It is noted that the experimental and empirical approach in hydroplaning studies has yielded valuable information on the various parameters that can affect hydroplaning and helps in the formulation of strategies to reduce hydroplaning occurrences. However, the qualitative and empirical models have done little in advancing pavement researchers’ understanding on the mechanisms involved in hydroplaning. Thus researchers have also looked into the problem from an analytical and numerical perspective since the 1960s.
The first analytical treatment of the hydroplaning problem was proposed by Moore (1967) in his discussion of the theory of viscous hydroplaning. In this analysis, a rubber sliding on a two-dimensional smooth sinusoidal asperity separated by a thin fluid film is modeled. A one-dimensional Reynolds equation solution was obtained in which inlets, central and outlet regions for the fluid film were treated separately. Correlation was obtained with expected values for load capacity, friction level and minimum clearance by the inclusion of many empirical constants in the formulation. The main weaknesses of the method are that many assumptions on the nature of the problem had to be made; there are limitations due to a two- dimensional asperity and a lack of consideration of side flow. This theory is thus strictly limited to the viscous hydroplaning situation.
Subsequent works in the theoretical and numerical modeling in the next two decades were sponsored by NASA. Martin (1966) considered the two-dimensional irrotational flow problems of rigid curved surfaces of arbitrary shape planning on an incompressible viscid fluid. Potential flow theory was employed and conformal mapping techniques were used to obtain the solution. A recovery factor of 0.8 was obtained as compared to 0.644 for NASA.
However, when the proper approximations were added to his theory so that the results could be
NASA (Browne, 1971). This is due to the fact that side flow and viscosity were totally neglected in his analysis, resulting in no formation of bow-wave, and the fact that no variation in gap in the direction perpendicular to the flow was incorporated.
Eshel (1967) considered the total dynamic hydroplaning using a three-region approach. Different simplifying assumptions were made to the nature of the flow in each region. The solutions obtained were coupled at the regional boundaries. Simple models of tire flexibility were coupled to the system to allow an elasto-hydrodynamic system. However, the model failed to consider the side flow in the inlet region under the wheel. Furthermore, the treatment of the problem as a two-dimensional problem is inappropriate. The assumption of a laminar parabolic velocity profile is not accurate as Browne (1971) has shown the flow to be turbulent.
Tsakonas et al. (1968) took a purely inviscid approach using the hydrofoil theory to solve the problem of a flat rigid surface of small aspect ratio in extremely shallow water. The only case for which a solution was obtained was for a plane flat rigid plate of low aspect ratio under which the pressure distribution of the pavement was a step function equal to the inflation pressure. However, this method is not appropriate because (1) the lift coefficient was small compared to experimentally measured values such as those by NASA; (2) the use of the inviscid theory is invalid for hydroplaning; and (3) the real tire deformation profile is never planar.
Browne (1971) proposed a two-dimensional treatment for a three-dimensional tire deformation model for hydroplaning, making use of the Navier-Stokes equations. In his model, inviscid, laminar and turbulent models were explored, and side flow was considered. The later parts of his work made use of solely the laminar flow model in the hydroplaning simulation.
However this method is not entirely appropriate since (1) the flow in the hydroplaning situation is turbulent (Schlichting, 1960); (2) the recovery factors of 0.56 in his model is low compared to the NASA experimentally measured values of about 0.644; (3) the model
flow and pavement surface in his numerical verification.
Browne and Whicker (1983) extended the analysis to include tire deformation by considering the interaction of the fluid flow module and the tire deformation module in the interactive procedure. This is one of the first numerical models of dynamic hydroplaning.
However, as explained in the preceding paragraph, the fluid flow model is plagued with the inability to model the NASA hydroplaning relationship.
Recent advances in computational fluid dynamics have prompted researchers to re- look into the problem of hydroplaning. Researchers began to analyze the problem of hydroplaning using two-phase flow. Groger and Weis (1996) proposed a simple mathematical two-phase model to describe the shape of the free-surface of the water around an automobile tire. Water was assumed to be incompressible and fully turbulent. The Navier-Stokes equations were solved using the finite-volume method (FVM). However, the model did not consider the effects of tire deformation during hydroplaning. Similarly, the research done by Aksenov and Dyadkin (1996) also neglected the effect of the tire deformation profile during hydroplaning.
The development of technology in fluid structure simulation has led to the use of commercial computer packages to model hydroplaning. Zmindar and Gradjar (1997) employed the ADINA fluid structure interaction package to simulate the aquaplaning of a tire using the finite element method (FEM). Although the idea was rather innovative, the flow was assumed to be laminar and there was no verification with any experimental data or the NASA equation.
Okano and Koishi (2000) made use of MSC.DYTRAN to simulate hydroplaning through fluid- structure interaction. However this study suffered a drawback in that the fluid flow was modeled using the potential flow theory. It is noted that recent research in this field is propelled by the tire industry whose main aim is to produce better tire tread design. No attention is being paid to the pavement surface characteristics and its influence to hydroplaning.
Andren and Jolkin (2003) made use of Reynolds equation without consideration of the stretch term and coupled it with ABAQUS finite element package for the tire deformation
microtexture depth. The analyses gave results that are rather incomprehensible since it showed that hydroplaning could not occur in speed from 0 to 200 km/h and the speed had to be increased to 1.6 x 103 m/s (5760 km/h) for the first full film regime to occur. Such findings could be due to a few problems. First, neglecting the asperities in micro-scale would cause the wedge effect developed by the film in micro-scale to be ignored and since viscous hydroplaning is a phenomenon associated with the microtexture of a plane surface, the assumption of a smooth surface is inappropriate. Second, the use of water as a lubricant could also cause complications. One would expect viscous hydroplaning to occur when the surface is slippery and this phenomenon tends to be associated with oil contaminated surface, rather than water. Unlike water whose density and viscosity are relatively stable at room temperature, oils have density and viscosity which vary with pressure even at room temperature. This would result in viscous hydroplaning at much lower speeds since the uplift force capable of separating the tire and asperity could be achieved when there is a thin film (of the order of micron and nanometers) of oil. Last, the problem is likely to be too large to be handled computationally since the actual dimensions of the tire differ from the film by at least three orders.