Radial Turbine
Radial Turbine: Theoretical Foundations
Overview
Is a radial turbine the turbine side of a turbocharger?
Yes. A radial inflow turbine has flow entering from the outer circumference towards the inner diameter and is discharged in the axial direction. It is compact and can achieve a high expansion ratio, making it widely used in automotive turbochargers and small gas turbines.
Total-to-Static Efficiency
How is the efficiency of a radial turbine defined?
Total-to-static efficiency is commonly used.
This definition is appropriate when the exit dynamic pressure is not recovered (free exhaust).
Velocity Ratio
What is the velocity ratio?
It is the ratio of the impeller peripheral speed $U$ to the isentropic expansion velocity $C_s$.
Maximum efficiency is obtained around $U/C_s \approx 0.7$. This corresponds to the condition where the swirl component at the blade inlet becomes optimal.
0.7 is an easy number to remember.
It is the most fundamental indicator for radial turbine design. Plotting the efficiency obtained from CFD against $U/C_s$ and checking if the peak is around 0.7 is the first checkpoint.
Specificities for Turbocharger Use
What are the specific challenges for radial turbines in turbochargers?
Response to exhaust pulses. Engine exhaust is intermittent, and the turbine inlet pressure fluctuates significantly with a cycle of a few milliseconds. Steady-state CFD can only predict time-averaged performance, so for higher accuracy, unsteady calculations with pulsating inlet pressure variations are necessary.
History of Radial Turbines — Establishment of Centripetal Turbine Design Theory (1930s-60s)
The theory and design methods for radial flow turbines (centripetal turbines) were established in the 1930s-40s, with Gehring et al. (1930s) developing high-efficiency centripetal turbine blade profile design theory based on de Laval's impulse steam turbine. The fundamental blade profile design methods for modern turbocharger radial turbines—optimization of backsweep angle, exit blade angle—were completed in the 1960s through joint research by NASA and GE Turbine (Rohlik 1968, etc.). Since then, over 60 years, CFD-based precision design has been layered on top of this foundational theory, leading to modern VGT turbine efficiencies reaching an astonishing 86-90%. Fluid machinery design is not born overnight; it is the product of a complex evolution where CFD refinement is layered upon over 60 years of accumulated experiments and theory.
Computational Methods for Radial Turbine
Model Configuration
How do you set up a CFD model for a radial turbine?
A typical configuration is as follows.
- Volute/Scroll: Stationary domain, non-axisymmetric
- Nozzle Vane (VGT): Stationary domain, blade row
- Turbine Wheel: Rotating domain
- Diffuser/Outlet Pipe: Stationary domain
For interface treatment, the volute-nozzle interface uses GGI (no pitch difference), and the Nozzle-wheel interface uses Frozen Rotor or Sliding Mesh.
VGT is a variable nozzle, right? Do you also analyze with different opening angles?
Yes. Change the VGT opening angle in 5-10 stages to create a map for each opening. Nozzle angle changes are done parametrically in BladeGen or CAD, and processed sequentially via automatic meshing → CFX batch calculation.
Mesh Generation
What should I be careful about when meshing a radial turbine?
| Domain | Method | Points to Note |
|---|---|---|
| Volute | Unstructured (Tetra+Prism) | Fine mesh at the tongue |
| Nozzle Vane | TurboGrid or Unstructured | Mesh strategy to accommodate variable opening |
| Turbine Wheel | TurboGrid (Structured Grid) | Curvature of inter-blade passage, splitter blade compatibility |
| Outlet Diffuser | Structured or Unstructured | Adequately resolve swirl flow decay |
Do turbine wheels have splitter blades?
Radial turbines often do not have splitters, but some high-performance designs include splitters to reduce blade loading. TurboGrid also supports topologies with splitters.
Turbulence Model
What turbulence model is suitable for radial turbines?
SST k-omega is standard. If transition on the turbine blade surface is important, add the Gamma-Theta transition model. For unsteady calculations of exhaust pulsations, SAS or SDES are also considered.
Radial Turbine CFD Numerical Settings — Transonic Flow and Mesh Resolution for Trailing Edge Shock Waves
Radial turbines used in small gas turbines and turbochargers often have exit velocities near sonic speed (Ma≈0.8~1.0), so proper numerical handling of transonic flow determines accuracy. To accurately capture the oblique shock wave generated from the blade trailing edge, the mesh near the trailing edge should be set to a cell size of at least 1/5 of the trailing edge thickness, and mesh alignment along the shock wave angle is necessary. For numerical schemes, the Roe Flux Differencing Scheme or HLLC (Harten-Lax-van Leer-Contact) scheme is recommended for shock wave capture accuracy, and Preconditioning (low Mach number preconditioning) is required in low Ma number regions (blade pressure surface). Neglecting these settings can lead to CFD overestimation of turbine efficiency by 3-5% compared to experiments, as reported in papers.
Radial Turbine in Practice
Turbine Map Composition
What format is a turbine map?
The horizontal axis is expansion ratio ($p_{01}/p_2$), the vertical axis is corrected mass flow rate $\dot{m}\sqrt{T_{01}}/p_{01}$. Lines for each rotational speed are drawn, with efficiency overlaid as a parameter.
How many calculation points are needed?
5 rotational speed levels × 6-8 expansion ratio points, totaling 30-40 operating points is standard. For VGT, a map is needed for each nozzle opening, so the total can exceed 100 points.
Method for Varying Expansion Ratio
How do you change the expansion ratio in CFD calculations?
There are two common approaches:
- Fix inlet pressure, vary outlet pressure: Simpler to implement, commonly used for quick parametric sweeps
- Fix rotational speed and inlet conditions, adjust outlet pressure iteratively: More realistic simulation of actual operating conditions, requires convergence loop
The second method is preferred for generating accurate performance maps.