# Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

## Abstract

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

- Authors:

- Publication Date:

- Research Org.:
- National Aeronautics and Space Administration, Cleveland, OH (USA). Lewis Research Center

- OSTI Identifier:
- 6516956

- Report Number(s):
- N-90-25948; NASA-TM-102402; E-5155; NAS-1.15:102402; ICOMP-89-29

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; UNSTEADY FLOW; COMPUTERIZED SIMULATION; COMPRESSIBILITY; CONSERVATION LAWS; CRAY COMPUTERS; DIFFERENTIAL EQUATIONS; KINETIC ENERGY; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; ROTORS; RUNGE-KUTTA METHOD; TIME DEPENDENCE; TURBULENCE; COMPUTERS; ENERGY; EQUATIONS; FLUID FLOW; ITERATIVE METHODS; MECHANICAL PROPERTIES; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; SIMULATION; 420400* - Engineering- Heat Transfer & Fluid Flow

### Citation Formats

```
Boretti, A A.
```*Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows*. United States: N. p., 1990.
Web.

```
Boretti, A A.
```*Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows*. United States.

```
Boretti, A A. Sun .
"Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows". United States.
```

```
@article{osti_6516956,
```

title = {Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows},

author = {Boretti, A A},

abstractNote = {Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.},

doi = {},

url = {https://www.osti.gov/biblio/6516956},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1990},

month = {7}

}