G. E. A. Meier

The influence of suction on the structure of turbulence in fully developed pipe flow

The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following. The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that the x -wise components are first affected, then the r -wise and lastly the ϕ-wise components. The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocity U τ . Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall. The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.

Wave splitting in a fluid of large heat capacity

The splitting of a single pressure discontinuity into a propagating two-wave system is studied for the case of saturated-liquid expansion (liquid-evaporation wave splitting) and vapour compression (vapour-condensation wave splitting). Experimental results from the Max-Planck-Institut fur Stromungsforschung and from Rensselaer Polytechnic Institute show that splitting occurs in test fluids of large molar heat capacity, such as iso-octane ( C v 0 / R ≈ 37). Each of the two forms of splitting results in a single-phase forerunner wave carrying a pressure discontinuity followed by a phase-change wave, also with a pressure discontinuity. The thermodynamic state between the forerunner wave and the phase-change wave is metastable (supersaturated liquid or vapour). The waves are quantitatively described by systems of adiabats, e.g. shock adiabats. It appears that nucleation processes are predominantly homogeneous. In vapour-compression shock-wave splitting, a combined wave (liquefaction shock) splits into discrete forerunner and condensation waves at a triple point, the intersection of a liquefaction shockfront, forerunner shock and condensation discontinuity: such a point occurs just at critical supersaturation (i.e. the Wilson-line state), where condensation is spontaneous and immediate. For shock waves that produce a metastable state of subcritical supersaturation, condensation is delayed, that is, the condensation discontinuity propagates more slowly; for a split-shock system, the condensation discontinuity propagates subsonically. The pressure amplitude of a real split-shock system is much larger than that predicted by an equilibrium model. In liquid-evaporation wave splitting, the forerunner wave is an acoustic expansion wave and the second wave an evaporation wave with a propagation velocity approximately determined by the Chapman-Jouguet condition for deflagration. Such evaporation wavefronts are increasingly distinct as the temperature approaches the critical-point value. The evaporation rates across the wavefront are comparable to those found in vapour explosions.

An experimental study of liquefaction shock waves

The existence of a liquefaction shock wave, a compression shock which converts vapour into liquid, has recently been predicted on physical grounds. The liquefaction shock was experimentally produced as the reflected shock at the closed end of a shock tube. Measurements of pressure, temperature, index of refraction and shock velocity confirm the existence of the shock and its general conformity to classical Rankine-Hugoniot conditions, with a discrepancy ∼ 10°C between measured and predicted liquid temperatures. Photographic observations confirmed the existence of a clear liquid phase and revealed the (unanticipated) presence of small two-phase torus-form rings. These rings are interpreted as vortices and are formed in or near the shockfront (∼ 50 rings/mm 2 are visible near the shockfront at any given time). Separate experiments with the incident shock under conditions of partial liquefaction produced a fog behind the shock: measurements of laser-beam attenuation yielded the thickness of the condensation zone and estimates of the droplet size (∼ 10 −7 m).

Complete Adiabatic Evaporation of Highly Superheated Liquid Jets

A nozzle expansion into a vacuum chamber was used to investigate the evaporation of highly superheated liquid jets. The large molar specific heat of fluids with high molucular complexity - in this caseC 6 F 14- is responsible for the new phenomena reported here. A modelwas developed to describe the basic physical effects. A cubic equation of state was used to describe the thermodynamic properties of the fluid. The evaporation was modelled as a sonic deflagration followed by an axisymmetrie supersonic expansion. As in the case of hypersonic gas jets the final state is reached by a normal shock. Forsufficiently high temperatures and expansion ratios a complete adiabatic evaporation of the liquid was found. At even higher temperatures the liquid evaporates completely within a rarefaction discontinuity. The predictions of the model are in good agreement with the experimental results.

Flow oscillations in a duct with a rectangular cross-section

A two-dimensional configuration has been investigated in which air flows through a convergent nozzle and expands abruptly into a rectangular duct of larger cross-section which terminates in a plenum chamber. Three different types of oscillation have been observed in the downstream duct. At low plenumchamber pressures an oscillation occurs towards the exit of the duct as the boundary layer of the flow becomes alternately separated and attached. At increasing plenum pressure a shock-pattern oscillation takes place in which a change from a normal shock to oblique shocks occurs during a cycle. At still greater plenum pressures a base-pressure oscillation occurs which influences the entire duct flow downstream of the abrupt change in cross-section. The amplitudes of the oscillation can be as high as 10% of the rest state, and the frequency of the base-pressure oscillations can be predicted approximately from one-dimensional gasdynamic theory. The unsteady duct phenomena have been studied by synchronizing instantaneous pressures measured by quartz pressure transducers with interferograms obtained with a Mach–Zehnder interferometer.

Automatic Evaluation Of Interferograms

A system for the automatic evaluation of interference patterns has been developed. After digitizing the interferograms from classical and holografic interferometers with a television digitizer and performing different picture enhancement operations the fringe loci are extracted by use of a floating-threshold method. The fringes are numbered using a special scheme after the removal of any fringe disconnections which might appear if there was insufficient contrast in the interferograms. The reconstruction of the object function from the numbered fringe field is achieved by a local polynomial least-squares approximation. Applications are given, demonstrating the evaluation of interferograms of supersonic flow fields and the analysis of holografic interferograms of car-tyres.

Evaporation Waves in Fluids of High Molar Specific Heat

In a fluid of high molar specific heat, i. e. composed of molecules with a large number of atoms, a complete phase transition can occur adiabatically because at high temperatures the energy stored in the large number of internal degrees of freedom of the molecules exceeds by a great margin the energy involved in the phase transition. Jet experiments were carried out to obverve the case of evaporation from an initially saturated state. The phenomena observed for the superheated liquid jets are partial and complete evaporation discontinuities with sonic outflow into an underexpanded supersonic jet and a new type of cylindrical recompression shock wave. A comparison of the experimental results is done with the theory for deflagration waves.

Flow Visualization of a Shock Wave by Simple Refraction of a Background Grid

Experiments with high-molecular-weight fluids yield large absolute density changes across gas-phase shock waves, producing correspondingly large changes in the index of refraction n. In the experiments described here, the change Δn across the shock is of order 10-2. Simple photography of the shock against a ruled background grid shows a visible shockfront by refraction of the grid lines. Comparison of the photographic image with an image generated by optical ray tracing yields a measurement of the density behind the shock.