Chenzhou Lian

Solution-limited time stepping to enhance reliability in CFD applications

A method for enhancing the reliability of implicit computational algorithms and decreasing their sensitivity to initial conditions without adversely impacting their efficiency is investigated. Efficient convergence is maintained by specifying a large global Courant (CFL) number while reliability is improved by limiting the local CFL number such that the solution change in any cell is less than a specified tolerance. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. An upper limit on the local solution change is attained by a proper non-dimensionalization of variables in different flow regimes within a single problem or across different problems. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results such as negative densities, temperatures or species mass fractions during the computation. The method is tested against a series of problems all starting from quiescent initial conditions to identify its characteristics and to verify the approach. The results reveal a substantial improvement in convergence reliability of implicit CFD applications that enables computations starting from simple initial conditions without user intervention.

Facility Development for Testing of Wave Rotor Combustion Rig

A Wave Rotor Combustion Rig (WRCR) is under development by a team including Purdue University, Rolls-Royce (LibertyWorks

Effects of Chamber Diameter on the Flowfield in Unielement Rocket Combustors

U NI-ELEMENT combustors embodying a single fuel oxidizer, injector pair constitute the smallest scale at which combustors can be tested in a rocket engine development program. These unielement systems provide fundamental information on combustor operation that cannot be obtained on larger sized rigs. The small scale provides an economical and safe test bed that allows more detailed instrumentation and much faster turn-around time than that for a practical larger scale combustor. The relatively simple geometry and construction is conducive to the application of advanced diagnostics while also lending itself to detailed computational fluid dynamics (CFD) analyses, both of which can aid in understanding and improving this most fundamental engine building block. Unielement testing is also useful for screening candidate injector types for a new engine, for diagnosing the performance of existing engines, or for fundamental academic studies into high-intensity combustion phenomena. A primary goal of unielement testing in an engine development program is to replicate as closely as possible the environment that a stream tube from an individual element will experience in the fullscale engine. Accordingly, unielement tests must be done with injector elements that are exact scaled copies of those to be used in the full-scale engine, both in terms of kinetic/kinematic and geometrical details. Additionally, the flow rates, oxidizer-to-fuel (O/F) ratios, and incoming propellant temperatures and pressures must match engine conditions, whereas the nozzle must be sized to ensure the proper chamber pressure. Finally, the length of the chamber should be matched to the distance from the injector face to the nozzle throat in the engine to ensure similar characteristic flow times. Clearly, interelement interactions and the intricate recirculation regions adjacent to the face of the full-scale engine cannot be replicated in unielement studies, but unielement combustors are widely used and accepted as an effective means for understanding rocket combustors and as an important precursor to subscale engine studies. A point of continuing controversy in unielement testing, however, concerns the cross-sectional size and shape of the chamber. A key argument has been that the unielement chamber should be sized to provide the cross-sectional area occupied by the stream tube from a single injector element in the full-scale engine, thereby reproducing the proper mean flowMach number. The impact of the cross section on instrumentation and optical diagnostics as well as on CFD modeling is, however, also an important concern that affects shape and size. Experimental configurations with optical access (which enables much more detailed quantitative measurements) drive the chamber cross section to larger sizes. Square chambers, such as those used in early experiments by Moser et al. [1], Foust et al. [2], and De Groot et al. [3], are most convenient for optical diagnostics but potentially introduce geometry-specific corner flows that are not present in engines and are difficult to represent in CFD analyses. Circular chambers eliminate concerns of corner flows and are also friendlier toward CFD modeling, but even with round chambers larger diameters facilitate optical access and advanced diagnostics. Increased chamber diameters, however, give rise to stronger recirculation regions adjacent to the injector face that eventually dominate flame attachment and the ensuing combustion processes. Despite these uncertainties, definitive experiments or computations concerning the effect of chamber Mach number and combustor diameter have never been attempted. The present paper represents a first attempt to address some of these issues. In the past decade, unielement combustors have been studied intensively, both experimentally [1–13] and computationally [14– 22]. The numerous experimental activities have provided detailed insights into, and visualization of, the flowmixing and combustion in unielement combustors. Important relationships between the physical phenomena and operating conditions, such as the momentum ratio and properties of the propellants, the density and velocity ratios of the jets, the temperature and pressure of the combustion chamber, and the role of the detailed local geometry, have been identified. In addition to physical understanding, there has been an emphasis on obtaining detailed experimental data for use in validating CFD models. Presented as Paper 2009-3897 at the 39th AIAA Fluid Dynamics Conference, San Antonio, TX, 22–25 June 2009; received 26 May 2011; revision received 12 December 2011; accepted for publication 14 December 2011. Copyright

Adaptive and Consistent Properties Reconstruction for Complex Fluids Computation

An efficient reconstruction procedure on adaptive Cartesian mesh for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh covering thermodynamic plane of interest that ensures function continuity across cell boundaries to C 0 , C 1 or C 2 levels. The C 0 and C 1 reconstructions fit the equation of state and enthalpy relations separately, while the C 2 reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD. The time required for evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations. Storage requirements are modest for today’s computers, with the C 1 method requiring slightly less storage than those for the C 0 and C 2 reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C 1 and C 2 methods are approximately a factor of two slower than the C 0 method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy levels.

Automatic Time Step Determination for Enhancing Robustness of Implicit Computational Algorithms

A method for enhancing the robustness of implicit computational algorithms without adversely impacting their efficiency is investigated. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. An upper limit on the local solution change is attained by a proper non-dimensionalization of variables in different flow regimes within a single problem or across different problems. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results during the computation. The method is tested against a series of problems to identify its characteristics and to verify the approach. The results reveal a substantial improvement in the robustness of implicit CFD applications that enables computations starting from simple initial conditions without user intervention.

Investigation of Effects of Radial Distortion on Transonic Fan Behavior

The flow analysis around blades of a transonic fan is presented for both clean and radially distorted inlets. Computations are shown for four-blade passages that are accomplished with a second order accurate code using a k-ω turbulence model. The mass flow rate along a speed line is controlled by varying a choked nozzle downstream of the fan. The results show good agreement with data for three speed lines. In the near-stall region, the flow first becomes unsteady and then unstable with the unsteadiness increasing at lower speeds. The four-blade simulations remained stable to lower mass flow rates than the single-blade simulations. In the near-stall vicinity, tip vortex breakdown occurred creating a low momentum zone near the blade tip on the pressure side that grew as the mass flow was decreased until it eventually blocked the passage. The presence of distortion reduced the operational range and moved the stall line to higher mass flow rates. At high speeds distortion reduced both the mass flow rate and total pressure ratio while at lower speeds, the choking mass flow rate was reduced, but the total pressure ratio was slightly improved. The flow separation near the hub on the suction side was caused by the distortion. Its size was decreasing with rotational speed.Copyright