Compressible Flow Simulations Over Basic Reusable Rocket Configurations

2003 ◽  
Author(s):  
Keiichiro Fujimoto ◽  
Kozo Fujii
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Compressible Flow ◽  
Simulation Method ◽  
Aerodynamic Characteristics ◽  
Pressure Level ◽  
The Body ◽  
Navier Stokes ◽  
Aerodynamic Coefficients ◽  
Flow Simulations

Compressible flow around the basic reusable rocket configurations are numerically simulated by Navier-Stokes computations. The study started with the simulations of Apollo configuration to validate the simulation method by the comparison of the aerodynamic data with NASA’s experiments, and the capability of CFD estimation are discussed. Computed aerodynamic coefficients for the Apollo agreed well with the experiments at subsonic to supersonic flow regime for whole angle of attack range. Then, the effects of the configuration parameters on the aerodynamic characteristics are numerically investigated and clarified in detail. It turns out that the aerodynamic characteristicsismainlyinfluenced by the separating position of the flow, shock wave on the surface and the pressure level behind the body. Large shoulder radius causes the strong Mach number dependency of the aerodynamic characteristics, and large fineness ratio strongly influences to the (CL)max.

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2161-2175 ◽  
Author(s):  
M Parmar ◽  
A Haselbacher ◽  
S Balachandar
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Propagation Speed ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Unsteady Force ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Cylinders And Spheres

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c ∞ t / R ≳10, where c ∞ is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

scholarly journals Numerical Investigation of Flow around Two Tandem Identical Trapezoidal Cylinders

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yupu Wang ◽  
Wenming Cheng ◽  
Run Du ◽  
Shubiao Wang ◽  
Yong Deng
Keyword(s):  
Flow Instability ◽  
Flow Characteristics ◽  
Simulation Method ◽  
Streamwise Velocity ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Mode Iii ◽  
Extended Body ◽  
Spacing Ratio ◽  
Volume Method

The trapezoidal beam structure is ubiquitous in giant engineering equipment, while their aerodynamic characteristics have not been clearly understood. Numerical simulation method was adopted to investigate the flow around two tandem identical trapezoidal cylinders. The study was conducted using a Reynolds number of 2.2 × 104, and with a spacing ratio varying from 0.5 to 10. The incompressible two-dimensional finite volume method was used for solving Reynolds-Averaged Navier–Stokes (RANS) equations with realizable k−ε model. The effects of cylinder geometry and spacing between the cylinders on aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics, and flow instability was studied. The results show that the flow around the two tandem trapezoidal cylinders is highly dependent on the spacing ratio. The flow modes can be classified into: extended-body regime (Mode I, S∗ ≤ 1), reattachment regime (Mode II, 2 ≤ S∗ ≤ 3), and binary regime (Mode III, S∗ ≥ 4). We explored their respective flow characteristics and distinctions through the force/pressure coefficients, time-average streamwise velocity, and the flow field evolution.

A 3-D Thin Layer Navier-Stokes Code for Supersonic Laminar and Turbulent Flows

2002 ◽  
Author(s):  
Omid Abouali ◽  
Mohammad M. Alishahi ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Mach Number ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Cross Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Laminar And Turbulent Flows ◽  
Circumferential Pressure

A 3-D Thin Layer Navier-Stokes (TLNS) code for solving viscous supersonic flows is developed. The new code uses several numerical algorithms for space and time discretization together with appropriate turbulence modeling. Roe’s method is used for discretizing the convective terms and the central differencing scheme is employed for the viscous terms. An explicit time marching technique and a finite volume space discretization are used. The developed computational model can handle both laminar and turbulent flows. The Baldwin-Lomax model and Degani-Schiff modifications are used for turbulence modeling. The computational model is applied to a hypersonic laminar flow at Mach 7.95 around a cone at different incidence angles. The circumferential pressure distribution is compared with the experimental data. The cross-sectional Mach number contours are also presented. It is shown that in addition to the outer shock, a cross-flow shock wave is also present in the flow field. The cases of supersonic turbulent flows with Mach number 3 around a tangent-ogive with incidence angles of 6° and a secant-ogive with incidence angles of 10° are also studied. The circumferential pressure distributions are compared with the experimental data and the Euler code results and good agreement is obtained. The cross-sectional Mach number contours are also presented. It is shown that in this case also in addition to the outer shock, a cross-flow shock wave is also present at the incidence angle of 10°.

Numerical Simulation on Aerodynamics of Ramjet Projectiles

2011 ◽  
Vol 201-203 ◽  
pp. 89-92 ◽  
Author(s):  
Jia Xian Zhang ◽  
Yan Na Wang ◽  
Rui Min Liu
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Pressure Center ◽  
Complex Wave ◽  
Center Increase

Three-dimensional Reynolds-averaged Navier-Stokes simulations have been performed to explore the aerodynamic characteristics of ramjet projectiles. The turbulence model used is the RNG k-ε model. The numerical algorithms termed total variational diminishing (TVD) was adopted. The complex wave structures of ramjet projectiles with different architecture at different inflow Mach number were achieved by numerical simulation. The influence of inflow Mach number on aerodynamic characteristics and pressure center of ramjet projectiles were analyzed. Results show that lift coefficient and pressure center increase with the argument of inflow Mach number. Ramjet projectiles with different architecture have different drag coefficient trend.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

Lift and drag in two-dimensional steady viscous and compressible flow

2015 ◽  
Vol 784 ◽  
pp. 304-341 ◽  
Author(s):  
L. Q. Liu ◽  
J. Y. Zhu ◽  
J. Z. Wu
Keyword(s):  
Mach Number ◽  
Viscous Flow ◽  
Compressible Flow ◽  
Velocity Component ◽  
Transverse Velocity ◽  
The Body ◽  
Far Field ◽  
Two Dimensional ◽  
Wide Range ◽  
Lift And Drag

This paper studies the lift and drag experienced by a body in a two-dimensional, viscous, compressible and steady flow. By a rigorous linear far-field theory and the Helmholtz decomposition of the velocity field, we prove that the classic lift formula $L=-{\it\rho}_{0}U{\it\Gamma}_{{\it\phi}}$, originally derived by Joukowski in 1906 for inviscid potential flow, and the drag formula $D={\it\rho}_{0}UQ_{{\it\psi}}$, derived for incompressible viscous flow by Filon in 1926, are universally true for the whole field of viscous compressible flow in a wide range of Mach number, from subsonic to supersonic flows. Here, ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$ denote the circulation of the longitudinal velocity component and the inflow of the transverse velocity component, respectively. We call this result the Joukowski–Filon theorem (J–F theorem for short). Thus, the steady lift and drag are always exactly determined by the values of ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$, no matter how complicated the near-field viscous flow surrounding the body might be. However, velocity potentials are not directly observable either experimentally or computationally, and hence neither are the J–F formulae. Thus, a testable version of the J–F formulae is also derived, which holds only in the linear far field. Due to their linear dependence on the vorticity, these formulae are also valid for statistically stationary flow, including time-averaged turbulent flow. Thus, a careful RANS (Reynolds-averaged Navier–Stokes) simulation is performed to examine the testable version of the J–F formulae for a typical airfoil flow with Reynolds number $Re=6.5\times 10^{6}$ and free Mach number $M\in [0.1,2.0]$. The results strongly support and enrich the J–F theorem. The computed Mach-number dependence of $L$ and $D$ and its underlying physics, as well as the physical implications of the theorem, are also addressed.

scholarly journals Method of approximation of ballistic missile aerodynamic characteristics at the powered flight segment depending on the Mach number and angle of attack

2021 ◽  
pp. 57-63
Author(s):  
P. A. Krasheninnikov
Keyword(s):  
Mach Number ◽  
Drag Coefficient ◽  
Angle Of Attack ◽  
Aerodynamic Characteristics ◽  
Ballistic Missile ◽  
Aerodynamic Coefficients ◽  
Calculation Process ◽  
The Impact

The paper describes the impact of aerodynamic coefficients on the ballistic target (BT) velocity and proposes a method of approximation of the dependence of ballistic target drag coefficient Cxa on the Mach number and angle of attack. The paper proves that the proposed approach allows to substantially reduce errors in drag coefficient simulation, but requires a more complicated calculation process.

Reynolds Number Effect Investigation of Shock Wave on Supercritical Airfoil

2014 ◽  
Vol 548-549 ◽  
pp. 520-524
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Reynolds Number Effects ◽  
Shock Location

The supercritical airfoil has been widely applied to large airplanes for sake of high aerodynamic efficiency. But at transonic speeds, the shock wave on upper surface of supercritical airfoil may induce boundary layer separation, which would change the aerodynamic characteristics. The shock characteristics such as location and intensity are sensitive to Reynolds number. In order to predict aerodynamic characteristics of supercritical airfoil exactly, the Reynolds number effects of shock wave must be investigated.The transonic flows over a typical supercritical airfoil CH were numerically simulated with two-dimensional Navier-Stokes equations, and the numerical method was validated with test results in ETW(European Transonic Windtunnel). The computation attack angles of CH airfoil varied from 0oto 8o, Mach numbers varied from 0.74 to 0.82 while Reynolds numbers varied from 3×106 to 50×106 per airfoil chord. It is obvious that shock location moves afterward and shock intensity strengthens as Reynolds number increasing. The similar curves of shock location and intensity is linear with logarithm of Reynolds number, so that the shock location and intensity at flight condition could be extrapolated from low Reynolds number.

Influencing Factors Analysis of the Shock-Induced Separation for Supercritical Airfoil

2013 ◽  
Vol 444-445 ◽  
pp. 221-226
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Mach Number ◽  
Influencing Factors ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Factors Analysis ◽  
Mach Numbers

The shock-induced separation easily occurred on the upper surface of supercritical airfoil at transonic speeds, which would change the aerodynamic characteristics. The problem of the shock-induced separation was not solved completely for the complicated phenomena and flow mechanism. In this paper, the influencing factors of shock-induced separation for supercritical airfoil CH was analyzed at transonic speeds. The Navier-Stokes equations were solved, in order to investigate influence of different attack angles, Mach numbers and Reynolds numbers. The computation attack angles of CH airfoil varied from 0oto 7o, Reynolds numbers varied from 5×106to 50×106per airfoil chord while Mach number varied from 0.74 to 0.82. It was shown that the shock-induced separation was affected by attack angles, Mach numbers and Reynolds numbers, but the influence tendency and areas were quite different. The shock wave location and intensity were affected by the three factors, and the boundary layer thickness was mainly affected by Reynolds number, while the separation structure was mainly determined by the attack angle and Mach number.

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