A one-dimensional supersonic CFD code was utilized to solve
for the required magnetic field strength, as a function of
conductivity, for fixed length and constant static enthalpy
magnetohydrodynamic generator and accelerator. The inlet
velocity and pressure to the generator were varied, while
requiring the exit Mach number of the generator to remain at
2.0. The flow after the generator proceeded through a simple
supersonic combustion process, and the bypassed energy was
then used in the accelerator to increase the flow velocity.
Results show that varying the conductivity between 7 and 70
mho/m and inlet velocity between 5000 and 14000 ft/s,
require magnetic fields in the generator between 1 and 12
Tesla with greater magnetic field strength required at lower
conductivities. It was also calculated that for the same
energy and conductivity used in the accelerator, a lower
magnetic field was needed.
[DH.002] Mixing Efficiency and Mean Temperature Measurements in a High Compressibility Mixing Layer
T. Rossmann, M. G. Mungal, R. K. Hanson (Stanford University)
The efficient mixing of fluids in two-stream mixing layers at compressible conditions is still of fundamental importance to high-speed propulsion. To further understand the role of compressibility on mixing, measurements of mixing efficiency, and mean temperature have been performed in a M_c = 2.64 mixing layer using a shock tunnel driven hypersonic mixing layer facility. The mean scalar field and mixing efficiency was measured using a ``cold chemistry'' technique utilizing the quenching of nitric oxide laser induced fluorescence signal to mark regions of molecularly mixed fluid. Several different quenching partners (O_2+Argon, Air, CO_2) were used to achieve statistically converged results using fewer images. The mixing efficiency (\delta_m/\delta) achieved in this study at Re_\delta = 2.6\times10^6 was 0.64, clearly following the trend of a slight increase with Reynolds number. Mean rotational temperature measurements were also made using the PLIF signal from two different excitation wavelengths, yielding the result that temperature no longer acts as a conserved scalar at high compressibility conditions.
[DH.003] The Fluid Dynamics of a Pulse Detonation Engine-II
K. Kailasanath, Gopal Patnaik, Chiping Li (Naval Research Laboratory)
Pulsed Detonation Engines (PDEs) have received considerable attention recently because they have the potential to make a major impact in aerospace propulsion. Last year, we showed that the fluid dynamics of an idealized PDE, consisting of a tube closed at one end and open at the other is quite complex and depends strongly on the boundary conditions at the open end. In this talk, detailed simulations of a method to enhance the performance of the engine is presented. The underlying mechanism for the enhanced performance is shown to be the presence of a quasi-steady shock in the section of the tube that does not have any fuel. The implications of these results on the development and potential application of the PDE will also be presented.
[DH.004] Growth-Rate Suppression in Simulated Compressible Mixing Layers
W.-Y. Kwok, R. Moser (University of Illinois at Urbana-Champaign)
Turbulent mixing layers exhibit striking compressibility
effects. In particular, at modest Mach numbers, the growth
rate of compressible mixing layers is significantly reduced
from that of incompressible mixing layers. In this research,
we investigate the relationship of this growth rate
reduction to the commonly observed large-scale structures in
the mixing layer. This is accomplished by performing direct
numerical simulation of compressible time developing mixing
layers. Two fields from the fully developed incompressible
mixing layer simulations of Rogers amp; Moser (Phys. of
Fluids 6:903-923) were used to construct initial
conditions, one from the natural (unforced) simulation and
one from the "strongly forced" simulation, which has much
more prominent two-dimensional mixing layer structures.
Cases were run at convective Mach numbers of 0.4 and 0.8. It
is found that significant compressible growth rate
reductions occur only in the cases in which the
two-dimensional structures are prevalent. Further, the
growth rate reduction is accompanied by a reduction in the
magnitude of the cross-stream velocity fluctuations, as
suggested by the results of Rogers amp; Moser; all suggesting
that pairing is being suppressed. Explanation for these
compressibility effects is sought by studying the
interaction of vortical and acoustic modes in the
compressible simulations, and direct comparison to the
corresponding incompressible simulations.
[DH.005] The Wiener Stochastic Expansion
William C. Meecham (Dept. Of Mech. and Aerospace Eng., Univ. Of California, Los Angeles, CA 90024)
The Wiener stochastic expansion is used for Boussinesq buoyancy (axisymmetric) turbulence; the scaleless 5/3 law energy spectrum is found, further exhibiting the 5/3 robustness.
Dimensional analysis, in situations where the number of objects (parameters plus variables) is limited, gives algebraic spectra. In interesting turbulence applications the result is scaleless. For ordinary, nearly incompressible turbulence the objects are: Energy spectrum,E(k); the wavenumber k (equal to 2 \pi / \lambda with \pi the eddy size), \epsilon the time rate of decay of turbulent kinetic energy per mass; k_0, the energy range wave number where most of the kinetic energy resides; and v the fluid kinetic viscosity; for buoyancy problems we have also the Brunt-V\ddot\mathrm ais\ddot\mathrm al\ddot\mathrm a frequency n = - g \partial < \rho _\mathrmpot / \partial z where < \rho _\mathrmpot is the potential. If as for isotropic turbulence, only the parameters k and \epsilon remain, the Kolmogorov-Obukhov (K-O) 5/3 law is forced. The threat is the entry of k_o which would destroy the scaleless behavior. We use the energy transfer, T(k) to see early changes in the spectrum. For k's less than the viscous cut-off the viscosity doesn ’t enter in the transfer. We use the stochastic (Wiener-Hermite, aka WH) expansion to represent nonlinear, but near to Gaussian, processes; developed turbulence is of this form. The energy transfer is of cascade form with a sharp plus/minus peak, cancelling peak for wavenumbers near k (of the form early proposed by Kraichnan for isotropic, homogeneous turbulence). It is seen that the dependence on k_0, drops out; this is surprising since the integrand might appear to be largest in the energy range. The N is small and appears as a multiplicative coefficient, not affecting the spectral form. Thus, the equilibrium energy spectrum must be of the K-O, 5/3 form. A model of compressible flow has previously been considered. For large Re^\prime (fluctuation Reynolds number) and if Ma^\prime, the fluctuation Mach number is moderate, the energy spectrum retains its 5/3 form. For example, Re^\prime 106, and Ma^\prime < 0.2 persistence of the 5/3, scaleless, energy spectrum law under these very diverse circumstances is impressive.
[DH.006] Application of higher order compact schemes to LES of compressible turbulent boundary layers
Santhanam Nagarajan, Joel Ferziger, Sanjiva Lele (Stanford University)
Staggering improves robustness of higher order compact
schemes for large eddy simulation of compressible turbulent
flows. The staggered arrangement of variables allows us to
solve the fully conservative form of the compressible LES
equations with lower aliasing errors. These schemes have now
been coupled with implicit time integration to expand their
range of applicability to wall bounded flows. Grid
clustering near walls causes increased stiffness which is
overcome using an implicit (Crank-Nicholson) time
integration scheme for the acoustic and viscous terms in the
wall normal direction. The less restrictive terms of the
governing equations are integrated using a Runge-Kutta
scheme. Lower order differencing is used for the left hand
side of the implicit scheme and subiteration at each
Runge-Kutta substep allows us to regain time accuracy. This
method is applied to the flat plate boundary layer flow at
subsonic Mach numbers. The test case is that of a the growth
of a small amplitude disturbance in a boundary layer.
Results are compare with other simulations and with theory.
The scheme is being applied to LES of turbulent boundary
layers.
[DH.007] Direct Numerical Simulation of a spatially evolving supersonic boundary layer.
Sergio Pirozzoli, Francesco Grasso (University of Rome ``La Sapienza''), Thomas Gatski (NASA Langley Research Center)
Results from a direct numerical simulation of a spatially
evolving supersonic turbulent boundary layer at Mach 2.25
are presented. The numerical procedure used is a finite
difference discretization that uses a fifth-order accurate
weighted-eno scheme for the inviscid flux, a fourth-order
compact difference approximation for the viscous flux, and a
fourth-order explicit Runge Kutta time integration
algorithm. Results are compared with previous studies that
used temporal formulations that assumed slow variation of
the mean boundary layer in the streamwise direction as well
as previous attempts at a full spatial simulation. Mean and
turbulent flow quantities are analyzed with focus on the
validity of the relationships comprising the strong Reynolds
analogy. In addition, heat and mass flux variation across
the boundary layer are examined as well as dilatational
effects and Prandtl number variability.
[DH.008] Direct Numerical Simulation of Isotropic Compressible Turbulence: Numerical and Physical Considerations
Donatella Ponziani, Sergio Pirozzoli, Francesco Grasso (Universita' di Roma "La Sapienza", Dipartimento di Meccanica e Aeronautica)
Compressible turbulence is characterized by a wide disparity of length and time scales and by the occurrence of eddy shocklets as the turbulent Mach number increases. Consequently, its numerical simulation is a demanding task for any numerical scheme which must also have the capability to resolve flow discontinuities (shock waves and/or eddy shocklets).
In the present work we discuss the application of
weighted-eno and optimized weighted-eno schemes for the
direct numerical simulation of compressible turbulence.
Weighted-eno schemes have originally been developed for high
resolution of flows characterized by shock waves and for
aeroacoustics applications. More recently, optimized
weighted-eno schemes have been designed to improve the
resolution in wave number space for the linearized Euler
equations. In the present work we have extended the latter
approach to the nonlinear case. The properties of the scheme
have been first evaluated with reference to the case of
decaying isotropic turbulence analyzed by Spyropoulos and
Blaisdell for a turbulent Mach number 0.4. In the paper we
then analyze the effects of the compressibility by varying
the turbulent Mach number and the compressibility ratio, and
the Reynolds number based on the Taylor microscale.
[DH.009] Linear Stabilty of a Laminar Boundary Layer with Shock Boundary Layer Interaction at Ma=4.8
Alessandro Pagella, Ulrich Rist, Siegfried Wagner (Institut f. Aero und Gasdynamik, University of Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany)
The stability behavior of a laminar boundary layer at Ma=4.8
with shock boundary layer interaction and small amplitude
disturbances is investigated by linear stability theory for
compressible flows (Mack 1969) and direct numerical
simulation. The effect of the shock strength is assessed.
The numerical scheme is based on the unsteady, compressible,
three-dimensional Navier-Stokes equations. In streamwise
direction, high order split type compact finite differences
are used, while in wall normal direction central differences
for viscous and alternating one-sided finite differences for
convective terms, in spanwise direction, a spectral Fourier
Series expansion are applied. Numerical oscillations, caused
by high gradients of the flow variables at the shock, are
damped by an implicit filter of high order in streamwise
direction. For the results obtained by the simulation
without impinging shock wave, non-parallel effects could be
identified and quantified. Taking these non-parallel effects
into account, linear stability theory could represent
stability behavior of wall distant disturbance amplitude
maxima with small obliqueness angles of the disturbances for
the investigated cases with shock. The impinging shock wave
locally influences stability behavior of the boundary layer,
which is dependent on its shock-strength, applied
disturbance frequency and disturbance propagation angle. A
separation bubble locally displaces the boundary layer in
wall normal direction. Hence, viscous instability becomes
weaker and the inviscid instability picks up.
[DH.010] Numerical Simulation of Secondary Instability in Hypersonic Boundary Layers
Chong Whang, Xiaolin Zhong (University of California, Los Angeles)
Secondary Gortler instability in a Mach 15 flow over a blunt
wedge with a concave surface is investigated using direct
numerical simulation (DNS). Initial forcing disturbances in
the simulation are obtained from linear stability theory
(LST), and subsequent linear and nonlinear development of
the hypersonic Gortler vortices and their secondary
instability are studied by computing the full Navier-Stokes
equations using a fifth order finite difference upwind
scheme and a shock fitting method. The nonlinear development
of Gortler vortices distorts the mean flow and leads to
highly inflectional profiles not only in wall normal
direction, but also in spanwise direction which induce the
secondary instability. In the break-down process of Gortler
vortices, unsteady fluctuations appear in the vortices. Such
a process is through a secondary instability mechanism.
Nonlinear development of Gortler vortices in the Mach 15
flow has been studied by imposing strong disturbances
obtained from LST at the inlet of computational domain. A
two-dimensional linear stability code is applied for the
distorted mean flow in order to find secondary modes of
hypersonic Gortler vortices. The mode obtained by linear
stability analysis is imposed at the entrance of the
computational domain. Subsequent development of the
secondary mode is carried out by solving the full
Navier-Stokes equations. The numerical results of nonlinear
development of hypersonic gortler vortices show the
inflectional profiles in boundary layers. The numerical
results of secondary instability show that the interaction
of Görtler vortices with the strong varicose mode leads to
the development of a horseshoe vortex.
[DH.011] Particle Image Velocimetry Measurements of Turbulent Jets at Different Mach Numbers
Zhexuan Wang, Yiannis Andreopoulos (Department of Mechanical Engineering, The City College of CUNY)
Compressibility and density effects in subsonic turbulent jets have been investigated experimentally. Helium, Nitrogen and Krypton gases were used in the jet flow issuing into still air at Mach number 0.3, 0.6 and 0.9 respectively. PIV (Particle Image Velocimetry) based on Cross-Correlation and Auto-Correlation methods was carried out, with double-pulse laser being the light source for visualization and quantitative measurements, and talcum powders being the seeding particles. The velocity distribution obtained indicated that the decay of Helium is the fastest, while the decay of Krypton is the slowest. Correspondingly, the level of turbulence fluctuation is also higher in case of Helium Jets indicating better mixing with the ambient air. The results cooperate very well with previous pressure measurements.
Sponsored by NASA Grant #NAG-1590
[DH.012] Large Eddy Simulation of Stagnation Point Heat Transfer Under Free-Stream Turbulence
Zhongmin Xiong, Sanjiva K. Lele (Department of Mechnanical Engineering, Stanford University, Stanford, CA 94305)
An implicit dual time stepping scheme with linearized subiterations is developed for efficient solution of the compressible Navier-Stokes equations. The LU decomposition is employed in the subiteration scheme in conjunction with spatially varying pseudo time step; the resultant algorithm is five times faster in comparison with the conventional approximate factorization method. Large eddy simulation based on this method is performed to investigate the effect of free stream turbulence on the stagnation point heat transfer. The pre-computed homogeneous isotropic turbulence is introduced upstream of a compressible leading edge impinging flow. The interaction between free-stream turbulence and the leading edge involves three distinct processes: free turbulence decay, inviscid distortion and viscous interaction. The energetic streamwise vortical structures formed near the surface are found to be temporally persistent, and spatially characterized by a spanwise scale of the order of the local boundary layer thickness. They are identified as the direct cause of the large heat transfer enhancement in the presence of free-stream turbulence.