Differences In Space Research Articles

Rotor free-wake modeling using a pseudoimplicit relaxation algorithm

A pseudoimplicit predictor-cor rector relaxation algorithm with five-point central differencing in space has been developed for the solution of the governing differential equations of the helicopter rotor free-wake problem. This new approach is compared and contrasted with more conventional explicit-type free-wake algorithms. A convergence analysis shows that the new algorithm provides for much more rapid convergence characteristics compared to explicit methods, with improvements in numerical efficiency and predictive accuracy. Nomenclature be = spatial boundary condition vector CT = rotor thrust coefficient, Tlp7rR2([lR)2 c = blade chord, m E — shift operator i,/, k = unit vectors in the x, y, and z directions, respectively L = spatial discretization operator / = length of discretized vortex element, m Nh = number of blades N.t. = number of vortex filaments P = iteration scheme operator R = rotor radius, m r(. = vortex core radius, m r, = spanwise location from which vortex filaments are trailed, m r = position vector of a point on a vortex filament, m S = source vector T = rotor thrust, N / = time, s V.,_ — freestream velocity, m/s V = time invariant flowfield velocity, m/s Vind = induced velocity, m/s Vloc = local velocity at a point in space, m/s VH = tangential velocity, m/s Cartesian coordinate system, origin at hub center rotor shaft angle (negative forward), deg )3() = blade coning angle, deg r = circulation, m2/s Ar = nth iteration position-vector correction f = distance along trailed wake filament (wake age), rad A.- = uniform-induced inflow ratio

Large‐eddy simulation of turbulent flow and heat transfer in plane and rib‐roughened channels

AbstractLarge‐eddy simulation results are presented and discussed for turbulent flow and heat transfer in a plane channel with and without transverse square ribs on one of the walls. They were obtained with the finite‐difference code Harwell‐FLOW3D, Release 2, by using the PISOC pressure‐velocity coupling algorithm, central differencing in space, and Crank‐Nicolson time stepping. A simple Smagorinsky model, with van Driest damping near the walls, was implemented to model subgrid scale effects. Periodic boundary conditions were imposed in the streamwise and spanwise directions. The Reynolds number based on hydraulic diameter (twice the channel height) ranged from 10 000 to 40 000. Results are compared with experimental data, k‐ϵ predictions, and previous large‐eddy simulations.

Implicit particle simulation of electromagnetic plasma phenomena

A direct method for the implicit particle simulation of electromagnetic phenomena in magnetized, multi-dimensional plasmas is developed. The method is second-order accurate for ω Δt < 1, with ω a characteristic frequency and time step Δt. Direct time integration of the implicit equations with simplified space differencing allows the consistent inclusion of finite particle size. Decentered time differencing of the Lorentz force permits the simulation of strongly magnetized plasmas in the limit of zero perpendicular temperature. A Fourier-space iterative technique for solving the implicit field corrector equation, based on the separation of plasma responses perpendicular and parallel to the magnetic field and longitudinal and transverse to the wavevector, is described. Wave propagation properties in a uniform plasma are in excellent agreement with theoretical expectations. Applications to collisionless tearing and coalescence instabilities further demonstrate the usefulness of the algorithm.

A Comparison of Two Explicit Time Integration Schemes Applied to the Transient Heat Equation

Abstract The forward-central (forward in time, central differencing in space) scheme and the Dufort-Frankel scheme applied to the transient heat equation are discussed here. The Dufort-Frankel scheme is shown to be unable to damp the oscillation of the high oscillatory 2Δx wave. It can even become unstable for this wave which may be produced by the initial conditions, nonlinear interactions, or other forcing. On the other hand, the forward-central scheme works well if μ<0.5. Examples of the applications of these schemes in fluid dynamics are also presented in this paper. It is also noted that none of the schemes are accurate for the high-frequency short wave.

Increase of random errors in temperature forecasts by numerical method and limiting period of reliable forecasts

It is shown that random errors of temperature observations increase in the course of forecasting temperature field by numerical method. The forecast equation under test is the advection equation for temperature with 'forward, differencing in time and 'centred' differencing in space, under an assumption that errors in temperature and wind at neighbouring grid-points are statistically uncorrelated :with one another. An analytical expression has been derived for its growth as a function of wind speed, time step, grid distance, temperature gradient and random errors in wind and temperature. The analytical result has also been verified by numerical experiment. With a grid of 200 n. miles and time step of 20 min., in a wind regime of 20 kt, the standard deviation of initial random error doubles itself in about 12 days.