A fully coupled RANS Spalart–Allmaras SUPG formulation for turbulent compressible flows on stretched-unstructured grids

Wervaecke, Christelle; Beaugendre, Héloïse; Nkonga, Boniface

doi:10.1016/j.cma.2012.04.003

Cited by 15 publications

(7 citation statements)

References 36 publications

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“…For the shock-capturing operator, two choices described in [13,12] are retained, and are described using four sensors. The first sensor is based on the relative density variation and it is defined, in each element, as…”

Section: Stabilization By Artificial Viscositymentioning

confidence: 99%

See 1 more Smart Citation

Shock Capturing Computations With Stabilized Powell-Sabin Elements

Giorgiani¹,

Guillard²,

Nkonga³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Stabilization By Artificial Viscositymentioning

confidence: 99%

“…The second sensor is based on the relative gradient according to the principle axes and is written [ U ] (1−β) e [A ∇U ] −β e . In [12], it is suggested to use β = 1 is for smooth shocks and β = 2 for strong shocks. A compromise between the two definitions is proposed,…”

Section: Stabilization By Artificial Viscositymentioning

confidence: 99%

Shock Capturing Computations With Stabilized Powell-Sabin Elements

Giorgiani¹,

Guillard²,

Nkonga³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…The free convection flow over isogrid elements is more analogous to the flow behavior over discrete obstruction elements such as backward-facing steps, forward-facing steps, ribs, and fences shown in Numerical simulations and comparisons with experimental data have been completed for each of these typical geometries, including the effects of heat transfer. Experimental and numerical simulations for flows over backward-facing steps are discussed in [11][12][13][14][15]. Details of the flow entering into a forward-facing step have been investigated in [16].…”

Section: Boundary-layer Modeling Over Walls With Obstruction Elementsmentioning

confidence: 99%

Effect of Isogrid-Type Obstructions on Thermal Stratification in Upper-Stage Rocket Propellant Tanks

Faure

Oliveira

Chintalapati

et al. 2014

Journal of Spacecraft and Rockets

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Analytical models for propellant thermal stratification are typically based on smooth wall flow correlations. However, many propellant tank walls have a mass-saving isogrid, which alters the boundary layer. This work investigates the boundary-layer behavior over walls with obstruction elements that are representative of isogrid or internal stiffener rings. The experimental studies reveal that the thickness of the velocity boundary layer over an isogrid wall is more than 200% thicker than a smooth wall at full-scale upper-stage tank Reynolds numbers. For buoyancy-induced free convection flows, the computational-fluid-dynamics models demonstrate that the velocity boundary layer over a wall lined with obstruction elements may be thicker or thinner than the equivalent boundary layer over a smooth wall, whereas the thermal boundary layer is always thicker for the rough wall. A Rayleigh number scaling analysis is presented for a range of fluids, tank and obstruction sizes, heat loads, and acceleration levels. When the results are applied to a full-scale liquid-hydrogen tank with obstruction elements, the stratification layer is 18% thicker, and the stratum fluid is 31% warmer than the corresponding results for the smooth wall tank. The increase is attributable to the augmented heat transfer area and enhanced mixing of fluid due to the obstruction element. Nomenclature c p = specific heat at constant pressure, J∕kg · K Gr = Grashof number (based on temperature difference) Gr = modified Grashof number (based on heat flux) g = local gravitational acceleration, m∕s 2 H = initial liquid fill level, m h = obstruction height, m L = tank height, m l = length between obstruction, m _ m = mass flow rate, kg∕s N = number of obstruction elements Nu = Nusselt number P = pressure, N∕m 2 Pr = Prandtl number _ q = heat flux, W∕m 2 R = tank radius, m Ra = Rayleigh number (based on temperature difference) Ra = modified Rayleigh number (based on heat flux) Re = Reynolds number S = run length along the obstruction elements, m s = obstruction element center-to-center spacing distance, m t = time, s; or isogrid element thickness, m U, u = velocity, m∕s x, y, z = length, m α = thermal diffusivity, m 2 ∕s β = volumetric thermal expansion coefficient, 1∕K Δ = thickness of stratified layer, m δ = 99% of U e boundary-layer thickness, m δ = boundary-layer displacement thickness, m ε = obstruction parameter ζ = nondimensional velocity η = yU e ∕νx 1∕2 , nondimensional boundary-layer variable θ = temperature difference between wall and fluid, K; or boundary-layer momentum thickness, m κ = thermal conductivity, W∕m · K μ = dynamic viscosity, N · s∕m 2 ν = kinematic viscosity, m 2 ∕s ξ = nondimensional temperature ρ = density, kg∕m 3 τ = implicit time step, s χ = boundary-layer energy flow rate, J∕s ω = spacecraft rotational spin rate, deg ∕s Subscripts b = bulk fluid bl = boundary layer e = external to boundary layer s = stratum td = touchdown distance behind backward-facing step trans = laminar to turbulent boundary-layer transition distance u = ul...

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“…This allows to directly set the Dirichlet value to the unknown associated to the non-zero shape function. Moreover, from (11) and (12) derives that the other two shape functions have zero derivative in the directions the two edges concurring in V l . In particular, using the notation depicted in Figure 2 …”

Section: Imposition Of the Boundary Conditionsmentioning

confidence: 99%

“…For the shock-capturing operator, the choices described in [12,13] are followed: three sensors are used to set up the artificial viscosity to be used to stabilize discontinuities. The first sensor is based on the relative density variation and it is defined, in each element, as…”

Section: Stabilized Approximation Of the Isothermal Euler Equationsmentioning

confidence: 99%

A Powell-Sabin finite element scheme for partial differential equations

Giorgiani

Guillard²,

Nkonga³

2016

ESAIM: Proc.

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Abstract. In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C 1 continuity. Critical issues when dealing with PS splines, and described in this work, are the construction of the shape functions and the imposition of the boundary conditions. The PS finite element method is used at first to solve an elliptic problem describing plasma equilibrium in a tokamak. Finally, a transient convective problem is also considered, and a stabilized formulation is presented.

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A fully coupled RANS Spalart–Allmaras SUPG formulation for turbulent compressible flows on stretched-unstructured grids

Cited by 15 publications

References 36 publications

Shock Capturing Computations With Stabilized Powell-Sabin Elements

Shock Capturing Computations With Stabilized Powell-Sabin Elements

Effect of Isogrid-Type Obstructions on Thermal Stratification in Upper-Stage Rocket Propellant Tanks

A Powell-Sabin finite element scheme for partial differential equations

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