Viscous flow in a mixed compression intake

Kotteda, V. M. Krushnarao; Mittal, Sanjay

doi:10.1002/fld.2423

Cited by 12 publications

(9 citation statements)

References 24 publications

(39 reference statements)

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“…The second series of element level integrals in the formulation given by Equation are the shock‐capturing terms that stabilize the computations in the presence of sharp gradients. The stabilization coefficients δ and τ are defined as

τ = max (0, τ_{a} - τ_{δ}),

τ_{a} = {((), {((), \frac{2 ∥ boldu ∥}{h_{e}})}^{2} + {((), \frac{12 ν}{h_{e}^{2}})}^{2})}^{- \frac{1}{2}} boldI,

τ_{δ} = \frac{δ}{2 {(c + ∥ boldu ∥)}^{2}} boldI,

δ = ([], ((), \frac{\partial {boldU}^{h}}{∂t} + {boldA}_{i} \frac{\partial {boldU}^{h}}{\partial x_{i}} - \frac{\partial}{\partial x_{i}} ((), {boldK}_{ij}^{h} \frac{\partial {boldU}^{h}}{\partial x_{j}})) \cdot {boldA}_{0}^{- 1} ((), \frac{\partial {boldU}^{h}}{∂t} + {boldA}_{j} \frac{\partial {boldU}^{h}}{\partial x_{i}} - \frac{\partial}{\partial x_{j}}))

…”

Section: Finite‐element Formulationmentioning

confidence: 99%

“…Most studies that use the stabilized finite‐element method, for computing compressible flows, employ first‐order shape functions . Higher‐order methods provide geometric flexibility and are more efficient than low‐order methods, for problems that involve wave propagation, vortex‐dominated flows including high‐lift configuration.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, the stabilized finite‐element formulation is employed with quadratic interpolation. The stabilization coefficients for the linear triangular interpolation are the ones that were used in our earlier work and similar to those employed by Aliabadi and Tezduyar . These definitions are extended to quadratic elements.…”

Section: Introductionmentioning

confidence: 99%

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Stabilized finite‐element computation of compressible flow with linear and quadratic interpolation functions

Kotteda

Mittal

2014

Numerical Methods in Fluids

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SUMMARYThe unsteady compressible flow equations are solved using a stabilized finite‐element formulation with C0 elements. In 2D, the performance of three‐noded linear and six‐noded quadratic triangular elements is compared. In 3D, the relative performance is evaluated for 6‐noded linear and 18‐noded quadratic wedge elements. Results are compared for the solutions to Euler, laminar, and turbulent flows at different Mach numbers for several flow problems. The finite‐element meshes considered for comparison have same location of nodes for the linear and quadratic interpolations. For the turbulent flow, the Spalart–Allmaras model is used for closure. It is found that the quadratic elements yield better performance than the linear elements. This is attributed to accurate representation of the stabilization terms that involve second‐order derivatives in the formulation. When these terms are dropped from the formulation with quadratic interpolation, the numerical results are similar to those obtained with linear interpolation. The absence of these terms result in added numerical diffusion that seems to give the effect of a relatively reduced Reynolds number. For the same location of nodes, the computations with the linear triangular and wedge elements are approximately 20% and 100% faster than those with quadratic triangular and wedge elements, respectively. However, if the same quadrature rule for numerical integration is used for both interpolations, the computations with quadratic elements are approximately 20% and 45% faster in 2D and 3D, respectively. Copyright © 2014 John Wiley & Sons, Ltd.

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τ = max (0, τ_{a} - τ_{δ}),

τ_{a} = {((), {((), \frac{2 ∥ boldu ∥}{h_{e}})}^{2} + {((), \frac{12 ν}{h_{e}^{2}})}^{2})}^{- \frac{1}{2}} boldI,

τ_{δ} = \frac{δ}{2 {(c + ∥ boldu ∥)}^{2}} boldI,

δ = ([], ((), \frac{\partial {boldU}^{h}}{∂t} + {boldA}_{i} \frac{\partial {boldU}^{h}}{\partial x_{i}} - \frac{\partial}{\partial x_{i}} ((), {boldK}_{ij}^{h} \frac{\partial {boldU}^{h}}{\partial x_{j}})) \cdot {boldA}_{0}^{- 1} ((), \frac{\partial {boldU}^{h}}{∂t} + {boldA}_{j} \frac{\partial {boldU}^{h}}{\partial x_{i}} - \frac{\partial}{\partial x_{j}}))

…”

Section: Finite‐element Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilized finite‐element computation of compressible flow with linear and quadratic interpolation functions

Kotteda

Mittal

2014

Numerical Methods in Fluids

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“…Performance characteristics of inlet in cases of extensive maneuvering range [3,4], unstart [5], buzz phenomenon, and application of boundary-layer bleed [6][7][8][9][10][11][12][13][14] have recently been investigated. In addition to these experiments, many computational studies have been accomplished on the supersonic inlet ow and buzz phenomenon as well as ow control methods [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Effects of Shock Wave/Boundary-Layer Interaction on Performance and Stability of a Mixed-Compression Inlet

Soltani¹,

Daliri²,

Sepahi-Younsi³

2016

Scientia Iranica

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Abstract. Experiments were conducted to study various kinds of Shock wave/BoundaryLayer Interaction (SBLI) in an axisymmetric mixed-compression inlet. Experimental ndings were compared and veri ed by numerical solutions where possible. Di erent types of SBLI relevant to the mixed-compression inlets are classi ed. Interactions of normal shock wave/boundary-layer at subcritical condition and in buzz condition are investigated using Schlieren and shadowgraph ow visualization as well as unsteady pressure recordings. The data is compared with the CFD predictions. Interactions of cowl lip re ected oblique shock and the terminal normal shock with the spike boundary-layer at both critical and supercritical operations, which lead to pseudo-shock phenomena, are also studied. Experimental pressure recordings are used for validation and discussion. For near-critical throttling values, interaction of internal compression oblique shocks with boundary-layer and pseudo-shock phenomenon is dominant. Formation of lambda shock due to interaction of separated boundary-layer with normal shock wave is investigated. Each type of ow interaction phenomena has di erent e ects on the stability and performance of the inlet. Interaction of terminal normal shock with internal duct boundary-layer causes pseudoshock phenomenon that increases ow distortion and reduces total pressure recovery. Interaction of normal shock with cone boundary-layer causes buzz instability and degrades inlet performance.

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“…SST were used for the evaluation of turbulent ow quantities. Kotteda and Mittal [14] solved unsteady viscous ow in a two-dimensional mixed compression inlet with a stabilized nite-element method. In this study, the e ect of bleed on the control of buzz instability and starting/unstarting of the inlet was investigated.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Back Pressure and Free-stream Effects on a Mixed Compression Inlet Performance

Ebrahimi

Chavoshi

2017

Scientia Iranica

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Abstract. Inlet performance has an important role in the operation of air-breathing propulsion systems. In this study, performance of a supersonic axisymmetric mixedcompression inlet in the supercritical operating condition is numerically studied. The e ects of free-stream Mach number and engine-face pressure on performance parameters, including mass ow ratio, drag coe cient, total pressure recovery, and ow distortion, are investigated. For this sake, a multi-block density-based nite volume CFD code is developed, and Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras oneequation turbulence model are employed. The code is validated by comparing numerical results against other computational results and experimental data for two test cases of inviscid ow in a two-dimensional mixed-compression inlet and ow in an external compression inlet. Finally, the code is utilized for the investigation of a speci c supersonic mixed-compression inlet with the design Mach number of 2.0 and length-to-diameter ratio of 3.4. Results revealed that the increment of free-stream Mach number leads to the decrease in total pressure recovery and drag coe cient, while mass ow ratio and ow distortion increase. The e ects of engine-face pressure on performance parameters showed that by increasing the engine-face pressure, mass ow ratio and drag coe cient remain constant, while total pressure recovery increases and ow distortion decreases.

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Viscous flow in a mixed compression intake

Cited by 12 publications

References 24 publications

Stabilized finite‐element computation of compressible flow with linear and quadratic interpolation functions

Stabilized finite‐element computation of compressible flow with linear and quadratic interpolation functions

Effects of Shock Wave/Boundary-Layer Interaction on Performance and Stability of a Mixed-Compression Inlet

Numerical Investigation of Back Pressure and Free-stream Effects on a Mixed Compression Inlet Performance

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