The starting flow structures and evolution of a supersonic planar jet

Zhang, Huanhao; Chen, Zhihua; Jiang, Xin; Huang, Zhengui

doi:10.1016/j.compfluid.2015.02.013

Cited by 17 publications

(9 citation statements)

References 46 publications

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“…Free supersonic jet flow is widely studied. A simplified 2-D planar jet, which was proposed by Zhang et al [44], is used here to test high order GKS. A Mach 1.4 jet is injected through a width L = 0.01m entrance into a square computational domain with the size 10L × 10L.…”

Section: (B) a Planar Jet Under High Reynolds Numbermentioning

confidence: 99%

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A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

Zhao

Shyy

et al. 2018

Journal of Computational Physics

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Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The main advantage of this kind of approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which is very time and memory consuming for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages, once the time derivatives of the flux function is used. For the traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the secondorder or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd-to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th-order and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a multidimensional scheme with incorporation of both normal and tangential spatial derivatives of flow variables at a cell interface in the flux evaluation. The scheme can be extended straightforwardly to viscous flow computation in unstructured mesh. It provides a promising direction for the development of high-order CFD methods for the computation of complex flows, such as turbulence and acoustics with shock interactions.

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Section: (B) a Planar Jet Under High Reynolds Numbermentioning

confidence: 99%

“…(a) Schematic of the computational domain (b) Case 3 result at t=0.15msFigure 12: (a) The sketch of a planar jet case proposed in[44]. (b) The 2-D result without entrance perturbation in[44], at t=0.15ms. The numerical schlieren-type images are plotted for visualization.…”

mentioning

confidence: 99%

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

Zhao

Shyy

et al. 2018

Journal of Computational Physics

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“…The compressible LES equations can be obtained by Favre filtering the multi‐component compressible Navier–Stokes equations in the Cartesian coordinate system [15]. For closing the multi‐component LES equations, the stretched‐vortex subgrid scales model [16–19] is chosen to approach the unresolved subgrid terms.…”

Section: Numerical Methods and Physical Modelmentioning

confidence: 99%

Mixing characteristic ofboth subsonic and supersonic unsteady circular jets

Zhang

Chen

Sun

et al. 2018

J. eng.

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“…[1][2][3] Also, because of many important physical phenomena, the starting flow fields of supersonic jets have been studied previously. 4,5 Moreover, interaction of the starting flow fields of supersonic jets with rigid bodies are found in many areas of aerospace and mechanical engineering; however there are not many works reported in this field. This paper focuses on unsteady supersonic flows and is concerned with the development of a simple implicit pressure correction method for computing compressible fluids and extending it to the ability of handle supersonic axisymmetric flows, which contain strong shocks.…”

Section: Introductionmentioning

confidence: 99%

“…6 In the starting flow of a supersonic jet, the shock diffraction leads to the misalignment of the pressure and density gradients and makes a vortex ring which moves downstream like a mushroom head. 5,7 The interactions of the acoustic wave and the mushroom head with the rigid body lead to propagate the acoustic waves from the impingement region out and toward the nozzle exit. Also, overexpansion of the flow occurs at the cylinder lip.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the Supersonic Starting Jet Flow Interactions with a Rigid Body

Azizian¹

2017

AAOAJ

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The interaction of starting flow fields of an axisymmetric supersonic under-expanded jet with the cross section of a cylinder is simulated. To achieve this goal, an implicit pressure correction algorithm based on a finite volume method on a collocated grid for simulation of compressible flows is presented. A two dimensional test problem, the supersonic flow through a wind tunnel with a step, is simulated and the numerical outcomes agree very well with previous results. Then, the method is extended to axisymmetric flows and validated for a supersonic circular jet flow. Finally, the proposed method is used to analyze the concerned problem. To describe the evolution of the starting flow fields, the Mach number, pressure, density and temperature contours evolutions through time are investigated. Also, the evolution of total force and temperature distribution on the cylinder cross section surface are studied during the collision of mushroom head of supersonic jet with the surface of cylinder. Keywordswhere γ is the ratio of specific heats, and by using this equation in energy equation (eq. 3), the number of variables are reduced.In the aforementioned governing equations, the conservation forms are used that the fluxes of mass, momentum and energy into and out of the control volume, themselves become important dependent variables rather than just the primitive variables. This is due to the fact that there are discontinuities in primitive variables across the shock; however, the fluxes are constant across the shock wave. 9To non-dimensionalization, the reference variables are used as follow:Where , r r u ρ and L are reference velocity, density and length, respectively. In this way, the non-dimensional governing equations are: AlgorithmThe variables are collocated in space at the center of control volumes. Moreover, the numerical method is implicit in time. The governing equations can be discretized by integrating over a control volume and using the Gauss theorem as follows:. . . .where the superscripts denote the time steps. Also, the subscripts c,v and face represent the values at the center of control volumes and the values that located on the control volume surfaces, respectively.Here, V and face A determine the volume and surface area of the control volumes. Furthermore, i g is the momentum in the direction of i and N u is the face normal velocity, which is acquired by projection and nor that interpolation. 10To find the values on the control volume surfaces, which there are in the convection term of the governing equations, the following scheme is used:Where Q can be each of the terms on the control volume surfaces. At the vicinity of discontinuity w i takes the value of +1 and -1 depends on the flow direction, but in the rest of the domain it takes the value of zero.Adapted from the researches of Hou & Mahesh, 10,11 the algorithm is based on a pressure-correction method, which the face normal velocities are projected to satisfy a constraint on the divergence that is determined by the energy equation. Thi...

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The starting flow structures and evolution of a supersonic planar jet

Cited by 17 publications

References 46 publications

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

Mixing characteristic ofboth subsonic and supersonic unsteady circular jets

Simulation of the Supersonic Starting Jet Flow Interactions with a Rigid Body

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