The following is an incomplete description of active research projects in his research group. Please refer to list of publications for more details.
Adaptive grid generation
Finite difference, finite volume and finite element methods all use a computational mesh to approximate a continuum problem. In areas of large gradient of velocity, pressure, temperature or other flow parameters, such as in the neighborhood of a shock wave, very small grid sizes are required. In other areas, such as in the far field where the flow is rather uneventful, fewer grid points can be used without degrading the computational accuracy. For many practical problems the precise location of shock waves or other flow features are not known a prior. It is highly desirable to have a computational method that can automatically detect the areas of high and low flow gradients and refine and coarsen the computational mesh accordingly. A grid generation method has been proposed that can provide precise control of the mesh size distribution. This research will develop the method for arbitrary computational domains and couple it with a flow solver for steady and unsteady flow calculations. 

Multigrid method for solving the Reynoldsaverage NavierStokes
equations with advanced turbulence models
We are interested in developing efficient numerical methods for simulating high Reynolds number flow with complex geometry. A staggered finite volume method with multigrid has been developed for the compressible Reynoldsaveraged NavierStokes equations with algebraic and twoequations turbulence models. Multigrid method is applied to accelerate the convergence rate for both the solution of the NavierStokes and the turbulence model equations. Both upwind and central difference type algorithms are employed to discretize the differential equations in space. The resulting semidiscrete equations are marched in time by an explicit multistage method which are highly suitable for parallel processing.


Computation of Unsteady
Flow in Turbomachinery Blade Rows
Almost all design methods for turbomachinery cascades such as the compressor
and turbine blades in a jet engine have been based on steady flow calculations
and experimental correlation. Yet, turbomachines are essentially unsteady
machines. Indeed, they depend on flow unsteadiness to produce work. Unsteady
flows are extremely important to the performance, heat transfer, aeroelasticity
and noise of jet engines. We have develop a parallel, multigrid, multiblock
NavierStokes code that can
simulate unsteady flow through single and multiple turbomachinery blade rows.
Such calculation take a
lot of computer time and memory, even on massively parallel computers. Improved
numerical algorithms are continuously sought to reduce the demand on
computational resources while increasing the accuracy. At the same time,
the computational code is used to study fundamental fluid flow, heat
transfer, combustion, and fluidstructure interaction problems that
exist in gasturbine blade rows. 

Aeroelasticity
We are developing efficient numerical methods for calculating fluid/structure interactions.
See The AGARD IWing 445.6


Aerodynamic Optimization of Turbine Blade Rows
via CFD and Control Theory Current aerodynamic design procedures involve
long hours of manual iteration by a designer.
The optimality of a design rests heavily on the designer's knowledge
and skills and is not in any way guaranteed.
This usually leads to nonoptimal machines with
long design cycle and large developmental costs.
With the advance of computational fluid dynamics and nonlinear
optimization theory, this research attempts
to replace this manual
iteration by a systematic computer optimization procedure based on
rigorous mathematical and fluid dynamics principles, that is, by
solving the fundamental fluid dynamic equations and using advanced
nonlinear optimization methods.
By formulating an aerodynamic shape optimization problem
into a nonlinear control problem, the computational effort in
achieving an improved design can be dramatically reduced compared to
conventional sensitivity analysis.
Gradient information needed for optimization can be obtained by
solving a linear adjoint equation to the original nonlinear
governing equations, the Euler or the NavierStokes
equations.
The optimization theory
is combined with a fast and accurate
NavierStokes analysis code for turbomachinery flows.
The proposed research will explore various two and
threedimensional
shape optimization of compressor and turbine blades. 

GasTurbine Cycle Innovation: TurbineBurner Engines
In a conventional gasturbine engine, fuel is burned in the main combustor before the heated highpressure gas expands through the turbine.
A turbineburner concept is proposed in which combustion is continued inside the turbine
to increase the efficiency and the specific thrust of the turbojet engine or
the specific power of a groundbased power gasturbine. This concept includes not only continuous
burning in the turbine (Continous TurbineBurner: CTB) but also 'discrete' interturbineburners
(ITB) as an intermediate option. Thermodynamic cycle analyses are performed to compare the relative performances of the conventional engine
and the turbineburner engine with different combustion options for both turbojet and turbofan
configurations and groundbased gasturbine engines. Turbineburner engines are shown to provide significantly higher
specific thrust with no or only small increases in thrust specific fuel consumption compared to conventional engines.
Turbineburner engines also widen the operational range of flight Mach number and compressor pressure ratio.
Coupled with regeneration or other hybrid cycles, the CTB and ITB engines
offer exceptional improvements in both efficiency and power density for
groundbased gasturbine engines. Due to reduced combustion temperature, the CTB and ITB engines also
have the potential of reducing NOx emission. Recent studies indicate potential longer endurance of turbine blades due to reduced
turbine inlet temperatures during operation of a turbineburner engine. Like most innovations, there are also tremendous challenges for this technology to become a reality. Among them are the following that are of fundamental importance.
Theoretical, computational, and experimental studies in the above topic
areas are being performed at UCI. The turbineburner engine has caught major
attention from the Air Force Research Laboratory and recently NASA Glenn
Research Center along with a number of engine companies. Realistic mission
studies are being performed for commercial and military, subsonic and
supersonic, and ground and aerial applications. Experimental studies are also
being performed or planned at those facilities. 

Flame Propagation over
Liquid Fuel pools under microgravity
To be detailed. 

Stability of Leadingedge Separation Vortices over
Slender Delta Wings and Conical Bodies at High Angle of Attack
To be detailed. 