ACFDStudyofDiffuserPerformanceofGasDynamicLaser.pdf

Proceedings of ICEAE 2009

Email addresses: [email protected] (S D Ravi), [email protected] (M A Sriram) [email protected], (P S Kulkarni), [email protected] (N K S Rajan) 1,4Corresponding author

A CFD Study of Diffuser Performance of Gas Dynamic Laser System

S D Ravi1, M A Sriram2, P S Kulkarni3 and N K S Rajan4 1,2,3,4Department of Aerospace Engineering, Indian Institute of Science, Bangalore

Abstract: Based on the an earlier CFD analysis of the performance of the gas-dynamically controlled laser cavity it was found that there is a possibility of optimizing the geometry of the diffuser that can bring about reductions in both size and cost of the system by examining the critical dimensional requirements of the diffuser for two cases i.e. case 1 is 1kg/sec and case 2 is 15kg/sec of mass flow rate. Consequently, an extensive CFD analysis has been carried out for a range of diffuser configurations by simulating the supersonic flow through the arrangement including the laser cavity driven by a bank of converging – diverging nozzles and the diffuser. The numerical investigations with 3D-RANS code are carried out to capture the flow patterns through diffusers past the cavity that has multiple supersonic jet interactions with shocks leading to complex flow pattern. Varying length of the diffuser plates is made to be the basic parameter of the study. The analysis reveals that the pressure recovery pattern during the flow through the diffuser from the simulation, being critical for the performance of the laser device shows its dependence on the diffuser length is weaker beyond a critical lower limit and this evaluation of this limit would provide a design guideline for a more efficient system configuration. The observation based on the parametric study shows that the pressure recovery transients in the near vicinity of the cavity is not affected for the reduction in the length of the diffuser plates up to its 10% of the initial size, indicating the design in the first configuration that was tested experimentally has a large factor of margin. The flow stability in the laser cavity is found to be unaffected since a strong and stable shock is located at the leading edge of the diffuser plates while the downstream shock and flow patterns are changed, as one would expect. Results of the study for the different lengths of diffusers in the range of 10% to its full length are presented, keeping the experimentally tested configuration used in the earlier study [1] as the reference length. The conclusions drawn from the analysis is found to be of significance since it provides new design considerations based on the understanding of the intricacies of the flow, allowing for a hardware optimization that can lead to substantial size reduction of the device with no loss of performance.

Key words: Nozzles, Gas Diffusers, Numerical Grid Generation, CFD, Turbulence

Performance of Gas Dynamic Laser System


INTRODUCTION Computational studies have been carried out for a two design configuration systems involving a parametric study of Gas Dynamics Laser (GDL) using a 3D-RANS code. Parametric study is done based on the configurations selected for the analysis from practical system which involves aerodynamically controlled laser cavity which is further used for generation of high powered laser beams. The parametric study in this arrangement, in order to produce an active lasing medium, rapid and deep cooling of mixture of gases from a combustion chamber (CO2-N2-H2O) is achieved by allowing the gases to expand in a set of convergent - divergent nozzles, allowing the supersonic jets to drive the cavity used as the zone for the laser activity. This cavity would have a distribution of CO2 in non-equilibrium condition with many quantum levels, providing a favorable condition for the lasing activity. The bank of nozzles followed by the cavity and further by a diffuser section for stable operation, makes the main parts of the aerodynamically controlled cavity which is considered in the present analysis and a 3D view of the configuration has been shown in Fig.1. The simulation of flow in a Gas Dynamics Laser system is done using an industrially standard CFD tool 3D-RANS code. The process of the modeling is taken up in steps of increasing complexity to ensure the numerical stability and computational consistency. The different stages have provided clarity on different parameters that include the optimal grid distribution and the optimal initial flow profiles to obtain a stable and consistent solution. The details of the analysis are explained below. An approach with multiple geometrical blocks that are matching to the geometry of the unit considered at different locations, depending on its complexity, is used with their matching surfaces blended so as to generate a good computational mesh. The structured mesh is preferred since the geometry is more complex and the flow computations need to capture supersonic, transonic and subsonic zones over the same computational domain. Optimization of number of computational nodes is done by allowing the cluster of grids in critical zones, at places expected to have larger gradients in the flow parameters and in places where the geometry is more complex. It is observed that nearly 3.6 to 5.6 lakh computational nodes are required for 10% of initial length to full length of the case-1 design configuration and 6.28 to 11.46 lakh computational nodes are required for 10% of initial length to full length of the case-2 design configuration. Fig. 2 gives view of a sample of the computational mesh generated near in cavity at the upstream of the diffuser.

The computational flow Analysis made during the preliminary stage of the study includes flow analysis through a single nozzle followed by flow analysis through a set of four nozzles and thereafter analysis of flow through of a set of nozzles along with a set of two diffuser vanes. In its final stage the computations were taken up to capture the flow through multiple nozzles and the diffusers. The method of analysis, the results obtained at different stages been presented and discussed in the following sections of the paper.

THE CONFIGURATION AND THE APPROACH The basic configuration of the system considered

for the analysis, scheme of computation, code validation with experimental data and other basic aspects of the study have been brought out in detail in an earlier work [1], and this work is an extension of this reported work. However, for clarity, the arrangement of the system configuration is shown in Fig. 1. In the present analysis, all the other hardware elements except the diffuser plates are kept unchanged, in order to have a focused parametric study. Further for simplicity of analysis, the downstream element of the diffuser – the acoustic control device is taken off from computation domain.

A 3D-RANS code having upwinding implicit scheme and k–ω approach for turbulence is used for the numerical solution. The Reynolds-Averaged Navier-Stokes Equations are solved for steady, compressible viscous flow. The governing equations used are the conventional standard sets that include:

Continuity equation: 0U jx j

∂=

∂ Momentum equation:

( ) ( ) ( )PU U U u ui i j ij i jt x x xj i jρ ρ τ ρ∂ ∂ ∂ ∂ ′′ ′′+ =− − +

∂ ∂ ∂ ∂

Energy equation: ( ) ( ) ( )h U h Q u hj j jt x xj j

ρ ρ ρ∂ ∂ ∂ ′′ ′′+ =− +∂ ∂ ∂

The boundary conditions and initial conditions used include (a) no slip, impermeable and adiabatic walls; (b) inlet pressure and temperature of the fluid entering the system to be an assigned boundary value (typical outlet of a rocket combustion chamber with storable liquid propellants) and (c) the outlet from the diffuser set to match the ambient conditions. Diminishing residual criteria of the variables is used for the convergence with a limit of RMS residuals falling below 10-4.

RESULTS AND DISCUSSION Results from the study given in the Figs. 3 and 4

shows the Mach plot for single and set of four nozzle. It can be seen that the details of a choked flow is obtained with the transonic transients captured well, a first exercise carried out for validating the approach. Figs. 5 (a), (b) and (c) belongs to a case-1 (with 1 kg/s flow rate) and Figs. 6 (a), (b) and (c) belongs to a case-2 (with 15 kg/s flow rate) provide the results of the studies made for the established design configurations with the diffuser, specified to have built for the experimental tests and based on empirical designs. The different plots show the distributions of important aerodynamic parameters – Mach number, Pressure and velocity (as streamline plot) of the system. It can be observed that the reflected shocks within the diffuser plates are adequately strong enough that the pressure recovery occurs dominantly beyond the trailing edge of the diffuser plates, ensuring a ‘safe’ operating pressure in the aerodynamic lasing cavity, eliminating the chances of the back pressure affecting the flow in the cavity. The predate pressure in the aerodynamic cavity is

S D Ravi, M A Sriram, P S Kulkarni, N K S Rajan


found to be close experimentally reported values of the hardware built elsewhere.

Having observed that multiple shock reflections are found within the diffusers, it was inferred that the plate lengths could be brought down with no loss in the performance as regards to the aerodynamic cavity is concerned. A more detailed study was taken up to investigate the possibility of the extent of reduction of the diffuser plate lengths that could be a significant contribution to reduce the size and weights of the integrated system.

The results shown in Figs. 5 (d) to (i) and Figs. 6 (d) to (i) show the behaviors of the case-1 and case-2 of the corresponding aerodynamic characteristics with sets of selective diffusers with reduced plate lengths of 80% , 60% and 30%. One can observe that only the downstream flow structure is affected as compared to the initial configuration and flow in the laser cavity is not affected. This and above data sets are run for the identical inlet conditions (28atm chamber pressure, upstream of the nozzle bank) of the reference design set. From the stabile flow in the cavity zone in all the cases, it could be clearly made out that the length of the diffuser plates can be significantly reduced. Though an alternate arguments could be made that the built system can handle much larger range for flow rates since the diffuser are ‘over designed’ since the requirements of the cavity conditions demand a fairly narrow range of working pressures for a favourable laser activity, the flow rates permissible in the system is limited to correspondingly narrow range. In this point of view, one can infer that the device could be optimized by reducing the diffuser plate lengths as can be seen by the results.

To make a sensitivity analysis of the diffuser performance based on its dependence on the inlet pressure, a set of analysis was made taking the case of a 10% plate length being the most critical among other cases. A variation in the inlet pressure of about 7.5% was chosen for this study. It was found that the higher side of the pressure did not change the flow pattern categorically, while the lower pressure provided a significantly unstable flow structure with the solution strongly oscillating. Figs. 5 (j), (k) and Figs. 6 (j), (k) show the both case studies having stable flow structure that belong to the standard pressure. Results shown in Figs. 5 (l), (m) and Figs. 6 (l), (m) belong to a case with reduced inlet pressure. One can see that the flow structure is not fully formed and the solution is found to be strongly unstable for both the two cases. It was also found that in this condition of reduced pressure, a steady state flow solution could not be reached. This behavior is visibly shown up clearly in the two plots shown in Figs. 7 and 8 that show the history of RMS residuals of the computational parameters with an inference that with the reduced pressure the solution has been quite oscillating and is instable. It was found that further reduction in the inlet pressure did not proceed numerically, leading to an inference that with the transients of the flow instability being strong enough not allowing for a steady state

solution. These aspects and observation further lead to infer the existence of the operating limit of the inlet pressure in the device. The analysis makes it clear that for a specified geometry that the working range for the device is associated with the length of the diffuser plate.

A consolidated plot of pressure recovery and Mach numbers over the diffuser plates for both the case-1 and case-2 are provided in Figs. 9 to 12 and it shows that for a specified working pressure, it is possible to arrive at an optimally lower length of diffuser plate than what was used in the empirical designs based on the trends of the pressure recovery transients, in the near–downstream of the cavity that are not disturbed by reduction in the plate lengths up to about 10% of its original length. This leads to a consideration that the design of the device can have a reduction in the length of the diffuser and the sizes of its associated hardware significantly, that could lead to a major advantage in the usability and cost of the device. The outcome of the analysis also signifies the extent of analysis that CFD tools have given with an insight of the flow behavior and to provide good guidelines for the design.

CONCLUSION The CFD Analysis using ICEM–CFD and ANSYS–CFX for the complex geometry considered for an aerodynamically driven laser cavity and capturing of the flow details have shown a distinct insight of the physical behavior of the configuration studied. The observations based on the parametric study show that the pressure recovery transients in the near vicinity of the cavity, the most functionally critical part of the device, is not affected with a reduction in the length of the diffuser plates up to 10% of the empirical design size. A validation of the approach is made by checking the cavity pressure close to experimental values and other flow parameters agreeing broadly on the their behavioral patterns. The analysis makes it clear that the configuration based on the empirical design has a large factor of margin that can be reduced significantly and that there exists a limit in the operating range for the device. The conclusions drawn from the analysis is expected to be significant since it provides new design considerations, allowing for a hardware optimization with substantial size reduction in the device with no loss of performance. REFERENCE 1. “Complex Flow Analysis through a Multiple Nozzle

Driven Laser Cavity” M.A.Sriram, N. K. S. Rajan and P. S. Kulkarni Symposium on Applied Aerodynamics and Design of Aerospace Vehicle (SAROD-2007) November 22-23, 2007, Thiruvananthapuram, India.

2. “Gas Dynamic Lasers”; an Introduction by John F Anderson.

3. David A. Russell Dept. of Aeronautics and Astronautics, Univ. of Washington, “First of the high-power machines, the gasdynamic laser still has a



dazzling performance capability; but future development will most likely come in hard-won incremental steps,”

4. “Compressible flow through a converging-diverging Nozzle” by S. J. Phillipson.

Fig. 1, A general view of the initial configuration

Fig. 2, Computational Mesh Model

Fig. 5(a), Mach Contours (case1, full length)

Fig. 5(b), Pressure Contours (case1, full length)

Fig. 5(c), Streamlined Plot (case1, full length)

Fig. 3, Mach Contour (single nozzle)

Fig. 4, Mach Contour (set of four nozzle)

Fig. 6(a), Mach Contours (case2, full length)

Fig. 6(b), Pressure Contours (case2, full length)

Fig. 6(c), Streamlined Plot (case2, full length)



Fig. 5(d), Mach Contours (case1, 80% Plate length)

Fig. 5(e), Pressure Contours (case1, 80% Plate length)

Fig. 5(f), Mach Contours (case1, 60% Plate length)

Fig. 5(g), Pressure Contours (case1, 60% Plate length)

Fig. 5(h), Mach Contours (case1, 30% Plate length)

Fig. 5(i), Pressure Contours (case1, 30% Plate length)

Fig. 6(d), Mach Contours (case2, 80% Plate length)

Fig. 6(e), Pressure Contours (case2, 80% Plate length)

Fig. 6(f), Mach Contours (case2, 60% Plate length)

Fig. 6(g), Pressure Contours (case2, 60% Plate length)

Fig. 6(h), Mach Contours (case2, 30% Plate length)

Fig. 6(i), Pressure Contours (case2, 30% Plate length)



Fig. 5(j), Mach Contours (case1, 10% Plate length)

Fig. 5(k), Pressure Contours (case1, 10% Plate length)

Fig. 5(l), Mach Contours (case1, with 7.5% lower pr)

Fig. 5(m), Pressure Contours (case1, with 7.5% lower pr)

Fig. 7, RMS Residual History (std pressure)

Fig. 6(j), Mach Contours (case2, 10% Plate length)

Fig. 6(k), Pressure Contours (case2, 10% Plate length)

Fig. 6(l), Mach Contours (case2, with 7.5% lower pr)

Fig. 6(m), Pressure Contours (case2, with 7.5% lower pr)

Fig. 8, RMS Residual History (Lower pressure)



Fig. 9, Consolidated plot of Pressure Recovery over the diffuser plates of different length (Case1 study)

Fig. 10, Consolidated plot of Pressure Recovery over the diffuser plates of different length (Case 2 study)

Fig. 11, Mach number over the diffuser plates of different

length (Case 1 study)

Fig. 12, Mach number over the diffuser plates of different length (Case 2 study)

S D Ravi has post graduate education at Visvesvaraya Technological University and has been working as a project assistant at CGPL, Dept of Aerospace Engineering Indian Institute of Science. His current

interests are R&D, CFD, combustion, Gasification, and energy.

M A Sriram is doing post graduate education at KTH, Royal institute, Sweden. and had been working as a project assistant at CGPL, Dept of Aerospace Engineering Indian Institute of Science. His current

interests are R&D, CFD, propulsion and combustion.

P S Kulkarni has Ph.D. in Faculty of Engineering (Aerospace engineering), Indian Institute of Science and has been working as a Principal Research Scientist at Dept of Aerospace Engineering Indian Institute of

Science. His current interests are Advanced Computational Fluid Dynamics and propulsion.

N K S Rajan has Ph.D. in Faculty of Engineering (Aerospace engineering), Indian Institute of Science and has been working as a Principal Research Scientist at Dept of Aerospace Engineering, Indian Institute of

Science. His current interests are Heat Transfer, Fluid Dynamics, combustion, Gasification, propulsion, energy, Development of Prototype, Development of algorithm, Computer Networking and Instrumentation.

ACFDStudyofDiffuserPerformanceofGasDynamicLaser.pdf

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