Charles L. Merkle

Reduction of Turbulent Skin Friction by Microbubbles

Measurements of the effect of microbubbles on a zero pressure gradient turbulent boundary layer generated on the test section wall of a water tunnel are described. Microbubbles are created by injecting air through a 0.5 μm sintered stainless steel plate immediately upstream of a floating element drag balance. At the downstream edge of the balance the length Reynolds number is as high as ten million. Integrated skin friction reduction of greater than 80% is observed. The drag balance results are confirmed by measurements with a surface hot‐film probe. For the case in which buoyancy tends to keep the bubbles in the boundary layer, the skin friction data are shown to collapse when plotted against the ratio of air to water volume flow rate. The effects of buoyancy on skin friction reduction are also documented.

Measurements of local skin friction in a microbubble-modified turbulent boundary layer

Abstract : Local skin friction reductions have been measured using an array of flush-mounted hot-film probes in a microbubble-modified, zero pressure gradient, turbulent boundary layer. The results of earlier integrated skin friction measurements, that showed the reduction to be a function of plate orientation, gas flow rate and freestream velocity, have been confirmed both qualitatively and quantitatively. With the measurement plate above the boundary layer, it is shown that skin friction is reduced monotonically for all air flow rates at each of three freestream velocities between 4 and 17 m/sec. For the plate below the boundary layer, however, it is possible for increasing gas injection to lead to smaller local skin friction reduction at the lowest speeds. Drag reduction appears to persist for as much as 60-70 boundary layer thicknesses downstream of the injection region. It is further shown, using a probe flush mounted just upstream of the injection section, that there is no apparent upstream interference due to the gas injection. Spectral measurements indicate that microbubbles can cause a reduction of high frequency shear-stress fluctuations. This suggests a destruction of some of the turbulence in the near wall region. Skin friction, microbubble, turbulent boundary layer.

Cavity Flow Predictions Based on the Euler Equations

An Euler solver based on artificial-compressibility and pseudo-time stepping is developed for the analysis of partial sheet cavitation in two-dimensional cascades and on isolated airfoils. The computational domain is adapted to the evolution of the cavity surface and the boundary conditions are implemented on the cavity interface. This approach enables the cavitation pressure condition to be incorporated directly without requiring the specification of the cavity length or the location of the inception point. Numerical solutions are presented for a number of two-dimensional cavity flow problems, including both leading edge cavitation and the more difficult mid-chord cavitation conditions. Validation is accomplished by comparing with experimental measurements and nonlinear panel solutions from potential flow theory. The demonstrated success of the Euler cavitation procedure implies that it can be incorporated in existing incompressible CFD codes to provide engineering predictions of cavitation. In addition, the flexibility of the Euler formulation may allow extension to more complex problems such as viscous flows, time-dependent flows and three-dimensional flows.

Numerical Modeling of the Thermodynamic Effects of Cavitation

A Navier-Stokes solver based on artificial compressibility and pseudo-time stepping, coupled with the energy equation, is used to model the thermodynamic effects of cavitation in cryogenic fluids. The analysis is restricted to partial sheet cavitation in two-dimensional cascades. Thermodynamic effects of cavitation assume significance in cryogenic fluids because these fluids are generally operated close to the critical point and also because of the strong dependence of the vapor pressure on the temperature. The numerical approach used is direct and fully nonlinear, that is, the cavity profile evolves as part of the solution for a specified cavitation pressure. This precludes the necessity of specifying the cavity length or the location of the inception point. Numerical solutions are presented for two-dimensional flow problems and validated with experimental measurements. Predicted temperature depressions are also compared with measurements for liquid hydrogen and nitrogen. The cavitation procedure presented is easy to implement in engineering codes to provide satisfactory predictions of cavitation. The flexibility of the formulation also allows extension to more complex flows and/or geometries.

Microbubble Drag Reduction in Liquid Turbulent Boundary Layers

The interactions between a dense cloud of small bubbles and a liquid turbulent boundary layer are reviewed on the basis of available experimental observations to understand and quantify their capability for reducing skin friction. Gas bubbles are generally introduced into the boundary layer by injection through a porous surface or by electrolysis. After injection, the bubbles stay near the wall in boundary-layer-like fashion giving rise to strong gradients in both velocity and gas concentration. In general, the magnitude of the skin friction reduction increases as the volume of bubbles in the boundary layer is increased until a maximum skin friction reduction of typically 80–90% of the undisturbed skin friction level is reached. The volumetric gas flow required for this maximum is nominally equal to the volume flow of the liquid in the boundary layer. Bubble size estimates indicate that in most microbubble experiments the bubbles have been intermediate in size between the inner and outer scales of the undisturbed boundary layer. Additional studies with other nondimensional bubble sizes would be useful. However, the bubble size is most likely controlled by the injection process, and considerably different conditions would be required to change this ratio appreciably. The trajectories of the bubble clouds are primarily determined by the random effects of turbulence and bubble-bubble interactions. The effects of buoyancy represent a weaker effect. The trajectories are unlike the deterministic trajectory of an individual bubble in a time-averaged boundary layer. Bubbles are most effective in high speed boundary layers and, for the bubble sizes tested to date, produce an effect that persists for some one hundred boundary layer thicknesses. Modeling suggests that microbubbles reduce skin friction by increasing the turbulence Reynolds number in the buffer layer in a manner similar to polymers. Although the effects of microbubbles are consistent and reproducible, their primary practical limitation is the volume of gas needed. Studies aimed at reducing the volumetric gas flow requirements are recommended. Potential applications would favor high speed vehicles operating near the surface where pumping work is minimized.

Bubble characteristics and trajectories in a microbubble boundary layer

Optical and photographic surveys of microbubble boundary layers are presented. The results show that the outer edge of the bubble cloud diffuses away from the wall as the bubbles are swept downstream. The plate‐on‐bottom orientation contains a bubble‐free region near the wall that cannot be discerned for the plate‐on‐top configuration. Skin friction measurements made when the bubble‐free region extends to y+=200 show there is no longer any Cf reduction present suggesting bubbles are not effective when they are outside the near‐wall region of the boundary layer. Bubble sizes, which increase with airflow and distance from the injection section and decrease with free‐stream velocity, were measured to be between 150 and 1100 μm.

The relation between flux vector splitting and parabolized schemes

Abstract The relationship between PNS and thin layer Navier-Stokes algorithms is used to develop traditional as well as new PNS procedures. The use of characteristics-based flux vector splitting gives rise to a parabolized system that is based on the predominant physics of the flow, while pressure-gradient-based flux vector splitting is shown to give the traditional parabolized scheme of Vigneron. Comparisons with TLNS results show the characteristics-based PNS system gives results that are at least as accurate as the more traditional pressure-gradient-split PNS system. The use of a safety factor in the pressure-gradient splitting is shown to cause inaccuracies and should be avoided. The interpretation of PNS procedures as the first sweep of a TLNS ADI procedure also suggests an obvious global pressure iteration method that is mathematically well posed and, hence, leads to an efficient rapidly converging global iteration procedure.

Microbubble Drag Reduction

Over the past twenty-five years there has been extensive and sustained research aimed both at determining techniques for reducing skin friction drag and at explaining how successful techniques work. Certainly, one reason for pursuing this research is because of our need to drive systems faster and farther for the same power, but this is only part of the motivation. An important additional rationale for the work is bound up with our continuing fascination with boundary layers -- particularly turbulent boundary layers -- with what makes them work the way they do and how we might intervene and change them.

A comparison of shear stress fluctuation statistics between microbubble modified and polymer modified turbulent boundary layers

Shear stress fluctuation statistics, as measured by flush mounted hot film probes, are presented for both microbubble and polymer injection into the same zero pressure gradient turbulent boundary layer. At equivalent values of drag reduction, the moments of the probability distribution are remarkably similar. For drag reductions larger than about 40%, the deviation of the skewness and kurtosis values from their pure water values argue against simple scaling explanations of the drag reduction phenomenon.

Characteristics of Tip-Clearance Flows of a Compressor Cascade and a Propulsion Pump

Tip-leakage flows for a linear compressor cascade and a one-stage shrouded pump rotor are discussed in this paper. A numerical method solving the Reynolds averaged Navier Stokes equations is used to explore various detail features of the tip-leakage flows. Calculation results for the cascade provide an assessment for predicting flow past a non-rotating blade passage with zero and 2% chord clearances. On the other hand, the pump rotor configuration provides a swirling passage flow with the complication of a trailing-edge separation vortex mixed with the tip-clearance and passage vortices and produces a very complex three-dimensional flow in the rotor wake. The physical aspects of the tip-clearance flows are discussed including suction-side reloading and pressure-side unloading due to a tip clearance and formation and transportation of the tip-leakage vortex. Detailed velocity comparisons in the blade passage and the tip gap region are shown to indicate the difficulty of predicting tip-leakage flow. The pressure at the core of the tip vortex is also examined to evaluate the strength of the tip-leakage vortex. Some computational guidelines for design usage are provided for these tip-leakage flow calculations.Copyright