## Book Volume 1

##### Abstract

Fluid drag or friction depends on the physical characteristics of the fluid and solid surface. It is very important to control fluid flow and achieve drag reduction. To this end, it is necessary to understand the phenomenon of drag reduction from the viewpoint of energy saving in hydraulic transportation systems. Studies on flow drag have greatly contributed to the development of hydraulics and fluid mechanics. Although we can compute the drag of a blunt body or pressure loss of a channel in various sorts of fluid flow by using the systematized knowledge gained thus far, still some unexplained phenomena have occurred in actual flow-field. Thus, it can be considered that there are two research directions; one concerns energy saving in practical applications; and the other involves the clarification of the phenomenon due to changes in the physical characteristics of fluids and surfaces during experiments. With regard to energy saving, it is possible to design and construct apparatus for simulating drag reduction by using experimental data. In this section, a drag reduction technique employing either drag reducing additives or drag reducing walls is explained. In addition, some existing experimental data on the characteristics of drag reducing walls used in laminar drag reduction are summarized.

##### Abstract

Laminar drag reduction, which occurs through apparent fluid slip, was shown for Newtonian liquids flow in a pipeline system with a highly water-repellent wall pipe by measuring the pressure drop and the velocity profile. The same hydrophobic pipe was also used in experiment for a circular pipe flow, shown in Fig. 4 in Chapter 1. It is 14% in the drag reduction ratio for 12 mm diameter pipe. The friction factor formula for a pipe with fluid slip at the wall was derived analytically using the Navier-Stokes equation and Navier’s hypothesis for fluid slip of the boundary condition. The result obtained using the friction factor formula agrees well qualitatively with the experimental data. It was experimentally clarified that the relation between the slip velocity and the wall shear stress is a substantially linear relation. Because the sliding constant is given by the gradient of an approximated straight line from Navier’s hypothesis, the comparisons between the experimental data and the analytical result are quantitatively enabled by substituting the value for the friction factor formula. Measurement result of the velocity profile shows the occurrence of slip velocity at the wall, and the cause of slip is discussed It can be considered that the micro bubble has no effect for the slip velocity since this flow system size is order of 10mm. Experimental result of surfactant solutions without the laminar drag reduction suggests the existence of air-liquid interface at the wall.

##### Abstract

High molecular weight polymer solutions or surfactant solutions are typical examples of complex fluids. They exhibit nonlinearity in viscosity and drag reduction occurs in the turbulent pipe flow even if the concentration is very dilute. They are generally known as non-Newtonian fluids. By applying a hydrophobic wall pipe to reduce drag on the flow of polymer solutions, a flow system was constructed, wherein drag reduction was obtained in both the laminar and turbulent flow ranges. In discussions of Newtonian fluid in Chapter 2, we dealt with apparent slip flow analytically using Navier’s hypothesis, and the result was compared with the experimental findings of the friction factor. The experimental results of PEO (polyethylene oxide) aqueous solutions with a concentration range of 30-1000 ppm and the analytical result for the friction factor of a power-law fluid with fluid slip were analyzed by applying the modified boundary condition on fluid slip, as described in this chapter.

##### Abstract

The laminar flow in a duct can be found by the exact solution of the Navier- Stokes equation. An experimental apparatus that changes the flow using a detachable channel side plate can be used to measure the velocity profile or pressure drop in order to find the dominant determiner of the wall’s characteristics. In this section, the mechanism of the apparent fluid slip is discussed by comparing the experimental test results from two ducts having hydrophobic walls with different structural characteristic but almost the same water-repellency characteristics. Different kinds of hydrophobic walls were produced for duct wall, and the laminar drag reduction was examined by measuring the pressure drop.

##### Abstract

The flow pattern between two coaxial rotating cylinders changes from Couette flow to Taylor vortex flow with an increase in the rotation speed. The flow systems described here are Couette flow and laminar Taylor vortex flow. Even though Couette flow is one of the simple shear flows, because it a reasonably good model for certain kinds of friction bearings, it is significant to experimentally clarify the drag reduction phenomenon with fluid slip for the frictional torque acting on a rotating shaft for the practical applications. In the Taylor vortex flow range, the effect of the apparent fluid slip on the vortex formation is examined analytically and experimentally.

##### Abstract

Flow near a rotating disk with constant angular velocity is a typical example of a three dimensional boundary-layer flows. In the case where the flow around a disk is rotating in a housing, i.e., when the rotating disk is enclosed, we can apply the flow model of a turbo-machinery impeller in a casing to estimate the frictional torque. Thus, many studies have been performed to clarify the characteristics of such flow. In this chapter, experiments were carried out to measure the velocity profile and frictional torque acting on a rotating disk with fluid slip in a Newtonian fluid filled chamber. A disk with a highly water-repellent wall gave rise to the drag reduction phenomenon when the moment coefficient was in the laminar flow range. Analysis of the moment coefficient by using momentum integral equations with the fluid slip boundary condition revealed results that qualitatively agreed with the experimental results.

##### Abstract

Flow patterns for a circular cylinder with fluid slip have been described experimentally using a cylinder with a highly water-repellent surface with Reynolds numbers Re-ranging from Re = 20 to 150. In addition, the stream lines of the flow past a circular cylinder have been analyzed in the Reynolds numbers 20 and 50 by using the fluid slip boundary condition described in Chapter 1. The analytical results agreed well with the experimental results obtained by the flow visualization. Flow separation can often result in increased increasing drag, particularly pressure drag which is caused by the pressure differential between the front and rear surface of the cylinder as it travels through the fluid. The delay in the flow separation is associated with a significant reduction in the drag. The results showed that the separation point of a cylinder with a highly water-repellent surface moves downstream compared to that of a smooth surface cylinder. This phenomenon is conducive to drag reduction with a fluid slip. The drag reduction ratios for tap water obtained from this calculation are 15% and 10% at Re = 20 and 50, respectively. The Strouhal number of a cylinder with fluid slip increases in comparison with the value for a smooth surface cylinder with no fluid slip.

##### Abstract

Drag reduction for a uniform velocity flow past a sphere with highly waterrepellent
surface and a gas liquid interface has been investigated experimentally and
analytically for Reynolds numbers ranging from 10 to 10^{4}. The surface of a sphere had
high water repellency (contact angle of ~150°) and the gas liquid interface exists at the
surface with many fine grooves. Experimental results showed that the separation point
of the boundary layer around a sphere moved downstream compared with that of a
smooth surface sphere. It was also shown, by measuring the sphere drag, that drag
reduction for a sphere with highly water-repellent surface occurs at Reynolds numbers
less than 10^{4} and that the maximal drag reduction ratio is 28.5 % at Re = 7.2. By
considering that such a phenomenon occurs due to an apparent fluid slip at the gas
liquid interface of a hydrophobic surface, the flow patterns around a sphere were
analyzed by applying the gas liquid two-phase model at the surface proximity. Results
of numerical simulations were obtained for Reynolds number ranging from 100 to 450.
The boundary condition for fluid slip was given by assuming an effective slip boundary
condition of the surface. A comparison of the simulation results with the experimental
results shows a close agreement concerning the flow patterns of the wake and drag
coefficient.

## Introduction

The phenomenon of resistance to motion through a fluid is believed to be a function of fluid-wall interaction. This theory is based on the assumption that under certain conditions a real fluid does not usually slip on the wall in contact with it and displays laminar flow. This set of conditions is known as a ‘no slip boundary condition’. But if a fluid is passed alongside a wall, the drag reduction in the laminar flow region can be calculated. In Laminar Drag Reduction, the frictional drag of an internal or an external fluid flow along a certain kind of hydrophobic wall is investigated. An analytic approach towards the mechanism of drag reduction is employed using Navier-Stokes existence and smoothness equations. The experimental results presented in this book show that frictional drag of a fluid alongside this hydrophobic wall decreases in comparison with fluid flow along a conventional wall or surface. This form of laminar drag reduction represents a relatively new area of research, where the laminar flow can be controlled by microscopic surface modifications, allowing fluid flows to slip over a wall. Laminar Drag Reduction brings information about some interesting phenomena related to fluid slippage on a highly water-repellent surface. Readers, physics graduates and senior researchers alike, can benefit from the information presented in this book to tackle more challenging questions in fluid mechanics research.