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At least 379 records · Page 21

A comparison of numerical flux formulas for the Euler and Navier-Stokes equations

Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.

Van Leer, Bram↗

Burst vortex/boundary layer interaction

Several configurations of delta wing vortex generator and boundary layer test plate were tested, and two final ones selected. Sample measurements and flow visualizations in the candidate configurations, together with more detailed measurements in one of the two final arrangements, which were selected so that a pure vortex bursts repeatably and then interacts, in as simple fashion as possible, with a simple turbulent boundary layer, are included. It is concluded that different intensities of bursting or breakdown, like different strengths of shock wave or hydraulic jump, can be produced by minor changes of configuration. The weaker breakdowns do not produce flow reversal. The initial measurements were done with a fairly weak, but repeatable, breakdown. Basic measurements on the second final arrangement, with a stronger breakdown, are in progress.

Bradshaw, P.↗

Computation of viscous transonic flow over porous airfoils

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the total airfoil surface, and is located near the shock. Both an interactive boundary layer (IBL) algorithm and a thin-layer Navier-Stokes (TLNS) algorithm have been modified for use in studying the outer flow, whereas a stream-function formulation has been used to model the inner flow in the small cavity. The coupling procedure at the porous surface is based on Darcy's law and on the assumption of a constant total presusre in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to consider the transpired turbulent boundary layer in the TLNS approach, and the Cebeci-Smith turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but it can also increase viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline patterns of passive-shock and boundary-layer interaction are revealed in this study.

Chow, Chuen-Yen↗

Quasiconical free interaction between a swept shock and a turbulent boundary layer

Previous observations that fin-generated interactions are quasi-conical in nature were further confirmed by surface pressure measurements spanning Mach 2.5-3.5, which encompassed unseparated through strongly separated interactions. For strongly separated interactions in which the shock wave is bifurcated into a lambda-foot structure, the conical free interaction hypothesis was validated through an appropriate scaling of the far-field surface pressure distribution. The behavior of the lambda-foot structure, such as the decrease of the slope of the separation shock with interaction strength, was explained by invoking the conical free interaction hypothesis. Through the conical free interaction hypothesis, it was further shown that the triple-shock intersection behaves in a complicated manner with changes in interaction strength.

Lu, Frank K.↗

The sheath/ionosphere boundary layer at Venus

At Venus the interaction of the shocked solar wind and cold planetary ions takes place in the dayside mantle. The shocked solar wind is a warm, drifting Maxwellian plasma whereas the planetary plasma is cold; the plasma in the mantle is strongly magnetized. The coexistence of these two populations is unstable, and it leads to wave excitations that organize the energy and momentum exchange between the shocked solar wind and the plasma of planetary origin. The source of the free energy is the solar wind. The intensive wave activity seen in the 100 Hz channel of the wave instrument onboard the Pioneer-Venus Orbiter in the dayside mantle region of Venus can be identified as almost electrostatic VLF waves excited by the kinetic branch of the modified two-stream lower hybrid instability. The waves interact with the particles, and the planetary plasma is heated and accelerated outside the ionosphere, close to its upper boundary. This way solar wind scavenges the ionosphere, and planetary ions leave the planetary magnetosphere. A portion of the wave energy is capable of penetrating directly into the ionosphere and heating it.

Szego, K.↗

Shock-Wave/Boundary-Layer Interactions in Hypersonic Low Density Flows

Results of numerical simulations of Mach 10 air flow over a hollow cylinder-flare and a double-cone are presented where viscous effects are significant. The flow phenomena include shock-shock and shock- boundary-layer interactions with accompanying flow separation, recirculation, and reattachment. The purpose of this study is to promote an understanding of the fundamental gas dynamics resulting from such complex interactions and to clarify the requirements for meaningful simulations of such flows when using the direct simulation Monte Carlo (DSMC) method. Particular emphasis is placed on the sensitivity of computed results to grid resolution. Comparisons of the DSMC results for the hollow cylinder-flare (30 deg.) configuration are made with the results of experimental measurements conducted in the ONERA RSCh wind tunnel for heating, pressure, and the extent of separation. Agreement between computations and measurements for various quantities is good except that for pressure. For the same flow conditions, the double- cone geometry (25 deg.- 65 deg.) produces much stronger interactions, and these interactions are investigated numerically using both DSMC and Navier-Stokes codes. For the double-cone computations, a two orders of magnitude variation in free-stream density (with Reynolds numbers from 247 to 24,7 19) is investigated using both computational methods. For this range of flow conditions, the computational results are in qualitative agreement for the extent of separation with the DSMC method always predicting a smaller separation region. Results from the Navier-Stokes calculations suggest that the flow for the highest density double-cone case may be unsteady; however, the DSMC solution does not show evidence of unsteadiness.

Moss, James N.↗

Supersonic flow visualization of a nacelle in close proximity to a simulated wing

A flow visualization study was made in the 9 x 9 inch supersonic wind tunnel at Wichita State University to examine shock and boundary layer flow interaction for a nacelle in close proximity to the lower surface of a simulated wing. The test matrix included variations of angle of attack from -2 degrees to +4 degrees, nacelle-wing gap from 0.5 to 3-nacelle inlet diameter (0.12 inch), and Reynolds number based on nacelle length (1.164 inch) from 1.16 x 10(exp 6) to 1.45 x 10(exp 6) at a nominal Mach number of 2. Schlieren pictures of wing and nacelle flowfield were recorded by a video camera during each tunnel run. Results show that the nacelle inlet shock wave remains attached to the inlet lip and its impingement does not significantly affect the wing boundary layer. At the nacelle trailing edge location, the wing boundary layer thickness is approximately one nacelle inlet diameter at alpha = 0 degrees and it decreases with increase of angle of attack.

Biber, Kasim↗

On the interaction between the shock wave attached to a wedge and freestream disturbances

A study of the interaction of small amplitude, unsteady, freestream disturbances with a shock wave induced by a wedge in supersonic flow is presented. These disturbances may be acoustic waves, vorticity waves, or entropy waves (or indeed a combination of all three). Their interactions then generate behind the shock disturbances of all three classes, an aspect that is investigated in some detail, our motivation being to investigate possible mechanisms for boundary-layer receptivity, caused through the amplification and modification of freestream turbulence through the shock-body coupling. Also, the possibility of enhanced mixing owing to additional vorticity produced by the shock-body coupling is investigated.

Duck, Peter W.↗

The dynamics and control of fluctuating pressure loads in the reattachment region of a supersonic free shear layer

The primary aim is to investigate the mechanisms which cause the unsteady wall-pressure fluctuations in shock wave turbulent shear layer interactions. The secondary aim is to find means to reduce the magnitude of the fluctuating pressure loads by controlling the unsteady shock motion. The particular flow proposed for study is the unsteady shock wave interaction formed in the reattachment zone of a separated supersonic flow. Similar flows are encountered in many practical situations, and they are associated with high levels of fluctuating wall pressure. Wall pressure fluctuations were measured in the reattachment region of the supersonic free shear layer. The free shear layer was formed by the separation of a Mach 2.9 turbulent boundary layer from a backward facing step. Reattachment occurred on a 20 deg ramp. By adjusting the position of the ramp, the base pressure was set equal to the freestream pressure, and the free shear layer formed in the absence of a separation shock. An array of flush-mounted, miniature, high-frequency pressure transducers was used to make multichannel measurements of the fluctuating wall pressure in the vicinity of the reattachment region. Contrary to previous observations of this flow, the reattachment region was found to be highly unsteady, and the pressure fluctuations were found to be significant. The overall behavior of the wall pressure loading is similar in scale and magnitude to the unsteadiness of the wall pressure field in compression ramp flows at the same Mach number. Rayleigh scattering was used to visualize the instantaneous shock structure in the streamwise and spanwise direction. Spanwise wrinkles on the order of half the boundary layer thickness were observed.

Smits, A. J.↗

On the scale of surface features in hypersonic swept shock boundary-layer interactions

A parametric study of a Mach 8 fin-induced shock interaction with a turbulent boundary layer was performed in a shock tunnel using surface oil-dot visualization and surface pressure measurements. The study showed that the interaction was separated and secondary separation was detected for the strongest cases studied. Although the inviscid shock wave was close to the fin, the interaction was spread over large angular extents. The interaction showed inception to conical symmetry at the highest shock strengths. Additionally, the surface pressure distribution showed an extensive plateau region, with no distinct dip associated with strongly separated interactions. Between the fin and the inviscid shock, the surface pressure rose rapidly but did not approach the downstream inviscid shock, the surface pressure rose rapidly but did not approach the downstream inviscid value.

Pace, E. G.↗

SC3 - A wing concept for supersonic maneuvering

A supersonic wing design concept that overcomes the problems associated with nonlinear inviscid pressure distribution is presented together with a summary of the supporting theoretical and experimental development program. The key design feature is a conical panel supporting a controlled supercritical conical camber (SC3) crossflow expansion and recompression which permits lift on the upper surface to be obtained without producing an adverse pressure gradient or crossflow shock wave strong enough to separate the boundary layer. The role of aerodynamics in the design implementation is discussed, as are the concept development, the initial design validation on a fabricated and tested SC3 design, and the body and canard interaction effect. The design and testing of an isolated wing with a planform and thickness distribution representative of a practical application are described. Wind-tunnel results show that significant performance gains can be obtained for fighter aircraft using this concept.

Mason, W. H.↗

Unsteady pressure measurements on a supercritical airfoil at high Reynolds numbers

Steady and unsteady pressures were measured on a 14 percent supercritical airfoil at transonic Mach numbers at Reynolds numbers from 6,000,000 to 35,000,000. Instrumentation techniques were developed to measure unsteady pressures in a cryogenic tunnel at flight Reynolds numbers. Experimental steady data, corrected for wall effects show very good agreement with calculations from a full potential code with an interacted boundary layer. The steady and unsteady pressures both show a shock position that is dependent on Reynolds number. For a supercritical pressure distribution at a chord Reynolds number of 35,000,000 laminar flow was observed between the leading edge and the shock wave at 45 percent chord.

Hess, R. W.↗

Interactive boundary-layer calculations of a transonic wing flow

Results obtained from iterative solutions of inviscid and boundary-layer equations are presented and compared with experimental values. The calculated results were obtained with an Euler code and a transonic potential code in order to furnish solutions for the inviscid flow; they were interacted with solutions of two-dimensional boundary-layer equations having a strip-theory approximation. Euler code results are found to be in better agreement with the experimental data than with the full potential code, especially in the presence of shock waves, (with the sole exception of the near-tip region).

Kaups, Kalle↗

Experimental Investigation of 'Transonic Resonance' with Convergent-Divergent Nozzles

Convergent-divergent nozzles, when run at pressure ratios lower than the design value, often undergo a flow resonance accompanied by the emission of acoustic tones. The phenomenon, different in characteristics from conventional 'screech' tones, has been studied experimentally. Unlike screech, the frequency increases with increasing supply pressure. There is a 'staging' behavior; 'odd harmonic' stages resonate at lower pressures while the fundamental occurs in a range of higher pressures corresponding to a fully expanded Mach number (M(sub j)) around unity. The frequency (f(sub N)) variation with M(sub j) depends on the half angle-of-divergence (theta) of the nozzle. At smaller theta, the slope of f(sub N) versus M(sub j) curve becomes steeper. The resonance involves standing waves and is driven by unsteady shock/boundary layer interaction. The distance between the foot of the shock and the nozzle exit imposes the lengthscale (L'). The fundamental corresponds to a quarterwave resonance, the next stage at a lower supply pressure corresponds to a three-quarter-wave resonance, and so on. The principal trends in the frequency variation are explained simply from the characteristic variation of the length-scale L'. Based on the data, correlation equations are provided for the prediction of f(sub N). A striking feature is that tripping of the boundary layer near the nozzle's throat tends to suppress the resonance. In a practical nozzle a tendency for the occurrence of the phenomenon is thought to be a source of 'internal noise'; thus, there is a potential for noise benefit simply by appropriate boundary layer tripping near the nozzle's throat.

Zaman, K. B. M. Q.↗

Computation of viscous blast wave solutions with an upwind finite volume method

A fully conservative, viscous, implicit, upwind, finite-volume scheme for the thin-layer Navier-Stokes equations is described with application to blast wave flow fields. In this scheme, shocks are captured without the oscillations typical of central differencing techniques and wave speeds are accurately predicted. The finite volume philosophy ensures conservation and since boundary conditions are also treated conservatively, accurate reflections of waves from surfaces are assured. Viscous terms in the governing equations are treated in a manner consistent with the finite volume philosophy, resulting in very accurate prediction of boundary layer quantities. Numerical results are presented for four viscous problems: a steady boundary layer, a shock-induced boundary layer, a blast wave/cylinder interaction and a blast wave/supersonic missile interaction. Comparisons of the results with an established boundary layer code, similarity solution, and experimental data show excellent agreement.

Molvik, Gregory A.↗

Numerical investigation of internal high-speed viscous flows using a parabolic technique

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Anderson, O. L.↗

Evaluation of Industry Standard Turbulence Models on an Axisymmetric Supersonic Compression Corner

Reynolds-averaged Navier-Stokes computations of a shock-wave/boundary-layer interaction (SWBLI) created by a Mach 2.85 flow over an axisymmetric 30-degree compression corner were carried out. The objectives were to evaluate four turbulence models commonly used in industry, for SWBLIs, and to evaluate the suitability of this test case for use in further turbulence model benchmarking. The Spalart-Allmaras model, Menter's Baseline and Shear Stress Transport models, and a low-Reynolds number k- model were evaluated. Results indicate that the models do not accurately predict the separation location; with the SST model predicting the separation onset too early and the other models predicting the onset too late. Overall the Spalart-Allmaras model did the best job in matching the experimental data. However there is significant room for improvement, most notably in the prediction of the turbulent shear stress. Density data showed that the simulations did not accurately predict the thermal boundary layer upstream of the SWBLI. The effect of turbulent Prandtl number and wall temperature were studied in an attempt to improve this prediction and understand their effects on the interaction. The data showed that both parameters can significantly affect the separation size and location, but did not improve the agreement with the experiment. This case proved challenging to compute and should provide a good test for future turbulence modeling work.

Turbulent Boundary Layer↗