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Status of turbulence modeling for hypersonic propulsion flowpaths

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Abstract

This report provides an assessment of current turbulent flow calculation methods for hypersonic propulsion flowpaths, particularly the scramjet engine. Emphasis is placed on Reynolds-averaged Navier–Stokes (RANS) methods, but some discussion of newer methods such as large eddy simulation (LES) is also provided. The report is organized by considering technical issues throughout the scramjet-powered vehicle flowpath, including laminar-to-turbulent boundary layer transition, shock wave/turbulent boundary layer interactions, scalar transport modeling (specifically the significance of turbulent Prandtl and Schmidt numbers), and compressible mixing. Unit problems are primarily used to conduct the assessment. In the combustor, results from calculations of a direct connect supersonic combustion experiment are also used to address the effects of turbulence model selection and in particular settings for the turbulent Prandtl and Schmidt numbers. It is concluded that RANS turbulence modeling shortfalls are still a major limitation to the accuracy of hypersonic propulsion simulations, whether considering individual components or an overall system. Newer methods such as LES-based techniques may be promising, but are not yet at a maturity to be used routinely by the hypersonic propulsion community. The need for fundamental experiments to provide data for turbulence model development and validation is discussed.

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Abbreviations

C f :

Skin friction coefficient

C p :

Specific heat at constant pressure

d :

Distance from wall

D :

Nozzle exit diameter

D t :

Turbulent species diffusivity

h :

Static enthalpy

H :

Fuel injector ramp height for scramjet test case

k :

Turbulent kinetic energy

k t :

Turbulent thermal conductivity

K :

Pressure gradient parameter

M :

Mach number

M t :

Turbulent Mach number

P :

Static pressure

\({\mathcal{P}_k}\) :

Production of turbulent kinetic energy

\({\dot{q}_{w}}\) :

Rate of wall heat flux

Pr t :

Turbulent Prandtl number

R y :

Turbulent Reynolds number based on wall distance = \({\rho y \sqrt{k}/\mu}\)

R t :

Turbulent Reynolds number = \({\rho k/\mu \omega}\)

Re x :

Plate Reynolds number

\({Re_{\nu}}\) :

Vorticity-based Reynolds number = \({\rho y^{2}\Omega/\mu}\)

s :

Streamline coordinate

S ij :

Rate of strain tensor

Sc t :

Turbulent Schmidt number

St :

Stanton number

t :

Time

T :

Static temperature

T r :

Temperature ratio

T t :

Stagnation temperature

T w :

Wall static temperature

U j :

Velocity vector

U ∞ :

Freestream velocity

W ij :

Vorticity tensor

x, y, z :

Cartesian coordinates

y + :

Wall normal coordinate

\({\epsilon}\) :

Turbulent dissipation rate

\({\epsilon_s}\) :

Solenoidal turbulent dissipation rate

\({\mu}\) :

Dynamic viscosity

\({\mu_t}\) :

Dynamic eddy viscosity

\({\omega}\) :

Specific turbulent dissipation rate = \({\epsilon/\beta^{*}k}\)

\({\Omega}\) :

Vorticity magnitude

\({\phi}\) :

Fuel equivalence ratio

\({\rho}\) :

Density

\({\rho_{\infty}}\) :

Freestream density

\({\tau^{T}_{ij}}\) :

Turbulent stress tensor

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  1. NASA Glenn Research Center, Cleveland, OH, 44135, USA

    Nicholas J. Georgiadis, Dennis A. Yoder & Manan A. Vyas

  2. Embry Riddle Aeronautical University, Daytona Beach, FL, 32114, USA

    William A. Engblom

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  1. Nicholas J. Georgiadis
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Georgiadis, N.J., Yoder, D.A., Vyas, M.A. et al. Status of turbulence modeling for hypersonic propulsion flowpaths. Theor. Comput. Fluid Dyn. 28, 295–318 (2014). https://doi.org/10.1007/s00162-013-0316-z

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