Numerical Simulations Using TVD Schemes of Two-Dimensional Supersonic Flow in Chemical Equilibrium

2017 ◽  
Vol 14 (02) ◽  
pp. 1750020
Author(s):  
J. Saldía ◽  
S. Elaskar ◽  
J. Tamagno
Keyword(s):  
Steady State ◽  
Chemical Equilibrium ◽  
Blunt Body ◽  
Steady State Solution ◽  
Two Dimensional ◽  
Tvd Schemes ◽  
Adaptive Use ◽  
Contact Discontinuities ◽  
Yee Scheme ◽  
Accuracy Of Results

A numerical scheme for the solution of both unsteady and steady-state, two-dimensional Euler equations considering gas in chemical equilibrium, is presented. Three alternatives of the Total Variation Diminishing (TVD) Harten–Yee scheme are implemented. One of them is a technique based on the adaptive use of different limiter functions in each wave of the inter-cell Riemann problem. With this technique, the undesirable effects of the artificial viscosity on the capture of contact discontinuities are reduced, without loss of robustness in nonlinear waves resolution. In order to verify the accuracy of the proposed scheme, results of the unsteady flow in cylindrical explosions, and of the steady-state solution of hypersonic flow over a blunt body, are presented. Finally, comparisons considering accuracy of results and convergence properties between the three Harten–Yee schemes are carried out.

The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

Free Convection in a Two-Dimensional Porous Loop

1986 ◽  
Vol 108 (2) ◽  
pp. 277-283 ◽  
Author(s):  
L. Robillard ◽  
T. H. Nguyen ◽  
P. Vasseur
Keyword(s):  
Steady State ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Outer Boundary ◽  
Convective Motion ◽  
Steady State Solution ◽  
Temperature Fields ◽  
Maximum Temperature ◽  
Two Dimensional ◽  
Convective Cells

A study is made of the natural convection in an annular porous layer having an isothermal inner boundary and its outer boundary subjected to a thermal stratification arbitrarily oriented with respect to gravity. For such conditions, no symmetry can be expected for the flow and temperature fields with respect to the vertical diameter and the whole circular region must be considered. Two-dimensional steady-state solutions are sought by perturbation and numerical approaches. Results obtained indicate that the circulating flow around the annulus attains its maximum strength when the stratification is horizontal (heating from the side). This circulating flow is responsible for an important heat exchange between the porous layer and its external surroundings. The flow field is also characterized by the presence of two convective cells near the inner boundary, giving rise to flow reversal on this surface. When the maximum temperature on the outer boundary is at the bottom of the cavity, the convective motion becomes potentially unstable; for a Rayleigh number below 80, there exists a steady-state solution symmetrical with respect to both vertical and horizontal axes; for a Rayleigh number above 80, an unsteady periodic situation develops with the circulating flow alternating its direction around the annulus.

An Experimental and Numerical Study of the Isothermal Flowfield Behind a Bluff Body Flameholder

1997 ◽  
Vol 119 (2) ◽  
pp. 328-339 ◽  
Author(s):  
C. N. Raffoul ◽  
A. S. Nejad ◽  
R. D. Gould ◽  
S. A. Spring
Keyword(s):  
Steady State ◽  
Bluff Body ◽  
Recirculation Zone ◽  
Numerical Study ◽  
Steady State Solution ◽  
Accurate Solution ◽  
State Solution ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Reynolds Stresses

An experimental and numerical investigation was conducted to study the turbulent velocities and stresses behind a two-dimensional bluff body. Simultaneous three-component laser-Doppler velocimeter (LDV) measurements were made in the isothermal incompressible turbulent flowfield downstream of a bluff body placed at midstream in a rectangular test section. Mean velocities and Reynolds stresses were measured at various axial positions. Spanwise velocity measurements indicated that the flow is three dimensional in the recirculation zone of the bluff body. Confidence in the accuracy of the data was gained by calculating the mass fluxes at each axial station. These were found to agree with each other to within ±3 percent. A parallel Computational Fluid Dynamics (CFD) study was initiated to gage the predictive accuracy of currently available CFD techniques. Three solutions were computed: a two-dimensional steady-state solution using the standard k-ε model, a two-dimensional time-accurate solution using the standard k-ε model, and a two-dimensional time-accurate solution using a Renormalized-Group (RNG) k-ε turbulence model. The steady-state solution matched poorly with the data, severely underpredicting the Reynolds stresses in the recirculation zone. The time-accurate solutions captured the unsteady vortex shedding from the base of the bluff body, providing a source for the higher Reynolds stresses. The RNG k-ε solution provided the best match to the data.

Flow Past Rotating Cylinders: Effect of Eccentricity

2000 ◽  
Vol 68 (4) ◽  
pp. 543-552 ◽  
Author(s):  
S. Mittal
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Steady State Solution ◽  
Rotating Cylinder ◽  
Computational Results ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Mean Values ◽  
Flow Past

Computational results are presented for flows past a translating and rotating circular cylinder. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. To validate the formulation and its implementation certain cases, for which the flow visualization and computational results have been reported by other researchers, are computed. Results are presented for Re=5, 200 and 3800 and rotation rate, (ratio of surface speed of cylinder to the freestream speed of flow), of 5. For all these cases the flow reaches a steady state. The values of lift coefficient observed for these flows exceed the limit on the maximum value of lift coefficient suggested by Goldstein based on intuitive arguments by Prandtl. These observations are in line with measurements reported, earlier, by other researchers via laboratory experiments. To investigate the stability of the computed steady-state solution, receptivity studies involving an eccentrically rotating cylinder are carried out. Computations are presented for flow past a rotating cylinder with wobble; the center of rotation of the cylinder does not match its geometric center. These computations are also important from the point of view that in a real situation it is almost certain that the rotating cylinder will be associated with a certain degree of wobble. In such cases the flow is unsteady and reaches a temporally periodic state. However, the mean values of the aerodynamic coefficients and the basic flow structure are still quite comparable to the case without any wobble. In this sense, it is found that the two-dimensional solution is stable to purely two-dimensional disturbances.

On the Squat of a Ship

1984 ◽  
Vol 28 (02) ◽  
pp. 107-117 ◽  
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Differential Equations ◽  
Froude Number ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Sinkage And Trim

The problem of the squat of a "two-dimensional" ship is solved using a nonlinear steady-state solution of the differential equations of the theory of a directed fluid sheet. Particular attention is focused on the prediction of the sinkage and trim of the ship, and the results for a model ship qualitatively agree with available experimental data. Specifically, the solution presented here predicts the experimentally observed dependence of the sinkage and trim on the equilibrium depth of the water (regarded here as an incompressible, inviscid fluid), and predicts a nonzero drag for subcritical ship speeds (corresponding to the values of depth Froude number F < 1). The solution also exhibits certain detailed features of the sinkage curves which apparently were not observed in the experiments mentioned above. In this connection, additional relevant experiments are suggested.

A Nonlinear Theory of Sloshing in Rectangular Tanks

1974 ◽  
Vol 18 (04) ◽  
pp. 224-241 ◽  
Author(s):  
Odd M. Faltinsen
Keyword(s):  
Steady State ◽  
Power Series ◽  
Boundary Value Problem ◽  
Nonlinear Theory ◽  
Reasonable Agreement ◽  
Steady State Solution ◽  
State Solution ◽  
Two Dimensional ◽  
The Stability ◽  
Theory And Experiment

A two-dimensional, rigid, rectangular, open tank without baffles is forced to oscillate harmonically with small amplitudes of sway or roll oscillation in the vicinity of the lowest natural frequency for the fluid inside the tank. The breadth of the tank is 0(1) and the depth of the fluid is either 0(1) or in-finite. The excitation is 0(ε) and the response is 0(ε1/3). A nonlinear, inviscid boundary-value problem of potential flow is formulated and the steady-state solution is found as a power series in ε1/3 correctly to 0(ε). Comparison between theory and experiment shows reasonable agreement. The stability of the steady-state solution has been studied.

A Simplified Direct Method for Cyclic Strain Calculation: Repeated Rolling/Sliding Contact on a Case-Hardened Half Plane

1996 ◽  
Vol 118 (2) ◽  
pp. 329-334 ◽  
Author(s):  
C.-C. Yu ◽  
B. Moran ◽  
L. M. Keer
Keyword(s):  
Steady State ◽  
Contact Problem ◽  
Direct Method ◽  
Strain Range ◽  
Cyclic Strain ◽  
Direct Analysis ◽  
Steady State Solution ◽  
Computational Effort ◽  
Sliding Contact ◽  
Two Dimensional

A direct analysis method for problems in repeated elastic-plastic rolling/sliding contact is presented. The method is shown to be an efficient technique for the determination of the steady-state solution under proportional or nonproportional cyclic loading and can provide such results as residual stress, residual strain, and cyclic strain range. Furthermore, the method is valid for both elastic and plastic shakedown. A two-dimensional rolling/sliding contact problem is considered with emphasis on the calculation of cyclic plastic strains. Several numerical techniques are employed to simplify and reduce the computational effort. These techniques consist of an operator split, the modified incremental projection method, middle-loading state, and decomposition into residual steady-state and cyclic parts. The resulting scheme is highly efficient and is ideally suited for parameter studies. To demonstrate the practical application of the approach, a two-dimensional contact problem, assuming a case-hardened material, is solved.

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