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Effect of Streamline Curvature on Three-Dimensionality of Transitional Near-Wall Flow in a Linear Hydrofoil Cascade: A DNS Investigation


The laminar flow on a curved surface transits to turbulent induced by streamline curvature which generates pressure gradient field and separated shear layer flow. We performed a direct numerical simulation investigation on transitional flow through a linear cascade consist of S-shaped S3525 hydrofoil which has different curvature variations on the two surfaces, i.e., concave-to-convex and convex- to-concave in the streamwise direction. The objectives are to quantitatively assess the effects of streamline curvature of the hydrofoil surface on the three-dimensionality of the separated and transitional flow, including the patterns of separation and reattachment, formation and development of three-dimensional boundary layer flow, and statistics on non-homogeneous turbulent near-wall flow. Comparisons between the near-wall flows of the two surfaces demonstrate the effect of streamline curvature and its associated influential mechanisms such as pressure gradient field. Numerical data reveal that transition and occurrence of three-dimensional flow are observed earlier for the concave-to-convex surface; intermittent flow is generated in the concave section near the leading edge and convex section near the trailing edge where three-dimensionality of flow and turbulent fluctuations are the most pronounced. However, the boundary layer and near-wall flow for the convex-to-concave surface is quite stable until the concave section, thus three-dimensionality of separation and reattachment, boundary layer flow and turbulent behaviors are only notable near the trailing edge.

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Angle of attack


Adverse pressure gradient


Boundary layer flow

C :

Chord length of the hydrofoil

C f :

Skin friction coefficient

C p :

Pressure coefficient


Favorable pressure gradient


Intermittent flow




Permanent forward flow


Permanent reversed flow

Re :

Reynolds number

s :

Local streamwise coordinate

t :



Turbulent kinetic energy

u, v, w :

Pvelocity components and pressure

u′, v′, w′:

Fluctuating velocity

U 0 :

Velocity of incoming flow

x, y, z :

Cartesian coordinate


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The work was supported by NSFC (52176047 and 51706205).

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Zhang, W. Effect of Streamline Curvature on Three-Dimensionality of Transitional Near-Wall Flow in a Linear Hydrofoil Cascade: A DNS Investigation. Flow Turbulence Combust 109, 603–625 (2022).

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  • Hydrofoil cascade
  • Direct numerical simulation
  • Near-wall flow
  • Laminar-turbulent transition
  • Three-dimensionality