Hypersonic Flow Over a Flat Plate: CFD Comparison with Experiment

Lofthouse, Andrew J.; Boyd, Iain D.

doi:10.2514/6.2009-1315

Cited by 9 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These results also agree qualitatively with trends observed computational fluid dynamics simulations [37] and measurements [38] of hypersonic flow over a flat plate. The results showed that the skin friction and boundary-layer thickness decreased as the momentum accommodation coefficient decreased, which corresponds to an increase in K.…”

Section: Fluid Flow Resultssupporting

confidence: 89%

Falkner-Skan Flow over a Wedge with Slip Boundary Conditions

Martin

Boyd

2010

Journal of Thermophysics and Heat Transfer

View full text Add to dashboard Cite

The Falkner-Skan solution for laminar boundary-layer flow over a wedge is modified to allow for a slip boundary condition. A modified boundary-layer Knudsen number K is introduced, and the coordinate system is transformed from one-dimensional to two-dimensional to allow for the loss of self-similarity in the flow. A marching scheme is used 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.

show abstract

Section: Fluid Flow Resultssupporting

confidence: 89%

Falkner-Skan Flow over a Wedge with Slip Boundary Conditions

Martin

Boyd

2010

Journal of Thermophysics and Heat Transfer

View full text Add to dashboard Cite

show abstract

“…This calculation does a better job at matching experimental normal stress and suggests that the accommodation coefficient in experiments varied spatially. Similar trends were noted by Lofthouse and Boyd [13]. These are discussed in Sec.…”

Section: B Uncertainties In the Surface Fluxessupporting

confidence: 85%

“…The uncertainty in the accommodation coefficient is expected to be large because the coefficient depends on surface properties, surface finish, temperature, chemistry, and molecular gas properties that are difficult to measure experimentally and may change in flight. By comparing their numerical simulations of Mach 11.9 nitrogen flow above a flat plate to Cecil and McDaniel's experiments [12], Lofthouse and Boyd [13] showed that, near a LE, an accommodation coefficient of 0.5 reproduces the experimental slip velocities accurately but an accommodation coefficient of 0.75 provides a better match 12.5 mm from the LE. On the other hand, the accommodation coefficient should be decreased in the downstream direction to best reproduce the normal velocity components.…”

Section: Introductionmentioning

confidence: 98%

Modeling Uncertainties in Direct Simulation Monte Carlo Calculations of Hypersonic Leading-Edge Flow

Kulakhmetov

Alexeenko

2012

Journal of Spacecraft and Rockets

View full text Add to dashboard Cite

The effects of uncertainties in the gas-surface and intermolecular interaction models on a hypersonic boundarylayer development are investigated by propagating these uncertainties through direct simulation Monte Carlo calculations of Mach 10 and 20 flows. The model input uncertainties considered are the momentum accommodation coefficient in the Maxwellian gas-surface interaction model, surface temperature and the viscosity exponent in the variable hard sphere molecular model. The effects of the input uncertainties are quantified by computing produced uncertainties in the flowfield temperature, flowfield density, surface shear, pressure, and heat flux. A nonintrusive generalized polynomial chaos expansion is used to propagate the uncertainties; reconstruct the probability density functions; and calculate the mean, standard deviation, and skewness of the output variables. It is shown that the polynomial chaos expansion with just three flowfield samples can propagate uncertainties with an accuracy equivalent to Monte Carlo methods with 10 million samples. The uncertainty analysis shows that the surface fluxes and the flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient uncertainty than surface temperature or viscosity exponent uncertainty. An input uncertainty of 19% in the accommodation coefficient results in a 20% uncertainty in the flowfield temperature at Mach 10 and a 31% uncertainty at Mach 20. This input uncertainty results in 22 and 28% uncertainties in the surface fluxes at the two Mach numbers. The produced uncertainties generally increase with Mach number, and the effect of introduced uncertainty diminishes away from the leading edge. Nomenclature a n = generalized polynomial chaos expansion coefficient C = Chapman-Rubesin constant w T 1 = 1 T w f y = probability distribution function of a dependent variable f z = probability distribution function of an independent variable I = order of Gaussian expansion M = Mach number N = order of the generalized polynomial chaos expansion N s = number of samples Re x = Reynolds number based on distance from leading edge T r = rotational temperature T t = translational temperature T w = wall temperature T 1 = freestream temperature V = rarefaction parameter M C=Re x p w i = Gaussian weight x = spatial coordinate Y = direct simulation Monte Carlo output y = independent variable y = mean of an independent variable Z = independent random variable with an arbitrary interval z = independent random variable scaled to 1; 1 interval = momentum accommodation coefficient = skewness of a dependent variable = mean free path w = coefficient of viscosity at wall temperature 1 = coefficient of viscosity at freestream temperature = density = standard deviation of a dependent variable n = orthogonal polynomial of order n ! = viscosity exponent in variable hard sphere model

show abstract

“…For example, the tangential and energy accommodation factors affect the CFD solutions. Tangential accommodation values of 0.5 seem to provide accurate results near the leading edge, whereas values between 0.75 and 1.0 yield the best agreement further along the plate [6]. The same author in another publication [7] claimed that the difficulty of defining these slip conditions is in determining the correct values for the coefficients mentioned above and other empirical terms required for the implementation.…”

Section: Recent Trends In Computational Science and Engineeringmentioning

confidence: 99%

“…Consider the Integro-Differential Model (IDM) as it is applied to the computational solution to the NSE (1)(2)(3)(4)(5)(6)(7)(8). In general, the IDS solution of a given fluid dynamic problem is built on an interconnecting set of spatial and temporal fluid cells.…”

Section: The Ids Fluid Modelmentioning

confidence: 99%

Evaluating the Hypersonic Leading-Edge Phenomena at High Reynolds and Mach Numbers

Ferguson¹,

Mendez²,

Dodoo-Amoo³

2018

Recent Trends in Computational Science and Engineering

View full text Add to dashboard Cite

Computational Fluid Dynamics (CFD) solutions have played an important role in the design and evaluation of complex problems where analytical solutions are not available. Among many practical applications, hypersonic flows have been an area of intense research because of the important challenges found in this flow regime. The numerical study conducted herein, focuses on solving the hypersonic flat plate problem under realistic conditions, at high Reynolds and Mach numbers. The numerical scheme implemented in this study solves the two-dimensional unsteady Navier Stokes Equations, using a novel technique called Integro-Differential Scheme (IDS) that combines the traditional finite volume and the finite difference methods. Moreover, this scheme is built on the premise of reducing the numerical errors through the implementation of a consistent averaging procedure. Unlike other numerical approaches, where free molecular effects are considered, this study enforces no-slip and fixed temperature as boundary conditions. The IDS approach accurately predicted the physics in the vicinity of the hypersonic leading edge at such realistic conditions. Even though there are slight discrepancies between the numerical solution and the available experimental data, the IDS solution revealed some interesting details about the flow field that was previously undiscovered.

show abstract

Hypersonic Flow Over a Flat Plate: CFD Comparison with Experiment

Cited by 9 publications

References 9 publications

Falkner-Skan Flow over a Wedge with Slip Boundary Conditions

Falkner-Skan Flow over a Wedge with Slip Boundary Conditions

Modeling Uncertainties in Direct Simulation Monte Carlo Calculations of Hypersonic Leading-Edge Flow

Evaluating the Hypersonic Leading-Edge Phenomena at High Reynolds and Mach Numbers

Contact Info

Product

Resources

About