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Flow Characteristics of Curved Rotor Stator Systems Using Large Eddy Simulation

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Abstract

In this paper, the new idea of application of a curved rotor disk in rotor stator systems is presented and analyzed by using the large eddy simulation technique. The geometry of the examined rotor-stator system consists of a stationary flat disk (stator), a rotating curved disk (rotor) and a stationary enclosing cylinder (shroud). A hole in the center of stator allows the flow to enter the cavity, and the clearance between the shroud and rotor enables the flow to exit the cavity. Employing elliptical bumps with different geometrical parameters on the rotor disk (creating a curvature on the rotor), the rotating curved disk is parametrized. Three cavity cases (one with a flat rotor disk, another with the maximum outflow total pressure, and the third with the highest mass flow rate) are selected for LES analysis and more detailed investigation of flow and turbulence structures. The Favre-filtered governing equations for LES analysis of compressible turbulent flows are solved for all three cases. Radial and circumferential flow velocities as well as shear and normal Reynolds stresses in different cavity regions are studied. The flow in a rotor-stator cavity is simultaneously affected by the inlet flow, rotor rotation, and the bump on rotor disk. Creating a bump on rotor disk causes increase of both the radial pressure gradient and the mass flow rate of fluid that enters the rotor-stator cavity.

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Abbreviations

a :

Semi-minor axis of elliptical bump (m)

b :

Semi-major axis of elliptical bump (m)

C w :

Non-dimensional mass flow rate

e :

Total energy (J)

G :

Gap ratio

G c :

Shroud clearance ratio

h :

Distance between the center of elliptical bump and rotation axis (m)

K :

Entrainment coefficient

l :

Inlet radius (m)

M :

Moment applied on rotor (N m)

Ma :

Mach number

\( \dot{m} \) :

Mass flow rate (kg s−1)

∆P :

Total pressure difference between inlet and outlet (bar)

p :

Static pressure (bar)

Pr :

Prandtl number

q j :

Heat flux vector (W m−2)

R :

Disk radius (m)

Re θ :

Rotational Reynolds number

R ij :

Reynolds stress tensor with i, j = (r,θ, z)

r, θ, z :

Cylindrical coordinate

S :

Distance between disks (m)

S c :

Clearance between rotor and shroud (m)

\( {\overset{\sim }{S}}_{ij} \) :

Resolved strain rate tensor

T t :

Total temperature (K)

T :

Static temperature (K)

t :

Time (s)

u i :

Cartesian velocity components (m s−1)

V r, V θ, V z :

Radial, circumferential and axial velocity components (m s−1)

\( {v}_r^{\prime },{v}_{\theta}^{\prime },{v}_z^{\prime } \) :

Fluctuation of radial, circumferential and axial velocity components (m s−1)

x i i-th:

Cartesian coordinates (m)

DNS :

Direct numerical simulation

FD :

Finite difference

ILES :

Implicit large eddy simulation

LES :

Large eddy simulation

RANS :

Reynolds averaged Navier-Stokes

RMS :

Root mean square

SVV :

Spectral vanishing viscosity

SGS :

Sub-grid scale

α :

Turbulent stress on the scalar level

β :

Sub-grid scale pressure-velocity

γ :

Specific heat ratio

δ ij :

Kronecker delta

ε :

Rate of dissipation

η :

Kolomogorov length scale

κ :

Sub-grid scale turbulent dissipation rate

λ T :

Turbulent flow parameter

μ :

Dynamic viscosity (N s m−2)

ν :

Kinematic viscosity (s−1 m2)

π :

Sub-grid scale pressure-dilatation

ρ :

Fluid density (kg m−3)

σ ij :

Viscous stress tensor

τ ij :

Sub-grid scale stress tensor

Ω :

Rotational speed (rpm)

b :

Basic cavity configuration (flat rotor)

m :

Modified cavity configuration (rotor with elliptical bump)

\( \overline{.} \) :

(Filtering)

\( \overset{\sim }{.} \) :

Favre filtering

\( \widehat{.} \) :

Indicates that the quantity is based on filtered variables

\( \overset{=}{.} \) :

Shows the unit surface normal

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The result of this article is a part of ongoing PhD research thesis and there was no funding for this research.

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  1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Mohammad Darvish Damavandi & Amir Nejat

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  1. Mohammad Darvish Damavandi
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Correspondence to Amir Nejat.

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Damavandi, M.D., Nejat, A. Flow Characteristics of Curved Rotor Stator Systems Using Large Eddy Simulation. Flow Turbulence Combust 103, 111–140 (2019). https://doi.org/10.1007/s10494-018-0001-9

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