STABILITY OF LAMINAR VISCOUS FLOWS WITH A BODY FORCE
Body force effects on the hydrodynamic stability of a fully developed laminar channel flow for symmetric and asymmetric basic flows
LAMINAR FLOW↗
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Implementing Chiral Three-Body Forces in Terms of Medium-Dependent Two-Body Forces
Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many- body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of Vmed from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range 2π-exchange term, a mid-range 1π-exchange component and a short-range contact-term. Several applications of V med to the equation of state of cold nuclear and neutron matter, the nucleon single-particle potential in nuclear matter, and the nuclear quasiparticle interaction are discussed. We also explore differences in using local vs. nonlocal regulating functions on 3N forces and make direct comparisons to exact results at low order in perturbation theory expansions for the equation of state and single-particle potential. We end with a discussion and numerical calculation of the in-medium NN potential V med from the next-to-next-to-next-to-leading order (N3LO) chiral 3N force, which consists of a series of long-range and short-range terms.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Investigation of Body Force Effects on Flow Boiling Critical Heat Flux
The bubble coalescence and interfacial instabilities that are important to modeling critical heat flux (CHF) in reduced-gravity systems can be sensitive to even minute body forces. Understanding these complex phenomena is vital to the design and safe implementation of two-phase thermal management loops proposed for space and planetary-based thermal systems. While reduced gravity conditions cannot be accurately simulated in 1g ground-based experiments, such experiments can help isolate the effects of the various forces (body force, surface tension force and inertia) which influence flow boiling CHF. In this project, the effects of the component of body force perpendicular to a heated wall were examined by conducting 1g flow boiling experiments at different orientations. FC-72 liquid was boiled along one wall of a transparent rectangular flow channel that permitted photographic study of the vapor-liquid interface at conditions approaching CHF. High-speed video imaging was employed to capture dominant CHF mechanisms. Six different CHF regimes were identified: Wavy Vapor Layer, Pool Boiling, Stratification, Vapor Counterflow, Vapor Stagnation, and Separated Concurrent Vapor Flow. CHF showed great sensitivity to orientation for flow velocities below 0.2 m/s, where very small CHF values where measured, especially with downflow and downward-facing heated wall orientations. High flow velocities dampened the effects of orientation considerably. Figure I shows representative images for the different CHF regimes. The Wavy Vapor Layer regime was dominant for all high velocities and most orientations, while all other regimes were encountered at low velocities, in the downflow and/or downward-facing heated wall orientations. The Interfacial Lift-off model was modified to predict the effects of orientation on CHF for the dominant Wavy Vapor Layer regime. The photographic study captured a fairly continuous wavy vapor layer travelling along the heated wall while permitting liquid contact only in wetting fronts, located in the troughs of the interfacial waves. CHF commenced when wetting fronts near the outlet were lifted off the wall. The Interfacial Lift-off model is shown to be an effective tool for predicting the effects of body force on CHF at high velocities.
Zhang, Hui↗
Task III: Development of an Effective Computational Methodology for Body Force Representation of High-speed Rotor 37
A framework for an effective computational methodology for characterizing the stability and the impact of distortion in high-speed multi-stage compressor is being developed. The methodology consists of using a few isolated-blade row Navier-Stokes solutions for each blade row to construct a body force database. The purpose of the body force database is to replace each blade row in a multi-stage compressor by a body force distribution to produce same pressure rise and flow turning. To do this, each body force database is generated in such a way that it can respond to the changes in local flow conditions. Once the database is generated, no hrther Navier-Stokes computations are necessary. The process is repeated for every blade row in the multi-stage compressor. The body forces are then embedded as source terms in an Euler solver. The method is developed to have the capability to compute the performance in a flow that has radial as well as circumferential non-uniformity with a length scale larger than a blade pitch; thus it can potentially be used to characterize the stability of a compressor under design. It is these two latter features as well as the accompanying procedure to obtain the body force representation that distinguish the present methodology from the streamline curvature method. The overall computational procedures have been developed. A dimensional analysis was carried out to determine the local flow conditions for parameterizing the magnitudes of the local body force representation of blade rows. An Euler solver was modified to embed the body forces as source terms. The results from the dimensional analysis show that the body forces can be parameterized in terms of the two relative flow angles, the relative Mach number, and the Reynolds number. For flow in a high-speed transonic blade row, they can be parameterized in terms of the local relative Mach number alone.
Tan, Choon-Sooi↗
Treatment of body forces in boundary element design sensitivity analysis
The inclusion of body forces has received a good deal of attention in boundary element research. The consideration of such forces is essential in the desgin of high performance components such as fan and turbine disks in a gas turbine engine. Due to their critical performance requirements, optimal shapes are often desired for these components. The boundary element method (BEM) offers the possibility of being an efficient method for such iterative analysis as shape optimization. The implicit-differentiation of the boundary integral equations is performed to obtain the sensitivity equations. The body forces are accounted for by either the particular integrals for uniform body forces or by a surface integration for non-uniform body forces. The corresponding sensitivity equations for both these cases are presented. The validity of present formulations is established through a close agreement with exact analytical results.
Saigal, Sunil↗
Implementation of a Body Force Model in OVERFLOW for Propulsor Simulations
We present an implementation of a propulsor model based on body force method into the OVERFLOW computational fluid dynamics code to model turbofan engines and propulsors of similar type. The model estimates the forces imparted on the fluid by the blade camber surfaces as a body force source terms in the momentum and energy equations over grids that represent the rotor and stator of a fan stage. We tested the implementation on three cases: 1) Source Diagnostics Test (SDT) fan with R4 rotors, which has extensive test data on aerodynamic performance and rotor wake surveys, 2) A stand-alone Aeronaut TF8000 propulsor which is an off-the-shelf propulsor used on model aircraft and 3) The D8 aircraft model with TF8000 propulsors placed in a wind tunnel. Despite missing some of the features in the velocity profiles near the endwalls (i.e. hub and casing surfaces), the OVERFLOW simulations with body force model predicted area-averaged flow speed and total pressure rise through the SDT propulsor within a few percent of the LDV (Laser Doppler Velocimetry) measurements. In the case of TF8000 propulsor on the D8 airframe, the model under-predicted mechanical power coefficient by several percent of the wind tunnel test results when the horizontal force balance condition over the airframe is targeted by tuning rotor speed. By investigating the upstream influence of the rotor swirl, it was found out that the induced swirl velocity effects upstream were relatively small and they rapidly vanished before reaching one fan diameter upstream of the fan face. The body force model provided insights on aerothermodynamics and aeromechanics of boundary layer ingesting propulsor; these insights could not be obtained by using the uniform pressure jump model.
Propulsor↗
Probing Gravitational Sensitivity in Biological Systems Using Magnetic Body Forces
At Brown University, we are developing the use of magnetic body forces as a means to simulate variable gravity body forces on biological systems. This tool promises new means to probe gravi-sensing and the gravi-response of biological systems. It also has the potential as a technique for screening future systems for space flight experiments.
Guevorkian, Karine↗
The effect of power-law body forces on a thermally driven flow between concentric rotating spheres
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
Macaraeg, M. G.↗
The effect of power law body forces on a thermally-driven flow between concentric rotating spheres
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
Macaraeg, M. G.↗
An analysis of laminar free-convection flow and heat transfer about a flat plate paralled to the direction of the generating body force
The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.
Ostrach, Simon↗
On Fully Developed Channel Flows: Some Solutions and Limitations, and Effects of Compressibility, Variable Properties, and Body Forces
An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flow has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force (e.g., gravity), an exact fully developed gas flow results. For a liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a Couette flow. In the liquid case two solutions (not a new result) can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations.In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection (due to, say, a wall temperature gradient) and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case (or quasi-incompressible case for free-convection flows) considered by many authors. Finally there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only a such form that independent variables are separable. For the case where the streamwise velocity varies inversely as the square root distance along the channel a solution is given.
Maslen, Stephen H.↗
Distribution of resistive body-force in curved free-surface flow
The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant (1871) model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory (1978), however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. Its variable distribution is determined as well as its magnitude for use in the curved-flow equations. This variable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.
Sivakumaran, N. S.↗
Body force circulation and the Antarctic Ozone minimum
A dynamical mechanism, which is relevant to the ozone-depletion problem and which involves a 'body force' circulation discussed by Eliassen (1951), is considered. The body force problem and its application to 'generic' upper-tropospheric wave-driving are discussed theoretically. Following a review of the interhemispheric differences in the winter and early-spring circulation, the elliptic equation governing the residual mean meridional streamfunction is derived, and its analytic-solution properties in negligible shear are discussed. Finally, a numerical solution is derived using the observed August winds under the assumption of radiative equilibrium, and the effect of diabatic heating is discussed.
Dunkerton, Timothy J.↗
Film Condensation with and Without Body Force in Boundary-Layer Flow of Vapor Over a Flat Plate
Laminar film condensation under the simultaneous influence of gas-liquid interface shear and body force (g force) is analyzed over a flat plate. Important parameters governing condensation and heat transfer of pure vapor are determined. Mixtures of condensable vapor and noncondensable gas are also analyzed. The conditions under which the body force has a significant influence on condensation are determined.
Chung, Paul M.↗
A Study of Laminar Compressible Viscous Pipe Flow Accelerated by an Axial Body Force, with Application to Magnetogasdynamics
A study is made of the steady laminar flow of a compressible viscous fluid in a circular pipe when the fluid is accelerated by an axial body force. The application of the theory to the magnetofluidmechanics of an electrically conducting gas accelerated by electric and magnetic fields is discussed. Constant viscosity, thermal conductivity, and electrical conductivity are assumed. Fully developed flow velocity and temperature profiles are shown, and detailed results of the accelerating flow development, including velocity and pressure as functions of distance, are given for the case where the axial body force is constant and for the case where it is a linear function of velocity. From these results are determined the pipe entry length and the pressure difference required.
Martin, E. Dale↗
Melting ablation for two-dimensional and axisymmetric blunt bodies with a body force
Melting ablation for two dimensional and axisymmetric blunt bodies with body force, predicting gas-liquid interface temperature for free stream conditions
Chen, C.-J.↗
Two dimensional wave front shape induced in a homogeneously strained elastic body by a point perturbing body force.
Two dimensional wavefront shape induced in finitely strained elastic body by impulsive point body force
Payton, R. G.↗
Stability of a Horizontal Fluid Layer with Unsteady Heating from Below and Time-Dependent Body Force
The stability of a horizontal layer of fluid in an accelerated container heated unsteadily from below was investigated theoretically, assuming an incompressible fluid with small density changes resulting from heating. The critical Rayleigh numbers based on the over-all density differential are much higher than for the static case, are dependent only on the density distribution, and instantaneous value of the acceleration, and are independent of Prandtl number and rate of change of temperature and body force field. The initial motion corresponds to approximately the same cell shape as for the static case. Rate of transition of temperature perturbations from a stable to an unstable condition is proportional to the rate of increase of the temperature gradient in the region well removed from the walls; rate of transition of the slow motion is proportional to the Prandtl number and rate of increase of the body force field.
Goldstein, Arthur W.↗