTypeMain CFD ChallengesRecommended Meshing Method
Low (100-200)Centrifugal (Low Flow)Diffuser loss, RecirculationTurboGrid + Volute Unstructured
Medium-Low (200-400)Centrifugal (Standard)Jet/Wake StructureTurboGrid
Medium (400-600)Mixed FlowEffect of Meridional CurvatureTurboGrid (Axial-Radial Mixed)
High (600-1000)Axial Flow (Large Hub Ratio)Tip Leakage, Secondary FlowTurboGrid
Very High (>1000)Axial Flow (Small Hub Ratio)Incompressible Flow, StallTurboGrid or Unstructured
🧑‍🎓

Is CFD for mixed-flow pumps particularly difficult?


🎓

Because the meridional curvature is large, the mesh in the inter-blade flow passage is prone to distortion. It's important to select J-type or L-type topologies in TurboGrid and set them to follow the meridional curvature.


Relationship Between Specific Speed and Efficiency

Related Simulators

Experience the theory firsthand with the interactive simulator for this field

All Simulators

Related fields

Rate this article
Thank you for your feedback!
Helpful
More details
Report error
Helpful
0
More details
0
Report error
0
Written by NovaSolver Contributors
Anonymous Engineers & AI — Sitemap