Numerical Treatment of Polar Coordinate Singularities

Mohseni, Kamran; Colonius, Tim

doi:10.1006/jcph.1999.6382

Cited by 275 publications

(207 citation statements)

References 27 publications

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“…For the treatment of the axis singularity, the method proposed by Mohseni and Colonius [48] is used, and to increase the time step the effective azimuthal resolution is reduced near the jet centerline [49]. The LES approach is based on the explicit application of a relaxation filtering to the flow variables [50] to take into account the dissipative effects of the subgrid scales.…”

Section: B Numerical Methodsmentioning

confidence: 99%

Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation

2011

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An initially laminar overexpanded round jet at an exit Mach number of 3.30 and a Reynolds number of 10 5 is calculated by compressible large-eddy simulation. The near field obtained by large-eddy simulation is also propagated to the acoustic far field by solving the full Euler equations to take into account the nonlinear propagation effects. Both computations are performed using low-dissipation finite differences in combination with an adaptive shock-capturing method. The jet originates from a straight pipe nozzle of radius r e , including lips of thickness 0:05r e . At the pipe exit, Blasius mean flow profiles are imposed, and static pressure and temperature are equal to 0:5 10 5 Pa and 360 K, resulting in fully adapted and acoustic Mach numbers, respectively, of 2.83 and 3.47. The jet flowfields, as well as the acoustic near and far fields, are described in detail and compared with data of the literature. The turbulent mechanisms developing in the jet are investigated, using spectral and azimuthal decompositions of the velocity fluctuations along the shear layers. Same analyses are applied to the acoustic fields, in order to discuss the properties of jet noise components. In this way, Mach waves, shock-associated noise, screech tones, and turbulent mixing noise are identified. = first shock location on the jet axis = specific heat ratio r = mesh size in the radial direction z = mesh size in the axial direction = boundary-layer thickness in the pipe nozzle 0:5 = jet half-width e = exit molecular viscosity e = exit density = radiation angle measured according to the flow direction

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Section: B Numerical Methodsmentioning

confidence: 99%

Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation

2011

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“…The singularity at the centerline (pole) of the system is removed by the finite volume method because all terms in the equations are multiplied by the Jacobian r 2 sin θ (for example, see [17]). The grid is non-uniform in the streamwise direction which allows for accurate calculation near the orifice without using too many grid points in the far-field.…”

Section: Computational Geometry and Numerical Schemementioning

confidence: 99%

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Agrawal

Boersma

Prasad

2005

Flow Turbulence Combust

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Abstract. Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, crossstream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.

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“…We solve the Navier-Stokes equations for compressible flow in cylindrical coordinates using a conservative formulation. The centreline singularity of the governing equations is treated by a method proposed by Mohseni & Colonius [5]. This approach uses a shifted grid in the radial direction and thus avoids placing a grid point at the polar axis (r = 0).…”

Section: Simulation Techniquesmentioning

confidence: 99%

Assessment of high‐order discretization schemes for the DNS of compressible swirling mixing layers

Müller

Kleiser

2007

Proc Appl Math and Mech

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We report on results of highly accurate Direct Numerical Simulations (DNS) solving the Navier-Stokes equations in cylindrical coordinates. The DNS code computes a compressible swirling mixing layer at Mach number Ma = 0.8. We present two simulations differing in the spatial discretization schemes for the convective terms. On the same grid, comparisons of flow simulations using different discretization schemes for otherwise identical conditions can be performed quantitatively and improve the understanding of the effects of numerical errors and in particular numerical dissipation. Simulation techniquesWe report on a compressible swirling mixing layer (i.e. a circular mixing layer with an additional swirl component which is present only in the shear layer) at Mach number M a = 0.8 and Reynolds number Re = 5000 (based on the jet radius and centerline quantities as reference quantities). This flow incorporates the nonlinear disturbance development and transition to turbulence of the laminar layer perturbed at the inflow by viscous spatial instabilities.The differences of the computational schemes are shortly outlined as follows. One discretization uses compact fifth-order accurate upwind-biased schemes (see Adams & Shariff [1]) in all spatial directions for the convective terms combined with fourth-order accurate boundary closures. For the diffusive terms, up to tenth-order central compact finite differences (Lele [2]) in the radial and axial directions and a Fourier spectral method in the azimuthal direction are employed. Towards the boundary the schemes are of sixth order at the second next-to-boundary nodes, of fifth order at the next-to-boundary nodes and of third order at boundary points, resulting in an overall fourth-order scheme. The corresponding modified wavenumbers (Lele [2]) are improved at all scales (compared to an explicit finite-difference scheme).The other discretization applies the (up to tenth-order) compact centered schemes and Fourier spectral method to all flux terms, combined with an additional secondary filter operation, corresponding toQ 5Ĝ in the approximate deconvolution model (ADM) relaxation term (RT), see Ref.[3]. The high-order filter is applied every second time step to ensure numerical stability.Our computational code is based on a conservative formulation of the compressible Navier-Stokes equations expressed in generalized coordinates (see Adams [4]). The governing equations are non-dimensionalized using the jet radius r * j = D * j /2, the jet centreline exit velocity W * j , density ρ * j , dynamic viscosity µ * j and temperature T * j (quantities with an asterisk denote dimensional quantities). The Reynolds number is given by Re = ρ * j W * j r * j /µ * j and the Mach number by M a = W * j / γ * R * T * j 1/2 where γ * is the isentropic coefficient and R * is the gas constant for air. We solve the Navier-Stokes equations for compressible flow in cylindrical coordinates using a conservative formulation. The centreline singularity of the governing equations is treated by a method pr...

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Numerical Treatment of Polar Coordinate Singularities

Cited by 275 publications

References 27 publications

Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation

Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Assessment of high‐order discretization schemes for the DNS of compressible swirling mixing layers

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