Michael James Martin

Momentum and Heat Transfer in a Laminar Boundary Layer with Slip Flow

Flow in a laminar boundary layer is modeled using a slip boundary condition. The slip condition changes the boundary layer structure from a self-similar profile to a two-dimensional structure. Although the slip condition generally leads to decreased overall drag, two-dimensional effects cause local increases in skin friction. Other effects include thinner boundary layers, delayed transition to turbulence, and changes in the heat transfer at the wall. Without a thermal jump condition, slip will lead to increased heat transfer. When a thermal jump boundary condition is added to simulate real gases, the heat transfer decreases to below the no-slip values.

Blasius Boundary Layer Solution With Slip Flow Conditions

As the number of applications of micro electro mechanical systems, or MEMS, increase, the variety of flow geometries that must be analyzed at the micro-scale is also increasing. To date, most of the work on MEMS scale fluid mechanics has focused on internal flow geometries, such as microchannels. As applications such as micro-scale flyers are considered, it is becoming necessary to consider external flow geometries. Adding a slip-flow condition to the Blasius boundary layer allows these flows to be studied without extensive computation.

Falkner-Skan Flow over a Wedge with Slip Boundary Conditions

DOI: 10.2514/1.43316 TheFalkner–Skansolutionforlaminar boundary-layer flowoverawedgeismodifiedtoallow foraslipboundary condition. A modified boundary-layer Knudsen number K is introduced, and the coordinate system is transformed fromone-dimensionaltotwo-dimensionaltoallowforthelossofself-similarityinthe flow.Amarchingschemeisused to solve the boundary-layer equations in the rarefied flow regime. The results of this solution show decreased skin friction, boundary-layer thickness, velocity thickness, and momentum thickness because of the presence of the slip boundary condition. When the energy equation is solved using a temperature-jump boundary condition, the heat transfer increases for slightly rarefied flows, and then decreases as the Knudsen number increases.

Momentum and Heat Transfer in Laminar Slip Flow over a Cylinder

The vorticity transport and energy equations are solved numerically in a laminar gas flow past a circular cylinder. The slip boundary condition and temperature jump are applied at the cylinder wall. The changes in heat transfer and slip velocity at the cylinder wall due to Knudsen and Reynolds number variations are calculated. The velocity at the wall increases as the Knudsen number increases due to the slip condition. The separation point moves downstream as slip increases. As the Knudsen number increases, the slip increases at the wall and the heat flux between the cylinder wall and the flow decreases. These results show that the heat transfer coefficient and the Nusselt number decrease as the slip increases. When hot wires are used for temperature measurements, failure to include a slip boundary condition will also lead to an error in the temperature measurement.

Stagnation-Point Heat Transfer Near the Continuum Limit

H EAT and momentum transfer at the stagnation point is a problem of theoretical and practical interest. Solution of the Navier–Stokes equations at the stagnation point is one of oldest known solutions to the Navier–Stokes equations [1,2] and is closely related to boundary-layer flow [3]. Once the fluid flow is computed, the heat transfer can be computed in both 2-dimensional [4] and axisymmetric [5] geometries. The importance of stagnation-point heat transfer in problems such as atmospheric reentry [6] and other rarefied hypersonic flows [7] make estimating the heat transfer a problem of practical engineering interest. Initial attempts to solve stagnation-point flow and boundary-layer flow with a slip boundary condition using perturbation methods [8] suggested that the slip condition would not affect shear stress or heat transfer. Amore complete thermal analysis partially contradicted this result, suggesting that heat transfer in a laminar boundary layer decreased in the presence of a slip boundary condition [9]. The apparent lack of a change in shear stress due to the slip condition led to the conclusion that the terms added by the slip boundary condition were smaller than the discarded second-order terms in the boundary-layer equations [10]. This led to the conclusion that slip could be ignored in both laminar boundary-layer and stagnationpoint flows. These conclusions were challenged by numerical results, including solution of the linearized Boltzmann equation for stagnation-point flow [11], solution of stagnation-point flow with slip [12], and solution of the Blasius boundary-layer equations with slip flow that incorporated the loss of self-similarity [13]. All of these analyses showed decreased shear stress and boundary-layer thickness. When heat transfer was incorporated in the boundarylayer analysis, the heat transfer decreased from the equilibrium values. The present work extends previous analysis of the fluid flow and heat transfer in the presence of a slip boundary condition [12,14] to cover rarefied flow, in which the temperature jump and slip boundary conditions are coupled. This analysis provides an estimate for change in heat transfer due to rarefied-flow effects for a range of Knudsen and Prandlt numbers for both monatomic and diatomic gases.

Design of a Low-Turbulence, Low-Pressure Wind-Tunnel for Micro-Aerodynamics

A novel wind-tunnel facility has been designed for measurement of lift and drag on micromachined airfoils. The tunnel is designed to operate with pressures ranging from 0.15 to 1.0 atmosphere, over a velocity range of 30 to 100 mls, allowing for independent control of Reynolds and Knudsen number. The tunnel is designed for testing of airfoils with chords of 10 to 100 microns, giving a range of Reynolds numbers from 10 to 600, with Knudsen numbers reaching 0.01. Due to the structural constraints of the airfoils being tested, the wind tunnel has a 1 cm cross-section. This small size allows the use of a 100-1 contraction area, and extremely fine turbulence screens, creating a low turbulence facility. Computational fluid dynamics is used to show that an ultra-short 100-1 contraction provides uniform flow without separation, or corner vortices. Velocity data obtained with impact and hot-wire probes indicate uniform flow and turbulence intensities below 0.5%.

Measurement of Continuum Breakdown During Disk Spindown in Low-Pressure Air

The deceleration torque during spindown of a disk is measured across a range of air pressures on three aluminum disks. The diameters of the disk are 0.15, 0.17, and 0.21xa0m; the range of pressures is 0.71xa0Pa to atmospheric pressure; and the angular velocities range approximately from 400 to 3300xa0rpm. The results are compared to computational fluid dynamics for the continuum flow regime and analytical results for the free molecular flow regime. The torque is nondimensionalized using dynamic viscosity of air, instantaneous angular velocity, and the disk diameter and is plotted against Reynolds number. Results show that the nondimensional curves from atmospheric pressure through 100xa0Pa collapse on each other for all disk diameters and agree with computational-fluid-dynamics results. At low pressures, the nondimensional torque does not change with Reynolds number. The analytically obtained free molecular flow torque is compared with the experimental results at the lowest ambient pressures, and the value of mom...

Fabrication of beam structures with micro-scale cross-sections and meso-scale spans

To allow testing of micro-scale aerodynamics, a process was created to manufacture beam structures that combine spans of 1 cm with a cross-section of 5 µm by 100 µm. The structural considerations limiting the fabrication of a structure combining macro-scale spans with a micro-scale cross-section are analyzed. Limiting considerations include forces during operation, fluid forces during release, vibrational limitations and beam buckling. Based on these results, a fabrication process for creating a beam structure for large spans without support structures is devised, incorporating the use of back-side etches and extra handling wafers to avoid stiction. This process is used to successfully fabricate the desired structure. (Some figures in this article are in colour only in the electronic version)

Design of a Low-Turbulence Facility for Micro-Scale Aerodynamics

A novel wind-tunnel facility has been designed for measurement of lift and drag on micromachined airfoils. Due to the structural and geometric constraints of the airfoils being tested, the wind tunnel has a 1-centimeter cross-section. This small size allows the use of a 100-1 contraction area, and extremely fine turbulence screens, creating an ultra-low turbulence facility. Preliminary velocity data obtained with a hot-wire probe indicate a successful design, with uniform flow, and turbulence intensities below 1%.Copyright

Measurement of Viscous Drag on a Disc Rotating in a Low Pressure Gas

Viscous drag on a rotating disc under different air-pressures is measured experimentally. Disc spin-down experiments are carried out from atmospheric pressure through a vacuum pressure of 1333 Pa. Deceleration torque was plotted as a function of angular velocity at the various pressures. Torque was nondimensionalized using dynamic viscosity of the air, angular velocity and the characteristic dimension of the disc. The results obtained could approximately be classified into two sets of self-similar curves, the first set between atmospheric pressure and 13332 Pa, and the second set between 13332 Pa and 1333 Pa.