Experimental results on aerofoil manipulators at high subsonic speeds

An extensive series of measurements of the boundary layer development and drag downstream of aerofoil manipulators have been made in the high speed tunnels at Cambridge. This work forms part of a combined study with the University of Poitiers into the possible drag reducing properties of manipulators and was supported by Airbus Industrie. Overall the test results showed that the reduction in turbulent skin-friction downstream of the device did not compensate for the drag of the device itself in any of the cases studied, thus no overall drag saving was possible although in certain cases the overall drag penaly was small. This finding suggests that such devices may have a use in regions where a local reduction in skin-friction (and hence possible heat transfer) is needed and a low level of loss can be accepted. However, the actual drag reduction obtained was found to be extremely sensitive to changes in the aerofoil shape and incidence.     

Influences of wind tunnel parameters on airfoil characteristics at high subsonic speeds

The influences of several wind tunnel parameters on airfoil characteristics are experimentally investigated in a transonic wind tunnel. Quantified as Mach number errors they show decisive effects and confirm that they have to be taken into consideration in a valuation of test results. Differences in data gained in measurements of several wind tunnels can be partly explained thereby.List of symbols C chord length - C _d drag coefficient - C ₀ d drag coefficient at zero lift - C ₁ lift coefficient - C _{1 max} lift coefficient at maximum lift - C _p pressure coefficient - D divergence - M Mach number - P ₀ stagnation pressure - Re Reynolds number - S _h suction along the horizontal walls - S _v suction along the vertical walls - X axial coordinate - X _ref position of the reference point - X _s shock position - angle of attack     

Drag measurements on long thin cylinders at small angles and high Reynolds numbers

Measurements of the drag caused by turbulent boundary layer mean wall shear stress on cylinders at small angles of attack and high length Reynolds numbers (8×10⁶<Re_L<6×10⁷) are presented. The use of a full-scale, high-speed towing tank enabled the development of turbulent boundary layers on cylinders made of stainless steel, aluminum, titanium, and polyvinyl chloride. The diameter of all cylinders in this experiment was 12.7 mm; two cylinder lengths, 3.05 m and 6.10 m, were used, corresponding to aspect ratio values L/a=480 and 960, respectively. Materials of various densities were towed at critical angles, resulting in linear cylinder geometry for tow speeds ranging from 2.6 m/s to 20.7 m/s and angles between 0° and 12°. Towing angles were measured with digital photography, and streamwise drag was measured with a strut-mounted load cell at the tow point. The measured tangential drag was very sensitive to small increases in angle at all tow speeds. A momentum thickness length scale is proposed to scale the tangential drag coefficient. The effects of the cross-flow resulting from the small angles of tow have a significant effect on the tangential drag coefficient values. A scaling for the orthogonal force on the cylinders was determined and provides a correction to published normal drag coefficient values for pure cross-flow. The presence of the axial turbulent boundary layer has a significant effect on these orthogonal forces.     

Heat transfer to surfaces of some lifting bodies at high supersonic speeds

Results are presented of an experimental study of the heat transfer and gas flow on the surface of a semicone and of planar wings with a break in the leading edges at Mach number M=5. It is shown that with the interaction of the gas streams flowing about various portions of the surface of such bodies there may occur local, relatively narrow zones of high or low values of the specific heat flux.Temperature indicating paints were used to measure the heat fluxes, and smearable paints applied to the surface in the form of individual dots were used for flow visualization.     

Drag measurements on V-grooved surfaces on a body of revolution in axial flow

In water flows with velocities of up to 9 m/s the friction drag of a body of revolution in axial flow was investigated for dependence on the body surface structure. This was done for different types of riblet film fixed on the surface with the riblet direction aligned with the flow. The lateral spacing between the triangular shaped riblets varied between 0.033 mm and 0.152 mm. In all cases the riblet spacing was equal to the riblet height. For comparison a smooth reference film was used.Depending on the Reynolds number and the non-dimensional riblet spacings ⁺, a turbulent drag reduction of up to 9% could be achieved with riblets in comparison with the flow over a smooth surface.In the region of transition to turbulent flow and with non-dimensional riblet spacings ofs ⁺10–15 drag reductions of up to 13% were obtained. It is therefore conjectured, that in addition to hampering the near wall momentum exchange, the riblets can delay the development of initial turbulent structures in time and space.     

Three-dimensional numerical simulation of the wake flow of an afterbody at subsonic speeds

We numerically investigate the wake flow of an afterbody at low Reynolds number in the incompressible and compressible regimes. We found that, with increasing Reynolds number, the initially stable and axisymmetric base flow undergoes a first stationary bifurcation which breaks the axisymmetry and develops two parallel steady counter-rotating vortices. The critical Reynolds number (Re _cs) for the loss of the flow axisymmetry reported here is in excellent agreement with previous axisymmetric BiGlobal linear stability (BiGLS) results. As the Reynolds number increases above a second threshold, Re _co, we report a second instability defined as a three-dimensional peristaltic oscillation which modulates the vortices, similar to the sphere wake, sharing many points in common with long-wavelength symmetric Crow instability. Both the critical Reynolds number for the onset of oscillation, Re _co, and the Strouhal number of the time-periodic limit cycle, St_sat, are substantially shifted with respect to previous axisymmetric BiGLS predictions neglecting the first bifurcation. For slightly larger Reynolds numbers, the wake oscillations are stronger and vortices are shed close to the afterbody base. In the compressible regime, no fundamental changes are observed in the bifurcation process. It is shown that the steady state planar-symmetric solution is almost equal to the incompressible case and that the break of planar symmetry in the vortex shedding regime is retarded due to compressibility effects. Finally, we report the developments of a low frequency which depends on the afterbody aspect ratio, as well as on the Reynolds and on the Mach number, prior to the loss of the planar symmetry of the wake.     

Velocity profiles for plate withdrawal at high speeds

A simplified Navier-Stokes equation is applied to the solution of the velocity profile in the liquid meniscus adhering to long flat supports withdrawn continuously from baths of quiescent liquids. The inertial term is included using an Oseen approximation, the inhomogeneous boundary condition is transformed, and the resulting differential equation is solved by the method of eigenfunction expansions. The series describing the velocity profile and volume flowrate are both found to be rapidly convergent.     

Drag measurements at Mach 5 using a stress wave force balance

The stress wave force balance, which has been used for measurements of drag on short models in hypersonic impulse facilities, is investigated here for its suitability for drag measurements on a longer, axisymmetric model. The sensitivity of the balance to loading distribution is investigated and results are reported for experiments on a 5° semi-angle cone, 425 mm in length and of 1.71 kg mass. Experimental drag measurements are shown to be in good agreement with theoretical levels. An investigation into the period over which the stress wave force balance can be used is addressed and, for the present model, the balance is shown to be suitable for measurements in flows of durations of one to several milliseconds with an estimated accuracy of ±10%.     

Lift force on rotating sphere at low Reynolds numbers and high rotational speeds

The lift force on an isolated rotating sphere in a uniform flow was investigated by means of a three-dimensional numerical simulation for low Reynolds numbers (based on the sphere diameter) (Re&lt;68.4) and high dimensionless rotational speeds (Г5). The Navier-Stokes equations in Cartesian coordinate system were solved using a finite volume formulation based on SIMPLE procedure. The accuracy of the numerical simulation was tested through a comparison with available theoretical, numerical and experimental results at low Reynolds numbers, and it was found that they were in close agreement under the above mentioned ranges of the Reynolds number and rotational speed. From a detailed computation of the flow field around a rotational sphere in extended ranges of the Reynolds number and rotational speed, the results show that, with increasing the rotational speed or decreasing the Reynolds number, the lift coefficient increases. An empirical equation more accurate than those obtained by previous studies was obtained to describe both effects of the rotational speed and Reynolds number on the lift force on a sphere. It was found in calcttlations that the drag coefficient is not significantly affected by the rotation of the sphere. The ratio of the lift force to the drag force, both of which act on a sphere in a uniform flow at the same time, was investigated. For a small spherical particle such as one of about 100μm in diameter, even if the rotational speed reaches about 10^6 revolutions per minute, the lift force can be neglected as compared with the drag force.     

Experimental observations of a flexible slider crank mechanism at very high speeds

A slider crank mechanism has been constructed and operated for the purpose of investigating steady state rod bending vibration induced by a very high speed crank. Features include a combination flywheel and adjustable length crank, a thin aluminum connecting rod, and a piston sliding on steel rod slide axes. A strain gage on the rod and magnetic pickup on the crank sensed rod strain and crank speed, respectively.For this system configuration, experimental results are categorized as small, intermediate and large crank length response. Small and intermediate cranks response was amplified due to a large superharmonic component of twice the crank speed frequency and at crank speeds near 1/2 the first natural frequency of the rod. Beyond that speed, period doubling occurred over a range of speeds for intermediate length cranks. The occurrence of period doubling was experimentally sudden and audibly noticeable, and characterized by the onset of frequency components of 1/2, 3/2, 5/2, and 7/2 times the crank speed. For large crank sizes of 0.5, 1, and 2 inches an amplified response also appeared in each at a certain speed, but at speeds lower than in the small and intermediate crank cases. Larger cranks required more frequency components to describe the response than smaller cranks. Experimental responses were correlated with computer simulations of a one mode nonlinear ordinary differential equation model, and over a wide range of speeds and for a representative of a small, intermediate, and large crank length.     

Method of calculating unsteady aerodynamic characteristics of a lifting surface at high subsonic speed

A method is presented for calculating the unsteady aerodynamic characteristics of harmonically oscillating thin wings traveling at high subsonic speed. The medium is assumed ideal. The aerodynamic coefficients are expressed in terms of the rotational derivatives, which are determined for a Strouhal number of zero. The calculation of the rotational derivatives of the aerodynamic coefficients in a compressible medium reduces to the conversion of the corresponding characteristics of a transformed wing, determined in an incompressible medium for altered boundary conditions. To calculate the aerodynamic characteristics of the transformed wing in the incompressible medium we use a technique based on replacement of the lifting surface by a system of discrete unsteady vortices. The problem is solved in general form, and together with the new relations for the rotational derivatives with dots we derive the known formulas for the rotational derivatives without dots.     

Experience in making rheological measurements at high pressures

Summary We review the difficulties encountered in the design and operation of apparatus for rheological studies on liquids at pressures up to 900 MN m^–2 and temperatures from –30 to 120°C. Such rheological information is required in connection with elastohydrodynamic lubrication in which high pressures and shear rates are encountered.With 3 figures     

Tire slip-angle force measurements on winter surfaces

Tire lateral force data on winter surfaces cannot be obtained with the traditional laboratory test technique of an instrumented tire on a moving belt surface. Furthermore, changing snow and ice conditions can drastically change the tire/surface interaction. In this study the Cold Regions Research and Engineering Laboratory’s (CRREL’s) Instrumented Vehicle (CIV) was used in a unique configuration to measure tire lateral force versus slip-angle data on ice and snow at various temperatures, moisture contents, depths, and densities. The vehicle is instrumented to record longitudinal, lateral, and vertical force at the tire contact patch of each wheel as well as vehicle speed, tire speed, and front tire slip angle. The tests were conducted at the Keweenaw Research Center (KRC) in northern Michigan in February 2005 and March 2006. Tests were conducted on ice, packed snow from 0.50 to 0.58 g/cc, remixed snow depths of 2.5–20.3 cm at 0.43 to 0.48 g/cc and freshly fallen snow with depths of 0.5–17 cm at 0.07 to 0.23 g/cc. Surface air temperatures during testing ranged from −14 to 1.6 °C. The data collected show that peak lateral force and the shape of the lateral force versus slip-angle curve are related to snow properties and depths.     

Boundary layer receptivity measurements on compliant surfaces

This paper describes receptivity measurements in a pre-transitional boundary layer flowing over either a rigid or a compliant surface. Fluctuating velocities and frequency spectra were determined on one rigid and nine compliant surfaces. The results showed that the near wall receptivity grows linearly with Re_θ. An empirical correlation of the gain frequency spectrum for a rigid wall was also established. For the compliant surfaces, the near wall gain is increased markedly near the leading edge of the plate due to the amplification of high and mid-frequencies. These frequencies are dissipated though as the flow progresses over the compliant surface such that the receptivity is lower on all the compliant surfaces than on the rigid surface at the trailing edge. An empirical correlation for the ratio of the gains on compliant and rigid surfaces in terms of the compliant surface coefficient ζ²/Eρ_CSL² and Re_θ was established. This correlation indicates that compliant surfaces can suppress receptivity by up to 25% for a Re_θ = 400.     

Dynamic measurements of initiation toughness at high loading rates

An experimental method is described for measuring the dynamic initiation toughness of a sharp stationary crack. A plane specimen is utilized which consists of a central region 50-mm wide and 200-mm long with integral dog-bone ends. The loading is accomplished by the detonation of four small explosive charges which produce two tensile stress waves upon reflection from the dog-bone ends. The stress waves meet at the midpoint of the specimen and reinforce to produce a relatively large, uniformly stressed region with a very high loading rate. The crack is positioned at the midpoint of the specimen at the location where the reinforcing tensile stress waves meet. A series of photoelastic experiments were conducted using Homalite 100 as the model material to observe, in a full-field view, the arrival of the dilatational waves, the subsequent development of the stress field at the tip of the stationary crack and the initiation of the crack. The isochromatic fringe pattern was also used to determine the instantaneous value of the stress-intensity factorK(t) after the characteristic fringe loops developed in the region near the crack tip. Finally,K(t) was measured using a single strain gage positioned and oriented so that its signal output was proportional toK(t) and independent of the next two higher order terms in the series representation of the strain field. A method was developed to determine the instant of initiation from the strain-time trace. Results obtained from the photoelastic and strain measurements of the dynamic-initiation toughnessK _ID were consistently higher than the static value ofK _IC . Paper was presented at the 1987 SEM Fall Conference on Experimental Mechanics held in Savannah, GA on October 25–28.     

A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds

We show that the mean wall-shear stresses in wall-modeled large-eddy simulations (WMLES) of high-speed flows can be off by up to \(\approx 100\%\) with respect to a DNS benchmark when using the van-Driest-based damping function, i.e., the conventional damping function. Errors in the WMLES-predicted wall-shear stresses are often attributed to the so-called log-layer mismatch, which, albeit also an error in wall-shear stresses \(\tau _\mathrm{w}\), is an error of about \(15\%\). The larger error identified here cannot be removed using the previously developed remedies for the log-layer mismatch. This error may be removed by using the semi-local scaling, i.e., \(l_\nu =\mu /\sqrt{\rho \tau _\mathrm{w}}\), in the damping function, where \(\mu \) and \(\rho \) are the local mean dynamic viscosity and density, respectively.     

Bodies of revolution with minimal drag coefficient and low heat transfer at high supersonic speeds

On the basis of modified Newtonian theory and the theory of selfsimilar hypersonic flows we study the form of the optimal contour of a body of revolution with minimal drag coefficient at hypersonic speeds. It is shown that bodies of optimal form also have a small heat transfer coefficient, much smaller than for a conical body. It is established experimentally that the optimal properties of these bodies of revolution are also retained for moderate supersonic flight speeds.In concluslion the author wishes to thank V. V. Sychev for valuable discussions of this problem.