Modeling the Effect of Stability Bleed on Back-Pressure in Mixed-Compression Supersonic Inlets

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Lv Yongzhao ◽  
Li Qiushi ◽  
Li Shaobin
Keyword(s):  
Mach Number ◽  
Flow Rate ◽  
Stokes Equations ◽  
Functional Relation ◽  
Back Pressure ◽  
Normal Shock ◽  
Navier Stokes ◽  
Correction Coefficient ◽  
Navier Stokes Equations ◽  
Plenum Pressure

To stabilize the terminal normal shock on high-static pressure at outlet, called back-pressure pout, stability bleed slots are used in the throat of mixed-compression supersonic inlets. In this paper, a model for the functional relation between the bleed flow rate mbl and back-pressure pout is established based on a bleed flow rate model (BFRM) in order to study the effect of stability bleed on the back-pressure in mixed-compression supersonic inlets. Given the inlet flow parameters Min, pin*, and Tin*, the plenum pressure ppl at slots' outlet, the terminal normal shock position xs in this model, the bleed flow rate mbl, Mach number M¯out, and back-pressure pout were derived one by one from the basic laws of conservation. To study the effect of plenum pressure ppl on subsonic flow of the divergent section behind the terminal normal shock, a correction coefficient κ is introduced to modify the Mach number M¯out. Furthermore, numerical simulations based on Reynolds-Averaged Navier–Stokes equations were performed to analyze the functional relation between the bleed flow rate mbl and back-pressure pout. Computational fluid dynamics (CFD) results show that the present model agrees with the data.

A quasi one-dimensional bleed flow rate model for terminal normal shock stability in mixed compression supersonic inlet

2014 ◽  
Vol 228 (14) ◽  
pp. 2569-2583 ◽  
Author(s):  
Li Qiushi ◽  
Lv Yongzhao ◽  
Li Shaobin
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Normal Shock ◽  
Navier Stokes ◽  
Rate Model ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Supersonic Inlet ◽  
The Stability

Ninety-degree (normal) bleed slots have been used to stabilize the terminal normal shock in the throat of a mixed compression supersonic inlet. In this study, a quasi-one-dimensional bleed flow rate model, consisting of a constant-area channel with a pair of normal slots symmetrically located along the upper and lower endwalls, is developed. The bleed flow rate is shown to be a function of the terminal normal shock position within the slot. Some key factors, such as the bleed discharge coefficient, taken from the Bragg model, were derived from the basic laws of conservation for a one-dimensional simplification. Furthermore, numerical simulations based on Reynolds-averaged Navier–Stokes equations were performed to analyze the flow characteristics around the bleed slots. The predictions of the bleed flow rate model agree well with computational fluid dynamics results. This method may be helpful to predict the stability of the terminal normal shock in mixed compression supersonic inlets.

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

scholarly journals On the Low Mach Number Limit for Quantum Navier--Stokes Equations

2020 ◽  
Vol 52 (6) ◽  
pp. 6105-6139
Author(s):  
Paolo Antonelli ◽  
Lars Eric Hientzsch ◽  
Pierangelo Marcati
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

scholarly journals A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

2015 ◽  
Vol 771 ◽  
pp. 520-546 ◽  
Author(s):  
Nicola De Tullio ◽  
Anatoly I. Ruban
Keyword(s):  
Mach Number ◽  
Boundary Layers ◽  
Asymptotic Theory ◽  
Stokes Equations ◽  
Roughness Element ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Compressible Boundary Layers ◽  
Tollmien Schlichting ◽  
Low Amplitude

The capabilities of the triple-deck theory of receptivity for subsonic compressible boundary layers have been thoroughly investigated through comparisons with numerical simulations of the compressible Navier–Stokes equations. The analysis focused on the two Tollmien–Schlichting wave linear receptivity problems arising due to the interaction between a low-amplitude acoustic wave and a small isolated roughness element, and the low-amplitude time-periodic vibrations of a ribbon placed on the wall of a flat plate. A parametric study was carried out to look at the effects of roughness element and vibrating ribbon longitudinal dimensions, Reynolds number, Mach number and Tollmien–Schlichting wave frequency. The flat plate is considered isothermal, with a temperature equal to the laminar adiabatic-wall temperature. Numerical simulations of the full and the linearised compressible Navier–Stokes equations have been carried out using high-order finite differences to obtain, respectively, the steady basic flows and the unsteady disturbance fields for the different flow configurations analysed. The results show that the asymptotic theory and the Navier–Stokes simulations are in good agreement. The initial Tollmien–Schlichting wave amplitudes and, in particular, the trends indicated by the theory across the whole parameter space are in excellent agreement with the numerical results. An important finding of the present study is that the behaviour of the theoretical solutions obtained for $\mathit{Re}\rightarrow \infty$ holds at finite Reynolds numbers and the only conditions needed for the theoretical predictions to be accurate are that the receptivity process be linear and the free-stream Mach number be subsonic.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Steady streaming in a turbulent oscillating boundary layer

2007 ◽  
Vol 571 ◽  
pp. 265-280 ◽  
Author(s):  
PIETRO SCANDURA
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Time Average

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

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