Modified GHS Model Compared With the VHS Collision Model in DSMC Computations

The generalized hard sphere (GHS) collision model was introduced by Hash and Hassan (1993). It is a generalization of the Sutherland collision model proposed by Kuscer (1989). At low temperatures, where the attractive intermolecular forces are important, the GHS collision model produces a more accurate variation of viscosity with temperature than the standard variable hard sphere (VHS) collision model. In spite of this, the GHS model remains virtually unused owing to its computational expense. A slight modification of the GHS model, described by Macrossan and Lilley(2003), makes it no more than 15% more computationally expensive than the VHS model. In this 'modified GHS' model the total collision cross-section is set proportional to 1/g for collision speeds g T_m. This "Maxwell cross-section" for low speed collisions is more physically reasonable than the original GHS cross-section. The latter gives an unrealistic collision rate that approaches infinity as g approaches zero. We compare the modified GHS and VHS models for a blunt body flow with stagnation temperature T_o = 1300 K. We calculate the supersonic flow of argon, with a freestream temperature of 100 K, around a flat plate normal to the freestream. The wall temperatures were 1300 K (front) and 500 K (rear), with diffuse reflection. The model parameters were chosen to give the two collision models identical viscosities at the freestream and stagnation temperatures. In the recirculation region behind the flat plate, where the temperature is approximately 500 K, the local mean free path was about 12% greater for the GHS compared to the VHS model. The pressure and heat transfer to the front wall (near the stagnation region) were found to be virtually identical for the two models. There was a slight difference in pressure on the rear wall, but again the heat transfer was virtually identical for the two models. The results imply that good results can be obtained with the VHS model provided the model parameters are selected to match the desired viscosity as closely as possible, over the temperature range in the flow

Modified GHS Collision Model Compared with VHS Model

The generalized hard sphere collision model (GHS) was introduced by Hassan and Hash [Physics Fluids A, 5, 738-744, 1993]. At low temperatures, where the attractive intermolecular forces are important, the GHS collision model produces a more accurate variation of viscosity with temperature than the standard Variable Hard Sphere (VHS) collision model. In spite of this, the GHS model remains virtually unused because of its great computational expense compared to the VHS model. A slight modification of the GHS model, described in [Macrossan and Lilley, Journal of Thermophysics Heat Trans, 17, 289-291, 2003], makes it no more than 5-15% more computationally expensive than the VHS model. We compare the GHS and VHS models for a blunt body flow with T0 = 1300 K. We calculate the supersonic flow of Argon, with a freestream temperature of 100 K, around a flat plate normal to the freestream. The wall temperatures were 1300 K (front) 500 K (rear), with diffuse reflection. The viscosity for the modified GHS and VHS models used here are compared in Fig. 2 with the recommended argon viscosity [3], over the range of temperatures in the flow. The temperature in the wake region is approximately 500 K, so the viscosity of the two models differs most there. This leads to small differences in the temperature field and the size of the re-circulation region. The GHS model required only 5% more CPU

Viscosity of argon at temperatures >2000 K from measured shock thickness

Mott-Smith's approximate theory of plane 1D shock structure (Phys. Rev., 82, 885-92, 1951; Phys. Rev., 5, 1325-36, 1962) suggests, for any intermolecular potential, the average number of collisions undergone by a molecule as it crosses the shock quickly approaches a limit as the Mach number increases. We check this with DSMC calculations and show that it can be used to estimate the gas viscosity at high temperatures from measurements of shock thickness. We consider a monatomic gas(gamma = 5/3) for five different collision models and hence five different viscosity laws mu = mu(T). The collision models are: the variable hard sphere, sigma ~ 1/g^upsilon, with three values of upsilon; the generalized hard sphere; and the Maitland-Smith potential. For shock Mach numbers M_1 greater than 4.48, all these collision models predict a shock thickness Delta = 11.0 lambda_s, where lambda_s is a suitably defined 'shock length scale', with a scatter approximately 2.5% (2 standard deviations). This shock length depends on the upstream flow speed, downstream density and a collision cross-section derived from the viscosity of the gas at a temperature T_g, characteristic of the collisions at relative speed g = u_1-u_2 between upstream and downstream molecules. Using Delta = 11 lambda_s and the experimental measurements of shock thickness in argon given by Alsmeyer (J. Fluid Mech. {74}, 498-513, 1976), we estimate the viscosity of argon at high values of T_g. These estimated values agree with the viscosity of argon recommended by the CRC Handbook of Chemistry and Physics (2001) at T approximately equal to 1,500 K. For T>2,000K, for which there appears to be no reliable direct measurements of viscosity, our estimated values lie between the extrapolated values recommended by the CRC Handbook and those predicted by the simple power law mu = mu__ref(T/T_ref ^0.72, with T_ref = 30 K and mu_ref = 2.283e-5 Pa s. Taking the error in the experimental measurements of Delta as the scatter in the results of Alsmeyer plus or minus 2%, we estimate the uncertainty in the viscosity deduced from the shock thickness measurements as less than plus or minus 5%. To this accuracy, our results agree with the power law predictions and disagree with the CRC Handbook values, for T > 3,000K

Modeling Vibrational-Dissociation Coupling with the Macroscopic Chemistry Method

We test the recently developed macroscopic approach to modeling chemistry in DSMC [Lilliley & Macrossan, Physics of Fluids, 16(6), 2054-2066 (2004)], by simulating the flow of rarefied dissociating nitrogen over a blunt cylinder. In this macroscopic method, chemical reactions are decoupled from the collision routine. Molecules are chosen to undergo dissociation at each time step, after the collisions are calculated. The required number of reaction events is calculated from macroscopic reaction rate expressions with macroscopic information taken from the time-averaged cell properties. One advantage of this method is that "state-of-the-art" macroscopic information about reaction rates can be used directly in DSMC in the same way as in continuum codes. Hybrid Navier-Stokes/DSMC codes can therefore easily use the same chemical models in both rarefied and continuum flow regions. Here we show that the macroscopic method can capture dissociation-vibration (DV) coupling, which is an important effect in vibrationally cold blunt body flows because it results in increased surface heat fluxes. We use the macroscopic method with Park's two-temperature rate model, often used in continuum studies, to capture DV coupling in DSMC. This produces a flowfield in reasonable agreement with that calculated using the conventional collision-based threshold line dissociation model

A Macroscopic Chemistry Method for the Direct Simulation of Gas Flows

In most chemistry methods developed for the direct simulation Monte Carlo (DSMC) technique, chemical reactions are computed as an integral part of the collision simulation routine. In the macroscopic chemistry method developed here, the simulation of collisions and the simulation of reactions are decoupled; reactions are computed independently, after the collision routine. The number of reaction events to perform in each cell is calculated using the macroscopic reaction rates k+, k- and equilibrium constant K*, calculated from the local macroscopic flow conditions. The macroscopic method is developed here for the symmetrical diatomic dissociating gas. For each dissociation event, a single diatomic simulator particle is selected with a probability based on its internal energy, and is replaced by two atomic particles. For each recombination event, two atomic particles are selected at random, and are replaced by a single diatomic particle. The dissociation energy is accounted for by adjusting the translational thermal energies of all particles in the cell. The macroscopic method gives density profiles in agreement with experimental data for the chemical relaxation region downstream of a strong shock in nitrogen. In the non-equilibrium regions within the shock, and along the stagnation streamline of a blunt cylinder in rarefied flow, the macroscopic method gives results in excellent agreement with those obtained using the most common conventional DSMC chemistry method in which reactions are calculated during the collision routine. The number of particles per computational cell has a minimal effect on the results provided by the macroscopic method. Unlike most DSMC chemistry methods, the macroscopic method is not limited to simple forms of k+, k- and K*. Any forms may be used, and these may be any function of the macroscopic conditions. This is demonstrated by using a two-temperature rate model, and a form of K* with a number density dependence. With the two-temperature model, the macroscopic method gives densities in the post-shock chemical relaxation region that also agree with the experimental data. For a form of K^* with a number density dependence, the macroscopic method can accurately reproduce chemical recombination behavior. In a primarily dissociative flow, the number density dependence of K* has very little effect on the flow. The macroscopic method requires slightly less computing time than the most common DSMC chemistry method

Explorations, Vol. 4, No. 3

Articles include: Cover: Trophy: MooseHorn, from the Trophy Series, by Caellaigh B. Desrosiers. Editorial Reflections, by Carole J. Bombard North Cascade Glacier Climate Project, by Mauri Pelto Stained Glass Molecules, by Anne P. Sherblom Lobsters Inside-Out: A Guide to the Maine Lobster Community Forestry: UMaine Cooperative Extension Service, by Nancy E. Coverstone and William D. Lilley Where Are They Now? — Robert F. LaPrade, M.D. ’81 Little Critters with a Big Job: Ciliated Protozoa and the Gulf of Maine Food Chain, by Marcia Gauvin from a paper by Charles Gregory The Innovation of Tradition: Low-Cost, Low-Input Alternatives for Maine Farmers, by Marcia Gauvin Just What IS An Animal? Preschoolers Investigate Merging Two Cultures: Our Cover Artist, by Caellaigh Bennett Derosiers Freezing and Photosynthesis, by Steven R. Dudgeon, Ian R. Davison, and Robert L. Vada

Modified Generalised Hard Sphere Collision Model for Direct Simulation Monte Carlo Calculations

The generalised hard sphere collision model (GHS) was introduced by Hassan and Hash [Physics of Fluids A, v5(3), 738-744 (1993)] and is a generalization of the Sutherland collision model suggested by Kuscer [Physica, v158, 784-800 (1989)]. Despite its superior modelling of realistic gas viscosities, compared to the Variable Hard Sphere collision model, the GHS model is rarely used because of its great computational expense compared to the VHS model. We show here how a slight modification of the GHS model makes it no more than 15% more computationally expensive than the VHS model, while retaining its superior viscosity modelling. All that is required is that the collision probability be limited for collision speeds approaching zero, rather than increase to infinity as it does for the original GHS model. A particularly simple modification is to use a Maxwell collision cross-section (equal probabilities) for collision energies less than the attractive energy of a realistic molecular model (characteristic temperature T* approximate 90 - 150 K). For temperatures above T*, the GHS viscosity is retained, while for temperatures less than T* the viscosity is slightly different from the GHS viscosity, but arguably more realistic

Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators

Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P_0 is α times that of a scaled-up microscale resonator at a reduced pressure α P_0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales

A direct role for SNX9 in the biogenesis of filopodia.

Filopodia are finger-like actin-rich protrusions that extend from the cell surface and are important for cell-cell communication and pathogen internalization. The small size and transient nature of filopodia combined with shared usage of actin regulators within cells confounds attempts to identify filopodial proteins. Here, we used phage display phenotypic screening to isolate antibodies that alter the actin morphology of filopodia-like structures (FLS) in vitro. We found that all of the antibodies that cause shorter FLS interact with SNX9, an actin regulator that binds phosphoinositides during endocytosis and at invadopodia. In cells, we discover SNX9 at specialized filopodia in Xenopus development and that SNX9 is an endogenous component of filopodia that are hijacked by Chlamydia entry. We show the use of antibody technology to identify proteins used in filopodia-like structures, and a role for SNX9 in filopodia