An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity). A critical ‘penetration’ thickness T is defined. When the annulus thickness is greater than T, the annular jet behaves like a full liquid jet; the only unstable perturbations are axisymmetric, and their growth rate is independent of thickness. When the annulus thickness is less than T, the jet behaves like a two-dimensional liquid sheet; the most unstable perturbations are antisymmetric and their growth rate increases as the jet thickness decreases. Therefore, an annular liquid jet with a sufficiently small ring thickness will disintegrate into spherical shells much faster than a full liquid jet disintegrates into drops, in accordance with existing experimental data. Non-dimensional expressions for the penetration thickness are given for both viscous and inviscid jets.

While plain vanilla OpenFOAM has strong capabilities with regards to quite a few typical CFD-tasks, some problems actually require additional bespoke solvers and numerics for efficient computation of high-quality results. One of the fields requiring these additions is the computation of large-scale free-surface flows as found e.g. in naval architecture. This holds especially for the flow around typical modern yacht hulls, often planing, sometimes with surface-piercing appendages. Particular challenges include, but are not limited to, breaking waves, sharpness of interface, numerical ventilation (aka streaking) and a wide range of flow phenomenon scales. A new OF-based application including newly implemented discretization schemes, gradient computation and rigid body motion computation is described. In the following the new code will be validated against published experimental data; the effect on accuracy, computational time and solver stability will be shown by comparison to standard OF-solvers (interFoam / interDyMFoam) and Star CCM+. The code’s capabilities to simulate complex “real-world” flows are shown on a well-known racing yacht design.

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Periodic leading-edge spanwise blowing was tested on a 60-deg swept delta-wing fighter aircraft model in a low-speed wind tunnel, up to an angle-of attack of a = 60 deg. At low frequencies, lift and drag coefficients correspond to the pulsating blowing pressure: when the valve is open, they reach the same values as with continuous blowing, and when it is closed, they agree with the no-blowing values. A lag in the response time is observed, which is equal at low incidences to the freestream convective time, but increases to 30 convective times at a = 30-40 deg. This response time is much longer when the valve closes than when the valve opens at a = 20-30 deg. These features are similar to those of delta wings in unsteady flows, such as in pitching or plunging motions. They are insensitive to the flow parameters and are valid at low blowing frequencies. At high frequencies, lift and drag coefficients do not correspond to the pulsating pressure, but remain at an intermediate value between those of continuous and no blowing. In both cases, the mean lift and drag coefficients are equal to the values obtained by continuous blowing at the same mean momentum coefficient. Nomenclaturenozzle internal diameter / = blowing frequency k = reduced blowing frequency, 2nf • c/V m -jet mass flux P = static pressure downstream of the valve q = freestream dynamic pressure r = relative pulse length (pulse/period ratio) R c = chord Reynolds number, V • c/v S = wing planform area T = pulsating period t = time t r = response time of the aerodynamic coefficients r* = dimensionless response time, t r /t Q t$ = convective time of the freestream on the wing, c/ V V = freestream velocity Vj = jet exit velocity a = angle of attack v = kinematic viscosity

Three cruciform wings were tested on a body at five roll angles and up to three longitudinal positions in a lowspeed wind tunnel, up to an angle of attack of a = 90 deg. The roll angle affects significantly the fin normal force coefficient. The normal force on the upper fins decreases to zero, at a > 40 deg, possibly because the vortex breakdown on the lower fins induces separated flow over the upper fins. As a consequence, a strong rolling moment is induced at these incidences at asymmetric roll angles. This rolling moment is independent of the wing axial position but proportional to the wing planform area, similarly to the fin normal force coefficient. This rolling moment is much larger than the rolling moment induced on symmetrical configurations by the asymmetric body vortices. The wing contribution to the side force is small compared with the body contribution at asymmetric roll angles. As a result, the maximum side force is not higher than that obtained at symmetric + and X attitudes. Nomenclature= normal force coefficient, based on area S TQf = fin normal force coefficient, based on area ,S ref = fin normal force coefficient, based on area S* = yawing moment coefficient, based on area S ref and diameter d = rolling moment coefficient, based on area 5 ref and diameter d = rolling moment coefficient, based on area S* and diameter d ?= side force coefficient, based on area S Kf = body diameter; reference length for moment coefficients, m = Reynolds number, based on diameter d =body maximal cross section; reference area for force and moment coefficients, unless otherwise defined, m 2 = planform area of one pair of joined wings, m 2 = one fin planform area; reference area for CN* and C*. ,m 2 = fin longitudinal center of pressure, measured from the fin root chord apex, m = main normal force center of pressure, measured backward from the moment reference center, at 4.5d from the body nose, m =fin lateral center of pressure, measured from the root chord, m =model angle of attack, deg = azimuthal angle, measured clockwise from the windward edge of the body when looking forward, cf. Fig. 1, deg <| ) = model roll angle, positive clockwise when looking forward, zero at + attitude, cf. Fig. 1, deg Subscripts B=value of a coefficient for the body alone B(W) =body contribution to a coefficient W(B) = wing contribution to a coefficient